Biophysical Chemistry: Techniques and Applications 9783031376818

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C. Kalidas M.V. Sangaranarayanan

Biophysical Chemistry Techniques and Applications

Biophysical Chemistry

C. Kalidas · M. V. Sangaranarayanan

Biophysical Chemistry Techniques and Applications

C. Kalidas Department of Chemistry Indian Institute of Technology Madras Chennai, India

M. V. Sangaranarayanan Department of Chemistry Indian Institute of Technology Madras Chennai, India

ISBN 978-3-031-37681-8 ISBN 978-3-031-37682-5 (eBook) https://doi.org/10.1007/978-3-031-37682-5 Jointly published with Ane Books Pvt. Ltd. The print edition is not for sale in South Asia (India, Pakistan, Sri Lanka, Bangladesh, Nepal and Bhutan) and Africa. Customers from South Asia and Africa can please order the print book from: ANE Books Pvt. Ltd. ISBN of the Co-Publisher’s country edition: 978-93-90658-81-7 1st edition: © Authors 2022 © The Author(s) 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface The subject of Biophysical Chemistry is relatively new in the Indian context although it is well established in the Western world. This perspective is based on the experience of one of the authors viz. the institute where he spent a year (1968–69) was “Max-Planck Institute für Physikalische Chemie, Göttingen, Germany” but was later renamed as “Max-Planck Institute für Biophysikalische Chemie” by 1976–77 when he visited the same institute again as a senior fellow of Alexander von Humboldt Foundation. This reflects the importance of the subject which opened up a wide variety of areas of research such as molecular biology, cellular biochemistry, physical biochemistry, neurobiology, and ultra fast dynamics to name a few. Realizing the importance of this area, the authors embarked on the preparation of this book. The book “Biophysical Chemistry” provides a pedagogical outline of various topics with a few selected applications. The essential objective in this endeavour has been to include a large number of diverse topics customarily covered in any physical chemistry course, albeit with a biochemical flavour. In view of this, extensive courage of the entire amount of biophysical chemistry is not pursued here. Nevertheless, it is hoped that the present text will provide essential elements of biophysical chemistry which will enable the reader to delve deeper into various advanced level monographs. There exist many classical textbooks in biophysical chemistry (for example, Biophysical chemistry, D. Klostermeier and Markus G. Rudolph). However, the present book is intended to cover most of the physical chemistry contents, essential for comprehending biophysical phenomena viz. non-equilibrium thermodynamics (chapter 2), bioenergetics (chapter 11),

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chemical kinetics (chapters 18 to 21). It is quite difficult to decouple physical chemistry concepts from structural considerations of biological phenomena. In view of this, Part I, provides an elementary description of the structure of the cell (cell and its biochemical setup (chapter 1)), carbohydrates (chapter 3), lipids (chapter 4), amino acids (chapter 5), peptides (chapter 6), proteins (chapter 7), nucleosides and nucleotides (chapter 8), enzymes (chapter 9), co-enzymes and vitamins (chapter 10). The emphasis in these chapters consists in providing structural considerations pertaining to diverse components of the cell. In Part II, different bioanalytical techniques have been described with illustrative applications viz. electrochemical methods (chapter 12), spectroscopic techniques (chapters 13, 16, 17, 22, 29 to 31), calorimetric methods (chapters 23 and 24) analytical methods based on mobility (chapters 14, 15, 25 to 28). The recently discovered genome editing is briefly summarized in chapter 32. In each chapter, different types of questions have been provided. In some cases, numerical questions with detailed solution have been provided. In the opinion of authors, this book will be of interest to students of a variety of disciplines such as physical chemistry, biochemistry, medicine and neurobiology, etc. The authors and publishers have made sincere efforts to trace the copyright holders. If any copyright material has not been acknowledged, it may please be brought to our notice so as to rectify this inadvertent omission in future reprints. The authors request that such omissions be brought to their attention so that due acknowledgements maybe made subsequently. Thanks are due to D.V. Kirana, K.V. Akshaya, P.P. Archana, Dr. Hema Chandra Kotamarthi and Prof. K.M. Muraleedharan of IIT Madras, Dr. A. Muthukrishnan of IISER Thiruvananthapuram and Prof. Nandita Madhavan of IIT Bombay for helpful suggestions. It is a pleasure to acknowledge Ane Books Pvt. Limited for their consistent support during the entire preparation of the book. The authors thank their families for the understanding, patience and support given during this methodic, painstaking and formidable effort. C. Kalidas M.V. Sangaranarayanan

Table of Contents List of Figures .............................................................................................. List of Tables ................................................................................................. List of Symbols and Acronyms . . . . . . . . . . . . . . . . . . . . . . .

Part I 1

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xvii xxv xxix

Different Types of Biomolecules

Cell and its Biochemical Setup 1.1 Introduction ...................................................................... 1.2 Structure of an Animal Cell . . . . . . . . . . . . . . . . . 1.3 Composition of Human Cell . . . . . . . . . . . . . . . . . 1.4 Eukaryotic and Prokaryotic Cells . . . . . . . . . . . . . . 1.5 Membrane-Bound Organelles . . . . . . . . . . . . . . . . 1.6 Comparison Between Lysosome and Ribosome . . . . . . 1.7 Types of Cells in Human Body . . . . . . . . . . . . . . . 1.8 Peripheral Proteins 17 1.9 Transport Across Cell Membrane . . . . . . . . . . . . . . 1.10 Facilitated Diffusion . . . . . . . . . . . . . . . . . . . . . 1.11 Permeability of Molecules Across Phospholipid Bilayers 1.12 Thermodynamic basis of Transport . . . . . . . . . . . . . 1.13 Examples of Antiport and Symport System . . . . . . . . 1.14 Ca2+ ATPase . . . . . . . . . . . . . . . . . . . . . . . . . .

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Thermodynamic Aspects of the Cell 2.1 Introduction .............................................................................. 2.2 Enthalpy and Free Energy Changes in Biochemical Processes .............................................................

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2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 3

Biophysical Chemistry

Effects of Electrochemical Changes . . . . . . . . . . . . . . Distribution of Ions Across Membranes . . . . . . . . . . . Distribution of Ions Near Charged Membranes and Macromolecules . . . . . . . . . . . . . . . . . . . . . . Osmotic Effects . . . . . . . . . . . . . . . . . . . . . . . . . Role of Chemical Potential . . . . . . . . . . . . . . . . . . . Effects of Different Molecular Environments and Phases on Energy and Entropy . . . . . . . . . . . . . . . . . . . . . Surface Free Energies and Surface Tension . . . . . . . . . . Molecular Aggregation . . . . . . . . . . . . . . . . . . . . . Non-equilibrium Thermodynamic Treatment of Bacterial Cells . . . . . . . . . . . . . . . . . . . . . . . . . . Bacterial Cell as a Thermodynamic System . . . . . . . . . Physical and Chemical Features of the Cell and Environment . . . . . . . . . . . . . . . . . . . . . . . . Concept of Steady State . . . . . . . . . . . . . . . . . . . . Non-equilibrium Thermodynamics in Microbiology . . . . Linear Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . Force and Flows in Living Systems . . . . . . . . . . . . . . Chemical Potential and Mass Transfer: Activated Support Applicability of Linear Laws . . . . . . . . . . . . . . . . . . Non-linear Descriptions . . . . . . . . . . . . . . . . . . . . Simple Cell Functions in Non-equilibrium Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . Batch Cultures . . . . . . . . . . . . . . . . . . . . . . . . . . Thermodynamic Concepts . . . . . . . . . . . . . . . . . . .

Carbohydrates, their Reactions, Thermochemistry and Energetics 3.1 Introduction . . . . . . . . . . . . . . . . . . . . 3.2 General Properties of Monosaccharides . . . . 3.3 Other Monosaccharides . . . . . . . . . . . . . 3.4 Glycosides . . . . . . . . . . . . . . . . . . . . . 3.5 Oligosaccharides . . . . . . . . . . . . . . . . . 3.6 Polysaccharides . . . . . . . . . . . . . . . . . . 3.7 Cell Walls of Bacteria . . . . . . . . . . . . . . . 3.8 Thermochemistry of Carbohydrates . . . . . . 3.9 Gibbs Free Energy Changes for Reactions . . . 3.10 Enolic Phosphate . . . . . . . . . . . . . . . . . 3.11 Guanidinium Phosphates . . . . . . . . . . . . 3.12 Carbohydrates and Microbial Fuel Cells . . . .

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Lipids 4.1 Introduction . . . . . . . . . . . . . . . . . . . 4.2 Properties of Lipids . . . . . . . . . . . . . . . 4.3 Bonding in Lipids . . . . . . . . . . . . . . . . 4.4 Classification . . . . . . . . . . . . . . . . . . . 4.5 Reactions . . . . . . . . . . . . . . . . . . . . . 4.6 Analysis of Lipids . . . . . . . . . . . . . . . . 4.7 Nomenclature of Phospholipids . . . . . . . . 4.8 Lipoproteins . . . . . . . . . . . . . . . . . . . 4.9 Role of Lipids in Cell Function . . . . . . . . 4.10 Distribution of Lipids . . . . . . . . . . . . . . 4.11 Physicochemical Data on Lipids . . . . . . . . 4.12 Lipid Bi-layers . . . . . . . . . . . . . . . . . . 4.13 Glycolipids on the Surface of all Membranes 4.14 Interfacial Studies of Lipid Bilayers . . . . . .

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Amino Acids 5.1 Introduction . . . . . . . . . . . . . . . . . 5.2 Classification of Amino Acids . . . . . . . 5.3 Chirality of Amino Acids . . . . . . . . . . 5.4 Acid-base Properties . . . . . . . . . . . . 5.5 Reactions of Amino Acids . . . . . . . . . 5.6 Biochemical Importance of Amino Acids 5.7 Electrochemical Studies of Amino Acids .

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Peptides 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . 6.2 Classes of Peptides . . . . . . . . . . . . . . . . . 6.3 Functions of Peptides . . . . . . . . . . . . . . . . 6.4 Acid-Base Properties of Peptides . . . . . . . . . 6.5 Peptides as Biosensors . . . . . . . . . . . . . . . 6.6 Current-Voltage Characteristics of Peptide Films

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Proteins 7.1 Introduction . . . . . . . . . . . . . . 7.2 Composition of Proteins . . . . . . . 7.3 Some Characteristics of Proteins . . 7.4 Classification of Proteins . . . . . . . 7.5 Nature of Bonds in Protein Structure 7.6 Structure of Proteins . . . . . . . . . 7.7 Role of Amino Acids in Proteins . .

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Biophysical Chemistry

7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 7.18 8

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Examples of Proteins . . . . . . . . . . . . . Hemoglobin . . . . . . . . . . . . . . . . . . Antibodies . . . . . . . . . . . . . . . . . . . Hormones . . . . . . . . . . . . . . . . . . . Denaturation of Proteins . . . . . . . . . . . Helix-Coil Transitions in Proteins . . . . . . Kinetics of Helix-Coil Transformation . . . Membrane Proteins . . . . . . . . . . . . . . Modelling of Tertiary Structure of Proteins Levinthal Paradox . . . . . . . . . . . . . . . Proteins in Nutrition . . . . . . . . . . . . .

Nucleosides and Nucleotides 8.1 Introduction . . . . . . . . . . . . . . . . . 8.2 Biological Function (DNA & RNA) . . . . 8.3 Examples of Nucleotides . . . . . . . . . . 8.4 Naming of Nucleosides and Nucleotides

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Enzymes 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Different Types of Enzymes . . . . . . . . . . . . . . . . . 9.3 Nature of Enzyme Action . . . . . . . . . . . . . . . . . . 9.4 Michaelis-Menten Mechanism . . . . . . . . . . . . . . . . 9.5 Effect of Temperature on Enzyme-catalysed Reactions . . 9.6 Specificity of an Enzyme . . . . . . . . . . . . . . . . . . . 9.7 Classification of Enzymes . . . . . . . . . . . . . . . . . . 9.8 Inhibitors of Enzymes . . . . . . . . . . . . . . . . . . . . 9.9 Reversible Inhibition . . . . . . . . . . . . . . . . . . . . . 9.10 Uncompetitive Inhibition . . . . . . . . . . . . . . . . . . 9.11 Allosteric Enzymes . . . . . . . . . . . . . . . . . . . . . . 9.12 Oligomeric Enzymes . . . . . . . . . . . . . . . . . . . . . 9.13 Isoenzymes . . . . . . . . . . . . . . . . . . . . . . . . . . 9.14 Bifunctional Oligomeric Enzymes . . . . . . . . . . . . . . 9.15 Multienzyme Complexes . . . . . . . . . . . . . . . . . . . 9.16 Modification of the Specificity of an Oligomeric Enzyme 9.17 Measurement of Enzymatic Activity of Lactose Dehydrogenase (LDH) obtained from Different Organisms . . . . . . . . . . . . . . . . . . . . . 9.18 Turn Over Rates (T.O.R) of Some Enzymes . . . . . . . . 9.19 Immobilisation of Enzymes . . . . . . . . . . . . . . . . .

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181 181 181 181 188 189 190 191 192 193 194 197 200 202 202 203 206

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Table of Contents 

10 Co-Enzymes and Vitamins 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 10.2 Relation between Co-enzymes and Vitamins . . . . 10.3 Vitamins . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 Biochemical Functioning of the B-Vitamin Group . . 10.5 Biochemical Function of Biotin . . . . . . . . . . . . 10.6 Adsorption of Riboflavin . . . . . . . . . . . . . . . . 10.7 Surface Tension Data of Complexes with Vitamin-A

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217 217 220 220 223 230 235 240

11 Bioenergetics 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Metabolism . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Coupled Reactions . . . . . . . . . . . . . . . . . . . . 11.4 ATP as an Energy Source . . . . . . . . . . . . . . . . . 11.5 High Phosphoryl Capacity of ATP . . . . . . . . . . . 11.6 Significance of Phosphoryl Transfer Potential (PTP) . 11.7 Intracellular Conditions Pertaining to ATP Hydrolysis 11.8 Methods by which ATP Transfers Energy . . . . . . . 11.9 Citric Acid Cycle . . . . . . . . . . . . . . . . . . . . . 11.10Reactions of the TCA Cycle . . . . . . . . . . . . . . .

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245 245 245 246 247 247 248 249 252 253 253

12 Biosensors 12.1 Introduction . . . . . . . . . . . . . . . . . . 12.2 Components of a Biosensor . . . . . . . . . 12.3 Different Types of Biosensors . . . . . . . . 12.4 Electrochemical Biosensors . . . . . . . . . 12.5 Enzymatic Sensing of Glucose . . . . . . . . 12.6 Estimation of Michaelis-Menten Constants 12.7 Non-enzymatic Sensing of Glucose . . . . . 12.8 Enzymatic Sensing of Urea . . . . . . . . . .

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263 263 263 264 266 267 270 271 271

Part II

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Biochemical Techniques

13 Surface Plasmon Resonance Spectroscopy 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 13.2 Details of SPR Set Up . . . . . . . . . . . . . . . . . . 13.3 Surface Plasmon Resonance and Refractive Indices . 13.4 Kinetic Applications of SPR Spectroscopy . . . . . .

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279 279 280 281 284

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Biophysical Chemistry

14 Affinity Chromatography 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 14.2 Methodology . . . . . . . . . . . . . . . . . . . . . 14.3 Types of Affinity Chromatography (A.C.) . . . . . 14.4 Kinetic Applications of Affinity Chromatography

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287 287 288 294 297

15 Capillary Electrophoresis 15.1 Introduction . . . . . . . . . . . . . . . 15.2 Basic Instrumentation . . . . . . . . . . 15.3 Capillary Diameter and Joule Heating 15.4 Various Types of Electrophoresis . . . 15.5 Chiral Recognition . . . . . . . . . . .

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301 301 301 303 303 309

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16 NMR Technique in the Elucidation of Biochemical Problems 16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2 Basics of NMR . . . . . . . . . . . . . . . . . . . . . . . . . 16.3 Applications of NMR . . . . . . . . . . . . . . . . . . . . . 16.4 Applications of NMR in Biomedical Research . . . . . . .

17 Applications of ESR 17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.2 Advances in Magic Angle Spinning (MAS) NMR . . . . . . 17.3 Protein Structure Determination . . . . . . . . . . . . . . . 17.4 Electron Nuclear Double Resonance Spectroscopy (ENDOR), Electron Spin Echo Envelope Modulation (ESEEM) and Hyperfine Sub-Level Correlation (HYScore) Spectroscopic Techniques . . . . . . . . . . . . . . . . . . . 17.5 Structural and Dynamical Information of Biological Systems . . . . . . . . . . . . . . . . . . . . . . . 17.6 Topology of Proteins . . . . . . . . . . . . . . . . . . . . . . 17.7 SDSLEPR Methods Under High Fields/ High Frequencies . . . . . . . . . . . . . . . . . . . . . . . . 17.8 Double Site-Directed Spin Labeling Methods . . . . . . . . 17.9 Other Important Biological Systems . . . . . . . . . . . . . 18 Flow Methods for the Kinetic Study of Fast Biochemical Reactions 18.1 Introduction . . . . . . . . . . . . . . . . 18.2 Experimental Arrangement . . . . . . . 18.3 Reactions Studied Using this Technique 18.4 Applications to Unimolecular Reactions

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Table of Contents 

18.5 Applications Involving Competitive Reactions . . . . . . . 18.6 Applications Involving Multi-step Reactions . . . . . . . . 19 Temperature Jump Relaxation Technique 19.1 Introduction . . . . . . . . . . . . . . . . . . . 19.2 Schematic Diagram of the Apparatus . . . . . 19.3 Follow Up of the Change in Concentration of Reactants by Spectrophotometry . . . . . . . 19.4 Applications . . . . . . . . . . . . . . . . . . .

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20 Flash Photolysis Technique 20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.2 Principle of the Method . . . . . . . . . . . . . . . . . . . . 20.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . .

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21 Pressure Jump Relaxation Method 21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Experimental Arrangement and Methodology . . . . . . . 21.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . .

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22 Circular Dichroism as a Tool for the Analysis of Biochemical Reactions 22.1 Introduction . . . . . . . . . . . . . . . . . . . 22.2 Principle . . . . . . . . . . . . . . . . . . . . . 22.3 Experimental Set Up . . . . . . . . . . . . . . 22.4 Methodology . . . . . . . . . . . . . . . . . . 22.5 Disadvantages as Limitations . . . . . . . . . 22.6 Applications . . . . . . . . . . . . . . . . . . .

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23 Applications of Isothermal Calorimetry 23.1 Introduction . . . . . . . . . . . . . . 23.2 Experimental Set Up . . . . . . . . . 23.3 Applications . . . . . . . . . . . . . . 23.4 Mutational Studies . . . . . . . . . . 23.5 Interaction of Transducer Fragments

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24 Principles of Differential Scanning Calorimetry 24.1 Introduction . . . . . . . . . . . . . . . . . . . 24.2 Experimental Set Up . . . . . . . . . . . . . . 24.3 Methodology . . . . . . . . . . . . . . . . . . 24.4 Illustrative Application of DSC . . . . . . . .

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25 Applications of Gel Filtration Technique in the Separation of Biomolecules 25.1 Introduction . . . . . . . . . . . . . . . . . . 25.2 Methodology of Gel Filtration . . . . . . . . 25.3 Principle of Gel Filtration . . . . . . . . . . 25.4 Applications . . . . . . . . . . . . . . . . . .

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26 Gel Electrophoresis and its Applications to Biochemical Analysis 26.1 Introduction . . . . . . . . . . . . . . . . 26.2 Nature of Gels Commonly Employed . 26.3 Experimental Arrangement . . . . . . . 26.4 Applications of Gel Electrophoresis . . . 26.5 Isoelectric Focusing (IEF) . . . . . . . . .

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401 401 402 403 404 407

27 Uses of Analytical Ultracentrifugation Methods 27.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 27.2 Details of the Apparatus . . . . . . . . . . . . . . . . . 27.3 Detection Method and Data Collection . . . . . . . . . 27.4 Rayleigh Interference Optics . . . . . . . . . . . . . . . 27.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . 27.6 Determination of Sedimentation Coefficient . . . . . . 27.7 Effect of Association on Sedimentation Coefficient . . 27.8 Active Enzyme Sedimentation . . . . . . . . . . . . . . 27.9 Estimation of Diffusion Coefficients . . . . . . . . . . 27.10Estimation of Molar Mass . . . . . . . . . . . . . . . . 27.11Thermodynamic Parameters of Association Reactions 27.12Sedimentation in Biological Environments . . . . . . . 27.13Density Gradient Sedimentation Equilibrium . . . . .

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409 409 409 410 411 411 413 414 415 415 416 417 418 418

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421 421 421 423 426 426 426 427

28 Ion Exchange Chromatography 28.1 Introduction . . . . . . . . . . . . . . . . 28.2 Mechanism of Ion Exchange . . . . . . . 28.3 Applications . . . . . . . . . . . . . . . . 28.4 Purification of Adenovirus . . . . . . . . 28.5 Separation of Membrane Phospholipids 28.6 Separation of Soyabean Proteins . . . . 28.7 Choice of Column Media . . . . . . . . .

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Table of Contents 

29 Surface Enhanced Raman Scattering 29.1 Introduction . . . . . . . . . . . . 29.2 Principle of SERS . . . . . . . . . 29.3 Experimental Aspects . . . . . . . 29.4 Applications of SERS . . . . . . .

xv

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429 429 429 431 433

30 Mass Spectrometry and its Applications in the Analysis of Biomolecules 30.1 Introduction . . . . . . . . . . . . . . . . . . 30.2 Principle of the Technique . . . . . . . . . . 30.3 Basic Components of a Mass Spectrometer 30.4 Ionisation Methods in Mass Spectrometry . 30.5 Applications . . . . . . . . . . . . . . . . . . 30.6 Analysis of Glycoproteins . . . . . . . . . . 30.7 ESI of Equine Apomyoglobin . . . . . . . . 30.8 Analysis of Phosphoproteins . . . . . . . . 30.9 Protein Ladder Sequencing . . . . . . . . . 30.10Specific Examples of Biomolecules . . . . . 30.11Peptides, Proteins and Polynucleotides . . 30.12Polysaccharides . . . . . . . . . . . . . . . .

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441 441 441 442 442 443 444 444 445 445 446 447 448

31 X-Ray Studies in the Elucidation of Structure of Biomolecules 31.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Bragg’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Structural Determination of Proteins . . . . . . . . . . . . . 31.4 X-ray Structures of Haemoglobin and Myoglobin . . . . . . 31.5 Photosynthetic Reaction Centers . . . . . . . . . . . . . . . 31.6 Ribosomal Subunit . . . . . . . . . . . . . . . . . . . . . . .

451 451 452 456 456 457 457

32 CRISPR-CAS-9, A Method for Genome Editing 32.1 Introduction to CRISPR-CAS-9 . . . . . . . . 32.2 Genesis of the Discovery . . . . . . . . . . . . 32.3 Details on Enzyme “CAS-9” . . . . . . . . . . 32.4 CAS-9 Mechanism . . . . . . . . . . . . . . . 32.5 Target DNA Binding and Cleavage by CAS-9

459 459 460 460 461 464

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Appendix A: Donnan Membrane Potential

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465

xvi 

Biophysical Chemistry

Appendix B: Nernst Planck Equation B.1 Nernst–Planck Equation from Onsager’s Linear Flux-Force Relation ..................................................................

469

Appendix C: Goldman-Hodgkin-Katz Voltage Equation

473

Appendix D: Salient Aspects of COVID-19 D.1 Introduction ............................................................................... D.2 Composition of the COVID-19 Virus . . . . . . . . . . . . . D.3 Symptoms and Other Effects of COVID-19 . . . . . . . . . D.4 Remedial Measures

475 475 475 476 476

Notes and Bibliography

479

470

List of Figures 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 2.1

Components of animal cell. . . . . . . . . . . . . . . Parts of the human cell. . . . . . . . . . . . . . . . . . Two types of cells: (a) Eukaryotic cell and (b) Prokaryotic cell. . . . . . . . . . . . . . . . . . . . Components of the cell. . . . . . . . . . . . . . . . . . Lysosome. . . . . . . . . . . . . . . . . . . . . . . . . Structure of phospholipid. . . . . . . . . . . . . . . . Structure of a phospholipid bilayer. . . . . . . . . . . Representation of a cell membrane. . . . . . . . . . . Simple diffusion across the cell. . . . . . . . . . . . . Facilitated diffusion. . . . . . . . . . . . . . . . . . . Na+ /K+ pump. . . . . . . . . . . . . . . . . . . . . . Three forms of endocytosis. . . . . . . . . . . . . . . Exocytosis is endocytosis in reverse. . . . . . . . . . Pancreatic acinar cells. . . . . . . . . . . . . . . . . . Relative permeability of a phospholipid bilayer. . . Mediated transport: (a) Passive transport and (b) Active transport. . . . . . . . . . . . . . . . . . . . Secondary active transport. . . . . . . . . . . . . . . Scheme for transport of Na+ and K+ by Na+ /K+ ATPase. . . . . . . . . . . . . . . . . . . . . . . . . . . Scheme for the active transport of Ca2+ by the Ca2+ ATPase. . . . . . . . . . . . . . . . . . . . . . . . . . . Boltzmann distribution of permeating cations and anions. . . . . . . . . . . . . . . . . . . . . . . . .

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4 6

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8 11 12 13 13 16 18 19 20 22 23 23 25

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25 26

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28

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35

xvii

xviii 

2.2 2.3 2.4 2.5

4.1 4.2 4.3 4.4 5.1 5.2 6.1

7.1 7.2 7.3 7.4 7.5 7.6 7.7 8.1 8.2 8.3 8.4 8.5 8.6 8.7 9.1 9.2 9.3 9.4

Biophysical Chemistry

Distribution of ions on negatively charged surfaces. . . Permeability of cations and anions. . . . . . . . . . . . . The surface free energy of water. . . . . . . . . . . . . . (a) The equilibria among a lipid monomer, (b) a vesicle containing N molecules and (c) a microscopic lipid bilayer. . . . . . . . . . . . . . . . . . . . . . . . . . Schematic representation of hydrophobic and polar groups in soaps. . . . . . . . . . . . . . . . . . . . Schematic depiction of lipid bilayers. . . . . . . . . . . . Energetically favourable structures of bilayers. . . . . . Structure of cholesterol in free state and fluid region. . . Fischer projection and ball-stick model. . . . . . . . . . Potentiometric titration of aqueous alanine solution. . . Structure of tetrapeptide containing Val-gly-Serine-Ala with L-Valine being at left end and L-Alanine at the right end. . . . . . . . . . . . . . . . . . . . . . . . . . . . Structure of α-helix. . . . . . . . . . . . . . . . . . . . . . Quaternary structure of a complex globular protein (dimer). . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structure of hemoglobin. . . . . . . . . . . . . . . . . . . Schematic depiction of helix-coil transitions in proteins. Shapes of proteins under different coordinates. . . . . . An energy diagram of a two-state folding event. . . . . (i) Native and (ii) a compact structure of amino acid chain lengths 16. . . . . . . . . . . . . . . . . . . . . . . . Structure of nucleoside, nucleotide, nucleoside di and tri phosphates. . . . . . . . . . . . . . . . . . . . . . . . . Structures of purines. . . . . . . . . . . . . . . . . . . . . Structures of pyrimidines. . . . . . . . . . . . . . . . . . The structural elements of the nucelosides and the phosphate bearing nucleotides. . . . . . . . . . . . . . . Scheme depicting electrochemical reduction of adenine. Electro-oxidation of guanine. . . . . . . . . . . . . . . . Helical structure of DNA. . . . . . . . . . . . . . . . . . Schematic depiction of enzyme - substrate complex. . . Energy diagram with and without the presence of enzymes. . . . . . . . . . . . . . . . . . . . . Dependence of the reaction rate on concentrations of (a) enzyme and (b) substrate. . . . . . . . . . . . . . . . Lineweaver-Burke plot. . . . . . . . . . . . . . . . . . . .

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36 37 40

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40

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90 106 106 106 115 118

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129 149

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150 152 154 155 156

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166 167 167

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167 168 168 169 182

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182

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185 186

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 xix

List of Figures

9.5

Variation of the rate of enzyme-catalysed reaction with pH. . . . . . . . . . . . . . . . . . . . . . . . . 9.6 Positioning of a substrate to an active site. . . . . . . . . . . 9.7 Graph showing the variation of reaction rate with substrate concentration. . . . . . . . . . . . . . . . . . . . . 9.8 Graph showing the variation of reaction rate: (i) without inhibitor; (ii) competitive and (iii) non-competitive inhibitor. . . . . . . . . . . . . . . . . . 9.9 Variation of the reciprocal velocity with reciprocal substrate concentration. . . . . . . . . . . . . . . . . . . . . 9.10 Dependence of the maximum velocity on the substrate concentration. . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Conversion of an apoenzyme to a holoenzyme. . . . . . . . 10.2 Conversion of an active enzyme with substrate to yield an enzyme with products. . . . . . . . . . . . . . . . . . . . 12.1 Sketch of a typical biosensor. . . . . . . . . . . . . . . . . . . 12.2 Applications of biosensors. . . . . . . . . . . . . . . . . . . . 12.3 Schematic diagram of thermometric biosensor. . . . . . . . 12.4 Sketch of an optical biosensor. . . . . . . . . . . . . . . . . . 12.5 Schematic variation of amperometric current with time. . . 13.1 Air-Solution interface. . . . . . . . . . . . . . . . . . . . . . 13.2 Reflection of wave for gold film in air. . . . . . . . . . . . . 13.3 Variation of SPR angle with refractive index. . . . . . . . . 13.4 Binding of rabbit lgG to protein A and anti-rabbit to lgG to FAB . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.5 Illumination-induced activity of G-protein and its desorption form the membrane. . . . . . . . . . . . . . . . . 14.1 Separation procedure in affinity chromatography. . . . . . 14.2 Variation of absorbance with time. . . . . . . . . . . . . . . 14.3 Structure of agarose. . . . . . . . . . . . . . . . . . . . . . . 14.4 Structure of silica. . . . . . . . . . . . . . . . . . . . . . . . . 14.5 Dependence of eluted amount with elution volume. . . . . 14.6 Different types of immobilization methods. . . . . . . . . . 14.7 Immobilization by N-hydroxy succinimide method. . . . . 14.8 Immobilization using carbonyl diimidazole method. . . . . 14.9 Target protein identification using affinity chromatography. . . . . . . . . . . . . . . . . . . . . . . . . 14.10 Application of high performance affinity chromatography in estimating rate constants. . . . . . . . . . . . . . . . . . .

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190 192

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196

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197 217

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218 263 264 265 266 269 280 282 282

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282

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283 288 289 290 290 292 292 293 294

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297

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xx



Biophysical Chemistry

14.11 Binding of D-tryptophan with a HPAC column containing immobilized HSA. . . . . . . . . . . . . . . . . . . . . . . . . 15.1 Diagram of a capillary electrophoresis unit. . . . . . . . . . . 15.2 Effect of pH on electro osmotic flow. . . . . . . . . . . . . . . 15.3 Separation of components using electrophoretic. . . . . . . . 15.4 Migration of charges using isoelectric focusing method. . . . 15.5 Separation of proteins using isoelectric focusing method. . . 15.6 Size separation using capillary gel electrophoresis. . . . . . . 15.7 Physical and chemical gels. . . . . . . . . . . . . . . . . . . . 15.8 Capillary gel electrophoresis of thymidine synthetic polymer. . . . . . . . . . . . . . . . . . . . . . . . . . 15.9 Isotachophoresis of a mixture of anions. . . . . . . . . . . . . 15.10 Separation of chiral amino acids using MECC. . . . . . . . . 16.1 Basic features of NMR. . . . . . . . . . . . . . . . . . . . . . . 16.2 Protein sequence formed by connecting peptide bonds. . . . 17.1 Energy-changes in electron spins in the absence and presence of a magnetic field. . . . . . . . . . . . . . . . . . . . 17.2 Magnetic Resonance Imaging principle of body and tissues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.3 Protein structure determination using solid state NMR. . . . 17.4 Block diagram of a EPR spectrometer. . . . . . . . . . . . . . 17.5 Structure of MTSL and the resulting side chain produced by reaction with cysteine residue of the protein. . . . . . . . . 17.6 Molecular structure of vimentin. . . . . . . . . . . . . . . . . 17.7 Three pulse ESEEM spectra with T = 200 ns of the I + 2 and I + 3 labelled Leu for AchR M-282 helical peptide in lipid bilayer and Ubiquitin β-sheet peptide in solution. . . . . . . 17.8 Identification of transmembrane region of α-helical nature of C99 amyloid precursor protein in proteoliposomes. . . . . 17.9 EPR spectra and corresponding simulations at three fields (or frequencies) of the radical intermediate in the Phycocyanobilin—Ferredoxin oxidoreductase system. . . . . 18.1 A simple experimental set up for flow methods. . . . . . . . 18.2 Technique of stopped flow method. . . . . . . . . . . . . . . . 18.3 Rapid interaction between apotransferrin and Zn2+ . . . . . . 18.4 (a) Variation of intensity of fluorescence with time in the kinetic study of high mobility protein with cisplatin modified DNA and (b) Variation of k obs with concentration of HMGI domain. . . . . . . . . . . . . . . . . . . . . . . . . . .

298 302 303 304 305 305 306 306 307 308 310 314 315 320 322 323 323 325 326

328 329

331 335 336 338

338

List of Figures

19.1 19.2 20.1 21.1 22.1 22.2 22.3 22.4 22.5 23.1 23.2 23.3 24.1 24.2 24.3 25.1

25.2 25.3 25.4 26.1 26.2 26.3 27.1 27.2 27.3 27.4

 xxi

Schematic diagram of a temperature jump apparatus developed by Eigen and his group. . . . . . . . . . . . . . . . Variation of concentration of species with time following a temperature jump. . . . . . . . . . . . . . . . . . . . . . . . A flash photolytic unit. . . . . . . . . . . . . . . . . . . . . . . Experimental arrangement of a pressure jump unit. . . . . . Different types of CD spectra. . . . . . . . . . . . . . . . . . . CD spectra of flavoproteins in the near UV and visible region. . . . . . . . . . . . . . . . . . . . . . . . . . CD spectra of isocitrate lyase from E.coli. . . . . . . . . . . . . CD spectra of the same species in the near UV region. . . . . CD spectra of α-lactalbumin (a) and (b) represent far UV and near UV spectra at pH = 7.0. . . . . . . . . . . . . . . . . Experimental set up of an isothermal heat flow calorimeter. . . . . . . . . . . . . . . . . . . . . . . . . . . Binding curve obtained from unprocessed data. . . . . . . . Thermodynamic profiles of HIV proteanase inhibitors. . . . Block diagram of a heat flux differential scanning calorimeter. . . . . . . . . . . . . . . . . . . . . . . . Single heat flux source in DSC. . . . . . . . . . . . . . . . . . Curve trace obtained with the solution of Arg96 → His mutant of the lysozymes of T4 phage. . . . . . . . . . . . . . . . . . . Schematic picture of (A) a bead with enlargement, (B) sample molecules diffusing into bead and (C) separation process. . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of elution. . . . . . . . . . . . . . . . . . . Typical elution pattern of dialysis (on Sephadex G25). . . . . Separation of RNAase from protease in pancreatic extract using Sephadex G-75 column. . . . . . . . . . . . . . . . . . . Experimental set-up of gel electrophoresis. . . . . . . . . . . Agarose gel electrophoresis pattern for cleavage of supercoiled PUC DNA. . . . . . . . . . . . . . . . . . . . . . . Scheme depicting the separation of molecules by charge differences. . . . . . . . . . . . . . . . . . . . . . . . Schematic depiction of ultracentrifuge pattern. . . . . . . . . Movement of the boundary in a sedimentation experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Estimation of the sedimentation coefficient. . . . . . . . . . . Concentration dependence of weight average “S” for DIP-α chymotrypsin. . . . . . . . . . . . . . . . . . . . . . . .

346 347 352 356 362 366 366 367 369 376 378 381 388 388 390

396 397 398 398 403 405 407 410 412 414 415

xxii 

27.5 28.1 28.2 28.3 28.4 28.5 29.1 29.2 29.3 29.4 29.5 29.6 29.7

29.8 30.1 30.2 30.3 30.4 30.5 30.6 30.7 30.8 31.1 31.2 31.3 31.4

Biophysical Chemistry

Dependence of the apparent molar mass of DNA on concentration. . . . . . . . . . . . . . . . . . . . . . . . . . Separation based on the binding of analytes to positively or negatively charged groups on the stationary phase. . . . . Separation mechanism in ion exchange. . . . . . . . . . . . . Schematic depiction of charged variants of monoclonal antibodies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two examples illustrating the use of BioMAB column for identification of c-terminal truncation on heavy chains. . . . High resolution of a mixture of proteins with a wide range of isoelectric points. . . . . . . . . . . . . . . . . . . . . . . . . Electromagnetic and chemical enhancement mechanism. . . SERS enhancement and enhancement mechanism. . . . . . . Metals exhibiting SERS and their wave length ranges. . . . . Schematic depiction of SERS for spherical aggregates. . . . . Field of a point dipole. . . . . . . . . . . . . . . . . . . . . . . SERS of dopamine in silver colloidal solution. . . . . . . . . . (A) Scheme of an immuno assay system using two different SERS Labels. (B) SERS signatures of three types of reporter labeled immuno gold colloid (a) MBA/goat anti-rat IgG, (b) NT/goat antirat IgG, (c) TP/goat anti rabbit IgG and (d) goat anti rat IgG. . . . . . . . . . . . . . . . . . . . . . . . Cleavage of single nucleotides and attachment to colloidal silver or gold clusters. . . . . . . . . . . . . . . . . Components of a mass spectrometer. . . . . . . . . . . . . . . ESI of equine apomyoglobin. . . . . . . . . . . . . . . . . . . Distribution of charged states characteristic of native and denatured proteins. . . . . . . . . . . . . . . . . . . . . . Denaturation of myoglobin in an acidic environment. . . . . ESI of cytochrome-C and glucagon. . . . . . . . . . . . . . . . Fragmentation pattern of protonated peptide in FAB/MS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mass spectrometry of nucleotide structures. . . . . . . . . . . Pattern of mass spectrum in polysaccharides. . . . . . . . . . Schematic diagram of an X-ray diffractometer. . . . . . . . . Reflection of X-rays in ( hkl ) planes of a crystal. . . . . . . . . Diffraction angle of X-rays. . . . . . . . . . . . . . . . . . . . . (a) X-ray camera and (b) X-ray film showing diffraction lines. . . . . . . . . . . . . . . . . . . . . . . . . . .

417 422 423 424 425 425 430 430 431 432 433 434

435 437 442 444 445 446 447 447 448 449 452 452 453 453

List of Figures

31.5 31.6 32.1 32.2 32.3 32.4 32.5 A.1 D.1

Lines corresponding to planes of different cubic structures. . . . . . . . . . . . . . . . . . . . . . . . . X-ray structure of Myoglobin obtained at high resolution. . . . . . . . . . . . . . . . . . . . . . . . Parts of a bacterial immune system: Genomic DNA, CAS-9, target sequence and guide RNA. . . . . . . . . . . The six domains of CAS-9. . . . . . . . . . . . . . . . . . . Single strand of RNA forming a T-shaped molecule. . . . CAS-9 complex (inactive) and target complimentary region of guide RNA. . . . . . . . . . . . . . . . . . . . . . CAS-9/guide RNA and target DNA leading to CAS-9/guide RNA complex bound to target DNA. . . . . Schematic depiction of the Donnan membrane potential. Schematic depiction of Corona virus. . . . . . . . . . . . .

 xxiii

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455

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457

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459 461 462

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462

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463 465 475

List of Tables 3.1 75 3.2 3.3 3.4 4.1 5.1 5.2 6.1 6.2 6.3 6.4 6.5 7.1 7.2 7.3 7.4 7.5 7.6

Enthalpy of formation (ΔH ◦f ) and ΔHc◦ at 298K and S◦ . . . . Gibbs energy of formation (ΔG ◦f ) of carbohydrates ................................................................................. Thermodynamic datatheir for anomeric conversions Redox reactions and E◦ and ΔG values. . at . . 298 . . K. . . . . Examples of a few fatty acids. . . . . . . . . . . . . . . . . . . Classification of amino acids based on polarity. . . . . . . . . Isoelectric point of a few amino acids. . . . . . . . . . . . . . Residues, their sources and amino acid sequences. . . . . . . Critical Aggregation Concentration (CAC) of a few peptides and their diffusion coefficients. . . . . . . . . . . . . . . . . . Variation of the MB peak current with time. . . . . . . . . . . Rate constant data for the effective cleavage rate of MB in the peptides TA-1 and MA-1 Current potential response of peptides from cyclic voltammetry at a scan rate of 500 mv sec−1 at 25◦ C. . . . . . Classification of proteins based on structure. . . . . . . . . . Equilibrium constants, Kh−c for helix-coil transformation. . . Electrophoretic mobility data of a few typical proteins. . . . Kinetic parameters for unfolding of S6 in SDS. . . . . . . . . Thermodynamic data of polypeptides in proteins relating to helix-coil transformation in aqueous solutions. . . . . . . . . Equilibrium constants (Khel −nonhel ) for some natural amino acids in nine globular proteins. . . . . . . . . . . . . .

75 80 90 116 119 132 134 138 138 138 144 153 155 157 158 159

xxv

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7.7

8.1 8.2 8.3 8.4 8.5 8.6 8.7

8.8 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 10.1 10.2 10.3 10.4 10.5 10.6 10.7

Biophysical Chemistry

A( p, q) values which arise from the counting of ‘hydrophobic-polar’ contacts for a square lattice of 16 sites, assuming periodic boundary conditions. . . . . . . . Comparison of nucleosides and nucleotides. . . . . . . . . . Typical polarographic data for the reduction of adenine, cytosine and guanine. . . . . . . . . . . . . . . . . . . . . . . . Functional importance of a few nucleotides. . . . . . . . . . . Sites of protonation and pKa ’s of four nucleobases and the ribose-phosphate backbone. . . . . . . . . . . . . . . . . . . . pKa data and ΔG ◦ values of nucleotides. . . . . . . . . . . . . Conductivity data of nucleotides and nucleotides at 400 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermodynamic parameters for DNA duplex formation in 4 MNaCl and 4 M choline dihydrogen phosphate (Choline dhP). . . . . . . . . . . . . . . . . . . . . . . . . . . . Stability constant data of the complexes formed between the nucleotides and polyamines in aqueous solution at 25◦ C. . . Kinetic data on some reactions catalysed by enzymes (or inhibited in presence of inhibitors). . . . . . . . . . . . . . Kinetic expressions for different inhibition types. . . . . . . . Conversion of zymogens to active enzymes. . . . . . . . . . . Data on glycolic enzymes. . . . . . . . . . . . . . . . . . . . . Activation parameters for the reactions of some enzymes. . . Enzymatic activity of lactose dehydrogenase. . . . . . . . . . Turn over numbers for selected enzymes. . . . . . . . . . . . Some industrial processes using enzymes. . . . . . . . . . . . Illustrative examples of industrial catalysts. . . . . . . . . . . Michaelis-Menten constants for some enzyme substrate reactions. . . . . . . . . . . . . . . . . . . . . . . . . Typical combinations of enzyme-co-enzyme systems in presence of vitamins for their effective functioning. . . . . Water soluble vitamins along with their co-enzymes and their physiological functions. . . . . . . . . . . . . . . . . Fat soluble vitamins and their physiological function. . . . . Typical examples of fat-soluble vitamins and their source. . . Water soluble Vitamins: Vitamins B-1 to B-7, B-9, B-12, Vitamin C and their source. . . . . . . . . . . . . . . . . . . . List of reactions catalysed by nicotinamide nucleotides. . . . Redox potential data on water soluble B-Vitamins. . . . . . .

160 165 168 170 173 175 175

177 178 187 195 199 201 204 207 208 209 210 212 219 221 222 223 223 225 227

List of Tables

10.8 10.9 10.10 10.11 10.12 10.13 10.14 10.15 10.16

10.17 10.18 10.19

10.20 10.21 11.1 11.2 11.3 11.4 11.5 11.6 12.1 12.2

 xxvii

Typical examples of enzymes (belonging to group of flavoproteins) and reactions catalysed by them. . . . . . . . . Half wave potential data of a few vitamins and related compounds. . . . . . . . . . . . . . . . . . . . . . . . . Average dissociation constant of thiamine at different temperatures. . . . . . . . . . . . . . . . . . . . . . . Kinetic data on the reaction of hydrated e− with cobalamine. . . . . . . . . . . . . . . . . . . . . . . . . . Redox potential of cobalamines. . . . . . . . . . . . . . . . . . Redox potential data against S.H.E. at pH = 7.0. . . . . . . . . Kinetic data on the oxidation of pyridoxine. . . . . . . . . . . Protonation constants of folic acid and stability constants of metal complexes. . . . . . . . . . . . . . . . . . . . . . . . . Conductances of the metal complexes formed at two points of addition in the titration of 25 ml of metal ions (1 × 10−3 M) with folic acid (0.01 M). . . . . . . . . . . . . . . Values of surface tension and conductivity at the inflection point pertaining to the formation of 1: 1 complex. . . . . . . Association constant (Ka ) and thermodynamic parameters of different Vit-β-cyclodextrin inclusion complexes. . . . . . . . Distribution constants (K) and Gibbs free energy changes (ΔG ◦ ) of Vitamin E partitioned between dry reversed micelles of surfactants and non-polar organic solvents. . . . . . . . . . . Optical data of Vit-K2 and Vit D3 in ethanol. . . . . . . . . . . Zeta potential data of loaded liposomes. . . . . . . . . . . . . Standard Gibbs energies of hydrolysis (ΔG ◦ ) of some phosphorylated compounds. . . . . . . . . . . . . . . . . . . Standard Gibbs free energies of phosphoesters. . . . . . . . . Gibbs free energy changes for ATP hydrolysis in various organisms under different physiological conditions. . . . . . Enthalpy changes of reactions involving ATP and related compounds. . . . . . . . . . . . . . . . . . . . . . . . . Dissociation constants and enthalpy changes for reactions involving ATP. . . . . . . . . . . . . . . . . . . . . . . . . . . . Gibbs free energy changes of reference compounds. . . . . . Typical range of detection accomplished for analytes using chemically modified electrodes. . . . . . . . . . . . . . Illustrative examples of analytes and corresponding enzymes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

229 234 235 236 236 237 238 238

239 239 239

239 241 241 249 250 251 256 257 257 268 270

xxviii 

14.1 14.2 14.3 16.1 23.1 23.2 23.3 23.4

23.5 23.6 26.1 30.1

Biophysical Chemistry

Examples of pre-activated products for immobilizing ligands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Examples of commonly used lectins for isolation of carbohydrates and polysaccharides. . . . . . . . . . . . . . List of chelating agents and corresponding metal ions. . . . Mass numbers, atomic numbers and spin quantum numbers. . . . . . . . . . . . . . . . . . . . . . . . Enthalpy–entropy compensation in the binding of F4E to 7 methyl-GpppG. . . . . . . . . . . . . . . . . . . . . . . . Binding constants and thermodynamic data of tyrosyl phosphopeptides with different SH2 domains at 298 K. . . Thermodynamic data for binding in ATP in presence of various mutants. . . . . . . . . . . . . . . . . . . . . . . . Thermodynamic parameters of citrate binding to CitAPhis at 298 K in 50 mM phosphate buffer at different pH’s as determined by ITC. . . . . . . . . . . . . . . . . . . . . . Thermodynamic parameters of citrate binding at different concentrations of MgCl2 . . . . . . . . . . . . . . . . . . . . . Thermodynamic parameters pertaining to binding affinities. . . . . . . . . . . . . . . . . . . . . . . . . Illustrative examples of various gels. . . . . . . . . . . . . . General range of applications of different MS methods. . .

.

291

. .

295 296

.

314

.

380

.

382

.

383

.

384

.

384

. . .

385 402 446

List of Symbols and Acronyms ΔH ◦ γ Ψ ε A aX dζ dq Ji (4 Fe-4S)+ 1,2, diacyl DPPC 1,3-BPG A,B,C,D NP’s A.C ADP3− Acetyl CoA ACTH ADP Ala AMP AN Arg AoT

Enthalpy change between the products and reactants surface tension Electrical potential dielectric constant Affinity Activity of X Degree of advancement of a reaction Heat exchanged by a system heat flux of species Ji iron-sulfur cofactors 1,2 diacylphosphatidylcholine 1,3-bisphosphoglycerate A, B, C, D natriuretic peptides Affinity chromatogrphy Adenosine diphosphate anion Acetyl coenzyme A Adrenocorticotropic hormone Adenosine diphosphate Alanine Adenosine monophosphate Acetonitrile Arginine Sodium bis (2-ethylhexyl) sulfosuccinate

xxix

xxx



Biophysical Chemistry

Asn ATP B0 BCCP bipy BLES C.M.R.F CAC CDTA DEER DHAP DHF DNA DPPC DSPE e− hyd E.coli EDTA EAK-16-II ECF E1/2 ENDOR ENO EOF EPC EPR ER FAD+ FADH FBA FMN FUM GLn GLP-1 Glu Gly GMP GSH GSSG

Asparagine Adenosine triphosphate Strength of magnetic field Biotin carboxyl carrier protein Bipyridyl Bovine lipid extract sulfactant Carbomethoxy riboflavin Critical aggregation concentration Trans,1,2-cyclohexyl ethylene dinitrilo tetraacetic acid, C14 H22 N2 O8 Double electron-electron resonance Dihydroxyacetone phosphate Dihydrofolic acid Deoxyribonucleic acid Dipalmitoyl phosphatidylcholine Distearoyl (Phosphatidylethanolamine) hydrated electron Escherichia coli Ethylenediaminetetraacetic acid (Ala-Gln-Ala-Gln-Ala-Lys-Ala-Lys)2 Extracellular fluid Half wave potential Electron nuclear double resonance spectroscopy Enolase Electroosmotic flow Egg phosphatidylcholine electron paramagnetic resonance Endoplasmic reticulum Flavin adenine dinucleotide Reduced form of Flavin adenine dinucleotide Fructose 1,6-bisphosphate aldolase Flavin mononucleotide Fumarate hydratase Glutamine Glucose like peptide 1 Glutaric acid Glycine Guanosine-5’-monophosphate Reduced form of glutathione Oxidised form of glutathione

List of Symbols and Acronyms

HA IEF IF Ilc IMP In IPP ITP Km L.A LDH Lecithin Leu LipS2 LTAB LTAC malonyl coA MAS Mb mC MDH MECC MRI NAD+ NADH NADP+ NAG NC NHS Nm−1 NoE NRPS ODN OEC PTP PAGE Pc PE PEG PELDOR

Dehydroascorbic acid Isoelectric focusing Interstitial fluid Isoleucine Inosine-5’-monophosphate Inhibitor (also Imb) Isoleucine-Proline-Proline Isotachophoresis Michaelis-Menten constant Lipoic acid Lactic dehydrogenase L-α-phosphatidylcholine Leucine LipoylS2 Lauryl trimethyl ammonium bromide Lauryl trimethyl ammonium chloride malonyl coenzyme A Magic angle spinning Myoglobin Millicoulomb malate dehydrogenase Micellar electrokinetic capillary chromatography Magnetic resonance imaging Nicotinamide adenine dinucleotide Reduced form of NAD+ Nicotinamide adenine dinucleotide phosphate N-acetyl glucosamine Noncompetitive inhibition N-hydrosuccinimide Newton per meter Nuclear Overhauser effect Nonribosomal peptide synthetase Oligodeoxyncleotide Oxygen evolving complex Phosphoryl transfer potential Polyacrylamide gel electrophoresis Phosphatidylcholine Phosphotidylethanolamine polyethylene glycol Pulse electron double resonance spectroscopy

 xxxi

xxxii



Biophysical Chemistry

PEP PET PFK PGD PGI PGM Phe PHI PI Pi PPY R5PI RBP RDC RNR rRNA SA SAM SDS SDSL Ser SM Succinyl CoA 5THF Thr TOR TPI TPP Tyr UC Vitamin A Vitamin B12 Vitamin B1 Vitamin B2 Vitamin B5 Vitamin B6 Vitamin B7 Vitamin B9 Vitamin C Vitamin D3 Vitamin E Vitamin K

Phosphoenolpyruvic acid 3’-ethyl phosphate Phosphofructokinease Phosphogluconate dehydrogenase Phosphoglycerate isomerase Phosphoglycerate mutase Phenylalamine peptide histidine isoleucine pH at isoelectric point Phosphate group Pancreatic polypeptide Ribose-5-phosphate isomerase Ribflavin binding protein Residual dipolar coupling Ribonucleotide reductase ribosomal Ribonucleic acid Stearic acid Self assembled monolayer Sodium dodecyl sulfate Site Directed Spin Label Serine Sphingomyelin Succinyl coenzyme A Tetrahydrofolic acid (or Tetrahydrofuran) Threonine Turn over rate Triosephosphate isomerase Thiamine pyrophosphate Tyrosine Uncompetitive inhibition Retinol Cyanocobalamine Thiamine Riboflavin Pantothenic acid Pyridoxin Biotin Folic acid Ascorbic acid cholecalciferol Tocoferol Phylloquinone

Part I

Different Types of Biomolecules

1

Cell and its Biochemical Setup 1.1

Introduction

All living things are composed of cells, which are bound by a membrane and which contain the fundamental molecules of life. A single cell is a complete organism in itself examples of which being yeast or a bacterium. When cells mature they acquire special functions. When these cells cooperate with other special cells, they become building blocks of large multi cellular organisms such as humans and other animals. Cells are much larger than atoms and some single celled organisms are spheres with a diameter of 0.2 μm. Human cells have a mass 4 × 105 larger than the mass of a single micoplasma bacterium, have a diameter of about 20 μm and have a mass of one nanogram.

1.2

Structure of an Animal Cell

The main components of an animal cell are shown in the following diagram (refer Fig. 1.1).

1.2.1

Principal Structures of an Animal Cell

Cytoplasm surrounds the cells specialized structures or organelles. Ribosomes, the site of protein synthesis are found free in the cytoplasm or attached to the endoplastic reticulum through which materials are

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_1

3

4



Biophysical Chemistry

Figure 1.1 Components of animal cell.

transported throughout the cell. Energy needed by the cell is released by the mitochondria. The Golgi complex, stacks of flattened sacs, processes and packages materials to be released from the cell in secretory vesicles. Digestive enzymes are contained in lysosomes. Peroxisomes contain enzymes that detoxify dangerous substances. The centrosome contains the centriols which play a role in cell division. The microvilli are finger-like extensions found on certain cells. Cilia, hair-like structures that extend from the surface of many cells, can create the movement of surrounding fluid. The nuclear envelope, a double membrane surrounding the nucleus, contains pores that control the movement of substances into and out of nucleoplasm. Chromatin, a combination of DNA and proteins that coil into chromosomes make up much of the nucleoplasm. The dense nucleolus is the site of ribosome production.

1.2.2

Structure of a Human Cell and its Functions

A cell is a fully operational living entity. Human beings are composed of multicellular organisms with different types of cells operating together to sustain life. The human body contains other noncellular components such

Cell and its Biochemical Setup

 5

as water, macronutrients like carbohydrates, lipids, proteins and micronutrients like minerals, vitamins and electrolytes. Tissue is composed of a collection of cells and they perform many activities apart from other specific functions of the body.

1.3

Composition of Human Cell

The cell contains a variety of structural components, it known as organelles required to maintain life. The organelles are suspended in a gelatinous matrix known as cytoplasm, which is contained within the cell membrane. The main organelles of the cell may be listed as (i) cell membrane, (ii) nucleus, (iii) mitochondria, (iv) endoplastic reticulum, (v) golgi apparatus, (vi) lysosomes, (vii) peroxisomes, (viii) microfilaments, and (ix) microtubules. The red blood cells of the human body lack organelles. A sketch of the human cell is given in the Figure 1.2. The functions of the various components are briefly described below cell membrane. It is an outer coating of the cell and contains cytoplasm and its contents and organelle. It is a double layered membrane containing proteins and lipids. The lipid molecules on the outer and inner part of the lipid bilayer allow it to transport substances in and out of the cell.

1.3.1

Human Cell

The functions of the human cell vary depending on the type of cell and its location in the body. Organelles are the most basic functional units and they cannot exist or operate without a cell. All organelles work together to keep the cell alive and help it to carry out its specific function. They are highly specialized and have various sizes, shapes. The functions of organelles include intake of nutrients and other substances, their processing, production of new substances, cell replication and energy generation.

6



Biophysical Chemistry

Figure 1.2 Parts of the human cell.

In motile cells like sperm cells, tail like projections allow for cellular locomotion.

1.3.2

Nucleus

The nucleus controls the cell. It contains genes, bunches of DNA which determine all aspects of human anatomy and physiology. The DNA which is organized into chromosomes also contains the blue print specific for each type of cell. It also allows proliferation of the cell. There is an area known as nucleolus in the nucleus, which is an accumulation of RNA and protein. It is also a site where the ribosomal RNA is transcribed from DNA and assembled.

1.3.3

Mitochondria

They are power houses of the cell and break down nutrients to yield energy. They also produce the high energy compound ATP. They are composed of two membranous layers: (i) an outer membrane that surrounds the structure and (ii) an inner membrane that provides sites for energy production. The inner membrane has many folds forming shelves where enzymes attach and oxidize nutrients. The mitochondria also contain DNA which replicates when necessary.

Cell and its Biochemical Setup

1.3.4

 7

Endoplastic Reticulum (ER)

It is a membranous structure that contains a net work of tubules and vesicles. Its structure permits substances to move through it and keep isolated from the rest of the cell until all the manufacturing processes within it are completed. Two types of ER are present: (i) rough (granular) and (ii) smooth (agranular). The smooth ER does not have any attached ribosomes. Its function is to synthesize different types of lipids and it also plays a role in carbohydrate and drug metabolism.

1.3.5

Golgi Apparatus

It is a stacked collection of flat vesicles. Substances produced in ER are transported as vesicles in Golgi apparatus. Products from ER are stored in it and converted into different substances necessary for cell’s various functions.

1.3.6

Lysosomes

They are vesicles that break off from Golgi apparatus. They vary in size and function depending on the type of cell. Lysosomes contain enzymes which help in the digestion of nutrients in the cell. They also break down any cellular debris or invading microorganisms like bacteria. Secretory vesicle is a structure similar to lysosome and it contains enzymes which are used outside the cell. For example, secretory vesicles of pancreatic acinar cell release digestive enzymes which help in the digestion of nutrients in the gut.

1.3.7

Peroxisomes

These organelles are similar to lysosomes and contain enzymes. The enzymes act in the form of H2 O2 to neutralize substances toxic to the cell. Perioxisomes are formed from endoplastic reticulum.

1.3.8

Microfilaments and Microtubules

These are rigid proteinous substances that form the internal skeleton of the cell known as cytoskeleton. Some microtubules also make up centrioles and mitotic spindles within the cell. They are responsible for the division of the cytoplasm when the cell divides. The microtubules are the central component “Cilia” which are small hair like projections that protrude from the surface of certain cells. It is also the central component of specialized

8



Biophysical Chemistry

celia like the tail of sperm cells which acts in a manner as to allow the cell to move in a fluid.

1.4

Eukaryotic and Prokaryotic Cells

Eukaryotes are organisms whose cells possess a nucleus enclosed within a cell membrane. They include multicellular organisms such as plants, animals and fungi. Prokaryotic cells do not possess membrane bound cellular components such as nuclei. They include bacteria and Archaea. The structures of eukaryotic and prokaryotic cells are given in the Figure 1.3.

1.4.1

Similarities and Differences Between the Two Types of Cells

Similarities (i) Cell membrane: Both types of cells have a lipid bilayer which is an arrangement of phospholipids and proteins that acts as a selective barrier between the internal and external environment of the cells. (ii) Genetic material: Eukaryotic and prokaryotic cells use DNA as the basis for their genetic information. The genetic material is needed to regulate the cell function through creation of RNA by transcription followed by the generation of proteins through translation.

Figure 1.3 Two types of cells: (a) Eukaryotic cell and (b) Prokaryotic cell.

Cell and its Biochemical Setup

 9

(iii) Ribosomes: They facilitate RNA translation and creation of protein which is essential to both types of cells. (iv) Cytoplasm: The cytoplasm is the medium in which the biochemical reactions of the cell take place, of which cytosol is the primary component. In eukaryotic cells, the cytoplasm covers all material between plasma membrane and the nuclear envelope including organelles. The material within the nucleus is known as nucleoplasm. In prokaryotes, the cytoplasm encompasses everything within the plasma membrane including the cytoskeleton and genetic material. Differences (i) Cell size: Eucaryotic cells have a size of 10–100μm while prokaryotic cells have size in the range 1–10μm. (μm = 1 micrometer = 10−6 m). (ii) Cell arrangement: Eucaryotes are multicellular whereas prokaryotes are unicellular. However, some unicellular eukaryotes exist such as amoebas, yeast and paramecium. (iii) Membrane bound nucleus: Eucaryotic cells have a true nucleus bound by a double membrane. It contains DNA related functions of the large cell in a small enclosure. This ensures close proximity of materials and increases efficiency for cellular communication and functions. In contrast, the smaller prokaryotic cells have no nucleus. The materials are close to each other and there is a “nucloid” which is the central open region of the cell where the DNA is located. (iv) DNA structure: Eukaryotic DNA is linear and complexed with proteins called “histones” which organize into a number of chromosomes Prokaryotic DNA is circular and is not associated with histones or chromosomes. This cell is simpler and requires far fewer genes to function than an eukaryotic cell. Therefore, it contains only one circular DNA molecules and various smaller DNA circlets (Plasmids).

1.5

Membrane-Bound Organelles

Eukaryotic cells contain many membrane enclosed organelles, which are large and complex and in the cytoplasm. Prokaryotic cells do not contain membrane bound organelles. This is an important difference because it allows to a large level of intracellular division and contributes to the highly complex character of eukaryotic cells. The larger size of eukaryotic cells and the confinement of certain cellular processes to a smaller area increases the efficiency of communication and movement within the cell.



10

Biophysical Chemistry

Eukaryotes only possess a membrane bound nucleus and organelles such as mitochondria, lysosomes, golgi apparatus, peroxisomes and ER. (i) Size of Ribosomes: Both types of cells contain many ribosomes but the ribosomes of eukaryotic cells are larger than prokaryotic cells. Eukaryotic ribosomes also show more complexity than prokaryotic cells. They are formed from five kinds of ribosomal RNA and about eighty kinds of proteins. Prokaryotic ribosomes are composed of three kinds of RNA and about fifty kinds of proteins. (ii) Cytoskeleton: This is a multi-component system in eukaryotes composed of microtubules, active filaments and intermediate filaments. It is required to maintain cell shape, provide internal organization and mechanical support. It is also important for cell division and movement. (iii) Sexual reproduction: Most eukaryotes undergo sexual reproduction whilst prokaryotes reproduce asexually. Prokaryotes reproduce clones of themselves via binary fission and relies more on horizontal genetic transfer for variation. (iv) Cell division: This occurs by mitosis for eukaryotic cells and binary fission for prokaryotic cells. Eukaryotic cells undergo mitosis and then cytokinesis but this involves several stages. The nuclear membrane disintegrates and then the chromosomes are sorted and separated to ensure that each daughter cell receives two sets of chromosomes. Following this, the cytoplasm divides to form two genetically identical daughter cells a process known as Cytokinesis. On the other hand, prokaryotes undergo a simple process of binary fission. This is faster than mitosis and involves DNA replication, chromosomal segregation and ultimately cell separation into two daughter cells genetically identical to the parent cell. Unlike mitosis, this process does not involve the nuclear envelope and centromere and spindle formation.

1.6

Comparison Between Lysosome and Ribosome

To understand the above, we briefly consider the cell and its components. Let us now consider the differences between lysosome and ribosome. A cell contains different types of organelles which perform different roles in the cell and they help in the survival of living organisms. As cell components, lysosomes and ribosomes perform different functions in the cell. Lysosomes are found only in eukaryotic cells but ribosomes are found in both eukaryotic as well as prokaryotic cells.

Cell and its Biochemical Setup 

11

Figure 1.4 Components of the cell. Lysosomes are membrane bound cell organelles and contain different types of digestive enzymes. Lysosome is also known as garbage disposal system of cells which destroy unwanted materials from the cell. Lysosomes are capable of degrading all types of polymer of the cell because they have a variety of digestive enzymes.

1.7

Types of Cells in Human Body

The diverse types of cells in the body may be listed as: (i) stem cells, (ii) bone cells, (iii) blood cells, (iv) muscle cells, (v) fat cells, (vi) skin cells, (vii) nerve cells, (viii) endothelial cells, (ix) sex cells, (x) pancreatic cells, and (xi) cancer cells. The cells in human body are innumerable and come in all shapes and sizes. These tiny structures are the basic unit of all living organisms comprise of tissues, tissues make up organs and organs form

12



Biophysical Chemistry

Figure 1.5 Lysosome. organ systems. The organ systems work together to create an organism and keeps it alive. Each type of cell in the body is specially equipped for its role. For example, the cells of digestive system are very different in structure and function from cells of the skeletal system. Cells of the body depend on each other to keep the body functioning as one unit. A brief account of types of cells is given below: (i) Stem cells: Stem cells originate as unspecialized cells and have the ability to develop into specialized cells which can build specific organs or tissues. They can divide and replicate many times in order to replenish and repair the tissue. (ii) Bone cells: Bones are a type of mineralized connective tissue which is a major component of skeletal system. Bones are made up of a matrix of collagen and calcium phosphate minerals. There are three types of bone cells in the body i.e., osteoclasts, osteoblasts and osteocytes. Osteoclasts are large cells that decompose bone for resorption and assimilation while they heal. Osteoblasts regulate bone mineralization and produce osteoid, an organic substance of the bone matrix, which mineralizes to form bone. Osteoblasts mature to form osteocytes which aid the formation of bone. Osteocytes help maintain calcium balance. (iii) Blood cells: They transport oxygen throughout the body to fight infection. They are produced by bone marrow. There are three major types of cells in blood: (a) red blood cells, (b) white blood cells and

Cell and its Biochemical Setup 

Figure 1.6 Structure of phospholipid.

Figure 1.7 Structure of a phospholipid bilayer.

13

14



Biophysical Chemistry

(c) platelets. Red blood cells determine blood type and are responsible for transporting oxygen. White blood cells are immune system cells that destroy pathogens and provide immunity. Platelets help in clotting of blood and prevent blood loss due to damaged blood vessels. (iv) Muscle cells: They form muscle tissue which enables the body movement. There are three types of muscle cells—(i) Skeletal, (ii) Cardiac and (iii) Smooth.

• Skeletal muscle tissue attaches to bones to facilitate voluntary movement. The muscle cells are covered by connective tissue which protects and supports muscle fibres. • Cardiac muscle cells form involuntary muscle and are found in the heart. These cells aid in heart contraction and are joined to one another by intercalated discs that allow for heart beat synchronization. • Smooth muscle is an involuntary muscle that lines body cavities and forms walls of many organs like kidneys, intestines, blood vessels and lung airways. (v) Fat cells: These cells are a major cell component of adipose tissue and they are also called “adipocytes”. Adipocytes contain drops of stored fat (triglycerides) that can be used for energy. Adipose cells have also a critical endocrine function. They produce hormones, influence sex hormone metabolism, blood pressure regulation, insulin activity, blood clotting and cell signaling. (vi) Skin cells: The skin is composed of a layer of epithelial tissue (epidermis) that is supported by a layer of connective tissue (dermis) and an underlying subcutaneous layer. The outer most layer of the skin is composed of flat, squamous epithelial cells that are closely packed together. The skin covers a wide range of roles, such as protecting internal structures of the body from damage, prevents dehydration, acts as a barrier against germs, stores fat, and produces vitamins and hormones. (vii) Nerve cells: Nerve cells or neurons are most basic for the nervous system. Nerves send signals between the brain, spinal cord and other body organs via nerve impulses. Structurally, a neuron consists of cell body and nerve processes. The central cell body contains neuron’s nucleus, associated cytoplasm and organelles. Nerve processes are finger like projections that extend from the cell body and transmit signals.

Cell and its Biochemical Setup 

15

(viii) Endothelial cells: These form the inner lining of the cardiovascular system and lymphatic structures. They make up the inner layer of blood vessels, lymphatic vessels and organs like the brain, lungs, skin and heart. Endothelial cells are responsible for the creation of new blood vessels. They also regulate the movement of macromolecules, gases and fluid between the blood and surrounding tissues as well as manage the blood pressure. (ix) Sex cells: Sex cells are reproductive cells created in male and female gonads that bring new life into existence. Male sex cells (or sperm) are motile and have long, tail like projections called flagella. Female sex cells or ova are non-motile and relatively large in comparison to male gametes. In sexual reproduction, sex cells unite during fertilization to form a new species, while other body cells replicate by mitosis, gametes reproduce by miosis. (x) Pancreatic cells: Pancreas functions both as exocrine and endocrine organ indicating that it discharges hormones both through ducts and directly into other organs. Pancreatic cells regulate blood glucose levels and also are important for digestion of proteins, fats and carbohydrates. Exocrine acinar cells, produced by pancreas, secrete digestive enzymes that are carried by ducts into small intestine. A small percentage of pancreatic cells have an endocrine function or secrete hormones into cells and tissues. Pancreatic endocrine cells are found in small clusters. Hormones produced by these cells include insulin, glucagon and gastrin. (xi) Cancer cells: Cancer cells work to destroy the body. Cancer results from the development of abnormal properties that cause cells to divide uncontrollably and spread to other locations. Cancer cell development originates from mutations arising from exposure to chemicals, radiation, UV light. Cancer can also have genetic origins such as chromosome replication errors and cancer causing viruses of the DNA. Cancer cells spread rapidly because they develop decreased sensitivity to anti-growth signals and proliferate quickly. They lose the ability to undergo programmed cell death making them even more formidable. The cell membrane is a very adjustable structure composed primarily of phospholipids (lipid bilayers). Cholesterol I also present in the membrane and it contributes to the fluidity of the membrane. There are also other proteins embedded in the membrane which have different functions.

16



Biophysical Chemistry

A simple phospholipid molecule has a ‘phosphate’ head group and two side-by-side chains of fatty acids that make up the lipid tails as shown in Figure 1.7. The phosphate group is negatively charged and is thus polar, hydrophilic. The lipid tails are uncharged, nonpolar and hydrophobic. They consist of saturated and unsaturated acids, and contribute to the fluidity of the tails which are in motion. Phospholipids are amphipathic (containing both hydrophilic and hydrophobic groups). The cell membrane consists of two adjacent layers of phospholipids. The lipid tails of one layer face the lipid tails of the other layer, joining at the interface. The phospholipid heads face out and one layer exposed to the interior of the cell, with the other layer being exposed to the exterior. The lipid bilayer forms the basis of the cell membrane and also contains various proteins. The cell membrane is associated with two different types of proteins, namely integral and peripheral proteins. An integral protein is one that is embedded in the membrane. A channel protein selectively allows certain species such as ions to pass in or out of the cell. Another important group of the integral proteins is known as ‘recognition proteins’, which serve to mark a cell’s identity. A receptor is a cell recognition protein. Recognition proteins can selectively bind a specific molecule outside the cell and this binding induces a chemical reaction within the cell. A ligand is a specific molecule that binds to and activates a receptor. Some integral proteins serve as both a receptor and an ion channel. An example of a receptor-ligand interaction is the receptors on nerve cells that bind neurotransmitters such as dopamine. When a dopamine

Figure 1.8 Representation of a cell membrane.

Cell and its Biochemical Setup 

17

molecule binds to a dopamine receptor protein, a channel within the transmembrane protein opens to allow certain ions to flow into the cell. Some integral membrane proteins are glycoproteins which have carbohydrate molecules attached that extend into extracellular matrix. The attached carbohydrates aid in cell recognition. The carbohydrates that extend from membrane proteins and from membrane lipids form what is known as “Glycocalyx”. The “glycocalyx” is a coating around the cell from glycoproteins and other carbohydrates attached to the cell. It has several roles (i) it allows the cell to bind to another cell, and (ii) it may contain receptors for hormones or it may have enzymes to break down nutrients.

1.8

Peripheral Proteins

Peripheral proteins are generally found on the inner or outer surface of the lipid bilayer but may also be attached to the internal or external surface of an integral protein. These proteins perform a specific function for the cell. For example, some peripheral proteins on the surface of intestinal cells act as digestive enzymes to break down nutrients to sizes such that they can pass through the cells into blood stream.

1.9

Transport Across Cell Membrane

An important aspect of cell membrane is its ability to regulate the concentrations of substances inside the cell, such as ions like Na+ , K+ , Ca2+ , Cl− ; nutrients like sugars fatty acids, amino acids and waste products like CO2 (which must leave the cell.) The membrane’s lipid bilayer structure provides the 1st layer of control. The phospholipids are tightly packed together, and the membrane has a hydrophobic interior. This structure causes the membrane to be selectively permeable. Because of this, only certain substances meeting specific criteria can pass through it unaided. Thus only relatively small non-polar materials like the gases O2 , CO2 and also some lipids can move through the lipid bilayer. Water soluble substances like glucose, electrolytes and amino acids require assistance to cross through the membrane because they are repelled by the hydrophobic tails of the lipid bilayer. The passage of all substances across the membrane occurs by two (general) methods depending upon whether energy is required or not for such a process; (i) Passive transport, and (ii) Active transport. For passive transport, no cellular energy need be expended for the movement of substances across the membrane.

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Biophysical Chemistry

Figure 1.9 Simple diffusion across the cell. But for active transport i.e., the movement of substances across the membrane, energy from ATP is used. Some details for passive or active transport of substances across the membrane are given below.

1.9.1

Passive Transport

This transport occurs via diffusion across a semipermeable cell membrane whenever there is a concentration gradient across the membrane. Substances like O2 , CO2 , which can easily diffuse across the bilayer, do so with the O2 diffusing into the cell (because it is more concentrated outside the cell) and CO2 diffuses out of the cell (because it is more concentrated inside the cell). It may be mentioned that O2 is rapidly used up during metabolism and hence there is a lower concentration of the same within the cell while CO2 is a product of metabolism and its concentration is higher with in the cell. Large polar or ionic species (which are hydrophilic) cannot easily cross the phospholipid bilayer. Charged species of any size cannot cross the cell membrane by diffusion because they are repelled by the hydrophobic tails in the interior of the lipid bilayer.

1.10

Facilitated Diffusion

Facilitated diffusion is the diffusion process used for such substances that cannot cross the lipid bilayer due to their size, charge or polarity. This diffusion of substances crossing cell membrane takes place with the help of proteins such as channel proteins and carrier proteins. Channel proteins

Cell and its Biochemical Setup 

19

Figure 1.10 Facilitated diffusion.

are less selective than carrier proteins and discriminate mildly between their cargo based on size and charge carrier proteins are more selective often allowing only one particular type of molecule to cross. A good example of facilitated diffusion is the movement of glucose into the cell where it is used to make ATP. Its simple diffusion through the cell is not possible because of its size and polarity but is made possible via a specialized carrier protein called glucose transporter. As an example, even though Na+ are highly concentrated outside the cells, they cannot pass through the non-polar lipid layer due to their charge. Their diffusion is facilitated by membrane proteins that form sodium channels (or pores) so that these ions can move down their concentration gradient from outside to inside the cells. Facilitated diffusion is a passive process and does not require any energy expenditure from the cell. Water can also move freely across the cell membranes of all cells either through protein channels or by slipping between the lipid tails of the membrane. The movement of water molecules is not regulated by cells, hence, it is important that cells are exposed to an environment in which the concentration of solutes outside the cells (i.e., in the extracellular fluid) is equal to the concentration of the solutes inside the cells (in the cytoplasm). Another mechanism (besides diffusion) to passively transport materials between compartments is filtration. Filtration uses a hydrostatic pressure gradient that pushes the solution from a higher pressure area to a lower pressure area and is an important process in the body. For example, the circulatory system uses filtration to move plasma and other substances across the endothelial lining of capillaries and into surrounding tissues supplying cells with nutrients. Filtration pressure in kidney provides the mechanism to remove wastes from blood stream.

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Biophysical Chemistry

Figure 1.11 Na+ /K+ pump. It is found in many cell membranes. It is powered by ATP, moves Na+ and K+ ions in opposite directions, each against its concentration gradient. In a single cycle of the pump, 3Na+ ions are extruded and 2K+ are imported into the cell.

1.10.1

Active Transport

During active transport, ATP is required to move a substance across a membrane with the help of protein carriers against its concentration gradient. One of the common types of active transport involves proteins that serve as “pumps”. Energy from ATP is required for these membrane proteins to transport substances (molecules or ions) across a membrane against their concentration gradient. The Na+ /K+ pump, also called Na+ /K+ ATPase transports Na+ out of a cell while moving potassium ions into the cell. The Na+ /K+ pump is found in the membranes of many cells. These pumps are abundant in nerve cells which constantly pump out sodium ions and pull in K+ ions to maintain an electrical gradient across the cell membranes. In nerve cells, the electrical gradient exists between the inside and outside of the cell with the inside being −vely charged (at about −70 mV) relative to the outside. The −ve electrical gradient is maintained because each Na+ /K+ pump moves three Na+ ions out of the cell and pushes in two K+ ions into the cell for each ATP molecule that is used. This process is important for nerve cells and it accounts for the majority of their usage. Active transport pumps can work together with other active or passive transport systems to move substances across the membrane. For example, the Na+ /K+ pump maintains a high concentration of Na+ ions outside the

Cell and its Biochemical Setup 

21

cell. If the cell needs the ions, it has to open a passive sodium channel and drive Na+ ions into the cell which is facilitated by the concentration gradient. When active transport powers the transport of another substance, it is called secondary active transport. Symporters are secondary active transport systems that move two substances in the same direction. For example, the sodium-glucose symporter uses Na+ ions to pull glucose molecules into the cell. Because cells store glucose for energy, it is at a higher concentration inside the cell than outside. But, due to the action of Na+ /K+ pump, Na+ ions diffuse easily into the cell when the symporter is opened. The flood of Na+ ions through the symporter provides the energy that allows glucose to move into the cell against its concentration gradient. Antiporters are secondary active transport systems that transport substances in opposite directions. For example, the Na− hydrogen ion antiporter uses the energy from the inward flow of ions to move H+ ions out of the cell. This antiporter is used to maintain pH of the cell interior. Other forms of active support do not involve membrane carriers. Endocytosis is the process of a cell ingesting material by enveloping it in a portion of its cell membrane and pinching off that portion of the membrane. Once pinched off, the portion of the membrane and its contents become an independent, intracellular vesicle. (A vesicle is a membranous sac-a spherical and hollow organelle bounded by a lipid bilayer membrane) Endocytosis brings materials into the cell that must be broken down or digested. Phagocytosis (cell eating) is the endocytosis of large particles. Many immune cells engage in phagocytosis of invading pathogens. In contrast to phagocytosis, pinocytosis, (cell drinking) brings fluid containing dissolved substances into a cell through membrane vesicles. Phagocytosis and pinocytosis take in large portions of extracellular material and they are not highly selective in the substances they bring in. Cells regulate the endocytosis of specific substances via receptor mediated endocytosis (receptor mediated endocytosis is endocytosis by a portion of cell membrane that contains many receptors that are specific for a given substance). Once the surface receptors have bound sufficient amounts of the specific substance, the cell will endocytose the part of the cell membrane containing receptor-ligand complexes. Example: Iron is bound to a protein called transferrin in the blood. Specific transferrin receptors on red blood cell surfaces bind the ion-transferrin molecules and the cell endocytoses the receptor-ligand complexes.

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Biophysical Chemistry

Figure 1.12 Three forms of endocytosis. Endocytosis is a form of active transport in which a cell envelops extra cellular materials using its cell membrane. (a) In phagocytosis, which is relatively non-selective, the cell takes in a large particle, (b) In pinocytosis, the cell takes in small particles in fluid, (c) Receptor mediated endocytosis is quite selective. When external receptors bind a specific ligand, the cell responds by endocyting the ligand. In contrast with endocytosis, exocytosis (taking out of the cell) is the process of a cell exporting material using vesicular transport. Many cells manufacture substances that must be secreted. These substances are packaged into membrane bound vesicles with in the cell. When the vesicle membrane fuses with the cell membrane, the vesicle release its contents into the interstitial fluid. The vesicle membrane then becomes part of the cell membrane. Cells of the stomach and the pancreas produce and secrete digestive enzymes through exocytosis. Endocrine cells produce and secrete hormones that are sent throughout the body and certain immune cells produce and secrete large amounts of histamine, a chemical important for immune responses. Pancreatic cells enzyme secretion products. They produce and vesicles secrete many enzymes.

1.11

Permeability of Molecules Across Phospholipid Bilayers

Most molecules diffuse across a protein free lipid bilayer down its concentration gradient over a period of time. The diffusion rate depends on the size of the molecule and its relative solubility in oil. Generally, a smaller

Cell and its Biochemical Setup 

23

Figure 1.13 Exocytosis is endocytosis in reverse. Material to be exported is packaged into a vesicle inside the cell. The membrane of the vesicle fuses with the cell membrane and the contents are released into the extracellular space.

Figure 1.14 Pancreatic acinar cells. molecule which is more soluble in oil (i.e., more hydrophobic and nonpolar) diffuses rapidly across a cell membrane. Small, non-polar molecules such as O2 , CO2 dissolve in cell membrane and thus diffuse rapidly across where as small, uncharged polar molecules like water or urea also diffuse but at a slower rate (ethanol diffuses readily). It may however be said that

24



Biophysical Chemistry

lipid bilayers are highly impermeable to ions and this is due to their charge, size and hydration. Because of these factors, such molecules are prevented from entering the lipid bilayer. These bilayers are 109 times more permeable to water than even to Na+ or K+ ions.

1.12

Thermodynamic basis of Transport

The diffusion of a substance X, across a membrane represented by x (outside membrane) → x (inside membrane) is associated with the Gibbs free energy change in the standard state

[μ¯ x − μ¯ 0 ( x )] = RT ln a x

( a x = activity of x )

(1.1)

where μ0 ( x ) is the standard chemical potential μ x (in) − μ x (out) = ΔGx = RT ln

a x (in) a x (out)

(1.2)

¯ x is negative, the spontaneous flow of x will be from If μ x (out) > μ x (in) , ΔG outside to inside. ¯ x is +ve, and an inward only if an exergonic If μ x (in) > μ x (out) , ΔG process, such as ATP hydrolysis is coupled to it make the overall free energy change negative. The transmembrane movement of ions also depends on charge differences across the membrane, there by generating an electrical potential difference, Δψ = ψ(in) − ψ(out) (1.3) where Δψ is termed as the membrane potential. Therefore, if x is ionic, the equation for ΔG( x) must be corrected to include the electrical work required to transfer a mol of x from outside to inside as Δ G¯ x = RT ln

[ a x ](in) + z x FΔψ [ a x ](out)

(1.4)

where a’s are the activities and Zx is the charge on x and F is the Faraday constant. ΔGx is now referred as the electrochemical potential of X.

1.12.1

Secondary Active Transport

This type of transport (also called co-transport uses energy to transport molecules across a membrane; however, there is no direct coupling to ATP (unlike in primary active support), instead the electrochemical potential difference created by pumping out of true cell is instrumental.

Cell and its Biochemical Setup 

25

Figure 1.15 Relative permeability of a phospholipid bilayer.

Figure 1.16 Mediated transport: (a) Passive transport and (b) Active transport.

1.13

Examples of Antiport and Symport System

An example of an antiport system is the Sodium–Calcium exchanger which allows three Na+ ions into the cell to transport one Ca2+ ion out. An example of symport system is glucose symporter SGLTI which cotransports one glucose (or galactose) molecule into the cell for every two Na+ ions it imports into the cell.

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Biophysical Chemistry

Figure 1.17 Secondary active transport.

1.13.1

(Na+ /K+ ) ATPase

This active transport system is found in the plasma membranes of higher eukaryotes. This transmembrane protein consists of two types of subunits: a 110 kD non glycosylated sub unit that contains the enzyme’s catalytic activity and ion binding sites and a 55 kD glycoprotein β-sub unit of unknown function. The α-sub unit has eight transmembrane α-helical segments and two large cytoplasmic domains. The β-sub unit has a single transmembrane helix and a large extracellular domain. The protein many function as an (αβ) tetramer in vivo. The Na+ /K+ ATPase is also called as the Na+ /K+ pump because it pumps 3Na+ out of and 2K+ in both directions across the membrane in presence of hydrolyzing ATP. The overall reaction is 3Na+ (in) + 2K+ (out) + ATP + H2 O → 3Na+ (out) + 2K+ (in) + ADP + Pi (1.5) + + The important feature of Na /K ATPase is the phosphorylation of a specific Aspartate residue of the transport protein which phosphorylates only in the presence of Na+ whereas the aspartyl phosphate residue is subject to hydrolysis only in the presence of K+ . Hence it has two conformations named E1 and E2 . They operate in the following way: (1) The protein in the E1 state has three high affinity Na+ binding sites and two low affinity K+ binding sites accessible to the cytosolic surface of the protein. Hence E1 binds 3Na+ ions inside the cell and then binds ATP to yield an E1 . ATP.3Na+ complex.

Cell and its Biochemical Setup 

27

Figure 1.18 Scheme for transport of Na+ and K+ by Na+ /K+ ATPase. Ion pumping by Na+ /K+ ATPase involves phosphorylation, dephosphorylation and conformational change. In this case, hydrolysis of E2 -intermediate powers E2 → E1 conformational change and simultaneous transport of two K+ ions inward. (2) ATP hydrolysis produces ADP and a ‘high energy’ aspartyl phosphate intermediate E1 -P.3Na+ . (3) This ‘high energy’ intermediate relaxes to its ‘low energy’ conformation E1 ∼ P.3Na+ and relaxes its bound Na+ outside the cell. (4) E2 -P binds two K+ ions from outside the cell to form E2 -P.2K+ complex. (5) The phosphate group hydrolyses to yield E2 .2K+ (P = Phosphate group) (6) E2 .2K+ changes conformation, releases its 2K+ ions inside the cell and replaces them with three Na+ ions thereby completing the transport cycle.

1.14

Ca2+ ATPase

Eucaryotic cells maintains a low conc of free Ca2+ in the cytosol (10−7 M) where as extra cellular concentration is very high on the opposite face

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Biophysical Chemistry

Figure 1.19 Scheme for the active transport of Ca2+ by the Ca2+ ATPase. Here, (in) refers to the cytosol and (out) refers to the outside of the cell for plasma membrane Ca2+ ATPase on the lumen of the endoplastic reticulum (or sarcoplastic reticulum) for the Ca2+ ATPase of the membrane.

(10−3 M). Thus a small influx of Ca2+ significantly increases the conc of free Ca2+ is the cytosol and the flow of Ca2+ ions down its steep concentration gradient in response to extra cellular signals is one of the means of transmitting these signals across the plasma membrane. The Ca2+ ATPases are commonly found in muscle cells and neurons. Ca2+ transporters are the common examples of P-type transport of ATPase. It is also known as Ca2+ pump or Ca2 ATPase. These transporters actively pump Ca2+ out of the cell and help in maintaining the gradient. The structure of Ca2+ pump has an asymmetrical arrangement of transmembrane and cytosolic domains that undergo movements during Ca2+ transport. It contains ten transmembrane α-helices and two cytoplasmic loops between transmembrane α-helices. The transmembrane αhelices form Ca2+ binding site which binds two Ca2+ ions from cytosol. The two cytoplasmic loops form three separate domains nucleotide binding domains that binds ATP, actuator domain that contains catalytic phosphorylation site and P-domains which is important for transmission of conformational changes between cytosolic and transmembrane domains. In unphosphorylated state, the two helices are disturbed and form a cavity for binding of two Ca2+ ions from the cytosolic side of the membrane. ATP also binds to a binding site on the same side of the membrane and

Cell and its Biochemical Setup 

29

the subsequent transfer of the terminal phosphate group of ATP to an Aspartic acid of an adjacent domain lead to a drastic rearrangement of the transmembrane helices. This rearrangement disturbs the Ca2+ ion binding site and releases Ca2+ ions on the other side of the membrane i.e., into the lumen of SR (SR = Sarcoplastic Reticulum). The mechanism of Ca2+ ATPase in the SR membrane may be understood through the following steps: (1) The protein is E1 conformation has two high affinity binding sites for Ca2+ ions accessible from the cytosolic side and ATP binds to a side on cytosolic surface. (2) In the presence of Mg2T , the bound form of ATP is hydrolysed to ADP and phosphate. Subsequently, the liberated phosphate is transferred to a specific aspartate residual in the protein forming the high energy acyl phosphate bond given by El ∼ P. (3) The protein then undergoes a conformational change and forms E2 , which has two low affinity Ca2+ binding sites accessible to the SR human. (4) The free energy of E1 ∼ P is greater than E2 − P and this leads to E1 → E2 conformational change. Simultaneously, the Ca2+ ions also dissociate from the low affinity sites to enter the SR humen following which the aspartyl phosphate bond is hydrolysed. (5) De-phosphorylation then leads to E2 → E1 conformational change and E1 is ready to transport two more Ca2+ ions.

Questions (1) The mass of a E.coli organism me.c yeast my and mh.c mass cell are in the order (a) me.c > my > mh.c (c) mh.c > my > me.c (b) my > me.c > mh.c (d) mh.c > me.c > my (2) (a) Eukaryotes are cells enclosed in a cell membrane (b) Prokaryotes are cells enclosed in a cell membrane (c) Eukaryotes are not multicellular organisms (d) Prokaryotes are larger in size than eukaryotes

30



(3) (a) (b) (c) (d)

Biophysical Chemistry

Mitochondria do not produce ATP There is only a single membrane layer in mitochondria Mitochondria do not contain DNA DNA is present in mitochondria and replicates as needed.

(4) (a) The rough endoplastic reticulum contains only carbohydrates. (b) The rough endoplastic reticulum synthesizes difference types of lipids. (c) The rough endoplastic reticulum does not synthesize proteins. (d) The smooth endoplastic reticulum does not have ribosome with in it. (5) (a) (b) (c) (d)

Ribosome is a membraneous of organelle Lysosome is a membraneous organelle Lysosomes are smaller in size than ribosomes Lysosomes are present in the cytoplasm of eukaryotic and prokaryotic cells

(6) (a) Ribosome contains an enzyme (b) Protein synthesis does not occur in ribosomes (c) Lysosomes always remain separate from each other while ribosomes are grouped together (d) None of the above statements are true. (7) (a) Cholesterol is not part of lipid bilayer (b) In a lipid bilayer, the phosphate group is negatively charged and hydrophilic (c) Lipid molecules in bilayer are amphiphilic (d) Phospholipids contain only hydrophilic groups (8) (a) Glycoproteins are integral proteins (b) Peripheral proteins do not act as digestive enzymes (c) Dopamine attached to a receptor is an example of a peripheral protein (d) Cell recognition proteins are peripheral proteins (9) (a) For permeability across a membrane through passive transport, cellular energy is spent. (b) For active transport across a membrane energy from ATP is required. (c) Na+ /K+ pump is an example of passive transport. (d) Filtration is not a method adopted by a cell for passive transport.

Cell and its Biochemical Setup 

31

(10) (a) Sodium glucose symporter uses Na+ ions to move substances like sugar and KCl from inside to outside of cell. (b) Na+ -K+ pump is a hindrance for transport of Na+ into the cell. (c) Na-H+ antiporter maintains pH of the interior of a cell. (d) Antiporters are primary active systems for moving sugar. (11) (a) Endocytosis requires membrane carriers for trimming part of sugar of glucose outside cell. (b) Phagocytosis is not synonymous with the endocytosis of large particles. (c) Immune cells do not use endocytosis to identify pathogens. (d) Endocytosis of large molecules is referred as phagocytosis. (12) (a) Iron bound to the protein transferrin uses endocytosis for transfer of the complex into or out of cell. (b) Exocytosis refers to the process of a cell bringing material into it. (c) Pancreatic and stomach cells do not create digestive enzymes through exocytosis. (d) Immune cells secret histone through the process of endocytosis. (13) The Gibbs free energy ΔGx of a substance from outside to the inside of a cell given by a x (in) Δ G¯ x = RT ln a x (out) (a’s are the “activities” of the cell inside (a x (in)) and outside (a x (out)) indicates the spontaneous of the process in the cell when (a) (b) (c) (d)

μ x (inside) = μ x (outside) μ x (inside) = μ x (outside) μ x (outside) > μ x (inside) none of the above

(14) (a) Sodium-Calcium exchanger is an example of antiport system. (b) Glucose symporter is not an example of port system. (c) Na+ -K+ ATPase is not present in plasma membrane of higher eukaryotes. (d) Corticosteroids do not bind to the surface of (Na+ -K+ ) ATPase (15) The study of ion transport across membranes is a frontier area of research in biochemistry. In a lipid bilayer membrane, the magnitude of the concentration gradient is 50 mol m−4 . Estimate the ionic flux. The diffusion coefficient of K+ ions is 8.7 × 10−5 cm2 s−1 .

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Biophysical Chemistry

Solution: According to Fick’s first law of diffusion, the flux ( J ) can be written as J = − D (∂C/∂x ) x=0

= −8.7 × 10−5 cm2 s−1 (−50) mol m−4 = 4.35 × 10−3 mol m−2 s−1 (16) Draw a sketch of a human cell and indicate the parts. Explain their function. (17) What are eukaryotic and prokaryotic cells? Describe the similarities and differences between the two types of cells. (18) Explain what are Liposomes and Ribosomes? Bring out a comparative account of these organelles. (19) List out the types of bone cells in human body and give a brief description of their role in the body. (20) Show the structures of phospholipid and lipid bilayers. Name the proteins in the bilayer and their function. (21) What are the general modes of transport of non-polar and polar molecules across lipid bilayer and explain their mode of operation. (22) Briefly describe the following: (i) Na+ /K+ pump (ii) Endothelial cells (iii) Phagocytosis and (iv) Exocytosis. (23) Give an example each of symport and antiport systems and explain their function. (24) Explain the transport of Ca2+ ions across the lipid bilayer with Ca2+ ATPase by means of a diagram and give details of the transport mechanism.

2

Thermodynamic Aspects of the Cell 2.1

Introduction

The variables such as temperature, concentration (more correctly, activity), nature of ions in electrolyte solutions dictate diverse phenomena viz. osmosis across semipermeable membranes, diffusion of reactants, phase changes, molecular aggregations etc. These processes are essential for comprehending the structure and function of human or animal cells. Both thermodynamic and non-equilibrium thermodynamic (or thermodynamics of steady state) studies are useful to an understanding of the cell functions as well as its interaction with the surroundings. The following examples in plants and animals may be considered: (2.1)

(2.2)

A consideration of the entropy changes in the biosphere reveals that the earth absorbs the solar energy at a rate of 5 × 1016 W (J/sec) so that the rate of entropy input is 5 × 1016 W/6000 K ≈ 8 × 1012 WK−1 (assuming that

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_2

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Biophysical Chemistry

the sun’s core temperature is 6000 K). If the earth radiates heat at the same rate, the rate of output of entropy is 5 × 1016 /293 ≈ 2 × 1014 (assuming an average temperature of earth as 20◦ C). Thus, the rate of entropy production in the biosphere is about 2 × 1014 WK−1 . Living cells of all types contribute only a small part of this entropy.

2.2

Enthalpy and Free Energy Changes in Biochemical Processes

In biochemical processes at 1 atm pressure without any gas phase, the P − V work is negligible. In a biochemical context, a molecular volume change of one (nanometer)3 [i.e., (10−9 m3 ) = 10−27 m3 ] is quite large but the P − V work is only 10−23 J molecule−1 . Biochemical reactions often take place at constant temperature T. From the relation G = H − TS = U + PV − TS any change in the state of the system, can be expressed as ΔG = ΔH − TΔS

(at constant T)

The term TΔS refers to the heat gained at a given temperature and in a biochemical process it is the entropic contribution to the Gibbs energy change ΔG.

2.3

Effects of Electrochemical Changes

In an electrolyte solution, positive ions tend to accumulate in the regions of low electrical potential Φ where their electrical potential energy is low. For an ion of energy q the electrical potential energy is q × Φ. Under equilibrium conditions, +ve ions accumulate preferentially in regions of low electrical potential, whereas negative ions (anions) have higher concentrations at high values of Φ. The equilibrium distribution of ions is given by Boltzmann distribution law, given by C = C0 ε−zFΦ/RT

(2.3)

where z represents the ionic charge, F indicates the Faraday constant and C0 denotes the concentration of the ions at Φ = 0.

Thermodynamic Aspects of the Cell 

2.4

35

Distribution of Ions Across Membranes

The cytoplasm of a cell has a lower electrical potential than the external solution. Considering the Cl− ions in the cytoplasm, their concentration is lower in the cell than outside at equilibrium. In the case of cations permeating into the cytoplasm of a cell, their concentration is higher in the cytoplasm than outside. Large molecules such as glucose and proteins do not permeate while others cross the membrane under certain conditions. The negative potential in the cytoplasm is maintained in part by pumps i.e., mechanisms that by expending energy produce a flux of specific ions in a particular direction. This distribution (or mechanism) is illustrated in the following diagram.

Figure 2.1 Boltzmann distribution of permeating cations and anions. Boltzmann distribution explains the equilibrium distribution of permeating cations and anions across a membrane. For a permeating cation, the left side has lower electric potential (low Φ) while for permeating anions it is on the right. The highest entropy state would require equal concentrations every where. Many of the intracellular anions required to

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Biophysical Chemistry

approach electro-neutrality are found on non-permeating species including macromolecules while the extra cellular solution will also contain many cations that are expelled from the cell by active energy using processes.

2.5

Distribution of Ions Near Charged Membranes and Macromolecules

In the vicinity of a negatively charged surface of a membrane or a macromolecule, the concentration of cations in the solution is higher than in the bulk of the solution. Since the surfaces of many membranes are −ve charged, there is usually an excess of cations and a depletion of anions near the membrane. Many macromolecules also have a small excess of negative charge and are therefore surrounded by excess cations as shown in the Figure 2.2.

Figure 2.2 Distribution of ions on negatively charged surfaces. In figure 2.2(a) the layer of excess +ve charges (i.e., electrical double layer) near the interface counteracts the above at sufficiently large distance. (b) and (c) show how the electrical potential Φ and the ionic concentrations C+ and C− vary near the surface but approach their bulk concentration at large distance X from the charged surface. The electric charge of the ions has another effect that contributes to their distribution i.e., the Born energy. The Born energy of an ion is the energy associated with the field of the ion and it depends on the nature of the medium, being lower in polar media (like water) than in non-polar media (such as the hydrophobic regions of lipids or other macromolecules). Thus ions are found in negligible concentrations in the hydrocarbon interior of membranes where Born energy is high. This energy also affects the distribution inside the pores in aqueous medium. If the ion is sufficiently close (in nm range) to a non-polar region of the membrane it has still a high Born energy because of the penetration

Thermodynamic Aspects of the Cell 

37

of the field into non-polar regions. The Born energy and Boltzmann distribution act in such a way that the concentration of either cations or anions is lower both in non-polar regions and also in polar aqueous solution near such regions. Thus the equilibrium distribution has a small excess of negative charge and is therefore surrounded by excess cations as shown in the Figure 2.2. Thus, the equilibrium distribution of the ions is a compromise between minimizing the Born energy (i.e., ions keeping away from non-polar regions) and maximizing entropy (uniform distribution of ions). Electrical interactions are weaker in solution than in pure water because ions of opposite sign tend to accumulate near charges and screen their effects. Further electrical effects in pure water are much weaker than in vacuum because of the dipolar nature of water.

2.6

Osmotic Effects

Osmosis refers to the movement of a solvent through a semipermeable membrane from a region of low solute concentration to a region of high solute concentration. Note that a semipermeable membrane is one in which

Figure 2.3 Permeability of cations and anions.



38

Biophysical Chemistry

the pores are so small that water molecules can pass through them but not solute particles (because of their much larger size). Many membranes are permeable to water but impermeable to macromolecules, sugars and some ions as well. In figure 2.3(a) the membrane is permeable to water but not to solutes. Water flows from the solution of low concentrations into that of higher concentrations. This flow stops when the osmotic pressure in the concentrated solution equals to that on the other side. (b) The entropy of the system will be maximized if the membrane bursts and the solutions mix freely. For the osmotic equilibrium, the value of the hydrostatic pressure difference required to stop from their flow into the solution side: The equilibrium pressure difference = P = Osmotic pressure = RTCs where Cs denotes the concentration of the solute in mol liter−1 (or kmol m−3 ). If the solute concentration = 1 mol liter−1 of non-ionic solute, I I ≈ P = 0.082 × 300 × 1 = 24.63 atm = 24.63 × 1011.325 = 24.9kPa = 2.5 MPa at 300 K. The semi permeability of membranes is not the only factor that prevents solutes and water mixing completely. Solutes of large size cannot enter the narrow spaces between closely packed macromolecules or membranes. When cells are dehydrated (by extracellular freezing or air-drying) the highly concentrated solutions produce very large osmotic effects.

2.7

Role of Chemical Potential

The Boltzmann equation is given by C = C0 e−ΔE/RT

(2.4)

or ln C = ln C0 − ΔE/RT RT ln C0 = RT ln C + ΔE

(2.5) (2.6)

where ΔE is the energy difference between the given state and the reference states. ΔE may also include P − V work or electrical energy etc. Considering the P − V work as the only energy term, the chemical potential μ may be expressed as μ = μ◦ + RT ln C + PV

= μ0 + RT ln C0

(2.7) (2.8)

Thermodynamic Aspects of the Cell 

39

where μ◦ = chemical potential in the standard state. It is the value of μ in some reference state with a concentration C0 .

2.8

Effects of Different Molecular Environments and Phases on Energy and Entropy

For a solid, the average intermolecular energy of attraction is kT; in a gas, it is kT; in a liquid, it is comparable to kT. The entropy of the three phases of a substance Ssolid < Sliq < Sgas . In the case of energy also, it increases from solid to gas due to supply of the latent heats of fusion and evaporation. Thus, the coexistence of two phases in equilibrium such as ice  aqueous solution or solution  vapour are examples of entropy-energy compromise. The energy of a solute molecule is different in different solvents. If the molecule is non-polar, its energy is different when it is in aqueous solution than when it is partitioned in the interior of a membrane. These differences may be considered in terms of the chemical potential. If molecules of a substance are in equilibrium at a temperature T and pressure P. According to Gibbs phase rule, μ (phase 1) = μ (phase 2) μ1◦

+ RT ln C1 + PV1 =

μ2◦

+ RT ln C2 + PV2

(2.9) (2.10)

When the energy in terms of electrostatic potential energy is also included, the equation for chemical potential may be written as μ = μ◦ + RT ln C1 + PV + ZeΦ

(2.11)

Molecules diffuse from a region of high chemical potential to regions of low chemical potential at a rate that increases with the gradient in Φ.

2.9

Surface Free Energies and Surface Tension

An important free energy difference in cellular biology is that between water molecules at the surface and the water molecules in the interior of the solution. At surfaces between two pure fluids having an interfacial tension, γ, the extra work done in introducing a molecule of area “a” to the interface is “γa” i.e., the surface free energy per unit area. In the bulk solution, water molecules are H-bonded to their neighbours. A water molecule at an air-water interface has fewer neighbours with which to form H-bonds. So, its energy is higher. Because the molecules

40



Biophysical Chemistry

Figure 2.4 The surface free energy of water. will tend to rotate to form bonds with their neighbours, the surface is more ordered and thus have a lower entropy per molecule. These effects give the water surface a relatively large free energy per unit area which gives rise to hydrophobic effect. The work done per unit area of a new surface is numerically equal to γ.

2.10

Molecular Aggregation

A single molecule has an energy of translation which may be related to the entropy associated with its freedom to diffuse through at the available volume. When molecules aggregate to form polymers, the entropy of translation is shared among N participating molecules. Hence entropy per molecule is obtained by dividing the number by N. Consider a simple lipid molecule in water with its standard chemical potential μ◦ , in equilibrium with a micelle or vesicle containing N molecules. The standard chemical potential μ◦N in the aggregate is much lower because the aggregate has a smaller hydrocarbon-water interface per molecule. The membrane may be subject to a tensile force per unit length, Y, and this may do work by changing the area.

Figure 2.5 (a) The equilibria among a lipid monomer, (b) a vesicle containing N molecules and (c) a microscopic lipid bilayer.

Thermodynamic Aspects of the Cell 

41

The equilibrium in terms of change in chemical potential may be given as μ1◦ + kT ln X1 = μ◦N +

kT ln N



XN N



= μ◦m − γa /2

(2.12)

where μ◦m is the standard chemical potential of lipids in the membrane, X1 , X N are the number fraction of lipids in the monomer and vesicle state respectively. The factor 12 in eqn. (2.8) arises because each lipid molecule has an area “a” in only one face of the membrane. If the lipid has more or longer hydrocarbon tails, then the extra energy difference due to the hydrophobic effect will increase (μ1◦ − μ◦N ) resulting in a lower monomer concentration. Increasing the tensile stress in the membrane (larger Y) makes the last term (equation 2.12) more −ve, so monomers and vesicle will move into the membrane increasing the area and relaxing the stress. Alternatively changing the area of a membrane causes a transient mechanical change in Y and results in the transfer of membrane contents between the membrane and a reservoir of material. It is possible that such processes occur in some cell membranes where regulation or homeostasis of membrane tension and cell area. Homeostasis is the state of steady internal, physical and chemical conditions maintained by living systems. It is a condition of optical functioning for the organism and includes many variables such as body temperature and fluid balance being kept within certain preset limits. Humans rely on homeostasis to keep this temperature around 98.4◦ F.

2.11

Non-equilibrium Thermodynamic Treatment of Bacterial Cells

Bacteria in their natural habitat have an environment whose physical and chemical nature change little with time. Living higher animals in whose organs or tissues various bacterial species are found, have been endowed with a homeostatic capability. A bacterium is an open system from a thermodynamic standpoint. The theory of non-equilibrium thermodynamics (which applies to open systems) is also applicable to bacteria.

2.12

Bacterial Cell as a Thermodynamic System

An individual bacterial cell bounded by the outer cell wall is the thermodynamic system under consideration. A living bacterium grows and at some point, during growth it divides into two bacteria whose size varies

42



Biophysical Chemistry

during growth. The relative size of the two daughter cells varies but there are upper and lower limits to cell volume. Bacterial life is thus a cyclic process beginning with the newly separated daughter cell and starting again when the next generation grows as a free species. A single cell or the sum of all cells in a culture is an open system in a thermodynamic sense. Matter, energy and entropy flow into the system followed by physical and chemical changes within the system which are accompanied by net production of entropy. Conversely matter, energy and entropy flow from the system to the environments. The environment includes aqueous solutions of cell nutrient, any substances discarded by the cells and any gases above the solution.

2.13

Physical and Chemical Features of the Cell and Environment

2.13.1

Physical Features

The system is composed of three major physical components: (i) the outer most part of the cell wall which limits the volume of the cell; (ii) a very thin membrane lying beneath the cell wall, its major function being to control the flow of molecules into and out of the cytoplasm; (iii) the cytoplasm which is an aqueous solution containing molecules such as glucose, ions like Na+ , K+ and Cl− in the interior of the cell. Other organelles of different kinds are also present in the cell.

2.13.2

Chemical Features

The bacterial cell wall, cytoplasmic membrane, the cytoplasm contain many substances in the environment of growing cells. The concentrations of some molecules (e.g., glucose), electrolytes (e.g., NaCl, KCl) in the cell’s environment decrease steadily with time. It is therefore necessary that nutrient molecules enter the bacterial cell so that chemical reactions occur to produce additional bacterial material in the cell. Within the cell system, nutrients undergo reactions that produce macromolecular components resulting in an increase of bacterial cell mass and volume. The energy required for the syntheses is obtained from the reactions of nutrient molecules in which some energy is lost as heat. Such chemical reactions that produce complex molecules (from relatively simple ones occur in a coordinated sequence of reactions), each producing one molecule more complex than the one utilized. The entropy produced in the cells flow into the environment.

Thermodynamic Aspects of the Cell 

43

As the thermodynamic system (i.e., the bacterial cell) functions, it is observed that some low molecular weight substances also appear and their concentration increases with time. This is due to cell metabolism. For example, CO2 produced by metabolism of carbohydrates does not accumulate in the system but is released to the environment. A bacterial mass (composed of many individual cells) must contain many cells in every physiological state between two cell divisions. Due to this, the available data are averages over cell growth and division cycle. If one has cultures in which growth of cells is perfectly synchronized with respect to the physiological state of individual cells, they could be chemically analyzed (at any chosen physiological state). For a mass of synchronously growing cells, it would in effect be amplifying the response of a single cell by a certain factor i.e., the number of cells per unit volume. Even though one works with average values of the desired physical and chemical properties of a system, some thermodynamic properties of the system can be employed to study the system. Hinshelwood et al., have considered the chemical species in the bacteria, the reactions producing them and the kinetics of the reactions. These studies led to the proposals of reaction sequences starting with nutrient molecules and ending with the formation of bacterial substances and waste products. Many molecular entities appear as members of more than one sequence thus providing a way for the coupling of sequences. The sequence of physical and chemical processes comprising bacterial growth (derived from kinetic studies) is associated with a decrease of Gibbs free energy. When a system of bacteria is studied under growth as a batch culture, it has the disadvantage of living under continually changing environment. The supply and environmental concentration of nutrient molecules (except O2 ) diminish rapidly as the system enlarges cell division while concentration of waste molecules rises rapidly. Thus, the system is (thermodynamically) an open system and the effect of these rapid, drastic environmental changes requires constant changes in the system to maintain life. Ultimately cell replication ceases and the disintegration of the system begins.

2.13.3

Continuous Culture

Continuous culture of bacteria under time-invariance provides chemostatic conditions. These conditions provide only the desired approximate environmental conditions. It is preferable to use chemically defined media to obtain accurate and continuous control of nutrient chemical species in the environment so that the identification and quantification of molecules discarded by the system is easy.

44



Biophysical Chemistry

As bacteria multiply in a continuous culture apparatus, the population density of the cells become established at a fixed level in a short time. New cells replace those that leave with the effluent because the thermodynamic system (i.e., the bacterial cell) has attained a steady state of growth and replication.

2.14

Concept of Steady State

In steady state, there are no changes of intensive variables of the system with time. Thermodynamic potential differences between the system and environment are maintained at a positive value because of constraints applied through the system. Some examples of the constraints are chemical potential difference of solutes, pressure and temperature gradients. As stated above, time-invariance of the constraints is necessary if the system is to achieve a steady state. Altering the magnitude of an external constraint after the system reaches steady state results in changes of the thermodynamic parameters of the system until the system reaches a new steady state. The distinction between steady state condition and equilibrium may be resolved by considering an isolated system, where it can neither exchange matter or energy with its environment. A system in a steady state would undergo changes for a while after it was isolated but for a system at equilibrium there would be no change at all.

2.15

Non-equilibrium Thermodynamics in Microbiology

The condition for the spontaneity of a reaction ΔGT,P < 0 is not applicable to bacteria because reactions associated with bacterial cells such as cell growth require variation of pressure or temperature as external constraints. The only criterion of spontaneity in such cases is the entropy change accompanying such processes. It is known that this quantity always increases in a spontaneous (or irreversible) processes. The entropy change can occur in two ways: (i) entropy flow between the system and the environment, and (ii) production of entropy within the system. Nonequilibrium thermodynamics concerns with the quantitative evaluation of entropy production within the system. Entropy per unit time permit volume is a sum of terms, each of which is defined as the product of a flow and the conjugate force that drives the flow. For example, entropy production accompanying the flow of heat has a temperature gradient as the conjugate force. Similarly, affinity is the driving force for a chemical reaction.

Thermodynamic Aspects of the Cell 

45

Simple free-living microorganisms have numerous metabolic pathways to follow. The utilization of these pathways implies flows of matter and heat into and out of the system that is also associated with entropy production. The variety of chemical reactions occurring within the organism is a accompanied by further production of entropy. To apply the principles of non-equilibrium thermodynamics to the study of these organisms, it is necessary to assume simple possible sequence of metabolic reactions of all those that occur in cell species.

2.16

Linear Laws

It is possible to apply linear laws relating flows and forces whose product is the entropy of the total process of bacterial life. The set of phenomenological equations that describe the bacterial growth must include: (i) equations for chemical reactions within the cell, (ii) equations describing the entry of nutrient materials and exit of waste materials, and (iii) equations relating energy exchange with the environment. Consider the functioning of some cells maintained in a time invariant nutritional environment as described by the following set of linear laws. J1 = L11 X1 + L12 X2 + L13 X3 + L14 X4

(2.13)

J2 = L21 X1 + L22 X2 + L23 X3 + L24 X4

(2.14)

J3 = L31 X1 + L32 X2 + L33 X3 + L34 X4

(2.15)

J4 = L41 X1 + L42 X2 + L43 X3 + L44 X4

(2.16)

where Ji = flow of heat, chemical substance (diffusion) or rate of a chemical reaction (i = 1, z, . . . , n). X j = force conjugate to flow Ji (temperature gradient), difference of chemical potential [or affinity ( J = 1, z, . . . , n)]. Lij = Onsager’s (straight) coefficients if i = j; Onsager’s cross coefficients if i = j, Lij = L ji . Equations (2.13 to 2.16) indicate that one must determine experimentally (and simultaneously) each of the flow’s Ji occupying when each force X j has a known value that one may calculate the values of the constants Lij . Onsager’s reciprocal relations are useful in this context. Experimentally, one requires the use of a continuous flow culture apparatus to fulfil the conditions of time invariant change of nutritional environment. When one

46



Biophysical Chemistry

deals with bacteria, it is difficult to determine directly the chemical potential of any substance inside a bacterial cell. Such difficulties can be circumvented by employing equations reciprocal to equations (2.13 to 2.16), i.e., X1 = R11 J1 + R12 J2 + R13 J3 + R14 J4

(2.17)

X2 = R21 J1 + R22 J2 + R23 J3 + R24 J4

(2.18)

X3 = R31 J1 + R32 J2 + R33 J3 + R34 J4

(2.19)

X4 = R41 J1 + R42 J2 + R43 J3 + R44 J4

(2.20)

where Rij =

[ Lij ] , [ Lij ] [ L]

being the minor determinant corresponding to the coefficient Lij and [ L] the determinant of the matrix of all the coefficients Lij . The Onsager reciprocal relation apply to Rij (i = j). Equations (2.17) to (2.20) give the forces as functions of the flows. The fluxes of particular chemical species into or out of the cell can be determined with suitable chemical techniques. The importance of equations (2.13 to 2.16) and (2.17 to 2.20) arises from the fact that by proper manipulation of the experimental of condition one or more of the flows or forces can be held to zero value. This leads to simpler relationships among constants and experimental quantities and it is easier to evaluate specific constants. If, for example, the temperature of the environment (and hence of the cell) be set at set new value in a chosen sequence, it may be determined that one or more specific numerical constants, Lij , take on new values for each temperature. With these changes, the same forces and flows may serve to describe the functioning of the bacteria. If one uses the steady states sustained by bacterial growth in a continuous culture (as affected by the concentration of the nutrient in the environment) to determine the phenomenological coefficients for a single organism, one is able to compare the efficiency of utilization of those carbon sources by the organism under the specified conditions. Changes in numerical values of phenomenological coefficients would signal alterations of relative importance of metabolic reactions.

2.17

Force and Flows in Living Systems

2.17.1

Temperature and Heat Flow

There is a temperature difference between the interior of a living bacterial cell and the medium that surrounds the cell. Heat moves from a point

Thermodynamic Aspects of the Cell 

47

at higher temperature to a point of lower temperature, nutrient medium surrounding growing bacteria becomes heated. It is the driving force of a small amount of heat flow and the product of the force and heat flow contribute to entropy production. The rate of heat flux flow with in the cell will be affected by the temperature drop across cell boundaries and the heat conductivity of the cell and its boundary layers. Consequently a steady state of internal temperature will be attained after a sufficient length of time. The internal temperature at the steady state characteristic of a bacterial species will govern the rates of reactions with in the cell and the metabolic diffusion rates (with in the cell) and across the boundary. The temperature difference between the environment and the cell interior can be considered in terms of non-equilibrium thermodynamics and it can also explain the observations that bacteria are able to live at temperatures where most enzymes are inactive. By the temperature drop across cell boundaries and the heat conductivity of the cell and its boundary layers. Consequently, a steady state of internal temperature will be attained after a sufficient length of time. The internal temperature at the steady state characteristic of a bacterial species will govern the rates of reactions within the cell and the metabolic diffusion rates (within the cell) and across the boundary. The temperature difference between the environment and the cell interior can be considered in terms of non-equilibrium thermodynamics and it can also explain the observations that bacteria are able to live at temperatures where most enzymes are inactive. Thermophilic organisms (i.e., heat living organisms which can thrive above 55◦ C) are stable at their observed temperature because at that temperature the thermodynamic force (related to temperature difference between the environment and the cell interior) is compatible with other thermodynamic forces, e.g., affinity of the system. The contribution of temperature gradient to the flow of substances through the cell membranes of bacteria and its influence on metabolic processes differs widely for different membranes.

2.18

Chemical Potential and Mass Transfer: Activated Support

Another combination of flows and forces contributing to entropy productions by microorganisms is mass flow and difference in chemical potential. Nutrients and metabolic products pass through the exterior layers of

48



Biophysical Chemistry

the cell at a rate that depend, on the nature of the cell wall, the specific substances and their chemical potential differences across the exterior layers. The amount of flow of any one substance caused by non-conjugate forces may be small or large and the flow of the substance driven by nonconjugate forces may be in the same or opposite direction as that of the force.

2.19

Applicability of Linear Laws

Biological membranes have been examined using the theory of nonequilibrium thermodynamics. This formalism has been employed to describe the function of ascites tumor cell membranes and also to transport through toad skin. Synthetic membranes are capable of demonstrating some of the properties of living membranes. Linear equations with constant phenomenological coefficient have been used to describe their behavior. These equations help in describing the coupling of an enzymatic reaction to transmembrane flow of electric current in a synthetic active transport system involving enzymes.

2.20

Non-linear Descriptions

The linear kinetic equations yield results in agreement with experiments in cases near equilibrium (near equilibrium assumption). In such cases, affinities of the involved chemical reactions are small.

2.20.1

Systems Involving Large Affinities

Prigogine et al., have shown that in some systems, there are steady states both near equilibrium and far from equilibrium. In these cases, the same chemical reactions account for events under both circumstances. In one model proposed, two substances A and B are initially transformed into two final products D and E, through two intermediates X and Y by the action of the catalysts C, W, V and V following the general scheme: (2.21) (2.22)

Thermodynamic Aspects of the Cell 

49

The following reactions are assumed to take place (2.23)

(2.24)

(2.25) The above model is satisfactory in a steady state near equilibrium. The requirements of linear irreversible thermodynamics are met with in this case. Consider equations (2.17) and (2.18). The carbon source (analogous to B) serves as a precursor to bacterial mass “D” and for discarded molecules (E) from which energy is extracted for combining (A) and (B) and for all other reactions requiring energy. The reactant A represents the nitrogen source and other substances required for cell function. In order that the system may function, certain catalysts in enzymes (C, W, V, V ) must be present as one produces new bacterial mass only from preexisting living bacterial mass. Prigogine et al., have shown that oscillations around an unstable steady state is a typical phenomenon of systems far away from equilibrium. It is believed that bacterial cell growth and division is a single process which can be interpreted as a process of oscillation about an unstable steady state. Cyclic processes in open systems with constant external constraints can be understood in terms of the theory of non-equilibrium thermodynamics.

2.21

Simple Cell Functions in Non-equilibrium Thermodynamics

Non-equilibrium thermodynamics provides a reasonable basis for understanding the operation of a living cell. The chemical reactions that occur in cell growth are not at equilibrium. The appearance of non-homogeneities i.e., the production of cell membranes, cell walls as a result of these processes indicates that these phenomena involve non-equilibrium stationary states far from equilibrium. In different growth media, chemical and physical properties of bacteria within a strain (of one species) show marked differences.

50



Biophysical Chemistry

Growth temperature is a significant variable in continuous culture of a yeast and bacteria. The E.Coli B observations on S. cerevisiae LBGH 1022 and on a bacterium Aerobactor cloacae demonstrate that for a given set of time-independent external constraints, there results (in continuous cultures) a single characteristic cell population density.

2.22

Batch Cultures

The theory of non-equilibrium thermodynamics has been developed under the postulate of time independent boundary conditions and its practical application to bacteria cell growth, divisions and function is only possible when such conditions are present. The “lag phase” in batch cultures is that period during which the condition of time in variant external constraints is nearly met. The “lag” ends with the first division of the cells of the inoculum. Prior to division, the cells of the inoculum have attained an unstable stationary state of growth; departure from the unstable state is initiated by some perturbation such as an enzyme function. The “exponential phase”, the stationary phase and the phase of decline of batch cultures are artifacts of the batch culture. The exponential phase is a steady state of growth. The fundamental condition of time invariant external constraints is not met in batch cultures in all the phases. In batch cultures, the reduction in nutrient concentration in extracellular environment (as a result of cellular growth) will cause a reduction in affinities of some substances which causes cessation of growth. In some cases, end products of metabolism appear outside the cell as –COOH anions. The apparent toxicity of metabolic end products increases with decreasing pH in batch cultures. The uncharged carboxylic acid molecules pass more easily through the cell’s negatively charged exterior layers than does the anions. The cell’s internal concentration of the acid or anion will rise as –COO and reenters leading to lowered affinity of the metabolic reaction producing it.

2.23

Thermodynamic Concepts

(1) Entropy change: The change in entropy of a closed system is greater than zero for all irreversible processes and may be expressed as di S ≥ 0

(2.26)

with equality sign being valid for a reversible process The entropy changes of an open system (Example: a single bacterial cell) may be

Thermodynamic Aspects of the Cell 

51

given as dS = de S + di S

(2.27)

where dS = total entropy change of the system; de S = the entropy change resulting from exchange of energy and matter between the system and environment, di S = total entropy change due to physical or chemical changes within the defined system, it may be zero or positive. The entire time span of cell life is a sum of incremental time periods during which the incremental changes occur. If a bacterial cell is divided into two subsystems such as cell cytoplasm (I) and cell covering (II) the entropy production of the entire system is di S = di ( S I + S I I ) ≥ 0

= di S + di S I

II

(2.28) (2.29)

The entropy production by every macroscopic region of the system must separately be greater than zero i.e. di S I ≥ 0,

di S I I ≥ 0

(2.30)

Entropy production must occur in a single volume element. It is manifest in metabolizing systems through the coupling of reactionsproduction by one reaction in a sequence of a molecule required in the next reaction of the sequence. Coenzymes are thus thermodynamic necessities; because they exist it is possible to carry out chemical reactions in controlled steps, the sites of the steps being well separated as in all living system. Non-equilibrium thermodynamics is concerned with the quantitative evaluation of d1S for spontaneous processes. Changes of this nature can be exemplified by conformational changes in proteins. Such reactions are involved in the growth and function of bacteria. (2) The Gibbs equation: It is given by dS =

1 P ∑ μr du + dv − dnr T T r T

(2.31)

where the terms have their usual significance. The Gibbs equation is developed for systems at equilibrium. In non-equilibrium thermodynamics (systems not in equilibrium), it is postulated that there exists at every point a state of local equilibrium for which the local entropy is given by the Gibbs equation.

52



Biophysical Chemistry

(3) Entropy production: The total entropy change of a system dS varies with time as dS/dt. But dS de S di S = + dt dt dt

(2.32)

where ddte S = entropy exchanged with environment (in unit time). Entropy produced within the system per unit time. If the whole volume of a system is considered as the sum of many volume elements, di S may be considered as the sum of internal entropy production in their volume elements. In each volume element the entropy produced is called the “local entropy production” symbolized by σ. It can be divided into three parts: (i) Production of pure entropy = heat flow × gradient of temperature function, (ii) production of entropy by diffusion of one or more substances present, and (iii) production of entropy due to chemical reactions occurring with in the system. Each of these three parts (components) is a product of two terms, one a flow and the other a force. (i) production of pure entropy = heat flux × gradient of temperature function, (ii) production of entropy by diffusion process = flow of matter by diffusions × gradient of chemical potential, and (iii) production of chemical reaction entropy = rate of a chemical reaction × a function of the affinity of the chemical reaction. We may summarize the above by writing σ=

∑ Ji Xi

i = 1, 2, 3, . . . , n

(2.33)

Once a flow is described, the primary force associated with it is fixed by certain thermodynamic requirements. Ji is said to be the flow conjugate to the force Xi . The primary idea of the local entropy production is to establish the flows and forces involved in the irreversible processes occurring in the system under consideration. (4) Linear Law: They may be illustrated by an example of “thermo couple”. It measures a potential difference to measure the temperature difference between two junctions. This might seem strange, for a potential difference between two points by Ohm’s law, is associated with the flow of electricity between two points and it does not say anything about temperature differences. Further, Fourier’s law relates temperature difference to heat flow and does not consider electrical potential differences. The conclusion is that when there is a difference there is a heat flow and when there is a potential difference, there is a current flow. It is observed that if one forces an electric current (DC) through a thermocouple whose junctions are at the same temperature,

Thermodynamic Aspects of the Cell 

53

the junctions do not remain at the same temperature, one becomes warmer and the other becomes cooler. The interrelationship of these four quantities–heat flow, electric current flow, temperature gradient and potential difference may be expressed by the following equations:

( T2 − T1 ) (φ − φ1 ) + L12 2 T T2 ( T2 − T1 ) (φ2 − φ1 ) Electric current = L12 × + L12 T T2 Heat flow = L11 ×

(2.34) (2.35)

These equations indicate the following: (1) Each flow in the system is a function of both forces operating in the system. Both forces involve the average temperature: one is ΔT/T2 and the other is Δφ/T. These forces meet the requirement of being those conjugates to the flow to which they are primarily related. (2) The dependence of the flow on each force is linear (i.e., it depends on the first power of the source). (3) There is a proportionality constant connecting each flow with the corresponding driving force. These equations can be summarized in the following mathematical form: Ji =

n

∑ Lik Xk ,

k =1

i = 1, 2, 3, . . . , n

(2.36)

Since these equations are based on experimental observations an describe the chosen phenomena, these are often designated as phenomenological relations. (5) Phenomenological coefficients and Onsager reciprocal relations: From the postulates of non-equilibrium thermodynamics, the phenomenological coefficients are constant over the range where the linear laws hold good. In equations (2.34 and 2.35), the coefficient L11 is identified as the thermal conductivity of the metal junction and L22 is the electrical conductivity. The other two coefficients L12 and L21 are called “cross coefficients”. They are independent of both L11 and L22 but are not independent of each other. Infact L12 = L21 (as proved by Onsager) and are called Onsager reciprocal relations. (6) Degree of advancement of a reaction: This concept applies to both physical and chemical processes. It is a number between zero and one that expresses how far the process has gone from inception to completion. It is given the symbol ξ. Consider the reaction CO2 + H2 O FGGGB GGG H2 CO3

(2.37)

54



Biophysical Chemistry

The degree of advancement of the reaction at the time of instant exposure of CO2 to water is zero. As CO2 dissolves in water, the degree of advancement reaches unity as a steady state is established under the given experimental conditions. The change in degree of advancement unit time is the reaction velocity dζ = Velocity dt

(2.38)

(7) Affinity: For a spontaneous or irreversible reaction occurring at constant T and P, it is possible that a certain amount of heat is released to the surroundings which is proportional to ξ. For this, one may write the equation dQ = Adξ ≥ 0

(2.39)

The proportionality constant A is called affinity. The heat produced by the irreversible reaction is a direct measure of the entropy produced. The affinity A may be defined as A=−

∑ vγ μγ v

(2.40)

in which vγ is the stoichiometric coefficient (negative for reactants and positive for products) and μγ is the chemical potential of the species participating in the given reaction. As an example, consider the reaction N2 (g) + 3H2 (g) FGGGB GGG 2NH3 (g)

(2.41)

The stoichiometric coefficient for N2 = −1, H2 = −3 and NH3 = +2A is given by A = − ∑(−μN2 − 3μH2 + 2μNH3 )

(2.42)

The properties of A are: (i) it is a function of state, (ii) always has the same algebraic sign of the rate of reaction, (iii) if A = 0, the system is in equilibrium, and (iv) it is possible for A to be very high but the rate is very close to zero. This is a case of false equilibrium. (8) Coupling of reactions: If there are several reactions going on at the same time in a system, the total entropy produced per unit time per

Thermodynamic Aspects of the Cell 

55

unit volume is the sum of the entropies produced of all individual reactions i.e., P=

di S 1 = dt T

∑ Ae Ve

e = 1, 2, 3, . . .

(2.43)

e

where e refers to each reaction involved. In a system where two reactions occur in a local region, it is possible to have A1 V1 < 0, A2 V2 > 0 provided that A1 V1 + A2 V2 ≥ 0

(2.44)

The first reaction is called the coupled reaction and the second reaction is the coupling reaction and because of thermodynamic coupling, the coupled reaction may proceed in a direction, opposite to that dictated by its affinity. An example is the synthesis of carbohydrate coupled to the combustion of elemental hydrogen in Bacillus pycnoticus. The coupled reactions involved are: Coupled reaction CO2 + 0.931H2 O →

1 C6 H12 × 0.93106 + 1.931O2 6

(2.45)

Coupling reaction 2H2 + O2 → H2 O

(2.46)

The coupled reaction indicated by subscript 1 in equation (2.44) is so designated because a carbohydrate similar in formula weight to glucose was observed to accumulate with time in the bacterium when it grew in a solution of H2 , O2 and CO2 . Hydrogen plays the role of a metabolite, for the mass present decreases as a result of combustion with oxygen. The hydrogen combustion is the coupling reaction [indicated by subscripts in equation (2.44)]. The affinities of the reaction and their velocities were found to be A1 = −105.1 kcal, V1 = 0.543 × 10−3 A2 = +108.5 kcal, V2 = 2.377 × 10−3

(2.47)

If inequality of equation (2.44) holds, there is an upper limit on A1 V1 ≤

| A2 |V2 | A1 |

(2.48)

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Biophysical Chemistry

substituting the experimental value given in equation (2.47) the equation (2.48) is verified accordingly. 0.543 × 10−3
27◦ C and increase with the hydrocarbon chain lengths. It is well known that (mono and poly) unsaturated molecules melt at much lower temperatures in comparison with their saturated analogues. As anticipated, the lowest melting temperatures occur when the C==C bonds are located near the centre of the hydrocarbon chain. Hence these molecules form viscous liquids, even at room temperature. The hydrophobic character of the hydrocarbon chain of fatty acids is more prominent than the hydrophilic nature of the –COOH group, resulting in lower solubility of these molecules in water. For example, at 25◦ C, the solubility of fatty acids ∼ μg per gram of water. However, this solubility exhibits an exponential decrease with the addition of each carbon atom to the hydrocarbon chain. From thermodynamic considerations, this behaviour is a manifestation of Gibbs free energy changes involved in the transfer of molecules from the organic solvent to water. In other words, upon incorporation of each CH2 group, more energy is required to orient water molecules around the hydrocarbon chain of the fatty acid. In aqueous solutions, the dissociation occurs as given by the equation R − COOH −→ RCOO− + H+ , with R representing the hydrocarbon chain; the degree of dissociation is quite small ( 1). The negatively charged –COO− ions are more polar than the undissociated acid. The dissociation equilibrium can however be controlled by systematic addition of a base such as NaOH. This leads to the replacement of H+ by Na+ ions so as to yield the salt of the fatty acid (soap). The detergent property of soaps arises since RCOO− anions in spontaneously form micelles. The interior of these structures essentially consisting of hydrocarbon chains, serves as an efficient medium wherein grease etc., can be sequestered. The diameter of each spherical micelle is nearly double the length of the extended fatty acid. The dispersions of micelles in water are stable. The formation of bubbles, foams on the surface of these soap dispersions is the consequent outcome of the adsorption of

Lipids 

89

RCOO− ions at air-water interfaces. It is hence no wonder that the entire arsenal of thermodynamic, spectroscopic, electrochemical and microscopic tools becomes available to unravel the nature of air-water interfaces.

4.3

Bonding in Lipids

The reactive acidic –COOH group of RCOOH form esters (RCOOR’) with alcohols R’OH, the ester bond being the primarily covalent in nature. A less frequent occurrence is the ether bond (R’-O–R) in lipids. All cell membranes consist of lipid bilayers. Each lipid bilayer contains two layers of fat cells which encompass two sheets. The boundaries of all the cells are dictated by the barrier provided by the lipid bilayer components and hence comprehending the structure and functioning of lipid bilayers is of paramount importance. The interfacial tension varies from 0.2 to 6 dynes cm−1 while the thickness ranges from 4 to 7 nm. In view of the lipid bilayers possessing capacitance (∼ 1μFcm−2 ), dielectric constant (< 4) and conductance (∼ 10−8 mho m−2 ) electrochemical techniques are especially suited to probe their properties.

4.4

Classification

They may be classified as: (a) fatty acids, (b) acylglycerides, (c) waxes, (d) phospholipids (or phosphoglyceride), (e) sphingolipids, (f) glycolipids, and (g) terpenoids lipids. A brief account of the above classes is given below.

4.4.1

Fatty Acids

They are carboxylic acids with hydrocarbons (carbon atoms ranging from 4 to 30) in straight chain mostly with 16 to 18 number of carbon atoms. The chain is generally linear but may be branched also. The compounds may contain double bonds from one to six always (nearly) with a cis configuration. For compounds with one double bond, the usual position is C-9 and C-10 and for compounds with many double bonds the most common positions are C-9, C-12 and C-15 (mostly unconjugated). The saturated fatty acids are waxy solids while the unsaturated ones are oily. A few fatty acids starting from lauric acid are listed below.

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Acid

Lauric Myristic Palmitic Stearic Oleic Linoleic

Table 4.1 Examples of a few fatty acids. Structure Number of carbons and double bonds CH3 (CH2 )10 COOH 12 : 0 CH3 (CH2 )12 COOH 14 : 0 CH3 (CH2 )14 COOH 16 : 0 CH3 (CH2 )16 COOH 18 : 0 CH3 (CH2 )7 CH = CH(CH2 )7 COOH 18 : 1 (position of = is 9) CH3 (CH2 )4 (CHCHCH2 )2 (CH2 )6 COOH 18 : 2 (position of = is 6)

If a trans configuration occurs in a structure, it is started as for example 18: 3(6-C, 9-C, 12-C) 6, 9, 12 being positions of double bonds. Animal fatty acids are mostly straight chain compounds containing upto six double bonds. Bacterial fatty acids may be saturated, branched chain compounds while plant fatty acids have a more complex structure. Naturally occurring fatty acids having 1 to 8 carbon atoms are liquid, while those with more carbon atoms are solid. Addition of a double bond to fatty acid lowers the melting point.

4.5

Reactions

4.5.1 Fatty Acids They react with base to form salts, known as soaps. For example, CH3 (CH2 )14 COOH + NaOH →CH3 (CH2 )14 COONa + H2 O

(4.1)

Sodium palmitate (soap)

Figure 4.1 Schematic representation of hydrophobic and polar groups in soaps.

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91

Such salts have a polar head (carboxyl group) and a non-polar tail (hydro carbon). Soaps form micelles where the hydrophobic tail points away from water while the polar heads point towards water as shown in Figure 4.1. A major portion of acids are found as esters in the cells and the ester bonds undergo hydrolysis in presence of acids or bases. The acid hydrolysis is a reversible reaction, but the base hydrolysis is not. For example, the base hydrolysis of triacylglycerol is as follows:

(4.2) The pKa ’s of most fatty acids range between 4.8 to 5.0.

4.5.2

Geometric Isomerism

When a double bond exists in the hydrocarbon chain, geometric isomerism occurs. For example

(4.3) Oleic acid is a bent molecule for the following reasons: (i) It has a cis 9, 10 double bond; (ii) The combination of a cis form and the presence of sigma and pi bonds in the double bond; (iii) The bent structure may be represented as:

(4.4)

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Biophysical Chemistry

Another bent form of oleic acid (CH3 (CH2 )7 CH = CH(CH2 )7 COOH). In linoleic acid, which has two double bonds in the hydrocarbon chain, it is more severely bent. It may be mentioned that animal and plant cell membranes are rich in polyunsaturated acids. Naturally occurring polyunsaturated fatty acids may contain a nonconjugated double bond like

−CH2 − CH = CH − CH2 − CH = CH − CH2 (non-conjugated) but also

−CH2 − CH = CH − CH = CH − CH = CH − CH2 (conjugated) An important poly unsaturated fatty acid, alpha-elaeostearic acid, which is the principal acid in tung oil, has a conjugated triene group given by

(CH3 )(CH3 )3 CH = CH − CH = CH − CH = CH(CH2 )7 COOH The two types of double bonded systems have important differences in their reactivity. The conjugated double bonded systems are more reactive than their non-conjugated double bounded systems because of the delocalization of pi-electrons. Fatty acids with conjugated double bonds undergo extensive polymerization, which is of great value in paint industry. Such systems, which are biochemically important, are retinol and carotenes and they have important role in visual processes of retina.

4.6

Analysis of Lipids

Gas liquid chromatography and thin layer chromatography are some methods used in analysis of lipids.

4.7

Nomenclature of Phospholipids

Let us consider glycerophosphoric acid as an example.

(4.5)

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93

(a) The numbers 1 and 3 cannot be interchangeably used for the same primary alcoholic group. (a) As can be seen, the second hydroxyl group (in I) is shown to the left of C-2 in the Fischer projection and the carbon above C-2 is referred as C-1 and the one below as C-3. This stereo specific numbering is indicated as “Sn” as prefix before the name of the compound. Thus glycerol is labeled as

On this basis, compound I (in equation 4.5) is Sn-glycerol-3-phosphoric acid. Its special antipode is

A mixture of both is called racemic glycerol-3-phosphoric acid. There are several phospholipids, which contain glycerol, fatty acids and a nitrogeneous base and are considered derivatives of phosphatidic acid whose structure is

(4.6) A few representative phospholipids containing different bases are given below. Bacteria, animal and plant tissues contain phospholipids. Cell membranes contain choline. They are amphipathic since they contain polar and non-polar groups.

Polar Base component

Choline

Amino-ethanol

Non-polar Component fatty acid

Stearic or palmitic (R1 ) polyunsaturated (R2 )

Stearic or palmitic ( R1 ) polyunsaturated (R2 )

Lecithin (3-Sn-phosphatedyl) choline

Cephalin (3-Sn-phosphatidyl) amino-ethanol

Structure



Name of Phospholipid

94 Biophysical Chemistry

Non-polar Component fatty acid

Polar Base component

Plasmalogen (3-Sn-Phosphital amino-ethanol

Unsaturated ether (α), Linoleic (α)

Amino-ethanol

Inositol-phosphor-lipid (3-Phosphotidylinositol)

Palmitic (R1 ) Arachidonic (R2 )

Myo-Inositol

Structure

Lipids 

Name of Phospholipid

95

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Biophysical Chemistry

There are three other classes of lipids of importance, which must be mentioned: (a) sphingolipids, (b) glycolipids, and (c) terpenoids. They are briefly discussed below: (a) Sphingolipids: The main compound is known as 4-sphnigenine which has the structure

Two important products formed from 4-sphingosine are

(b) Glycolipids: They are derivatives of carbohydrates and glycerol and do not contain phosphate. They are present in chloroplasts; galacto

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97

and sulpholipids are also found in chloroplasts. Two important compounds of this class are:

(c) Terpenoids: Terpenoids are an important group of compounds made of a simple repeating unit, the isoprenoid unit. This unit by appropriate condensation with other molecules gives rise to compounds like rubber, carotenoids, steroids and terpenes. The active biological (counter part of isoprene is isopentyl pyrophosphate which is formed by a series of enzymatically steps from squalene. Squalene condenses with itself to form cholesterol. The structures of squalene (C30 H50 O) and isopentyl pyrophosphate are:



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Biophysical Chemistry

Another important terpenoid product is beta-carotene which has the structure as shown earlier. β-Carotene belongs to carotenoid family and is a constituent of colouring pigment for deep yellow and orange fruits and vegetables. It occurs in natural form in strawberries, cantalopes, broccoli, carrots etc. It is a powerful antioxidant and boosts immune system. Other important members of beta-carotenoid family are lycopene, alpha-carotene etc.

4.8

Lipoproteins

These are classes of bio molecules in which the lipid components are triacylglycerol, phospholipid and cholesterol or its esters. The protein components have relatively high proportion of non-polar amino acid residues which can participate in binding of lipids. The main binding force between the protein and lipid is the hydrophobic interaction between the apoproteins and lipids. The hydrophobic interaction implies the tendency of the hydrophobic components to associate with each other in aqueous medium. Lipoproteins are found in membranes of mitochondria endoplasmic reticuli and nuclei. The electron transport system is mitochondria contains large amounts of lipoproteins. Lamellar lipoproteins occur in chloroplasts and membranes of bacteria.

4.9

Role of Lipids in Cell Function

Lipids serve as storage forms of energy and they are also part of the structure of cell membranes. They participate in many metabolic activities such as (i) a major source of energy in animals and birds, (ii) activators of enzymes such as glucose-6-phosphatase,

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99

(iii) enabling electron transport in mitochondria. (iv) For example, the isoprenoid compound, undecaprenyl phosphate acts as a lipophilic carrier of a glycosyl moiety in the synthesis of bacterial wall lipopolysaccharides and peptidoglycan,

(v) Phosphotidylserine is decarboxylated by a specific decarboxylase to Phosphatidylethanolamine and in the process CO2 is released.

4.10

Distribution of Lipids

The composition of lipid differs in prokaryotic and eukaryotic cells. In prokaryotic cells, a bacterial cell wall has over 95% of its total lipid associated with cell membrane. The remaining 5% is distributed between its cytoplasm and cell wall. Bacteria are limited in their capacity to synthesize conventional polyunsaturated acids. They produce only saturated or branched chain fatty acids. Plants: Seeds of higher plants have a fixed composition of fatty acids. The maturing seed synthesizes its different fatty acid, at different rates and at different periods during maturation. The exotic fatty acids are found as triacylglycerols in the mature seed and are not found in chloroplast. Higher plants synthesize a wide range of polyunsaturated fatty acids. Animals: Lipids of animal cells are complex and their composition is characteristic of a particular cell. For example, a nerve cell is rich in sphingolipids, glyceryl ethers and phospholipids. An adipose cell consists mainly of triacylglycerols. A special feature, which is unique to lower and higher forms of animal life, is their inability to form polyunsaturated fatty acids. Animal cells introduce “cis” double bonds into hydrocarbon chain towards carboxyl end where as plant cells always introduce double bonds towards the methyl end.

100



4.11

Biophysical Chemistry

Physicochemical Data on Lipids

Interfacial tension data of some single component bi-layer membranes with different lipids.

β-carotene belongs to carotenoid family and is a constituent of colouring pigment for deep yellow and orange fruits and vegetables. It occurs in natural form in straw berries, cantaloupes, broccoli, carrots etc. It is a powerful anti-oxidant and boosts immune system. Other important members of this family are lycopene, alpha-carotena etc.

Lipids 

4.11.1

101

Physicochemical Data on Lipids

I. Interfacial tension data of lipid-cholestrol (1 : 1) complex in bi-layer lipid membranes. Complex Interfacial tension (Nm−1 )

Pc - Ch 2.17 × 10−3

PE - Ch 2.38 × 10−3

Cer - Ch.SM - Ch 2.33 × 10−3 4.48 × 10−3

II. Interfacial tension data of lipid-lipid (1 : 1) in bi-layer lipid membrane. Complex Interfacial tension (Nm−1 )

Pc - PE 2.58 × 10−3

SM - Cer 1.62 × 10−3

III. Interfacial tension data for lipid-fatty acid and lipid-amine complexes (1 : 1) in bi-layer lipid membranes. Complex Pc - SA Interfacial 7.16 × 10−3 tension (Nm−1 )

PC - DA 7.25 × 10−3

PC - ST 6.04 × 10−3

PC - DE 3.63 × 10−3

IV. Interfacial tension data for lipid-amino acid complexes (1 : 1) in bilayer lipid membranes. Complex Pc - Tyr Interfacial 1.75 × 10−3 tension (Nm−1 )

PC - Ile 1.91 × 10−3

PC - Val 2.04 × 10−3

PC - Phe 3.69 × 10−3

V. Interfacial tension data of some single component bi-layer membranes with different lipids.

Interfacial tension (Nm−1 )

Phosphatidylcholine (PC) 1.62 × 10−3 Phenylalanine (Phe) 5.30 × 10−3

Ceramide (CER) 1.29 × 10−3

Cholesterol (Ch) 4.72 × 10−3

Phosphatidylethanolamine (Pe) 3.34 × 10−3

Decanoic acid (DA) −4.2 × 10−3

Decylamine (DE) −7.5 × 10−3

Valine (Val) 7.0 × 10−4

Sphingomyelin (SM) 1.72 × 10−3

Tyrosine (Tyr) −3.5 × 10−3

Stearic acid (SA) −1.54 × 10−3

Stearylamine (ST) 4.40 × 10−3

Isoleucine (Ile) −2.7 × 10−3



Name of lipid Interfacial tension (Nm−1 ) Name of lipid Interfacial tension (Nm−1 ) Name of lipid Interfacial tension (Nm−1 ) Name of lipid

102 Biophysical Chemistry

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103

VI. Physico-chemical parameters of one component bi-layer lipid membranes. Component

pKa

pKb

Isoelectric point

PC PE PS SM

2.58 2.42 2.58 2.59

5.69 5.98 9.55 5.31

4.12 4.18 3.80 4.01

Interfacial Tension at Isoelectric Point (Nm−1 ) 3.53 4.06 2.94 4.42

VII. Conductivity of phospholipid (used as lecithin) cholesterol membranes as a function of pH. Concentration of phospholipid = 5 × 10−6 mol ml−1 = 5 × 10−3 mol liter−1 . Lipid: PE

X (Mole fraction of cholesterol) 0.20 0.80

Conductance (mho cm−2 ) pH = 5.0 pH = 6.0 − 5 2 × 10 8 × 10−6 − 5 5 × 10 1 × 10−5

Lipid: PC

X (Mole fraction of cholesterol) 0.20 0.80

Conductance (mho cm−2 ) pH = 5.0 pH = 6.0 − 5 1 × 10 0.2 × 10−5 − 5 6 × 10 4.0 × 10−5

VIII. Dependence of membrane conductance on carrier concentration. Concentration of Valinomycin = 10−8 M Lipid Conductance (mho cm−2 )

PG 10−4

PE 10−7

DC 10−7

PG = Phosphatidyl glycerol; PE = Phosphatidyl ethanolamine; DC = 7-dehydro-cholestrol IX. Critical micelle concentration of lipids. The CMC of a surfactant (in this case, a lipid) is the concentration at which surfactant micelles form. Below CMC, a surfactant exists as monomers in solution but above CMC micelles are present.

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Lipid = PC 5:0 10 : 0 16 : 0 Lipid = PG 10 : 0 14 : 0

CMC 90 mM 0.005 mM 0.46 nM CMC 14.0 mM 0.011 mM

Lipid = PS 8:0 10 : 0

CMC 2.28 mM 0.096 mM

X. Temperature dependence of CMC. Lipid : PC 10 : 0 14 : 0

Temp (20◦ C) 8 × 10−3 moles liter−1 7 × 10−5 moles liter−1

Temp (40◦ C) 7 × 10−3 moles liter−1 8.5 × 10−3 moles liter−1

Spontaneous self-assembly of phospholipids in water is essential to the stability of biological membranes and to life itself. It is controlled by thermodynamics, specifically the tendency of hydrophobic lipid chains to segregate from contact with water coupled with the structural requirement to form a thin, flexible membrane. The membrane forms a tight permeability barrier to polar solutes in aqueous environment. This requires a strong interplay of lipid polar head-groups and their hydrocarbon acyl chains, which lead to the formation of lipid bi-layer membranes. ◦ , ΔH ◦ , ΔS◦ data for some saturated acyl lysophosphatidyl XI. ΔGtr tr tr cholines (n : 0) and diacetyl phosphatidyl cholines (n : 0)2 of different chain lengths, n, from their monomeric state in water to their respective micellar states at different temperatures.

Lipid studied (10 : 0) LPC (14 : 0) LPC

◦ /kJmol−1 ΔGtr 20◦ C 40◦ C −21.5 −22.5 −35.0 −36.5

◦ /kJmol−1 ΔS◦ /Jk−1 mol−1 ΔHtr tr 10◦ C 30◦ C 10◦ C 30◦ C 9.0 2.5 150.0 100.0 5.0 −7.0 140.0 90.0

◦ for 1, 2 diacetyl phosphatidyl cholines ( n : 0) XII. Dependence of ΔGtr 2 from water to micellar state at 25◦ C.

Chain length 8 10 12

ΔGt◦ /Jmol−1 −30.0 −40.0 −52.0

Formula of the compound C42 H80 NO8 P

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105

XIII. Surface charge density (σ ) of various lipids. Compound 1, 2 dipalmitoyl-3-trimethyl ammonium propane (DPTAP) 1, 2 dipalmitoyl phosphatidyl ethanolamine (DPPE) 1, 2 dipalmitoyl phosphatidyl glycerol (DPPG)

4.11.2

σ 15.1 ± 1−2 mCm−2 5.3 ± 5 mCm−2 Δσ = −44.0 ± 9 mCm−2

Waxes

Waxes are esters of fatty acid, with long chain monohydric alcohol group. Natural waxes are mixtures of such esters and may also contain hydrocarbons. The formulae of three well-known waxes are given below, the under lined part being the carboxylic acid moiety. Compound Spermaceti Bees wax Carnauba wax

Formula CH3 (CH2 )14 COO − (CH2 )15 CH3 CH3 (CH2 )24 COO − (CH2 )29 CH3 CH3 (CH2 )30 COO − (CH2 )33 CH3

The leaves and fruits of many plants have waxy coatings which protect them from dehydration and small insects. The feathers of some birds and furs of some animals have similar coatings which serve as water repellents. Waxes are highly insoluble in water and have no double bonds in their chains.

4.12

Lipid Bi-layers

The lipid bi-layer is established as the basis for cell membrane structure. The bi-layer structure is attributable to the special properties of lipid molecules which cause them to assemble spontaneously into bi-layers. Lipid molecules constitute about 50% of the mass of most animal cell membranes, the remainder being protein. There are approximately 5 × 106 lipid molecules in a (one μm)2 i.e., 10−12 m2 area of a bi-layer. All of lipid molecules in cell membranes are amphiphilic (or amphipathic) i.e., they have hydrophilic or polar end and a hydrophobic or non-polar end. Cylinder shaped phospholipid molecules form bi-layers. Lipid molecules form any of the above structure in H2 O depending on their shape. In this energetically most favourable arrangement, the hydrophilic

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Biophysical Chemistry

Figure 4.2 Schematic depiction of lipid bilayers. heads face water and the hydrohobic tails are shielded from water inside. A small tear in a bi-layer creates a free wedge with water. This being energetically unfavourable, the lipids spontaneously rearrange to eliminate the wedge. In such a case, they form a sealed compartment by closing on themselves, which is fundamental to the creation of a living cell.

Figure 4.3 Energetically favourable structures of bilayers. Different spectroscopic techniques such as ESR, NMR have been used to measure the motion of individual lipid molecules. Lipid molecules

Figure 4.4 Structure of cholesterol in free state and fluid region.

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107

rapidly exchange places with their neighbours within a monolayer (107 times per second). This gives rise to lateral diffusion with a diffusion coefficient of 10−8 cm2 sec−1 which means that the average lipid molecule diffuses the length of a large bacterial cell (2μ m) in about one second. The lipid bi-layer of many cell membranes contains not only phospholipids but also often cholesterol and glycolipids. Eucaryotic plasma membranes contain large amounts of cholesterol i.e., upto one molecule of cholesterol for every phospholipid molecule. The lipid composition of two different cell plasma membranes is given below. Lipid PE PS PC Cholesterol

Liver cell plasma membrane 7 4 24 17

Red blood cell plasma membrane 18 7 17 23

In the above, PS carries a net negative charge while the others are electrically neutral at physiological pH carrying one +ve and one −ve charge.

Asymmetry of the Lipid Bi-layer The liquid compositions of the two-lipid bi-layer in many membranes are strikingly different.

4.13

Glycolipids on the Surface of all Membranes

The glycolipids with the most extreme asymmetry in the distribution of membranes are the sugar containing lipid molecules called glycolipids. They are found exclusively in the non-cytosolic monolayer of the lipid bi-layer. The glycolipids tend to self-associate partly through H-bonds between their sugars and partly through Van der Waals forces between their long saturated hydrocarbon chains. Glycolipids occur in all animal cell plasma membranes where they generally constitute about 5% of lipid molecules in the outer monolayer. They are also found in some intracellular membranes. In voltammetric studies, glassy carbon electrodes are modified by deposition of a hydrophobic coating of a lipid. For example, the lipid asolectin, which is negatively charged, modifies the glassy carbon electrode by selectively accumulating organic molecules depending on their charge and the hydrophobic-hydrophilic balance.

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Dipalmitoyl Phosphatidylcholine

Structure of dipalmitoyl phosphatidylcholine C40 H80 NO8 P; Mol. Weight = 734.05g/mol; CMC = 4.6 × 10−10 M 1, 2 diacyl phosphatidylcholine or 1, 2-diacyl-Sn-glycero-3-phosphocholine Formula-C42 H80 NO8 P

4.14

Interfacial Studies of Lipid Bilayers

The cyclic voltammetric and impedance analysis are especially powerful in this context since they can provide all the system parameters pertaining

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109

to electron and ion conduction. However, it is essential to choose systems which mimic the structure and components of lipid bilayers. As mentioned earlier, in view of the phosphate ions and lipid molecules together forming a bi-layered system, the nomenclature bilayer lipid membrane is invoked. Such bilayer lipid membranes are the scene of action for many important processes e.g., transport of species, charge transfer. The interior of membranes is non-polar and hence the transfer of hydrophilic substances is energetically un-favourable. However hydrophobic molecules (and ions such as tetra alkyl ammonium and tetraphenyl borate) can pass though the membrane, in a facile manner. Comprehending the mechanism of such transport is of paramount importance in so far as the extent of the drug delivery of the species is crucially dependent on energetic considerations. The electric-field assisted transport consists of (i) adsorption of the species and (ii) transfer across the interface. For each of these steps, the Gibbs free energies can be formulated and interpreted. The construction of suitable thermochemical cycles can be of immense help in estimating the overall Gibbs free energy changes involved. In view of the adsorption step (i) above, it is essential to compute the surface coverage of the lipids using appropriate adsorption isotherms such as Henry isotherm represented as θ = BCads Langmuir isotherm viz θ = BCads 1−θ Frumkin isotherm viz

θezaθ = BCads 1−θ

In the above equations, θ is the surface coverage while B denotes the adsorption equilibrium constant, Cads being the bulk concentration of the adsorbate. The parameter ‘a’ known as the Frumkin interaction constant is solely dependent upon the nearest neighbour interaction energies and its value if > 2 indicates the onset of phase transitions. It is well known that the Henry and Langmuir isotherms will be unable to predict the phase transitions since these do not incorporate interaction energies. For adsorption of phloretin onto the bilayer lipid membranes, the most suitable

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Biophysical Chemistry

adsorption isotherm remains un-settled. This limitation arises because of the inability to quantitatively incorporate dipole-dipole, non-electrostatic and van der Waals type interactions. Among several studies in this context, adsorption of phloretin on phosphatidylcholine (PC) and phosphatidylethanolamine (PE) deserves mention in view of the unusual dependence of the surface coverage of phloretin on the bulk concentration. Furthermore, adsorption also induces dipole potentials whose magnitude ranges from 100 to 300 millivolts. Analogously, the analysis of the step (ii) involving ion transfer across dissimilar interfaces is a non-trivial task. In this case, the most effective experimental strategy consists in constructing cyclic voltammograms. Here, the hydrophilic ions of BLM yield distinct voltammetric features, wherein the peak height is a quantitative measure of the amount of the ionic species while the peak potential is a qualitative measure of the nature of the species involved. On account of the difficulties involved in mimicking the structure and properties of natural membranes, it has been customary to model a simpler system such as water/organic solvent interface wherein the ionic species can be dissolved in the aqueous solvent, with the hydrophobic species being present in the organic phase. Hence the entire paraphernalia of charge transfer processes across liquid/liquid interfaces can be employed to unravel all the events of relevance pertaining to biological processes.

Questions (1) Which of the following is correct regarding palmitic acid? (a) saturated (b) unsaturated

(c) linear (d) branched

(2) Identify the correct statement regarding Linoleic acid and Linolenic acid. Both are (a) Essential fatty acids (b) Micelles

(c) Inorganic compounds (d) Cholesterol

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111

(3) Identify the following structure:

(a) phospholipid (b) glycolipid

(c) sphingolipid (d) glycerophospholipid

(4) For the oxidation of the fatty acid, palmitic acid, CH3 (CH2 )14 COOH give by CH3 (CH2 )14 COOH + 23O2  16CO2 (g) + 16H2 O(l) ΔG = −856 kJ mol−1 . Given that ΔG ◦f (CO2 ) and ΔG ◦f (H2 O, l) =

−394.4 kJ mol−1 and −237.2 kJ mol−1 respectively, what is ΔG ◦f of the acid? Solution:

−856 = ΔG ◦f (CO2 ) × 16 + ΔG ◦f (H2 O, l) × 16 × −237.2 − ΔG ◦f (palmitic acid) − 0 or ΔG ◦f (palmitic acid) = −394.4 × 16 + 16 × −237.2 + 856

= 16(−394.4 + (−237.2) + 856) ΔG ◦f (palmitic acid) = 16 × −631.6 + 856 = −10105.7 + 856

= −9249.6 kJ mol−1

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(5) Explain briefly, giving reasons, as to why the interfacial tension of phosphatidyl ethanolamine (PE = 3.34 × 10−3 Nm−1 ) is much higher than phosphatidyl choline. Solution: The head group in phosphatidyl ethanolamine is more polar than that in phosphatidyl choline. Further the lipid membrane of PE is also much more viscous than in phosphatidyl choline. These differences may be largely responsible for the difference in interfacial tension between the two lipids. (6) (a) Assuming phosphatidyl choline to be bronsted base, represent its dissociation equilibrium in aqueous solution. (b) Given its pKb =5.76, calculate the Gibbs energy change of the above reaction at 300K. Solution: ΔG ◦ = − RT ln Kb = −8.314 × 10−3 × 300 × 2.303 × log Kb

= +8.314 × 10−3 × 300 × 2.303 × 5.76 = 1421.7 kJ (7) For a spherical micelle aggregate, estimate the approximate radius if its volume is 100 cm3 , the area inside the aggregate being 0.1 cm2 . Solution: V = 100 cm3 ; q = 0.1 cm2 Rsphere = 3 V/a Rsphere = 3 × 100 cm3 /0.1 cm2 Rsphere = 3000 cm (8) A electrochemical cell containing a lipid bilayer membrane (BLM) was formulated as follows: SCE− (in gel)|BLM|Ag+ (1M)|Ag Its voltage was found to be 0.660 V. Given (ESCE = +0.22V) and (E Ag,Ag+ ( M) = +0.800V). What is the potential difference across thelipid dilayer. Solution: 0.660 = ER − EL + EBLM

= 0.800 − 0.220 + EBLM EBLM = 0.660 − 0.800 + 0.220

= 0.08V

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113

(9) Among the following, which possesses higher stacking characteristic?

(10) Fill up the blanks with suitable phrases: (a) 1,2-Diacyl-sn-Glycero-3-Phosphocholine is a ................................... (b) 1-Acyl-2-Acyl-sn-Glycero-3-Phosphocholine is an example of ................................... (c) Linoleic acid is an ................................... (11) Describe the intermolecular forces present in the lipid bilayer membranes. (12) Write the structure of a simple triglyceride. (13) Give a schematic diagram of a cell and indicate its components which serve to transfer information across the cell.

5

Amino Acids 5.1

Introduction

Amino acids are organic compounds containing an amino group(–NH2 ) and a carboxyl group(–COOH) along with a side chain (–R) specific to each amino acid. Among the many known naturally occurring amino acids about 20 are important because they occur are coded genetically. They can be classified according to the core (structural) functional groups locations such as α−, β−, γ−, δ–amino acids. The general formula of a naturally occurring amino acid may be represented as

Figure 5.1 Fischer projection and ball-stick model. Amino acids are soluble in water but are insoluble in non-polar organic solvents such as chloroform or ether. They have high melting points.

5.2

Classification of Amino Acids

One way of classifying amino acids is based on the polarity of the R-group. They may be classified into four groups.

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_5

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Biophysical Chemistry

Table 5.1 Classification of amino acids based on polarity. Group-I Group-II Group-III Group-IV Non-polar Polar but uncharged Acidic amino Basic amino amino acids amino acids acids acids

Group

Examples Alanine

Glycine Non-polar amino acids

Leucine

Valine

H

H

H

H

H2N „ C „ COOH

H2N „ C „ COOH

H2N „ C „ COOH

H2N „ C „ COOH

H

CH3

H „ C „ CH 3 CH3

CH2 1 H „ C „ CH CH3

Methionine

Creatine

NH H2N

O

CH3

It plays a crucial role in protein biosynthesis Group

Polar uncharged amino acids

OH

N

Examples Serine

Asparagine

Glutamine

H

H

H

H2N „ C „ COOH

H2N „ C „ COOH

H2N „ C „ COOH

CH2 OH

CH2

CH2 CH2

3

Amino Acids 

Group

Examples Tyrosine

Threonine

Polar uncharged amino acid

(Note: pKa of phenolic group in tyrosine is 10.1) Group

Examples Aspartic acid

Glutamic acid

Acidic amino acids

(Note: Ghutamate is an excitory neurotransmitter in the central nervous sytesm)

Group

Examples Lysine

Arginine

Histidine

Basic amino acids (The pKa i.e., acid dissociation constant of guanidinium group is 13.8 ± 0.1)

(It makes up the active sites of protein enzymes)

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118

5.3



Biophysical Chemistry

Chirality of Amino Acids

Except glycine, all other amino acids are chiral. They exist in optically active enantiomeric forms (D and L) that are mirror images of each other. It is interesting to note that the amino acids found in proteins are mostly of L-configuration. Enzymes responsible for protein synthesis utilise only L-configuration. D-amino acids are found in cell walls of bacteria and in several antibiotics.

5.4

Acid-base Properties

Amino acids are amphoteric molecules (because they contain both amino and carboxylic acid groups). For example, an aqueous solution of alanine is neutral and there is no migration of ions under the influence of an electric field. Thus, although it is a neutral molecule it is best represented as a zwitterion. H H3C

C

COO

NH3 (zwitterion of alanine)

In the potentiometric titration of an aqueous solution of alanine with NaOH, the pH vs. NaOH curve shows a typical curve with a pKa = 9.7 upon titrating with it is titrated with HCl, a curve with a pKa = 2.3 is obtained as shown below.

Figure 5.2 Potentiometric titration of aqueous alanine solution. at pH = 9.7: a group capable of furnishing protons is half neutralized. at pH = 2.3: a group of accepting protons is half neutralized.

Amino Acids 

119

The reactions occurring may be represented as:

It may be seen from the above scheme that alanine in acid solutions, migrates to the negative electrode (anodes) in an electric field and to the positive electrodes in alkaline solutions. Because of the zwitterionic nature, amino acids, dissolve easily in water. The Zwitterionic nature of amino acids is also proved by the reaction with formaldehyde.

The secondary and tertiary amines formed are weaker bases (or stronger acids). This is shown by the lowering of pKa of the amino group in presence of formaldehyde. The pH at which an amino acid behaves predominantly as neutral is known as isoelectric point (pI). The piso (pH at isoelectric point) may be approximated as half way between the two points of strongest buffering capacity and is given by pI =

1 1 (pK1 + pK2 ) = (2.3 + 9.7) = 6.0 2 2

Table 5.2 Isoelectric point of a few amino acids. Amino acid Glycine Alanine Valine Leucine Methionine Threonine Cysteine

pKa1 2.34 2.34 2.32 2.36 2.28 2.09 1.96

pKa2 9.60 9.69 9.62 9.60 9.21 9.10 8.18

pI 5.97 6.00 5.96 5.98 5.74 5.60 5.07

Amino acid Proline Phenylalanine Tryptophan Asparagine Glutamine Serine Tyrosine Aspartic acid Glutamic acid Lysine Arginine Histidine

pKa1 1.99 1.83 2.83 2.02 2.17 2.21 2.20 1.88 2.19 2.18 2.17 1.82

pKa2 10.60 9.13 9.39 8.80 9.13 9.15 9.11 9.60 9.67 8.95 9.04 9.17

pKa3 6.30 5.48 5.89 5.41 5.65 5.68 5.66 3.65 4.25 10.53 12.48 6.00

pKa1 = −ve log10 of 1st –COOH group, pI = pH at isoelectric point. pKa2 = −ve log10 of NH3+ group. pKa3 = −ve log10 of second –COOH group.

pI

2.77 3.22 9.74 10.76 7.59

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Biophysical Chemistry

In amino acids having more than one –COOH group or −NH2 group there are different pKa values for them. For example, the pKa of alphacarboxyl group of aspartic acid is 1.88 while the pKa of the second carboxyl group is 3.65 and that of −NH3 group is 9.60. The sulphydril group of cysteine dissociates with a pKa of 8.18 according to the reaction.

5.5

Reactions of Amino Acids

(a) Reactions of carboxyl group (i) The carboxyl group may be esterified with alcohols

(ii) Using PCl5 or POCl3 , the –COOH group may be converted to an acyl chloride

The acyl chloride formed is very reactive and can react with a second amino acid to form a peptide bond.

(iii) The carboxyl group of amino acids may be decarboxylated either chemically or biologically to yield the amine.

Amino Acids 

121

In all the above, for example, histamine is produced from histidine in this way. The biological significance of histamine is that it stimulates the flow of gastric juice in stomach. (b) Reactions of amino group (i) Oxidising agents like HNO2 react with amino acids liberating N2 . The reaction is stoichiometric and is used for the estimation of alpha-amino group in the amino acid.

(ii) Other milder oxidising agents like ninhydrin may be used to oxidise the amino group.

This reaction is characteristic of amino acids having alpha-amino group. The reaction can be used to quantitatively determine amino acids. (iii) Reaction with 1–fluoro –2, 4 dinitrobenzene

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Biophysical Chemistry

By this method, one can identify the terminal amino acid in a polypeptide chain. (c) Reaction with isothiocyanates: Isothiocyanates are used to degrade polypeptide chains and to identify the −NH2 terminal amino acid in the polypeptide chain. For example, the reaction of an amino acid with phenyl isothiocyanate is given by

5.6

Biochemical Importance of Amino Acids

Our body needs twenty different amino acids to maintain good health. Among them, people have to obtain nine essential amino acids through foods such as eggs, tofu, soyabean, meat, quinoa and dairy products. The body itself makes the remaining eleven amino acids. Amino acids perform diverse functions in the body such as: (i) build muscles, (ii) cause chemical reactions in the body, (iii) transport nutrients, (iv) prevent illness. Deficiency of amino acids results in decreased immunity, digestive problems, low mental alertness, depression etc. Each amino acid has a different role in the body. They are enumerated below: (i) Lysine: It plays important role in building muscle, maintain bone strength, fast recovery from injury or surgery, regulates hormones and enzymes. This amino acid is present in meat, eggs, soyabean, black beans, quinoa and pumpkin seeds. (ii) Histidine: It promotes growth, creation of blood cells and tissue repair. Our body metabolises histidine into histamine, which is very important for immunity build up, digestion and reproductive health. Its deficiency can cause anaemia and low blood levels in the body and kidney disease. Meat, fish, nuts, seeds and whole grains are good sources of histidine.

Amino Acids 

123

(iii) Threonine: It is necessary for healthy skin and teeth. It helps in metabolising fat and digestion. It helps in controlling depression. Cottage cheese and wheat germ are good sources of threonine. (iv) Methionine and cysteine: They play a role in the health of skin and hair. They also aid in the proper absorption of selenium and zinc. This amino acid i.e., methionine is present in eggs, grains, nuts and seeds. (v) Valine: It is essential for muscle co-ordination, mental focus and emotional stability. It is present in soyabeans, cheese, peanuts, mushroom, vegetables and whole grains. (vi) Leucine: It helps regulate blood sugar levels and aids growth and repair of muscle and bone. It is also necessary for wound healing. Its deficiency leads to skin rashes, hair loss and fatigue. Dairy, soybeans, legumes, beans are good sources of this compound. (vii) Isoleucine: It is useful in faster wound healing, immunity, blood sugar regulation and production of hormones. It is present in muscle tissue. Meat, fish, poultry, eggs, cheese, lentils are plentiful in this amino acid. (viii) Phenylalanine: It is important in the body for effective use of proteins and enzymes. It is converted in the body to tyrosine, which is necessary for specific brain functions. Its deficiency causes eczema, fatigue and memory loss in adults. It is used in the artificial sweetener, Aspartame. People with the genetic disorder, phenyl ketonuria are unable to metabolise this amino acid. It is present in dairy, meat, fish, soyabeans and beans. (ix) Tryptophan: Infants need it for good growth. It is a precursor of seritonin and melatonin. The former is a neurotransmitter, regulates appetite and pain. Melatonin is a sleep aid and hence used as a sedative. It improves mental energy and emotional well being in women. Deficiency of this amino acid causes a condition known as pellagra, which can lead to dementia. It also causes skin rashes and digestive problems. It is present in most high-energy foods such as cottage cheese and wheat germ.

Foods with Essential Amino Acids Meat, eggs, tofu, dairy products contain all essential amino acids. However, people who eat vegetarian or vegan diets can also get their essential amino acids from plant foods such as rice and beans.

124

5.7



Biophysical Chemistry

Electrochemical Studies of Amino Acids

The conversion of amino acids into peptides has been studied extensively for the past few decades, on account of its importance in evolution of life. The diversity in the products arising from the anodic oxidation, can be ascribed to the nature of amino acids, the molar concentrations and pH dependence. The products may vary from aldehyde and ammonia to carbon dioxide. In contrast to conventional homogeneous chemical oxidations, electrochemical oxidations are versatile and the product formation can be controlled by (i) nature of electrodes; (ii) choice of electrolytes and solvents; (iii) potential window; (iv) bulk concentration; (v) choice of experimental technique and (vi) electrode geometry. Among various amino acids for which the complete equilibrium and kinetic data are available, the following deserve mention: alanine, glycine, guanine, L-arginine, L-lysine, asparagine, etc. The electrode potentials are often be expressed either using half wave potentials or formal potentials. The half wave potentials are approximately equal to the standard electrode potentials since the diffusion coefficients of oxidised and reduced species are nearly the same. However, the formal potentials and standard potentials are substantially different due to the effect of pH and activity coefficients. Thus, it is customary to report the formal potentials of compounds having biological significance. The mechanistic elucidation for comprehending such studies requires not only elaborate experimental techniques but also density functional theories of diverse genre. The theoretical calculations are required in order to rationalise the experimentally observed products. The oxidations can be studied using noble metals, carbon paste and glassy carbon electrodes. In addition, various nanoparticles or polymer-coated electrodes can be employed. It is of interest to note that for oxidation studies, carbon-based electrodes are preferable since metals lead to oxide formation in the same potential range in which amino acids undergo oxidation. In cyclic voltammetric studies, the absence of electron transfer peak is an indication of adsorption of amino acids (with or without polymerization). A collateral advantage consists in selective and sensitive detection of amino acids using different steady state and transient electrochemical experiments. The differential pulse voltammetry and amperometry provide an estimate of sensitivity, linear calibration range and lowest detection limits pertaining to different biosensors. These aspects have been briefly discussed in Chapter 12.

Amino Acids 

125

Glycine being the simples amino acid, its behaviour at electrode surfaces has been extensively investigated. On noble metals, the oxidation products include CO, CN− and [O=C=N]− ions. The identification of products can not solely be identified from electrochemical studies; instead several in situ spectroscopic techniques become essential. The adsorption of amino acids such a tryptophan on surfaces may also form self-assembly which can then be exploited for several applications. An important aspect in this context is the enantiomeric separation of amino acids which can be accomplished by chiral electrodes.

Questions (1) Which of the following is the aprotic and aliphatic amino acid? (a) tryptophan (c) Lysine (b) alanine (d) cysteine (2) Which of the following is a neutral pH amino acid (a) Glutamate (c) Methionine (b) Arginine (d) Valine (3) Proline is known as (a) α-helix terminator (b) α-helix initiator

(c) α-helix responder (d) α-helix sensor

(4) Methionine is a (a) Sulphur-containing amino acid (b) Nitrogen-containing amino acid (c) Imino acid (d) Polypeptide (5) Arginine is (a) Positively charged (b) Negatively charged

(c) Neutral (d) Non-polarisable

(6) Aromatic amino acids with aromatic nature can be identified at a wave length of (a) 320 nm (c) 280 nm (b) 440 nm (d) 380 nm

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Biophysical Chemistry

(7) An amino acid which is both glucogenic and ketogenic are (a) Lysine (c) Homocystine (b) Isoleucine (d) Cysteine (8) Amino acid involved in carbon skeleton catabolism releases (a) Acetoacetyl CoA (c) Acetoacetyl CoB (b) Acetone (d) Acetic acid (9) Glycine and proline are the most abundant amino acids in (a) Hemoglobin (c) Insulin (b) Myoglobin (d) Collagen (10) Lysine has one carboxylic and two amino groups whose dissociation constants are 6.61 × 10−3 , 1.12 × 10−9 , 2.95 × 10−11 (the latter two are for NH3+ group). The PI value of the molecule is (a) 5.56 (b) 6.35

(c) 9.74 (d) 7.42

(11) The PI values of valine (I), cysteine (II) and histidine (III) are 5.96, 5.07 and 7.59 respectively. The increasing order of their migration in an electrophoresis experiment towards cathode at pH = 7.0 is (a) I < II < III (b) III < I < II

(c) II < II < III (d) I < III < II

(12) Given Ka(1) and Ka(2) of cysteine as 1.1 × 10−2 and 6.61 × 10−9 , calculate its isoelectric point. Solution: pKa = 1.96, pKb = 8.18 Isoelectric point =

pKa + pKb 1.96 + 8.18 10.14 = = = 5.07 2 2 2

(13) Calculate the pH of a 0.05 M solution of glycine given its pKa (of – COOH group) is 2.34 at 298K. (14) A solution of 25 ml of 0.1 M alanine is titrated with 25 ml of 0.1 M NaOH. The potentiometric titration yields a curve with pKa = 9.7 when 12.5 ml of NaOH are added. When the same solution is titrated with 0.1 M HCl the curve with pKa = 2.3 was deduced. Draw the potentiometric curve obtained in the two cases as a pH vs. volume of acid and volume of base. What are the reactions in the two cases?

Amino Acids 

127

pKa = 9.7

pH pKa = 2.3 12.5 0

0.1 M HCl

CH3  CH  COOH

H+

0.1 M NaOH

CH3  CH  COOH



NH3

12.5

OH

NH2 CH3  CH  COO  H2O NH2

(15) Classify the following amino acids into various categories: Arginine, Glutamine, Threonine, Valine and Creatine. Answer: Arginine: Basic amino acid Glutamine: Polar uncharged amino acid Threonine: Polar uncharged amino acid Valine: Non-polar amino acid Creatine: Non-polar amino acid (16) Draw the structure of the tetrapeptide valine-glycine-serine-alanine in neutral solution.

6

Peptides 6.1

Introduction

Peptides are short chains of amino acids linked by peptide (or amide) bonds. They are classified as di, tri, tetra and poly peptides. A polypeptide is a long, continuous, unbranched peptide chain. Peptides are different from proteins on the basis of their size and they contain upto 50 amino acids in their chain. Amino acids that are incorporated into peptides are termed as “residues”. All peptides except cyclic peptides have a N-terminal (amino group) and a C-terminal (Carboxyl group) residue at the end of the peptide. Example:

Figure 6.1 Structure of tetrapeptide containing Val-gly-Serine-Ala with LValine being at left end and L-Alanine at the right end.

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_6

129

130



6.2

Biophysical Chemistry

Classes of Peptides

Peptides are classified on the basis of their source and function. Some groups of peptides include plant, bacterial, fungal, invertebrate, venom, cancer/anticancer, vaccine, endocrine, ingestive and gastrointestinal, cardiovascular, renal, respiratory, opiatic, blood-brain peptides. Some organisms produce peptides as antibiotics. Peptides undergo reactions such as phosphorylation, hydroxylation, sulfonation, glycosylation and disulfide formation. Non-ribosomal peptides (NRP’s) are a kind of peptide secondary metabolites which are synthesized by multidomain mega enzymes named non-ribosomal peptide synthetases f (NRP’s) without the need for the cell ribosomal machinery and messenger RNA’s. They are naturally synthesized by microorganisms such as bacteria and fungi. An example is glutathione, which is a component of anti-oxidant defenses of many aerobic organisms, plants and fungi.

6.2.1

Different Classes of Peptides Classification of peptides

Antimicro bial peptides (Example: Magainin family)

Tachykinin Vaso Pancreatic Opioid family’ active peptides and (such as intestinal related such as neuropeptides prodypeptides kinin A) (such as VIP (such as norphin peptide PHI27 NPY, PPY) peptides Secretin)

Self assembled peptides, such as amphiphilic biomimetic peptide

The abbreviations are explained as follows: VIP = Vasoactive intestinal peptide; PHI = Peptide histidine isoleucine 27; NPY = Neuropeptide Y; PPY = Pancreatic polypeptide. Other peptides include lactotripeptides, natriuretic peptide, Lactotripeptides are two naturally occurring milk peptides; IsoleucineProline-Proline (IPP) and Valine-Proline-Proline (VPP). They are derived from casein, which is a milk protein found in dairy products.

6.2.2

Natriuretic Peptides (NP’s)

There are four different groups of NP’s identified as: (i) atrial natriuretic peptide (ANP), (ii) B-type natriuretic peptide (BNP), (iii) C-type natriuretic

Peptides 

131

peptide (CNP) and a D-type natriuretic peptide (DNP) each with its own characteristic functions. They are hormones which are mainly secreted from heart. A polypeptide is a single linear chain of many amino acids held together by amide bonds. An oligopeptide consists of two to forty amino acids. Oligopeptides are classified according to molecular structure as aeruginosins cyanopeptolins, microcystins, microviridins, microginins, anabaenopeptins, and cyclamides.

6.3

Functions of Peptides

The function that a peptide carries out depends on the types of amino acids involved in the chain and their sequence as well as the specific shape of the peptide. Peptides often act as hormones and thus constitute biological messengers carrying information from one tissue to another through blood. There are two classes of hormones known as peptide hormones and steroid hormones. The former are produced in glands and other tissues such as stomach, intestines, and brain. Examples of peptide hormones are those involved in blood regulation, including insulin, Glucose like Peptide1 (GLP-1) and those regulating appetite including Ghretin. Ghretin is produced and released by the small intestine and by stomach, pancreas and brain. Peptides are found in every cell of human body and perform a wide range of functions mentioned above. Maintenance of appropriate concentration levels of peptides is necessary to achieve homeostasis and maintain health. A few common natural peptides are given in Table 6.1.

6.4

Acid-Base Properties of Peptides

All peptides have, at least, two ionisable groups, the carboxyl group of Cterminal residue and the amino group of N-terminal group. Further, there may be ionisable groups inside chains of some amino acids forming part of the peptide. It is important to predict the charge carried by a peptide since this helps to know how it travels during an electrophoresis experiment. The charge on a peptide depends on pH due the acid groups present in amino acid part.

Hypothalamic neurohormone. It is involved in the regulation of the hypothalamic pituitary thyroid axis

Biophysical Chemistry

TRH(3) peptide i.e., Thyrotropin releasing hormone (tripeptide) (C16 H22 N6 O4 )



Table 6.1 Residues, their sources and amino acid sequences. Source or function Amino acid sequence Living cells, they stimulate tissue NH3 CH(COO− )CH2 CH2 CONHCH growth (CH2 SH)CONHCH2 COOH

132

Name and residues Glutathione (3)

Name and residues Glucagon: It is 29 amino acid peptide hormone secreted from the alpha cells of the pancreas Insulin

Source or function It is generated from the cleavage of proglucon by protein convertase 2 in pancreatic islet α cells

Amino acid sequence Its structure in humans is NH2 -His-Ser-Gln-Gly-Thr-PheThr-Ser-Asp-Tyr-Ser-Lys-Tyr-Leu-Asp-Ser-Arg-Arg-AlaGln-Asp-Phe-Val-Gln-Trp-Leu-Met-Asn-Thr-COOH. It has molar mass of 3485 daltons.

It helps control blood glucose levels by signalling the liver and muscle and fat cells to take in glucose from the blood. Thus, it helps cells to take in glucose to be used for energy. It is a pancreatic hormone.

It is composed of two peptide chains referred as A chain and B chain. These chains are linked together by two disulfide bonds, and an additional disulfide is formed within the A chain. In most species, the A chain consists of 21 amino acids and the B chain of 30 amino acids. The structure is given below.

Peptides  133

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Biophysical Chemistry

To find the overall charge on a peptide, one has to identify—(i) all ionisable groups, (ii) charge on each group at a given pH. Let us consider, for example, the compound (Val-Ile-Leu-Met). O

O

O

H2N  CH  C  NH  CH  C  NH  CH  C  OH CHCH3

CH2

CH2

CH3

CH

CH2

H3C

CH3

S CH3

The ionisable groups in the above compound are the −NH2 group (pKa of NH3 groups 9.0) and the carboxyl group (pKa = 3.0) at each end of the compound. The net charge on the peptide at three different pH’s is distributed as follows: pH

Charge on functional group C-terminus N-terminus Overall charge

2.0 7.0 12.0

0 −1 −1

+1 0

+1 0 −1

Table 6.2 Critical Aggregation Concentration (CAC) of a few peptides and their diffusion coefficients. Name of the compound EAK 16-II Alzheimer’s beta amyloid oligo peptide Human Serum albumin Bovine Serum albumin

CAC gram liter−1 0.1

moles liter−1 6.035 × 10−5 2.5 × 10−5

0.05

7 × 10−7

0.05

7 × 10−7

Diffusion coefficient (m2 sec−1 )

D.C. of A Beta 42 = 1.35 × 10−10 CAC of Ab 42 = 9.2 × 10−8 M

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135

Among the many peptides, EAM16-II (molar mass = 1656.8 g) is an important 16-residues peptide (Ala-Glu-Ala-Glu-Ala-Cys-Ala-Cys)2 . It has a characteristic β-sheet circular dichroism spectrum in water. Upon addition of salts, the peptide spontaneously assembles to from a macroscopic membrane. The critical aggregation constants and diffusion coefficients of EAK-II and a few other peptides are given in Table 6.2. Based on the amino acid sequence of bovine serum albumin, its molar mass is 66430.3 daltons which is equivalent of 66430.3g mol−1 . Albumin found in human blood. It is the most abundant protein in human blood plasma. It has a molar mass of 66.5 k Da i.e., 66500 daltons or 66,500 a.m.u Name of compound λTAPP (human islet amyloid polypeptide) a 37 amino acid peptide hormone. Its structure is: Lys, Cys, Asn, Thr, Ala, Thr, Cys, Ala, Tur, Gln, Arg, Leu, Ala, Asn, Phe, Leu, Val, His, Ser, Ser, Abn, Asn, Phe, Gly, Als, Ile, Leu, Ser, Ser, Thr, Asn, Val, Gly, Ser, Asn, Thr, Thr

6.4.1

CMC 3.25 × 10−6 (by conductance and fluorescence measurements)

ΔG associated with the incorporation of protein into membrane is determined by the hydrophobic effect and is about −63 kJ mol−1

Expansion of Symbols

Lys = lysine (K), Cys = Cysteine (C), Asn = Asparagine (N), Thr = Threonine (T), Ala = Alanine (A), Gln = Glutamine (a), Arg = Arginine (R), Leu = Leucine (L), Phe = Phenylalanine (F), Val = Valine (V), His = Histidine (H), Ser = Serine (S), Gly = Glycine (G), Ala = Alanine (A), Ile = Isoleucine (I). The single letters in brackets are one letter abbreviations. It is secreted by beta cells and functions to control hyperglycemia.

6.5

Peptides as Biosensors

Peptides also find applications as biosensors upon immobilisation of certain amide sequences on electrode surfaces, such as Au, Ag etc.

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Biophysical Chemistry

Structure of the ionic complimentary peptide EAK 16-II. It contains alternating hydrophobic (alanine, A) and hydrophilic (glutamic acid, E and lysine, K) residues producing amphiphilic structure that is hydrophobic on one side and hydrophilic on the other. The charged residues are arranged as type-II − − + + − − ++, where pairs of −vely (E) and +vely charge (K) residues alternate. Formula of EAK 16-II: C70 H121 N21 O25 . Mol.Wt = 1657 g.

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137

Structure of MA-1

Structure of TA-1

Using voltammetric studies, the time-dependent variation of the peak current for various compositions of TA-1 and MA-1 was studied and the results are shown in Table 6.3. The TA-1 probe was taken in a buffer of pH = 7.4 and then Trypsin was added.

6.6

Current-Voltage Characteristics of Peptide Films

Using cyclic voltammetric studies, the current-potential response of F-mocLL and F-moc-YL was studied. The increase in current with potential was observed (see Table 6.3). The specific conductances of the peptide are also shown in Table 6.5.

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Biophysical Chemistry

Table 6.3 Variation of the MB peak current with time. Time (min) % change in signal using TA-1 MA-1 0.0 0.0 0.0 10.0 −12.0 −30.0 20.0 −28.0 −43.0 30.0 −38.0 −48.0 40.0 −46.0 −50.0 58.0 −50.0 −52.0 78.0 −53.0 −54.0 96.0 −60.0 −58.0 Table 6.4 Rate constant data for the effective cleavage rate of MB in the peptides TA-1 and MA-1. Compound Rate constant (min−1 ) TA-1 7.7 × 10−2 MA-1 3.8 × 10−2 Table 6.5 Current potential response of peptides from cyclic voltammetry at a scan rate of 500 mv sec−1 at 25◦ C.

Peptide F-moc-LL

F-moc-YL

Potential (V) −2.0 −1.0 +0.5 +1.0 +2.0 −2.0 −1.0 −0.5 +1.0 +2.0

Current (μA) −0.25 −0.10 0.00 0.00 0.10 −0.75 −0.50 −0.30 +0.10 +0.45

Electrode length/space (in mm)

Specific conductance (mho cm−1 )

12/3

4.2 × 10−5

12/3

2.2 × 10−4

F-moc-LL: N-(fluorenyl - 9 methoxy carbonyl)-leucine-leucine F-moc-YL: N-(fluorenyl - 9 methoxy carbonyl)-tyrosine-leucine-leucine

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139

It is well known that peptides possess the ability to form self-assembled monolayers on suitable electrode surfaces. These self-assembled monolayers (SAMs) are the vital source of information for the functional behaviour of peptides. Furthermore, it is possible to tailor-make peptide sequences of desired characteristics. In this context, Au electrodes modified using peptides with sulphide moiety offer the most desirable surfaces. The investigations pertaining to the structure and dynamics of SAMs on surfaces have several facets viz. (i) applicability as sensors; (ii) directional charge transport; (iii) opto-electronic devices and (iv) biomedical applications. (i) In the case of electrochemical biosensors, various types of peptides serve as bio recognition elements for detection of antibodies and proteins. A pre-requisite for employing these peptide-based biosensors is the correct choice of peptide sequences that possess unique ability of excellent affinity and satisfactory selectivity towards the target (analyte) protein. Since the peptides themselves are electro-inactive, modified electrodes of diverse types (SAMs, carbon nanotubes, graphene, conducting polymers etc.) have been employed. (ii) A particularly innovative approach consists in employing negatively (e.g., glutamic acid) and positively charged amino acids (e.g., histidene) on Au. This arrangement upon suitable anchoring is shown to yield secondary structures-amenable for fundamental and medicinal applications. In the case of directional charge transport, the system donor-peptide-acceptor is chosen wherein the electron transfer mechanism designated as ‘super exchange’ operates. The corresponding operator is known as ‘super exchange operator’. An alternate mechanism of electron transfer deduced using current-potential response of molecular junctions is electron hopping which occurs in the selfassembly of cyclic peptide nanotubes. In the electron hopping mechanism, the mobility is significantly higher than the conventional electron transfer processes. (iii) In order to function as opto-electronic devices, electron or photon responses of the system are essential. In view of the self-assembly properties as well as chemical and electrochemical activity of the peptides, these constitute potential opto-electronic devices. Under suitable conditions, the peptides can serve as spacers between the donor and acceptor moieties. Due to the availability of diverse peptide functional groups viz oligothiophene, oligopyrrole, oligoaniline etc., these systems function as light emitting diodes, electrochromic device, solar cells etc.

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Biophysical Chemistry

(iv) Peptides function as biorecognition elements in diverse amperometric and voltammetric biosensors on account of their selectivity and satisfactory adhesion to electrodes. Among several analytes employed in this context, mention may be made of proteins, nucleic acids, antibodies. The most commonly employed electrochemical technique in this context is differential pulse voltammetry, in view of its sensitivity and low detection limits.

Questions (1) Which of the following is true regarding the nature of the peptide bonds? (a) Covalent (c) Metallic (b) Ionic (d) Three centre-two electron (2) Which of the following is true regarding complete proteins? They are (a) conjugated (c) saturated (b) unconjugated (d) unsaturated (3) When a protein denatures, it undergoes (a) folding (c) oxidation (b) un-folding (d) reduction (4) For a peptide given by the sequence Glu-Cys-Asn-Met-Lys Met-GluThr-Arg-Trp Ile-Tyr, the reagent for specific cleavage is (a) Trypsin (b) Chymotrypsin

(c) Pepsin (d) Renin

(5) Myoglobin has a (a) Primary structure (b) Secondary structure

(c) Tertiary structure (d) Quaternary structure

(6) Cysteine has (a) Azo bond (b) Disulphide bond

(c) Thiol bond (d) Hydrogen bond

(7) The rate constant for the cleavage of methylene blue in the peptide TA-1 is 7.7 × 10−2 min−1 . Calculate the time required for 90 percent cleavage of the same. (8) Draw the structure of a tetrapeptide and indicate the end groups in it.

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141

(9) Give the chain of amino acids linked in EAK 16-II. What are the special features of the peptide. (10) Calculate the percent aggregation of EAK 16-II after 1200 sec given its aggregation rate constant is 1.14 × 10−4 min−1 . (11) With illustrative examples, explain the application of peptides as biosensors.

7

Proteins 7.1

Introduction

Proteins are essentially linear polymers built of monomer units of amino acids. The function of a protein is dependent on its three-dimensional structure. Proteins fold up spontaneously into three dimensional structures that are determined by the sequence of amino acids in its chain. They are versatile macro molecules in living systems and have crucial functions in all biological processes. They act as catalysts, transport and store molecules like O2 and provide immune protection.

7.2

Composition of Proteins

Proteins are built from around twenty amino acids. The amino acids are linked by peptide bonds to poly peptide chains in a primary structure and subsequently these chains fold into other structures like α-helix, beta sheets and loops. Proteins contain a wide range of functional groups and they may be alcohols, thiols, carboxylic acids and also a variety of basic groups. This array of functional groups, when combined in various sequences accounts for a broad spectrum of protein function. The chemical reactivity associated with these groups is essential to the function of enzymes.

7.3

Some Characteristics of Proteins

Proteins can interact with one another and with other biological macromolecules to form complex assemblies. Proteins within these assemblies

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_7

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Fibrous proteins (i) They are linear (long fibrous) in shape

Globular proteins (i) They are spherical in shape and are tightly folded into this shape.

(ii) For this class of proteins, secondary structure is a most important functional structure. (iii) They are tough and strong.

(ii) Tertiary structure is very important in them.

(iv) They are insoluble in water. (v) They form long fibres or sheaths. (vi) Examples: Insulin, Haemoglobin, DNA, and RNA polymerase.

(iii) They are softer than fibrous proteins. (iv) They are soluble in water. (v) They form antibodies, enzymes and hormones. (vi) Examples: Collagen, myosin, silk, keratin.

Intermediate proteins (i) Their structures intermediate between linear and globular proteins. (ii) They are short and linear shaped.

(iii) They are soluble in water. (iv) They are blood clotting proteins. (v) Examples: Fibrinogen.

Biophysical Chemistry

Table 7.1 Classification of proteins based on structure.

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can act (in synergy) to generate capabilities not afforded by individual components. For example, human insulin is a protein hormone crucial for maintaining blood sugar levels at proper levels. Its structure with chains of amino acids is a specific sequence defines its function. The protein lactoferrin undergoes conformational changes on binding with iron that allow other molecules to distinguish between iron free and iron bound forms.

7.4

Classification of Proteins

Proteins are classified on the basis of the following three criteria: (i) based on the structure of proteins, (ii) based on composition of the proteins and (iii) based on functions of the protein.

Classification Based on Composition (a) Simple proteins composed only of amino acids: They possess relatively simple structure. They may be fibrous or globular. Example: Collagen, Myosin, Insulin, Keratin. (b) Conjugated proteins: They are complex. They contain some nonamino acid components. The protein part is tightly or loosely bound to one or more non-protein parts which are called prosthetic groups. The prosthetic groups may be metal ions, carbohydrates, lipids, phosphoric acids, nucleic acids. These groups are essential for the biological function of the proteins. Conjugated proteins are globular in shape and are water soluble. Most enzymes belong to this class. Based on the nature of prosthetic groups, conjugated proteins are further classified as follows: – Phosphoprotein: In this case, the prosthetic group is phosphoric acid. – Chromoproteins: In this case, the prosthetic group is pigment or chrome. Example: Hemoglobin, Phytochrome, Cytochrome. – Lipoproteins: Prosthetic group is lipids. Example: Membrane proteins. – Flavoproteins: Prosthetic group is FAD (i.e., Flavin adenine dinucleotide). Example: Proteins of electron transport system. – Metalloproteins: Prosthetic group is metal ions. Example: Nitrate reductase.

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Classification Based on Functions (a) Structural proteins: Most of these proteins are fibrous proteins insoluble in water. Example: Collagen, Keratin, Elastin. Collagen and Elastin are found in connective tissues such as tendons and ligaments. Keratin is found in hair, feathers and beaks. Collagen is recognized as the most abundant protein in mammals. It has a triple helix structure and is not α-helix. It contains specific amino acids: glycine, proline, hydroxyl proline and arginine. (b) Enzymes: They are biological catalysts. They speed up reactions by reducing the activation energy of reactions. Many of them are globular conjugated proteins. Example: DNA polymerase, Lipase, Nitrogenase. (c) Hormones: These include proteinaceous hormones in cells. Example: Insulin, Glucagon, ACH. (d) Respiratory pigments: They are coloured and are conjugated proteins containing pigments as prosthetic groups. Example: Haemoglobin, Myoglobin. (e) Transport proteins: They transport material in cells, form channels in plasma membranes. They form one of the components of blood and lymph in animals. Example: Serum albumin. (f) Contractile proteins: They are force generators in muscles. They can contract with expense of energy from ATP molecules. Example: Actin, Myosin. (g) Storage proteins: They store metal ions and amino acids in cells. They are found in seeds, egg, milk and pulses (legume seeds). Example: Ferritin which stores iron, casein, ovalbumin, gluten of wheat. (h) Toxins: They are toxic proteins. Example: Snake venom.

7.5

Nature of Bonds in Protein Structure

The polypeptide bonds present in proteins fold into specific structures so as to get a proper conformation. Many types of bonds support and stabilize the specific shapes and conformations. Important types of bonds that contribute to the conformation are peptide bonds, ionic bonds disulphide bonds, H-bonds and bydrophobic interactions. The various bonds are discussed below.

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(1) Peptide bond: It is a covalent bond formed between the amino group of one amino acid and carboxyl group of another amino acid. The bond has high dissociation energy and is also planar since the electrons are delocalised to give double bond character to the C–N bond.

(a) During protein synthesis, this bond is formed. (b) The resulting compound after the

formation is a di-peptide. (c) Several amino acids combine to form polypeptides having many peptide bonds

(d) Peptide bond formation is favoured by the enzyme peptidyl transferase. Two amino acids react according to

(2) Ionic bonds: The ionic bonds are formed between the ionized acidic ¯ (−COO− ) or ionised basic O

⎛ + ⎞ ⎜ − N H3 − ⎟ ⎝ ⎠ groups of amino acids. The R-groups of some amino acids, may contain additional



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The ionic bonds may break down by a change of pH. Example: Denaturation of protein. Tertiary or quaternary structures of proteins are stabilized by ionic bonds. (3) Disulphide bonds: This bond is covalent and hence quite strong. The covalent bond formed between two thiol groups of two cysteine residing in a protein is an example. Disulphide bonds stabilize the tertiary structure of protein.

(4) H-bonds: It is formed by electrostatic attractions between a H atom which is covalently linked to atoms such as O or N. Example: H : O : H. The H atoms carry a partial +ve charge due to attraction of highly electro negative oxygen atom. The same is true with nitrogen. Example: NH3 . The H-bonds give regular shape to the dipeptide chain such as α-helix. H-bond is not very strong. These bonds stabilize the secondary and tertiary structure of proteins. (5) Hydrophobic interactions: The non-polar R-groups in some amino acids are hydrophobic and they repel water. Example: alanine, valine, leucine, methionine. In an aqueous environment (inside a cell) the linear polypeptide chain will fold in such a way that the hydrophobic groups come together and exclude water due to hydrophobicity. The hydrophilic groups form a shell over the hydrophobic moieties and point towards water in the interior of the cell.

7.6

Structure of Proteins

Research on protein structure resulted in the conclusion that a specific configuration, the right handed a α-helix, is favourable for its stability. The α-helixes are stabilised due to H-bonding between an −NH group in the helix and the C=O group of the form the amino acid down the chain. The α-helix, a common structural motif of proteins consists of a right handed helix with a repeat length of 3.6 amino acid residues per helical turn. The α-helix is stabilised by H-bonds between an amide hydrogen of one amino acid and a carbonyl hydrogen four amino acids away. The side chains of the amino acids, R, protrude from the surface of the helix core, allowing interaction of these functional groups with other proteins

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Figure 7.1 Structure of α-helix. structural motifs or with H-bonding sites in the major or minor grooves of the DNA. The amino acids, glycine, proline, serine, glutamine, threonine and asparagines are α-helix breakers because they have Nα atom in a rigid ring structure.

7.7

Role of Amino Acids in Proteins

(1) Cysteine: It can cross link with another cysteine sulfhydril group in the same or on different polypeptide chains by oxidation to a covalent disulphide bond. The structure of insulin is a good example of the importance of disulphide bonds. Thioether bridges occur in cytochrome C between the iron protoporphyrin groups and two cysteine residues of the protein. (2) Histidine: The lone pair of electrons in the ring nitrogen may serve as a potential ligand as in the iron containing proteins in haemoglobin and cytochrome C. (3) Lysine: It is involved in binding pyridoxal phosphate, lipoic acid and biotin. Like in serine and histidine, it may serve in making up the active site of an enzyme like muscle aldolase.

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(4) Serine: It serves as a nucleophile in a number of proteolytic enzymes. Along with histidine residue, a specific serine residue serves as a component of the active site of chymotrypsin. It may be mentioned that chymotrypsin is a digestive enzyme which breaks down proteins in the small intestine (it is secreted by pancreas and converted into an active form by trypsin). Serine residues also serve as active sites of phosphoryl groups which modify the activity of a number of enzymes. (5) Proline: It forces a bend in polypeptide chain and disrupts α-helicity due to its rigid rang. Polar amino acids such as glutamic acid, aspartic acid, arginine, lysine are ionised over a wide pH range and can form ionic bonds in protein structure. Protein, being a complicated macro molecule, is defined in terms of four basic structural levels. (a) Primary structure: It is a linear sequence of amino acid residues making up its polypeptide chain. (b) Secondary structure: It refers to the structure of a polypeptide or a protein may possess from H-bond inter actions between amino acid residues which are fairly close to one another in primary structure. (c) Tertiary structure: This structure refers to the tendency of the polypeptide chain to undergo extensive coiling or folding to produce a complex rigid structure. Folding occurs between amino acid residues relatively far apart in the sequence. (d) Quaternary structure: This defines the structure resulting from interactions between separate polypeptide units of a protein containing more than one sub unit. Thus the enzyme phosphorylase “a” contains two identical sub units that alone are catalytically inactive but when joined as a dimer form the active enzyme.

Figure 7.2 Quaternary structure of a complex globular protein (dimer).

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151

Examples of Proteins

(1) Blood proteins: About 60 proteins have been identified and characterized in blood plasma. They are divided into carbohydrate free proteins and glycoproteins. Among the predominant carbohydrate free proteins is albumin which constitutes 50% of total serum protein. It serves as a carrier protein because of high concentrations of fatty acids and anions in it. Serum albumin controls the osmotic pressure of blood as well as maintaining the buffering capacity of blood pH. It is a globular protein with a molar mass of 69,000. (2) Glyco proteins: They occur widely in nature. In these proteins, a covalent link exists between carbohydrate polymer and N-or acylglyconyl linkage. They are classified into three categories based on carbohydrate composition, linkage of carbohydrate to protein. (i) Plasma glycoproteins: They are found in blood sera.

After NH-C and vertical double bonded O. (ii) Mucin glycoprotein protein

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(iii) Mucopolysaccharide

7.9

Hemoglobin

It is a respiratory protein in all vertebrates and is localized in erythrocytes. It reacts reversibly with O2 and transports O2 from lungs to all parts of body. It is a conjugated heterogeneous tetrameric protein composed of different subunits (α and β). Each monomeric unit (Molar mass = 16,000) contains a heme group linked to protein via the imidazole nitrogen of the histidine residues in the monomer of protein. There are four iron atoms in each molecule of hemoglobin which can bind four oxygen atoms. Globin contains two linked pairs of polypeptide chains.

Figure 7.3 Structure of hemoglobin.

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7.10

153

Antibodies

A large group of glycoproteins, classified as immunoglobulins are found in blood plasma. Some of these proteins are produced in the spleen and lymphatic cells in response to a foreign substance called antigen. The newly formed protein is called “antibody”. Each immunoglobulin is made of two pairs of polypeptide chains, a pair of short and a pair of long chains.

7.11

Hormones

These polypeptides are small proteins found in low concentrations in animal tissues. Among these, the important ones are pituitary hormones (oxytocin), large protein (glucagon) and insulin.

7.11.1

Nutrient Proteins

The essential amino acids (in proteins) are readily synthesized by plant but must be acquired by humans.

7.12

Denaturation of Proteins

Proteins are maintained in their native state (i.e., their natural 3D configuration) by stable secondary, tertiary and quaternary structures. Denaturation takes place when the folded native structures break down because of extreme temperatures, pH changes which disrupt the stabilizing structures. Under these conditions, the structure becomes random and disorganised. Most proteins are biologically active over a temperature range of 0 to 40◦ C only. Heat is often used to kill organisms and deactivate their toxins. Heat denaturisation is used to prepare vaccines against some diseases. Denaturation can also be caused by α-helices packed on one side. Other methods such as treatment with organic solvents, strong acids or bases, detergents and heavy metal ions like Hg2+ , Pb2+ , Ag+ . Table 7.2 Equilibrium constants, Kh−c for helix-coil transformation. Amino acid residue Glycine L-serine L-alanine L-leucine

Kh−c 0.62 0.79 1.06 1.14

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Biophysical Chemistry

Equilibrium constants, Kh−c for helix-coil transformation in some proteins having amino acid residues at 30◦ C.

7.13

Helix-Coil Transitions in Proteins

The helix form dominates at low temperatures. As temperature is raised, the random form dominates. More often, the transition occurs over a narrow range of temperatures indicating that the helix unwinds suddenly rather than gradually. A plot of fractional helicity (in terms of optical rotation) as a function of temperature for protein chains of different length (N) is depicted in Figure 7.4.

Figure 7.4 Schematic depiction of helix-coil transitions in proteins. Note: Tc is the temperature in the midpoint of the transition when half of the total number of chains are helical.

7.14

Kinetics of Helix-Coil Transformation

Using small synthetic polypeptides rich in alanine, temperature jump studies were carried out and the mechanism was deduced as consisting of two steps: (i) a very fast step in which amino acids at either end of the helical segments undergo transitions to coil regions and (ii) a slower (rate determining step) that corresponds to the co-operative melting of the rest of the chain and loss of helical content. Using X and Y to denote an amino acid

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residue as belonging to a helical and coil region the mechanism may be written as

The relaxation time of the slow step, measured by laser T-Jump techniques for an alanine rich polypeptide chain (containing 21 amino acids) around 290 K was found to be 160 ns (or 160 × 10−9 sec). Table 7.3 Electrophoretic mobility data of a few typical proteins. Protein pH Electrophoretic mobility (10−4 cm2 v−1 sec−1 ) Ribonuclease A 7.0 0.55 Lysozyme at an ionic strength of 0.2 9.6 −0.24

7.15

Membrane Proteins

Integral membrane proteins, also called intrinsic proteins, have one or more segments that are embedded in the phospholipid bilayer. Many integral proteins contain residues with hydrophobic side chains that can interact with fatty groups of the membrane phospholipids thus anchoring the proteins to the membrane. Membrane proteins perform several functions vital to the survival of organisms. They relay signals between the cells internal and external environments. Effect of micellar structure, electrostatic effects and activation barrier on detergent mediated unfolding of 101-residue monomeric mixed α-helix S6 protein.

Figure 7.5 Shapes of proteins under different coordinates.

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Biophysical Chemistry

Ribosomal protein S6 (sub unit 6) is a small α/β protein consisting of 101 amino acids with a molar mass of about 12 kDa. S6 is constructed from 4β-sheets and two α-helices. S6 has two different conformations; it is either folded or unfolded with no intermediate states. It follows two-state folding event from the denatured state (D) to the native state (N) with the energy diagram shown in Figure 7.6. Its 3D structure consists of 4 stranded antiparallel β-sheets with two.

Figure 7.6 An energy diagram of a two-state folding event. The protein crosses an energy barrier, the transition state, to pass from denatured state to the native state without populating any intermediate states. The energy difference between the “D” state and “N” state corresponds to the difference in ΔGD− N and the reaction co-ordinate is the total difference in exposed surface area, Δm D− N (divided from m f and mu ). The reaction rate from the denatured state to TS is seen as the folding rate (k f ) and the opposite direction, from the native state to TS as the unfolding rate (k u ). The detergents used in these studies are sodium dodecyl sulfate (SDS), lauryl trimethyl ammonium bromide (LTAB) and lauryl trimethyl ammonium chloride (LTAC). Two schemes were proposed for the unfolding of S6

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Table 7.4 Kinetic parameters for unfolding of S6 in SDS. Concentration of NaCl (M)

−1 kmodel un f ( s )

K1 ( M − 1 )

−1 kSDS 0.5m ( s )

CMC (mM)

0.0 0.02 0.06 0.15 0.30 0.40

19.5 12.3 4.34 2.49 -

364 303 445 177 -

31.3 43.8 67.6 88.9 125.2 162.0

2.0 1.7 1.0 0.5 -

Conditions: Temperature 25◦ C, pH = 7.0. K1 = association constant between micelles (of surfactants) and free protein. CMC values (of surfactants) in presence of S6 at the given NaCl concentration and 25 mM Tris HCl, pH = 8.0. The kinetic runs were made using stopped flow technique.

7.16

Modelling of Tertiary Structure of Proteins

As mentioned earlier, the sequence of amino acids dictates the primary structure of proteins. The secondary structures often comprise α-helices and β-sheets, while the three-dimensional arrangement of peptides constitutes the tertiary structure. Interestingly, diverse types of long-range and short-range interactions predominantly influence the tertiary structures. In fact, it is this presence of electrostatic and non-electrostatic along with van der Waals type interactions that poses a major challenge in the prediction of the structures. Consequently, it is imperative to employ minimalistic approaches for comprehending the structures from the constituent amino acids sequences. The mysterious connection between the native structures of proteins and their most stable sequences vis a vis the mechanism underlying the energy landscape remains formidable even today. It is hence essential to formulate the fundamental rules governing the native protein structures, in a hierarchical manner. The lowest-energy state is identified as the native state of the protein; among different conformations available for a given sequence, the folded state is often referred to as the most compact structure. The Hydrophobic-Polar (HP) model for a chain of N amino acid residues is a simple but powerful approach to analyze the conformations of proteins. The energies and degeneracies of 2N states need to be computed for identifying the native states. Since exact enumeration is feasible only for small values of N (< 16), Monte Carlo simulations as well as graph

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Table 7.5 Thermodynamic data of polypeptides in proteins relating to helix-coil transformation in aqueous solutions.

theoretical procedures have been employed for larger values of N (∼ 100). The tertiary structures of proteins is dictated solely by the topological arrangement of the H-P sequences. The H-P lattice models are analyzed in both two and three dimensions, for deducing the designable protein sequences vis a vis conformations. Furthermore, these models correctly predict the temperature dependence of the coil to globule transition, thus

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Table 7.6 Equilibrium constants (Khel −nonhel ) for some natural amino acids in nine globular proteins. Amino acid Glu Ala His Met Lys Phe

N 62 165 54 20 106 56

helix/N 0.63 0.57 0.56 0.50 6.44 0.38

ΔG ◦ /JK−1 mol−1 −611.7 −236.2 −324.7 -

exp(−ΔG ◦ /RT) 1.28 1.10 > 1.0 > 1.0 1.14 > 1.28

Note: N = number of residues of the amino acid in 9 globular proteins (myoglobin, α and β chains of haemoglobin, lysozyme, ribonuclease, αchymotrypsin, papain, subtilisin, carboxypeptidase)

demonstrating their remarkable validity. The input in these lattice models is the pair-wise interaction energies between H-H, P-P and H-P contacts. There are several versions of H-P models, depending upon the energies ( E) assigned for H-H, H-P and P-P contacts. In the original HP model due to Dill et al., in 1989, the interaction energy between H-H contacts (EH − H ) was assumed to be negative (i.e., favorable) while the H-P (EH − P ) and P-P (EP− P ) energies were assigned zero. Subsequently, other parametrization schemes for the interaction energies were envisaged e.g., negative values for both EH − H and EH − P with EP− P = 0. Typically, for two-dimensional H-P lattice models of N amino acid chains, containing hydrophobic and polar residues, the total number of sequences is 2N . In an amino acid chain of length ‘N’, let ‘p’ be the number of hydrophobic residues and q be the number of hydrophobic-polar contacts. The enumeration of A( p, q) indicating the total number of ways in which the H-P contacts can arise for a given composition of proteins is a non-trivial task even for N = 16 since the total number of states allowed is 216 . In the parlance of graph theory, this enumeration is known as the counting of black-white edges. Table 7.7 provides the values of A( p, q), for a square lattice of 16 sites. It is easy to verify that the addition of all the entries of Table 7.7 yields 216 (65,536). This enumeration becomes tedious when the chain length of amino acids increases. As an illustrative example, consider a sequence HHHPHHPHHHHPHHP with the chain length N = 16, with p = 4 (black circles denoting the polar part). It has been demonstrated that the structures (i) and (ii) are the native and compact structures for this sequence.

160 Biophysical Chemistry

Note: ‘p’ denotes the number of polar residues and ‘q’ denotes the number of polar-hydrophobic contacts.



Table 7.7 A( p, q) values which arise from the counting of ‘hydrophobic-polar’ contacts for a square lattice of 16 sites, assuming periodic boundary conditions.  q  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 p   0 1 1 2 4 16 16 6 32 32 8 88 96 24 8 24 96 88 10 256 256 192 96 64 0 64 96 192 256 256 12 208 736 688 704 624 768 624 704 688 736 208 14 576 1664 1824 1920 1600 1920 1824 1664 576 16 228 1248 2928 3680 4356 3680 2928 1248 228 18 448 1568 3136 3264 3136 1568 448 20 128 768 1392 2112 1392 768 128 22 64 512 576 512 64 24 56 96 120 96 56 26 0 64 0 28 16 0 16 30 0 32 2

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Figure 7.7 (i) Native and (ii) a compact structure of amino acid chain lengths 16 within the two-dimensional HP lattice model framework.

7.17

Levinthal Paradox

The process by which a given amino acid composition chain acquires a three-dimensional shape is customarily designated as ‘protein folding’. The folding of any protein into its native structure remains a challenging problem, and the complexity can be comprehended with a typical example. For a chain length N = 100 undergoing three-dimensional random walk, the total number of conformations is ∼ 1077 . Given these astronomically large numbers, ferreting out the native protein structure by any algorithmic methodologies will consume billions of years even with the fastest computers. On the other hand, the protein folding often occurs within the time scale of a few seconds, implying that the protein folding does not occur by any systematic search among all the conformations. This is known as Levinthal paradox. One of the strategies by which this paradox can be resolved consists in assigning first order kinetic rate constants to the process by which the native state arises. This clever method entirely eliminates the enumeration protocols.

7.18

Proteins in Nutrition

Protein is found in plants and animals. Two kinds of amino acids must be considered for the body. Essential amino acids are required for normal body function but they can not be directly made by the body and must be obtained from food. Nine amino acids out of 20 are considered essential. The non-essential amino acids can be made by the body from the essential amino acids consumed in food. Proteins are found in a variety of foods such as beans, peas, eggs, nuts and seeds, meat, sea-food and soy products. Proteins provide energy for the body. They are a component of every cell in the body and are necessary for proper growth and development. Protein helps the body build and repairs cell and body tissue.

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Protein foods are important sources of vitamins and minerals, such as B-vitamin, choline, iron, phosphorus and selenium. They are also a sources of vitamins D, E and zinc. The daily value for protein is 50 gms per day based on 2000 calories diet.

Questions (1) If the electrophoretic mobility of ribonuclease A is 5.5 × 10−5 cm2 v−1 sec−1 , how much distance will it travel under a potential gradient of 20 V cm−1 in 60 min. Solution: Distance travelled in 1 sec = 5.5 × 10−5 cm sec−1 × 20V cm−1

= 11.0 × 10−4 cm In 60 minutes, distance travelled = 11.0 × 10−4 cm × 60 × 60

= 11.0 × 36 × 102 × 10−4 = 396 × 10−2 = 3.96 cm (2) The rate constant for the unfolding of S6 proteins in 0.5 M sodium dodecyl sulfate (SDS) is 31.3 sec−1 . Given that the equilibrium constant for the reaction kfold S6 + SDS FGGGGGGGGB GGGGGGGG S6(SDS) kunfold is 364 sec−1 , calculate the rate constant for the folding of S6. Solution: K = 364 =

kfold kunfold

kfold = 364 × 31.3 = 41410.5 liter M−1 sec−1 (3) For the polypeptide, poly-L-Lysine, the enthalpy and entropy changes ΔH ◦ and ΔS◦ associated with the helix-coil transformation are −3.4 kJ mol−1 and −10.04 J deg−1 mol−1 respectively. Calculate the equilibrium constant at 300K.

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Solution: ΔG ◦ = − RT ln K ΔG ◦ = ΔH ◦ − TΔS◦ = −3400 − (300 × −10.04)

= −3400 + 3012 = −388 J −388 = −8.314 × 300 × 2.303 log K 388 log K = = 0.0675 8.314 × 300 × 2.303 K = 1.17 (4) Classify proteins on the basis of their structure and describe their properties. (5) Discuss briefly the various types of bonds observed in proteins. (6) Write the structure of haemoglobin and explain its role in human body. (7) Describe briefly (a) denaturation of proteins and (b) helix-coil transition. (8) Discuss the effect of temperature on helix-coil transformation in proteins. (9) Consider the square lattice model for a protein of 16 amino acids, with equal number of hydrophobic and polar parts. Show that the total number of hydrophobic-polar contacts is 4356.

8

Nucleosides and Nucleotides 8.1

Introduction

A nucleoside consists of a nitrogenous base covalently linked to a 5-carbon sugar (ribose or deoxyribose) but having no phosphate group. A nucleotide consists of a nitrogenous base sugar (ribose or deoxyribose) and one to three phosphate groups. A comparison of the two is given in Table 8.1. Table 8.1 Comparison of nucleosides and nucleotides. Chemical Medical Examples composition significance Nucleoside Nucleoside sugar Many Cytidine, uridine, + base. When the nucleoside adenosine, phosphate group analogues are guanosine, of a nucleotide is used as thymidine removed by antiviral or and inosine hydrolysis, the anti-cancer structure of agents nucleoside remains Nucleotide Sugar + base + The All names as phosphate malfunctioning given above and nucleotides is with inclusion of one of the main phosphate. For causes of all example 5’-uridine cancers monophosphate

Compound

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_8

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Biophysical Chemistry

Biological Function (DNA & RNA)

Nucleotides are building blocks of nucleosides. A nucleic acid contains a chain of nucleotides linked together with covalent bonds to form a sugar phosphate backbone with protruding nitrogenous bases. For example: DNA contains two chains spiraling round each other in the shape of a double helix. The two chains in the double helix are held together along their length by H-bonds that form between the base, on one chain and the bases on another.

8.3

Examples of Nucleotides

Nucleic acids are made of monomers known as nucleotides. A nucleotide has three parts as mentioned earlier. I. A 5-carbon sugar ring: For example, deoxyribose in DNA: ribose in RNA; ribose in ATP. II. Phosphate group: In RNA and DNA the phosphate group binds to another nucleotides carbon forming the backbone of the molecule. In ATP, there are three phosphate groups that store energy. III. A nitrogenous base: The bases in DNA, are adenine, guanine, cytosine, and thymine. The bases in RNA are adenine, guanine, cytosine and uracil. The base in ATP is always adenine. 





Figure 8.1 Structure of nucleoside, nucleotide, nucleoside di and tri phosphates.

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167

Figure 8.2 Structures of purines.

Figure 8.3 Structures of pyrimidines.

Figure 8.4 The structural elements of the nucelosides and the phosphate bearing nucleotides. (i) The reduction of adenine involves a primary potential controlling reduction of the N(1) = C(6) double bond to give 1, 6-dihydro-6 amino purine. It is reduced again is a 2e¯ − 2H + process to give 1, 2, 3, 6-tetrahydro-6-amino purine. The scheme of reduction is given in Table 8.2.

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Biophysical Chemistry

Table 8.2 Typical polarographic data for the sine and guanine. Compound Nature of polarographic wave Adenine Single diffusion-controlled wave Cytosine Single diffusion-controlled wave

reduction of adenine, cytoHalf wave potential (V)

−0.975 to 0.084 in the pH range 1 to 6 −1.125 to 0.073 in the pH range 4 to 6

Figure 8.5 Scheme depicting electrochemical reduction of adenine. (ii) The basic reaction pattern for cytosine involves a rapid protonation at the N(3) position to form the electro active species A 2electron reduction of the N(3) = C(4) bond leads to the carbanion. The protonation of the latter followed by de-amination, regenerates the N(3) = C(4) bond giving 2-oxypyrimidine. The protonation and subsequent one-electron reduction of 2-oxypyrimidine gives a free radical which then dimerizes to give 6-6’ bis (3, 6) dihydropyrimidone-2. In the case of guanine, the mean potential for oxidation is 0.99 V and the scheme of oxidation is shown below.

Figure 8.6 Electro-oxidation of guanine.

Nucleosides and Nucleotides 

8.4

169

Naming of Nucleosides and Nucleotides

Nucleotides are commonly abbreviated with 3 letters (4 or 5 in case of deoxy or dideoxy-nucleotides). The first letter indicates the identity of the nitrogenous base (for example: A for adenine, G for guanine), the second letter indicates the number of phosphates (mono, di, tri) and the third letter “P” denotes phosphate. Nucleoside triphosphates that contain ribose as the sugar are abbreviated as NTPS, while nucleoside triphosphates containing deoxyribose as the sugar are abbreviated as DNTPs (example: dATP refers to deoxyribose adenine triphosphate) NTPs are the building blocks of RNA and dNTPs are the building blocks of DNA. The carbons of the sugar in a nucleoside triphosphate are numbered around the carbon atom starting from the original carbonyl of the sugar. By convention, the carbon numbers in a sugar are followed by the prime symbol ( ) to distinguish them from the carbons of the nitrogenous base. The nitrogenous base is linked to the 1 carbon through a glycosidic bond and the phosphate groups are covalently linked to the 5 carbons. The 1st phosphate linked to the sugar is termed as α-phosphate, the second is βphosphate and the third is the γ-phosphate.

Figure 8.7 Helical structure of DNA.

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Compound Adenosine triphosphate

Importance It is a most important energy form for all organisms and is the cells energy currency

Structure

Biophysical Chemistry

Table 8.3 Functional importance of a few nucleotides.

Compound Ribonucleic acid (RNA)

Structure

 



 



Nucleosides and Nucleotides 

Table 8.3 (Continued) Importance It is a single stranded molecule composed of building blocks called ribonucleotides. A ribonucleotide is composed of 3 parts (i) a ribose i.e., ringed 5 carbon (ii) sugar nitrogeneous base and (iii) a phosphate group. In RNA, the bases present are adenine, guanine, cytosine and uracil. There are three functionally different RNA’s; messenger RNA (mRNA), transfer RNA (tRNA), ribosomal RNA (rRNA) mRNA carries information about a protein sequence to ribosomes, the protein synthetic factories in the cell. t-RNA is a small RNA chain of 80 nucleotides that transfers a specific amino acid to a growing polypeptide chain. rRNA is the catalytic component of ribo somes.

171

Structure

 Biophysical Chemistry

Table 8.3 (Continued) Importance DNA is made up of molecules called nucleotides. Each nucleotide contains a phosphate group, a sugar group and a nitrogen group. The four types of nitrogen bases are Adenine (A), Thymine (T), Guanine (G) and Cytosine (C). The order of these bases is what determines DNA’s instructions, or genetic code. Each nucleic acid strand contains nucleotides that appear in a certain order within the strand, called its base sequence. The base sequence of DNA is responsible for carrying and retaining the hereditary information in a cell.

172

Compound Deoxyribonucleic acid (DNA)

Nucleosides and Nucleotides 

173

Table 8.4 Sites of protonation and pKa ’s of four nucleobases and the ribose-phosphate backbone. Reaction pKa1 pKa2 1. 3.50 —

2.

1.60

9.20

3.

4.20

—

4.

9.2

—

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pKa and ΔG ◦ (kJmol−1 /at 298 K of the nucleotides 3’-ethyl phosphate [d | rN Pet] (1a-5a and 1b-5b, scheme-1) and 3’, 5’-bisethyl phosphate [Etp (d | rN) pEt] (6a-10a and 6b-10b), scheme-1 in both 2’-deoxy (dN) and ribo (rN) series using NMR technique

1a : B = A, R = H 2a : B = C, R = H 3a : B = T, R = H 4a : B = U, R = H 5a : B = G, R = H 1b : B = A, R = OH 2b : B = C, R = OH 3b : B = T, R = OH 4b : B = U, R = OH 5b : B = G, R = OH

Explanation of symbols:

6a : B = A, R = H 7a : B = G, R = H 8a : B = U, R = H 9a : B = T, R = H 10a : B = C, R = H 6b : B = A, R = OH 7b : B = G, R = OH 8b : B = U, R = OH 9b : B = T, R = OH 10b : B = C, R = OH

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175

Table 8.5 pKa data and ΔG ◦ values of nucleotides. Nucleotide pKa (nucleo base) ΔG ◦ (kJmol−1 ) 1a 3.35 19.1 2a 4.12 23.5 3a 9.92 56.6 4a 9.35 53.3 5a 9.40 53.6 6a 3.82 21.8 7a 9.59 54.7 8a 9.58 54.6 9a 10.12 57.7 10a 4.34 24.8 1b 2b 3b 4b 5b 6b 7b 8b 9b 10b

3.11 3.84 9.66 9.21 9.23 3.72 9.29 9.26 9.78 4.25

17.1 21.8 55.1 52.5 52.7 21.2 53.0 52.9 55.8 24.2

Examples of symbols in explanation:

Table 8.6 Conductivity data of nucleotides and nucleotides at 400 K. Nucleosides Nucleotides − 11 − 13 − 1 − 7 10 to 10 mho cm 10 to 10−12 mho cm−1

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Solid State Conductivity of Dry DNA It shows a small semi conductivity based on the equation x = x0 e−Δε/RT where Δε = 2.42 electron volts, log10 ( x0 , mho cm−1 ) = 3.4

DNA Duplex and the Thermodynamic Parameters Associated With It Duplex DNA is another name for double stranded DNA. This means that the nucleotides of two DNA sequences have bonded together and then coiled to form a double helix. This double stranded structure facilitates the stable duplication of genetic material, a requirement for cell division. A strand of DNA is composed of nucleotides each of which consists of a nitrogen base bonded to a sugar and triphosphate group. When two of these strands are antiparallel, meaning lagging end of one strand is aligned with the other strands leading end, hydrogen bonds form between complementary nitrogen base pairs of adenine and thymine (A–T) or guanine and cytosine (G–C). This allows two separate DNA segments to fuse together to create a ladder-like structure, where the sugar and the phosphate group are the vertical sides and the complementary nitrogen base pairs serve as the ladder’s rungs. The DNA molecule is technically classified as a biopolymer, which means that it contains two polymer chains that link up to form the larger molecule. Each of these polymer chains is composed of a DNA monomer, or nucleotide whose structure is formed from a phosphate group, a deoxyribose sugar and a nitrogen containing base. Areas mentioned below: (i) Better crops (drought and heat resistant), (ii) recombinant vaccines (i.e., hepatitis B), (iii) prevention of sickle cell anaemia, (iv) prevention of cystic fibrosis, (v) production of clotting factors, (vi) production of insulin, (vii) plants that produce their own insecticides.

More Explanatory Information on (ITS)1 and (ITS)2 Internal transcribed spacer (ITS) is the spacer DNA situated between the small sub-unit ribosomal RNA (rRNA) and large subunit rRNA genes in the chromosome or the corresponding transcribed region in the polycistronic rRNA processor transcript.

Nucleosides and Nucleotides 

Table 8.7 Thermodynamic parameters for DNA duplex formation in 4 MNaCl and 4 M choline dihydrogen phosphate (Choline dhP). Medium Nucleotide ΔG ◦ /kJ mol−1 ΔH ◦ /kJ mol−1 TΔS◦ /kJ mol−1 Tm (◦ C ) 4 M NaCl Oligonucleotide with 9 chains −35.1 −195.0 −159.8 38.6 (0 DN 9) 4 M NaCl Oligonucleotide with 10 chains −53.4 −228.8 −175.7 63.0 (0 DN 10) Choline DhP 0 DN 9 −42.2 −279.5 −237.2 43.6 Choline dhP 0 DN 10 −35.1 −200.0 −164.8 38.2

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Details of ITS-1 and ITS-2 Terms In bacteria and archaea, there is a single ITS located between the 16S and 23S rRNA (ribosomal RNA, S = Svedberg unit = 10−13 sec). In contrast there are two ITS’s in eukaryotes: ITSI is located between 18S and 5.8S rRNA genes, while ITS2 is between 5.8S and 28S rRNA genes. ITSI corresponds to the ITS in bacteria and archaea while ITS2 originated as an insertion that interrupted the ancestral 23S rRNA gene. Table 8.8 Stability constant data of the complexes formed between the nucleotides and polyamines in aqueous solution at 25◦ C. Nucleotide AMP

Polyamine (en) (r = 2) 2.61

log (Kr) CdV ptr (r = 2) (r = 2) 2.22 2.24

Spd (r = 2) (r = 3) 2.52 3.04

UMP

(r = 2) 2.64

(r = 2) 2.04

(r = 2) 2.1

(r = 2) (r = 3) 3.13 3.17

IMP

(r = 2) 2.73

(r = 2) 2.31

(r = 2) 2.3

(r = 2) (r = 3) 3.54 3.51

GMP

(r = 2) 2.65

(r = 2) 1.95

(r = 2) 1.61

(r = 2) (r = 3) 3.09 3.24

Sper (r = 2) (r = 3) (r = 4) 2.63 3.44 4.09 (r = 2) (r = 3) (r = 4) 2.67 3.19 3.76 (r = 2) (r = 3) (r = 4) 3.19 3.21 4.04 (r = 2) (r = 3) (r = 4) 2.70 3.01 4.04

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179

Questions (1) Which of the following statements is true of Duplex DNA (a) It has no relation to the genetic material. (b) It does not convey any information about the bonding of the nucleotides in DNA. (c) It is another name for double stranded DNA. (d) Cell division does not require participation of DNA. (2) Indicate the correct answer: (a) Ribonucleic acid contains the nitrogenous bases adenine, guanine cytosine and uracil. (b) Ribonucleic acid contains adenine, six membered sugar, thymine and uracil. (c) Ribonucleic and deoxyribonucleic acids are nucleosides. (d) There is no relation between the order of presence of nitrogenous bases and genetic code. (3) The pKa ’s of adenosine, guanosine and cytosine are 3.50, 1.60 and 4.20 respectively. Hence, their acidic strength lies in the order (a) (b) (c) (d)

adenosine > guanosine > cytosine guanosine > adenosine > cytosine cytosine > guanosine > adenosine cytosine > adenosine > guanosine

(4) What are the essential components of ribonucleic acid (RNA). Give the structure of a RNA fragment? (5) Draw the helical structure of DNA and indicate the positions of amines and the sugar phosphate backbone. (6) State the compositions of a nucleoside and nucleotide and indicate their medical significance. (7) Write down the dissociation of adenosine and guanosine acids. If their pKa ’s are 3.50 and 1.60, what are their percent dissociations values at 0.1 M.

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(8) Estimate the vertical electron affinity of adenine using the following data: (a) Standard enthalpy of formation of the neutral form = 1.0042 eV (b) Standard enthalpy of formation of the anion radical = 1.5607 eV (c) Total tautomeric energy = 1.3034 eV

9

Enzymes 9.1

Introduction

Enzymes are mostly proteins that accelerate the reaction rates. They are vital for life and execute diverse functions in the body such as: (i) aiding the digestion and (ii) assist metabolic processes. Enzymes are made from amino acids. An enzyme is formed by stringing together about 100 to 1000 amino acids in a specific and unique order. This chain of amino acids folds into a unique shape.

9.2

Different Types of Enzymes

Three different kinds of enzymes are known (i) Amylase and carbohydrase enzymes: They break down starch into sugar. (ii) Protease enzymes: They break down proteins into amino acids. (iii) Lipase enzymes: They break down lipids into fatty acids and glycerol.

9.3

Nature of Enzyme Action

Some enzymes break large molecules into smaller ones which are more easily absorbed by the body. Other enzymes bind two molecules together to form a new molecule. Enzymes are very selective catalysts. They react

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_9

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Figure 9.1 Schematic depiction of enzyme - substrate complex. with compounds known as substrates. The substrates bind to a region on the enzyme referred as active site. Figure 9.1 depicts the enzyme-substrate complex, schematically. The energy diagram of the reaction may be represented as shown below:

Figure 9.2 Energy diagram with and without the presence of enzymes. It is seen from Figure 9.2 that the activation energy of the reaction gets lowered from ΔE to ΔE thereby enhancing the reaction rate.

9.3.1

Examples of Digestive Enzymes

(i) Amylase is produced in the mouth and helps in breaking down starch into smaller sugar molecules. (ii) Pepsin is produced in the stomach and helps to break down proteins in the food. (iii) Trypsin, lipase, DNA and RNA are produced in pancreas. (iv) Lactose, found in mammalian milk,

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183

breaks down the sugar lactose. Nature of enzyme action: Applying chemical kinetic principles, a chemical reaction may be expressed as occurring according to the scheme. X+Y    Reactants



. . Y ∗ X . 

−→

Transition State

Z + Z    Products

The quantitative measurement of the relation between rate and substrate concentration in an enzyme catalyzed reaction is due to Michaelis and Menten. According to them, an enzyme catalyzed reaction involves the formation of an enzyme-substrate complex in an equilibrium step which then decomposes to give the enzyme and products. The reaction scheme may be represented as k1 k2 BG ES FGGGGGGGB E + S  FGGGGGG GGGGG GGGGGGG E + P k −1 k −2

(9.1)

where k’s represent the rate constants of the appropriate steps. After the enzyme and substrate are brought together, the concentration of E-S complex builds up under condition when “S” is in large excess and k1 >> k2 i.e., under steady state conditions. In this case, the rate of decomposition of E-S complex balances the rate of its formation. Thus, Rate of formation of [ES] = Rate of decomposition of [ES] k1 [ E][S] + k −2 [ E][ P] = k −1 [ ES] + k2 [ ES]

(9.2) (9.3)

From equation (9.3),

[ E]{k1 [S] + k −2 [ P]} = [ ES]{k −1 + k2 }

(9.4)

[ ES] k [ S ] + k −2 [ P ] k1 [S] k [ P] = 1 = + −2 [ E] k −1 + k 2 k −1 + k 2 k −1 + k 2

(9.5)

To simplify equation (9.5), the initial stage of reaction can be determined when the concentration of P will be small. In this case, the rate of formation of ES from E and S will be small. Thus, the second term of equation (9.5) can be neglected, i.e., k −2 [ P ] =0 (9.6) k −1 + k 2 Thus

[ ES] k1 [S] = [ E] k −1 + k 2

(9.7)

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Biophysical Chemistry

By defining

k −1 + k 2 = Km k1

(9.8)

[ E] Km = [ ES ] [S]

(9.9)

eqn. (9.8) may be written as

The total enzyme concentration, Et = [ E] + [ ES]

[ E] = [ Et ] − [ ES]

or

(9.10)

Substituting equation (9.10) in equation (9.9), we get

[ Et ] − [ ES] Km = [ ES] [S]

(9.11)

[ Et ] Km −1 = [ ES] [S]

(9.12)

or

The maximum initial velocity, Vmax , is obtained when the total enzyme, Et , is completely complexed with saturating amounts of S or Vmax = k [ Et ]

(9.13)

where k is a rate constant for this reaction. Also, the initial velocity of the reaction (V ) is given by V = k [ ES] (9.14) at a given concentration of S. Thus,

[ Et ] Vmax = V [ ES]

(9.15)

Comparing equations (9.12) and (9.15), it is seen that Vmax Km −1 = V [S]

or

Km Vmax −1 = +1 V [S]

or V Km [S]

+1

=

Vmax Km +[S] [S]

=

Vmax [S] Km + [ S ]

(9.16)

(9.17)

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185

Km of equation (9.8) is known as Michaelis–Menten constant. Some conditions may be considered which give interesting results for equation (9.17). (i) when [S] is very large, Km (in equation 9.17) becomes negligible. Then V = Vmax

(9.18)

In such a case, it is seen that V is independent of [S] or it becomes a zero order reaction. (ii) when V = Vmax /2, equation (9.17) may be written as Vmax [S] Vmax = 2 Km + [ S ]

or

Km + [ S ] =

Vmax [S] × 2 = 2[ S ] Vmax

or

Km = [ S ]

(9.19) It is to be noted that under these conditions, the dimensions of Km is mols/ liter. If Km >> [S] Vmax [S] V= (9.20) Km Now V depends on concentration of [S] as a first order dependence. Graphically, the above conclusions may be represented as in Figure 9.3.

Figure 9.3 Dependence of the reaction rate on concentrations of (a) enzyme and (b) substrate. In the above diagram, it is assumed that the concentration of enzyme is constant and the concentration of substrate is increasing.

9.3.2

Significance of Km

The rate limiting steps in a biochemical reaction can be predicted by using Km values which is similar to suggesting rate determining steps of ordinary chemical reactions.

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For example, consider

In the above scheme, L → P, at low concentrations of L (< 10−4 M lower), the rate L → M will be very low and controls the overall change L → P. It may be mentioned that Km may be defined as the equilibrium constant of an enzyme-catalysed reaction because k −1 ES FGGGGGGGB GGGGGGG E + S k1

or

Ks =

[ E][S] k = −1 [ ES] k1

(9.22)

and

k −1 + k 2 k1 Thus Km >> Ks . It is to be noted that Km depends on ionic strength and temperature. Km =

Lineweaver-Burke Plot Taking reciprocal of equation (9.17), it follows that   1 Km 1 1 = + V Vmax [S] Vmax From the slope and intercept values, Km and Vmax can be evaluated.

Figure 9.4 Lineweaver-Burke plot.

(9.23)

Enzymes 

Table 9.1 Kinetic data on some reactions catalysed by enzymes (or inhibited in presence of inhibitors). Substrate Enzyme Km (μmol/L) Ki (μmol−1 ) Inhibitor Ribulose diphosphate Ribulose diphosphate 1.2 × 10−4 4.2 × 10−3 Phosphate (C) carboxylase (spinach) Bicarbonate ion (HCO3− ) Ribulose diphosphate 2.2 × 10−2 9.5 × 10−3 3-phosphoglyceric acid (C) carboxylase (spinach) Fructose 1, 6 diphosphate Fructose 1, 6 diphosphate 3 × 10−4 2 × 10−4 L-Sorbose-1 Phosphate (C) aldolase (yeast) Ethanol Alcohol dehydrogenase 1.3 × 10−2 6.7 × 10−4 Acetaldehyde (NC) (yeast) Succinate ion Succinate dehydrogenase 1.3 × 10−3 4.1 × 10−5 Malonate (C) (bovine heart) D-glyceraldehyde 3 Triose phosphate 9.0 × 10−3 3.0 × 10−6 1, 3-diphosphoglycerate (C) phosphate de-hydrogenase (rabbit muscle) Glucose-6-phosphate Glucose-6-phosphatase (rat 4.2 × 10−4 6 × 10−3 Citrate (C) liver) (C) = Competitive inhibitor; (NC) = Non-competitive inhibitor

187

188

9.4



Biophysical Chemistry

Michaelis-Menten Mechanism

Two types of mechanisms have been suggested: (i) ordered and (ii) random. In the ordered type, it is suggested that the substrates must be added to enzyme before any products are released. The sequence of release of products is also precise. In the random mechanism, the substrates add to the enzyme and the products are released randomly. A few reaction schemes under the above categories are given below. Ordered reaction mechanism: Consider the reaction

(In equation 9.24, E = Enzyme, L, M = Substrates, X, Y = Products). The scheme (9.24) states that E first forms a complex with L and only then M can form the complex ELM. After catalysis, first X and then Y are released (in that order). The reaction, CH3 CH2 OH + NAD+

alcohol + (9.25) FGGGGGGGGGGGB GGGGGGGGGGG CH3 CHO + NADH + H dehydrogenase

is a typical example of scheme. The kinetic analysis of reaction (9.25) may be given as

An example of a reaction following random mechanism is

An example of such a mechanism is

Ping-Pong mechanism: A typical reaction sequence of this type is

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189

The enzyme complexes formed in this case are EL, FX, FM and EY, with L being converted to X and then M to Y, F being designated as a modified enzyme (of X). F combines with M with a subsequent transfer of X to M so as to form Y, the product with simultaneous regeneration of Y. The reaction Acetyl CoA + ATP + HCO3− −→ Malonyl CoA + ADP + Pi

(9.30)

is an example of the above scheme.

9.5

Effect of Temperature on Enzyme-catalysed Reactions

Consider a chemical reaction with an activation energy of 58.5 kJmol−1 and an enzyme catalysed reaction with an activation energy of 25.0 kJmol−1 . By using Arrhenius equation, it is possible to calculate by what factor the enzyme catalysed reaction proceeds faster vis a vis the chemical reaction. For the chemical reaction log k c = log A −

58.5 58.5 = log A − = log A − 23.6 2.48 8.314 × 10−3 × 298

For the enzyme catalysed reaction, 25.0 8.314 × 0.001 × 298 25.0 = log A − = log A − 10.1 2.48 log k e − log k c = −10.1 + 23.6 = 13.5 log k c = log A −

or log

ke = 13.5 or kc

ke = 1013.5 kc

It is seen that the enzyme catalysed reaction is 1013.5 faster than the chemical reaction. Although it is possible to increase the rate of a reaction by raising the temperature, this is not favourable in the case of a reaction in the cell because the protein in the enzyme may undergo denaturation making the enzyme lose its activity. One must choose an optimum temperature which takes into consideration the increasing rate with temperature and the decreasing activity of the enzyme at higher temperature.

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Effect of pH Since the change in pH profoundly affects the ionic character of amino and carboxyl groups in proteins, they markedly affect the catalytic sites. Apart from the ionic effects, low or high pH may cause denaturation and the enzyme loses its activity. It may also be noted that many substrates are ionic in nature (NAD+ , amino acids) and the active site of an enzyme may require specific ionic species for optimal activity. The effect of pH on enzyme catalysed reactions may be shown in the following diagram.

Figure 9.5 Variation of the rate of enzyme-catalysed reaction with pH.

9.6

Specificity of an Enzyme

An enzyme will select only specific compounds with which it can combine. This is necessitated by the requirements such as the conformation of the complex protein in the enzyme, the uniqueness of its active site and the structure of the substrate. An enzyme often exhibits group specificity in a group of substrates. Another aspect of enzyme specificity is its stereospecificity towards substrates i.e., an enzyme may prefer to react with an L- or D-isomer. For example, D-amino acids

O2 α-keto acids + NH3 + H2 O (9.31) FGGGGGGB GGGGGG D-amino acid oxidase

A similar reaction for L-amino acids may be applied using L-amino acid oxidase. alanine BG D-alanine L-alanine FGGGGGGGGGGGG (9.32) GGGGGGGGGGG racemase

Enzymes 

9.7

191

Classification of Enzymes

There are six classes of enzymes: (i) Oxidoreductase (ii) Transferases, (iii) Hydrolases, (iv) Lyases, (v) Isomerases, and (vi) Ligases. A brief account of these is given below. (i) Oxidoreductases: These are concerned with biological oxidation reduction reactions. Respiration and fermentation processes are thus included in this category. Also, dehydrogenases, oxidases and peroxydases (which use H2 O2 as oxidant) are part of this category. Hydrolysates, and oxygenases which introduce −OH groups and molecular O2 (in place of a double bond) are also included. (ii) Transferases: These enzymes catalyse the transfer of one carbon group (example: methyl group), aldehydic or ketonic groups, P-containing and S-containing groups also. (iii) Hydrolases: Examples of this class are phosphatases, peptidases and glycosidases. (iv) Lyases: This class includes aldolases, dehydratases, decarboxylases. They remove groups from their substrates leaving or adding double bonds. (v) Isomerases: Some enzymes in this class are cis-trans isomerases, racemases, intramolecular oxidoreductases and intra molecular reductases. (vi) Ligases: These enzymes catalyse the joining of two molecules coupled with the breakdown of a pyrophosphate bond in ATP or other similar PO34− groups.

Conditions (to be fulfilled) for Specific Interactions Between Enzyme and Substrate Three conditions must be fulfilled for a reaction between an enzyme and substrate: (i) The substrate must be associated with the enzyme in a a specific orientation at least at three sites. (ii) The reactivities of the three enzymic sites must be different. (iii) The compound may have two groups (x1 and x2 ) affected by the enzyme and two different groups (y1 and y2 ) which are associated with a central carbon atom C. For example, in the synthesis of citrate from acetyl CoA and oxaloacetic acid only x1 is derived from CoA and x2 , y1 and y2 come from oxaloacetate.

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However, citrate in solution is optically inactive since it has a plane of symmetry. The following diagram shows the positioning of a substrate to its active site on the surface of the enzyme.

Figure 9.6 Positioning of a substrate to an active site.

9.8

Inhibitors of Enzymes

Inhibitors are compounds which have the ability to combine with some enzymes reversibly or irreversibly and thereby inhibit the catalysis by that enzyme. There are a variety of compounds like drugs, antibiotics and metabolites which can act as inhibitors. An irreversible inhibitor forms a covalent bond in the enzyme often an amino acid residue which may be associated with the catalytic activity of the enzyme. Some enzyme inhibitors physically block the active site. Scheme depicting non-competitive inhibition

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193

In a kinetic sense, the rate of the enzyme-catalyzed reaction is lowered in proportion to the concentration of the inhibitor. This is known as noncompetitive inhibition. A specific case is the reaction of the inhibitor, iodoacetate, which reacts with the sulfhydryl group of an enzyme, triosephosphate dehydrogenase according to E − SH + ICH2 COOH → E − S − CH2 COOH + HI

(9.35)

Another type of irreversible inhibition is that a latent inhibitor becomes an active inhibitor by binding to the active site of the enzyme. This newly formed inhibitor reacts chemically with the enzyme leading to its irreversible inhibition. For example, the inhibition of D-3-hydroxyl decanoyl ACP dehydrase (of E-coli) by the latent inhibitor D-3-decenoyl-N-acetyl cystamine to form an active inhibitor proceeds according to the following scheme.

(9.36)

9.9

Reversible Inhibition

This type of inhibition involves establishment of equilibrium between the enzyme and inhibitor, the equilibrium constant, Ki , being a measure of the inhibitor to the enzyme. There are three types of reversible inhibition: (i) Competitive inhibition (CI), (ii) Non-competitive inhibition (NC), and (iii) Uncompetitive inhibition (UC). In the first category (CI), the inhibitor and the substrate compete for the same active site on the enzyme which may be represented as

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Biophysical Chemistry

Scheme showing competitive inhibition

here, complexes ES and EInh are formed but the complex EInh.S. It may be noted that high concentrations of “S” will overcome the inhibition by causing the reaction to shift to the right. In non-competitive inhibition (NC), compounds that bind reversibly with either the enzyme or E-S complex are designated as non-competitive inhibitors. The following scheme depicts this reaction.

In this case, the inhibitor can combine with ES while S can combine with E.Inh to form E.Inh.S in both cases, the value of Km is not altered in this case since the inhibitor binding site is not identical to the active sites nor does it modify the latter directly.

9.10

Uncompetitive Inhibition

In the case of uncompetitive inhibition (UC) compounds that combine only with ES complex but not with the free enzyme are called UC inhibitors. The reaction scheme in this case is Scheme showing uncompetitive inhibition

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195

Comparing schemes (9.38) and (9.39), it is seen that a part of uncompetitive inhibition (UC) is always a component of non-competitive inhibition as E.Inh.S is formed in both cases. The kinetic expressions in all three cases (CI; NC; UC) may be worked out in a similar way to MichaelisMenten derivation and the results are summarized below. Table 9.2 Kinetic expressions for different inhibition types. Inhibition type No inhibitor CI NC UC

Equation V = Vmax [S]/ (Km + [S]) V = Vmax × [S]/ {(Km (1 + 1/Ki ))} + [S] V = Vmax × [S]/ (Km + [S])(1 + 1/Ki ) V = Vmax × [S]/ (Km ) + [S](1 + 1/Ki )

Vmax -

Km -

No change

Increases

Decreases

No change

Decreases

No change

The variation of rate of reaction (V ) with substrate concentration in all the above cases is shown in Figure 9.7.

Figure 9.7 Graph showing the variation of reaction rate with substrate concentration. In the case of NC (curve b), there is no change in Km (see the curves “no inhibitor and NC”) but Vmax shifts to the top in the case of NC. In the case  but there is no change in V . of curve for (a), there is a change in Km to Km m

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Biophysical Chemistry

Figure 9.8 Graph showing the variation of reaction rate: (i) without inhibitor; (ii) competitive and (iii) non-competitive inhibitor.  and V  In this case Km decreases to Km max decreases to Vmax . A typical reciprocal plot of 1/V vs. 1/[S] in the case of CI is shown below:

Figure 9.9 Variation of the reciprocal velocity with reciprocal substrate concentration.

Negative Feed Back Inhibition This inhibition is caused by interaction of a product with enzyme early in the sequence of its formation. This is similar to the type of competitive inhibition.

Enzymes 

9.11

197

Allosteric Enzymes

They are enzymes that change their conformational isomers upon binding an effector. Every enzyme contains an active site where it catalyses its specific reactions. However, allosteric enzymes contain a second site called allosteric site. This site, through its binding of a non-substrate molecule influences the activity of the enzyme. Such enzymes play crucial role in many fundamental biological processes like cell signaling and regulation of metabolism.

Kinetic Aspects of Allosteric Enzymes A normal hyperbolic curve in a velocity [S] plot is obtained when a molecule of substrate has no effect on the intrinsic dissociation constant of vacant sites. However, if the binding of one substrate molecule induces structural changes that result in altered affinities for vacant sites, the velocity curve does not follow. Michaelis-Menten Kinetics. Allosteric enzymes yield a sigmoid type of velocity [S] curves. The binding of one substrate facilitates the binding of he next substrate (or effector) molecule by increasing the affinities of the vacant binding sites. This phenomenon is called co-operative binding. The following diagram shows a typical sigmoid curve vis a vis a normal hyperbolic velocity curve.

Figure 9.10 Dependence of the maximum velocity on the substrate concentration.

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Biophysical Chemistry

It is to be noted that between [S] = 0 and [S] = 3.0, the hyperbolic curve decelerates but still rises to 0.75 Vmax . In the same limits, the sigmoid curve acelerates but reaches only about 0.1 Vmax . However, the sigmoidal curve increases from 0.1 Vmax to 0.75 Vmax with only an additional 2.3 fold increase in [S]. But for the same increase the hyperbolic curve requires 27 fold increase in [S]. Cofactors in enzyme catalysis: Many enzymes require an additional component before it can carry out its catalytic functions. The cofactors may be divided into three groups: (i) Prosthetic groups, (ii) Co-enzymes, and (iii) metal activators. A prosthetic group is a cofactor firmly bound to enzyme protein. For example, the porphyrin moiety of the hemoprotein peroxidase is a prosthetic group. It may be represented as

A co-enzyme is a small organic molecules stable to heat, which readily dissociates off an enzyme protein and can be dialysed away from the protein. Examples of Co-enzymes are NAD+ , NADP+ , thiamine phosphate. The function of a co-enzyme to interact with different co-enzymes is shown below:

(9.41) The metal activator group is necessitated by the requirement of a large number of enzymes for mono or divalent cations like K+ , Mn2+ , Mg2+ , Ca2+ and Zn2+ ions. These ions may be loosely or firmly bound to an enzyme protein by chelation with phenolics phosphoryl or carboxyl groups.

Enzyme (Zymogen) Trypsinogen Chymotrypsinogen A Pepsinogen Procarboxypeptidase A

Activating agent Enterokinase Chymotrypsin H+ or pepsin Trypsin

Active enzyme Trypsin α-chymotrypsin Pepsin Carboxypeptidase A

Inactive peptide + hexapeptide + amino acid residues + fragments + fragments

Table 9.3 Conversion of zymogens to active enzymes.

Enzymes  199

200



Biophysical Chemistry

Enzymes as proteins: There are three groups of this class: (1) The monomeric enzymes, (2) Oligomeric enzymes, (3) Multi-enzyme complexes. (1) First category: They are enzymes with only one polypeptide chain in which the active site resides. Examples of this class include Lysozyme (Egg white: Molar mass = 14,600; amino acid residues = 129) Trypsin (Molar mass = 23,800, amino acid residues = 223); Carboxypeptidase A (Molar mass = 34,600, amino acid residues = 307). (2) Second category: The enzymes contain 2 to 60 more sub-units firmly associated to form catalytically active enzyme protein. (3) Third category: In this case, a number of enzymes engaged in a sequential series of reactions in the conversion of substrate to product are strongly associated. Attempts to dissociate these enzyme complexes leads to deactivation. This class contains only a small number of enzymes and they catalyse hydrolytic reactions. They are highly reactive proteases and cannot be biosynthesized in the active form in the cell as the cell is damaged in this process. They are, therefore, synthesized in an inactive form known as “Zymogens” and transported out of the cell into the digestive tract where they are again converted into the active form. The enzymes, chymotrypsin, trypsin, and elastase are called serine proteases since their catalytic sites contain highly reactive serine residue.

9.12

Oligomeric Enzymes

These enzymes include proteins with molar masses ranging from 35,000 to a few millions. They contain a number of polypeptide combinations and form catalytically active enzymes. Since these enzymes contain multipolypeptide structures, they exhibit properties necessary for proper functioning of metabolic activities. Some important aspects of the enzymes are given below: (a) The dissociation of many oligomeric enzymes into sub-units results in complete loss of their activity. (b) The association of many sub-units may yield an active site involving amino acid residues contributed by different components. Thus, the widely separated amino acid residues in ribonuclease constitute the active sites of its monomeric enzyme structure. (c) The association of two sub-units with different individual enzyme activity often yields appropriate enzyme reaction (Example: Tryptophan synthetase system).

Enzymes 

201

(d) In a number of enzymes, a sub-unit serves as a specific carrier of a substrate. For example, the two sub-units, biotin carboxylase and transcarboxylase in the enzyme acetyl CoA carboxylase of E.coli catalyse the following reactions. (i) Biotin carboxylase carrier protein

(9.42) (ii) Catalysis using transcarboxylase

(9.43) (e) Many oligomeric enzymes are regulatory in nature with regulatory sites and catalytic sites residing on separate sub-units. (f) An assembly of enzymes would allow highly efficient movement of intermediates between reactants and products (than individual enzymes).

9.12.1

Glycolytic Enzymes

These enzymes convert glucose-6-phosphate and nicotinamide adenine dinucleotides (NAD+ ) to pyruvate and NADH by producing two Table 9.4 Data on glycolic enzymes. Enzyme Phosphorylase A Phosphofructokinase Fructose diphosphatase Glyceraldehyde-3Phosphatase dehydrogenase Creatine kinase Lactic dehydrogenase Pyruvic kinase

Number of of sub units 4 2 2 2 2

Molar mass 92,500 78,000 29,000 37,000 72,000

Total molar mass 3,70,000 1,90,000 1,30,000

2 4 4

40,000 35,000 57,200

80,000 1,50,000 2,37,000

1,40,000

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Biophysical Chemistry

molecules of ATP according to C6 H12 O6 + 2NAD+ + 2ADP + 2P → 2CH3 C

= OCOOH (Pyruvic acid) + 2ATP + 2NADH + 2H+

(9.44)

Each enzyme in this group is not a simple monomeric type of protein but oligomeric type consisting of varying number of sub-units.

9.13

Isoenzymes

An enzyme which has multiple molecular forms in the same organism catalyzing the same reaction is known as isoenzyme. An example of this class is lactic dehydrogenase (LDH) which occurs in five forms in organs of many vertebrates. One type predominates in the heart and known as heart LDH. The other one is characteristic of skeletal muscles and is referred as muscle LDH. While the heart LDH consists of four identical monomers, called H sub-units, muscle LDH consists of four identical M units, each sub-unit being enzymatically inactive. Both types of sub-units have different amino acid compositions and different immunological properties. The two sub-units are believed to be produced by different genes.

9.14

Bifunctional Oligomeric Enzymes

A typical enzyme in this category is Tryptophan synthetase of E.coli. It consists of two proteins designated as A and B. The complete tryptophan synthetase consists of two A proteins and one B protein designated as α2 β 2 . The α2 β 2 protein catalyses the reaction. α2 β 2 Indole-3-glycerophosphate + L-SerineGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGA in presence of pyridoxal phosphate L-Tryptophan + glyceraldehyde-3-phosphate

(9.45)

Individually, the α and β proteins catalyse the reactions. α BG Indole+glyceraldehyde-3-phosphate Indole-3-glycerophosphate FGGGGG GGGG (9.46)

Enzymes 

β2 Indole + L-SerineGGGGGGGGGGGGGGGGGA L-Tryptophan pyridoxylsulfate

9.15

203

(9.47)

Multienzyme Complexes

In this case, a number of complexes are described which consist of an organized mosaic of enzymes in which each component enzyme is so located as to allow effective use of individual reactions catalysed by them. For example, the E-coli pyruvic acid dehydrogenase complex catalyses the oxidation of pyruvic acid to acetyl CoA and CO2 . The total complex (Mol. Mass 40 × 106 ) consists of three separate catalytic active components EI, EII and EIII named pyruvic dehydrogenase, dihydrolipoyl transacetylase and dihydrolipoyl dehydrogenase. The manner in which this complex enzyme acts is shown below: Scheme depicting the catalytic activity of components E1 , E2 and E3

An even more complex multienzyme system is the fatty acid synthetase complex which occurs as a tightly knit group responsible for the conversion of acetyl CoA and malonyl CoA to palmitic acid. These complexes are found in animal and yeast cells. In bacteria and plants, these enzymes are completely separable and are easily purified.

204



Table 9.5 Activation parameters for the reactions of some enzymes. ΔG  ΔH  TΔS (kJ mol−1 ) (kJ mol−1 ) (kJ mol−1 ) 127.1 92.5 −34.7

For the same reaction above, in presence of enzyme cytidine deaminase (from E.Coli)

58.6

62.3

3.8

56.1

−42.2

k (rate constant for hydrolysis) 3 × 10−10 s−1

kcat = 300 s−1

Biophysical Chemistry

Reactions

Reactions

Table 9.5 (Continued.) ΔG’ (kJ mol−1 )

ΔH’ (kJ mol−1 ) 113.4

k (rate const. for hydrolysis)

Enzymes 

ΔG0 (binding) of cytidine with the enzyme cytidine deaminase = −22.0 kJ mo1−1 TΔS◦ = −31.8 kJ mol−1 (at 298 K), K for binding = e−ΔG0 /RT = 9.12 × 103

TΔS’ (kJ mol−1 ) −3.4

205

206



9.16

Biophysical Chemistry

Modification of the Specificity of an Oligomeric Enzyme

The enzyme lactose synthetase catalyses the synthesis of lactose by the reaction UDP-galactose + glucose  UDP + Lactose (9.48) in the mammary gland. This enzyme (isolated from raw milk) is separable into proteins A and B. None of them catalyse reaction (9.48). Protein A, however, catalyses the reaction UDP galactose + N - acetylchol glucose amine

←→ N-acetyl lactosamine + UDP

(9.49)

The addition of protein B inhibits the reaction (9.49) and in presence of glucose allows catalysis of reaction (9.48). Thus protein B modifies the substrate specificity of protein A by combining to form lactose synthetase complex. Protein B is alpha-lactalbumin found only in mammary glands while protein A is distributed widely in animal tissues. This leads to the formation of lactose in mammary glands.

9.17

Measurement of Enzymatic Activity of Lactose Dehydrogenase (LDH) obtained from Different Organisms

LDH catalyses the interconversion of pyruvate and lactate with concomitant interconversion of NADH and NAD+ . The reaction scheme is

Table 9.6 Enzymatic activity of lactose dehydrogenase. Enzyme

Muscle type LDH D-glyceraldehyde-3-phosphate dehydrogenase D-glyceraldehyde-3-phosphate dehydrogenase Muscle glycogen phosphorylase-b Muscle glycogen phosphorylase-b

Animal

Temp (K)

kJ mol−1

Vmax (μ mol substrate)

J mol−1 K−1

ΔG ± 52.3 36.8 62.3

ΔH ± 52.3 36.8 77.0

ΔS± −10.5 −56.5 47.3

Rabbit Tuna Rabbit

308 308 308

1080 4500 180

Ea 54.8 39.1 79.5

Cod

308

225

60.7

61.9

58.1

−12.1

Rabbit Lobster

303 303

60 70.8

88.7 66.5

63.6 63.2

86.2 64.0

74.5 3.4 Enzymes  207

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Biophysical Chemistry

The above data pertains to the following reaction

9.18

Turn Over Rates (T.O.R) of Some Enzymes

T.O.R is defined as the number of substrate molecules that can be converted to the product by a single molecule of enzyme (per unit time). T.O.R is also given by T.O.R = k cat =

Vmax [ ET ]

where ET = total enzyme concentration.

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Table 9.7 Turn over numbers for selected enzymes. Enzyme T.O.R (moles of product sec−1 mol enzyme−1 ) Carbonic anhydrase 6 × 105 Catalase 9.3 × 104 β-galactosidase 2.0 × 102 Chymotrypsin 100.0 Tyrosine 1.0 Staphylococcal nuclease 95.0 Cytidine deaminase 299.0 Triose phosphate isomerase 4300 Cyclophilin 13,000

Enzymes 

209

Table 9.7 (Continued) T.O.R (moles of product sec−1 mol enzyme−1 ) Ketosteroid isomerase 66,000 3-ketosteroid isomerase 2.8 × 105 Acetylcholinesterase 2.5 × 104 Penicillinase 2.0 × 103 Lactate dehydrogenase 1.0 × 103 DNA polymerase I 15 Tryptophan synthetase 2 Lysozyme 0.5 Enzyme

(10) (11) (12) (13) (14) (15) (16) (17)

9.19

Immobilisation of Enzymes

Immobilised enzyme systems “fix” the enzyme in warm solution of agar, which on cooling sets to a gel. This gel can be cut off into small pieces and can be used to catalyse a reaction. The enzyme can be recovered after the reaction and can be reused. Because of the advantage to recover them again, they find extensive application in industry. Once a biocatalyst has been immobilised, it can be put to use in a range of continuous flow reactors enabling a continuous supply of substrate that can be converted to product. Table 9.8 Some industrial processes using enzymes. Industrial process High fructose col syrup Lactose hydrolysis Aspartame production L-aspartic acid production Semisynthetic penicillin production Acrylamide production Transesterification of food oils

Enzyme used Glucose isomerase Lactase Thermolysin Aspartase Penicillin acylase Nitrile hydratase Lipase

Rate of production (in tons year−1 ) 107 105 104 104 104 105 105

210

Alkaline proteases

(3)

Amino acylase

(4) (5)

Amyloglucosidase β-galactosidase

(6)

α-amylase

(7)

Glucose isomerase

(8)

Penicillin acylase

(9)

L-Asparaginase

(10)

Urokinase

Biophysical Chemistry

(2)

Table 9.9 Illustrative examples of industrial catalysts. Reaction Source Application Protein digestion Aspergillus niger Coagulation of milk in cheese Kluyveromyces lactis manufacture Protein digestion Bacillus species Detergents and washing powders Hydrolysis of acylated Aspergilus species Production of L-amino acids L-amino acids Dextrin hydrolysis Aspergillus species Production of glucose Lactose hydrolysis Aspergillus species Hydrolysis of lactose in milk or whey Starch hydrolysis Bacillus species Conversion of starch to glucose or dextran Conversion of glucose to Spectromyces species High fructose syrup production fructose Penicillin sidechain E.Coli 6-APA formation for production cleavage of semisynthetic pencillins Enzymes as therapeutic agents Removal of L-Asparagine E.Coli Cancer chemotherapy, essential for tumor growth especially for leukemia Plasminogen activation Human Removal of fibrin clots from blood stream



(1)

Name of enzyme Acid proteases

Name of enzyme (11) (12)

Glucose oxidase Peroxidase

(13)

Urease

(14)

Luciferase

(15)

Lysozyme

(16)

Nucleases

(17)

DNA polymerases

Table 9.9 (Continued) Source Enzymes as Analytical Reagents Glucose oxidation Aspergillus niger Dye oxidation using H2 O2 Horse radish Reaction

Hydrolysis of urea to CO2 and NH3 Biduminescence Hydrolysis of 1, 4-glycosidic bonds Hydrolysis of phosphodiester bonds DNA synthesis

Jack bean Marine bacteria or firefly Egg white (Hen) Various bacteria Thermus aquaticus

Application Detection of glucose in blood Quantification of hormones and antibodies Urea quantification in blood

Enzymes 

Bioluminescent assay involving ATP Disruption of mucopeptide in bacterial cell walls Enzymes used in genetic manipulation to cut DNA DNA amplification in polymerase chain reaction

211

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Biophysical Chemistry

Table 9.10 Michaelis-Menten constants for some enzyme substrate reactions. Enzyme Substrate Km (mM) (a) Carbonic anhydrase CO2 12 (b) Hexokinase Glucose 0.15 Fructose 1.5 (c) β-galactosidase Lactose 4 (d) Glutamate dehydrogenase NH4+ 57 Glutamate 0.12 NAD+ 0.025 NADH 0.018 (e) Aspartate amino Aspartate 0.9 transferase α-ketoglutarate 0.1 Oxaloacetate 0.04 Glutamate 4 (f) Threonine deaminase Threonine 5 (g) Pyruvate carboxylase HCO3− 1.0 Pyruvate 0.4 ATP 0.06 (h) Penicillinase Benzyl penicillin 0.05 (i) Lysozyme Hexa-N-acetyl glucosamine 0.006

Illustrative Calculation of Km The estimation of Km can be demonstrated with the following examples: Reaction of horse radish peroxidase with H2 O2

Keq =

k2 = 2 × 10−8 k1

k1 = 1.2 × 107 lmol−1 sec−1 ; k2 = 2 × 10−8 × 1.2 × 107 = 0.24 sec−1 ; k3 = 5.1 sec−1 Km =

k2 + k3 0.24 + 0.51 5.34 = = = 4.45 × 10−7 7 k1 1.2 × 10 1.2 × 107

It is essential to point out that other interpretations of Km also exist such as the one given by Briggs and Haldane. According to them, Km represents the ratio between the sum of the two unimolecular rate constants and the bimolecular rate constant representing the formation of the enzyme substrate complex.

Enzymes 

213

Questions (1) The activation energy of a chemical reaction is 60 kJ mol−1 . An enzyme employed as a catalyst for the same reaction has an activation energy of 30 kJ mol−1 . Calculate the ratio of the rate constants. (Assume that the frequency factor is the same in both cases). (The temperature may be taken as 27◦ C). Solution: k che Ae− Eche /RT e− Eche /RT = = k enz Ae− Eenz /RT e− Eenz /RT or k che − Eche Eenz = + k enz RT RT −60 30 = + − 3 8.313 × 10 × 300 8.313 × 10−3 × 300 1 = (−60 + 30) 2.494 = +0.4 × −30 = −12 −12 k log che = = −5.21 k enz 2.303 k log che = 6.17 × 10−6 k enz ln

(2) In an enzyme catalyzed reaction, a substrate was analyzed with time, its initial concentration being 10−4 M. After 10 min of the reaction, 5 percent of the substrate reacted. Calculate the amount of product formed after 30 min. (Assume a 1st order decomposition of substrate). Solution: a 2.303 log t a−x 10−4 2.303 log = −4 10 10−4 − 10100×5

k = 364 =

10−4 2.303 log −4 10 10 − 5 × 10−6 10−4 2.303 log = − 4 10 1 × 10 − (5 × 10−4 × 10−2 )

=

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Biophysical Chemistry

10−4 23.3 log 10 (1 − 0.05) × 10−4 1 2.303 2.303 log = = × 0.0223 10 0.95 10 = 0.00513 min.

k=

after 30 min, 10−4 2.303 log 0.00513 = 30 (a − x)  −4  0.00513 × 30 10 log = = 0.0668 a−x 2.303  −4   1 × 10−4 10 = 1.166 or ( a − x ) = a−x 1.166

= 0.8576 × 10−4 amount reacted = 1 × 10−4 − 0.8576 × 10−4

= 0.1424 × 10−4 or product formed = 1.424 × 10−5 M (3) Write the balanced equation for the combination of oxaloacetate (OAA) and the acetyl group from acetyl coenzyme A (ACCOA), in the presence of H2 O, to form citrate ions, thiol coenzyme, and hydrogen ions. Solution: ACCOA0 + OAA2− + H2 O  CIT3− + COAS− + 2H+ (4) Identify all the products in the hydrolysis of ATP given below. ATP4− + H2 O  product Solution: ATP4− + H2 O  ADP3− + HPO24− + H+ (5) The membrane potential is 50 mV during the transport of K+ ions. If the equilibrium potential is 59 mV and the current is −0, 5μA cm−2 , estimate the ionic conductance in S cm−2 .

 + Kout RT ln VK+ = + F Kin

Enzymes 

215

Solution: Current I = g(Δφ − VK+ )

−0.5 × 10

−6

A cm

−2

= g(0.05 − 0.059) V

Conductance g = 5.56 × 10−5 S cm−2 (6) Write down the reaction between an enzyme and a substrate leading to a product. Derive the equation relating the velocity of the reaction to the Michaelis–Menten constant. (7) Describe briefly the various modes of inhibition exhibited by certain compounds on the activity of an enzyme. (8) What are allosteric enzymes? Discuss their mode of reaction with a substrate. (9) Write the equation for the net flux in the following scheme assuming Michaelis-Menten mechanism: k +1 k +2 A + E FGGGGGGGB GGGGGGG C FGGGGGGGB GGGGGGG B + E k −1 k −2

10

Co-Enzymes and Vitamins 10.1

Introduction

Co-enzymes are substances that enhance the action of enzymes. They are small organic non-protein molecules that bind with a protein molecule (apoenzyme) to form the active enzyme (holoenzyme). They can not by themselves catalyse a reaction but they can help enzymes to do so. Coenzymes are a type of cofactors that temporarily bind to an enzyme to change its configuration or shape.

Figure 10.1 Conversion of an apoenzyme to a holoenzyme.

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_10

217

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Biophysical Chemistry

Once the enzyme is in an active form, it can build upon or break down reactents to products.

Figure 10.2 Conversion of an active enzyme with substrate to yield an enzyme with products.

Functioning of Co-enzymes Co-enzymes bind temporarily to apoenzymes and detach themselves easily after a biochemical reaction takes place. Other types of cofactors, known as “Prosthetic groups” which work as co-enzymes, are metal ions bind more tightly to their apoenzymes through covalent bonding and cannot easily detach themselves from the enzyme. Once the cofactor (enzyme or metal ion prosthetic group) and apoenzyme form the complex, it becomes a holoenzyme (active form of the enzyme). Co-enzymes help transfer of compounds between enzymes and also connect compounds to the active site of enzyme.

10.1.1

Importance and Need for Co-enzymes

Co-enzymes are mainly responsible for the transfer of functional groups, electrons, hydrogen atoms or ions and energy. Some enzymes won’t function in the absence of vitamins. Vitamin deficiencies arise when some vitamins are converted into co-enzymes. Some combinations of enzyme-coenzyme systems in presence of vitamins for effecting some functions are given below.

10.1.2

Support for Proper Enzyme Function

Many diseases arise in the body due to nutritional deficiencies. Though co-enzymes function at molecular level, co-enzymes and their vitamin precursors are very important for health. The vitamin precursors are found in

Co-Enzymes and Vitamins 

Table 10.1 Typical combinations of enzyme-co-enzyme systems in presence of vitamins for their effective functioning. Co-enzyme Enzyme Vitamin Function Precursor Methyl cobalamin (B-12) Methionine synthase B-12 Transfers methyl group NAD (nicotinamide adenine Malate dehydrogenase, pyruvate B-6 Transfers electrons and H-atoms dinucleotide) dehydrogenase FAD (Flavine adenine D-lactate dehydrogenase B-2 Transfers electrons and H-atoms dinucleotide) Co-enzyme Q (Ubiquinone) Cytochrome C-oxido reductase B-5 Transfers electrons and H-atoms Biotin Propionyl-CoA carboxylase Biotin Carries carboxyl groups

219

220



Biophysical Chemistry

whole foods, plant foods, nuts, peanuts, beans etc. Considering the correct cofactor form of vitamin B12 , it is necessary to check for methylcobalamin as the body uses this enzyme to detoxify the tissues of homo cysteine to convert into methionine. Adenosyl cobalamine is another active form of B12 which is vital for the metabolism, proteins and fats. These two cobalamines are important for vascular and brain health.

10.2

Relation between Co-enzymes and Vitamins

Many enzymes are simple proteins consisting of one or more amino acid chains. Other enzymes contain a non-protein component called a cofactor that is necessary for the functioning of enzyme. There are two types of cofactors: (i) inorganic ions like Zn++ , Cu2+ , and (ii) organic compounds known as co-enzymes. Most co-enzymes are vitamins or derived from vitamins.

10.3

Vitamins

10.3.1

Definition and Types

They are nutrients needed by the body to function and fight disease; types of vitamins are: (i) Fat soluble vitamins and (ii) Water soluble vitamins. The first category are stored in fat cells of the body where as the second category are not stored in the body. They need to be replaced daily. Vitamins are not a source of energy but help enzymes which generate energy from nutrients such as carbohydrates and fats.

10.3.2

Some Specific Functions of Vitamins

1. Vit-A: Production of retinol which is used in the rods and cones of eyes to sense light and prevent night blindness. Also, it is important for healthy teeth, bones, skin and immune system. 2. Vit-B: Aid in energy production in the body, making of red blood cells, making of new DNA cells, needed for healthy nerve and brain function, and also needed for intestinal and cardiovascular health. 3. Vit-C: Is an antioxidant, helps prevents cell damage and reduces heart disease and risk of certain cancers. It is a vital ingredient information of collagen. Also it helps in faster wound healing.

Co-Enzymes and Vitamins 

Table 10.2 Water soluble vitamins along with their co-enzymes and their physiological functions. Vitamin Co-enzyme Function of co-enzyme Deficiency causes Vit-B1 (Thiamine) Thiamine Pyrophosphate Decarboxylation reactions Beriberi Vit-B2 (Riboflavin) Flavin mono nucleotide or Oxidation reduction reactions — Flavin adenine dinucleotide involving two H-atoms Vit-B3 (Niacin) NAD or NADP Oxidation-reduction reactions Pellegra involving hydride ion Vit-B6 (Pyridoxin) Pyridoxyl phosphate Many reactions including — transfer of amino groups Vit-B12 (Cyano cobalamine) Methyl cobalamin or Intramolecular rearrangement Pernicious anaemia deoxyadenosylcobalamin reactions Biotin Biotin Carboxylation reactions — Folic acid Tetrahydrofolate Carrier of one carbon units such Anaemia as formyl group Pantothenic acid Co-enzyme-A Carrier of acyl groups — Vit-C (Ascorbic acid) None Antioxidant, formation of Scurvy collagen proteins found in tendons, ligaments and bone

221

222

 Note: Vitamins C and E as well as provitamine β-carotene act as antioxidants in the body. Antioxidants prevent damage from free radicals. It is known that such radicals form through metabolic reactions involving O2 but they can also form by environmental factors such as pollution and radiation. β-carotene is known as a provitamin because it is converted to Vitamin-A in the body.

Biophysical Chemistry

Table 10.3 Fat soluble vitamins and their physiological function. Physiological function Effect of deficiency Formation of vision pigments and Night blindness differenciation of epithelial cells Vit-D (Chole calciferol) Improves the body ability to absorb calcium Softening of bones (Osteomalacia), rickets and phosphorus in children Vit-E (Tocopherol) Fat soluble antioxidant Damage to cell membranes Vit-K (Phylloquinone) Formation of prothrombin, a key enzyme in Longer time required for blood clotting blood clotting process Vitamin Vit-A (Retinol)

Co-Enzymes and Vitamins 

223

Table 10.4 Typical examples of fat-soluble vitamins and their source. Vitamins Source of the vitamins Vit-A Orange coloured fruits, vegetables, dark leafy greens like kale Vit-D Fortified milk, dairy products, cereal, sunshine is a good source of this vitamin Vit-E Fortified cereals, green leafy vegetables, nuts and seeds Vit-K Dark green leafy vegetables, turnip or beet greens Table 10.5 Water soluble Vitamins: Vitamins B-1 to B-7, B-9, B-12, Vitamin C and their source. Vit-B-1 (Thiamin) Whole gains, enriched grains, nuts Vit-B-2 (Riboflavin) Whole grains, enriched grains and dairy products. Vit-B-3 (Niacin) Meat, fish, poultry, whole grains Vit-B-5 (Pantothenic acid) Meat, poultry, whole grains Vit-B-6 (Pyridoxine) Fortified cereals, soy products Vit-B-7 (Biotin) Meats and fruits Vit-B-9 (Folic acid) Leafy vegetables Vit-B-12 (Cyanocobalamin) Fish, poultry, meat, dairy products Vit-C Citrus fruits like oranges, grape fruits, red, yellow and green peppers

10.4

Biochemical Functioning of the B-Vitamin Group

10.4.1

Niacin

The biochemically active form of this vitamin is nicotinamide whose structure is

It is widely distributed in plant and animal tissues. The co-enzyme forms are nicotinamide nucleotides. The nicotinamide nucleotides are co-enzymes for the “dehydrogenases” enzymes that catalyse oxidationreduction reactions. For example, alcohol dehydrogenase, catalyses the

224



Biophysical Chemistry

oxidation of ethanol with simultaneous reduction of NAD+ according to CH3 CH2 OH + NAD+  CH3 CHO + NADH + H+

(10.1)

The equilibrium constant K of the above reaction is 10−4 at pH = 7.0 and at pH = 9.0 is 10−2 . The shift in the equilibrium constant towards right is due to the replacement of H+ ions by OH− at higher values of pH.

The enzymes possess several functional roles. The dehydrogenases that require NAD+ and NADP+ catalyse the oxidation of alcohols, aldehydes, α-amino acids and α-, β-hydroxy carboxylic acids. Some reactions catalysed by nicotinamide nucleotides (enzymes) are given in Table 10.6. The reduction of acetaldehyde to ethanol by yeast (in presence of alcohol dehydrogenase) is linked to the oxidation of glyceraldehyde-3phosphate (in presence of glyceraldehyde-3-phosphate dehydrogenase, according to the scheme.

(a) (b) (c) (d) (e)

(g) (h)

Co-Enzymes and Vitamins 

(f)

Table 10.6 List of reactions catalysed by nicotinamide nucleotides. Enzyme Co-enzyme Substrate Product Alcohol dehydrogenase NAD+ Ethanol Acetaldehyde Glycerophosphate NAD+ Sn-glycerol-3Dihydroxyacetone phosphate dehydrogenase phosphate Lactic dehydrogenase NAD+ Lactate Pyruvate Malic enzyme NADP+ L-malate Pyruvate + CO2 + Glyceraldehyde-3-phosphate NAD Glyceraldehyde-31, 3-diphospho glyceric acid dehydrogenase phosphate + H3 PO4 Glucose-6-phosphate NADP+ Glucose-6-phosphate 6-Phosphogluconic acid dehydrogenase Glutathrone reductase NADPH Oxidised glutathione Reduced glutathione Quinone reductase NADH, NADPH p-benzoquinone Hydroquinone

225

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Biophysical Chemistry

Another way in which nicotinamide nucleotides function is in the reduction of flavin co-enzymes. For example, the reduction of oxidized glutathione (GSSG) by glutathione reductase in presence of NADH. The reaction is glutathione NAD+ + H+ + GSSG GGGGGGGGGGGGGGGGGA reductase NADH + 2 GSH (reduced glutathione)

(10.2)

The above reaction is facilitated by the presence FAD due to the large ΔG  required by reaction (10.2) and is broken down into two reactions of smaller ΔG  as shown below: NADH + H+ + FAD → NAD+ + FAD − H2 FAD − H2 + GSSG → FAD + 2GSH

(10.3) (10.4)

The nicotinamide nucleotides and their dehydrogenases are important in the kinetic and mechanistic study of enzyme reactions for two reasons: (i) These hydrogenases are available in highly pure crystalline forms; and (ii) Easy distinguishability of reduced nicotinamide nucleotide from its oxidized form because the reduced form absorbs strongly at 340 nm where the oxidized form does not absorb.

Co-Enzymes and Vitamins 

10.4.2

227

Riboflavin B2

It consists of ribitol attached to 7, 8-dimethyl alloxane. Its structure is

The vitamin occurs in nature as a constituent of two flavin prosthetic groups, flavin mono nucleotide (FMN) and flavine adenine dinucleotide (FAD). Riboflavin is produced in green plants, fungi and many bacteria.

Table 10.7 Redox potential data on water soluble B-Vitamins. Reaction Formal potential (V) NAD+ + H+ + 2e  NADH −0.32 + FAD + 2H + 2e  FADH2 −0.22 NADH + H+ + 12 O2  NAD+ + H2 O +1.44 The E0 values are against [H+ ] = 10−7 i.e., pH = 7 at 298K and is not with respect to standard hydrogen electrode (pH = 0).

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10.4.3

Biophysical Chemistry

Flavin Adenine Dinucleotides (FAD)

Riboflavin functions as a coenzyme because of its ability to undergo redox reactions.

These enzymes belong to a group of proteins termed flavoproteins. Some reactions catalysed by these enzymes are listed in Table 10.8.

10.4.4

Metalloflavoproteins

They are characterized by their multicomponent structure. They transfer electrons from substrate to oxygen, NO3− , NO2− , NAD+ and ferricytochrome C. A metalloflavoprotein is a single isolable enzyme moiety. The iron in metalloflavoproteins is a single isolable enzymemoiety. The iron in metalloflavoproteins is a single isolated enzyme moiety and is frequently of the non-heme type found in iron-sulphur proteins known as ferridoxins. In these molecules the iron atom is bonded to the sulfur atoms of cysteine residues and mutually linked by S-bridges.

10.4.5

Lipoic Acid

It exists both in oxidized and reduced forms due to the ability of the disulfide linkage to undergo reduction.

Yeast and liver are rich sources of this compound. Lipoic acid is bonded to the lysyl residues of the protein in lipoyl enzymes as for example in EN-lipoyl.

Note: Many flavoproteins react directly with molecular O2 to produce H2 O2 ; NHI = non hemetype.

Table 10.8 Typical examples of enzymes (belonging to group of flavoproteins) and reactions catalysed by them. Enzyme Electron donor Product Co-enzyme and other (substrate) components (1) D-amino acid and L-amino acid D- and L-amino α-keto acids + NH3 2 FAD oxidases acids (2) L-amino acid oxidase (kidney) L-amino acid α-keto acids + NH3 O2 → H2 O FMN (3) L(+)-lactate dehydrogenase (yeast) Lactate Pyruvate 1 FMN; 1 heme (cyt B5) (4) Glycolic acid oxidase Glycollate Glyoxalate FMN + (5) NAD ± cytochrome C-reductase NADH NAD 2 FAD, 2 MoNHI (6) Aldehyde oxidase (liver) Aldehydes Carboxylic acids FAD, Fe Mo (7) α-glycerol phosphate Sn-glycerol-3 Dihydroxy acetone FAD, Fe dehydrogenase phosphate phosphate (8) Succinic dehydrogenase Succinate Fumarate FAD, Fe, NHI (9) Acyl-CoA (C6 - C12 ) dehydrogenase Acyl-CoA Enoyl CoA FAD (10) Xanthine oxidase Xanthine Uric acid FAD, Mo, Fe (11) Lipoyl dehydrogenase Reduced lipoic acid Oxidised lipoic acid 2 FAD

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Biophysical Chemistry

L-lysine whose structure is

Lipoic acid is a cofactor of the multienzyme complexes, pyruvic dehydrogenase and α-glutaric dehydrogenase. In these complexes, the lipoyl containing enzymes catalyse the generation and transfer of acyl groups.

10.4.6

Biotin

It serves as a growth factor for yeast and bacteria. Egg white contains a basic protein known as Avidin and it has great affinity for biotin or its simple derivatives. Biotin + Avidin  Product with equilibrium constant ≈ 1015

(10.7)

This large value indicates that the equilibrium is entirely shifted to the right. The structure of Biotin is

Liver and yeast are excellent sources of Biotin. This vitamin occurs mainly in the form bound to protein E - N - Lysine moiety.

10.5

Biochemical Function of Biotin

The specific enzyme protein bound to Biotin is associated with many carboxylation reactions. The overall reaction catalysed by Biotin dependent carboxylase may be represented as

Co-Enzymes and Vitamins 

231

The conversion of acetyl CoA to malonyl CoA in E.coli follows the sequence in which three proteins participate: (i) biotin carboxylase, (ii) biotin carboxyl carrier protein (BCCP), and (iii) acetyl CoA, malonyl CoA carboxylase.

10.5.1

Thiamin

The structure of this compound is:

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Biophysical Chemistry

It occurs in the outer coats of the seeds of many plants including cereal grains. Unpolished rice and foods made of whole wheat are good sources of this vitamin. In yeast and animal tissues it occurs as the co-enzyme thiamine phosphate or co-carboxylase whose structure is

10.5.2

Biochemical Function

Thiamine pyrophosphate acts as a co-enzyme in α-keto acid dehydrogenases, pyruvic decarboxylase, transketolase, phosphoketolase. For example, Phospho D-xylulose-5-P+Pi FGGGGGGGGGGGGGGGGGGGGGGGGB GGGGGGGGGGGGGGGGGGGGGGGG Acetyl-P+glyceraldehyde-P ketolase, co-carboxylase (10.11)

10.5.3

Vitamin B-6 Group

The compounds belonging to this group are pyridoxal, pyridoxine and pyridoxamine whose structures are

Cereal grains are especially rich sources of this group of vitamins. Pyridoxal is converted to pyridoxal phosphate in the liver according to the scheme.

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233

Biochemical function: Pyridoxal phosphate is a versatile derivative which takes part in the catalysis of several important amino acid metabolisms known as transmission, decarboxylation and racemisation. It is inferred from the above data that the reduction of Vitamins D3, D2, E and α-tocopherol is favourable on the basis of Gibbs free energy considerations.

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 Biophysical Chemistry

Table 10.9 Half wave potential data of a few vitamins and related compounds. Vitamin Reaction E1/2 (V) vs. NHE Medium D group vitamins D3 (Cholecalciferol) D → Dox +1.45 CH3 CN, CH2 Cl2 E E → Eox +1.20 CH3 CN α-tocopherol Eox → Eox,2 +0.80 CH3 CN Vit-K Kred → K −0.60 CH3 CN + 50 mM H2 O Phylloquinone Kred,2 → Kred , Kred,2 → Kred −1.2, −0.5 CH3 CN + 7.2 M H2 O

Co-Enzymes and Vitamins 

10.6

235

Adsorption of Riboflavin

Using Langmuir isotherm in the form C 1 C = + a K as where C = equilibrium concentration of riboflavin, a = number of moles of riboflavin adsorbed per gm of clay, K = Langmuir adsorption coefficient. Thiamine has two ionizable groups viz. (i) amino and (ii) hydroxyl. The mean dissociation constant at different temperatures is provided in Table 10.10. Table 10.10 Average dissociation constant of thiamine at different temperatures. Temp (K) pKa 288 9.43 293 9.33 298 9.23 303 9.15 308 9.05 313 8.96

Scheme depicting catalytic decarboxylation of pyruvate by thiamine O OH

O H3C

C

COO + Thiamine

H3C

C

C CH3

H acetoin +CH3COCOO b

H a

CO2 + CH3CHO

O OH

CO2 + H3C C C CH3 COO (acetoacetate)

Rate of evolution of CO2 = 2.25 × 10−3 mols l−1 hr−1 . Rate of formation of acetoin = 1.13 × 10−3 mols l−1 hr−1 . From the above reaction, it is deducted that acetoin decomposes at a faster rate in comparison with its rate of formation through the reaction between pyruate and thiamine.

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Biophysical Chemistry

Table 10.11 Kinetic data on the reaction of hydrated e− with cobalamine. Rate constant Reaction (dm3 mol−1 sec−1 ) − e (hyd) + cyanocobalamin −→ Vit-B12 3.8 × 1010 · OH + cyanocobalamin −→ yellow brown compound 6.5 × 109 −· CO2 + hydroxocobalamine −→ product (carboxyl radical) 1.45 × 109 CO2− + Vitamin B12 r −→ cobalamin (Vit-B12 ’s) 8.2 × 108

− Note: ehyd and OH were generated by pulse radiolysis of water.

Redox chemistry of cobalamin and iron—sulphur containing cofactors (in tetra-chloroethylene reductase) of dehalobactorretus. (dehalobacter is a halogen removing rod shaped bacterium). Tetrachloroethene reductase is an enzyme specific for removing halogens from any compound like dehalobacter reductus. This substance contains cobalamine and iron—sulphur cofactors. It has a mass of 60 k Da = 60,000 Daltons = 60,000 a.m.u. Its reduction was studied by optical and electron spin resonance spectroscopy. Table 10.12 Redox potential of cobalamines. Reaction Redox potentials/V Co+1 −→ Co2+ + e −0.350 Co2+ −→ Co3+ + e 0.150 The redox chemistry of iron-sulphur containing cofactors in tetrachloro ethylene reductase dehalobactorretus can be represented as below:

[4Fe − 4S]1+ −→ [4Fe − 4S]2+ + e − 0.480 The above data is presented in decreasing order of redox potentials. Hence the Gibbs free energy changes too increase in the same order. In the case of NAD+ , NADH system, it can be deduced that the Gibbs free energy change has a large positive value. Folic acid gives a pair of well defined redox waves at a 2-mercapto benzothiazole self assembled gold electrode. It can bind strongly 2-MBT and form a closely packed monolayer whose average electron transfer rate is 0.085 sec−1 with a 2P, 2H+ transfer. The maximum surface coverage is 2.8 × 10−10 mol cm−2 and the adsorption equilibrium constant is 4 × 105 lmol−1 .

Co-Enzymes and Vitamins 

Table 10.13 Redox potential data against S.H.E. at pH = 7.0. Redox pair Eo (V) O2 /H2 O +0.82 Vit-E oxidized/reduced +0.37 Co-enzyme Q-10 oxidised/reduced +0.10 Vit-C oxidized/reduced +0.08 Cystine/cysteine −0.22 Glutathione oxidised/reduced −0.24 Lipoate oxidized/reduced −0.29 + + NAD , NADH, NADP /NADPH −0.32 H+ /H2 −0.42 Biotin reduction in aprotic solvents. −1.6 to −1.8 (V) vs. − The e is attached to –COOH group to Ferrocene/Ferricenium couple form a carboxylate anion Irreversible oxidation of pyridoxine in 0.50 AN

237

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Biophysical Chemistry

Table 10.14 Kinetic data on the oxidation of pyridoxine. Temp (K) 288 293 298 303 308 k c × 103 (dm3 mol−1 sec−1 ) 2.5 3.0 3.7 4.2 4.8 Kc (dm3 mol−1 ) 207 199 190 196 79 Table 10.15 Protonation constants of folic acid and stability constants of metal complexes. Metal ion log K1 ( M : 1) log K2 ( M : 2) log K3 ( M : 1) H+ 8.6 5.1 3.63 Al (III) 9.20 (1 : 1) 7.66 (1 : 2) 8.11 (1 : 3) Pb (II) 14.83 (1 : 2) 13.22 (1 : 3) Ba (II) 14.37 (1 : 2) 12.97 (1 : 3) Ca (II) 7.10 (1 : 1) Cel (II) 12.71 Co (II) 14.81 (1 : 1) 13.93 (1 : 2) 12.24 (1 : 3) Fe (III) 14.70 (1 : 1) 13.54 (1 : 2) 12.04 (1 : 3) Li (I) 2.50 (1 : 3) Mg (II) 14.05 (1 : 1) 12.76 (1 : 2) 10.01 (1 : 3) Ni (II) 14.37 (1 : 1) 13.60 (1 : 2) 11.85 (1 : 3) Cr (III) 8.12 (1 : 1) Sr (II) 14.42 (1 : 2) 12.92 (1 : 3) Th (IV) 12.92 (1 : 1) 9.53 (1 : 2) 7.14 (1 : 3) Zn (II) Cu (II) 14.06 (1 : 1) 11.59 (1 : 2) 8.62 (1 : 3)

Note: On titration with dilute KOH (0.2M), the maximum number of protons that can be released from folic acid is 3 in the pH range 2.8–12.0. Folic acid functions as a triprotic acid (H3 -FH), the protonic centers being 1st carboxyl group, 2nd carboxyl group and imino group of glutamic acid. One proton is released from 1st carboxyl group in the pH range 3.63–4.95, the second proton is released from 2nd carboxyl group in the pH range 5.10–8.40, the 3rd proton is released from the imuno group in the pH range 8.60–9.20. The equilibria established are H 3 − FA  H 2 FA− + H + ( pH = 3.63 − 4.95) H 2 − FA−  HFA2− + H + ( pH = 5.10 − 8.40) HFA2−  FA3− + H + ( pH = 8.60 − 9.20)

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239

Table 10.16 Conductances of the metal complexes formed at two points of addition in the titration of 25 ml of metal ions (1 × 10−3 M) with folic acid (0.01 M). Metal ion FA added Conductance (mho cm−1 ) ×106

Ca (II) 3ml 6ml

Co (II) 3ml 6ml

Cu (II) 3ml 6ml

Fe (III) 3ml 6ml

42

15

10

5

54

48

36

10

The addition of FA increases the specific conductance of the metal ions while passing from Cd2+ to Fe3+ . This suggests that the ionic character of the complex is enhanced due to the addition of FA. Table 10.17 Values of surface tension and conductivity at the inflection point pertaining to the formation of 1: 1 complex. Concentration Concentration γ/m K (sp. Cond.) − 3 − 1 of β-CD/mM mM 10 Nm mho m−1 4.81 5.19 nicotinic acid 73.13 5.42 × 10−3 4.94 5.06 ascorbic acid 72.98 10.65 × 10−3 Table 10.18 Association constant (Ka ) and thermodynamic parameters of different Vit-β-cyclodextrin inclusion complexes. Temp ΔH 0 ΔSe − 3 − 1 − 1 − 1 Vitamin (K) Ka × 10 /M (kJ mol ) (kJ mol−1 ) Nicotinic acid 298.15 1.25 −20.59 −9.96 308.15 0.92 Ascorbic acid 298.15 3.10 −21.67 −5.87 308.15 2.33

Table 10.19 Distribution constants (K) and Gibbs free energy changes (ΔG ◦ ) of Vitamin E partitioned between dry reversed micelles of surfactants and non-polar organic solvents. System K ΔGt◦ kJmol−1 Vitamin-E/AoT/n-heptane 10.6 −5.8 Vitamin-E/DDAB/n-heptine 130 −12.1 Vitamin-E/Lecithin/cyclohexane 80.2 −10.9 Vitamin-E/C12 E4 /n-heptane 53.00 −9.8

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Biophysical Chemistry

Note: 1. AoT = Sodium bis (2 ethyl hexyl) sulfosuccinate 2. DDHB = Didodecy dimethyl ammonium bromide 3. Lecithin = L-α-phophatidyl choline 4. C12 E4 = Tetra ethylene glycol monododecyl ether

10.7

Surface Tension Data of Complexes with Vitamin-A

BLES (Bovine Lipid Extract Surfactant) whose common brand name is Suvanter is used to treat respiratory distress syndrome, neonatal (prophylaxis and treatment). It is a natural lung surfactant and is a mixture of lipids and apoproteins. The surfactant reduces the surface tension of pulmonary fluids and thereby increases lung compliance. Compound BLES BLES + retinylacetate + ethanol

Surface tension, γ /nNm−1 37.5 36.2

Vitamin-KI: It is highly insoluble in water due to its long hydrocarbon chain. A substantial increase in its solubility was obtained in solutions of commercial surfactants containing carboxy methyl ethoxylates. Its solubilisation was studied by UV-Vis spectrometry. The CMC of aqueous Vitamin-A from studies of variation of γ with concentration is estimated as 6.0 × 10−9 M. The solute permeability (W ) of various permeants in the presence of liquid membranes generated by Vitamin-A (W1 ) along with control values (W0 ) when no Vitamin-A was used. Permeant Serine Threonine Arginine Histidine CaCl2 Na(Cl) KCl

Initial concentration (mg ml−1 ) 0.2 0.2 0.2 0.2 10.0 5.4 10.4

W0 × 105 (mols sec−1 N−1 ) 498.3 219.9 38.2 7.1 10.7 2.4 3.2

W1 × 105 (mols sec−1 N−1 ) 238.2 105.6 90.0 8.2 16.0 2.7 3.8

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241

Table 10.20 Optical data of Vit-K2 and Vit D3 in ethanol. Vitamin γ (Nm) Extinction coefficient ml/μg Cell length (cm) Vit-K2 320 0.008 1 Vit-D3 270 0.0444 1 Table 10.21 Zeta potential data of loaded liposomes. Concentration Zeta potential Zeta potential Zeta potential of chitosan in the absence (mV) of (mV) of (% V/v) of Vitamins solution-1 solution-2 0.0 −35.4 −38.4 −36.2 0.0025 (2.5 × 10−3 ) −22.4 −20.9 −31.9 − 3 6.25 × 10 −18.7 −19.8 7.5 × 10−3 −21.7 −20.3 1.0 × 10−2 −17.6 −20.2 Concentration of Vit-K2 used < 0.005% (V/V); Concentration of Vit-D3 = 32.4 mg in 5 ml of ethanol. Various forms of Vit-K: Natural forms: K1 and K2 Synthetic forms: K3 , K4 , K5 . Their structures are

As one of the four lipophilic vitamins, Vit-K is a group of vitamins structurally similar molecules that are essential cofactors for γ-glutamyl carboxylase, an enzyme that catalyses the carboxylation of glutamic acid residues in a number of proteins that are involved in blood coagulation. Vit-K also plays a role in bone metabolism and the regulation of blood calcium levels. In healthy individuals, like for any lipid compound, orally administered Vit-K is emulsified in the intestine by bile salts produced by

242



Fluorosein DSPE + PEG

Zeta potential (mv) −23.1

Diffusion coefficient of Vit-K in phosphate buffer μm2 sec−1 124

DSPE + PEG

−4.6

98

Biophysical Chemistry

Formulation Non-PEGylated (Egg phosphotidyl Choline (EPs)) + Glycocholate + Vit-K PEGylated EPC, DSPE + PEG Glycocholate and Vit-K DSPE = distearoyl phosphatidyl ethanolamine

Co-Enzymes and Vitamins 

243

liver to form mixed micelles with phospholipid to facilitate the absorption of Vit-K by enterocytes. However, in some cases, like new born patients with cholestasis showed that the absorption of Vit-K is low. Permeability coefficients for the transport of Vit-K loaded in mixed micelles (with and without PEG coating) through CaCo-2 cell Monolayers For non-PEGylated micells of Vit-K For PEGylaled micelles of Vit-K

Permeability coefficient 3.2 × 10−7 cm sec−1 1.1 × 10−7 cm sec−1

Note: The above results imply that the PEGylation reduced the transport of Vit-K loaded in mixed micelles through CaCo-2 cell monolayers. The cells have characteristics that resemble intestinal epithelial cells such as the formation of a polarised monolayer well defined brush order on the apical surface and intercellular junctions. Zeta potential of different Vit-K loaded mixed micelles (with and without PEG coating).

Questions (1) Explain the terms (i) Apoenzyme (ii) Holoenzyme. account of the functioning of co-enzymes.

Give a brief

(2) Calculate the Gibbs energy change for the reaction NAD+ + FADH2  NADH + FADH+ given E0 values for the reactions NAD+ + H+ + 2e  NADH and

FAD + 2H+ + 2e  FADH2

are −0.32 V and −0.22 V respectively. Is the above reaction spontaneous under the conditions? (Note that the E0 values are at pH = 7.0) while E0 of hydrogen electrode is −0.421 V. What will be the E0 values against S.H.E, that is when [ H + ] = 1.0 molar. (3) Calculate the pH of a 0.02 M solution of Nicotinic acid given its pKa = 4.75.

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Biophysical Chemistry

(4) Calculate the degree of dissociation and the dissociation constant of ascorbic acid at 298 K form the following data. Ascorbic acid (mol dm−3 ∧ (mho cm−2 ) eq −1

5.8 × 10−3 37.00

2.1 × 10−2 20.22

8.0 × 10−2 10.04

∧0 of the acid = 380.4 mho cm−2 eq−1 . (5) Calculate the molar mass of Nicotinic acid from the following data of the freezing points of its aqueous solutions K f (H2 O) = 1.86 K kg mol−1 . Concentration of acid/mol kg−1 ΔT f

0.0122 0.024

0.0239 0.046

0.0638 0.121

(6) Calculate the partial pressure of a 0.01 M solution of Nicotinic acid in water at 298 K, given the Henry’s law constant for the acid as 2.90 × 10−12 atm m3 mol−1 . (7) Explain the term “cofactor”. Give examples of co-enzymes and their combinations with vitamin B group that result in (i) decarboxylation of a reaction (ii) transfer of amino groups and (iii) carriers of acyl groups. (8) Classify vitamins. Give two examples in each category and explain their function in human metabolism. (9) Name the vitamins of vitamin B and elaborate on their biochemical functions. (10) What are the compounds belonging to vitamin B6 and B12 groups? Give their structure and explain their function. (11) Write down the structure of ascorbic acid. Given its pKa1 =4.2, calculate its degree of dissociation at a concentration of 0.1 M and its pH.

11

Bioenergetics 11.1

Introduction

The field of bioenergetics deals with diverse types of energy transformation in cells; in particular, the reactions involving adenosine triphosphate play a central role. The pathways in which the living organism produce and consume energies is central to various metabolic processes. Any analysis of bioenergetics will be incomplete without adequate description of thermodynamic concepts and kinetic principles. The Gibbs free energy changes in various processes involving ATP predict the thermodynamic feasibility; in this context, it is important to analyse the role of pH. Consequently, the Gibbs free energy changes too vary depending upon the nature of the electrolyte. Thus, the formal potentials of cell reactions need to be incorporated in this context rather than the standard electrode potentials-customarily invoked. Furthermore, the reaction rates pertaining to ATP hydrolysis and related reactions are functions of temperature.

11.2

Metabolism

Metabolism involves a series of interlinked chemical reactions that begin with a particular molecule which is converted into some other molecule (or molecules) in a chosen fashion. There are many such pathways in a cell.

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_11

245

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Biophysical Chemistry

For example, we consider the glucose metabolism as shown in the following scheme:

Metabolic pathways may be divided into two categories: (1) those that convert energy into biologically useful forms and (2) those that require input of energy to proceed. As an example of first category, the scheme below may be considered Fuels (Carbohydrates, fats) −→ CO2 + H2 O + useful energy

(11.1)

This class of reactions are described as “Catabolism” (Catabolic reactions). As examples of reactions of second category, which are referred as anabolic reactions (or anabolism) Useful energy + small molecules −→ Complex molecules

11.3

(11.2)

Coupled Reactions

This concept is of great importance in the study of bio-chemical reactions. This means that a thermodynamically unfavourable reaction (i.e., are which has a +ve ΔG ◦ ) can be driven by a thermodynamically favourable reaction (i.e., are which has a more negative ΔG ◦ value) to which it is coupled. The following example illustrates this principle. (11.3)

On combining the reactions, (11.4) The reaction (11.3) is driven by coupling it to the second reaction.

Bioenergetics 

11.4

247

ATP as an Energy Source

Most energy requiring processes such as biosynthesis, transport of species across membranes derive their energy from the free energy donor i.e., ATP. ATP consists of the units adenine, ribose and three phosphate units. The active form of ATP is usually a complex of ATP with Mg2+ or Mn2+ . The role of ATP as an energy barrier lies in its triple phosphate moiety. The presence of two phospho anhydride bonds in its triphosphate groups contributes to the energy rich character of ATP. Considerable amount of free energy is liberated when ATP is hydrolysed to ADP or AMP as may be noted from the following equations ATP + H2 O −→ ADP + Pi ATP + H2 O −→ AMP + PPi

ΔG ◦ = −30.5 kJ mol−1 ΔG ◦

= −45.6 kJ

mol−1

(11.5) (11.6)

where Pi is inorganic phosphate and PPi is inorganic pyrophosphate. Under the conditions of concentrations prevailing in cells, the ΔG ◦ values for the above hydrolyses are of the order of −50 kJmol−1 . Energyrequiring processes such as muscle contraction use the energy derived out of ATP hydrolysis. The ATP, ADP cycle is fundamental to the energy change in biological systems. Other analogous nucleoside phosphates whose hydrolysis is similar to ATP are guanosine phosphate (GTP), uridine triphosphate (UTP) and cytidine triphosphate (CTP). Enzymes catalyse the transfer of the terminal phosphoryl group from one nucleoside to the other. While the phosphorylation of nucleoside monophosphates is catalysed by the enzyme nucleoside monophosphate kinase, the phosphorylation of nucleoside diphosphate is catalysed by nucleoside diphosphate kinase. Thermodynamically, ATP acts as a coupling agent. This means that a thermodynamically unfavourable reaction can be converted into a favourable one by coupling it to the hydrolysis of sufficient number of ATP molecules. It may be shown that the hydrolysis of “n” ATP molecules changes the equilibrium quotient of the overall reaction by a factor of 108n .

11.5

High Phosphoryl Capacity of ATP

It is known that the transfer of phosphoryl group is a common way of energy coupling and it is extensively used in intracellular transmission of information. To understand the efficient transfer of phosphoryl group by ATP, the following two reactions [one of them being reactions] (11.5) and

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Biophysical Chemistry

(11.6) and the reaction Glycerol-3-phosphate + H2 O −→ Glycerol + Pi

ΔG ◦ = −9.2 kJmol−1 (11.7)

may be considered. Since ΔG ◦ for reaction (11.5) is much smaller than that of (11.7), one may conclude that ATP has a much stronger tendency to transfer its terminal phosphoryl group to water than glycerol-3-phosphate. Thus ATP has a higher phosphoryl group transfer potential than does glycerol-3-phosphate. Examination of the structures of ATP, ADP and Pi will give an explanation for the same. ADP and Pi, especially Pi has greater resonance stabilization than ATP. Apart from this, other factors like electrostatic repulsion and stabilization due to hydration must be considered. Further, orthophosphate has a number of resonance forms of nearly the same energy as shown below:

Another important reason is that water can bind more effectively to ADP and Pi than to phosphoanhydride part of ATP. This leads to stabilization of ADP and Pi.

11.6

Significance of Phosphoryl Transfer Potential (PTP)

ΔG ◦ of hydrolysis serves as a measure of comparing PTP of phosphorylated compounds. It is observed that some compounds in biological systems have a higher PTP than ATP. A few of such compounds are phosphoenol pyruvate (PEP); 1, 3-bisphosphoglycerate (1, 3-BPG) and creatine phosphate whose structures are shown.

Bioenergetics 

249

Table 11.1 Standard Gibbs energies of hydrolysis (ΔG ◦ ) of some phosphorylated compounds. Compound Phosphoenol pyruvate 1, 3-BPG Creatine phosphate ATP → ADP Glucose-1-phosphate Glucose-6-phosphate Glycerol-3-phosphate

ΔG ◦ /kJmol−1 −61.9 −49.4 −43.1 −30.5 −20.9 −13.8 −9.2

To understand the significance of the above data, we consider the reaction. creatine C.P. + ADP + H+ FGGGGGGGGGGGGB GGGGGGGGGGGG ATP + creatine kinase

(11.8)

C.P. in vertebrate muscle serves as a reservoir of high potential phosphoryl groups that can be readily transferred to ATP. This reaction occurs every time we exercise to generate ATP. The equilibrium constant of the above reaction is 162. When body muscle is resting, typical concentrations of the constituents in equation (11.8) are [ATP] = 4 × 10−3 M; [ADP] = 1.3 × 10−5 ; [C.P.] = 25 × 10−3 ; [Creatine] = 13 × 10−3 . The large amount of C.P. and its high P.T.P. relative to ATP makes it a highly effective phosphoryl buffer.

11.7

Intracellular Conditions Pertaining to ATP Hydrolysis

The value of ΔG due to ATP hydrolysis depends upon the activities (in dilute solutions, may be considered as concentrations) of the various species in the reaction. For example, in the reaction (11.5). Keq =

[ADP]eq /[IM] × [Pi]/[IM] [ATP]eq /[M] × [H2 O]eq /[55M]

(11.9)

ΔG ◦ = − RT ln Keq = −31.0 kJmol−1 Correcting for physiological concentrations ΔG =

[ADP]Phys /[IM]/[Pi]Phys [IM] [ATP]Phys

ΔG = ΔG ◦ + RT ln Q ≈ −60 kJmol−1

(11.10)

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11.7.1

Biophysical Chemistry

Hydrolysis Reaction O

Phosphoanhydride (acid-base) bond hydrolysis

O  P  OH O +1  OPO R

Reaction

ΔG ◦ (kJ/mol)

ADP + H2 O → AMP + Pi

− 31.0

ATP + H2 O → AMP + PPi

− 38.0

PPi + H2 O → 2Pi

− 24.0

Table 11.2 Standard Gibbs free energies of phosphoesters. ΔG ◦ Reaction (kJ/mol) 3-Phosphoserine + H2 O → Serine + phosphate −10.0 AMP + H2 O → Adenosine + phosphate −14.0 Dihydroxyacetonephosphate (DHAP) + H2 O → DHA +Phosphate −15.0 Fructose1, 6-biphosphate + H2 O → F6P + Phosphate −16.0 Glyceroldehyde-3-Phosphate + H2 O → Glyceraldehyde +Phosphate −17.0 Threoninephosphate + H2 O → Threonine + Phosphate −19.0 Fructose-6-phosphate + H2 O → Fructose + Phosphate −16.0 AcetylCoA + H2 O + Oxaloacetate → Citrate + CoA −31.4 5-adenonylmethionine + H2 O → Methylthioadenosine +homoserine −41.8 When the concentrations are farther from equilibrium values |ΔG | is larger. In practice, the physiological condition depends on the organism being studied, the time or the cell compartment under consideration and the energy demand for metabolic reactions. Thus ΔG values may vary widely. Gibbs free energy changes for ATP hydrolysis in various organisms under different physiological conditions are shown in the following table.

Bioenergetics 

Table 11.3 Gibbs free energy changes for ATP hydrolysis in various organisms under different physiological conditions. Concentration of Physiological condition of organism ATP ADP Pi ΔG/kJ mol−1 Standard conditions 1M 1M 1M −31.0 E.Coli aerobic exponential growth on glucose 10 mM 0.6 mM 20 mM −54.0 E.Coli anaerobic exponential growth on glucose 3 mM 0.4 mM 10 mM −54.0 E.Coli anaerobic exponential growth on glycerol 7 mM 0.7 mM 10 mM −55.0 S.Cerevisiae aerobic growth on glucose 2 mM 0.3 mM 22 mM −52.0 Spinach spinacia oleracea chloroplast stroma in light 2 mM 0.8 mM 10 mM −51.0 Spinach spinacia oleracea cytosol + mitochondria in light 3 mM 0.7 mM 10 mM −52.0 Homosapiens (resting muscle) 8 mM 9 μM 4 mM −68.0 Homosapiens (muscle recovery after exercise) 8 mM 7 μM 1 mM −72.0

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The calculations of ΔG require accurate measurement of relevant intracellular concentrations. NMR can be used in humans to measure concentrations of 31P in vivo because 31P has magnetic properties. In E. Coli, the concentrations of ATP can be measured by an ATP bioluminescence assay. The luciferase enzyme uses ATP in a reaction that produces light which can be measured using a luminometer and the ATP concentration can be inferred from signal strength.

11.8

Methods by which ATP Transfers Energy

Cells require chemical energy for three general tasks: (i) To drive metabolic reactions that would not occur automatically to transport substances needed across membranes and to do mechanical work such as moving muscles. ATP is not a storage molecule for chemical energy (it is the job of carbohydrates, glycogen and fats). (ii) When energy is needed by the cell, it is converted from storage molecules into ATP. ATP then serves as a shuttle delivering energy to places within the cell where energy consuming activities are taking place. ATP is a nucleotide that consists of three groups: the nitrogenous base glucose, adenine, the sugar ribose and a chain of three phosphate groups bound to ribose. (iii) The actual power source is the phosphate tail of ATP which the cell taps. When hydrolysis occurs, the phosphate tail is broken and one phosphate group is broken from ATP to yield energy i.e. ATP + H2 O −→ ADP + Pi

(11.11)

ATP is able to power cellular processes by transferring a phosphate group to another molecule (called phosphorylation). This process is carried out by special enzymes that couple the release of energy from ATP to cellular activities that require energy. As seen above, cells continuously break down ATP to obtain energy. ATP also gets synthesized from ADP and Pi through the process of cell respiration. This is facilitated by the enzyme ATP synthase which converts ADP and Pi to ATP. The enzyme ATP synthase is located in the membrane of cellular structures called mitochondria, inplant cells the enzyme is found in chloroplasts. The three processes of ATP production include glycolysis, oxidative phosphorylation and tricarboxylic acid cycle. In eukaryotic cells, the latter two processes, occur with in mitochondria. Electrons that are passed through the electron transport chain ultimately generate free energy capable of driving the phosphorylation of ADP.

Bioenergetics 

11.9

253

Citric Acid Cycle

Citric Acid Cycle is also known as CAC, TCA or Krebs Cycle. It is a series of chemical reactions used by aerobic organisms to release stored energy through oxidation of acetyl-CoA derived from carbohydrates, fats and proteins into ATP and CO2 . In addition, the cycle provides precursors of certain amino acids as well as the reducing agent NADH that are used in numerous other reactions. CH2 COOH This metabolic pathways is derived from citric acid HO C

COOH

CH2 COOH

that is consumed and regenerated by this cycle. The cycle consumes acetate (in the form of acetyl CoA) and water, reduces NAD+ to NADH and produces CO2 as waste product. The NADH produced in the cycle is fed into oxidative phosphorylation (electron transport) pathway. The net result of these two closely linked pathways is the oxidation of nutrients to produce energy in the form of ATP. In eukaryotic cells the TCA cycle occurs in the matrix of mitochondria. In prokaryotic cells, such as bacteria, the TCA cycle is performed in the cytosol with the proton gradient for ATP production being across the cell surface. The over all yield from the TCA cycle is three NADH, one FADH2 and one GTP.

11.10

Reactions of the TCA Cycle

The initial step of the cycle is catalysed by the citrate synthase in the matrix of mitochondria. This highly exothermic reaction commits acetyl groups to citrate formation and complete oxidation in the cycle. The reactions of the cycle are carried out by eight enzymes that completely oxidize acetate in the form of acetyl CoA into two molecules each of CO2 and H2 O.



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Biophysical Chemistry

NAD

Acetyl CoA

NADH +H+

CoASH

Malate dehydrogenase

Oxaloacetate

Citrate synthase

Citrate

L-malate H2 O

Aconitase

Fumarase

H 2O Summary of the citric acid cyle

Fumarate

Inputs FAD H2

Succinate dehyrogenase

FAD

Outputs

2(2C) acetyl groups

4CO2

6NAD+

6NADH

2FAD

2FADH2

2ADP + 2Pi

2ATP

cis-aconitate H 2C

Succinate

isocitrate

CoASH

GTP

NAD+

Pi CO2

GDP

CoA S α -keto glutarate

Succinyl CoA NADH + H+

NAD+

(Mass = 380 kDa) ucc Isocitrate alos dehydrogenase Ox inate

-

NADH + H+

CO2

Gibbs Free Energy Changes for Glycolysis Reactions and TCA ΔG ◦ of the reaction = −38 kJ mol−1 ΔG ◦ of isocitrate → α-ketoglutarate = −21.0 kJ mol−1 ΔG ◦ of α-ketoglutarate → succinyl CoA = −33 kJ mol−1 ΔG ◦ of succinyl CoA to succinate is −3.0 kJ mol−1 ΔG ◦ of L-malate → oxalo acetate is +29 kJ mol−1

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This endergonic reaction is pulled in the forward direction by the action of citrate synthase and other reactions which remove oxaloacetate.

One of the primary sources of acetyl CoA is from the break down of sugars by glycolysis which yield pyruvate that in turn is decarboxylated by the pyruvate dehydrogenase complex generating acetyl CoA according to ¯ + HSCoA + NAD+ CH3 C(=O)C(=O)O

−→ CH3 C(=O)SCoA + NADH + CO2

(11.12)

The TCA cycle is the final path way for breakdown of foods. It may be stated that the four, five, six carbon intermediates generated in the reactions of TCA cycle are important intermediates in the biosynthetic processes. Succinyl CoA, malate, oxalo acetate, α-ketoglutarates and citrate are all precursors in the biosynthesis of important cellular compounds.

The TCA cycle acts as a source of precursors for amino acid, fatty acid and glucose synthesis.

256

Table 11.4 Enthalpy changes of reactions involving ATP and related compounds.

− PGN3− + NADP3− + H2 O = RU5P2− + NADP4red + CO23− + 2H+

R5P− = R5P2− − − ISCIT3− + NADOX + H2 O = AKG2− + NAD2red + CO23− + 2H+

37.5 12.9 −26.3

Biophysical Chemistry

Reference reactions Glucose + ATP4− = glucose-6-phosphate−2 + ADP3− + H+ Glucose-6-phosphate (glu-6-p2− ) = Fructose-6-phosphate2− (F6P2− ) F6P2− + ATP4− = F16P4− + ADP3− + H+ F16P4− = DHAP2− + GAP2− GAP2− = DHAP2− F16P4− = 2 DHAP2− PG23− = PG33− PG23− = PEP3− + H2 O PYR− + ATP4− = PEP3− + ADP3− + H+ ISCIT3− = CIT3− − − LSCIT3− + NADP3OX + H2 O = AKG2− + NADP4red + CO23− + 2H+ 2− 4 − 2 − + 3 − GTP + Suc + CoAS- + H = GDP + HPO4 + SUCCoA− FuM2− + H2 O = MAL2− MAL2− + NAD2− = OAA2− + NAD2red + H+ − 4− 2− − NADOX + NADPred = NADred + NADP3OX 2− 4 − 3 − + ATP + H2 O = ADP + HPo4 + H G6P2− + H2 O = G65 + Pi2−



Name of reactions Glucokinase (GLK) Phosphoglucose isomerase (PGI) Phosphofructokinase (PFK) Fructose-1-6-bi phosphate aldolase (FBE) Triose phosphate isomerase (TPI) Fructose-1, 6-phosphate aldolase (FPA2) Phosphoglycerate mutage (PGM) Enolase (ENO) Pyruvate kinase (PYK) Aconitrate hydratase (ACON) Isocitrate dehydrogenase (IDH) Succinate CoA ligase (SCA) Fumarate hydratase (FUM) Malate dehydrogenase (MDH) NADP transhydrogenase (NPTH) ATPase (ATPS) Alkaline phosphatase hydrolysis G6P (G6PH) 6-Phosphogluconate dehydrogenase (PGD) Ribose-5-Phosphate isomerase (R5PI) Isocitrate dehydrogenase (IDH2)

Δr H ◦ / kJmol−1 −23.8 11.5 −9.5 49.0 2.7 51.70 28.0 15.1 5.4 −20.0 −22.2 −30.9 −13.2 51.3 −4.1 −20.5 0.91

Table 11.5 Dissociation constants and enthalpy changes for reactions involving ATP. Reactant Adenosine diphosphate (ADP3− ) Adenosine triphosphate (ATP4− ) 1, 3-bisphosphoglycerate-citrate (CIT3− ) Coenzyme A-SH (CoAS− ) Acetyl coenzyme A (ACoA◦ )

Abbreviation ADP ATP CIT CoAS ACoA

Zi (Charge) −3 −4 −3 −1 0

NH (No. of H’s) 12 12 5 0 3

pKH1 6.5 6.7 5.7 8.2 —

Δr + 1 −2 −2 −1.9 — —

Table 11.6 Gibbs free energy changes of reference compounds. GLC◦ −916.4 NAD− 0

ATP4− −2769.7 NADPH2− −809.2

P6P2− −1760.8 HPO24− −1096.1

F16P2− −2597.6 PG33− −1508.8

DHAP2− −1292.9 PG23− −1502.1

GAP2− −1285.9 PZP3− −1269.4

BPG4− −2354.5 ADP3− −1906.1

NADH2− 23.9 CoA5 0

ACoA◦ −188.5 CO23− −527.8

Bioenergetics 

Species Δ f Gi◦ /kJmol−1 Species Δ f Gi◦ /kJmol−1

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11.10.1

Biophysical Chemistry

Activity of TCA Cycle

TCA cycle is regulated by different factors. First, the supply of acetyl units, whether derived from pyruvate (by glycolysis) or fatty acids (by β-oxidation) is crucial in determining the rate of the cycle. Regulation of the pyruvate dehydrogenase complex, the transport of fatty acids into mitochondria and β-oxidation of fatty acids are effective determinants of cycle activity. Second, because of the dehydrogenases of the cycle are dependent on a continuous supply of NAD+ and FAD, their activities are very strongly controlled by the respiratory chain that oxidizes NADH and FADH2 . The activity of respiratory chain is dependent on the rate of ATP synthesis which is strongly affected by availability of ADP, phosphate and O2 .

Symbols Pertaining to CTA Cycle PG2− = 2-phospho-D-glycerate PG3− = 3-phospho-D-glycerate PEP3− = phosphoenol pyruvate PYR− = pyruvate ATP4− = adenosine triphosphate ADP3− = adenosine diphosphate ISCIT3− = isocitrate CIT3− = citrate AKG2− = α, ketoglutarate GTP4− = guanosine triphosphate Suc2− = succinate CoAS− = co-enzyme A-SH GDP3− = guanosine diphosphate SucCoA− = succinyl-CoA FuM2− = fumarate

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259

MAL2− = malate OAA = oxaloacetate G6P2− = D-glucose-6-phosphate GLC◦ = glucose PGN3− = 6-phosphogluconate Ru5P2− = ribulose-5-phosphate R5P− = ribose-5-phosphate

Questions (1) The standard Gibbs free energy change for the hydrolysis of ATP is given by ATP + H2 O  ADP + Pi where Pi = phosphate group is −31.0 kJ mol−1 . Calculate equilibrium constant of the reaction at 298K. State whether the reaction is spontaneous under these conditions. Solution: ΔG ◦ = − RT ln K = −8.314 × 10−3 × 298 × 2.313 log K

−31.0 = −8.314 × 10−3 × 298 × 2.313 log K = −5.17 log K 31.0 log K = = 5.43 5.71 K = 2.70 × 105 The reaction is spontaneous under the standard conditions. (2) The equilibrium constant of the reaction Creatine phosphate + ADP + H+  ATP + Creatine is 162 at 293K. Given that the concentrations of creatine = 13 × 10−3 , ATP = 4 × 10−3 , creatine phosphate = 25 × 10−3 and ADP = 1.3 × 10−5 in the muscle of the humans under rest conditions, what is the pH of the biological fluids therein.

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Solution:

[ATP][Creatine] [Creatine phosphate][ADP][H+ ] [4 × 10−3 ][13 × 10−3 ] 162 = [25 × 10−3 ][1.3 × 10−5 ][ H + ] 52 × 10−6 [ H+ ] = 32.5 × 10−8 [162] K=

= 0.00988 × 102 = 0.988 pH = − log[ H + ]

= − log 0.988 = −(−0.005) = 0.005 (3) Formulate the fuel cell in which glucose undergoes oxidation at the anode in alkaline medium as one electrode. The other electrode is an oxygen electrode with Pt for electrical contact. What are the anodic and cathodic half cell reactions (Express both as reduction reactions). Given their half cell potentials as −0.93V and +0.52V respectively. Calculate the Gibbs energy change of the reaction. Solution: Pt|C6 H12 O6 in alkaline medium containg CO23− ion

|alkaline medium|O2 (g, 1 atm)|Pt Half cell reactions 12H2 O + 6O2 (g) + 24e−  24 OH−

( E = +0.52V )

24H2 O + 6CO23− + 24e  C6 H12 O6 + 36 OH−

( E = −0.92V )

Ecell = ER − EL = +0.52 − (−0.93) = 1.45V ΔG ◦ = −nFE◦ = −24 × 96500 × 1.45

= −33582 × 102 J −33582 × 102 1000 = −3358.2 kJ =

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261

(4) If a kg of glucose produces 3200 kwh of energy, how much energy is generated by 11.1 moles of glucose. Express your answer in kJ. Solution: 1 kg= 5.55 moles of glucose or 2 kg=11.10 moles of glucose. Hence 2 kg of glucose produces 2 × 3200 = 6400 kWh. So 1 kWh = 3.6 × 106 J 2 kg glucose produces

= 6400 × 3.6 × 106 J = 64 × 3.6 × 108 J = 2304 × 108 J = 230.4 × 105 kJ (5) What is metabolism? Explain how glucose metabolises in the body. (6) Define “catabolic” and “anabolic” reactions. Give examples for each. (7) What is a coupled reaction? importance.

Give an example and outline its

(8) Explain the term phosphoryl capacity of ATP. How does it impact energy changes in a cell? (9) Write down all the steps in citric acid cycle and outline its importance.

12

Biosensors 12.1

Introduction

Biosensors are defined as analytical tools or devices, which include a system of biological detecting elements e.g., a sensor and a transducer. In medicinal chemistry, the need for affordable and selective sensing of analytes such as glucose, urea, dopamine, progesterone, anesthetics etc., is of paramount importance It is well known that L-cysteine is a prostate cancer biomarker, and its timely measurement is essential. Analogously, the qualitative and quantitative detection of trace elements such as arsenic, lead becomes essential in water analysis. Thus, it is no wonder that the field of biosensors today occupies a pivotal place in materials science and biophysical chemistry. The essential touchstones in this context are as follows: (i) selectivity; (ii) limit of detection; (iii) range of detection and (iv) real time monitoring.

12.2

Components of a Biosensor

The biosensor has mainly three components: (i) sensory element, (ii) transducer, (iii) necessary arrangement for transport of electrons. A sketch of biosensor is shown in the diagram below:

Figure 12.1 Sketch of a typical biosensor.

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_12

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The sensor in contact with the analyte of biological nature responds and the detector changes the resulting signal via transducer. It is amplified and displayed via a signal processor.

12.2.1

Working of a Biosensor

The electrical signal of the transducer is often quite low (due to low concentration of the detectable species) and a fairly long base line is observed. The signal processing includes the necessary correction for deducting the base line signal.

12.2.2

Applications

The applications of biosensors include: (i) food industries, (ii) agriculture and (iii) control of pollution in environment and ecology.

Figure 12.2 Applications of biosensors.

12.3

Different Types of Biosensors

Broadly, there are eight types of biosensors (a) to (h): (a) Piezoelectric: The platform of a piezoelectric sensor is a sensory element that works on the law of oscillations leading to a collection pump on the surface of a piezoelectric crystal. The biosensors have their surface modified with an antigen or an antibody and the detection parts are united by using nanoparticles.

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265

(b) Wearable: It is a digital device used to wear on a human body in different wearable systems like smart watches, tattoos which allow levels of blood glucose, rate of heartbeat etc. In humans, these sensors may allow premature recognition of health condition and prevent hospitalization. (c) Thermometric: There are various types of biological reactions that are connected with evolution or absorption of heat and this is the basis of this class of sensors. This sensor is used to measure or estimate the serum cholesterol. The heat of generated through the oxidation of cholesterol by the enzyme cholesterol oxidase is measured. This sensor is also used to estimate glucose, urea, uric acid, penicillin-G. A schematic diagram of this sensor is shown in Figure 12.3.

Figure 12.3 Schematic diagram of thermometric biosensor. (d) Optical: These biosensors use fiber optics as optoelectronic transducers. The sensors mainly involve antibodies and enzymes as the transducing elements. A sketch of this set up is also shown in next page. The optical biosensors permit a secure non-electrical inaccessible sensing of equipment. They also do not need reference sensors because the comparative signal can be produced by using similar light source like sampling sensor. Although a variety of sensors can be envisaged as shown above, the electrochemical biosensors viz.

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Biophysical Chemistry

Figure 12.4 Sketch of an optical biosensor. (e) amperometric; (f) potentiometric; (g) voltammetric and (h) impedimetric are more prominent in this context on account of the portability, ease of measurement and sensitivity. Hence the sensors based on electrochemical measurements are described in more detail below.

12.4

Electrochemical Biosensors

Generally, an electrochemical biosensor depends on a reaction that consumes or generates electrons (i.e., a redox reaction). The reaction could be an enzymatic or a non-enzymatic reaction. The basic set up in the biosensor involves a three-electrode system, i.e., a working electrode, a counter electrode and a reference electrode. The analyte gets reduced (or oxidized) and the product is sensed by the working electrode and the signal is detected by a device such as an oscilloscope.

12.4.1

Amperometric Biosensors

These are based on the measurement of current flowing between working and counter electrodes at a chosen potential. In the Clark’s oxygen electrode (used to measure O2 concentration in a metabolite such as blood),

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267

a silver electrode (as anode) and a platinum (as cathode) are immersed in an electrolyte, containing dissolved oxygen. An optimum voltage of about 0.7 V is applied between the electrodes. Oxygen is reduced at the cathode and silver is oxidized at the anode. The experimentally measured current reaches a plateau due to the rate being controlled by diffusion of O2 towards the electrode surface. The magnitude of the diffusion current is directly proportional to the bulk concentration of the analyte. The analytes (e.g., glucose, dopamine, urea, progesterone, ascorbic acid etc.) are dissolved in suitable solvents. Since the current is linearly related to the analyte concentration, an effortless method of estimating the amount with the help of a calibration curve/chart is envisaged. The practical feasibility of the sensors is studied using the calibration plot for deducing the linear detection range, by the constant addition method-well known in analytical chemistry. It is desirable to obtain the range of detection varying from nanomolar to micromolar. The other sensing parameters viz., sensitivity (S), limit of detection (LOD) and response time (τ) are also required for point of care analysis. The method of estimating the sensitivity (S) depends upon the experimental technique employed. For example, in amperometric sensors, S is calculated from the slope of the calibration curve viz. S=

ΔI ΔC

(12.1)

In the above equation S represents the change in amperometric current (or current density) for unit change in the analyte concentration (C ). The limit of detection (LOD) representing the lowest measurable concentration within a specified confidence interval is computed from the equation LOD = k

σ S

(12.2)

where σ denotes the standard deviation of the measurements and k = 3 indicates the confidence level of 99.6%, S being the slope of the calibration curve. The values lower than 3 in the above equation reflects a lower confidence interval.

12.5

Enzymatic Sensing of Glucose

The development of biosensors gained impetus from the need to monitor glucose levels in the blood of diabetics. In 1962, Leland Clark Jr. developed

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Table 12.1 Typical range of detection accomplished for analytes using chemically modified electrodes. Analyte Glucose Catechol Urea Cholesterol Progesterone Dopamine Procaine

Approximate range of detection (mM) 0.001 to 60 0.00015 to 0.075 50 to 250 0.005 to 0.1 1 × 10−6 to 1 × 10−3 0.001 to 0.4 0.0001 to 10

an enzyme electrode to estimate glucose levels in humans which is based on the reaction Glucose + O2 −→ Gluconic acid + H2 O2

(12.3)

In order to accelerate the rate of the above reaction as well as provide selectivity, glucose-oxidase (GOx ) enzymes are almost always employed. The method of immobilization of GOx on electrodes is a crucial factor in determining the efficiency of the sensor, in electrochemical methods. Since bare metal electrodes do not possess satisfactory sensitivity even in the presence of enzymes, it is customary to employ conducting polymerscoated electrodes for the sensing of analytes. There are several types of electrodeposition techniques to prepare such chemically modified electrodes. The simplest method is to polymerize the desired monomers (e.g., aniline, pyrrole, indole, thiophene. . ..) on any metal electrodes (e.g., stainless steel, Ni, Ag, Au etc.) by applying current for optimum duration of time. Any enzyme-based biosensor requires efficient immobilization on the chosen electrode surface. The modified surface should possess desirable characteristics for facile electron transfer.

12.5.1

Experimental Details

In a typical experiment, the desired monomer (e.g., pyrrole) is polymerized on the electrode surface (e.g., Au) by a suitable electrodeposition technique (potentiostatic/potentiodynamic/galvanostatic) in electrolytes such as para-toluene sulphonic acid. This procedure yields the modified electrode designated as (Au/PPy), where PPy refers to polypyrrole. A small amount (∼ 5% glucose oxidase enzyme in phosphate buffer solutions) is drop cast on Au/PPy, yielding the enzyme coated surface. This electrode then serves as the sensor for glucose.

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269

Figure 12.5 Schematic variation of amperometric current with time for equal additions of glucose when an enzyme-coated electrode is dipped in a suitable medium. A careful systematic addition of equal volume (often microliters) of glucose is then added to the solution and the chronoamperometric current is measured (Fig. 12.5). The stepwise decrease in current shown in Figure 12.5, for various concentrations are the typical features for the feasibility of amperometric sensors. The total number of steps then indicates the linear concentration range in which the sensor is functional.

12.5.2

Mechanism of Detection

The enzyme-catalyzed oxidation of glucose may be represented in the following manner: β-D-Glucose + GOx -FAD −→ GOx -FADH2 + δ-D-gluconolactone (12.4) GOx -FADH2 + O2 −→ GOx -FAD + H2 O2 H2 O2 −→ 2H+ + O2 + 2e−

(12.5) (12.6)

FAD refers to Flavin adenine dinucleotide (quinine form) and is a coenzyme essential for the functioning of glucose oxidase. FADH2 indicates the hydroquinone form of Flavin adenine dinucleotide. The gluconolactone hydrolyses to form gluconic acid. Upon adding the above three equations, eqn. (12.3) is again obtained.

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Biophysical Chemistry

The sensing of glucose can also be accomplished by the reduction of H2 O2 viz. H2 O2 + 2H+ + 2e− −→ 2H2 O

(12.7)

When eqn. (12.1) is applied for sensing of glucose using chemically modified electrodes, the sensitivity varies from 0.2 to 60 (μAcm−2 mM−1 ) depending upon the nature of the electrode and operating conditions. This number refers to the variation of the current density for one millimolar addition of glucose.

12.6

Estimation of Michaelis-Menten Constants

It is possible to estimate the Michaelis-Menten constants for ascertaining the efficacy of the chosen enzyme from amperometric measurements using a graphical procedure as shown below: K I (max ) = M +1 I C

(12.8)

where I and I (max ) denote respectively, the current and the maximum current respectively, C being the concentration of the glucose. The currents I and I (max ) are analogous to the initial and maximum velocities respectively in the Lineweaver-Burke plot. By plotting the ratio, Table 12.2 Illustrative examples of analytes and corresponding enzymes. Analyte Enzyme Reaction 1. Glucose Glucose oxidase β-D-glucose + O2 −→ gluconic acid + H2 O2 2. Ethanol Ethanol oxidase Ethanol + O2 −→ acetaldehyde + H2 O2 3. Lactic acid Lactase oxidase L-lactate + O2 −→ Pyruvate + H2 O2 4. Lactose Galactose oxidase Lactose + O2 −→ galactose dialdehyde derivative + H2 O2 5. Uric acid Uricase Uric acid + 2H2 O+ O2 −→ Allantoin + CO2 + H2 O2 6. Catechol Catechol oxidase Catechol + O2 = 1,2-benzoquinone + H2 O 7. Dopamine Tyrosinase Dopamine + O2 −→ indole 5,6 quinone

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271

I (max )/I versus 1/C, the Michaelis-Menten constant K M is deduced. Since the interaction of the chemically modified electrodes with the glucose oxidase enzyme is not identical, K M varies from 4 to 55 mM. These values pertain to different chemically modified electrodes.

12.7

Non-enzymatic Sensing of Glucose

Although enzyme-based biosensors exhibit remarkable selectivity and sensitivity, they suffer from high cost as well as inadequate storage stability. Hence recent investigations have focused on the fabrication of nonenzymatic sensing of analytes. In the case of glucose, a variety of electrochemical biosensors have been developed, without the use of glucose oxidase. Among them, mention may be made of the following: noble metals, oxides and hydroxides of transition metals.

12.7.1

Interference Studies

Although sensing of glucose may be the main objective, other analytes such as ascorbic acid, dopamine, urea, uric acid etc., may also be present in the sample. Hence, selective detection of glucose is of paramount importance. For ascertaining the selectivity of any biosensors, it is customary to add very large concentrations (about 50 times that of the analyte) of the so-called interfering agents. To evaluate the selectivity for sensing of glucose, various concentrations of other compounds ascorbic acid (AA), dopamine (DA), uric acid (UA) will be added and if there is no change in the chronoamperometric current response, it indicates the selectivity.

12.8

Enzymatic Sensing of Urea

Urea (also known as carbamide) is one of the final products in protein metabolism, having immense biological significance in clinical analysis and dairy industry. The normal level of urea in serum varies from 2.5–7.5 mM. Here too, enzymatic and non-enzymatic methods have been reported. Enzymatic sensors for urea make use of the enzyme urease on account of its specific binding characteristics as well as impressive catalytic performance. The sensing principle is based upon the detection of ammonium ions resulting from the hydrolysis of urea in the presence of the enzyme

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Biophysical Chemistry

urease viz. NH2 CONH2 + 3H2 O −→ 2NH4+ + HCO3− + OH−

(12.9)

As mentioned earlier, the cost factor and limited storage characteristics are the main limitations of enzymatic sensing. The shelf life of enzymebased sensors is not satisfactory. Non-enzymatic biosensors of urea either employ conducting polymers based metal electrodes or different nanostructures of Nickel.

12.8.1

Potentiometric Sensors

The potentiometric analysis is a passive technique wherein the potential between an indicator electrode and a reference electrode is measured, at zero current. The analysis is based on the Nernst equation for the reduction viz. Ox + ne− −→ Red

(12.10)

The cell potential is given by E = E0 − ( RT/nF ) ln

[Red] [Ox]

(12.11)

where E is the overall cell potential, E◦ is the standard potential, R denotes the universal gas constant, and T is the absolute temperature. Ion-selective electrodes are well-known examples of potentiometric sensors, and the choice of ion-selective membranes is the most essential component. A variety of liquid membranes are available to achieve selectivity and sensitivity. Among various ion-selective electrodes, the following deserve mention: (i) Glass membrane electrode for estimating pH and (ii) LaF3 electrodes for sensing of F− . A few the major limitations of potentiometric sensors are: (i) the linear range obtainable is very limited since the potential depends upon log of the activity or concentration (a change of ten times the analyte concentration changes the potential by about 59 millivolts); (ii) limited selectivity and (iii) cumbersome protocols for synthesis of ion-selective membranes.

12.8.2

Voltammetric Biosensors

In recent times, the voltammetric biosensors have gained prominence. Among the voltammetric techniques, the two most effective ones are: (i) cyclic voltammetry and (ii) differential pulse voltammetry. In cyclic

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273

voltammetry, current-potential response of an electrochemical system is recorded at an optimum potential and scan rates (typically 100 millivolts/ sec). The peak current (i p in amperes) is linearly related to the bulk concentration of the analyte (in mol cm −3 ) and is given by the so-called RandlesSevcik equation viz.  i p = 0.4463

F3 R

1/2

n3/2 AD01/2 C0∗ v1/2

(12.12)

where A denotes the area of the electrode in cm2 , D denotes the diffusion coefficient of the analyte (in cm2 /sec) and v denotes the scan rate (in V/sec), with R being the universal gas constant (in J K−1 -mol−1 ). The subtle difference between chronoamperometry and cyclic voltammetry should be noticed. In cyclic voltammetry, the potential is scanned at selected scan rates and the ratio (i p /v1/2 ) is often constant. In amperometric sensing, equal volume of the analytes were added in a controlled manner. In cyclic voltammetry, the construction of cyclic voltammograms (current vs. potential response) is feasible at all concentrations of the analyte with the proviso that the peak current should show appreciable change as the concentration is varied. Although this is a very simple and powerful technique, it is not selective since other analytes also interfere in sensing and hence distort the cyclic voltammograms. Nevertheless, this technique has been employed for sensing of analytes such as dopamine, urea, catechol, glucose, progesterone etc. Among voltammetric biosensors, the differential pulse voltammetry (DPV) occupies a pivotal role in view of its discriminating the voltammetric responses among analytes. This being a pulse technique wherein small amplitude voltage pulses are superimposed, by optimizing pulse width and pulse duration, selective sensing of analytes can be accomplished in a systematic manner.

12.8.3

Impedimetric Biosensors

The impedimetric biosensors constitute a specific application of the electrochemical impedance spectroscopy, often abbreviated as EIS. By applying a sinusoidal perturbation of a range of frequencies (ω ) to the potential ( E) viz. E = E0 sin(ωt)

(12.13)

different types of impedance spectra can be experimentally obtained. In view of the sinusoidal pulse, the resulting impedance behavior has a real

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and imaginary component. The most popular method of analyzing EIS data consists in drawing the Nyquist plots (imaginary part of the impedance vs. real part of the impedance). The frequencies are varied from 10−3 Hertz to 106 Hertz, thus providing a complete ‘spectrum’ of all the events happening in any electrochemical system. Hence, this technique is often called as ‘impedance spectroscopy’. The Nyquist plots provide semi-circles from which the charge transfer resistance and solution resistances can be deduced. Although both these resistances are directly proportional to the bulk concentration of the analyte, the solution resistance is more sensitive. The EIS analysis has been employed for the sensing of glucose, catechol, urea, dopamine etc.

Questions (1) The sensing of Dopamine was carried out using chronoamperometry at a carbon paste electrode. The steady state current was 0.71μA for a 5 mL solution containing unknown concentration of the analyte. Upon adding 0.005 mL of a solution containing 1500 ppb of Dopamine, the steady state current reached 1.54μA. Estimate the approximate concentration of Dopamine in the original solution. Solution: It is well known that the steady state current is linearly proportional to the bulk concentration of the analyte viz. Iss = constant × C (Dopamine) From the given two data, it is easy to construct the following equations: Iss (original) = kC (Dopamine) Iss (upon spiking)

=k

C (added)V (added) C (Dopamine)V (initial) + V (initial) + V(added) V (initial) + V (added)

Upon combining the above two equations and substituting the given data, 1.54 0.71 = C(Dopamine)5 C (Dopamine) + 1500 × 0.005 5.005

5.005

Thus, the concentration of dopamine in the given solution = 1.25 ppb.

Biosensors 

275

(2) The quantitative analysis of progesterone using a pencil graphite electrode yielded the following linear regression equation for the peak current in cyclic voltammetric studies: I p (mA) = 73.1C + 56.2 where C ranges from 0.105 to 1.825μM. For an unknown solution of progesterone, the peak current was 100.5 mA. Estimate the concentration of progesterone. Solution: Substituting the given data, 100.5 = 73.1C + 56.2 Concentration of progesterone = 0.606 μM.

Part II

Biochemical Techniques

13

Surface Plasmon Resonance Spectroscopy 13.1

Introduction

While well-known physico-chemical techniques can in principle be employed to all biochemical reactions and processes, there are certain experimental procedures which are especially applicable in the context of biophysical chemistry and molecular biology. This field is quite exhaustive, and hence a brief outline is provided here. The nature of the technique varies with the information sought. For example, the Surface Plasmon Resonance spectroscopy (SPR) provides valuable insights into non-covalent interactions of proteins. It also yields mechanistic details of the drug delivery process as well as immune response. Among the several techniques available for the study of biochemical reactions, the surface plasmon resonance spectroscopy (SPR) may be cited as a versatile and unique technique. It is a powerful, label free technique to monitor noncovalent molecular interactions in real time and in a noninvasive manner too. Being a label free technique, it does not require tags, dyes or special reagents (like enzyme-substrate complexes) to obtain a visible or fluorescent signal. It has important applications in the areas of electrochemistry, biochemistry, and medicinal chemistry. During the last 20 years, SPR has been applied to study non-covalent interactions of protein-DNA, DNA-DNA, DNA-RNA and cell-protein interactions. In addition, other studies such as protein-protein, proteincarbohydrate, protein-peptide and self-assembled monolayers and their

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_13

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interactions have been investigated. SPR has also been employed to study drug delivery and monitor an immune response against a therapeutic agent. It has been used to study the kinetics, affinity and changes in concentrations of selected molecules of a reaction.

13.2

Details of SPR Set Up

The following figure shows the essential details of this technique.

Figure 13.1 Air-Solution interface. A metal film (Ag or Au) is placed at the interface of two dielectric media. Medium 1 with a higher refractive index (n1 ) is a prism and medium 2 with a lower refractive index (n2 ) may be air or a solution of interest. A parallel beam of polarized light impinges on the medium of higher refractive index (n1 ) and travels to the medium of lower refractive index (n2 ). In doing so, the total internal reflection (TIR) can take place within the medium 1 as long as the incident angle θ is greater than the critical angle θc , where sin θ = n2 /n1 . Quickly fading (or evanescent) waves are formed in the medium of lower refractive index under conditions of TIR. The amplitude of these standing waves decays exponentially with distance upto the interface (interface of media 1 and 2). The evanescent wave is enhanced in the presence of a non-magnetic gold film (as in this case) of sufficient thickness, and it penetrates the gold film and enters the medium 2. The magnitude of the parallel wave vector, Levan,II is given by Levan,II = 2πn1 sin θ/λ

(13.1)

where λ = wavelength of incident wave, n1 = refractive index of medium 1 and θ = incident angle.

Surface Plasmon Resonance Spectroscopy 

13.2.1

281

Surface Plasmon

They are quanta of plasma, a surface electromagnetic wave whose propagation is confined to metal-dielectric interface. The magnitude of the wave vector of the surface plasmon ( LSP ) is related to the dielectric constants of both medium 2 and gold film. For non-absorbing media, the dielectric constant, ε = n22 . Thus LSP is determined by n2 and n g (n g = refractive index of gold film) and

LSP

13.3

  2 2 n n 2π   2 g = 2 λ n2 + n2g

(13.2)

Surface Plasmon Resonance and Refractive Indices

The surface plasmon can be excited by the evanescent wave and this phenomenon is referred as surface plasmon resonance. When resonance occurs, the intensity of the reflected wave decreases sharply. The decay of the excited surface plasmon includes energy conversion to photons (or phonons). For SPR to occur, LSP = Levan,II . Thus from equations (13.1) and (13.2),   2 2 n n 2π  2π  2 g n1 sin θ = 2 λ λ n2 + n2g   2 2 n n 1  2 g sin θ = 2 n1 n2 + n2g ⎛  ⎞  2 2  n × n 1 g 2 ⎠ θSPR = sin−1 ⎝  2 n1 n2 + n2g

(13.3)

(13.4)

(13.5)

The angle required for the resonance, θSPR , is related to n2 when n1 and n g are fixed. Adsorption, desorption processes on gold surface changes the refractive index of medium 2 near the metal-dielectric interface and thus the resonance angle changes. Hence, by monitoring change in SPR, adsorption–desorption, association–dissociation reactions occurring on gold surface can be studied. The intensity of reflected wave as a function of incident angle for gold film in air is shown in Figure 13.2.

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Intensity of reflected light (mV)

300

250

200

SPR angle (35.2°)

150 25

50

75

Incident angle (deg)

Figure 13.2 Reflection of wave for gold film in air. The variation of SPR angle with refractive index is shown in Figure 13.3.

Figure 13.3 Variation of SPR angle with refractive index.

Figure 13.4 Binding of rabbit lgG to protein A and anti-rabbit to lgG to FAB

Surface Plasmon Resonance Spectroscopy 

283

Some applications of SPR spectroscopy (1) Bovine rhodopsin (the light activated receptor) was incorporated into an egg phosphatidylcholine bilayer and this was deposited on a thin silver film. The tight binding and activation of its associated G-protein was established by SPR. (2) In another experiment, Streptavidin was bound to biotinylated-thiols in a mixed self-assembled monolayer (SAM) with an excess of ωhydroxy-undecanethiol (HTA) on the metal surface, which then get bound the biotinylated receptor to the surface through its extracellular N-terminus in a defined orientation. Following immobilization of the receptor and thorough washing with detergent, a supported lipid bilayer was formed around the receptors. The activity of the immobilized receptor was observed in SPR data following its illumination with light which was achieved by SPR. Illumination-induced activity of the G-protein was followed by its desorption from the membrane. Ligand binding was monitored and quantified from SPR data by adding IIcis-retinol with increasing concentrations to the immobilized and completely photolysed receptor. The above experiment is pictorially demonstrated below: (1) SPR has been used to characterize ligand binding to the human chemokine receptors CCR-5 and CXCR-4. These receptors have also been used to demonstrate important developments in SPR methods for purification, solubilization, reconstruction and functional analysis of GPCR’s.

Figure 13.5 Illumination-induced activity of G-protein and its desorption form the membrane.

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Biophysical Chemistry

(2) A novel receptor analyte configuration was used to characterize neurotensin receptor-I binding to the neurotransmitter peptide neurotin using 5PR. (3) Using the adenosine A2A receptor, a new approach called Biophysical Mapping (BPM) has been developed that combines a thermostabilized GPCR with SPR analysis of ligand binding to binding site mutants.

13.4

Kinetic Applications of SPR Spectroscopy

For a bimolecular reaction between two species S and L according to k1 BG SL S + L FGGGGGG GGGGG k −1

(13.6)

d[SL] = k1 [S][ L] − k −1 [SL] dt

(13.7)

where k1 and k −1 are forward and reverse rate constants. The concentration of SL is monitored by measuring the change in the refractive index at the surface of the sensor. By varying the concentration of L the SPR response for the system is fit to the integrated rate equation Rt =

 Rmax k1 [ L]  1 − e−(k−1 [ L]+k1 )t k 1 [ L ] + k −1

(13.8)

where Rt is the response measured at time t, Rmax is the maximum response obtained upon saturation of S with L. By varying the concentration of L, and by fitting the data to equation (13.7), k1 and k −1 can be determined. The binding of a target ligand (mass = 50, 000 a.m.u.) to immobilized chymotrypsin was studied. A number of antibodies-antigen interactions have been studied using SPR. The interaction rates of DNA-based aptamers with human immune globulin E have been studied. SPR has also been used to examine the interactions of human carbonic anhydrase-I with various sulfonamide inhibitors. SPR has been employed to investigate biological interactions that include reactions with second order rate constants in the range of 102 to 108 M−1 sec−1 and first order rate constants from 10−6 to 1 sec.

Surface Plasmon Resonance Spectroscopy 

285

Questions (1) The magnitude of the wave vector of surface plasmon Lsp is given by    2 2  2 2  n n n n λ  2 g λ  2 g (c) L = (a) Lsp = sp 2 2 2π n2 + n2g π n2 + n2g    2  2 2 2  n + n n n 2π  2 2π  g  2 g (b) Lsp = (d) L = sp 2 2 λ λ n2 n2g n2 + n2g (n2 = refractive of medium; n g = refractive index of gold film; λ = wavelength of the surface wave) (2) If the refractive indices of glass and gold film are 1.5 and 0.181 respectively, the SPR angle for resonance is (a) 10.5◦ (b) 7.4◦ Solution:

(c) 22.9 (d) 20.9   2 n × n2g 1  2 sin θ = n1 n22 + n2g

where n1 is refractive index of glass, n2 is refractive index of gold film, therefore  1 0.33 × 2.25 sin θ = 1.5 0.33 + 2.25  1 0.7425 = 1.5 2.58 = 0.667 × 0.536 = 0.357 θ = 20.9 (3) Explain the principle of surface plasmon resonance spectroscopy and discuss some applications of this technique. (4) Outline the applications of SPR spectroscopy in ligand binding to human chemokine receptors.

14

Affinity Chromatography 14.1

Introduction

Affinity chromatography is one of the most diverse and important methods for the purification of a given molecule or a group of molecules from complex mixtures. It is based on highly specific biological interactions between two molecules such as interactions between an enzyme and substrate, a receptor and ligand or antibody and antigen. These interactions, which are typically reversible, are used for purification by placing one of the interacting molecules, referred as affinity ligand, onto a solid matrix to create a stationary phase while the target molecule is in the mobile phase. A successful affinity purification requires some understanding of the nature of interactions between the target molecule to help determine the selection of an appropriate affinity ligand and purification procedure. Because this technique relies on this interaction between molecules, it can purify a molecule on the basis of its biological function or individual chemical structure. This technique can also be used for separation of biomolecules based on highly specific biological interactions between two molecules such as an enzyme and substrate. The biological interactions between the ligand and a target molecule can be a result of electrostatic or hydrophobic interactions, van der Waals forces or H-bonding.

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_14

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14.2

Biophysical Chemistry

Methodology

The separation procedure in affinity chromatography is illustrated in the following diagram which consists of four steps. The sample is applied under optimum conditions that form specific binding of the target molecules to the binding molecules (ligand). The desired molecules bind specifically but reversibly to the ligand and unbound molecules wash through the column. Target molecule is recovered by changing conditions that favour elution of the bound molecules. Elution is carried out specifically using a competitive ligand or non-specifically by changing pH, ionic strength or polarity. Target protein is collected in a purified, concentrated form. Affinity medium is re-equilibrated with binding buffer. In the following figure, a typical scheme is shown which shows the application of affinity chromatography. Affinity chromatography with biological ligands is referred as “bioaffinity chromatography”. A number of names have been proposed depending upon the wide application potential of affinity chromatography. Some of them are: (i) Immuno affinity chromatography, (ii) High performance affinity chromatography, (iii) Lectin affinity chromatography, (iv) Dye-ligand affinity chromatography, (v) Affinity electrophoresis, (vi) Avidin-Biotin immobilized system based affinity chromatography,

Figure 14.1 Separation procedure in affinity chromatography.

Affinity Chromatography 

289

Figure 14.2 Variation of absorbance with time. (vii) Membrane based affinity chromatography, (viii) Covalent affinity chromatography, and (ix) Hydrophobic chromatography. Some factors that influence the success of an affinity chromatographic experiment are: (i) Selectivity of ligand, (ii) Recovery process, (iii) Reproducibility, (iv) Stability, and (v) Economic criteria. Before the start of an experiment, the following factors need, therefore, to be considered: (i) Support material, (ii) Activation method, (iii) Ligand, (iv) Immobilization method, and (v) Conditions for adsorption and desorption. A brief description of each of the above factors is given below.

14.2.1

Support Material

It is necessary that the support in the column contains an affinity ligand capable of forming a strong complex with the solute of interest. Also, the support material must be chemically and biologically inert to avoid unspecific bindings. The material must also be hydrophilic as most reactions are carried in aqueous solution. Uniformity of particle size and ease of activation of support material are also important. The support materials can be

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Biophysical Chemistry

divided into three categories: (a) natural, such as agarose, dextrose, cellulose, (b) synthetics such as acrylamide, polystyrene, polymethyl methacrylate, (c) inorganic, such as silica, glass etc. Among the above materials, agarose is widely used. The structure of agarose may be represented as shown below. CH2OH

H O

HO

O

H

H O OH

H

O H

H

H

H

CH2OH O

O H

O

OH

Figure 14.3 Structure of agarose. Cellulose is another example of polysaccharides which is used as support in affinity chromatography. Other supports used are polystyrene, porous glass, silica. Silica based materials are used in high performance affinity chromatography because they are basically hydrophilic as can be seen by the structure of silica. OH Si

OH O

Si

OH O

Si

O

O

O

Si

Si

Si

Figure 14.4 Structure of silica. Membranes have been used in various forms such as stacked sheets, in rolled geometrics or as hollow fibers. Materials commonly used for membranes are cellulose, polysulfone and polyamide.

14.2.2

Ligand

Ligands are molecules that bind reversibly to a specific molecule enabling purification by affinity chromatography. These molecules play a major role in the specificity and stability of the system. The selected ligand must be capable of selectively and reversibly binding to the substance to be isolated and have also some groups which are available for modifications to

Affinity Chromatography 

291

be attached to the support material. There are a variety of ligands like dyes, amino acids, protein A, lectin, metal chelates as well as specific ligands such as enzymes, substrates, antibodies and antigen. These ligands can be synthetic or biological too. Biological ligands include RNA, DNA fragments, nucleotides, coenzymes, vitamins, binding or receptor proteins. Synthetic affinity ligands are generated by synthetic methods or by modification of existing structures like purine, pyrimidine structures, unnatural peptides, triazine based ligands, oligosaccharide ligands etc. Many parameters such as cost, selectivity, stability, toxicity have to be considered. Despite the advantages of the techniques its use is limited due to the high cost of affinity ligands and their biological and chemical instability. Biological ligands have high selectivity but their binding capacity is low. Synthetic ligands are in that sense preferable because they provide selectivity and are also inexpensive. Ligands which possess affinity to the immobilized protein are suggested as ligands. The selection of the ligand may be designed according to the structure of the target protein as well.

14.2.3

Immobilization of Ligand

Immobilized ligand is an essential factor that determines the success of the method. Several methods are available to couple a ligand to a preactivated matrix. Before the ligands are coupled, the matrix is activated. Commercially preactivated products are available in the market and a few are listed in Table 14.1. Table 14.1 Examples of pre-activated products for immobilizing ligands. Product name Functional group specificity Carbolink coupling resins CHO, C=0 Epoxy activated agrose 6B −NH2 , −OH, −SH Tresyl chloride activated agarose −NH2 , −SH

Ultra link iodoacetyl resin −SH Profinity epoxide resin −NH2, −OH, −SH EAH sepharose 4B −COOH, −CHO Thiopropyl sepharose 6B −SH

After the activation of the support material, it is ready for immobilization process of ligand. If the ligand is a small molecule, steric hindrance will occur between the immobilized support and the compound of interest. Use of supports having spacer arms before immobilization is recommended.

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Biophysical Chemistry

Ligand Amt eluted Spacer arm 0

5

10

15

20

25

Elution volume (ml)

Figure 14.5 Dependence of eluted amount with elution volume.

Spacer arms are used to improve binding between ligand and a target molecule by overcoming effects of steric hindrance. Compounds which have diamine groups such as hexanediamine, propane diamine, ethylenediamine are preferred spacer arms. The next step is the immobilization of ligands on the activated matrix. For this, esters like N-hydroxy succinimide esters are used. Immobilisation methods can be classified as follows. General types of immobilisation methods

Covalent methods

Nonspecific adsorption

Noncovalent methods

Biospecific adsorption

Co-ordination methods

Entrapment

Figure 14.6 Different types of immobilization methods. The simple adsorption of ligand to surface, binding to a secondary ligand, or ligand immobilization through a co-ordination complex belong to non-covalent immobilization method. In covalent immobilization method, it is necessary to activate the ligand or support first. Activating of the ligand can be carried when it is desired to couple this ligand through a specific region. An example is the immobilization of proteins through their amino group to supports activated with N-hydroxy succinimide or carbonyl diimidazole. Amine groups are often used to immobilize proteins and peptides. Reductive amination (also known as Schiff’s base method) couples’ ligands to activated periodate is used to oxidize diol groups on the surface of the support to give aldehydes.

Affinity Chromatography 

14.2.4

293

N-hydroxy Succinimide Method (NHS)

The NHS method is often employed when immobilizing biomolecules through amine groups. This gives rise to the formation of a stable amide bond. The immobilization via NHS is depicted below: O

O O

NH2 +

O

N

O

C

(CH2)n

C

O

O

N O

DMF O O NH2

C

O (CH2)n

C

O

N O

NHS activated support pH 7–8 Ligand O NH2

C

NH2

O (CH2)n

C

O

NH

Ligand

Figure 14.7 Immobilization by N-hydroxy succinimide method.

14.2.5

Carbonyl Diimidazole Method (CDI)

This reagent can be used to activate supports for the immobilization of amine containing ligands. This method is simple and easy to carryout. The immobilization using CDI is shown in Figure 14.8. There are several other methods for preparing affinity supports such as sulfhydryl reactive methods, haloacetyl method, maleimide method, pyridyl disulfide method etc.

14.2.6

Elution

Elution is a critical step for success of the experiment. After all non-retained components are washed off the column, the retained solute with the ligand as ligand-solute complex can be eluted by treating with solvent. Step gradient elution is the most common method employed in affinity chromatography.

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Biophysical Chemistry O COOH

+

N

Carboxyl containing matrix O C

N

C

N

N

Carbonyl diimidazole

O O

C

N

N

Carbamate support pH 9–10 Ligand

NH2

O C

NH

Ligand

Figure 14.8 Immobilization using carbonyl diimidazole method. Step elution method is employed if the ligand has high affinity for target molecule. There are also other factors to be considered such as strength of solute-ligand interaction, amount of immobilised ligand present and the kinetics of solute-ligand association which have influence on retention and elution of the compound. Obtaining stable biomolecules in high yield and purity is of utmost importance in elution process.

14.3

Types of Affinity Chromatography (A.C.)

Depending on the type of ligand used, several names have been given to affinity chromatography, such as Immuno affinity chromatography, Protein-A or Protein-G A.A, Lectin A.A, Dye-ligand A.A, metal-chelate A.A, etc. A brief account of these techniques is given below:

• Lectin A.C.: Certain types of carbohydrate residues may be separated by this method because all lectins have the ability to recognize and bind this type of compounds. The commonly used columns are concanavalin A, soybean lectin, and wheat germ agglutinin. Concanavalin A is specific for α-D-mannose and α-D-glucose while wheat germ agglutinin binds to D-N-acetyl glucosamine. Some commonly used lectins for isolation of compounds containing carbohydrates and polysaccharides are listed in Table 14.2.

Affinity Chromatography 

Table 14.2 Examples of commonly used lectins drates and polysaccharides. Lectin Source Sugar specificity Con A Jack bean α-D-mannose, seeds α-D-glucose WG A Wheat germ N-acetyl-β-Dglucosamine PSA Peas α-D-mannose LEL Tomato N-acetyl-β-Dglucosamine STL Potato N-acetyl-β-Dtubers glucosamine PHA Red kidney N-acetyl-β-Dbean glucosamine

295

for isolation of carbohyEluting sugar α-D-methyl mannose N-acetyl-β-Dglucosamine α-D-methyl mannose N-acetyl-β-Dglucosamine N-acetyl-β-Dglucosamine N-acetyl-β-Dglucosamine

Enzymes, cofactors, inhibitors, nucleic acids can be used as ligands in bio-affinity chromatography.

• Immuno A.C: In this technique, the stationary phase comprises of an antibody or antibody related agent. This technique is useful for analyzing natural food contaminants such as aflatoxins. First, the antibodies are immobilized on a support. To bind the ligand on the support properly, protein-A or protein-G is often used as a bridge which provides enough space for ligand protein binding. Initially, the antibodies should be purified prior to preparing the immunoaffinity column. Both large and small analytes can be determined using direct detection in A.C. Immuno A.C. is a highly specific form of bioaffinity chromatography. • Metal-Chelate A.C.: This technique exploits selective interactions and affinity between transition metal ions immobilised on a solid support (resin) via a metal chelator and amino acid residues in the protein of interest. Amino acids such as histidine, tyrosine, phenylalanine, tryptophane form complexes with transition metal ions. Adsorbents may be prepared by binding chelators onto the surface and metals to the chelators. Zn2+ , Na2+ , Cu2+ and Hard Lewis acids like Ca2+ , Mg2+ , Fe3+ , soft Lewis acids like Ag+, Cu+ are some of the common used metal ions. Ligands containing −COOH groups, aliphatic nitrogen groups in compounds like glutamine, phosphorylated amino acids, cysteine are the ligands of choice. For metal ions like Cu(II), Ni(II), Co(II), Zn(II) the target amino acids on the protein

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Biophysical Chemistry

surface are imidazoyl, thiol and indolyl groups. A list of chelating agents and the metal ions are given in Table 14.3. Table 14.3 List of chelating agents and corresponding metal ions. Chelating Salicyl aldehyde 8-hydroxy quinolone compound Metal ion Ca(II) Al(III), Fe(III), Yb(III) Co-ordination Bidentate Bidentate Imino diacetic acid Ortho phosphoserine Nitrilotriacetic acid Cu(II), Zn(II), Ni(II), Fe(III), Al(III), Yb(III), Ni(II) Co(II) Ca(II) Tridentate Tri-dentate Tetra-dentate N-N-Nt’-(tricarboxy methyl) ethylene diamine Cu(II), Zn(II) Penta-dentate

• Protein-A or Protein-G A.C.: These ligands are capable of binding to many types of immunoglobulins near about neutral pH. These two ligands differ in their ability to bind to antibodies from different species. They are good ligands for the separation of immuneglobulins. • Dye ligand A.C.: Some proteins bind triazine dye and this allows it to be used as an affinity adsorbent by immobilization. This method is especially popular for enzyme and protein purification. Procion Red HZ3b, cibacron Blue F3GA are some examples of dyeligands use for purification.

14.3.1

Applications

Affinity chromatography finds applications in pharmaceutical and biomedical analysis, drug discovery. This technique is useful in isolating and identifying target molecules for a specific ligand utilizing affinity between biomolecules such as antigen-antibody reactions. An example of a target protein isolated and identified by using this technique is given in Figure 14.9.

14.3.2

Purification of Specific Groups of Molecules

The diversity of antibody-antigen interactions available makes them useful for therapeutic and diagnostic applications as well as for immunochemical techniques. Affinity chromatography provides an important method for purification of antibodies and antibodies.

Affinity Chromatography 

NH H2N

O

H N N H

297

OH O

N H

O

O

Figure 14.9 Target protein identification using affinity chromatography. Protein-A and Protein-G are bacterial proteins, which upon coupling to Sepharose create very useful media for many applications. Examples include purification of monoclonal IgG type antibodies, purification of polyclonal IgG subclasses and adsorption and purification of immune complexes involving IgG.

14.4

Kinetic Applications of Affinity Chromatography

An important advantage of using AC or high-performance AC for kinetic investigations of biological reactions is its ability to use the same immobilized binding agent for many experiments. Two important advantages

Figure 14.10 Application of high performance affinity chromatography in estimating rate constants.

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Biophysical Chemistry

that this method offers are: (i) its reproducibility and (ii) variety of methods available for kinetic experiments. Second order rate constants ranging from 103 to 107 M−1 sec−1 and dissociation constants in the range 10−2 to 10−1 sec−1 have been measured. Various supports and surfaces can be used for immobilizing binding agent since detection is done after the target or other sample components have eluted from the column. For detection, absorbance, fluorescence, mass spectrometry have been used. The immobilisation methods involve the use of amines, thiols for immobilization of proteins. Two methods have been employed in H.P.A.C. and AC for determining the rate constants. They are depicted in the Figure 14.11. Analysis of band broadening in affinity chromatography provides information on the kinetics of interaction of an analyte with a given binding agent. The plate height method for kinetic studies makes use of a small quantity of target that is injected onto an affinity column as well as onto control column at several flow rates. This method was used to analyze the binding of D-tryptophan with an HPAC column containing immobilized HAS as shown in Figure 14.11.

Figure 14.11 Binding of D-tryptophan with a HPAC column containing immobilized HSA.

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299

Questions (1) (a) Explain the application of affinity chromatography in the separation of biomolecules. (b) What are the different types of affinity chromatography employed in the separation procedure. Give an account of support materials. (2) Describe the application of affinity chromatography in kinetic studies. (3) The technique of affinity chromatography is most useful for (a) synthesis of a compound from the required reactants. (b) purification of a compound from complex mixtures. (c) separation of a compound from mixtures containing high concentration of contaminants. (d) none of the above. (4) SPR spectroscopy is generally useful to study the rates of reactions of (a) first order reactions with rate constants of the order 10−8 sec−1 . (b) zero order reactions with rate constants of the order of 105 moles l−1 sec−1 . (c) second order reactions with the rate constants of the order of 102 to 108 l mol−1 sec−1 . (d) none of the above.

15

Capillary Electrophoresis 15.1

Introduction

This technique employs narrow bore capillaries whose internal diameters range from 20 to 200 μm to perform separations of a variety of molecules with high efficiency. The separations are carrier out using high voltage which generates electro osmotic and electrophoretic flow of buffer constituents and ions within the capillary. The format of Capillary Electrophoresis (CE) requires the following: (i) capillary tubing of the dimensions mentioned above, (ii) high electric field strengths of the order of 500 V/cm and (iii) modern detector technology. Its advantages are (i) requirement of very small samples, (ii) can be automated for precise quantitative analysis, (iii) user-friendly, (iv) use of small amounts of reagents, and (v) applicability to a wide selection of analytes.

15.2

Basic Instrumentation

(i) A fused silica capillary with an optical viewing window, (ii) A controllable high voltage power supply, (iii) Two electrode assemblies, (iv) Two buffer reservoirs, (v) An ultraviolet detector are the required components.

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A schematic diagram of a CE, unit is given in Figure 15.1.

Figure 15.1 Diagram of a capillary electrophoresis unit. After filling the capillary with buffer, the sample is introduced by dipping the capillary into sample solution and raising the capillary above the detector side buffer reservoir.

Useful Terminology in CE (i) Migration time (tm ), it is the time taken by a solute to move from the beginning of the capillary to the detector window. (ii) electrophoretic mobility (μeq which has units cm2 V −1 sec−1 ), (iii) electrophoretic velocity Vep (cm sec−1 ) and (iv) electrical field strength E (V/cm). The relation among them is given by μeq =

Vep L /tm = d E V/Lt

(15.1)

where Ld = length of capillary upto the detector, V = potential, Lt = total length of capillary.

Electro Osmosis This phenomenon is a consequence of the surface charge on the wall of the capillary. The fused silica capillaries have ionizable groups in contact with the buffer in the capillary. The electro osmotic flow is given by Vε0 =

εZJ E 4πη

(15.2)

ε = dielectric constant of the medium, η = viscosity of the buffer, J = zeta potential close to liquid-solid interface.

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The negatively charged wall attracts the +vely charged ions from the buffer which results in the electrical double layer. Under the influence of an applied potential across the capillary, cations in the diffuse portion of the double layer move towards the cathode carrying water with them. The net result is flow of buffer solution in the direction of negative electrode. This flow enables the simultaneous analysis of cations, anions and neutral species in a single analysis. The effect of pH on electro osmotic flow is shown below. Electroosmotic flow High pH + O+ O+ O+ O+

–

Low pH + OH O +

OH O OH – +

Figure 15.2 Effect of pH on electro osmotic flow.

15.3

Capillary Diameter and Joule Heating

The production of heat in CE is the result of application of high field strengths. The quantity of heat generated is proportional to the square of the field strength. Temperature gradients across the capillary are a consequence of heat dissipation. Both the electro osmotic flow and electrophoretic velocities are directly proportional to the field strength. Hence, use of highest possible voltages will result in shorter times of separation.

15.4

Various Types of Electrophoresis

The various types of electrophoresis have different operative and separative characteristics. The techniques are: (i) Capillary zone electrophoresis (CZE), (ii) Isoelectric focusing (IEF), (iii) Capillary gel electrophoresis (CGE), (iv) Isotachophoresis (ITP), and (v) Micellar electrokinetic capillary chromatography (MECC). A brief account of these types is given below. (i) Capillary Zone Electrophoresis (CZE): The separation mechanism in this technique is based on differences in charge to mass ratio. In CZE, it is important to maintain homogeneity of the buffer solution and constant field strength throughout the length of the capillary.

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After injection and application of voltage, the components of a simple mixture separate into discrete zones as shown below:

Figure 15.3 Separation of components using electrophoretic. The fundamental parameter, the electrophoretic mobility μeq is given by q μeq = (15.3) 6πηRhyd where q = net charge, Rhyd = hydrodynamic or Stokes radius, η = viscosity of the medium. The movement of a species in a CZE experiment depends upon the charge which in turn depends on pH of the medium. Zwitterions like those of amino acids, proteins, peptides exhibit charge reversal at their isoelectric points and hence shifts in the direction of electrophoretic mobility occur. For capillary material, fused silica is preferred because of its UV transparency and durability. The capillary must be conditioned before its use. Buffers: A wide variety of buffers are employed in CZE. Zwitterionic buffers such as bicine, tricine, MES and Tris are commonly employed in protein and peptide separations. These buffers have the advantage of low conductivity and reduced Joule heating. Sometimes, buffer additives can be employed to change the selectivity of separation. They also change the electrophoretic mobilities. Applications: Among the analytes hitherto-studied using CZE, mention may be made of the following: (i) proteins; (ii) β-lactoglobulin; (iii) myoglobin; (iv) ribonucleases; (v) Adenosine-5 [α − 32P] Triphosphate; (vi) α-chymotrypsin and (vii) collagens. (ii) Isoelectric Focusing (IEF): It is assumed in IEF that a charged molecule will migrate under the influence of an applied field. A gradient of electric field with low pH at anode and high pH at cathode is maintained in IEF. The pH is generated with a number of zwitterionic compounds known as carrier ampholytes. The ampholyte mixture gets separated under the field and they migrate to cathode

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or anode depending on the charge they carry. The pH will decrease at cathodic section and increase at anodic section. Ampholyte migration will cease once the isoelectric point of the ampholyte is reached. The migration of charges under the field is shown in Figure 15.4.

−

pI (Isoelectric point) Low pH

⊕ High pH

Figure 15.4 Migration of charges using isoelectric focusing method. The electro-osmotic flow and other convective forces must be suppressed for effective IEF. For this purpose, the capillary walls are coated with methyl cellulose or polyacrylamide IEF is used for high resolution separation of proteins and polypeptides. There are three basic steps in IEF: (i) loading, (ii) Focusing, and (iii) mobilization. After loading and focusing are completed, the gel is stained using traditional methods. In IEF, the bands must migrate past the detector. As mentioned earlier, a pH gradient is formed along the capillary. Applications: IEF is useful for separating immunoglobulins, hemoglobin variants, recombinant proteins. The isoelectric point of a protein can be determined. A diagram showing the separation of a protein mixture is given below:

Figure 15.5 Separation of proteins using isoelectric focusing method.

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(iii) Capillary Gel Electrophoresis (CGE): CGE is conducted in an anticonvective medium such as polyacrylamide or agarose. The gel suppresses the EOF. The composition of the media can also serve as a molecular sieve to perform size separations as shown below:

Figure 15.6 Size separation using capillary gel electrophoresis. Two classes of gels are employed in CGE: (i) physical gels and (ii) chemical gels. The physical gel attains its porous structure by entanglement of polymers and is quite rugged to changes in environment. An example of such gels is hydroxy propyl methyl cellulose. Chemical gels use covalent attachment to form porous structure.

Physical gel

Chemical gel

Figure 15.7 Physical and chemical gels. Cross linked polyacrylamide is commonly used as the gel forming agent along with urea and other buffer agents like Tris-borate-EDTA. CGE is usually carried in 50–100 μm capillaries of length 10 cms to 1 m. The applied voltage is restricted to less than 500 V/cm. Applications: (i) Protein separations: Proteins are initially denatured using 2mercapto ethanol and treated with SDS. Under these conditions, all the proteins have the same charge to mass ratio because the native charge is obscured by SDS binding. In the presence of SDS, all proteins become negatively charged and migrate towards anode. They unfold and have rod like structure allowing uniform molecular sieving for size separation. A calibration graph of mobility vs. molar mass permits size assignments of the fragments. Usually, 10–20 cm size capillaries

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are employed with field strengths in the range of 400 V/cm. Under these conditions the correlation of mobility with molecular weight is linear. The denaturing of proteins is usually done in 1% SDS and 2% mercapto ethanol for 30 minutes at 363 K. (ii) DNA: Separation of oligonucleotides and DNA sequence products are carried out in poly acrylamide gels. Separation of deoxy oligonucleotides such as poly (dA) 40–60 is accomplished in 8% T gel using a buffer of Tris-borate at pH = 8.3 in presence of 2 mMEDTA and 7 M urea. Determination of the purity of synthetic oligonucleotides is an important application of CGE. The CGE of thymidine synthetic homopolymer using buffer of Tris (25 × 10−3 M), boric acid (25 × 10−3 M), 7 M Urea and polyacrylamide gel, 7.5% T, 3.3% C is shown below:

Figure 15.8 Capillary gel electrophoresis of thymidine synthetic polymer. Double stranded DNA can be separated with physical gels. The separation of Hae-III restriction digest of OX174 DNA has also been carried out using CGE. (iv) Isotachophoresis (ITP): Like IEF, ITP is based on zero EOF and the buffer system is heterogeneous. The sample is injected after filling it with a leading electrolyte that has a higher mobility than any of the sample components to be determined. A terminating electrolyte, whose ionic mobility is lower than any of the sample components, occupies the opposite reservoir. The separation occurs in the gap between the leading and terminating electrolytes based on individual mobilities of analytes. Highly efficient separations result due to stable boundaries formed between individual components.

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Differential conductivity and an UV detection are commonly employed as detection techniques. The selection and optimization of the buffer are important factors to be considered in these studies. The ITP of a mixture of anions with conductivity detection is shown below:

Figure 15.9 Isotachophoresis of a mixture of anions. Capillary size: 105 μm id; fluorinated ethylene-propylene co-polymer leader; 10 × 10−3 HCl titrated to pH = 6.0 with histidine, 2 × 10−3 hydroxyethyl cellulose terminator; 5 × 10−3 MES, current = 10μA. Anions measured: L; Cl− ; 1: SO24 ; 2 : ClO3− ; 3: CrO24− ; 4: malonate; 5: adipate; 6: benzoates; 7: impurity; 8: acetate; 9: β-bromopropionate; 10: naphthalene, 2-sulfonate; 11: glutamate; 12: enantate, T, MES. In isotachophoresis, all bands move with the same velocity and bands are clear cut. EOF can be suppressed with 0–25% hydroxypropyl methyl cellulose. Leading electrolyte 5 × 10−3 H3 PO4 and 10−2 M Valine as terminating electrolyte are commonly employed. (v) Micellar Electrokinetic Capillary Chromatography (MECC): The use of micelle forming surfactant solutions can give rise to separations resembling reverse phase L.C.

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Among the surfactants, the anionic surfactant, SDS and cationic surfactant CTAB are most useful in MECC. Naturally occurring bile salts are also useful. Micelles have the ability to organize analytes at molecular level based on hydrophobic and electrostatic interactions. Even neutral molecules can bind to micelles since the hydrophobic core has strong solubilizing power. Surfactant solutions can serve as chromatographic mobile phase carriers with respect to MECC. The analyte can partition between micellar phase and bulk phase or between micellar and stationary phase as well. Separation mechanism: In neutral or alkaline pH, a strong EOF moves in the direction of cathode. In the presence of an anionic surfactant like SDS, the electrophoretic migration of the anionic micelle is towards anode. When an analyte is associated with a micelle, its overall migration velocity is slowed. Analytes that have greater affinity for micelle have slower migration velocities compared to analytes that spend more time in bulk phase. When using a cationic surfactant the EOF is reversed. Therefore, the electrode polarity must also be reversed to detect the analyte. Order of migration: In presence of SDS, the general migration order is anions, neutral molecules, cations. Anions spend more time in the bulk phase than in micellar phase because of electrostatic repulsions between the −ve surfactant and anions. Neutral molecules get separated due to hydrophobicity. Cations elute last due to strong electrostatic attraction due to the formation of ion pairs with micelles. Applications: The separation of some corticosteroids using NaClO3 as a surfactant has been demonstrated by MECC. Use of organic modifiers reduces EOF and the overall peak capacity of separation also increases. Modifier also makes the bulk solution more receptive to hydrophobic analytes. The commonly used organic modifiers are methanol and acetonitrile in the range 5 to 25%. Other solvents like DMSO, DMF are also used as modifiers.

15.5

Chiral Recognition

Additives such as optically active bile salts and cyclodextrins permit chiral resolution by stereo selective interaction with the solute. The interaction occurs with in the molecular cavity in the case of cyclodextrins by forming an inclusion complex. When an analyte is complexed with micellar or

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cyclodextrin additive, its migration velocity is slowed down relative to the bulk phase. Another approach to chiral selectivity is precapillary derivatisation. The analyte is derivatised with an optically active reagent to form covalently bound diasteromers. They are easily separable by MECC. The separation of chiral amino acids derivatised with Marfey’s reagent (1-fluoro-2, 4 dinitrophenyl-5-L-alanine) is shown in the Figure 15.10.

Figure 15.10 Separation of chiral amino acids using MECC. MECC has been applied to a variety of separation studies involving modified nucleic acids, penicillin, urinary porphyrins, water-soluble vitamins, β-lactum antibiotics, sulphonamides etc.

Questions (1) (a) Give a sketch of the capillary electrophoretic unit and indicate the various parts. (b) What is capillary zone electrophoresis and describe some of its applications. (2) Electroosmosis is due to (a) flow of ions of the buffer to the respective electrodes. (b) flow of ions of the analyte to the respective electrodes.

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(c) the presence of surface charges on the walls of the capillary. (d) the absence of electrical double layer in the analyte. (3) Explain the principle of capillary gel electrophoresis and outline its uses in separation of proteins and DNA. (4) What is Micellar electrokinetic capillary electrophoresis and discuss its applications. (5) Calculate the electrophoretic mobility of blood given its viscosity is 4.5 × 10−2 pascals and its hydrodynamic radius as 3 nm. (6) Calculate the electrophoretic mobility of a solute moving under an electrical field of strength 250 V cm−1 in which the length of the capillary is 10 cm (upto detector window) with the total length of the capillary being 15 cm. Under these conditions, the solute takes 30 min to migrate from the beginning of the capillary to the detector window. What is its mobility if the electric field strength is doubled?

16

NMR Technique in the Elucidation of Biochemical Problems 16.1

Introduction

NMR is a spectroscopic technique concerned with the magnetic properties of certain nuclei (NMR active) such as the nucleus of H atom or the C-13 isotope of carbon. Only those nuclei possessing non-zero nuclear spin have a nuclear magnetic moment which produces magnetic interactions with an external magnetic field. The NMR active nucleus will have the energy level splitting when placed in an external magnetic field. A radio frequency pulse of the right frequency would induce transitions of nuclei from the lower to higher energy levels. After the radio frequency pulse is switched off, the nucleus at the higher energy states relaxes to the lower energy states giving out signals. This is referred as Nuclear Zeeman effect. Since the energy level splitting is different for different nuclei, the frequency of the signal becomes a characteristic for a specific atom (Larmor frequency). Since the resonance frequency W0 of the radiation is proportional to ΔE, the energy of splitting which in turn is proportional to magnetic fields strength H, one may write W0 = γH

(16.1)

where γ is a proportionality constant known as gyromagnetic ratio and is a constant for a given atomic nucleus.

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Atoms such as 1 H, 2 H, 13 C, 15 N, 31 P are common nuclei studied using NMR in biomedical research.

16.2

Basics of NMR

The following diagram illustrates the basic features of NMR. B0 (Magnetic field strength)

off

1≠0 (nuclear spin)

on

on

ΔE = r B0

ΔE = hν

Energy level splitting ΔE

on

Relaxation

NMR signal + hν

Radio frequency pulse (υ )

Figure 16.1 Basic features of NMR. The nuclear energy level splits in an external magnetic field. The splitting ΔE is determined by the field strength B0 and the gyromagnetic ratio γ. The radio frequency pulse induces a transition of nuclei from low to high energy level. The nuclei at high energy level (excited state) would relax back to lower energy level and give NMR signal. It may be pointed out that the nuclei that exhibit NMR are those for which the spin quantum number I  is greater than zero and this, in turn, is associated with the mass number and atomic number as shown below: Table 16.1 Mass numbers, atomic numbers and spin quantum numbers. Mass number Even Even Odd

Atomic number Even Odd Even or odd

Spin quantum number 0 1, 2, 3, . . . 1 3 5 2, 2, 2, . . .

Hence, nuclei such as 12 C, 16 O have I  = 0 and hence are non-magnetic. Nuclei like 13 C, 31 P are magnetic nuclei.

16.3

Applications of NMR

NMR can be used to identify molecules and to study molecular interactions. It has been applied to the structure and function determination of

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 315

important biological molecules such as drugs and their interaction with targets. NMR has also been employed for identification of abnormal metabolites as biomarkers for specific diseases, also diagnoses of disorders by imaging particular tissues or organs. The interactions within pFMRP—Caprin-I biological condensates were proved by solution state NMR. It may be mentioned that there are four major interactions besides, the Zeeman interaction (discussed earlier), which include chemical shift, dipolar, paramagnetic and quadrupole interactions. These interactions are susceptible to molecular motion and chemical environment (such as chemical bonding, spatial arrangement of atoms in a molecule etc.) which in turn affect the position, intensity and splitting of NMR peaks. The size and motion of molecules also affect NMR relaxation properties. For example, the relaxation behavior in tissues has been utilized in magnetic resonance imaging (MRI) to take images of different parts of the body.

16.4

Applications of NMR in Biomedical Research

It is known that the main building blocks of our body are composed of proteins, nucleic acids, lipids and carbohydrates. Each class of these body blocks metabolise in different ways to provide energy to the body.

16.4.1

Determination of Protein Structure

Proteins account for more than 75% of the drug targets. They also are used as drugs to maintain our body. Knowledge of the structure of a particular protein helps in our understanding how it achieves its specific function. For example, the binding of APP9mer to the GABAB RI a single domain has been investigated with NMR. Proteins are biopolymers made of different amino acids in different orders and lengths and thus form different threedimensional structures. An example of a protein sequence is shown below: H

H

R1

N

C2

C′

N

C2

C′

N

C2

H

R1

O

H

H

O

H

RN O

C′

Figure 16.2 Protein sequence formed by connecting peptide bonds. It is not easy to assign each chemical shift to a specific atom in the amino acid sequence of amino acids due to the crowded nature of the one dimensional NMR (see Fig. 16.3). By using high field NMR one can obtain

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a spectrum of higher resolution and sensitivity at higher fields. Multidimensional NMR techniques enable correlation between neighboring atoms or residues. They facilitate the sequential assignment of proteins which is a first step in solving protein structure. These correlations are usually obtained through J coupling interactions between neighbouring atoms or through some relaxation mechanisms. Although chemical shifts have been used to predict protein secondary structures, more structural constraints are needed to build the structure of a protein.

300

200

100 13C

0

100

200

frequency (ppm)

While Karplus coupling predicts three bond scalar coupling values to molecule dihedral angles, RDC (residual dipolar coupling) enables dipolar coupling values 15N− H or 13C− H of proteins which helps us to figure out the orientation of these bonds with respect to molecular alignment axis.  H-NOE (nuclear overhauser effect) is used to measure the distance between two nuclei upto 5A◦ . The final protein structures are generally obtained by running a simulated annealing process such as Xplor with all chemical shift assignments and structural constraints.

Questions (1) An NMR instrument operates at 500 MHz frequency. Calculate the magnetic field strength required to observe resonance lines in the case of 13 C nucleus (g for 13 C nucleus = 1.404) β N = 5.02 × 10−27 J T−1 . Solution: r=

g · βN × BZ h

NMR Technique in the Elucidation of Biochemical Problems

BZ =

 317

rh gβ N

500 × 106 × 6.63 × 10−34 1.404 × 5.02 × 10−27 33.15 × 1026 = 7.05 × 10−27 = 4.7 × 10 = 47 gauss

=

(2) Discuss briefly the application of NMR technique in the elucidation of structure of proteins.

17

Applications of ESR Spectroscopy for the Solution of Biological Problems 17.1

Introduction

EPR spectroscopy is a very powerful tool that can provide valuable structural and dynamic information on a wide ranging biological systems. EPR spectroscopy requires the presence of an unpaired electron spin and a simple EPR active system consists of a single unpaired electron spin in a molecular orbital. The electron can exist in one of two spin quantum states, + 12 and − 12 . In the absence of a magnetic field, the two states are degenerate and have the same energy. When a magnetic field is applied, the − 12 state decreases in energy and the + 12 state increases in energy as shown in the Figure 17.1. EPR transitions occur when the energy in the microwave photons matches the splitting between two electron spin states. In the simplest case, this splitting is a function of the magnetic field. In a typical continuous wave (CW) EPR, a constant microwave frequency is applied and Bo , the magnetic field swept with spin-flop transition occurring when the energy separation between the two election spin states matches the constant microwave energy. Further to sweeping Bo , the field is modulated to enhance the signal to noise ratio. This gives rise to the derivative line shape (see Fig. 17.1) observed in EPR spectra. The block diagram of a simple ESR spectrometer is shown below.

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Figure 17.1 Energy-changes in electron spins in the absence and presence of a magnetic field.

The magnetic field at which this signal appears depends on the g value which governs the slope at which the energy levels for the two spin states changes are function of the magnetic field. In most biological systems, the effective g value depends on the orientation of the molecule with respect to the magnetic field. The EPR spectrum also depends on interactions between electron spin and any NMR active nuclei in the vicinity. This interaction is referred as for MRS, a one-dimensional spectrum of a particular location of the body is obtain using the magnetic field gradients in x, y, z direction. Many nuclear like 1 H, 31 F, 19 F, 13 C have been studied. The chemical stiff information can be used to distinguish between different species. In the MRI of brain, the commonly observed metabolites are N-acetyl aspartates creatinine, choline etc. MRI and MRS have been used in Alzheimer’s disease to diagnose and monitor the tumour in the brain. The relative changes in concentration of some MRS detectable metabolites like NAA, creatinine, choline have been studied and found useful in diagnosis of AD.

17.2

Advances in Magic Angle Spinning (MAS) NMR

This method allows the identification and characterisation of protein complexes such as transmembrane proteins and metalloproteins. MASNMR can be used to identify structural details at atomic level for T-355, DSbB, and FimA proteins. In addition to protein complexes, MASNMR has been used for analysis of nucleic acids and nucleic acid-protein interactions. MASNMR is also useful for analysis of molecular interactions in cellulose membranes, cytoskeleton components and activity of viral proteins

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and viral protein complexes. It was also used to study functions and conformational modifications of cyclophilin-A, a human protein which forms a composition with HIV capsid and affects HIV-I infecting capacity. MASNMR has also been employed for structural and functional analysis studies of bacteriophage proteins. Phospholamban can be studied by solid state NMR because it is a membrane protein and most of its interacting partners are membrane proteins too. Solid state NMR has also been used to study α-synuclein oligomers. Solid state NMR has successfully been used to study β-amyloid peptide structure which is of great use in understanding Alzheimer’s disease. NMR has been used to develop new drugs and also in synthesizing new molecules. In pharmaceutical research too, NMR contributed extensively NMR drug screening has been carried out by observing ligand resonance changes.

NMR Study of Metabolites Metabolites are intermediates or final products of different biochemical reactions occurring in a biochemical system. Metabolomics is a subset discipline of systems biology where the metabolites from a specific biological system are assessed, quantified to gain information on the system. NMR is a good tool to investigate the metabolites. Biofluids like urine, blood have been analysed by using NMR with strong magnetic fields and better probe designs. NMR has been successfully used to identify potential biomarkers in Alzheimer’s disease. HNMR spectroscopy has been used to compare the metabolomic profiles of different brain regions in wild type mice.

MRI or Magnetic Resonance Spectroscopy (MRS) of Body and Tissues MRI has now been developed to such an extent that it is now widely used in clinical diagnosis and spectra could be obtained on any part of a body non-invasively. In such studies, the sample has to be a kept in a homogeneous magnetic field to make NMR peak line width as narrow as possible. In MRI, the field gradients are purposely introduced across the sample so that the NMR frequency of the nucleus at different positions in the sample is slightly different and this information is used to map the location of the nucleus in the sample.

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–

+

Field gradient Gx Bz = B0 + Gxx

x

–

+

x

NMR frequency ν (x) = ν0 + yGx x/h

Figure 17.2 Magnetic Resonance Imaging principle of body and tissues. Optimizations and structural refinements, and averaging them the final 3D structure of the protein is arrived at. An example relates to the solution NMR study of the structure of Phospholamban (a protein in the sarcoplasmic reticulum (SR) membrane of cardiomyocytes) and its variants. NMR distance and dihedral angle constraints were used as inputs in X-plor and the final structure was generated. The structures obtained were used to predict the binding mode between phospholamban and calcium ATPase and explain why critical mutations are critical in phospholamban’s function.

17.3

Protein Structure Determination

A lot of biochemical reactions occur in solution phase. However, there are situations where studies have to be made in solid phase, for example, bones, teeth whose structure could be elucidated through NMR. Most protein drug targets are membrane proteins. They act as receptors or transporters to pass information in and out of membranes. There are interesting solid state protein structures in humans, bacteria, and viruses as well. For example, the virus capsid formed by capsid proteins has a unique structure and it has been studied by solid state NMR. Such studies may ultimately provide a cure for AIDS. In solid state NMR, the chemical shift is referred as chemical shift anisotropy. The chemical shift depends on orientation of each molecule causing broadening of peaks. This can be circumvented by aligning the molecules in the sample to have the same orientation. This method has been applied to study membrane proteins and phospholipid bilayer membranes. The protein molecules in the aligned sample have similar chemical shifts and narrower line widths. Hyperfine interaction (A) and it depends on three factors: (i) amount of election spin density on the nucleus, (ii) distance between electron spin and nucleus, (iii) angle between the two with respect to the magnetic field.

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Figure 17.3 Protein structure determination using solid state NMR.

Figure 17.4 Block diagram of a EPR spectrometer. It is possible to extract information on electron-electron couplings between two sets of spins and this provides valuable distance information between biological systems and zero field splitting in higher spin systems.

17.4

Electron Nuclear Double Resonance Spectroscopy (ENDOR), Electron Spin Echo Envelope Modulation (ESEEM) and Hyperfine Sub-Level Correlation (HYScore) Spectroscopic Techniques

In these spectroscopies, the electron spin is used as a detector to probe nuclei that are coupled to the unpaired electron spin. In ENDOR, nuclear

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transitions are directly driven using either continuous or pulsed radio frequency radiation. The effect on the EPR signal as a function of RF is monitored. Similar to ENDOR, ESEEM and HYScore are pulsed methods that are used to obtain information about nuclei in the vicinity of unpaired electron spin.

Double Electron-Electron Resonance (DEER) or Pulse Electron Double Resonance (PELDOR) Spectroscopy When there are two or more EPR active species in a system, there will be electron-electron dipolar interaction present. This interaction depends on the distance and the angle between the two paramagnetic species relative to the externally applied magnetic field. In DEER spectroscopy, this dipolar coupling is measured and thereby the distance between the two species can be measured in the range 20–80 A◦ . This technique has emerged as a powerful tool in structural biology.

Spin Label EPR With the advent of spin labelling, the potential use of EPR has been extended to any biological system because biological techniques are available to place stable radicals at specific locations in biological macromolecules. EPR spectroscopy has emerged as a powerful technique to obtaining structure and dynamic information on peptides, proteins, nucleic acids and macromolecules. EPR spectroscopy offers high sensitivity (at μM concentrations) and is not limited by the size of the protein. EPR measurements can be made on a variety of samples such as solutions of proteins, densely packed membrane suspensions, tissue samples. Analysis of EPR data for a series of spin labelled protein sequences allows modelling of protein structure.

Site-Directed Spin Labeling (SDSL) Methods Native biological systems cannot be studied by EPR because they are not EPR active. A reporter group or a label such as spin probe needs to be incorporated into the desired system to be detected by EPR. The site specific incorporation of unpaired electrons into biomolecules is known as SDSL. In SDSL experiments, all native non-disulfide bonded cysteines are removed by replacing them with another amino acid like alanine. A unique cysteine residue is then introduced into a recombinant protein via site

Applications of ESR  O S N O

S O

r4

CH3 + HS

CH2

r5

Protein

325

r2

S r3

C

r1

Protein

N O

Figure 17.5 Structure of MTSL and the resulting side chain produced by reaction with cysteine residue of the protein. r1 , r2 , r3 , r4 , r5 represent locations of five rotations about the chemical bonds. directed mutagenesis and subsequently reacted with a sulfhydryl specific nitroxide reagent to generate a stable paramagnetic EPR a dive side chain.

17.5

Structural and Dynamical Information of Biological Systems

The overall mobility of the spin label attached to a protein, or a peptide is a superposition of the contributions from: (1) the motion of the label relative to peptide back bone, (2) fluctuations of α-carbon back bone, and (3) rotational motion of the entire protein or peptide. Under the experimental conditions, these motions can be isolated from the EPR spectrum. The spin label side chain motion is used to study tertiary contacts and protein structure. For β-sheet proteins, the spin label motion is influenced by steric interactions with the nearest neighbours. The inverse line width of the central line provides a measure of relative stability. Scanning the inverse line width of the EPR spectrum against the amino acid sequence yields a periodic data profile that reflects the local secondary structure of the protein. This method also provides a strategy for identifying functional domains in high molecular weight proteins, membrane proteins and supra molecular complexes. The work done on Escherichia coli ferric citrate transporter FecA constitutes an excellent example of application of SDSLEPR. This FecA protein is involved in ferric iron—iron translocation across the outer membrane. Another example of SDSLEPR to probe the structural and dynamic properties of proteins is Vimentin. Vimentin is a type III intermediate filament protein found in many cells of mesenchymal origin. Mutations in IFgenes have been linked to different human diseases. Vimentin’s head domain structure is dynamic and changes with filament assembly.

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Figure 17.6 Molecular structure of vimentin.

Figure 17.6 shows vimentin molecular structure with a representation of protein domains of Vimentin. At the amino terminus is the head domain leading into rod domain-I. Black boxes represent linked 1-2 Rod 2B and Rod 1B are parallel helical structures of Rod 2A/linker 2 Panel.

17.6 Topology of Proteins Membrane proteins control bioenergetics, movement of ions across a cell and initiate signaling of pathways. Nitroxide base site directed spin labeling EPR can be used to obtain structural and dynamic information on membrane—protein assembly. EPR spin labels are very sensitive to the presence of other paramagnetic species which alter the relaxation properties. There are several biologically important membrane protein systems (e.g., Bacteriorhodopsin, ABC cassette transporter MsbA, cytochrome C oxidase subunit IV (Cox IV) and Ferric enterobactin receptor FepA) which have been studied using spin label EPR to investigate structural topology. A typical example of using CW-EPR power saturation data is to study the topology of KCNE-I membrane protein in proteoliposomes (KCNE-I is a single transmembrane protein that modulates the activity of KCNQI voltage gated K channel). These data showed that KCNE-I spans the full width of lipid bilayer with Leu-59 residue located near the center of membrane. Analysis of SDSLEPR line showed that the dynamic motion of the nitroxide spin label is slower in the membrane environment than in micelles and that residues within membrane are less mobile than that outside. An excellent example of using accessibility and mobility data to identify α-helical secondary structure is the study of lactose permease protein. Site directed spin labeling EPR studies to obtain periodicity of side chain mobility and accessibility to O2 showed that the transmembrane domain XII in the lactose permease protein adopts and α-helical conformation.

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CW-EPR at X-band has been used to study membrane topology of integrated membrane proteins inserted into aligned phospholipid bilayers. The membrane alignment technique coupled with dipolar broadening CW-EPR was used to determine the distance and relative orientation of two nitroxide spin labels on M-28 peptide of acetylcholine receptor (Ach R) in DMPC vesicles.

17.7

SDSLEPR Methods Under High Fields/ High Frequencies

EPR spectral line shapes can provide information on the secondary structure of a protein and on the orientation of its sub-units relative to each other. If the experiment is carried at more than one frequency, additional information about the tumbling of the protein and internal motion consisting of back bone fluctuations and side chain isomerization can be obtained. EPR spectra obtained at multiple frequencies provide unique perception on the molecular motions and give accurate descriptions of the dynamics of spin probe environment. EPR, as a biophysical tool, can be used to tackle the following three areas: (1) Structure and dynamics of large molecular weight proteins in solution, (2) Membrane and membrane associated proteins, structure, location, interaction with other membrane components or DNA or RNA, (3) Fast conformational transitions of proteins and RNA’s in solution protein folding and unfolding. Extending conventional EPR to higher frequencies, it is possible to obtain the following additional features: (1) (2) (3) (4) (5)

enhanced spectral resolution, enhanced orientational selectivity in disordered samples, enhanced low temperature electron spin polarization, enhanced sensitivity for probing fast motional dynamics, and enhanced detection sensitivity for restricted volume samples.

Multi frequency EPR has provided pertinent structural and dynamic information on myosin. It is known that myosin are involved in muscle contraction and a wide range of eukaryotic mobility processes. Multi frequency of EPR has also been used to study the dynamic properties of T4 lysozyme in solution. It is a globular protein composed of 164 amino acid residues with a molar mass of 18.7 kDa (i.e., 18700 atomic mass units).

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SDSL-ESEEM Methods ESEEM is a powerful pulsed EPR technique to study many different biological systems. It has been used to probe the site specific secondary structure of membrane peptides using microgram amounts of sample. The three pulse ESEEM data obtained for AChRM28α-helical peptide in a membrane and an ubiquitin β-sheet peptide in solution is shown in Figure 17.7.

Figure 17.7 Three pulse ESEEM spectra with T = 200 ns of the I + 2 and I + 3 labelled Leu for AchR M-282 helical peptide in lipid bilayer and Ubiquitin β-sheet peptide in solution.

Applications of ESR 

17.8

329

Double Site-Directed Spin Labeling Methods

It is possible to use EPR for measuring the distances between two spin labels in terms of either intramolecular distance between sites on different proteins. Using double labeling EPR techniques, distances can be measured to probe secondary, tertiary and quaternary structures. The CWEPR line broadening approach has been used to study the bacterial K + -translocating protein KtrB. Such proteins are found in bacteria fungi, plants and trypanosomes. In DEER, one set of spins are monitored, and another set of spins are excited with a second microwave frequency leading to the measurement of the coupling between the two spins and hence the distance between them. DEER can be used to probe the structure of biomacromolecules, globular proteins, membrane proteins, oligomer states and RNA. At high fields, DEER can be used to measure relative orientation of spins. The protein fluctuation dynamics and spin label rotameric motions have a significant contribution to DEER distribution width. The transmembrane region of α-helical nature C-99 Amyloid precursor protein in proteo-liposomes was identified by DEER. C-99 is a transmembrane carboxyl terminal domain of the amyloid precursor protein that is cleaved by r-secretase to release amyloid βpolypeptides which are involved in Alzheimer’s diseases. The curved nature of the transmembrane is important for C-99 interactions with rsecretase. CW-EPR power saturation data were used to confirm the spanning of transmembrane domain of C-99 and revealed that N-helices and Chelices are associated with membrane surface. DEER measurements on a dual labeled construct of CBD-12 indicated that the β-sandwich regions of CBD-1 and CBD-2 domains are widely separated at their N- and C-termini and are largely insensitive to Ca2+ binding.

Figure 17.8 Identification of transmembrane region of α-helical nature of C99 amyloid precursor protein in proteoliposomes.

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An illustrative example for measuring distance constraints with DEER is the Na+ /Proline transporter Put P Escherichia coli system. Proteins of this family utilize a sodium motive force to drive uphill transport of substrates such as sugars, amino acids, vitamins, myo-inositol and urea.

Protein-Protein Interactions EPR spectroscopy is a powerful technique to study protein-protein interactions and oligomeric states. It is pertinent to point out that protein-protein interactions are involved in all biological processes such as immune responses, cell signaling, translocation and regulation. DEER has emerged as a powerful tool to measure distance between spin labeled binding sites in a protein-protein complex. An example of application of CW-EPR and DEER spectroscopy is associated with the study of complicated proteinprotein complexes involving Cdb3|AnKD34 proteins. Both techniques were used to map the binding interfaces of these two proteins in the complex and to obtain the inter-protein distance constraints. Saturation transfer EPR was used to probe the homo- and hetero oligomeric interactions of the sarcoplastic reticulum Ca-ATPase (SERCA) and phospholamban (PLB).

Unpaired Spins in Biological Systems Structural information in biological processes can be obtained by EPR since electrons are almost intimate participant of these processes.

Naturally Occurring Radicals Many common biological radicals are those stemming from amino acid residues such as tyrosine, tryptophane, cofactors such as flavine and pigment molecules such as chlorophyll. They typically contain one unpaired electron spin residing in an aromatic molecular orbital. Higher field frequency instruments can be used to determine small anisotropies in “g” values. The deviation of “g” values is a characteristic for a given system and hence can be used to obtain information on identity and environment of electron spin. A few illustrative examples of how EPR and related methods have been used to answer important biological questions in systems containing organic based biological radicals are given below. (1) Ribonucleotide reductase: The Ribonucleotide Reductase (RNR) family of enzymes catalyses the conversion ribonucleotides to deoxyribonucleotides that are used in the synthesis of DNA in every living

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organism. The ribonucleotide reaction is believed to proceed via the creation of a tyrosine radical in the R2 submit by the di-iron center in the R1 sub-unit, followed by an electron transfer reaction. This creates a thyil radical near the substrate binding site and the subsequent reduction of ribonucleotide. (2) Phycocyanobilin—Ferredoxin oxidoreductase (PCYA) Phycocyanobilin: PCYA catalyses the reduction of biliverdin to 3Z/3E phycocyanobulin via a 4e− process. This system functions via a two step 4e− reduction with 181, 182-dihydro-biliverdin (DHBV) as an intermediate in the reaction. The small amount of “g” anisotropy present in many biological radicals precludes determination of the g values by conventional low field/frequency EPR. This can be seen in the case of radical intermediate in PCYA reaction as shown in Figure 17.9.

Figure 17.9 EPR spectra and corresponding simulations at three fields (or frequencies) of the radical intermediate in the Phycocyanobilin— Ferredoxin oxidoreductase system. The principal factor that gives rise to deviations in g values from that the free electron value is spin orbit coupling within the molecule. Spin orbit coupling is the interaction between the unpaired electron spin and low lying unoccupied excited states.

17.9

Other Important Biological Systems

Quinone based electron transport systems have been widely studied using EPR and ESEEM methods. These studies have helped in understanding Q-cycle in the complex III family of membrane bound electron transport systems. EPR methods were also used in furthering our understanding of two redox active tyrosine residues with in photosystem II. Many biological cofactors such as chlorophylls, flavins have also been studied by EPR.

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Oxygen Evolving Complex (OEC) in Photosystem-II (PS-II) Photosystem-II is a multi-submit membrane associated enzyme system which catalyses the light driven oxidation of water to molecular O2 releasing 4 protons. It has helps fuel the pH gradient that drives ATP synthesis and form e− in the form of reducing equivalents which eventually participate in the reduction of CO2 to sugar. The water oxidation occurs at the oxygen evolving complex (OEC) which consists of 4 Mn atoms and one atom each of Ca and Cl− . While EPR spectra can detect interactions between an unpaired electron spin and other electrons and nuclei in the vicinity, those interactions are often lost in the large inhomogeneously broadened EPR spectra of transition metal systems. The multi-line signal associated with S2 state of photosystem-II was investigated with 55 Mn ESE-ENDOR. The pattern of multiline signal arises from the coupling between S = 12 electrons spin and all of the nuclei in the vicinity with the isotopically prevalent 55 Mn I = 52 nucleus being the dominant interaction. ESEEM and ENDOR techniques have been very powerful in determining ligand identity to the OEC. Multifrequency ESEEM studies have shed light on the hyperfine couplings of the directly bound and second nitrogen of the imidazole ring and the nature of the histidine ligation to the OEC.

The FeMo Cofactor of Nitrogenase Nitrogen fixation is catalysed by the enzyme Nitrogenase. This process consists of two parts: (i) an electron delivery system, the Fe protein, which delivers an electron upon hydrolysis of two molecules of ATP and (ii) the FeMo protein which contains an iron-molybdenum cluster where the catalysis takes place. As with PS-II, many intermediate states have EPR spectra which are informative and also allow techniques such as ENDOR to be used to characterize them. The FeMo cluster where nitrogen fixation occurs is of interest. This cluster exists as a rhombic S = 32 system with of values as 4.32, 3.64 and 2.00. These EPR signals associated with nitrogenase system yield unpaired electron spins that can be used by techniques such as ESEEM, ENDOR and HYSCORE.

Metal Replacement Although there are large numbers of EPR active metal-based systems in nature, there are still many that are EPR silent. Of them, Mg and Zn are important. Many systems require Zn for function. It is a d10 system and

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333

has no unpaired electrons to study by EPR. However, they can be functionalized by substituting with Co (II) to give an EPR active probe within the system. One important biological system that has been studied in this manner is metallo-β-lactamase family of enzymes. These enzymes are a primary target for antibiotic drug design and have been well characterized by replacement of Zn (II) with Co (II) for EPR studies. This metal replacement has also enabled EPR studies of interaction of nucleic acids with Mg2+ . Thus, replacement of Mg2+ (which is EPR silent) by Mn2+ , gives a spectroscopic probe which has been widely utilized to understand the role of counter ions in the structure and function of nucleic acids.

Questions (1) (a) The g value of a species is independent of the magnetic field. (b) The g value depends on the orientation of the molecule with respect to the magnetic field. (c) The g value varies between + 12 and − 12 . (d) None of the above. (2) For a certain radical, the magnetic field strength is 3350 gauss and the frequency of the microwave is 9500 MHz. Calculate its g factor. Solution: g=

71.4484 in GHz B (in nT)

71.4484 × 9500 × 10−3 3350 × 10−1 = 2.026

=

The number of lines from the hyperfine interaction can be determined by the formula 2N I + 1 where N is the number of equivalent nuclei and I is the spin. (3) Calculate the number of lines to be expected for methyl radical CH3 . Solution: 2N I + 1 = 2 × 3 ×

1 +1 = 4 2

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Biophysical Chemistry

(4) Discuss briefly the usefulness of EPR spectroscopy in understanding the structure of biologically important radicals like ribonucleoside reductase. (5) Explain how the multi line signal associated with S2 state of photo system II can be understood using ESE-Endor?

18

Flow Methods for the Kinetic Study of Fast Biochemical Reactions 18.1

Introduction

The kinetic study of any reaction involves the start of the reactions by mixing the reactants and following the course of the reaction by monitoring the concentration change of a species by titrimetry or by following the change in physical property of the system as a function of time. Flow techniques, developed by the pioneering work of Hartridge and Roughton, are used to study reactions occurring on time scales of the order of seconds to milliseconds.

18.2

Experimental Arrangement

A simple experimental flow-set up or apparatus is given below: Reactant 1

Reactant 1 Fixed

Reactant 2

detector

Reactant 2 Movable detector

Movable injector

Figure 18.1 A simple experimental set up for flow methods.

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_18

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In the experimental set up shown above, reactants are mixed at one end of a flow tube and the composition of the reaction mixture is monitored at one or more positions along the tube. If the flow velocity is known, then measurements at different positions provide information on the concentrations at different times after initiation of the reaction. A different version of the method has the detector in a different position but a movable injector may be used to inject one of the reactants into the flow tube at different positions relative to the detector in order to study the time dependence of the composition of the reaction mixture. In a stopped flow method, a fixed volume of reactants flow rapidly in a reaction chamber and are mixed by the action of a syringe fitted with an end stop. The composition of the reaction mixture is then monitored by a physical technique (Spectrophotometrically or otherwise) as a function of time after mixing at a fixed position in the reaction vessel.

Figure 18.2 Technique of stopped flow method. It may be mentioned that the continuous flow methods have the disadvantage of requiring large quantities of the reactants as also high flow velocities of reactants to study fast reactions.

Importance of Study of Biological Reactions and their Rates Many biological reactions occur in the living systems. For example, enzymes catalyse reactions by binding and modifying substrates, transport proteins bind to and carry lipids, hormones within circulatory systems. Further, antibodies are utilized by the immune system to bind and remove foreign substances from the body.

18.3

Reactions Studied Using this Technique

Examples of biological interactions that have been studied using this technique include: (i) kinetics of protein folding, (ii) enzyme inhibition and (iii) binding of proteins or DNA to hormones or drugs. In these studies, a variety of molecules have been used like drugs, hormones, proteins, metal, ions etc.

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Commonly used detection techniques are absorbance and fluorescence. Reactants or products with a specific chromophore or fluorophore as in NADH, pyridoxal phosphate on tryptophan residues have been studied. Other techniques like NMR, small angle X-ray scattering, circular dichroism have been coupled to the stopped flow apparatus.

18.4

Applications to Unimolecular Reactions

Consider a reversible reaction involving a molecule which changes its conformation from one form to another. The reaction may be represented by k1 BG y x FGGGGGG GGGGG k −1

(18.1)

If the observed signal (b) is obtained as a function of time (t), it can be fitted to the equation b(t) = beq − (beq − b0 )e−kobs t

(18.2)

where b(t) = signal measured at time t, b0 = signal observed at the beginning of the experiment (i.e., at t = 0), beq = signal obtained after a sufficiently long time i.e., at equilibrium and beq − b0 = total change in signal during the reaction. k obs is equal to the sum of k1 and k −1 and if the equilibrium constant K of the reaction is known, both k1 and k −1 can be calculated. Reactions involving conformational changes in proteins often follow this type of kinetics. The dis oxygenation of haemoglobin according to Oxyhaemoglobin −→ Haemoglobin + O2

(18.3)

follows a first order kinetics with a t1/2 = 64.8 × 10−3 sec and k = 10.7 sec−1 . The reaction between the apoprotein and excess of Zn2+ has been followed by following the change in fluorescence intensity with time after mixing them. The fluorescence intensity changes with time are shown below. The rapid interaction given in curve (a) may be described by the equation k1 BG SL S + L FGGGGGG GGGGG k −1

(18.4)

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Biophysical Chemistry

Figure 18.3 Rapid interaction between apotransferrin and Zn2+ . while second and third processes can be expressed by the equation k1 BG S∗ S FGGGGGG GGGGG k −1

(18.5)

k obs = k1 [ xtotal ] + k −1 M−1

sec−1

(18.6) sec−1 .

and k −1 = 6 A Analysis of data gives k1 = 21 × stopped flow kinetic study of the binding of high mobility group domain proteins with cisplatin modified DNA was made using fluorimetric detection. The second order rate constant of the reaction from the slope is 1.1 × 8 10 M−1 sec−1 . The variation of fluorescent intensity with time is shown in Figure 18.4. 104

Figure 18.4 (a) Variation of intensity of fluorescence with time in the kinetic study of high mobility protein with cisplatin modified DNA and (b) Variation of k obs with concentration of HMGI domain.

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Other bimolecular reactions under pseudo first order conditions were: (1) binding of warfarin with human serum albumin, (2) reaction of isonicotinic hydrazide and its analogues mycobacterium tuberculosis catalase peroxidase (kat G),

with

(3) interaction of enzymes or coenzymes with peptides, (4) protein-protein interactions or protein binding with ATP.

18.5

Applications Involving Competitive Reactions

Consider the reaction k1 BG SL −→ (4); S + L FGGGGGG GGGGG k −1

k2 S + C FGGGGGGGB GGGGGGG SC k −2

(18.7)

In this scheme, “C” competes with “L” for the same site on “S”. Competition experiments in stopped flow analysis have been performed to study drug-protein, DNA-protein, protein-protein and enzyme peptide binding. As a specific example, phenyl butazone was used as a competing agent in kinetic studies of interactions of warfarin with HSA. In another case, podophyllotoxin (POD) was used as a competing agent to study binding by tubulin to two analogues of colchicine, TCB and TKB (2, 3, 4, trimethoxy4’-acetyl-1, 1’-biphenyl).

18.6

Applications Involving Multi-step Reactions

Consider the reaction scheme k1 k2 ∗ BG SL FGGGGGGGB S + L FGGGGGG GGGGG GGGGGGG SL k −1 k −2

(18.8)

when the concentration of L >> S, k obs2 =

k2 [ Ltot ] + k −2 K−1 + [ Ltot ]

(18.9)

where k obs2 = observed rate constant for the slower unimolecular reaction and K−1 is the dissolution equilibrium constant for the fast bimolecular reaction, i.e., K−1 = k −1 /k1 .

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Biophysical Chemistry

Several reactions such as: (1) J-binding protein 1 interaction with J-DNA- binding domain with DNA oligomers that contained glycosylated 5-hydroxyl methyl cytosine, (2) binding of phosphatidyl serine containing vesicles to lactadherin, (3) binding of Fe2+ and Zn2+ to human serum transferrin. Stopped flow method can be used to study first order reactions with rate constants ranging from 10−6 to 106 sec−1 and from 1 to 109 M−1 sec−1 for second order reactions. The rate of association of E (binding site of Lysozyme) with NADH viz. E + NADH ←→ E − NADH was studied by stopped flow method. The rate constant for the forward reaction was found to be 5 × 106 M−1 sec−1 at 276 K. The equilibrium and kinetic constants for the dissociation of ko f f LADH − NADH FGGGGGGGGB GGGGGGGG LADH + NADH k on

(18.10)

were also estimated, with the following values: Buffer Phosphate buffer pH = 7.0 Phosphate, pH + 50 mM NaCl

k on /M−1 sec−1 1.7 × 107 2.5 × 107

k o f f /sec−1 3.2 9.0

Questions (1) (a) Continuous flow methods required only small volumes of reactants. (b) Stopped flow methods can be conveniently used to study reactions in the time scale of a few seconds to milliseconds. (c) The reaction between H+ and OH− ions can be studied by stopped flow technique. (d) Continuous flow methods can be employed to study reactions with low flow rates. (2) (a) Pressure jump technique is used to study relatively faster reactions as compared to temperature jump method.

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(b) There are more methods for following the rates in pressure jump method than in temperature method. (c) The extent of displacement of equilibrium in a temperature jump experiment is dependent on the enthalpy change of the reaction. (d) The rate of neutralisation of H+ by OH− ions in aqueous solution can be studied by P-Jump method. (3) The reaction between myoglobin (MG) and O2 is given by R1 MG + O2 FGGGGGGB GGGGGG MGO2 R −1 for this reaction, 1 ¯ 2 ) + R1 . = R−1 (MG + O τ 1 ¯ 2 ) + R −1 . = R1 (MG + O (b) τ (a)

1 ¯ 2 ]. = R1 [MG] + R−1 [O τ 1 ¯ 2 ] + R−1 [MG]. = R1 [O (d) τ (c)

(4) The deoxygenation of oxyhemoglobin, according to the equation, oxyhemoglobin −→ hemoglobin + O2 is a first order process with a t1/2 = 65 millisec. Calculate the time for 90% deoxygenation to take place. Solution: 0.693 0.693 = = 10.66 sec−1 t1/2 65 × 10−3 a 2.303 2.303 2.303 log log 10 = k= = t a − 0.9a t t 2.303 t= = 0.216 sec = 216 m sec 10.66 k=

(5) Carbon monoxide reacts with haemoglobin (Hg) according to CO(g) + Hg(l)  COHg(l) The rate constant for forward reaction is 0.51 × 10−6 M−1 sec−1 . Assuming that the concentration of CO in blood is 1 × 10−3 M and the concentration of Hg is 2 × 10−2 M, calculate the time required for the concentration of CO to be reduced to 1 × 10−4 M.

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Solution: For a second order reaction k=

2.303 b( a − x ) log t( a − b) a(b − x )

In this case, let [HG]= a = 0.02 M; [CO]= b = 0.001M, x = 0.001 − 0.0001 = 0.0009 substituting the data 0.51×−6 = or 0.51×−6 = or

2.303 0.001(0.02 − 0.0009) log t(0.02 − 0.001) 0.02(0.001 − 0.0009)

0.0000191 2.303 2.303 log = × 0.98 t × 0.0019 0.000002 0.019 × t

2.303 × 0.98 = 2.32 × 106 sec 0.019 × 0.51 × 10−6 232.9 × 106 = = 6.47 × 104 hrs 3600

t=

(6) The association of E binding site of Lysozyme ( E) with NADH according to the reaction E + NADH  E − NADH was studied by a stopped flow method and the rate constant was found to be 5 × 106 liters mol−1 sec−1 . Assuming that both the species are at an initial concentration of 1 × 10−3 M, calculate the time required for the binding to be 75 percent complete. Solution: 1 t 1 5 × 106 = t 1 = t k=

· ·

x a( a − x ) 0.75 1 × 10−3 (0.01 − (75/100) × 0.001)

0.075 0.001 × 0.0002 0.075 t= 6 5 × 10 × 0.001 × 0.0025 0.075 = 5000 × 0.00025 0.075 = = 0.06 sec 1.25

×

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(7) The activation energy of the reaction between CO2 and ammonia according to the reaction CO2 + NH3 −→ NH2 COOH is 46.5 kJ mol−1 . Given that its rate constant at 313 K is 1000 L mol−1 sec−1 , what will be its value at 293 K? Solution:   1 E 1 k2 = − log k1 2.303 × R T1 T2   46.5 1 1 1000 = − log k1 2.303 × 8.314 × 10−3 293 313 46.5 20 = × = 0.5295 0.01915 293 × 313 1000 = 3.385 k1 1000 = 295.4 L mol−1 sec−1 k1 = 3.385 (8) The reaction between Zn2+ ions and apoprotein (AP) given by Zn2+ + AP  Zn2+ AP was studied fluorimetrically. The variation of fluorescence intensity in presence of excess of Zn2+ and at a concentration of apoprotein of 1 × 10−3 M is as follows: Time (sec) 0.01 0.015 0.020 0.030

Fluorescence intensity (arb units) 5 62.5 61.2 60.8

Calculate the rate constant of the reaction.

19

Temperature Jump Relaxation Technique for the Kinetic Study of Fast Biochemical Reactions 19.1

Introduction

A unique technique for rapidly disturbing the position of a chemical equilibrium is through a sudden change of temperature of the system and the temperature jump method (T-jump) is based on this principle. The displacement of the equilibrium of a reaction is based on the thermodynamic relation   ∂ ln K ΔH ◦ = (19.1) ∂T RT 2 P where K denotes the equilibrium constant of the reaction and ΔH ◦ is the standard enthalpy change of the reaction. This method is most versatile among all the relaxation methods because of several advantages, associated with this technique, as enumerated below.

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_19

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Advantages of this Technique (1) It covers a wide range of relaxation times from about 1 μsec to 1 sec. (2) A variety of experimental techniques such as: (i) (ii) (iii) (iv)

spectrophotometry, fluorimetry, conductivity, and polarimetry are available for following the course of the reactions.

(3) Various methods are available for bringing about a rapid heating of the solution. Some of these are: (i) (ii) (iii) (iv)

19.2

joule heating, optical heating, dielectric heating, and heating by flash lamp.

Schematic Diagram of the Apparatus

A schematic diagram of T-Jump apparatus developed originally by Eigen and co-workers in Germany is given below:

Figure 19.1 Schematic diagram of a temperature jump apparatus developed by Eigen and his group. In any given experiment, the condenser (C) is charged to a voltage of 20 to 100 kV. The spark gap (S.G.) is next fired so that the capacitor discharges through the cell containing the experimental solution. A temperature jump of 5 to 10◦ may be obtained in a time of 0.05 μsec to 0.5 μsec.

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Simultaneously, the oscilloscope is triggered and the relaxation curve is traced.

19.3

Follow Up of the Change in Concentration of Reactants by Spectrophotometry

The change in the concentration of a species ’i’ is related to the change in the intensity of the transmitted light ΔIi as ΔIi = Ii (t) − Ii (ref) = Ii (ref)[e−ε j ΔCi l − l ]

(19.2)

where ε j denotes the extinction coefficient of the species ’i’; ΔCi is the change in the concentration at time t and l indicates the path length of the cell. Upon linearizing the exponential term,

However,

ΔIi = −ε i ΔCi l Ii (ref)

(19.3)

ΔCi = ΔCi (t = 0)e−t/τ

(19.4)

where τ denotes the relaxation time. Substituting eqn. (19.4) in eqn. (19.3). ΔIi = −ε i l Iref



∂T ∂ ln K



ΔH ΔCi (0)e−t/τ RT 2

(19.5)

The variation of the concentration of a species I with time following a TJump may be shown below. Ii (ref)

Ii (t)

Ci (ref)

Ci (t) Ci

Ci (0)

Time

Figure 19.2 Variation of concentration of species with time following a temperature jump.

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19.4

Biophysical Chemistry

Applications

Many enzyme catalysed reactions and biochemical reactions involving phospholipids, dispersions have been studied. Other reactions include metal complex formation reactions, proton transfer reactions etc.

Specific Examples (1) The mechanism of an enzyme-substrate reaction may be given as k1 k2  BG ES FGGGGGGGB E + S FGGGGGG GGGGG GGGGGGG ES k −1 k −2

(19.6)

where ES and ES are the enzyme-substrate complex and another rearranged species of ES. The rate constants k1 and k −1 are of the order of 106 − 108 lmol−1 sec−1 and 10−4 to 106 sec−1 respectively. k2 and k −2 are found to be of the order of 103 − 104 sec−1 . For example, the conformational changes in β-lactoglobulin have been studied using spectrophotometric detection. (2) T-Jump kinetic study of the binding of imidazole by sperm whale Metmyoglobin. The relaxation of metmyoglobin ( Mb) containing imidazole ( Im) at constant pH has been expressed in terms of the mechanism k1( app) Mb + Im FGGGGGGGGGGB GGGGGGGGGG MbIm k −1( app)

(19.7)

for which the relaxation time τ is given by 1 ¯ + Im ¯ ) = k −1(app) + k1(app) ( Mb τ

(19.8)

The bars on Mb and Im represent equilibrium concentrations. τ was found to vary from 0.2 to 0.04 sec depending on pH and concentration ¯ ] ≥ [ Mb ¯ ]. At pH = 7.0 and T = 298 K, of Im. In all experiments [ Im − 1 − 1 the k1( app) = 170 M sec and k −1( app) = 5.4 sec−1 using imidazole as one reactant. When benzimidazole was used instead of imidazole, k1( app) = 509 M−1 sec−1 and k −1( app) = 8 sec−1 . (3) The biochemical reaction involving glyceraldehyde-3-phosphate dehydrogenase + β-NAD was investigated by T-Jump method. Three relaxation times τ1 = 1.43 × 10−4 sec. τ2 = 1.45 × 10−3 sec, τ3 = 5 sec have been observed. A general mechanism was put forward to explain the observed relaxation times.

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(4) (a) The kinetic study of the reaction of sperm whale myoglobin with O2 at pH 7.0 ( T = 293 K) was made by T-Jump method. The relaxation times were found to range from 0.0125 sec to 3 × 10−3 sec depending upon the equilibrium concentrations of the myoglobin and O2 . The following scheme k1 BG MGO2 MG + O2 FGGGGGG GGGGG k −1

(19.9)

was proposed where MG = myoglobin and MGO2 is its complex with O2 . The relaxation time is related to the rate constants k1 and k −1 according to 1 ¯ 2) ¯ +O = k − 1 + k 1 ( MG τ

(19.10)

¯ 2 )], the rate constants k1 From the variation of 1/τ with [(MG + O and k −1 were found to be k1 = 1.9 × 107 M−1 sec−1 and k −1 = 11 sec−1

(19.11)

(b) A temperature jump kinetic study of the reaction of O2 with β−SH and β PMB sub-units of human haemoglobin was made at pH = 7.0 (temperature = 293 K). The relaxation times ranged from 4.3 × 10−3 sec to 1.5 × 10−3 sec in the former case and from 1.13 × 10−3 to 4.8 × 10−4 sec in the latter case. The rate constants for the reaction of β−SH with O2 were calculated to be k1 = 6.5 × 107 M−1 sec−1 and k −1 = 16.0 sec−1 . The rate constants for the reaction of β PMB with O2 were found to be k1 = 8.3 × 107 M−1 sec−1 and k −1 = 156 sec−1 . The temperature was maintained at 293 K in all cases.

Questions (1) Derive an expression for the reciprocal relaxation time (1/τ ) for a general chemical reaction given by k1 BG C + D A + B FGGGGGG GGGGG k −1

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(2) The relaxation time of a polypeptide chain represented by YXXXX  YYYYY containing the amino acid alanine was measured by laser T-Jump technique and found to be 160 nanosec. If the relaxation is due to helix-coil transformation of the chain and its equilibrium constant is 1.10, calculate the forward and reverse rate constants for this change. (3) A certain proton transfer reaction involving an indicator, HIn, was studied by T-Jump method at 298 K. The reaction may be represented by k1 BG In− + H2 O HIn + OH− FGGGGGG GGGGG k −1 The relaxation times observed at two concentrations of the OH− ion and the calculated equilibrium concentration C¯ HIn + C¯ OH are given below: − COH 1.29 × 10−4 2.45 × 10−4

C¯ HIn + C¯ OH 3.20 × 10−4 4.35 × 10−4

1/τ × 10−4 (sec−1 ) 3.90 4.30

Derive the equation for 1/τ and calculate the rate constants k1 and k −1 . (4) Derive the equation



∂ ln K ∂P



=− T

ΔV ◦ RT

which relates the displacement of equilibrium by application of pressure on a system. ΔV ◦ represents the difference between standard molar volumes between the products and reactants. (5) The hydration of propionaldehyde, given by the reaction k1 BG CH3 CH2 CH(OH2 ) + H3 O+ CH3 CH2 CHO + H3 O+ + H2 O FGGGGGG GGGGG k −1 was studied by P-Jump technique and a relaxation time (τ ) of 2.5 sec was observed at pH = 3.30. τ is given by the expression   1 1 CH + = k1 1 + τ K where K is C¯ hydrate /C¯ aldehyde = 480. Calculate k1 and k −1 .

20

Flash Photolysis Technique for the Kinetic Study of Fast Biochemical Reactions 20.1

Introduction

The initiation of a reaction by photo irradiation is a powerful method for the study of rates and for detecting transient intermediates formed in the reaction. In this context, the flash photolysis technique, developed by Norrish and Porter in UK has proved to be very convenient not only to initiate the reaction but also for bringing about a considerable extent of reaction in a very short interval of time.

20.2

Principle of the Method

The reactant system is irradiated with an intense flash of light in UV or visible region to produce a measurable change of concentration in the system. The flash is usually of a very short duration, of the order of a few microseconds (i.e., short compared to the reactions that follow). The subsequent chemical changes are followed by what is known as kinetic spectrometry. In this method, the absorption is measured at a given wavelength as a function of time.

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Experimental Arrangement The following diagram illustrates the basic experimental setup. Photolytic flash

Photoelectric detector

Collimalting lens Source for for following reaction

Mono chromator

Reaction tube

Display device

G

Figure 20.1 A flash photolytic unit. A high intensity flash with energies ranging upto 2000 J is generated in an interval of 1 to 100 μsec or microsec. The emerging light is collimated onto reaction vessel through a series of mirrors. The change in absorbance of the solution is monitored by means of a monochromator and photocell and displayed on an oscilloscope. In recent years, lasers have been used as sources of photolysis flash.

20.3

Applications

(1) Reactions such as the triplet state of naphthalene in hexane, decay of duroquinone radical in viscous paraffin liquid have been studied. (2) The reaction of myoglobin with carbon monoxide has been investigated by this method at a pH = 7.1 and temperature of 296.5 K. The reaction is k1 BG MgbCo Mgb + Co FGGGGGG (20.1) GGGGG k −1 and was monitored at 540 μm. The reaction was found to be second order and the rate constant k1 is 5.5 × 105 l mol−1 sec−1 .

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 353

(3) The reaction between myoglobin and oxygen was also studied by this method and the rate constant for the combination reaction Mgb + O2 ←→ MgbO2

(20.2)

has been reported as 1.28 × 107 lmol−1 sec−1 at 296.5 K. (4) Flash photolysis technique was employed to generate a reactive aryl nitrene from N-(4-azido-2-nitrophenyl) 2-aminoethyl sulfonate (NAPtaurine) in the presence of the protein ribonuclease A. The reactive nitrene is inserted in about 2 ms into those C-H-bonds of the protein that are exposed to the solvent. On the basis of amino acid analysis, it appears that the residues of the native protein that are buried in the interior of the molecule do not react with the nitrene. But when these residues (even the non-reactive ones such as valine and proline) are exposed by the denaturation of the proteins, they react with nitrene. It is observed that the native ribonuclease A retains 90% of its enzymic activity when flashed in the absence of NAP-Taurine. This small loss in activity arises from the disruption of a limited portion of the native enzyme structure. The site of this limited disruption may be a portion of the enzyme surface near the cys-26-cys-84 disulfide bond.

Questions (1) The decay of the triplet state of naphthalene was followed by a flash photolysis technique at 410 nm. The first order rate constant for this process was found to be 6.3 × 105 min−1 . Calculate the time required for its concentration to be one tenth of its original value. (2) The reaction between myoglobin (Mgb) and carbon monoxide was studied by flash photolytic technique at 540 nm and the rate constant of the forward reaction k1 BG MgbCO Mgb + CO FGGGGGG GGGGG k −1 was found to be 5.5 × 105 l mol−1 sec−1 . Assuming that their initial concentrations are 1 × 10−4 M, calculate the time required for the “CO” concentration decrease to 1 × 10−5 M.

21

Pressure Jump Relaxation Method for the Kinetic Study of Fast Biochemical Reactions 21.1

Introduction

The use of pressure as a perturbing parameter to initiate and understand biochemical reactions has a long history. In the pressure jump technique, the pressure on a reaction system in solution is changed rapidly and the position of equilibrium thereby shifts adiabatically according to   ΔV ◦ Vα ΔH ◦ ∂ ln K (21.1) =− + · ∂P RT C p RT S where ΔV ◦ = change in molar volume between products and reactants under standard conditions, ΔH ◦ refers to difference in enthalpy between products and reactants under standard conditions, α is the coefficient of thermal expansion    1 ∂V V ∂T P C p is the heat capacity, R is universal gas constant. In aqueous solutions at 298 K, for moderate pressure changes of the order of 50 atm (≈ 50 bar), the contribution due to second term of equation (21.1) is quite small and hence the equation is adopted.   ∂ ln K P ΔV ◦ (21.2) =− ∂P RT S

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Experimental Arrangement and Methodology

There are two essential parts of a P-Jump unit: (i) a device for the production of a fast P-Jump, (ii) a suitable Wheatstone bridge net work with a fast recording device such as an oscilloscope to follow the change in conductivity (there are other physical parameters such as colour change which can be followed in a spectrophotometer) of the solution with time. The following diagram shows the set up commonly used in Pressure Jump experiments. The Wheatstone bridge employed in these studies is such that it measures only relative changes of cell resistance and hence its design is different from the bridge normally used in resistance measurements. It is also to be noted that the bridge frequency must be greater than the reciprocal of the smallest relaxation time to be measured.

Conductance cells

Bursting memberance

Auto clave

Inlet for pumping kerosene

50 kHz

Oscillator Potentiometer Oscilloscope

Figure 21.1 Experimental arrangement of a pressure jump unit.

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357

Two small conductivity cells (1 ml capacity) are placed inside the autoclave one filled with the experimental solution and the other with a reference non-relaxing solution like KCl or MgSO4 such that they nearly have the same resistance. The rest of the autoclave is filled with a non-conducting liquid like kerosene and the pressure is built up by pumping kerosine into the autoclave which is covered with a thin metallic disc. The disc ruptures when the pressure reaches around 60–70 atms and simultaneously the oscilloscope is triggered. The release of pressure to the atmospheric pressure takes about 50 μsec.

21.3

Applications

(1) Conformational changes of serum albumin: In this study, changes in intrinsic protein fluorescence and absorbance changes due to spectral shift in the benzyl orange dye spectrum are used to follow the isomerisation. A single relaxation time was observed and the rate constant was ∼ 6.0 sec−1 . (2) Equilibrium in myosin assembly: The equilibrium in myosin according to 100 myosin monomers ( M ) ←→ myosin filament assembly ( F ) (21.3) whose equilibrium constant is given by K er =

[ F] [ M]100

(21.4)

The experimental data was fitted to the second order equation 2M ←→ M2

(21.5)

and the second order rate constant was found to be ≈ 4 × 104 l gm−1 sec−1 at 298 K and a pH = 8.3. (3) The equilibrium concentrations of the reactants in the system Lactate + NAD+

Lactate + FGGGGGGGGGGGB GGGGGGGGGGG pyruvate + NADH + H dehydrogenase

(21.6)

were altered by change of pressure on the system by 150 atm. The total change in [NADH + NAD+ ] concentration was followed by UltravioletVisible spectroscopy at 340 nm. The relaxation time is found to be in the range of 50 msec in presence of phosphate buffer.

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In another experiment the P-Jump of 200 atm was applied and the overall lactate dehydrogenase equilibrium was monitored by protein fluorescence quenching and a relaxation time of 0.56 sec was observed for a slow step. (1) Several metal complex formation reactions in 2 : 2 and 3 : 2 electrolytes like BeSO4 , aluminium sulphate and gallium sulphate solution were studied by P-Jump technique. The hydration of pyruvic acid (CH3 COCOOH) was investigated by employing this technique and a relaxation time of 1 to 2 sec was observed. (2) The pressure-jump induced relaxation kinetics was used for studying the protein folding/unfolding of Y115W, a fluorescent variant of ribonuclease A. Pressure jumps of the order of 350–400 atoms were achieved and relaxation times of the order of a few minutes were observed. For the reaction given by ku Folded state FGGGGGGB GGGGGG Unfolded state kf

(21.7)

The data obtained are shown below: Temp (K) 303 323

pH 5.0 5.0

ΔGu◦ (kJmol−1 ) 34.5 10.2

P1/2 (MPa) 468 225

k obs at P1/2 (sec−1 ) 4.2 × 10−3 9.5 × 10−2

ΔVu= (ml · mol−1 ) −58.2 −17.5

where P1/2 = pressure at half transition. The observed rate constants at a pressure of 300 MPa are k f = 1.82 × 10−2 sec−1 at 300 K and k u = 8.1 × 10−2 sec−1 .

Questions (1) For the reaction k1 k3 BG Be(H2 O)SO4 FGGGGGG BG Be2+ SO24− Be2+ + SO24− FGGGGGG GGGGG GGGGG k −1 k4 the first step is very fast (to be studied by P-Jump) and the reciprocal relaxation time is given by 1 K0 (C¯ 1 + C¯ 2 ) = k4 + k3 τ 1 + K0 (C¯ 1 + C¯ 2 )

Pressure Jump Relaxation Method 

359

where C1 = C¯ Be2+ , C¯ 2 = C¯ SO2− . Given that 1/τ at concentrations 4 (C¯ 1 + C¯ 2 )1 = 0.002; (C¯ 1 + C¯ 2 )2 = 0.004 are 350 sec−1 and 400 sec−1 respectively and K0 = 100 M−1 . Calculate k3 and k4 .

22

Circular Dichroism as a Tool for the Analysis of Biochemical Reactions 22.1

Introduction

Circular dichroism (CD) spectroscopy is a spectroscopic technique where the CD of molecules is measured over a range of wavelengths. CD is the difference in the absorption of left-handed circular polarized light (LCPL) and right-handed circularly polarized light (R-CPL) and occurs when a molecule contains one or more light absorbing groups (or chiral chromophores). (22.1) CD = ΔA(γ) = A(γ)LCPL − A(γ)RCPL where γ = wavelength and A = absorbance. CD spectroscopy is widely used to study chiral molecules of all types and sizes but it finds most applications in the study of large biological molecules. Its primary use is in analyzing the secondary structure or conformation of macromolecules particularly proteins as secondary structure is sensitive to environment, pH and temperature. Structural, kinetic and thermodynamic information about macromolecules can be derived from CD spectroscopy.

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Biophysical Chemistry

Principle

The differential absorption occurs when a chromophore is chiral (or optically active) either (a) intrinsically by reason of its structure or (b) by being linked to a chiral centre or (c) by being placed in an asymmetric environment. In practice, the plane polarized light is split into two circularly polarized components by passage through a modulator subjected to an alternating electric field (50 kHz). The modulator consists of a piezoelectric quartz crystal and a thin plate of isotropic material (e.g., quartz) tightly coupled to the crystal. The alternating electric field induces structural changes in the quartz crystal which make the plate transmit circularly polarized light at the extremes of the field. If after passage through the sample, the LCPL and RCPL components are not absorbed, combination of the components would regenerate radiation polarized in original plane. If one of the components is absorbed by the sample to a greater extent than the other, the resultant radiation would now be elliptically polarized i.e., the resultant would trace out an ellipse. The CD spectropolarimeter does not recombine the components but detects the two components separately. It will then display the dichroism at a given wavelength of radiation as either the difference in absorbance of (γA = A L − A R ) or as ellipticity in degrees (θ )  the two components 

θ = tan−1 ba , where b and a are minor and major axes of the resultant ellipse. The relationship between θ and ΔA is θ = 32.98ΔA

(22.2)

Absorbance (A)

ACD spectrum obtained when the dichroism is measured as a function of wavelength is shown below: 1

2

3

Figure 22.1 Different types of CD spectra. Band 1 is not chiral; Band 2 has a positive CD spectrum with L absorbed more than R; and Band 3 has a negative CD spectrum.

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If two or more identical chromophores are in close proximity, the interaction between them can give rise to a sigmoidal CD spectrum. The exciton coupling model can be used to account for this behavior. Such coupling can occur from close pairs of Trp side chains or from more extended sets of chromophores in proteins. The latter situation is seen in the case of the ring 18B850 of bacterio-chlorophyll molecules in the LH2 light harvesting complex from photosynthetic bacteria. In much of biological work, the observed ellipticities are of the order of 10 milli degrees (i.e., the difference in absorbance between two circularly polarized components of the incident radiation is of the order of 3 × 10−4 absorbance units).

22.3

Experimental Set Up

The light source for conventional CD measurements is a xenon arc. It gives output over a range of wave lengths (178 to 1000 nm), a good range for studies on proteins. It is important to flush the instrument with N2 gas to remove oxygen from the lamp housing to prevent ozone formation and to allow measurements below 200 nm. The protein samples must be homogeneous and should be freed of scattering particles by centrifugation or passage through suitable filter. It is also important to minimize absorption due to other components of buffers (solvents, supporting electrolytes etc.). Sometimes, it may be necessary to run “blank” CD spectra to ensure that the buffer components do not lead to excessive noise or other artefacts in the spectra. It is also essential to know the protein concentration to within ±5% in order to enable the estimate of the secondary structure content of a protein from CD.

22.3.1

Units for CD

When CD data are expressed in terms of absorbance, ΔA = difference in molar absorbance = A L − A R , (i.e., cm−1 · M−1 ). When the data are expressed in terms of ellipticity, the mean residue ellipticity [θ ]mrw,λ at a given wavelength is given in units of deg · cm2 · d · mol−1 and is given by

[θ ]mrw,λ =

MRWθ 10d · C

(22.3)

where θ = observed ellipticity (deg), d is the path length, C is the concentration (in gm mol−1 ).

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At any given wavelength, θ and ΔA can be related according to θmrw = 3298ΔA

22.3.2

(22.4)

Amount of Sample Required

Considering that the cells used for far UVCD are about 0.01 to 0.05 cm, protein concentrations are in the range of 0.1 to 0.2 mg ml−1 . The CD signals in the near UV and visible regions are much weaker than in far UV indicating the much lower concentrations of chromophores compared to those of peptide bonds. Protein concentrations of the order of 0.5 to 2 mg ml−1 with a cell of length 0.5 to 2 cm are used. Recording of CD spectra at liquid nitrogen temperatures i.e., 77K give very useful information.

22.4

Methodology

Stopped flow technique was adopted in the initial stages and has been used to study early events in protein unfolding. Concentrations of the order of 0.55 M bring out sufficient changes in ellipticity in the far UV (225 nm) and near UV (290 nm) to get valuable information in the secondary and tertiary structure of proteins.

22.4.1

CD Studied by Using Synchrotron Radiation

Synchrotron radiation is generated when charged particles like electrons moving at velocities close to that of light are accelerated through magnetic fields. Intense radiation is produced covering a wide range of wavelengths from X-rays to IR. The key adavantage for CD in the generation of synchrotron radiation is the very large increase (over 1000 fold) in intensity in the far UV region (below 200 nm) compared with xenon arc sources.

22.5

Disadvantages as Limitations

Studies using CD have certain advantages over X-ray and NMR in that the measurements can be carried out fast and good quality spectra can be obtained in the near UV and far UV region in a short interval of 30 mins. Some examples illustrate this point. The changes in the far UVCD spectrum of a 58-residue DNA binding peptide derived from transcription factor GCN4 over 1000 fold range of concentrations has been interpreted in terms of a dimeric species with a high helical content (about 70%) dissociating upon dilution into two unfolded chains. Far UVCD studies required

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only small amounts of material. The technique is non-destructive and hence one can recover most of the solution and conduct multiple experiments on the same sample. Since cells of differing path lengths can be used, a wide range of protein concentrations can be employed. CD studies can be performed over a wide range of experimental conditions including pH and temperature. The main limitation of CD is that it only provides low resolution structural information. For example, although few UVCD can give reliable estimates of the secondary structure content of a protein (in terms of proportion of a-new and b-sheets and β-turns), the overall figures do not indicate which regions of the protein are of what type. CD gives little information on quaternary structure of protein.

22.6

Applications

CD has been employed widely in studies of protein unfolding and folding. The secondary and tertiary structural characteristics of a range of mutant proteins has been assessed rapidly by CD Mutations have not resulted in significant distortion of the structure when in two mutant forms of isocitrate lyase from Escherichia coli in which CYS 195 has been replaced by alanine or serine. In the case of phosphoglycerate mutase from schizosaccharomyces pombe, mutations of HIS163 to Gln leads to complete loss of activity. The CD spectra of isocitrate lyase from E.coli has been obtained. Although the ligand or cofactor has no CD signal, the observed CD signal in the complex indicate that the binding site of ligand or cofactor confers chirality. It should be noted that there is generally a much smaller change in absorbance of the cofactor on dissociation from the protein.

22.6.1

Effect of Cofactors and Ligands on CD

(i) Pyridoxal-5-phosphate: This cofactor is used by many enzymes such as amino transferases and decarboxylases in amino acid metabolism. It is also a cofactor in glycogen phosphorylase. CD was used in studies of two iso enzymes of aspartate aminotransferase which were used to study unfolding of proteins. The specific CD peaks at 365 nm (for cytoplasmic isoenzyme) and 355 nm (mitochondrial isoenzyme) were used to monitor loss of cofactor from the enzyme since free pyridoxal-5 -phosphate shows no significant CD signal in this region.

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(ii) Flavins: The two flavins (Flavin mononucleotide (FMN)) and flavin adenine nucleotide (FAN) play important redox roles in the electron transport chain as well as in a number of enzyme catalysed oxidation reactions of substrates such as amino and hydroxyl acids. Free flavins exhibit only very small visible CD and hence dissociation of cofactor leads to complete loss of the signal. The FMN containing E.coli flavodoxin shows negative ellipticity over 310–450 nm with a maximum visible signal at 365 nm (−160 deg cm2 · dmol−1 ). However, its redox partner flavodoxin reductase exhibits a +ve ellipticity over 300–420 nm with a maximum around 390 nm (+95 deg · cm2 · dmol−1 ).

Figure 22.2 CD spectra of flavoproteins in the near UV and visible region.

θ (deg. cm2. dmol–1)

15000 10000 5000 0 –5000 –10000

200

220

240

Wavelength (nm)

Figure 22.3 CD spectra of isocitrate lyase from E.coli.

260

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 367

2.0 1.0

0

–1.0 260

270

280

290

300

310

320

Wavelength (nm)

Figure 22.4 CD spectra of the same species in the near UV region. (iii) Haem: The Haem cofactor plays a number of roles in proteins such as binding of O2 in Haemoglobin cytochrome C-oxidase, a cofactor for hydro-peroxidases such as catalase or as a redox cofactor as incyto chromes b and c. CD has been used widely to study cytochrome P450 enzymes. The CD spectrum of a P-450 can be used to predict active site structural properties such as H-bonding and polarity.

22.6.2

Specific Examples

(1) Peptide bond: Peptide bond absorbs in far UV. Aromatic amino acid side chains (like phenyl alanine, tyrosine and tryptophan) absorb in the near UV range 250–290 nm studies in far UV can give information on the secondary structure. The tertiary folding of polypeptide chain can place these side chains in chiral environment giving rise to CD spectra which can serve as characteristic finger prints of the native structure. This bond absorbs primarily in the far UV region (240 nm to 190 nm). Studies of far UVCD can be used to assess the overall secondary structure of the protein quantitatively. (2) Aromatic amino acid side chains: The near UVCD of proteins arises from the environs of each aromatic amino acid side chain as well as possible contributions from disulphide bonds, or non-protein cofactors. Small model compounds of the aromatic amino acids exhibit CD spectra because the chromophore is linked to the nearby α-carbon atom. It may be noted that in the case of proteins in their native states the side chains of amino acids are placed in a variety of asymmetric environments characteristic of the tertiary structure of the folded protein. Some factors which influence CD spectra of aromatic amino

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acids are: (i) rigidity of protein, (ii) nature of environment such as Hbonding polar groups and polarisability, (iii) interactions among the amino acids, (iv) number of aromatic amino acids in a protein. (3) Non-protein chromophores: CD in the near UV, visible and near IR provides a great deal of information on the environments of cofactors or other. (4) Flavocytochromes: CD in the visible region provides a valuable spectroscopic probe of flavins in flavocytochromes. It may be mentioned that flavocytochromes are enzymes containing two redox cofactors i.e., FMN or FAD and a Haem group. For example, in nitrate reductase from chlorella, the flavin contribution is masked in the visible absorption spectrum of this molybdoprotein and Haem b containing enzyme. Positive CD signals from FAD are seen at 311 nm and 387 nm with negative CD signals at 460 nm and 487 nm. (5) Nucleic acid chromophores: The bases DNA and RNA do not show any intrinsic CD. The chirality of the sugar residues induces a small CD in the nucleotide units. The stacking of bases which occurs in helical structures adopted by oligonucleotides and nucleic acids gives rise to large CD signals due to exciton coupling between the bases. The CD spectrum in the range 230 to 300 nm is a very sensitive measure of secondary structure with the various forms of DNA and RNA. (6) Conformational changes in proteins: CD is an ideal technique to monitor conformational changes in proteins arising from experimental factors such as temperature, pH, binding of ligands. CD has proved to be very useful in studying the extent of conformational changes and the stability of the folded state of the protein. Far UVCD has been found to be a valuable tool for monitoring the transitions from α-helical to β-sheet structures in proteins and peptides. CD was used to monitor the binding of Ca2+ to troponin C, the protein which confers Ca2+ sensitivity to muscle. It was found that addition of Ca2+ led to an increase in the negative CD signal in the range 200 to 230 nm showing the increased stability of the helical regions of the protein. CD has been used to monitor the binding of the substrate ATP to a mutant form of the molecular chaperone GroEL. This protein consists of two stacked rings of seven sub-units with a central cavity within which the protein folding is assisted. Binding of ATP to K3E mutant was shown from the observation that addition of nucleotide led to a 50% increase in the size of the CD signals in the range 230 to

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190 nm. By contrast, addition of ATP does not lead to any increase in the far UVCD signal of the wild type protein. The near UVCD of the hexameric enzyme glutamate dehydrogenase was used to monitor the binding of NAD+ in the presence of a competitive inhibitor glutarate. Addition of NAD+ was found to change the near UVCD signal sharply at a point corresponding to half saturation of the sites. CD has also been employed to monitor the R ←→ T allosteric transition in haemoglobin. The CD spectrum of the protein shows the bands in the 270–300 nm region due to Tyr and Trp side chains and a large band at 260 nm due to Haem group. Deoxyhaemoglobin shows

Figure 22.5 CD spectra of α-lactalbumin (a) and (b) represent far UV and near UV spectra at pH = 7.0.

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Biophysical Chemistry

a negative band at 287 nm. Oxyhaemoglobin shows weak negative bands at 283 nm and 290 nm. The marked changes in the near UVCD spectrum were attributed to changes in environments of Trp-37 on the β-chain and Tyr-42 on the α-chain. A particularly important use of CD has been to characterize the overall structural states of proteins. For example, when lactalbumin is incubated at pH = 2.0, it retains its native secondary structure as shown by far UVCD. However, under these conditions, the near UVCD signal of the protein is very much reduced indicating that the native tertiary interactions are absent. (7) The refolding of proteins and peptides: An important problem of molecular biology is the mechanism of protein folding. An understanding of protein folding is necessary to learn about the disease states of the body which arise possibly from protein misfolding. In order to establish the mechanism of refolding of a protein, it is necessary to study the time scale of recovery of structure from the denatured state and to correlate the same with the recovery of biological state. The regaining of secondary structure is monitored by far UVCD and that of tertiary structure by near UVCD and fluorescence. Stopped flow CD has been widely used to examine the properties of early intermediates in protein folding. Studies showed that during the refolding of denatured ferricytochrome C and β-lactoglobulin, the native ellipticity in the far UVCD was regained in around 18 msec. However, the ellipticity in visible region for ferricytochrome C or near UV for β-lactoglobulin was regained over a period of few minutes. In a study of native and mutant forms of staphylococcus nuclease, it was found that a transient kinetic intermediate formed within 10 msec. This intermediate possessed only about 30% of native ellipticity at 225 nm. The relatively low amplitude indicated formation of the 5-stranded β-sheet structural core of N-terminal domain of the enzyme with the helices contributing bulk of the CD signal at 225 nm. In some detailed studies of protein folding and refolding on hen egg white lysozyme, it was shown that the form disulphide bonds are kept intact. Stopped flow CD and fluorescence were used to define the regions of protein where secondary structure and tertiary interactions have formed during refolding process. Further insights into the folding of lysozyme were obtained from stopped flow CD at far and near UV region. The near UV results at 289 nm show that the native

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ellipticity develops in a single kinetic process with a rate similar to the protection of β-sheets domain. Stopped flow CD in the far UV shows that about 80% of native ellipticity was regained at 225 nm. In a second phase which was complete after 80 msec the CD signal increases to about 150% of the native value in a third phase of t1/2 = 300 msec. (8) Protein and peptide design: CD is a very useful tool in characterizing peptide and protein fragments which have been designed to adopt specific structures and thus display special biological functions. Peptides based on a repeating unit AEAAKA having length in the range of 14 to 50 residues form helices as shown by far UVCD. The urea induced unfolding of these peptides has been monitored by CD and the energetics of the unfolding is shown to correspond with those of unfolding of helices in proteins like myoglobin. The far UVCD spectrum of peptide of the type AC-KAKAKAKAEAEAGA EA-NH2 show interesting structural changes at 20◦ C as shown by far UVCD. It was shown to form a stable macroscopic β-sheet in water which stains dyes like congored. There is an abrupt change in the CD spectrum on raising the temperature to 70◦ C which indicates that a helical structure is formed. (9) Membrane proteins: CD is an important technique in the study of membrane proteins especially to study the retention of native structure on extraction and purification. For example, in studies of extraction of myelin basic protein (MBP) from equine myelin, CD was used to assess the effect of several detergents on the protein. The solubilisation of bacteriorhodopsin in the non-ionic detergent octyl glucoside led to significant changes in secondary structure as indicated by for UVCD spectrum. The structural changes in the OMPA protein in the unfolded and folded state were monitored by far UVCD and protein fluorescence. The changes in CD signal at 206 nm showed that there were three phases to the folding and insertion process. Far UVCD studies showed that peptides are largely helical (78%). (10) Interactions between domains in proteins: Most polypeptide chains larger than 30 kDA (30,000 amu) tend to exist in multiple domains i.e., as independent folding units. Preparation of large quantities of protein corresponding to defined domains has been achieved by recombinant DNA technique. CD has been employed as a structural technique in such studies. Using CD signal at 218 nm to monitor the loss

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of structure caused by Gdmcl, the unfolding of intact enzyme and isolated N- and C-domains were found in phosphoglycerate kinase. CD studies helped to unravel the low rate of electron transfer between the redox centers of separate flavin and P-450 domains of BM3 flavocytochromes. The significant differences CD spectra in the near UV and visible regions in intact BM3 were ascribed to characteristic environments of the aromatic amino acid side chains and flavin and haem cofactors. In experiments with P-450 BM3, CD was used to compare the structural stability of the protein as measured by CD in the near and visible regions. CD studies of the LH2 complex from Rhodopseudomonas acidophila 10050 in the far UV region have shown that α- and β-polypeptides have high (50–60%) α-helical content. The absorption and CD spectra of LH2 show three main absorption peaks between 450 and 550 nm and they were ascribed to carotenoid molecules. The absorption peaks at 380 nm, 595 nm and in 750 to 900 nm region are due to Bchla (also known as B-800) and that at 863 nm is due to the inner set of 18 Bchla. When the carotenoid (of LH2 complex) is extracted and dissolved in organic solvents, there is no CD signal which reflects the symmetry of the molecule. CD can be used to assess the structural integrity of LH2 complexes. Comparison of CD spectra of native LH2 , B-850 complexes in both visible and near IR spectral regions showed that the inner core of carotenoids and Bchla-B850 were very similar. In addition, the CD of the reconstituted and native complex around 800 nm showed that the Bchla-B800 molecules had bound in the correct orientation in the reconstituted complexes. (11) Ligand binding and drug design: The binding of ligands to proteins gives rise to a CD signal due to asymmetric binding of the ligand. Such binding leads to conformational changes in proteins which can be detected by far UV and near UVCD. Studies of the helical content and thermal stability using CD were used to examine the effects of mutating amino acids involved in contact with the N-helix in the hydrophobic groove.

Circular Dichroism as a Tool for the Analysis of Biochemical Reactions

 373

Questions (1) In circular dichroism, the technique used is (a) light scattering (c) NMR (b) UV-Vis (d) ESR (2) The relation between ΔA (A-absorbance) and θ (ellipticity in degrees) is (a) θ = 35 × ΔA (c) θ = 3298 × ΔA Φ (b) ΔA = (d) θ = 45.82 × ΔA 40.5 (3) The far UVCD spectrum of α-lactalbumin (around pH = 2.0) shows a θ maximum (in nm) around (a) 310 (c) 305 (b) 250 (d) 420 (4) Circular Dichroism is best used for study of (a) (b) (c) (d)

acid-base dissociation potential changes in electrolytic solutions electro reduction of a species at metal or mercury surface conformational changes in proteins

(5) Far UV circular dichroism gives valuable information on (a) (b) (c) (d)

secondary structure of proteins lipid bilayer composition carbohydrate metabolism Phosphate groups in ATP

(6) Discuss the advantages and disadvantages of the technique of circular dichroism in the study of biomolecules. (7) Enumerate the applications of circular dichroism giving specific examples.

23

Applications of Isothermal Calorimetry in the Study of Biochemical Reactions 23.1

Introduction

Isothermal calorimetry (ITC) is a physical technique that measures directly the heat released or consumed in a bimolecular reaction. In this analytical technique the ligand comes in contact with a macromolecule (or any other) at constant temperature. From basic thermodynamic principles, whenever there is contact between two molecules, there is either heat evolution or absorption depending on the type of binding. The heat generated or absorbed during an interaction is measured. It is widely used for measuring the binding energetics of biological macromolecular interactions including protein—ligand and protein—protein interactions. Kinetic data of enzyme-catalysed reactions have also been obtained by employing this method. In recent years, ITC has been recognized as a reliable tool for obtaining thermodynamic parameters (of intermolar interactions) such as ΔH, ΔS and binding constants of protein-ligand interactions.

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_23

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Biophysical Chemistry

Experimental Set Up

The schematic presentation of a simple isothermal heat conduction calorimeter is given below. (a) Syringe holder (b) U-shaped holder (c) Ampoule made of glass (d) Aluminium cup (for sample) (e) Aluminium cup (for reference) (f) Thermocouples

Figure 23.1 Experimental set up of an isothermal heat flow calorimeter. In the above instrument there are two identical heat flow sensors, one for sample measurement and the other for a reference. On top of the sensors, aluminium cups are mounted into which the ampoules with the sample and reference are mounted and inserted for a measurement. The sensors are in intimate thermal contact with a relatively large aluminum heat sink. A syringe is mounted above the sample cup to enable introduction of a solution or liquid as reagent. The complete instrument is shielded from the surrounding by an insulation jacket. The voltage from the reference heat flow sensor is subtracted from the voltage from the measurement heat flow sensor. Heat that enters through the jacket will influence the measurement and the reference sides identically and thus will produce no net signal. Only a signal produced by the sample will be recorded. It is advantageous for the calorimeter to be equipped with a thermostatting position where a sample may be held for

Applications of Isothermal Calorimetry 

377

some time before being introduced into thermal contact with the thermocouples. Isothermal calorimeters are calibrated electrically with a resistance heater inserted into the measurement ampoule or attached to the ampoule holder.

23.3

Applications

(1) Thermodynamic data for characterization of ligand—target binding: According to the equation ΔG = ΔH − TΔS

(23.1)

changes in enthalpy and entropy account for the Gibbs free energy of ligand binding. When the conformation of a ligand becomes more rigid, ΔS becomes smaller indicating that the entropic loss of ligand target binding is getting smaller. If the ΔH becomes more negative, it means that more stronger interactions occur between the ligand and target. To evaluate which ligand is more enthalpy favourable, a quantity enthalpic efficiency (EE) equal to ΔH/Q is proposed where Q is number of heavy atoms or molar mass of a ligand. By analysing the thermodynamic profiling of inhibitors of HIV protease and the hydroxymethyl glutaryl co-enzyme A (HMG-CoA) reductase, it was possible to differentiate between the best in drug classes. The enthalpy change data serve as a key indicator to qualify ligands as candidates for best ligand-target studies. (2) ITC combined with ligand—protein complex structure: Rapid development of structural biology, especially in X-ray protein crystallography, provides a powerful approach to solving protein-ligand complex structures and reveal the actual binding site of compounds in the binding pocket of targeting proteins. Introduction of a H-bond or presence of hydrophobic interactions in protein ligand exchange are responsible for enthalpy/entropy gain or loss. The importance of thermodynamic data in the understanding of protein ligand interactions is explained through the following examples. (a) Phosphodiesterase type 5, an enzyme catalyzing the hydrolysis of CGMP to 5-GMP is an important drug target for treatment of diseases associated with low level of CGMP such as pulmonary arterial hypertension. ITC experiments were used to supplement the experimental results of the bonding of halogen (F, Cl, Br, I) substituted (in the 5th position) monocyclic pyrimidinones with the

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Biophysical Chemistry

residue of Y612 of PDE5. The crystal structures of PDES complex with compounds involving halogens (in pyrimidinones) showed a similar binding mode for the compounds with the enzyme. The binding free energies of the Cl, Br, I substituted compounds in pyrimidinones with PDE5 were found to be −34.9, −36.4, and −38.9 kJmol−1 respectively. A second example which takes advantage of the thermodynamic data supported by complex structures is the discovery of FABP4, which is a fatty acid binding protein responsible for transportation of saturated fatty acids to mediate cell signal path ways. It was shown that FABP4 (knocked out from mice) protects the mice from diseases such as atherosclerosis and type-2 diabetes. (b) A typical ITC experiment consists of three steps: (i) a ligand is titrated into a solution containing the bio macromolecule (e.g., a protein), (ii) measurement of the heat released or absorbed that is associated with the binding event, (iii) the resulting data is processed to obtain binding constant, Kb , free energy of binding, ΔGbin , enthalpy and entropy of binding (ΔHbin and ΔSbin ). A representative ITC data for the binding of cytidine 2’-monophosphate (2’ CMP) to RNase A is shown in Figure 23.2.

Figure 23.2 Binding curve obtained from unprocessed data. Heat of reaction per injection as a function of the ratio of total ligand concentration to the protein concentration. At pH = 5.5 and T = 301K, it was found that K B = 2.5 × 105 M−1 , ΔH = −12.98 kcal mol−1 for the reaction between 2’ CMP and RNASEA.

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(3) Application of ITC data in kinetic studies: ITC measurements can be used to obtain binding constant Km , k cat and Vmax of enzyme-substrate reactions and inhibition constant (Kc ) of enzyme-inhibitor binding. The development of a method, known as kinetic ITC technique, led to the possibility of measuring binding kinetics (k on and k o f f ) and the inhibitory constant Ki . The simple competitive enzyme inhibition model given by the following kinetic scheme was used. ko f f k1 k cat EI FGGGGGGGGB GGGGGGGG E + I + S FGGGGGGGB GGGGGGG ES −−→ E + P k on k −1

(23.2)

where E = enzyme, I = inhibitor, S = substrate, P = product, EI = enzyme inhibitor complex), k on = association rate constant, k o f f = dissociation rate constant, k cat = catalytic rate coefficient. The instantaneous rate of enzyme catalysis is given by MichaelisMenten equation as d[ P] d[S] k cat [S]([ E0 ] − [ EI ]) =− = dt dt Km + [ S ]

(23.3)

where [ E0 ] = total enzyme concentration, [ EI ] = concentration of enzyme-inhibitor complex, Km = Michaelis-Menten constant. Assuming that the inhibition follows 1st order kinetics, given by d[ EI ] = k on [ E][ I ] − k o f f [ EI ] dt

(23.4)

where [ E] = concentration of free enzyme. The heat flow generated Q(t) by catalysis is given by Q(t) = ΔHcat × Vcell ×

d[ P] dt

(23.5)

where ΔHcat = enthalpy of catalysis, V = Volume of the cell. The basis of this method is that ITC detects heat flow in real time and then gives a direct measurement of enzyme activity and its variation in response to inhibitor according to equations (23.3) and (23.5). The kinetic parameters of inhibitor binding to enzyme can be calculated from equation (23.4). The kinetic ITC technique enables the kinetic constants of inhibition, k on ≈ 103 to 107 M, and Kc in sub-nM values to be determined.

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Biophysical Chemistry

(4) Enzyme catalysed reactions: The enzyme glucose-6-phosphate dehydrogenase (G6PD) uses NAD+ or NADP+ as a cofactor and the enthalpy changes of this enzyme catalysed reaction varied with the type of buffer used in the reaction. When tris was used as buffer, ΔH ITC = −22.93 kJ mol−1 , but ΔH ITC (when phosphate buffer) was 19.4 kJ mol−1 for NADP+ linked reaction but the values were −11.7 kJ (tris) or 30.6 kJmol−1 (phosphate) for NAD+ reaction. (5) ITC application in RNA biochemistry: ITC has been used in the areas of small molecules binding to RNAs, RNA—protein interactions and in fundamental studies of protein folding. ITC was employed to study ligand binding to both natural purine riboswitch as well as synthetic riboswitch that responds to tetracycline. Binding has been shown to be enthalpically favourable and entropically opposed for all the species that can be accommodated in these riboswitches. Another group of small molecules—RNA interactions that has been studied by ITC are the aminoglycoside antibiotics. These agents are known to bind the 16SrRNA, HIV responsive elements and many other RNA’s. It was shown by ITC studies that the binding of neomycin to the 16SrRNA depends strongly on pH and buffer sensitivity. ITC was used to probe individual steps in the assembly pathway of the small subunits of bacterial ribosomes. ITC was employed to probe the binding of ELF4E to a 7-methyl-GpppG cap analogue. The temperature dependent analysis of this binding showed significant enthalpy-entropy compensation. The following table shows some data related to this binding. Table 23.1 Enthalpy–entropy compensation in the binding of F4E to 7 methyl-GpppG. Temperature (K) 290 300 310

ΔG ◦ (kJmol−1 ) −42.0 −40.0 −40.0

ΔH ◦ (kJmol−1 ) −70.0 −55.0 −40.0

(6) ITC use in biopharmaceutical development: Prox is a drug (prescribed as tablets) used for treating bacterial infection of skin tissue. ITC has been used to aid the development of additives for Prox. In this process, polysorbate-80 and phenol were examined as the additives. It may be

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mentioned that polysorbate-80 is a surfactant to prevent non-specific adsorption and aggregation of proteins. Fitting of the binding curve to a particular binding model can yield Kb , ΔH and n (number of ligands) from a single experiment. Kb can be obtained from ΔGbin . ΔSbin and ΔCP(bin) may similarly be obtained using the following relationships. ΔH(T ) = ΔH(T0) + ΔCP(bin) ( T − T0 ) ΔS(T ) = ΔS(T0) + ΔCP(bin) ln

T T0

(23.6) (23.7) 

ΔG(T ) = ΔH(T0) − TΔST0 + ΔCP(bin)

T − T0 − T ln

T T0

 (23.8)

where T = experimental temperature, T0 = reference temperature. ITC has been used to optimize HIV-I protease inhibitor binding by considering the thermodynamics of binding interactions. The figure below shows the thermodynamic profiles for a pair of HIV-protease inhibitors with the difference in the pair being a functional group. In this case, the replacement of a thioether on KNI-10033 by a sulfonyl on KNI-10075 results in a more negative enthalpy change (−3.9 kcal mol−1 ) and less entropy gain (−4.2 kcal mol−1 ). ΔG = −14.9, ΔH = −8.2; TΔS = −6.7 (all in kcal mol−1 )

HO H N

O

O

O N H

O

O N

N H

CH S

S

Figure 23.3 Thermodynamic profiles of HIV proteanase inhibitors. Another example of an ITC experiment is a study of exothermic interaction between a specific phosphotyrosyl peptide (concentration = 210μM) and Fyn SH2 domain (concentration = 21.0μM) at 293K. For this interaction, it was found that n = 1.1, K B (binding constant) = 2.42 × 106 M, ΔHB◦ = 30.9 kJmol−1 . ITC studies were performed on S-protein binding to seven forms of Speptide in which the methionine at position 13 (Met 13) was substituted by

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Biophysical Chemistry

different amino acids. At pH = 6.0 and 298K, ΔΔGB◦ values for the Met13 → isoleucine (ile) and Met13 → gly substitutions were 0.8 and 21.0 kJmol−1 respectively. (Note that ΔΔGB◦ = ΔGB◦ (mutant peptide) −ΔGB◦ (wild type peptide)). ITC studies were carried out on the formation of complex DNA structures corresponding to the intersection points of oligonucleotides. ITC has been used to determine the Δ B H ◦ at 298 K for the interaction of the Δ and Λ isomers of [Ru(phen)2 DPPZ]2+ with calf thymus DNA. Δ B H ◦ values of 0.8 kJmol−1 and 12.1 kJmol−1 were observed for Δ and Λ isomers respectively. ITC studies proved to be invaluable in understanding the specificity of proteins involved in intracellular signal transduction. Analysis of ITC data showed the subtle differences between the thermodynamic consequences of interactions between selected SH2 domain and specific (and non specific) tyrosyl phosphopeptides. Some thermodynamic data relating to these interactions is given below. ITC has been used to explore the interaction of molecules in receptor systems to elucidate the stoichiometry and thermodynamic parameters of interactions. The mode of binding of acidic fibroblast growth factor (aFGF) to its receptor was also investigated by ITC. It was shown that aFGF forms a 1 : 1 complex with its receptor. ITC data for the high affinity interaction of the immunosuppressive agent FK506 with the protein FKBP-12 also supported the relation between ΔCP( B) and surface area burial. The interactive surface between these two molecules is entirely hydrophobic. In the ternary complex TK: dT: ATP, the substrate dT and cofactor ATP are located in separate and well defined binding pockets of the enzyme. Table 23.2 Binding constants and thermodynamic data of tyrosyl phosphopeptides with different SH2 domains at 298 K. K B × 10−6 ΔB G◦ ΔB H◦ Δ B S◦ − 1 − 1 − 1 (M ) kJmol kJmol Jmol−1 SH2 domain-specific 1.6 −35.4 −35.3 +0.43 peptide Fyn SH2 domain-specific 1.4 −35.0 −35.6 −0.02 peptide P85SH2 domain-specific 2.3 −36.2 −39.2 −10.1 peptide LCK SH2 0.32 −31.3 −31.5 −0.37 domain-non-specific peptide

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383

The formation of the ternary complex may proceed through two sequential pathways (TK → TK: dT → TK: dT: ATP or TK → TK: ATP—TK: ATP: dT). In a random binding mechanism, all these reactions take place. To distinguish between ordered and random mechanism, ITC was used which confirmed the ordered binding mechanism (i.e., TK: dT → TK: dT: ATP) by titrating the preformed TK: binding complex with ATP. The reaction was found to be exothermic with K B = 3.9 × 106 M−1 and ΔHbin = −13.8 kcal mol−1 at 298 K.

23.4

Mutational Studies

The mechanism of substrate diversity observed with HSVTKL was investigated by a thorough mutational study, Kinetic measurement and ITC study. The residue triad H58/M128/Y172 was found to give a distinctive binding of a large variety of substrates to HSVTKL. Mutations in this trial have been prepared and analyzed by ITC. Table 23.3 Thermodynamic data for binding in ATP in presence of various mutants. Mutant (of HSVITK) ΔH/ ΔG/ TΔS/ KB kcal mol−1 kcal mol−1 kcal mol−1 (105 ) Wild type −26.3 −9.9 −16.4 229 M128F −8.1 −6.8 −1.3 1.04 M128F/Y172F/H58L −19.8 −7.4 −12.4 2.6

Specificity of Citrate Binding to the Histidine Autokinase CitA Receptor ITC was applied to describe the thermodynamic properties of citrate and citrate analogue binding to CitAPhis . Citrate binding to CitAPhis was found to be an exothermic process and could befit to a single-site binding model, yielding K D value, where K D = K1B of 5.5 × 10−6 M and ΔHobs = −18.3 kcal mol−1 . Depending on the pH, citrate exists in four species i.e., H3 -Citrate, H2 -Citrate, H-Citrate2− and Citrate3− with pK1 = 3.13, pK2 = 4.76 and pK3 = 6.40. In order to determine the preferred ligand species, the pH dependency of citrate binding constant to CitAPhis was studied in the pH range 4.0–9.0.

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Biophysical Chemistry

Table 23.4 Thermodynamic parameters of citrate binding to CitAPhis at 298 K in 50 mM phosphate buffer at different pH’s as determined by ITC. K B (104 KD ΔHobs ΔG (kcal TΔS pH N M−1 ) (μ M) (kcal mol−1 ) mol−1 ) (kcal mol−1 ) 4.0 0.98 6.26 16.7 −24.7 −6.5 −18.2 7.0 0.89 18.25 5.5 −18.3 −7.2 −11.1 9.0 0.83 6.47 15.5 −17.9 −6.6 −11.3 Table 23.5 Thermodynamic parameters of citrate binding at different concentrations of MgCl2 . ΔHobs ΔG TΔS MgCl2 K B (104 (kcal (kcal (kcal (mM) pH N M−1 ) K D (μ M) mol−1 ) mol−1 ) mol−1 ) 2.0 7.0 0.83 7.78 12.9 −18.9 −6.7 −12.2 10.0 7.0 0.85 2.47 40.5 −21.3 −6.0 −15.3 20.0 7.0 0.89 1.74 57.5 −21.4 −5.8 −15.6 The inhibitory influence of Mg2+ ions on citrate binding as seen from the above data (decrease of K B ) has been confirmed by ITC. From the tenfold decrease in K B at 20 mM Mg2+ , it was confirmed that that all citrate is complexed as Mg-Citrate2− . ITC was also used to localize amino acids involved in citrate binding by studying the influence of point mutations in CitAPhis . ITC was applied for investigating membrane bound protein-ligan interaction especially the serine receptor of Escherichia coli chemotaxis. ITC was employed to shed light on human apo- and holo-transferrin binding to the neisseria meningitides transferrin receptor.

23.5

Interaction of Transducer Fragments

Phototaxis of nitrosobacterium pharonis is mediated by two sensor rhodopsin SR-I and SR-II. SR-I enables bacteria to seek light conditions optimal for the function of light driven ion pumps and to avoid UV light. SR-II conveys negative phototaxis, which might enable the bacteria to evade harmful conditions of high oxygen concentration in presence of light. Both receptors are bound to membrane proteins (halobacterial transducers of rhodopsin, Htr-I and Htr-II). Light excitation of the SR-II: NpHtr-II complex leads to conformational changes in both proteins. Both SR-II and NPHtr-II form a tight 2 : 2 complex on membranes where as in micelles it dissociates to a 1 : 1 homodimer complex. ITC was used to elucidate the dimerisation as well as to determine the size of the receptor binding

Applications of Isothermal Calorimetry 

385

domain of transducer and also to determine K D of a series of the transducers to the receptor. Binding affinities of four shortened transducer fragments (NpHtr-II82, . . . ,101, NpHtr-II-114, . . . ,tr-II-157) to the receptor SR-II were determined using ITC. The relevant thermodynamic data are given below. Table 23.6 Thermodynamic parameters pertaining to binding affinities. ΔHobs ΔG ΔS Temp K B (106 KD (kcal (kcal (cal K−1 NpHtr-II (K) M−1 ) (nM) mol−1 ) mol−1 ) mol−1 ) 157 318 6.2 160 −4.3 −9.9 −17.6 114 318 4.32 240 −4.2 −9.6 −17.0 101 295 0.1 104 −1.4 −6.7 −18.2 5 82 295 < 0.01 > 10 — — — These data show that ITC is suitable to study membrane-protein interactions.

Questions (1) In an isothermal calorimetric experiment carried out in a cell of capacity 2 ml, the rate of the reaction in presence of an enzyme was found to be 0.1 moles liter−1 min−1 . Calculate the rate of heat flow of this enzyme catalyzed reaction. (2) Draw a neat sketch of an isothermal calorimeter and indicate the parts. (3) Describe the biochemistry.

application

of

isothermal

calorimetry

in

(4) Discuss the use of isothermal calorimetric data in kinetic studies.

RNA

24

Principles of Differential Scanning Calorimetry and its Applications in the Study of Biochemical Reactions 24.1

Introduction

It is a thermal analysis technique used to measure enthalpy changes due to changes in physical and chemical properties of a material as a function of temperature or time. It allows one to characterize materials and is a fast sensitive technique. In this technique the difference in energy inputs into a substance and a reference material is measured as a function of temperature while the substance and reference material are subjected to a controlled temperature program.

24.2

Experimental Set Up

Block diagram of a heat flux DSC is given in the Figure 24.1. The apparatus consists of a sample and reference holder, heat resistor heat sink and heater. The heat from the heater is supplied to the sample and reference through heat sink and heat resistor. The heat flow is proportional to the heat difference of heat sink and heat holders. Heat sink has enough heat capacity

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_24

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Sample

Heat sink Heater

C.P.U

Heat driven Thermo couple

Temp. control

Heat resistor

Amplifier

Temp. recording

Amplifier

Temp diff. that flux recording

Thermo couple

Figure 24.1 Block diagram of a heat flux differential scanning calorimeter. compared to the sample. In a case where the sample undergoes endothermic or exothermic process such as transition or a reaction, this process is compensated by heat sink. Thus the temperature difference between the sample and the reference is kept constant. The difference in the amount of heat supplied to the sample and reference is proportional to the difference in temperature of the two holders. By calibrating the standard material, quantitative measurement of unknown sample is possible. There are two types of DSC systems which are commonly used, i.e., heat flux DSC and power compensation DSC. A simple version of a single heat flux DSC is given below.

Figure 24.2 Single heat flux source in DSC.

Principles of Differential Scanning Calorimetry

 389

In heat flux DSC, the sample and reference are connected by a low resistance heat flow path (a metal disc). The assembly is enclosed in a single furnace. Enthalpy or heat capacity changes in the sample cause a difference in its temperature relative to the reference; the resulting heat flow is small because the sample and reference are in good thermal contact. The temperature difference is recorded and related to enthalpy change in the sample using calibration experiments. In power compensation DSC the temperatures of the sample and reference are controlled independently using separate but identical furnaces. The temperatures of sample and reference are made identical by varying the power input to the two furnaces; the energy required to do this is a measure of the enthalpy or heat capacity changes in the sample relative to the reference.

24.3

Methodology

In a scanning calorimeter, one measures the specific heat of a system as a function of temperature. For a solution, the apparent specific heat of the solute, C2 is given by the equation. C2 = C1 +

1 (C − C1 ) w2

(24.1)

where C1 = specific heat of solvent, C = specific heat of solution and w2 = weight fraction of the solute. In DSC, (C − C1 ) is directly measured. As an example, the DSC curve obtained in the reversible thermal denaturation of a globular protein is shown below. The apparent specific heat of the native form of the protein increases while that of the denatured form is independent of temperature. The integral of the Cex (where Cex = excess apparent specific heat is the amount by which the apparent specific heat during a transition involving the solute exceeds the base line specific heat) over the temperature gives the specific calorimetric enthalpy, Δhcal for the transition. The interpretation of DSC data is based on the thermodynamic relation 

∂ ln K ∂T



= P

ΔH RT 2

where ΔH denotes the van’t Hoff enthalpy.

(24.2)

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Biophysical Chemistry

Figure 24.3 Curve trace obtained with the solution of Arg96 → His mutant of the lysozymes of T4 phage.

24.4

Illustrative Application of DSC

Thermal Denaturation of Proteins Calorimetric analysis of thermal unfolding of proteins by DSC provides information concerning the fundamental nature of this process. The forces involved in the stabilization of native structures of proteins can be elucidated as well. (a) Two state denaturations with self dissociation or association: DSC was employed to study the dissociative unfolding of the protein streptomyces subtilisin inhibitor (SSI). At ordinary temperatures, this protein is dimeric. Its denaturation curves are slightly asymmetric and the values of tm (the temperature at which Cex reaches its maximum value Cex,max ) increase with increasing protein concentration. Analysis of DSC curves showed that the denaturation process follows the scheme A2 ↔ 2B. The native protein remains dimer upto 80◦ C. The core protein obtained by partial proteolysis from lac repressor of E.coli is tetrameric at ordinary temperatures. DSC data of the thermal denaturation of this protein, which is irreversible, gives three values of ΔHV H according to the methods given as follows: (i) curve fitting to the model A4 ↔ 4B gave ΔHvan t Hoff = 520 kcal mol−1 , (ii) calculation according to the equation 2 ΔHV H = ART1/2

Cex,1/2 Δhcal

(24.3)

where Δhcal = calorimetric specific enthalpy, T1/2 = t1/2 + 273.15 where t1/2 is the temperature in deg C at which the process is half

Principles of Differential Scanning Calorimetry

 391

completed, Cex,1/2 = excess specific heat at half life t1/2 , R denotes the universal gas constant and A = 4.00 gave ΔHV H = 585 kcal mol−1 and (iii) slope of van’t Hoff plot of ln ( L0 ) (where L0 is the total protein concentration) vs. 1/T1/2 with n = 4 in the equation ln K1/2 = constant t + (n − 1) ln( A0 ) + m ln( L0 ) = gave ΔHV H = 498 kcal mol−1 .

−ΔHV H + constant RT1/2 (24.4)

(b) Two-state denaturations with ligand dissociation: DSC was applied to protein/ligand association reactions involved in the binding of LArabinose and D-galactose to the Arabinose binding protein (ABP) of E.coli. The thermal denaturation of ABP is reversible both in the absence and presence of ligands. van’t Hoff plot of ln( L0 ) vs. 1/Tm ( L0 = Total ligand concentration) yielded the following values for both ligands: ΔHV H = 137 kcal mol−1 at 58◦ C and ΔHV H = 161 kcal mol−1 at 65◦ C. The value for ΔHcal in presence of glucose at 59◦ C was estimated as 200.7 kcal mol−1 . (c) Multistate denaturations: The thermal denaturation of taka-amylase A gives a DSC curve with a single asymmetric peak with ΔHV H /ΔHcal ≈ 0.17 indicating a multistate transition. This protein contains a single tightly bound Ca2+ ion in the absence of any added Ca2+ , its denaturation curves can be accurately resolved into the sum of two in dependent two state transitions including the dissociation of Ca2+ in the last step. Aspartyl transcarboxylase is a complex protein of six catalytic polypeptide chains and six regulatory chains per molecule of 310 × 104 a.m.u. The C6 r6 molecule can be separated into two catalytic subunits, C3 and three regulatory subunits, r2 . A DSC study of these units showed that the denaturation curve of C3 can be resolved into three two state components and that of r2 into two components. C6 r6 in composed of two separate peaks and was resolved into five two state components. The tm values for denaturation of r2 and C3 were found to be independent of concentration indicating that the poly peptide chains do not separate on denaturation. The tm for denaturation of C6 r6 increase with increasing concentrations showing that dissociation into C3 and r2 subunits accompanies denaturation. (d) Denaturation of mutant proteins: DSC measurements of Arg 96 → His mutant of lysosome of T4 bacteriophage indicated that the unfolding of this protein is reversible and the following results were obtained.

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Type of mutant Wild type Arg96-His

ΔH/kCal mol−1 5.97 + 2.35t −8.58 + 2.66t

T1/2 2.11 + 17.29t◦ (C) −19.84 + 21.31t◦ (C)

A DSC study of glutamine and serine replacements of Glu49 in the α-submit of tryptophane synthase showed decreases in the tm at pH = 7.0 and increases at pH = 9.3. Both proteins showed enthalpy of denaturation between 81 heal mol−1 at 45◦ C and 124 kCal mol−1 at 60◦ C. The denaturation curve for the α repressor of E.coli showed two separate peaks. The one at lower temperature is due to denaturation of the N-terminal portion of the molecule and the other at higher temperature is due to denaturations of the C-terminal portion. Seven mutant forms of the tail spike protein of phage P22 were studied by DSC. In this case, a maximum destabilization energy of +17.0 kCal mol−1 was determined. The Asp27 → Asn and AsP—Ser mutant forms of dihydrofolate reductase were studied using DSC. In each case, tm raises by 3.8◦ and 5.2◦ C respectively. The denaturation enthalpy increases by 15 kcal mol−1 in the former case and by 7 kcal mol−1 in the latter case. (e) Conformational transitions of nucleotides: The helix-coil transitions of oligo and polynucleotides have been widely studied by means of DSC. The enthalpy increase for this transition is about 8–10 kcal (mole of base pairs)−1 . DSC studies of the unfolding of a tRNA and the melting of several tRNA’s were made. DSC has been applied to the study of DNA ligand interactions also. The thermodynamics of transition from the right handed helical B form to the Z form has been determined for poly (dG-m5 dc) and for poly (dGdC). The B-helix-to-coil and Z-helixto-coil transitions of these polynucleotides occur at 125◦ C depending on experimental conditions. (f) Phase transitions of phospholipids and phospholipid mixtures: DSC has been employed to obtain thermodynamic data relating to phospholipid bilayers because they serve as simple models for complex biological membranes and also because they are interesting quasi two dimensional systems. Phospholipid phase transitions give two or more closely spaced DSC peaks. These transitions relate to gel-to-liquid crystal type. The addition of several compounds to a phospholipid bilayer lowers the phase transition temperature and also broadens the transitions. The cooperativity of a transition of a pure liquid is indicated by its sharpness and

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may be expressed in terms of the size of lipid molecule of the cooperative unit by the ratio ΔHV H ΔHcal where ΔHcal is the enthalpy of transition per mole of lipid (in calories). DSC has been employed to study phase transitions in twenty chemically related glycosphings lipids and also their mixtures with dipalmitoyl-phosphatidyl cholin and myelin basic protein. (g) Conformational transitions of polysaccharides: A widely studied process by DSC involving polysaccharides is the double helix-coil transition of iota- and kappa-carrageenan. The order-disorder transition of xanthan poly electrolyte, which is composed of a cellulosic backbone with trisaccharide side chains carrying carboxyl groups (some of which are on pyruvate residues condensed at the carboxyl group), has been investigated by DSC. It has been observed that the triple helical polysaccharide schizophyllan undergoes a sharp transition at 6◦ C and in studies in water DMSO mixtures this polysaccharide showed two transitions. The transition at the higher temperature is attributed to a triple helix-single coil change in conformation. (h) Applications to more complex systems: DSC was applied to the study of transitions involving plasma membrane Acholeplasma laidlawii. Two endothermic peaks were observed. The one at lower temperature was reversible and is due to phase transition of gel phase lipids while the higher temperature peak was attributed to the denaturation of membrane proteins. DSC was also employed in the study of human erythrocyte membrane. Four transitions were observed, two of which were attributed to simple unfolding transitions of proteins. The heat produced by suspension of murine macrophages was investigated by employing DSC. The total heat evolved in the range 10 − 37◦ C varied from 300 to 2500 × 10−12 Cal per cell in the scan range 1 K min−1 depending on cell density and glucose concentration. It was shown that 24% heat liberated is due to the conversion of glucose to lactic acid and an additional 14–41% is due to hydrolysis of ATP. The DSC curve observed on heating a suspension of photosystem-II in the temperature range 30–70◦ C was resolved into 5 two-state systems. The peak at 48.2◦ C was attributed to functional denaturation of oxygen

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evolving complex. The peak is very sharp with ΔHV H = 3 × 106 ΔHcal The thermally induced reversible polymerization of the coat protein of tobacco mosaic virus has also been studied by using DSC.

Questions (1) In a study of the denaturation of the protein SSI by differential scanning calorimetry, the excess specific heat (Cex1 , 12 ) of the calorimeter used is 0.380, the constant A = 4.00, Δhcal = calorimetric specific enthalpy = 0.8 cal and T1/2 = temperature in deg K at which denaturation is half complete = 383.1. Calculate the enthalpy change for the denaturation process. Solution: Cex , 1/2 Δhcal 4.00 × 0.002 × (383.1)2 × 0.380 = 0.8 = 558 k cal mol−1

2 ΔH = ART1/2

(2) Draw a neat sketch of a differential scanning calorimeter and describe the components. (3) Derive the relation



∂ ln K ∂T



= P

ΔH ◦ RT 2

(4) Discuss the applications of differential scanning calorimetry in understanding the denaturation of proteins. (5) Enumerate the use of differential scanning calorimeter in understanding (i) conformational transitions in nucleotides and phase transitions of phospholipids.

25

Applications of Gel Filtration Technique in the Separation of Biomolecules 25.1

Introduction

Gel filtration (also known as size exclusion chromatography, SEC) separates molecules based on differences in size as they pass through a gel filtration medium packed in a column. In this method, the molecules do not bind to the chromatography medium. As a result, one can vary the conditions to suit the type of sample or the requirements for further purification, analysis or storage without altering separation. Gel filtration is suitable for biomolecules that may be sensitive to a variety of conditions such as change in pH, concentration of metal ions or cofactors. It is used to separate proteins, peptides and oligonucleotides. It is widely used for molecular size analysis, separation of components of a mixture.

25.2

Methodology of Gel Filtration

At first the gel filtration medium is packed into a column to form a packed bed. The medium is a porous matrix of particles which are physically stable and chemically inert. The bed is equilibrated with a buffer which fills the pores of the matrix and the space between the particles. The liquid inside the pores is known as the stationary phase and is in equilibrium

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with the liquid outside the particles i.e., the mobile phase. The following figure illustrates the separation process of gel filtration. (A)

(B)

(C)

Figure 25.1 Schematic picture of (A) a bead with enlargement, (B) sample molecules diffusing into bead and (C) separation process. The two steps involved are as follows: (1) Sample is applied on the column, and (2) The smallest molecule is more delayed than the largest molecule. The largest molecule is eluted first from the column. Band broadening causes some dilution of the protein zones during chromatographic separations.

25.3

Principle of Gel Filtration

As shown in Figure 25.2, the separation of molecules is based on the basis of their molecular sizes. The molecular sieve properties of the porous resins are made use of. Large molecules elute first because they are completely excluded from pores, interstitial spaces and resin particles. The smaller molecules get distributed between the mobile phase inside and outside the beads and pass down the column at a slower rate. Thus they are eluted last. The distribution of a molecule in a column of cross linked beads is determined by the total volume of mobile phase inside and outside the beads.

Gel Filtration Media A polysaccharide, dextran, is cross linked to give small beads of a hydrophilic and insoluble in nature material. When they are placed in water, they swell and form an insoluble gel. It is known as Sephadex

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Figure 25.2 Schematic diagram of elution. Commercially. Sephadex has the property to exclude solutes of large molecular size but it is accessible for diffusion to molecules of small dimension. There are other types of filtration media such as polyacrylamide (BiogelPTM ), dextran polyacrylamide (SephacrylTM ) and agarose (sepharoseTM and Bio-gelATM ). They are available in a large range of pore sizes for separation of macromolecules of different sizes. A gel with a smaller range of pore sizes gives higher resolution while a gel with a wider range gives a lower resolution than the largest molecule. The largest molecule is eluted first from the column. Band broadening causes some dilution of the protein zones during chromatographic separation.

Elution Volume Relationships A fraction collector is attached to the system to collect fractions of elution and a detector connected to the collector analyses the separated fractions. The distribution coefficient (KX ) of an analyte may be expressed as KX =

(Ve − V0 ) (Vt − V0 )

(25.1)

where Ve = volume of buffer that elutes from the column before a particular peak appears in the elution profile; Vt = total column volume (or bed volume), V0 = volume of the space between gel particles (or void volume). Thus (Vt − V0 ) = volume occupied by gel including gel matrix (Vgel ).

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The distribution coefficient, KX of a molecule between the inner and outer mobile phase is a function of molecular size. If a molecule is sufficiently large to be completely excluded from the mobile phase between the beads then K = 0. On the other hand, if a molecule is very small that it accesses the inner most mobile phase deep in the beads, KX = 1. For in between situations, KX will vary between 0 and 1. The variation of KX between 0 and 1, enables separation of the molecules present in a mixture within a narrow molecular range.

25.4

Applications

Physical parameter

(1) A typical elution pattern of dialysis (on Sephadex G-25) to separate hemoglobin from the salt NaCl is shown in Figure 25.3: Haemoglobin

NaCl

Elution volume

Figure 25.3 Typical elution pattern of dialysis (on Sephadex G25). (2) Another example involves the separation of RNAase from a protease in pancreatic extract using Sephadex G-75 column. The elution pattern is depicted in Figure 25.4.

Enzyme activity

Protease RNAase

Elution volume

Figure 25.4 Separation of RNAase from protease in pancreatic extract using Sephadex G-75 column. (3) The distribution coefficient (KX ) varies with molecular weight for different proteins. Gel filtration method can be used for determination of

Applications of Gel Filtration Technique in the Separation of Biomolecules 

399

molecular weights. Depending upon the possible molecular weight, a suitable gel such as Sephadex G-100 (or G-200) is selected and a column is prepared with this gel. A calibration curve is obtained with pure proteins of known molecular weight by determining their elution volumes. Next, the protein whose molecular weight is under consideration is placed on the same column and its elution volume determined under the same conditions used as in calibration experiments. The molar mass of the unknown is read off from the calibration curve. Sometimes, instead of elution volume, K D is used. The K D -molecular weight data is given above. (4) The gel filtration of hemoglobin: A solution of methemoglobin and ferricyanide is applied to Sephadex column. Separation of brown hemoglobin is first observed. The methemoglobin then overtakes a previously added band of iron (II) salt and is reduced by it to purple haemoglobin. When the protein emerges from the reducing agent, it enters buffer saturated by air and becomes oxygenated to form scarlet oxyhemoglobin. Thus three distinct processes occur and a small tube of 8 cm is adequate for completing the separation. (5) Monoclonal antibodies (MAB) separation: An important step in MAB production and characterization is the analysis of aggregates and determination of purity of monomeric fraction. The separation of a monoclonal mouse lgG from its aggregates has been studied using Superdex 200 Increase 10/300 GL. Buffer used 0.1 M sodium phosphate solution. Buffer used = 100 × 10−3 Na3 PO4

Questions (1) Explain the principle of gel filtration technique. Discuss its applications in the separation of (i) haemoglobin and (ii) monoclonal antibodies. (2) Explain the principle of gel filtration technique with special reference to the media employed in this method.

26

Gel Electrophoresis and its Applications to Biochemical Analysis 26.1

Introduction

The term ‘Electrophoresis’ denotes the separation of charged molecules under the influence of an applied electric field. In particular by exploiting the differences in ionic mobilities, separation of species can be accomplished in a facile manner, for various biochemical contexts. Apart from mobilities, several other factors too play a significant role viz. charge to mass ratio, size and shape of molecules, viscosity and porosity of the matrix though which the species migrate.

Principle of the Technique It is well known that a mixture of charged molecules when placed in an electrical field of strength E (V/cm), migrates to the oppositely charged electrode surface. However, their ionic mobilities are not identical, dictated by several factors mentioned above, move at different rates depending upon the physical characteristics of the molecule.

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The velocity of v, of a charged molecule in an electric field may be expressed as q v = E× (26.1) f where q denotes the net charge on the species and f is the frictional coefficient which depends on mass, shape and compactness of the migrating particles, porosity of the matrix and viscosity of the medium. A simple method of estimating the frictional coefficient is to employ Stokes-Einstein equation approximately valid for dilute solutions and spherical particles. From the above equation, it can be inferred easily that the movement of the molecules will be more rapid if both the net charge and the applied field can be made large. On the other hand, the frictional coefficient will retard the velocity. Hydrated gels provide significant advantages over in gel electrophoresis since: (i) these can be used in horizontal/vertical columns in the form of slab gels or in tubes/capillaries and (ii) these are chemically inert and hence do not possess significant chemical interaction with biomolecules. Consequently, the separation essentially exploits physical rather than chemical differences between the components of the system.

26.2

Nature of Gels Commonly Employed

The matrix refers to the gel employed in electrophoresis and functions as a molecular sieve in the separation process based on their size. Among many gels, the following deserve mention (Table 26.1). Among several polysaccharide gel matrices, agarose is a typical one. The polymer agarose consists of repeating disaccharide units (known as agarobioses) and is extensively used in the separation of DNA constituents. The molar masses of DNA can be accurately estimated, from the mobility in agarose gels. In view of the facile polymerization of acrylamide, a stronger gel matrix results in this case and is useful in the separation of proteins as well as nucleic acids. In order to obtain a cross linked gel with tunable porosity, satisfactory mechanical strength and chemical inertness, it is customary to Table 26.1 Illustrative examples of various gels. Gel type Main uses Starch Isolation of proteins Agarose Proteins of large dimensions, nucleic acids, nucleoproteins Acrylamide Nucleic acids and proteins

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add optimal quantity of cross linked acrylamide with the help of N-N , methylene bisacrylamide. These gels are particularly suitable in order to accomplish high resolution separation of DNA and proteins, with varying ratios of molar masses. An important protocol in gel electrophoresis is the requiem for ‘staining’ the molecules separated in the gel matrix so as to view their locations. Several staining agents customarily used are as follows: (i) Amido black, (ii) Ponceau red, (iii) Coomassie blue, (iv) Nile red, and (v) Fluorosamine.

26.3

Experimental Arrangement

A sketch of the set up used in gel electrophoresis experiments is shown below: −

Sample wells

⊕

Figure 26.1 Experimental set-up of gel electrophoresis. The horizontal electrophoresis apparatus consists of two platinum electrodes, one at each terminal. The unit contains removable gel casting trays with rubber end caps for sealing off the ends of the tray during gel-casting. After the agarose gel is cast, the filled tray is immersed in an appropriate buffer-filled chamber for loading the sample under investigation. It has been demonstrated that for best resolution of fragments, a voltage of 5 volts per cm serves as the optimal value. Buffers used in these studies, especially for electrophoresis of duplex DNA, are TAE (Tris-acetate-EDTA) and TBE (Tris-borate-EDTA). They maintain the pH apart from providing satisfactory ionic conductivities.

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Types of Gel Electrophoresis There are two types of gel electrophoresis viz. (i) one-dimensional and (ii) two-dimensional. (i) The one dimensional gel electrophoresis may be further classified into three parts: (a) SDS-PAGE, (b) Native-PAGE, (c) IEF (isoelectric focusing). Several types of PAGE are known and they yield diverse information about proteins. SDS (Sodium dodecyl sulfate)—PAGE (Polyacrylamide gel electrophoresis) is capable of separating proteins based on their mass. The so-called Native—PAGE separates proteins using their mass: charge ratios. (ii) Two-dimensional PAGE (2D-PAGE) separates proteins from the information on the isoelectric points (IEF) in the first dimension and subsequently by mass in the second dimension. The samples are often treated with SDS-an anionic detergent. This denatures the protein by breaking the disulfide bonds and giving rise to negative charges to each protein in direct proportionality to its mass.

26.4

Applications of Gel Electrophoresis

Among diverse applications of gel electrophoresis, a few are described briefly below: (1) Agarose gel electrophoresis is widely used for the mechanistic analysis of the DNA cleavage of small molecules and for analysing the binding modes of the molecules with supercoiled DNA. It may be reiterated that an adequate comprehension of DNA cleavage is essential in drug designing. Natural plasmid DNA consists of (i) supercoiled (SC) pUC19 DNA; (ii) nicked circular (NC) and (iii) linear conformations (LC). It is possible to employ agarose gel electrophoresis for quantifying their relative efficiencies. By intercalating small molecules to plasmid DNA, the SC DNA form cleaves, thereby decreasing rate of mobilities. The DNA cleavage occurs either by hydrolytic or oxidative pathways. Hydrolytic cleavage agents do not require co-reactants and are thus more suitable in the designing of drugs. Consequently, they are more beneficial than oxidative cleavage agents.

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 405

Several metallonucleases have been investigated as regards their DNA cleavage properties. In particular, copper—amino acid/dipeptides containing complexes have been systematically studied in this context. Upon electrophoresis of SC DNA, rapid migration was observed for the intact SCDNA. If scission occurs essentially on only one strand, the SC form relaxes to yield a slower moving nicked circular (NC) form. As an illustrative example, the conversion of SC DNA to NC form has been studied at several concentrations of [Cu(II)(hist)(trp)]+ and [Cu(II)(hist)(try)] and is schematically represented below: H2 N

O

O

N H2

R

oled erco Sup NA D 37°C 7.2, pH =

Cu N N H

%NC 7 12 21 32 45 56 1 2 3 4 5 6 NC SC (a)

[Cu(II)(hist)(tyr)trp]+

%NC 10 21 35 42 49 53 1 2 3 4 5 6 NC SC

OH R= N H

(b)

Figure 26.2 Agarose gel electrophoresis pattern for cleavage of supercoiled PUC DNA. In some cases, kinetic data i.e., rate of cleavage of DNA as a function of time can also be deduced. (2) DNA analysis: The identification of DNA and DNA fragments constitutes an important application of Agarose gel or acrylamide gel electrophoresis. Upon applying optimal potential gradients, larger and smaller fragments of DNA begin to separate since they are affected differently on account of friction from the medium chosen. When the applied electric field is stopped, the fragments get frozen and can then be examined at high resolutions. (3) Molecular cloning: This term refers to the construction of recombinant DNA molecules which are integrated into diverse organisms so as to create genetic modifications. The outcome of these modifications is subtle. Applications of molecular cloning include adding fluorescent protein fusions to existing cellular proteins for identifying their locations in cells and creating new genetic circuits to carry out specific functions

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Biophysical Chemistry

such as breaking-down of toxins. Gel electrophoresis is a crucial step in quality control and production of DNA fragments in molecular cloning. It can analyse fragments arising from the polymerase chain reaction (PCR) to ensure that they are of correct dimensions. (4) Genetic finger printing: The identification of individuals based on their genetic codes is often known as genetic finger printing. In combination with with PCR, agarose gel electrophoresis remains as a powerful technique for genetic finger printing. The human genome is composed of several regions of short repeats, whose number varies uniquely among individuals. By targeting these regions with specific PCR primers, a profile of band on an electrophoresis gel corresponding to these regions gets created which is unique to an individual. This technique, designated as DNA finger printing is used in forensic analysis for criminal investigations, genealogy and parentage testing. (5) Diagnostic applications: Gel electrophoresis is useful for the screening of genetic disorders and for inferring abnormal proteins. DNA can be extracted not only from patients but also from embryos. It is then subjected to PCR and agarose gel electrolysis for qualitative analysis of genes or genetic abnormalities. In order to ascertain correct medical treatments, this method is also applied to some proteins to analyse the composition of blood.

Functioning of SDS-PAGE In this method, the proteins are dissolved in SDS and then subjected to electrophoresis. SDS binds to protein in a ratio of one SDS molecule to two amino acids. This protocol effectively masks the charge on the protein so that all proteins become uniformly negatively charged. The denatured proteins are then applied to one end of a layer of poly acrylamide gel which is submerged in a buffer. When an electric current is applied across the gel, the −vely charged proteins migrate to the +ve pole of the electrode surface. Since proteins of smaller lengths fit more easily in the pores of the chosen gel, they move faster, while the larger ones move slowly. On account of this difference in rate of migration (caused by size), smaller proteins move farther down the gel, while the larger ones stay closer to the origin. After a particular time duration, proteins become separated according to their sizes.

 407

Gel Electrophoresis and its Applications to Biochemical Analysis

26.5

Isoelectric Focusing (IEF)

This technique separates molecules by exploiting their electric charge differences. Here, proteins are separated by electrophoresis in a pH gradient based on their corresponding isoelectric prints (pI). A pH gradient gets generated in the gel when an electric potential is applied across the gel. At all values of pH other than pI, the proteins move to one of the electrodes dictated by the charges they possess. At the value of pI, protein molecules do not carry any net charge, and hence they accumulate or focus into a sharp band. (A) Low pH +

Figure 26.3 differences.

+ +

± +

− ±

Low pH

−

±

− ± High − pH − +

+

(B)

High pH

−

Scheme depicting the separation of molecules by charge

Questions (1) What is the principle of gel electrophoresis? Name the various gels used in this method and specify their uses. (2) What are the different types of gel electrophoresis and describe some applications of this technique. (3) Explain the terms: (i) DNA analysis (ii) Molecular cloning and (iii) Genetic finger printing.

27

Uses of Analytical Ultracentrifugation Methods in the Analysis of Biomolecules 27.1

Introduction

The analytical ultra centrifuge method is a versatile technique for the determination of the molecular weight and the hydrodynamic and thermodynamic properties of proteins or other macromolecules. Svedberg and Pedersen (1920) were the first workers to use ultracentrifuge for the study of macromolecules. Further rapid growth in this area became possible with advances in the field of molecular biology relating to manipulation of structures of DNA and proteins.

27.2

Details of the Apparatus

In an analytical ultracentrifuge, a rotor must spin at an accurately controlled speed and temperature and also it must be possible to record the concentration distribution of the sample at given times. High angular velocities are necessary to achieve rapid sedimentation and minimize diffusion. Velocities of the order of 60,000 rpm are employed. To reduce frictional heating and minimize aerodynamic turbulence, the rotor is spun in an evacuated chamber.

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A schematic sketch of ultracentrifuge results is depicted below:

Absorbance

Solvent meniscus Sample meniscus

Boundary region

Plateau

0 Top

Bottom

Sample reference

Figure 27.1 Schematic depiction of ultracentrifuge pattern. The sample solution is placed in one sector and a sample of the solvent (in dialysis equilibrium with the sample) is placed in the reference sector. The reference sector is filled slightly more than the sample sector so that the reference meniscus does not obscure the sample profile. In ultracentrifuge cells, the sample is placed within a sector shaped cavity sandwiched between two thick windows of optical grade quartz. The cavity is produced within a centerpiece of aluminum alloy or reinforced epoxy. Sector shaped sample compartments are essential in velocity work since sedimenting particles move along radial lines. Double sector cells allow the user to take account of absorbing components in the solvent and to correct for the redistribution of solvent components especially at high “g” values. A sample of the solution is placed in one sector and a sample of the solvent is placed in the second sector (see Fig. 27.1). The optical system measures the difference between the sample absorbance and reference sector solution absorbance. Double sector cells also facilitate measurements of differences in sedimentation coefficient and of diffusion coefficients.

27.3

Detection Method and Data Collection

The data is collected as a set of concentration measurements at different radial positions at a given time. Usually, the measurement of absorbance of the sample at a given wavelength at fixed position of the cell is followed.

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 411

Refractrometric methods are also used for obtaining concentration distributions as the sample solution has a greater refractive index than the pure solvent. Two different optical systems are employed for this purpose: (i) Schlieren system, and (ii) Rayleigh interference optic system. In the Schlieren system, light passing through a region in the cell will be deviated radically where the concentration (hence the refractive index) is changing. This optical system converts the radial deviation of light into a vertical displacement of an image at the camera. The displacement is proportional to the concentration gradient. The Schlieren image is thus a measure of the concentration gradient, dc/dr, as a function of radial distance. The change in concentration relative to that at some specific point in the cell can be determined at any other point by integration of the Schlieren profile.

27.4

Rayleigh Interference Optics

This technique depends on the fact that the velocity of light passing through a region of higher refractive index decreases. Monochromatic light passes through two fine parallel slits one below each sector of a double sector cell containing, respectively, a sample of a solution and a sample of solvent. Light waves emerging from the entrance slits and passing through the two sectors undergo interference to yield a band of alternating light and dark fringes. Modern absorption optical systems have increased sensitivity and wide wavelength range. It is possible to obtain absolute concentration at any point. The increase means that samples may be examined at concentrations too dilute for Schlieren or interference optics. For example, measurements below 230 nm allow examination of concentrations 20 times more dilute than can be studied with interference optics.

27.5

Applications

Molecular Weight Determination To determine the molecular weight, several quantities are required: (i) data of concentration distribution, (ii) density of solvent, (iii) partial specific volume of the solute (or more specifically, the specific density increment). Further to consider the effects of different solvents and temperatures on sedimentation behavior, (iv) the viscosity of the solvent and its dependence

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Biophysical Chemistry

on temperature are also required. The partial specific volumes of macromolecular solutes may be calculated from knowledge of their composition and the partial specific volumes of component residues. Alternatively, it is possible to estimate both M and V¯ from the data obtained using sedimentation equilibrium experiments. For some classes of compounds, the variation in V¯ with composition is not large and an average value of V¯ for Polysaccharides (0.61) not large and an average value of V¯ for Polysaccharides (0.61), RNA (0.53) and DNA (0.55) have been obtained. Two additional basic experiments are performed with the ultracentrifuge i.e., sedimentation velocity and sedimentation equilibrium. In the sedimentation velocity experiment, a uniform solution placed in the cell is subjected to a high angular velocity to cause rapid sedimentations of the solute to the cell bottom. This results in a depletion of the solute near the meniscus and a sharp boundary is formed between the depleted region and the uniform concentration of the sedimentating solute. From these experiments, the sedimentation coefficient S, which depends on the mass of the particles and the frictional coefficient can be obtained. Measurement of the rate of spreading boundary yields the diffusion coefficient, D, of the particles, which is given by RT D= (27.1) Nf where R denotes the universal gas constant, T being the absolute temperature, N represents the Avogadro number and f is the frictional coefficient which is linearly related to the viscosity of the medium and hydrodynamic radius of the compound. An illustrative diagram of the movement of the boundary in a sedimentation velocity experiment is given below.

Figure 27.2 Movement of the boundary in a sedimentation experiment.

Uses of Analytical Ultracentrifugation Methods

 413

Movement of the boundary in a sedimentation velocity experiment with a recombinant malaria antigen protein. As the boundary progresses down the cell, the concentration of the plateau region decreases from radial dilution and the boundary broadens from diffusion. The midpoint positions, rbud of the boundaries are shown. The ratio of the sedimentation to diffusion coefficient gives the molecular weight M. M=

S◦ RT ¯ ) D ◦ (1 − Vρ

(27.2)

where V¯ = partial specific volume, ρ= solvent density, S◦ = sedimentation coefficient and D ◦ = diffusion coefficient. Multiple boundaries indicate multiple sedimentating species.

27.6

Determination of Sedimentation Coefficient

If the sedimenting boundary is sharp and symmetrical, the rates of movement of solute particles in the plateau region may be considered close to the rate of movement of the mid points. The velocity of the boundary increases gradually with the movement of the boundary outwards. S≡

U dr /dt = int2 2 w r w r

(27.3)

Equation (27.3) can be written as ln(rint /rm ) = Sw2 t

(27.4)

where rm is the radial position of the meniscus. A plot of ln rint versus time (sec) yields a straight line whose slope is 2 Sw . This plot is for the recombinant dehydratase domain protein. From the slope of the graph, the sedimentation coefficient may be obtained. The sedimentation coefficient is dependent on the concentration, density of the solvent as well as its viscosity. Pure non-associating solutes show a decrease in the sedimentation coefficient with increase of concentration. The concentration dependence of “S” may be given as S=

S◦ (1 + k s C )

(27.5)

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1.88

ln r

1.84

1.80

20

40 60 Time (sec)

80

100

Figure 27.3 Estimation of the sedimentation coefficient. where S◦ = the limiting sedimentation coefficient, k s = concentration dependent coefficient, C = concentration of the substance. For globular proteins k s ≈ 5 mlgm−1 . In a sedimentation velocity experiment, the shape of the boundary is subjected to different influences, some of which are (i) Heterogeneity tending to spread out the boundary because different species move with different velocities. (ii) Diffusion also tends to spread the boundary. (iii) Concentration dependence of sedimentation coefficient also leads to self sharpening of boundaries. Most solutes display significant boundary spreading due to diffusion. When the concentration dependence of sedimentation coefficient is large, such as in the case of rod shaped virus particles or DNA, the boundary tends to sharpen itself overcoming the spreading due to diffusion. In a study of antigen-antibody interactions, it was shown that with absorption optics, a significant improvement to signal to noise ratio can be made by use of dc/dt values at fixed radial positions in determining the distribution of sedimentation coefficients.

27.7

Effect of Association on Sedimentation Coefficient

When a macromolecule undergoes association, the molecular weight of the particles increases and so “S” will increase with concentration. In the case of a monomer-dimer association, only one asymmetric boundary is produced. For monomer n, when n > 3, the boundary is bimodal i.e., two boundaries may be observed.

Uses of Analytical Ultracentrifugation Methods

 415

Figure 27.4 Concentration dependence of weight average “S” for DIP-α chymotrypsin.

27.8

Active Enzyme Sedimentation

Band sedimentation is suitable for the study of sedimentation behavior of enzyme activity in which a zone of enzyme solution is centrifuged through a supporting solution containing chromogenic substrate. Enzyme activity results in the migration of a moving boundary of product generated as the enzyme band migrates down the cell.

27.9

Estimation of Diffusion Coefficients

An accurate estimate of diffusion coefficient is needed for the determination of molecular weight from sedimentation coefficient. The analytical centrifuge can be used for measurement of diffusion coefficient. The best way is to use a boundary cell to create an initial sharp boundary the spread of which with time allows measurement of D. Under this condition, the solvent is layered over the solution as the rotor reaches about 4000–6000 rpm. Scans of the cell contents at different times allow measurement of the concentration in the plateau region (C p ) and the concentration gradient at the boundary (dc/dr )b by numerical differentiation of the data. If the boundary is symmetrical, its position will be that of maximum concentration gradient and will occur at the point C = C p /2. The diffusion coefficient is then given by 4π times the slope of the plot of [C p /(dc/dr )]2 against time in seconds. For human spectrin, by this method, D ≈ 3.91 × 10−5 cm2 sec−1 . Since the diffusion coefficient is concentration dependent, an extrapolated value of D ◦ , the limiting value as C → 0 must be determined.

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Biophysical Chemistry

Estimation of Molar Mass

In sedimentation equilibrium experiments, a small volume of uniform solution is centrifuged at low angular velocities. As solute begins to sediment towards cell bottom, its concentration at bottom increases and this process of diffusion opposes the process of sedimentation. Measurement of concentrations at different points leads to the determination of molar mass of the solute. When sedimentation equilibrium is reached, the diffusion flow balances sedimentation flow at every point in the cell. For a nonassociating solute. 2RT d ln C M= (27.6) ¯ )ω 2 × dr2 (1 − Vρ where M = molar mass of solute (in g/mol), ω = angular velocity of rotor and C = concentration of the solute (in gm/l) at a radial distance “r” from axis of rotation. A plot of log (concentration) vs. r2 for a solute at sedimentation equilibrium gives a linear graph whose slope is proportion to molar mass. This method is applicable for determination of molar masses of a wide range of solutes from a few hundreds to a few billions such as viruses. Sedimentation equilibrium in native solvents provides a method for the determination of molar masses of oligomeric structures. When several species with different molar masses are present, at sedimentation equilibrium, each will be distributed according to equation (27.6). Tangents to ln C vs. r2 plot at various points give weight average molecular weight, Mw , given by M C + M2 C2 ∑ Mi Ci = 1 1 (27.7) Mw = C1 + C2 ∑ Ci where C1 and C2 denote two concentrations of the solute respectively. Because of non-ideality due to size and charge of macromolecule, the apparent molecular weight is concentration-dependent and may be expressed as M Mapp = (27.8) 1 + B2 MC where B2 is referred to as the second virial coefficient. An extrapolated value for M from the plot of Mapp vs. C gives a molar mass of 5.15 × 105 for aspertin. For an association reaction 2A  A2 at sedimentation equilibrium,

√ 2 1 + 8KC √ Mw = M1 1 + 1 + 8KC

(27.9)

Uses of Analytical Ultracentrifugation Methods

 417

where Mw represents the weight average molar mass and K denotes the equilibrium constant, C being the concentration of the solute. From sedimentation equilibrium experiments, the apparent molar mass, MW,app was found to vary with concentration for the self association reaction of DNA binding protein. The variation is depicted in Figure 27.5.

Figure 27.5 Dependence of the apparent molar mass of DNA on concentration, studied at rotor velocity = 32000 rpm. The decrease at higher concentrations may be due to non-ideality.

27.11

Thermodynamic Parameters of Association Reactions

The temperature dependence of the equilibrium constant of an association reaction yields the enthalpy change from the relation. ln K =

ΔS◦ ΔH ◦ − R RT

(27.10)

A plot of ln K vs. 1/T gives ΔS◦ from the intercept and ΔH ◦ from the slope assuming that they are constant over the temperature range studied. The change in CP is also given by ΔCP =

∂ΔH ◦ T∂ΔS◦ = ∂T ∂T

(27.11)

The relative magnitudes of the thermodynamic parameters help in understanding the types of interaction.

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27.12

Biophysical Chemistry

Sedimentation in Biological Environments

The crowded molecular conditions encountered in Vi V0 in cells and biological fluids may have dramatic effects on macromolecular interactions. Non-ideal effects in concentrated solutions of macromolecules favor compact conformations and associated states. The pyruvate dehydrogenase complex of Azotobactor vinelandii exists in dilute solution as particles of sedimentation coefficient 17–20 S; in the presence of 3% polyethyleneglycol, these particles aggregate to form 50– 60 S clusters. The analytical ultracentrifuge is amenable to the study of crowding effects. These effects may be studied in model systems in which the macromolecule of interest is in the presence of a high concentration of an inert solute like sucrose, dextran or polyethylene glycol. Sedimentation equilibrium measurements allow investigation of both self interactions of macromolecules at high concentrations and the crowding effects of solutes like sucrose, or dextrin and conformation equilibrium as a model of crowding processes in Vi V0 . There is a method where by both sedimentation coefficient and molecular weight may be obtained from early stages of a sedimentation equilibrium experiment on the assumption that S is independent of C. This method gave satisfactory results for the molar masses of proteins.

27.13

Density Gradient Sedimentation Equilibrium

This method relies on the banding of a macromolecule within a gradient of density at a point 1 − vρ = 0. With this method it is possible to measure the buoyant density of a particle and to make analytical separations based on differences in buoyant density. In this experiment, a solution of the macromolecule in a proper concentration of density gradient solute (usually CrCl or Cs2 SO4 ) is centrifuged until equilibrium is attained. Redistribution of the density gradient solute leads to a density gradient from meniscus to the base and the macromolecules migrate to this position in the gradient. Knowledge of the initial concentration of the gradient material, its molar mass and v¯ and its activity coefficient as a function of concentration permits the calculation of equilibrium density and hence the buoyant density determination of the macromolecule. This technique has been used for the analysis of nucleic

Uses of Analytical Ultracentrifugation Methods

 419

acids. The method is sensitive to small density differences and has led to a greater understanding of nucleic acid replication. Differences in buoyant density may arise from differences in base composition of nucleic acids. Changes in buoyant density also arise from differences in solvation and ion binding. The buoyant densities of proteins are a function of pH values; deprotonation of carboxyl groups, for example, leads to increased binding of cs+ ions with an increase in buoyant density while deprotonation of lysine residues leads to loss of binding of chloride ions and hence to an increase in buoyant density. The width of the band of macromolecules is a function of molecular weight as well as the steepness of the local density gradient and the heterogeneity of the samples. For high density materials like DNA, the bands may be very narrow. Equilibrium density gradient sedimentation is useful in the examination of the assembly of complex macromolecular structures and also for heteromolecular associations e.g., protein-nucleic acid and protein-lipid interaction.

Questions (1) Define the term sedimentation coefficient. How is it determined? (2) Explain how the molar mass of a biomolecule is determined from sedimentation experiments. (3) Explain how sedimentation principle is useful in the analysis of cell and other biological fluids. (4) Serum alumin has a sedimentation coefficient of 4.5S (1S= 10−13 sec). ¯ as 0.73 ml Given the partial specific volume of the macro molecule (v) gm−1 and its frictional coefficient as 1.15, and density of water, ρ = 1.0 gm ml−1 , calculate its molar mass. (5) A protein has a molar mass of 1.5 × 105 Dalton (or amu) and its diffusion coefficient is 4.5 × 10−7 cm2 sec−1 . Given its partial specific volume as 0.73 cm3 gm−1 , calculate its sedimentation coefficient in the units of Svedberg (temperature may be taken as 293 K.)

28

Ion Exchange Chromatography and its Applications in the Separation of Biomolecules 28.1

Introduction

Ion Exchange Chromatography is one of the important adsorption techniques used in the separation of proteins, peptides, nucleic acids and related biopolymers. The separation of these charged molecules of different molecular sizes is based on the formation of ionic bonds between charged groups of biomolecules and an ion exchange support carrying the opposite charge. Biomolecules exhibit different degrees of interaction with charged chromatography media due to their varying charge properties. There are two mechanisms in this technique—(i) ion exchange due to competitive ionic binding and (ii) ion exclusion due to repulsion between similarly charged analyte ions and the ions fixed on the chromatographic support.

28.2

Mechanism of Ion Exchange

In ion exchange chromatography there are mobile and stationary phases. The mobile phase consists of an aqueous buffer system into which

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the mixture to be resolved is placed. The stationary phase consists of an inert organic matrix having ionisable groups (fixed ions) that carry a displaceable oppositely charged ion. The ions in equilibrium between the mobile and stationary phase may be cations or anions. The exchangeable matrix counter ions may be H+ , OH− , or singly charged alkali metal ions, or doubly charged alkaline earth metal ions (Ca2+ , Mg2+ ) and multiply charged anions like SO24− , PO34− , etc. Cations are separated on cation exchange resin column and anions on anion exchange resin column. Separation is based on the binding of analytes to positively or negatively charged groups on the stationary phase and which are in equilibrium with free counter ions in the mobile phase. This is depicted in Figure 28.1.

+++ − ++++ +++ ++

––– ⊕ –––– ––– ––

Negatively charged analyte (anion)

Positively charged analyte (cation)

(anion exchanger stationary phase particle)

(cation exchanger stationary phase particle)

Figure 28.1 Separation based on the binding of analytes to positively or negatively charged groups on the stationary phase. Ion exchange chromatography (I.E.C) involves separation of ionic and polar analytes using chromatographic supports having ionic functional groups that have charges opposite to that of analyte ions. The analyte ions and other similarly charged ions of the eluent compete with the oppositely charged ionic functional group on the surface of the stationary phase. In the case of exchanging ions (analytes and other ions in mobile phase) which are cations (C+ ) the exchange reaction may be written as SX CM

SXMC

(28.1)

In the above, the cation M+ of the eluent has replaced the analyte cation C+ bound to the anion X− which is fixed on the surface of the chromatographic support(s). In anion exchange chromatography, the exchanging ions are anions and the reaction S − X+ A− + B− ↔ S − X+ B− + A−

(28.2)

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The anion B− of the eluent has replaced the analyte A− ion bound to the X+ ion on the surface of the stationary phase. Molecules vary considerably in their charge properties and will exhibit different degrees of interaction with charged chromatography support depending upon the differences in their overall charge, charge density and surface charge distribution. The net surface charge of all molecules with ionisable groups is highly pH dependent.

28.3

Applications

This technique is often used for characterization of proteins in their native or active form and for purification. Proteins contain a variety of functionalities that can give rise to differences in charge. The overall charge is dependent on the pH of the Na⊕Cl– − SO3

⊕

−

⊕

SO3

− SO3 −

− SO3

SO3

⊕ ⊕

−

SO3 Na⊕ − ⊕ SO3 Na − SO3 −

−

⊕

⊕

Na

SO3 Na⊕

⊕

Cl

Cl

−

⊕

⊕

⊕ ⊕ Cl − ⊕ Cl −

−

SO3 Na⊕

⊕

Cl

⊕

−

⊕ Cl

⊕− Cl

⊕ Cl −

Figure 28.2 Separation mechanism in ion exchange.

Cl

−

−

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surrounding solution and this in turn will affect the ion exchange method that is used. The mobile phase must maintain a controlled pH throughout the course of separation and so aqueous buffers are used as eluents. Figure 28.2 shows the separation mechanism in ion-exchange. The technique of ion exchange is suitable for separating proteins with differing isoelectric points. It is equally valuable in separating charged iso forms of a single protein. In the important field of biopharmaceuticals, where proteins are manufactured through bioengineering and isolated from fermentation reactions, it is important to identify charged isoforms as these indicate a difference in primary structure of protein. A difference in primary structure could indicate a change in glycosylation or degradation path-way such as loss of C-terminal residues or amidation/deamidation. Ion exchange is used to separate and quantify charge variants during the development process and also for quality control and quality assurance during manufacture of biotherapeutics. With large molecules such as monoclonal antibodies (mAbs) it is also important to consider the size and structure of the molecule (mAbs are typically 150k Daltons), particularly as the chromatographic interaction will occur only with surface charges.

Figure 28.3 Schematic depiction of charged variants of monoclonal antibodies.

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Example 1: BioMAB column to identify C-terminal truncation on heavy chains

Figure 28.4 Two examples illustrating the use of BioMAB column for identification of c-terminal truncation on heavy chains. Example 2:

Figure 28.5 High resolution of a mixture of proteins with a wide range of isoelectric points.

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28.4

Biophysical Chemistry

Purification of Adenovirus

Ion exchange chromatography offers a powerful method for adenoviral fractionation because of its high capacity and resolution. I.E.C. exploits the charge that proteins carry on their surface. Their net charge varies with pH and the amino acids exposed in the protein surface. Adenoviral capsids are highly anionic in nature, making anionic exchange ideal for purifying them. Anion exchange resins carry positively charged groups such as diethylamino ethyl (DEAE) or quaternary amino ethyl, which bind anionic proteins which depends on pH. Elution may be accomplished by changing pH to eliminate ionic interaction with the protein.

28.5

Separation of Membrane Phospholipids

Biological membranes are anionic and hence are amenable to anionic exchange chromatography. Membrane phospholipids are either neutral or anionic (such as phosphatidic phosphalidic acid, phosphalidylserine, phosphatidylinositol, phosphatidylglycerol). All membranes have varying degrees of negative charge density and will bind to anion exchange columns. The higher the −ve charge density, the tighter the membrane binding. Membrane fractions are released from the column with either increasing retention time in the presence of a fixed anion (normally Cl− ions) concentration or by adding solutions of increased anion concentrations. The poorest binding membrane fraction has the lowest negative charge density and is the first to be released. The most negative membrane fraction is the tightest bound and is the last to be released.

28.6

Separation of Soyabean Proteins

Soyabean contains mainly 11S and 7S globulins. For separating them by High pressure ion exchange chromatography, the binary gradient approach was used with the mobile phase being a borate buffer of pH 9.0. The mixed proteins were eluted with the same buffer with the gradient starting with an isocratic step at zero percent B (buffer) for 2.5 min and 0 to 70% B in 14 minutes. The detection was UV spectroscopy at 254 nm. The stationary phase employed was an anion exchange perfusion column POROS HQ/10 packed with cross linked poly styrene divinyl benzene beads.

Ion Exchange Chromatography 

28.7

427

Choice of Column Media

In all chromatographic techniques, there is a range of columns to choose from. The first consideration is “should it be anion or cation exchange”. Also, there is a choice of strong or weak ion-exchange. In most circumstances, it is best to start with a strong ion exchange column. Weak ionexchangers can then be used to provide a difference in selectivity. The functional group in a strong cation exchange column is sulfonic acid resulting in the stationary phase being −vely charged. In an anion exchange column, however, the functional group is a quaternary amine group which is +vely charged. Strong ion exchange columns, therefore, have the widest operating range. Weak ion exchange sorbents (such as carboxylic acids in weak cation exchangers and amines in weak anion exchangers) are more strongly affected by the mobile phase conditions. The functionalities are not dissimilar to the charged groups on proteins and the degree of charge can be influenced by ionic strength as well as pH of the mobile phase. This can result in a change in resolution that may be subtly controlled and optimized through careful choice of operating conditions.

Questions (1) Discuss mechanistic aspects of ion exchange chromatography. (2) Explain the application of this method in (i) characterization of proteins (ii) purification of adenovirus. (3) Briefly explain the application of this method in (i) separation of membrane phospholipids and (ii) separation of soy bean proteins.

29

Surface Enhanced Raman Scattering and its Bioanalytical Applications 29.1

Introduction

The phenomenon of Raman scattering arises as a result of interaction of electromagnetic radiation with matter which results in the alteration of the frequency of the incident radiation. Raman spectroscopy has grown into a highly sensitive technique to probe the structural details of complex structures of biomolecules. However, its applications became restricted due to low scattering cross section achieved in this technique. Surface Enhanced Raman scattering (SERS) effect deals with the gigantic amplification of the weak Raman scattering intensity by molecules in the presence of a nanostructured metallic surface. The SERS enhancement factor may be defined as the ratio of Raman signals obtained from a given number of molecules in the presence of the metal nanostructure to that in the absence of the nanostructure and this ratio depends largely on the size and morphology of the nanostructures. Generally, this enhancement factor is around 106 .

29.2

Principle of SERS

Fleischmann and his co-workers at the university of Southampton carried out Raman spectroscopic study of the adsorbed molecules of a compound

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on a roughened metal electrode surface in 1974 and obtained high intensity scattering signals. They attributed the enhancement in Raman scattering intensity to an increase in the surface area of the electrode by the roughening method adopted. The following diagram explains the principle of Raman and Rayleigh scattering.

Figure 29.1 Electromagnetic and chemical enhancement mechanism. The technique is so sensitive that even a single molecule can be detected in addition to various electrochemical processes. The dominant contributor to SERS processes is the electromagnetic enhancement mechanism. The enhancement results from the amplification of the light by the excitation of localized surface plasmon resonances (LSPRS). This light concentration occurs preferentially in the crevices, gaps of the plasmonic materials which are generally coinage or noble metals (like Cu, Ag, Au) with nano scale features. Reproducible and robust structures that strongly enhance the electromagnetic field are preferred in SERS. Another mechanism involved in signal enhancement is chemical enhancement which involves charge transfer mechanism where the excitation wave length is resonant with the metal molecule charge transfer electronic states. The total SERS enhancement factor is the product of electromagnetic and chemical enhancement mechanisms. The enhancement factor may approach 1010 to 1011 for highly optimized surfaces.

Figure 29.2 SERS enhancement and enhancement mechanism.

Surface Enhanced Raman Scattering 

29.3

431

Experimental Aspects

The first parameter to be considered is the choice of enhancing substrate. Substrates range in structure from nano rods to three dimensional colloidal solutions with tunable Plasmon resonances and a range of enhancement factors. The largest enhancements are found in a few nanometers closest to the substrate surface. The second parameter to consider is a proper excitation source. It should enable efficient excitation of the Plasmon source. A laser tuned to the peak of Plasmon resonance for a substrate gives maximum enhancement of the signal. Following excitation of the Plasmon resonance and generation of SERS signal, the detection process is identical to normal Raman experiments. A long pass filter is used to reflect or absorb any Rayleigh scattering while allowing for the transmission of Raman signal and a spectrograph and detector are used to image Raman spectra across a wide spectral region. The third factor, one must consider, is the choice of plasmonic materials. The success of SERS is very much dependent on the interaction between absorbed molecules and the surface of plasmonic nanostructures which are often substrates of Au, Ag, or Cu. All the three metals have LSPRS (light supported Plasmon resonances) that cover most of visible and near infrared range where most Raman experiments are carried. The diagram below gives the wave length ranges of the three metals.

Cu Au Ag

200

300

400

500

600

700

800

900

1000 1100 1200

Wave length (nm)

Figure 29.3 Metals exhibiting SERS and their wave length ranges. In SERS molecules are attached to a nanostructure. SERS is not much of a “surface effect” but a “nanostructure effect”. Figure 29.4 shows another perspective of a SERS experiment. The nanostructure is an aggregate of spherical metal colloidal particles. In ’normal’ RS, the total Stokes Raman signal (P RS (vS )) is proportional to the Raman cross section σ R f ree , the excitation laser intensity I ( v L )

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Biophysical Chemistry

Figure 29.4 Schematic depiction of SERS for spherical aggregates. and the number of molecules in the chosen volume N. P RS (vS ) = N × σ R f ree × I ( v L )

(29.1)

To determine the SERS stokes power PSERS (vS ), equation (29.1) has to be modified to describe the specific effects of the metal nanostructures. Two effects need to be considered: (i) the scattering occurs in the enhanced local optical fields of the metallic nanostructures (i.e., the electromagnetic field enhancement), (ii) a molecule in contact with a metal nanostructure exhibits a “new Raman process” at a cross section larger than the Raman cross section of a free molecule (chemical or electronic enhancement) PSERS (vS ) = N  σ(Rads) | A(v L )|2 | A(vS )|2 I (v L )

(29.2)

In the equation (29.2), A(v L ) and A(vS ) represent enhancement facR is the tors for the Laser and for the Raman scattered field, σods increased cross section of the new Raman process of the adsorbed molecule and N  is the number of molecules involved in the SERS process which may be smaller than the number of molecules in the probed volume N. The concept of electromagnetic SERS enhancement is illustrated in the following diagram (Fig. 29.5). E M = E0 + ESp

(29.3)

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433

Molecule

d r

ε = ε ′ + iε ″ Metal sphere

Figure 29.5 Field of a point dipole.

( E = Field of a point dipole at the center of the sphere) ESp = r3

ε − ε0 1 E0 × ε + 2ε 0 (r + d )3

(29.4)

The metallic nanostructure is a small sphere with complex dielectric constant ε D in a surrounding medium of dielectric constant ε v . The diameter of the sphere 2r is small compared with the wave length of light. A molecule in the vicinity of the sphere is exposed to the field E M which is the superposition of the incoming field E0 and the field of a dipole ESp induced in the metal sphere. The field enhancement factor is the ratio of the field at the position of the molecule and the incoming field Field enhancement factor = A(v) =

EM (v) ε − ε0 = E0 (v) ε + 2ε 0



r (r + d )

3 (29.5)

A(v) is quite strong when the real part of ε(v) is equal to −2ε 0 . Further, for strong electromagnetic enhancement, the imaginary part of dielectric constant must be small. These conditions meet the resonant excitation of surface plasmons of the metal sphere.

29.4

Applications of SERS

SERS finds applications in biophysical/biochemical and biomedical fields. Many SERS experiments have been conducted on amino acids, peptides, purine and pyrimidine bases and also on large molecules like proteins, DNA and RNA. Intrinsically-colored molecules like chlorophyll and other pigments were also studied by SERS. SERS was also employed to detect and characterize biomolecules. It has also been used to monitor transport through membranes. SERS has been shown to discriminate between the movement of different molecules across a membrane. (1) Detection and identification of micro-organisms: SERS spectroscopy is a valuable tool for identifying bacteria based on their vibrational spectrum. This method has the advantage of needing only a small

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Biophysical Chemistry

amount of the material because of its high sensitivity. The SERS spectrum of the bacterium Escherichia coli on which colloidal silver particles were deposited, was first reported. SERS spectra of E.Coli K12 in contact with silver and gold colloidal particle have been obtained. (2) SERS study of neurotransmitters: The detection, identification and measurement of concentration changes of neurotransmitters like glutamate in central nervous system is very important in neurochemistry. SERS spectra of different neurotransmitters have been measured on silver colloidal particles in water. As an example, the SERS spectra of dopamine in silver colloidal solution is shown below:

Figure 29.6 SERS of dopamine in silver colloidal solution. Spectrum was obtained in 50 ms using 100 mW NIR excitation (NIR: near infrared SERS). Norepinephrine which has a similar structure to dopamine shows clear differences in SERS spectra. Such differences are due to small differences in the adsorption behavior of these molecules. SERS can thus show improved sensitivity and selectivity between structurally similar molecules. It is interesting to note that glutamate has been detected in microdialysis samples of rat brains in 0.4 − 0.5 × 10−6 M concentration. (3) Immunoassays employing SERS: (a) SERS has been first employed in an immunoassay of thyroid stimulating hormone (TSH). In this experiment, SERS-active substrate was silver film which was coated with anti TSH-bodies and then incubated with TSH. A second anti-TSH labelled with p-dimethyl amino benzene was added to bind the TSH. The SERS signal of the label was used to quantitatively determine TSH.

Surface Enhanced Raman Scattering 

435

(b) Detection of antigens by SERS: Colloidal gold particles supported on gold surface serve as SERS-active substrate. Antigens from solution are captured by immobilized antibodies on the gold surface. Gold nanoparticles labeled with specific antibodies and a specific reporter bind to the captured antigen. By immobilizing different antibodies and using specific reporters, the presence of different antigens can be detected by the characteristic SERS spectrum of the specific reporter molecules. In Figure 29.7, SERS spectra of three types reporter labeled immune gold colloids are shown along with the “empty” spectrum of commercial gold colloids conjugated with goat anti rat IgG.

Figure 29.7 (A) Scheme of an immuno assay system using two different SERS Labels. (B) SERS signatures of three types of reporter labeled immuno gold colloid (a) MBA/goat anti-rat IgG, (b) NT/goat antirat IgG, (c) TP/goat anti rabbit IgG and (d) goat anti rat IgG.

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Biophysical Chemistry

Antibodies immobilized on a solid substrate bind antigen (mouse IgG) which in turn binds to a second antibody labeled with peroxidase. When thee immuno complexes are reacted with o-phenylenediamine, azoaniline is formed. The reaction product is adsorbed on colloidal particles which results in a strong SERS spectrum of azoaniline. The signal strength is proportional to the concentration of antigen. The method of colloidal silver SERS has been successfully applied to detect and to quantify prostaglandin H synthase-1 and 2 (PGSH-1 and 2) in normal human hepatocytes and human hepatocellular carcinoma (HepGz) cells. (4) Probing of DNA and genes by SERS: Quantification of DNA and its fragments during polymerase chain reaction is important. A SERS based method for monitoring the concentration of double stranded (ds) DNA amplified by PCR was proposed. In this method, a DNA intercalator, 4’, 6-diamidino 2-phenylindole dihydrochloride (DAPI) was used to complex with ds-DNA. DAPI gives a strong SERS signal in colloidal silver solution. SERS labels offer some advantages for multiplex screening and simultaneous detection of different sequences in hybridization of DNA and its fragments. The use of SERS label in detecting the DNA hybridization is shown in Figure 29.7. SERS has been applied in hybridization experiments for detecting p(dA)18 . The oligonucleotides have been attached on a nitrocellulose surface. Nucleic acid fragments consisting of 18 deoxy ribonucleotide oligomers of Thymine, p(dT)18 , have been tagged with cresyl fast violet (CFV) as the SERS label. The hybridized oligomers were deposited on a SERS-active silver substrate. A strong SERS peak was observed from the labeled p(dT)18 . The effectiveness of the SERS gene technique has also been demonstrated in experiments dealing with human immunodeficiency virus (HIV) gag gene sequence. In experiments involving nucleic acids, structural changes such as denaturation were shown to occur when colloidal silver particles were used in SERS experiments. SERS on electrochemically etched (or roughened) silver surfaces was applied to detect a single mismatch in a ds-DNA fragment (290 base pairs) without the use of a label molecule. This observation agrees with SERS spectra measured for native and denatured DNA in which the appearance of strong adenine ring line confirmed denaturation. The target nucleic acids were applied in concentrations ranging from 10−5 to 10−8 mol lit−1 ) but the

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437

most interesting aspects of SERS on nucleic acids may be ascribed to the highly sensitive and single molecule capabilities of the method. The large non-resonant surface enhanced Raman cross sections provided by the strong field enhancement of colloidal clusters was exploited in single molecule experiments. The nucleotide bases show well distinguished SERS spectra. Thus, after cleaving single native nucleotides from a DNA or RNA strand into a medium of colloidal clusters detection and identification of single native nucleotides is quite possible because of the unique SERS spectra of their bases. The SERC spectra of nucleotide bases based on the idea of rapid sequencer base are shown in Figure 29.8.

Figure 29.8 Cleavage of single nucleotides and attachment to colloidal silver or gold clusters. (5) Studies inside living human cells using SERS: Colloidal particles of silver were incorporated inside the cells and SERS was applied to monitor intracellular distribution of drug in the whole cell and to study the anti-tumour drugs/nucleic acid complexes. These experiments show SERS spectra of the drug/DNA complexes represented by Raman lines of the drugs but no SERS spectra of the native cell constituents were detected. Strong SERS spectra attributed to dimethyl crocetin (DMCRT) in a living HL60 cell in contact with gold film showing weak SERS bands (due to phenylalanine and amide I and III bands) were detected. SERS mapping over a cell monolayer (intestinal epithelial cells HT29) with 1 μm lateral resolution shows different Raman spectra at all places which indicates inhomogeneous chemical constitution of the cells. The

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Biophysical Chemistry

Raman lines may be assigned to native chemical constituents in the cell’s nucleus and cytoplasm such as DNA, RNA, phenyl alanine, tyrosine etc. The evidence that cells are alive after treatment with colloidal gold comes from inspection of the cultures. The cultures show that cells incubated with colloidal gold are growing and there is no evidence of cell rounding or cell detachment from the growth surface when compared with monolayers. The above experiments and observations demonstrate the feasibility of measuring SERS of native constituents in a single cell using colloidal gold particles as SERS-active nanostructures and generating a surface enhanced Raman image inside a living cell. (6) Detection of bacteria original biomolecules: SERS is well suited for detection of bacteria from molecular to cellular level due to its sensitivity and selectivity. A new type of SERS chip, consisting of sandwich graphene (G)-AgNP–silicon nanohybrid has been developed which could achieve both molecular and cellular analysis in different samples. The chip could realize sensitive and accurate quantification of ATP with LOD of 1 pM and can also simultaneously capture, discriminate and inactivate the bacteria. By combining SERS with a microfluidic chip using nanoparticle clusters as labels, a universal platform for sensitive and specific detection of pathogen and antigens was established. LOD’s were 1 pgm/ml for Entamoeba histolytica antigen EHI 115350.

Questions (1) The intensity in Raman shift experiments for a 10−5 M solute of silver citrate in presence of sodium chloride is 11627 × 10−5 and that in the absence of the same is 8095 × 10−5 . Calculate the SERS enhancement factor (EF). Solution: EF =

11627 × 10−5 = 1.436 8095 × 10−5

(2) Outline the principle of surface enhanced Raman scattering with special reference to the contributing factors to SERS processes. (3) Discuss some applications of this method in biophysical biomedical fields.

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(4) How is this technique useful in (i) probing of DNA and genes (ii) detection of bacteria in biological molecules. (5) The incident Raman radiation in a Raman scattering experiment occurs at 104 nm and the scattered light has a wave length of 105 nm. ¯ Calculate the Raman shift in wave numbers (v). (6) The Raman shift in the DNA analysis of phosphate bond occurs at 785 cm−1 . What wave length does it correspond to when expressed in nm.

30

Mass Spectrometry and its Applications in the Analysis of Biomolecules 30.1

Introduction

Mass spectrometry is a very important analytical technique employed to quantitatively determine known materials and to identify unknown compounds within a sample. It is also used to elucidate the structure and chemical properties of different molecules. This technique is basically concerned with studies of the effect of ionization of energy on molecules. The actual process involves the conversion of the sample into gaseous ions, with or without fragmentation, which are then characterized by their mass to charge (m/z) ratios and relative abundances. Thus chemical reactions are considered in gas phase in which sample molecules are consumed during formation of ionic and neutral species.

30.2

Principle of the Technique

Multiple ions from the sample under consideration are generated in a mass spectrometer and it then separates them according to their specific mass to charge ratio (m/z) and then records the relative abundances of each ion type. The first step in the mass spectrometric analysis of any compound is the production of gas phase ions of the compound by electron ionization.

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The molecular ion formed undergoes fragmentation and the primary product formed from this ion undergoes further fragmentation. The ions are separated in the mass spectrometer according to their m/z ratio and are detected in proportion to their abundance. A mass spectrum of the molecule is thus produced and displayed as a plot of ion abundance vs. m/z ratio. The ions provide information concerning the nature and structure or the precursor molecule. In the spectrum of a pure compound, the molecular ion appears at the highest value of m/z, followed by ions of containing heavier isotopes and gives the molecular mass of the compound.

30.3

Basic Components of a Mass Spectrometer

There are three major components in a mass spectrometer: (i) Ion source: for producing gaseous ions from the substance under consideration. (ii) Analyser: for resolving the ions into their characteristic mass components according to their m/z ratio. (iii) Detector system: for detecting the ions and recording the relative abundance of each of the resolved ions. Further, a sample introduction system is necessary to introduce the samples to the ion source under high vacuum requirements (10−6 to 10−8 mm of Hg). For manipulating the data, a computer is required too. The block diagram of a mass spectrometer is shown in the Figure 30.1 given below:

Figure 30.1 Components of a mass spectrometer.

30.4

Ionisation Methods in Mass Spectrometry

There are many types of ionization methods adopted in mass spectrometry. The classical methods that chemists are familiar with are: (i) electron impact (EI) and fast atom bombardment (FAB). More modern methods

Mass Spectrometry and its Applications in the Analysis of Biomolecules

 443

such as atmospheric pressure chemical ionization (APCI), electro spray ionization (ESI), matrix assisted laser desorption ionization (MALDI) have now come into vogue. Both ESI and MALDI have greatly advanced our ability to analyse thermally labile molecules by providing an efficient means of generating intact gas phase ions. Moreover, both methods have been used to gain molecular weight information on biological samples with great speed, accuracy and sensitivity. ESI generates ions directly from solution (usually an aqueous or aqueous-organic solvent mixture) by creating a fine spray of charged droplets in the presence of a strong electric field. Subsequent vapourisation of charged droplets results in the formation of gaseous ions. Gas phase ions are generated by the laser vaporization of a solid matrixanalyte mixture in which the matrix (usually a small crystalline organic compound) strongly absorbs the laser radiation and acts as a receptacle for energy deposition. The concentrated energy deposition results in the vaporization and ionization of both matrix and analyte ions.

30.5

Applications

Both methods (ESI and MALDI) give mass accuracy of 1 part in 10,000 for proteins with molar masses less than 30 to 40 kD (i.e., 30,000 to 40,000 amu) and with a reduced mass accuracy for larger proteins. Proteins with molar masses upto 100 kD (i.e., 1,00,000 amu) can be analysed at picomole (10−12 mole) sensitivities to give simple mass spectra corresponding to intact molecule. Accurate measurements of molar mass of biopolymers are necessary for this analytical technique. A technique with high accuracy is MALDI time of flight (TOF) mass spectrometry. This technique provides the mass of a protein with on accuracy of 0.01%. In MALDI, proteins introduced as solid or in solution are converted into intact, naked ionised molecules in the gas phase. Subsequently in the mass analyser, the m/z ratios of the naked protein molecule ions are determined. When the measured mass of a protein agrees with that calculated from the gene sequence, one can conclude that the gene sequence is correct. An intense production of intact naked ionized protein molecules can be achieved when small amounts of proteins embedded in a solid matrix are bombarded with intense, short bursts or pulse of focused UV laser light usually 337 nm from a N2 laser. The solid matrix consists of low molar mass organic molecules that strongly absorb the UV irradiation.

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30.6

Biophysical Chemistry

Analysis of Glycoproteins

Peptides and oligonucleotides are composed of linear head to tail combinations of different amino acids and nucleotides. But oligosaccharides contain many isobaric monosaccharides that not only can be linked through different hydroxyl groups but can also form complex branching patterns. It is not enough to determine monosaccharide composition and sequence analysis to determine detailed primary structure. MALDI-TOF-MS has been introduced to study the ionization of large peptides and proteins. A combination of HPLC or Capillary Electrophoresis (CE) with MS peptide mapping of protein is ideal for evaluating the presence of modifications. Because FAB techniques cannot be applied to biomolecules of mass greater than 6000, ESI methods are applied to most biomolecules.

30.7

ESI of Equine Apomyoglobin

As a result of electrospray process a molecule is charged by one or multiple H+ and/or Na+ ions. This result appears as charge clusters i.e., m/z peaks which represents the same molecule, but with different charges, the pattern can be deconvoluted to the Mr which corresponds to the m/z peak with a single charge. The deconvolution pattern of m/z peaks of equine apo myoglobin to the m/z values of ∼ 17, 000 is shown below. 16950.584 2.5

M15+ M16+ 1130.7

2.0

M14+ 1211.5

M17+ 998.1

1.5 1.0

1304.7 1413.6

943.1 849.1

0.5 800

900

16930 16950 16970

1000

1100

1200

1300

1400

Figure 30.2 ESI of equine apomyoglobin. In a native protein, fewer basic residues become exposed and charged in the ESI process than in the corresponding denatured (unfolded protein).

Mass Spectrometry and its Applications in the Analysis of Biomolecules

ESI

Native protein

+

+ +

+

+

 445

+ + + + + + + + + + + + + ++ +++++ +++

m/z

+ Denatured protein

ESI

+ + + +

m/z

Figure 30.3 Distribution of charged states characteristic of native and denatured proteins.

30.8

Analysis of Phosphoproteins

Phosphoproteins have an important role in many intracellular processes including signal transduction and regulation of cell division. The recombinant protein of alpha catalytic subunit of CAMP-dependent protein kinase, which was isolated as a mixture of molecular species containing same peptide chain (but differing from each other in degree of phosphorylation at specific residues) was subjected to HPLC-electro spray MS. The molar masses of three isoforms of the protein were determined after desalting them in a form suitable for electrospray MS analysis. The isoforms differed from one another by the mass of a single - PO3 H group.

30.9

Protein Ladder Sequencing

The protein ladder sequencing method relies on the capabilities of matrix assisted laser desorption MS to measure the molar masses of proteins and peptides. The sequence defined fragments of a polypeptide chain have been analysed by using MALDI in a single operation as a protein ladder. The identity of a particular amino acid (based on the distinctive mass of each genetically coded amino acid) was established by the mass differences between consecutive peaks. The family of fragments found defines the sequence of amino acids in the original peptide chain.

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30.10

Biophysical Chemistry

Specific Examples of Biomolecules

Electron impact (EI) or chemical ionization (CI) are not useful to bring into vapour phase, the biomolecules, because of their high molar masses. Ionisation techniques such as fast atom bombardment (FAB), secondary ion mass spectrometry (SIMS), ESI and MALDI are required for this purpose. The general range of application of different MS methods is presented in Table 30.1. Because of the large molecular weights and the large number of atoms in the formula it is important to be aware of the effects of isotopes that contribute to the satellite peak pattern.

Table 30.1 General range of applications of different MS methods. Ionisation method

Detection limit (picomole)

Fast atom bombardment Electrospray (also with TOF) MALDI

1–50

Common application range of mass 6000

Precision (%)

0.01–0.10

< 1, 30, 000

0.01

0.001–0.01

< 3, 00, 000

0.05

0.05

Native hmb Denatured hmb 20+ Denatured apo Mb 20+

A

Denatured hmb

Native mb 11+

20+

B

Time

Denatured apo Mb C

600

800

1000

1200

1400

1600

1800

2000

m/Z

Figure 30.4 Denaturation of myoglobin in an acidic environment.

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 447

The denaturation process of the protein, myoglobin in an acidic environment can be followed with time and which results in the loss of heme factor. The resulting mass spectra are shown in Figure 30.4.

30.11

Peptides, Proteins and Polynucleotides

Fragmentation of positive ions of peptides and proteins once created by FAB, ESI or MALDI can occur spontaneously and be detected by separating the ions. It can also be induced by tandem mass spectrometry in which ions are made to undergo collisions with inert gas molecules like Ar at low pressure in an ion trap. Peptides and proteins tend to fragment near the amide bond. The fragmentation pattern is shown in Figure 30.5 and Figure 30.6.

Figure 30.5 ESI of cytochrome-C and glucagon.

Figure 30.6 Fragmentation pattern of protonated peptide in FAB/MS.

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Biophysical Chemistry A

100

C

A

T

G

C

C

A

T

G

G

C

A

T

G

90

472.4 70 50

425.1

531.6

[M – 11H]

608.0

30

709.1

386.3

10 0

[M – 6H]6–

300

350

400

450

500

550

600

650

700

750

800

Figure 30.7 Mass spectrometry of nucleotide structures. The bases in the structures of DNA and RNA are Adenine, guanine, cytosine, thymine (in DNA) and Uracil instead of Thymine in RNA. The MS of nucleotide structures is shown Figure 30.7.

30.12

Polysaccharides

Mass spectrometry of polysaccharides is more complex than that of proteins and polynucleotides. The pattern of MS is shown in Figure 30.8.

RO

O O

RO

O CH3 O O RO

O

O

OR

OR

848 B3

RO

O RO

OR

1484 O

O

OR NHAC 273 B1

OR

B5 1424

1136 561 576 B2

B4 1322

OR 500

1100 m/Z

Figure 30.8 Pattern of mass spectrum in polysaccharides.

1500

Mass Spectrometry and its Applications in the Analysis of Biomolecules

RO

RO RO

 449

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Biophysical Chemistry

Questions (1) Draw a neat sketch of a mass spectrometer indicating the various parts. (2) What are the different types of ionisation methods in mass spectrometry? Illustrate the electron spray ionisation method with a sketch of E.S.I. spectrum. (3) Outline the applications of mass spectrometry in understanding the structure of proteins, peptides and polysaccharides.

31

X-Ray Studies in the Elucidation of Structure of Biomolecules 31.1

Introduction

X-ray diffraction can be used to determine the crystalline structure and lattice parameters of a crystal. The information so obtained can be used to identify the material since each metallic element has a unique combination of lattice structure and parameter. When an X-ray beam is directed at a metallic crystal, the beam strikes the atoms and produces two types X-rays called white X-rays and characteristic X-rays. The characteristic X-rays, which are of interest, are caused by the ejection of an electron from the inner shell of an atom hit by the incident X-ray. When an outer shell electron moves to fill the space created in the inner shell, energy is emitted in the form of a X-ray photon. By applying Bragg’s law, it is possible to determine the crystal parameters from its characteristic X-ray pattern.

Sketch of an X-ray Diffractometer A schematic diagram of an X-ray diffractometer is given below (Fig. 31.1).

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_31

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Biophysical Chemistry

Figure 31.1 Schematic diagram of an X-ray diffractometer.

31.2

Bragg’s Law

The X-rays that strike a crystal have a wave length of about the same wave length as the space between the atoms in crystal lattice. If each plane acts as a surface which is struck by the incident X-ray beam, the beam is reflected in some cases and not reflected in other cases. In the case of reflection, the beams exiting the crystals are in phase and act to reinforce each other. This occurs when the incident beam hits the parallel planes at certain angles known as Bragg’s angle θ. In the non reflecting case, the waves leaving the crystal are out of phase and cancel each other. The reflection of X-rays from the planes of a crystal is shown in Figure 31.2.

Figure 31.2 Reflection of X-rays in ( hkl ) planes of a crystal. If the geometry of the reflected beam is examined (Fig. 31.3), the relationship between Bragg’s angle, the wavelength λ of the X-rays and the interplanar spacing, d, can be found.

X-Ray Studies in the Elucidation of Structure of Biomolecules  Incident x-rays

453

Reflected x-rays

O

θ

θ

M

θ 2θ

N

d

P

(hkl) planes

Figure 31.3 Diffraction angle of X-rays. The arbitrary planes of atoms whose indices are ( hkl ) and which has interplanar spacing “d” are shown in Figure 31.3. If the X-rays entering the crystal are in phase at OM and those reflected are in phase at ON, then the distance MPN must be qual to an integral number of wave lengths, nλ. It may be noted that MP = PN = d sin θ. Therefore for reflected X-ray beams nλ = 2d sin θ

(31.1)

where n = 1, 2, 3, . . .. In the powder method of X-ray diffraction, the material under consideration is placed in the camera as shown in Figure 31.4.

θ θ1 2

Monochromatic x-ray beam

θ4

θ5

Beam entrance

S Film Film holder Poly crystalline sample

Beam exit

S1 S2 S3 S4 S5

Figure 31.4 (a) X-ray camera and (b) X-ray film showing diffraction lines.

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Biophysical Chemistry

The specimen is placed at the center of camera with the film around in circle. When a monochromatic beam of X-rays is directed at the specimen diffraction takes place and characteristic X-rays are emitted in conical sections that intersect the film and expose it at different arcs. These arcs are seen as lines in the flattened film (Fig. 31.4). The Bragg angle of 90◦ corresponds to the distance between beam exit and entrance of the X-ray film. The Bragg angle of each characteristic line on the film can be found by using the ratio. Si θ = i (31.2) Sn θn where Si = distance from the exit to the line of interest, Sn = distance from the exit to the entrance, θi = Bragg angle of the line, θn = Bragg angle 90◦ from the exit to the entrance. After all the Bragg angles have been found, it is possible to determine the crystal structure of the sample by considering its geometry. For pure metals in a cubic structure dhkl = √

a h2 + k 2 + l 2

(31.3)

where dhkl = interplanar distance between ( hkl ) planes, “a” is the lattice parameter and h, k, l are Miller indices of the planes. Substituting eqn. (31.3) into equation (31.1), we get λ= √

2a sin θ h2 + k 2 + l 2

(31.4)

Let Q2 = h2 + k2 + l 2 and then λ2 =

4a2 sin2 θ Q2

(31.5)

Or,

Q2 λ2 = sin2 θ 4a2 Since λ2 /4a2 is a constant (C), equation (31.6) may be written as Q2 C = sin2 θ

(31.6)

(31.7)

From eqn. (31.7), it is seen that the squares of the sines of the angles that result in a diffraction peak (line on the film) occur in a certain ratio of whole numbers and this arises due to the structure factor of the lattice. These ratios can be used to determine the crystal structure.

X-Ray Studies in the Elucidation of Structure of Biomolecules 

455

Figure 31.5 Lines corresponding to planes of different cubic structures. Figure 31.5 shows the lines corresponding to the planes which diffract X-rays for cubic lattice structures. Once the crystal structure has been found, the lattice parameter can be found from λ a= √ 2 c Note that c=

(see eqn. 31.6)

sin2 θ Q2

(31.8)

(31.9)

From the lattice parameter and the lattice structure, it is possible to identify the metal from the corresponding standard table of crystal structures. Generally, an X-ray diffraction experiment is done in two parts (1) From a set of given data, determine the crystal structure and lattice parameter which will allow identification of the material. (2) From the camera and the strip of film, estimate true Bragg angles, crystal structure and lattice parameter. The data are tabulated as follows:

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31.3

Biophysical Chemistry

Structural Determination of Proteins

The first step in crystallographic studies is the production of single crystals. This is achieved by slowly bringing the sample from a state of supersaturation to the crystalline state. The crystallization process is affected by sample saturation, concentration of precipitants, ionic strength pH and buffer concentration. The X-ray diffraction experiments are next carried out using MIR (Multiple Isomorphous Replacement) or MAD (Multiple Wavelength Anomalous Dispersion) methods, the election density equation given ρ( x, y, z) =

1 NV

h

k

l

∑ ∑ ∑ f (s)ρ[−2πi (hx+ky+lz] e−iα

(31.10)

−h −k −l

is solved and an image for the molecular transform can be completed. In eqn. (31.10), V = Volume of the asymmetric cell, N = number of molecules in volume V. The electron density is only a rough outline of the crystallized sample and requires further interpretation using graphical and computational methods. Structural refinement uses geometrical factors such as proper bond lengths, bond and tetrahedral angles, planarity and backbone angles as guides.

31.4

X-ray Structures of Haemoglobin and Myoglobin

Haemoglobin and myoglobin, the first proteins for which 3-dimension structures were determined at high resolution, play a crucial role in oxygen transport and storage in muscle. This class of proteins consist entirely of α-helices. In Myoglobin, there are eight helices of which two are oriented such that they form a V-shaped pocket. In the holoenzyme the pocket contains haem group (prosthetic group or cofactors) a large heterocyclic ring containing four pyrrole rings. The center of haem is occupied by a Fe2+ cation. The histidine residue adjacent to the iron is important in mediating the non-cooperative binding of oxygen to the protein. In haemoglobin a similar arrangement of residues can be found in the haem binding pocket. However, oxygen binding and release is allosterically regulated by the pseudo-tetrameric arrangement (a dimer of dimers, d2 β 2 ) of the individual protein subunits.

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Figure 31.6 X-ray structure of Myoglobin obtained at high resolution.

31.5

Photosynthetic Reaction Centers

Photosynthetic reaction centers (RC) are important catalysts in the photosynthetic process, and they are important for this process in the biosphere. It is necessary to note that the conversion of light energy to chemical energy is a prerequisite for all higher life forms on earth. RC’s are large multiprotein complexes in the outer membranes of plants and bacteria. The X-ray structure of the reaction centre is the first structure of an integral membrane protein determined at high resolution. There are four protein chains, the H, L and M subunits and cytochrome C. The H chain has one transmembrane helix, while the L and M chains have five each. The cytochrome C subunit has no membrane spanning helix and it is anchored by proteins L and M. From the crystal structure, one can see how the photosynthetically active components bacteriochlorophyll, quinone and the haem groups are arranged. The spatial arrangement of these chromophores reveals the path and the order of the electron transfer steps.

31.6

Ribosomal Subunit

Ribosomes are large molecular assemblies (Cytoplasmic organelles) consisting of complexes of proteins and in eukaryotes upto four RNA

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Biophysical Chemistry

molecules. A large (50S) and a small (30S) subunit are loaded onto a mRNA molecule to mediate the translation of the genetic message into a specific sequence of amino acids or a polypeptide chain. The ribosomal proteins play only a subordinate architectural role and do not directly participate in the peptidyl transferase activity of the ribosome. X-ray crystallography provides proof that the ribosome is a ribozyme (catalytic RNA).

Questions (1) Give the schematic diagram of an X-ray diffractometer and indicate its parts. (2) Show the reflection of X-rays in (hkl) planes of a crystal. Write down the relation between the diffraction angle and wavelength of X-rays. (3) Describe briefly the structures of Haemoglobin and myoglobin determined by X-ray diffraction technique. ˚ impinge on a (111) plane of a silver lattice. (4) X-rays of wavelength 1.545A If the reflection from this plane occurs at 2θ = 38.5◦ , calculate its lattice parameter.

32

CRISPR-CAS-9, A Method for Genome Editing 32.1

Introduction to CRISPR-CAS-9

It is a gene editing mechanism derived from a primordial immune system in bacteria called “Clustered regularly interspersed short palindromic repeats” (CRISPR). The synthetic guide RNA (created by Emmanuelle Charpentier and Jennifer Doudna) is complementary to a target DNA sequence, directs the CAS-9 enzyme (see Fig. 32.1) to a specified location for DNA cutting. Some applications require an additional DNA template to fill in the cut. It allows the scientists to cut any strand of DNA. Since its creation in 2012, diverse experiments have been carried out using CRISPR to alter

Figure 32.1 Parts of a bacterial immune system: Genomic DNA, CAS-9, target sequence and guide RNA.

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5_32

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Biophysical Chemistry

DNA in organisms across the tree of life, mushrooms, tomatoes as well as tumours.

32.2

Genesis of the Discovery

The two scientists were inspired by a strange and little studied bacterial immune system. It is known that bacteria too have viral infections just like people do, and some bacteria used an enzyme called CAS-9 to chop up invading viruses and store molecular mugshots of them to quickly attack any repeat invaders. In 2011, these scientists worked out the details of how two bacterial RNA molecules called trace RNA and CrRNA controlled this process. They synthesized a new molecule called the single guide RNA which combines essential features of the two bacterial RNA’s to direct CAS-9 to a specific site in DNA for cutting. Their method is cheaper, faster and easier to use than previous gene-editing tools which are complex and costly. Today, scientists can readily order CAS-9 and guide RNA’s customized to target a specific sequence of DNA. CRISPR opened up gene editing to the masses. But CRISPR’s ease of access has its negative aspects. For example, in 2018, a Chinese scientist used CRISPR to edit two human embryos that were carried to term. The announcement of the first gene edited babies shook the world. The experiment crossed an ethical red line in the minds of many gene editing scientists. Even though CRISPR’s applications are in the realm of biology, the technique requires sophisticated and very complex chemistry. With new treatments for human genetic diseases in needy patients, the era of human genome editing has began.

32.3

Details on Enzyme “CAS-9”

This acts as a pair of molecular scissors that can cut the two strands of DNA at a specific location in the genome so that the bits of DNA can be added or removed. The scaffold part binds to DNA and the predesigned “sequenced guides CAS-9” to the right part of the genome. Its main function is to cut DNA and there by alter a cell’s genome. More scientifically, “CAS-9” is a dual RNA-guided endonuclease enzyme associated with CRISPR adaptive immune system in streptococcus pyogenes. It cleaves foreign nucleic acids bearing sequence complementary to the RNA loaded into the enzyme during bacterial adaptive immunity.

CRISPR-CAS-9, A Method for Genome Editing 

32.4

461

CAS-9 Mechanism

The key step in editing an organism’s genome is selective targeting of a specific sequence of DNA. Two biological micromolecules, the CAS-9 proteins and guideRNA, interact to form a complex that can identify target sequences with high selectivity. The CAS-9 protein is responsible for locating and cleaning target DNA, both in natural and artificial (CRISPR/CAS systems). The CAS-9 protein has six domains, REC-I, REC-II, Bridge helix, PAM interacting, HNH and RuvC. The REC-I domain is the largest and is responsible for binding guide RNA. The role of REC-II is not well understood. The arginine-rich bridge helix is crucial for initiating cleavage activity upon binding of target DNA. The PAM interacting domain confers PAM specificity and is therefore responsible for initiating binding to target DNA. The HNH and RuvC domains are nuclease domains that cut singlestranded DNA. They are highly homologous to HNH and RuvC domains found in other proteins. REC I

Bridge helix REC II

vC

HNH

Ru

M PA

ng

cti

ra nte

i

Figure 32.2 The six domains of CAS-9. The “CAS-9” protein remains inactive in the absence of guide RNA. In engineered crisper systems, guide RNA is comprised of a single strand of RNA that forms a T-shaped molecule which is comprised of one tetra loop and two or three stem loops. The guide RNA is engineered to have a 5’ end that is complimentary to the target DNA sequence.

462



Biophysical Chemistry Target complimentary region

Tetraloop

Stem loop 1 Stem loop 2 Stem loop 3

Figure 32.3 Single strand of RNA forming a T-shaped molecule comprising of one tetra-loop and stem-loops (1, 2 or 3). This artificial guide RNA binds to the CAS-9 protein and upon binding, induces a conformational change in the protein (see Fig. 32.4). The conformational change converts the inactive protein into its active form. The mechanism of conformational change is not fully understood but it is hypothesized that either steric interactions or weak binding between protein side chains and RNA bases may induce the change.

Figure 32.4 CAS-9 complex (inactive) and target complimentary region of guide RNA.

Figure 32.5 CAS-9/guide RNA and target DNA leading to CAS-9/guide RNA complex bound to target DNA.

CRISPR-CAS-9, A Method for Genome Editing  463

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Biophysical Chemistry

Once the CAS-9 protein is activated, it stochastically searches for target DNA by binding with sequences that matches its protospacer adjacent motif (PAM) sequence. A PAM is a two or three base sequence located within one nucleotide down stream of the region complementary to the guide RNA. PAMs have been identified in all CRISPR systems, and the specific nucleotides that define PAMS are specific to the particular category of CRISPR system. The PAM in Streptococcus pyogenes is 5t’-NGG-3. When the “CAS-9” protein finds potential target sequence with the appropriate PAM, the protein will melt the bases immediately upstream of the PAM and pair them with the complementary region on the guide RNA. If the complementary region and the target region pair properly, the RuvC and HNH nuclease domains will cut the target DNA after the third nucleotide base upstream of the PAM (Fig. 32.5).

32.5

Target DNA Binding and Cleavage by CAS-9

(1) CAS-9 scans potential target DNA for the appropriate CAM (Stars), (2) When the protein finds PAM, the protein-guide RNA complex will melt the bases immediately upstream of the PAM and pair them with the target complimentary region of the guide RNA, and (3) If the complimentary region and the target region pair properly, the RuvC and HNH domains will cut the target DNA after the third nucleotide base upstream of the PAM.

Questions (1) Explain the CAS-9 mechanism of editing an organism’s genome. (2) By means of a sketch, show the six domains of CAS-9. (3) How does the enzyme CAS-9 cleave the target DNA?

Appendix A

Donnan Membrane Potential In this Appendix, the equations pertaining to Donnan membrane potential will be derived for a polyion possessing a net negative charge. The Donnan membrane potential refers to the transport of all ions (except chosen macroions) across a semi-permeable membrane. For brevity, the macro polyion is assumed to possess a net negative charge (magnitude of charge = z). Consider an electrolyte designated as MX with anions ( X − ) and cations ( M+ ) being allowed to diffuse across the membrane. The polyanions ( Macro −z ) can however not diffuse across the membrane and is initially present in the compartment ‘a’. Hence the polyanion ( Macro −z ) provides excess negative charges in compartment a whereas the anions X − enter the right and the cations M+ towards the left as shown in the figure. a

b cations anions poly anion

Figure A.1. Schematic depiction of the Donnan membrane potential when the polyanion is impermeable across the membrane. The anions move to the right side while the cations move to the left till the equilibrium is established.

© The Author(s) 2023 C. Kalidas and M. V. Sangaranarayanan, Biophysical Chemistry, https://doi.org/10.1007/978-3-031-37682-5

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When the diffusion and migration effects balance each other, a potential difference Δϕ arises. Eventually, an equilibrium is reached in which a voltage difference (Δϕ) is balanced by diffusive forces. The accumulation of cations in the compartment ‘a’ and anions in compartment ‘b’ leads to the negative values of the interfacial potential. However, the Nernst equation provides the potential difference as a function of the concentration. For an 1:1 electrolyte, RT [ M+ ]b ln F [ M+ ]a RT [ X − ]b ln − Δϕ = F [X ]a Δϕ = −

(A.1) (A.2)

At equilibrium,

[ M+ ]b [ X − ] a = [ M+ ] a [ X − ]b

(A.3)

If the concentration of anions and cations in the two compartment obeys the above equation, it indicates the existence of the Donnan membrane potential. The principle of electroneutrality indicates that in the compartment designated as ‘a’

[ M+ ] a − [ X − ] a − z[ Macro −z ] = 0

(A.4)

Similarly in the compartment ‘b’, electroneutrality dictates that

[ M+ ]b = [ X − ]b

(A.5)

Furthermore, the concentrations of cations and anions are equal in this case. Hence the salt concentration cb can be introduced in stead of the individual concentrations. The cationic and anionic concentrations can then be written using the salt concentration. Hence cb = e− FΔϕ/RT [ M+ ]a cb = e FΔϕ/RT [X− ]a

(A.6) (A.7)

The above two equations are reminiscent of the Boltzmann distribution. Employing these equations in conjunction with eqn. (A.4), it is possible to

Appendix A: Donnan Membrane Potential 

467

obtain the following equation in terms of the interfacial potential difference Δϕ cb e FΔϕ/RT − cb e− FΔϕ/RT − z[ Macro −z ] = 0

(A.8)

The above equation can be rewritten as e2FΔϕ/RT −

z[ Macro −z ] FΔϕ/RT e −1 = 0 cb

(A.9)

Upon solving the quadratic equation and using the physically realistic positive root, the Donnan membrane potential follows as a function of the system parameters.

e FΔϕ/RT =

=

z[ Macro −z ]cb



z[ Macro −z ] + 2cb

 z[ Macro −z ] 2 cb

2 

+4

z[ Macro −z ] 2cb

(A.10) 2

+1

(A.11)

The Donnan membrane potential can now be estimated using the two concentrations [ Macro −z ] and the bulk concentration of the salt (cb ). The Donnan membrane potential alters the ionic concentrations in a significant manner. This is not the case for the Nernst equation wherein the ionic concentrations get altered to a minor extent for changes in the potential. It is well known that when the concentration ratio changes ten times, the potential is altered by about 59 millivolts, according to the Nernst equation.

Appendix B

Nernst Planck Equation The three conventional transport processes governing any physicochemical system are: (i) diffusion; (ii) migration and (iii) convection. The corresponding driving forces are chemical potential gradient, electrical potential gradient, and non-uniformity in velocities. Among these, diffusion and migration processes of charged species are more extensively pursued on account of their immense applicability in diverse fields. The phenomenological equations governing diffusion are Fick’s first and second laws while the migration effects can be described using Ohm’s law or non-linear current-potential equations. It is of interest to enquire the governing equations pertaining to the simultaneous occurrence of diffusion and migration. Although there are a hierarchy of equations for describing diffusion and migration together, the simplest ones are the Nernst–Planck equation and Donnan equation. A few salient features of Nernst Planck equation are provided below on account of its importance in estimating potential differences in membranes. The Donnan membrane potential has been described briefly in Appendix A. The classical Fick’s first law of diffusion for the one-dimensional flux ( Ji ) of the species i is represented as Ji = − Di

∂ci ∂x

(B.1)

Since the driving force for migration is the electrical potential gradient, it can be added to the flux thereby yielding the Nernst–Planck equation as:  zi F ∂Δφ ∂ci c (B.2) + Jion = − Di ∂x RT i ∂x

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for the ith ionic species. Di denotes the diffusion coefficient of i across the region of transport, Δφ being the potential difference, ∂x being the infinitesimal distance of transport. The above equation is valid for one-dimensional transport. It is easy to recognize the two different contributions to the overall flux. In biophysical chemistry, the Nernst–Planck equation describing the movement of charged species under concentration and electrical field gradients is of immense importance due to its usefulness in computing the diffusion potentials and ion transport across membranes. We emphasize the following limitations of the above equation viz. (i) neglect of activity coefficients; (ii) non-inclusion of interionic interactions and (iii) validity for dilute solutions.

B.1

Nernst–Planck Equation from Onsager’s Linear Flux-Force Relation

According to the linear flux-force formalism of Onsager, the ionic flux can be represented as Ji = Liv ( Xi − Xv ) (B.3) where Xi and Xv denote the driving forces at a site occupied by the ion and at vacant site respectively. Liv denotes the Onsager’s phenomenological coefficient. However, the driving force is the gradient of electrochemical potential and hence ∂ Xi = − (μiel ) ∂x where μiel is the electrochemical potential of the species with charge zi given by μiel = μ0,ch + RT ln ci + zi FΔφ (B.4) i and μ0,ch is the standard chemical potential of i. The driving force now i becomes  zi F dΔφ 1 dci (B.5) Xi = − RT + ci dx RT dx Similarly,

− RT dcv , (B.6) cv dx since the vacant sites are neutral. Consequently, the ionic flux equation becomes   1 dci zi F dΔφ 1 + + Jion = − Liv RT ci cv dx RT dx Xv =

Appendix B: Nernst Planck Equation 

471

For dilute solutions, the concentration of vacant sites is large (i.e., cv → ∞). Hence  zi F dΔφ 1 dci (B.7) Jion = − Liv RT + ci dx RT dx The Onsager’s coefficient is related to the diffusion coefficient in the following manner: Liv = ci Div /RT (B.8) For emphasizing the diffusion of ions through vacant sites within a lattice model framework, the subscript v is introduced for the diffusion coefficient and is not different from the conventional diffusion coefficient. Substituting equation (B.8) in equation (B.7),  Jion = − Div

z F dΔφ dci + i ci dx RT dx

(B.9)

which is one-dimensional Nernst–Planck equation. Employing the above, the diffusion potential can be deduced from the respective transference numbers of ions. The current density arising from the transport of ions of charge z is Current = i = zFJion The above description is made simple but in reality, the estimation of the steady state ionic flux as well as the time-dependence of ionic concentrations requires the numerical solution of the spatio-temporal diffusion migration equations with realistic boundary conditions, especially when the two and three dimensional transport is considered.

Appendix C

Goldman-Hodgkin-Katz Equation This equation is employed in cell membrane physiology to determine the potential across a cell’s membrane taking into consideration all the ions that are permeant through the membrane. Considering K+ , Na+ and Cl− ions inside and outside of a membrane, the membrane potential can be derived as Em =

p [K+ ]out − pNa [Na+ ]out + pCl [Cl− ]int RT ln K + zF pK[K ]in + pNa[Na+ ]in + pCl[Cl− ]out

where p s denote permeability coefficients of the respective ions, K+ , (out)

, Cl− represent the concentrations of the ions indicated outside Na+ (out) (out) the cell membrane and the “in” terms related to the concentrations of the ions inside the membrane. Although the above equation pertains to monovalent cations and anions, its generalization to other valencies is straight forward.

Questions (1) Calculate the membrane potential from the GHK equation for the skeletal muscle of a toad at 298K under the following conditions.

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Ions Na+ K+ Cl−

Permeability factor (cm/sec) 5 × 10−8 5 × 10−6 5 × 10−6

Intracellular concentration (in 10−3 moles/litre) 10 150 5

Extracellular concentration (in 10−3 moles/litre) 150 5 125

Solution: 

 pK [K+ ]ex + pNa [Na+ ]ex + pCl [Cl− ]in pK [K+ ]in + pNa [Na+ ]in + pCl [Cl− ]ex   25 × 10−9 + 750 × 10−11 + 25 × 10−6 = 0.0591 log 750 × 10−9 + 50 × 10−11 + 625 × 10−6

RT ln Em = F

= −0.081 V (2) The electrical mobility of the Li+ in water is 5 × 10−4 cm2 /sec-V at 25◦ C; the corresponding values of K+ and Br− are 7 × 10−4 and 8 × 10−4 . Using the Goldman equation, estimate the electrode potential across a film separating a 100-mM KBr solution from a 100-mM LiBr solution.

Appendix D

Salient Aspects of COVID-19 D.1

Introduction

Many countries all over the world are currently grappling with a virus which has presumably developed as an out break in China and referred as severe acute respiratory syndrome (SARS). The World Health Organization (WHO) identified it as SARS-CoV-2 as it is a common virus known as corona virus that infects the nose, respiratory tract and the sinuses of a person. It is currently referred as COVID-19 and was first reported in December, 2019.

D.2

Composition of the COVID-19 Virus

Corona viruses contain Ribonucleic acid (RNA) in their core which is akin to Deoxyribonucleic acid (DNA). The RNA acts as a molecular messenger which enables the formation and production of proteins which are required for the other parts of the virus. The following diagram provides a rough sketch of its structure.

Figure D.1. Schematic depiction of Corona virus.

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The viral envelope encapsulates or covers the RNA genome thus protecting the virus when it is outside its host i.e., the cell. The outer envelope constitutes a layer of lipids consisting of a long chain of saturated fatty acids such as palmitic acid (CH2 (CH2 )14 COOH), or stearic acid CH3 (CH2 )16 COOH. It is possible that unsaturated fatty acids such as oleic acid (CH3 (CH2 )7 CH = CH(CH2 )7 COOH) or linolenic acid also may form part of the layer of lipids. These lipid layers serve two purposes: (i) they serve as an anchor to the structural proteins required by the virus to infect the cells in the body (see the small closed circles in the diagram). (ii) the bulky projections protruding outside the cell are known as spike proteins which act as hooks for the virus to attach themselves to host cells and promote infections. A common observation is that corona viruses do not thrive or reproduce outside of a host cell.

D.3

Symptoms and Other Effects of COVID-19

The main symptoms of a person afflicted with this virus include: (i) fever, (ii) cough with shortness of breath, (iii) fatigue, (iv) body aches, (v) running nose and (vi) loss of smell or taste. The virus can lead to other more serious conditions like respiratory failure, heart and liver problems, septic shock and death. The virus can infect the immune system with proteins, known as cytokines and are thus inimical to the body. The disease spreads when a sick person sneezes or coughs. It is also possible that the virus can get into the body by touching a surface or a part of the body like mouth or the nose as it can live for several hours.

D.4

Remedial Measures

There are several ways by which one can get rid of the virus viz. (1) Washing or sanitizing hands regularly. It is also necessary to disinfect the surface, one is likely to touch or come in contact with. (2) By following social distancing i.e., keeping away from others by about six feet or wearing a face mask.

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(3) It is possible to prevent infection by getting vaccinated with a suitable vaccine. – Details of vaccines available till date: Currently, the vaccine developed by the Pfizer pharmaceutic company, known as Pfizer BioNTech COVID-19 vaccines is used for people 16 years or older. Apart from this, the vaccines developed by Moderna, Johnson and Johnson pharmaceutical companies are used. Usually two does of the vaccine are given to a person to compact the virus or its variants. – Vaccines based on Ribonucleic acid (RNA): The vaccines, developed by Pfizer BioNTech and Moderna generated messenger RNA (or mRNA) which works by instructing the cells to create a covid2 spike protein that stimulates the body to make antibodies. An unwanted development in using mRNA vaccines is that they triggered a response resulting in the breakdown of mRNA. However, Katalin Kariko at the University of Pennsylvania USA (and also at BioNTech, Mainz, Germany) and Drew Weissman also at University of Pennsylvania showed that replacing one type of molecule in mRNA, namely Uridine (C9 H12 N2 O6 ) by a similar one Pseudouridine (C9 H12 N2 O6 ) avoids the immune reactions.

Notes and Bibliography Chapter 1 – Figures 1.1–1.5 were adapted from M.G. Greenwood News-Medical Life Sciences (2014). – Figures 1.6–1.14 Open access book available: Download for free at https://openstax.org/details/books/anatomy-and-physiology. – Figures 1.17–1.25 are from NPTEL Biotechnology course-module 3.

Chapter 2 – I. Prigogine, Introduction to Thermodynamics of Irreversible Processes John Wiley & Sons Inc; Third edition (1968). – C. Kalidas and M.V. Sangaranarayanan, Non-Equilibrium Thermo dynamics-Principles and Applications MacMillan India (2002). – Onsager’s Reciprocity relations were derived in L. Onsager, Physical Review, 37, 405 (1931). – The importance of non-equilibrium thermodynamics for biochemical systems has been expounded in J. Wolfe, Cellular Thermodynamics: The molecular and macroscopic views, University of New South Wales, Australia 2015. – The concept of coupled reactions in biochemical processes has been lucidly illustrated in W. Bustin Mereer., Technical report 640, the living cell as an open thermodynamic system, Bacteria and Irreversible Thermodynamics, Department of Army, Fort Detrick, Maryland, May 1971.

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Chapter 3 – A comprehensive discussion of carbohydrates has been given in W. Pigman and D. Horton. (eds.), The carbohydrates, second edition, New York, Academic Press (1970). – Korneel Rabaey, Suzanne T Read, Peter Clauwaert, Stefano Freguia, Philip L Bond Linda L Blackall1 and Jurg Keller, The ISME Journal, 2, 519 (2008).

Chapter 4 – Tables of Interfacial tension data are from Petelska, Aneta. “Interfacial tension of bilayer lipid membranes”, Central European Journal of Chemistry, 10, 16 (2012). Open access https://doi.org/10.2478/s11532-0110130-7 – Robert Murray, Darryl Granner, Peter Mayes and Victor Rodwell. Harper’s Illustrated Biochemistry (LANGE Basic Science) 27th Edition (2009).

Chapter 5 – The potentiometric titrations to estimate the dissociation constants as well as equivalence points is a well-known technique in analytical chemistry. See for example Douglas A Skoog Fundamentals of Analytical Chemistry New York, Holt, Rinehart and Winston (1963). – Extensive tables containing isoelectric points of amino acids are available in several Handbooks. A partial list of isoelectric points is provided in CRC Handbook of Chemistry and Physics (84th Edition CRC Press (2003).

Chapter 6 The structures of MA1 and TA1 and all electrochemical data are from – Ayub Karimzadeh, Mohammad Hasanzadeh, Nasrin Shadjou and Miguel de la Guardia, Trends in Analytical Chemistry, 107, 1 (2018). – Ann K. Nowinski, Fang Sun, Andrew D. White, Andrew J. Keefe, and Shaoyi Jiang, J. Amer. Chem. Soc., 134, 6000 (2012). – Mordechay Mizrahi, Alexander Zakrassov, Jenny Lerner-Yardeni and Nurit Ashkenasy, Nanoscale, 4, 518 (2012).

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– Veronika Vanova, Katerina Mitrevska, Vedran Milosavljevic, David Hynek, Lukas Richtera and Vojtech Adam, Biosensors and Bioelectronics, 180, 113087 (2021). – Rajamouli Boddula and Surya Prakash Singh, J. Materials Chemistry C, 9, 12462 (2021). – Ruslan Garifullin A, Mustafa O. Guler, Materials Today Bio., 10, 100099 (2021). – Matteo Staderini, Eva González-Fernández, Alan F. Murray, Andrew R. Mount and Mark Bradley, Sensors and Actuators, B274, 662 (2018). Under Creative Common License.

Chapter 7 – One of the classic texts is by R.R. Sinden, DNA structure and function, Elsevier (1994). – M. VinothKumar, G Nandhini and M V Sangaranarayanan, J. Chem. Sci., 124, 105 (2012). Table 7.9 containing the values of hydrophobic-polar contacts is reproduced with permission from the Indian Academy of Sciences, Bengaluru. – New insights on Levinthal paradox have been provided in Robert Zwanzig, Attila Szabo and Biman Bagchi, Proceedings of the National Academy of Sciences, 89, 20 (1992).

Chapter 8 – A detailed account has been provided in Kim Gail Bioprocess Engineering Woodhead Publishing Limited (2013).

Chapter 9 – Several types of enzyme-substrate complex formation have been discussed in B. Chance, J. Biol. Chem., 152, 553 (1943). – Alternate methods of deducing Michaelis-Menten constants have been discussed in G.E. Briggs and J.B.S. Haldane, Biochemical Journal, 19, 338 (1925).

Chapter 10 – H. Sapper, Sa-Ouk Kang, Hans-Helmut Paul and Wolfgang Lohmann, Z. Naturforsch, 37C, 942 (1982).

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– H. Sapper, Sa-Ouk Kang, Hans-Helmut Paul and Wolfgang Lohmann, J. Pure Appl. Chem. Revs., 1, 11–17 (2012). – M. M. Mortland and J. G. Lawless, Clay and Clay minerals, 31, 433 (1983). – E. F.Roddy Yatco-Manzo , Frances Roddy, Ralph G Yount and David E. Metzler, J. Biol. Chem., 234, 733 (1959). – R. Blackburn, M. Kyaw, G. O. Phillips and A. J. Swallow, J. Chem. Soc. Faraday Trans I Physical Chemistry in Condensed Phases, 71, 2277 (1975). – Wolfram Schumacher, Christof Holliger, Alexander J.B Zehnder and Wilfred R Hagen, FEBS Lett., 409, 421 (1997). – S.V. Nivane and G. Gokavri, Inorganic Chemistry Communications, 14, 1102 (2011). – Subhadeep Saha, Aditi Roy, Kanak Roy & Mahendra Nath Roy, Nature Scientific Reports, 6, 35764 (2016). – Victor R Reedy and Ronald R-Watson (1981). Drug. Des. Devel. Ther., 2, 145 (2008). – B. Janssens, Encapsulation of Vit-D3 and Vit-K2 in chitosan coated liposomes, M.S. Thesis, University of Ghent (2017–18). – F. Sun., PhD. Thesis, Lipid based mixed micelles for oral delivery of Vitamin K, University of Utrecht, Netherlands (2018). – Yi Jung Ju et al., Organic and Biomolecular Chem., 15, 4417 (2017). – Hidetaka Ushijima, Hitoshi Okamura,Yasuzo Nishina and Kiyoshi Shiga, J. Biol. Chem., 105, 467 (1989).

Chapter 11 – Yijun Tang, Xiangqun Zeng and Jennifer Liang, J. Chem. Ed., 87, 742 (2010). – Simon G Patching, Biochimica et Biophysica Acta, 1838, 43 (2014).

Chapter 12 – A comprehensive account of all electrochemical techniques has been given in Cynthia Zoski Handbook of Electrochemistry Elsevier (2007). – The mathematical treatment of different electrochemical techniques is lucidly discussed in Alan J. Bard and Larry Faulkner Electrochemical Methods–Fundamentals and Applications John Wiley & Sons (2001). – An overview of electroanalytical techniques is given in Joseph Wang Analytical Electrochemistry John Wiley & Sons (2006).

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Chapter 13 – Figures 13.1 to 13.4 adapted from (Yijun Tang, Xiangqun Zeng and Jennifer Liang, J. Chem. Ed., 87, 742 (2010) are reproduced with permission from the American Chemical Society.

Chapter 14 – Sazia Iftekhar, Susan T. Ovbude and David S. Hage, Frontiers in Chemistry, 7, Article 673 (2019).

Chapter 15 – Figures 15.1 to 15.10 are adapted from Beckmann Coulter. Introduction to capillary electrophoresis- Handbook (open access).

Chapter 16 – J. Lu., NMR in Biomedical research, Materials and Methods, 3, 170 (2013).

Chapter 17 – Indra D Sahu, Robert M McCarrick, Kaylee R Troxel, Rongfu Zhang, Hubbell J Smith, Megan M Dunagan, Max S Swartz, Prashant V Rajan, Brett M Kroncke, Charles R Sanders and Gary A Lorigan, Biochemistry, 52, 6627 (2013).

Chapter 18 – Xiwei Zheng, Zhao Li, Sandya Beeram, Maria Podariu, Ryan Matsuda, Erika L. Pfaunmiller, Christopher J. White II, NaTasha Carter and David S Hage, J. Chromatography, B968, 49 (2014). – Claire Vallance, An Introduction to Chemical Kinetics Morgan and Claypool publishers (2007). – H. Gutheard et al., Ann. Rev. Biochem., 40, 315 (1971). – Xiwei Zheng, Cong Bi, Zhao Li, Maria Podariu and David S. Hage, J. of Pharm and Biomed Analysis, 113, 163 (2015).

Chapter 19 – S.L. Frien, E.S. Lewis and A. Weinberger (Eds), Techniques of organic chemistry. Vol. III, Part 2, Wiley (Interscience) (1963). – G. Czerlinski Ali and M. Eigen, Z. Electrochem., 63, 652 (1959).

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– C. Kalidas, Chemical Kinetic Methods, New Age International Publishers, New Delhi (2002).

Chapter 20 – J.M. Sturtevant, Ann. Rev. Phys. Chem., 38, 468 (1987). – J.E. Ladbury and B.Z. Chowdury, Chem. Biol., 3, 791 (1996).

Chapter 21 – J.S. Davis and H. Gutfreund, FEBS Letters, 72, 2 (1976).

Chapter 22 – S.M. Kelly and N.C. Price, Current Protein and Peptide Science, 1, 349 (2000).

Chapter 23 – Figure 23.1 reproduced with permission from (Thomas Hofelich, Lars Wadsö, Allan L. Smith et al., Journal of Chemical Education, 78, 1083 (2001). Copyright 2001 American Chemical Society.

Chapter 24 – R. Chang, Physical chemistry for the biosciences, University Science, New York (2005).

Chapter 25 – E.E. Conn and P.K. Stumpf, Outlines of Biochemistry, Fourth Edition John Wiley & Sons (1976). – H.B.F. Dixon, Biochemical Education, 13, 181 (1985).

Chapter 26 – Figures 26.1 to 26.3 are adapted from Pulimamidi Rabindra Reddy and Nomula Raju Gel Electrophoresis and its Applications Intech open access (2012).

Chapter 27 – G. Rabston, in Beckman Coulter (Life Sciences) Analytical Ultracentrifuge (open access) (2013).

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Chapter 28 – Figure 28.1 adapted from O.B. Acikara Ion exchange chromatography, Intech open access (2012).

Chapter 29 – Figures 29.1 and 29.2 adapted from Ujit Sur, Surface Enhanced Raman Scattering (2017) Intech Open access.

Chapter 30 – Thomas P. E. Hollenbeck, Gary Siuzdak and Robert D. Blackledge, J. Forensic. Sci., 44, 783 (1999).

Chapter 31 – Figure 31.9 adapted from Yunbeom Lee, Jong Goo Kim, Sang Jin Lee, Srinivasan Muniyappan, Tae Wu Kim, Hosung Ki, Hanui Kim, Junbeom Jo, So Ri Yun, Hyosub Lee, Kyung Won Lee, Seong Ok Kim, Marco Cammarata and Hyotcherl Ihee, Nature Communications, 12, 3677 (2021).

Chapter 32 – Figures 32.1 to 32.5 adapted from Cavanagh and Garrity, “CRISPR Mechanism”, CRISPR/Cas9, Tufts University (2014). https://sites.tufts.edu/crispr/

Index Active transport 17 Affinity Chromatography 287 Aldopentoses 66 Allosteric enzymes 197 Amperometric biosensors 266 Analysis of glycoproteins 444 Analysis of Lipids 92 Analytical Ultracentrifugation 409 Antibodies 153 Antiport 21 ATP hydrolysis 250 Basic components of a mass spectrometer 442 Basics of NMR 314 Bifunctional oligomeric enzymes 202 Biochemical function of Biotin 230 Boltzmann Distribution 35 Capillary zone electrophoresis, 303 CAS-9 Mechanism 461 Cellulose 73, 290 Chiral Recognition 309 chymotrypsin 284 Circular Dichroism 361

Circular Dichroism using synchrotron radiation 364 Classes of peptides 130 Classification of Amino Acids 115 Classification of Proteins 145 Co-enzymes 217 Cofactors in enzyme catalysis 198 Competitive inhibition 187 Composition of Proteins 143 Conformational changes in proteins 368 Continuous culture of bacteria 43 Coupling of reactions 54 CRISPR-CAS-9 459 Denaturation of Proteins 153 Deoxyribonucleic acid 475 Distribution of Lipids 99 Donnan Membrane Potential 465 Double site-directed spin labeling 323 Effect of cofactors and ligands on circular dichroism 365 Electro osmosis 302 Electro-reduction of adenine 168 Electrochemical biosensors 265

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Electron nuclear double resonance spectroscopy 329 electrophoresis 302 Endoplastic Reticulum 7 Enzymatic sensing of glucose 267 Enzymatic sensing of urea 271 Enzyme “CAS-9” 460 Eukaryotic cells 9 Examples of nucleotides 166 Examples of Proteins 151 Exocytosis 23

Immunoassays employing SERS 434 Impedimetric biosensors 273 Ion Exchange Chromatography 421 Ionisation methods in Mass spectrometry 442 Isoelectric focusing 303 Isothermal Calorimetry 375 Isothermal Heat Flow Calorimeter 376

Facilitated diffusion 18 Fick’s diffusion laws 469 Flash photolysis 351 Flavin Adenine Dinucleotides 228 Flow Methods 335

Joule Heating 303

Gel filtration 395 Gel filtration of hemoglobin 399 Geometric Isomerism 91 Gibbs free energy 43 Glycolipids 107 Glycolytic enzymes 201 Glycosides 68 Goldman-Hadgkin-Katz Equation 473

Linear laws 45 Lineweaver-Burke Plot 186 Lipid Bi-layers 105 Lipoproteins 98

Helix-Coil Transitions 154 Hemoglobin 152 High performance affinity chromatography 288 High phosphoryl capacity of ATP 247 Immobilisation of enzymes 209 Immobilization by N-hydroxy succinimide method 293

Ketohexoses 67 Kinetics of Helix-Coil Transformation 154

Magic angle spinning 320 Mass spectrometry 441 Membrane Proteins 155 Metal complexation studies 358 Metal-Chelate Affinity Chromatography 295 Metalloflavoproteins 228 Methodology 389 Micellar electrokinetic capillary chromatography 303 Michaelis–Menten constant 185 Michaelis-Menten constants for enzymatic biosensors 270 Mitochondria 6 Molecular aggregation 40 Molecular cloning 405

INDEX 

Molecular Weight Determination 411 Multi-substrate enzyme reactions 188 Multienzyme complexes 203 Mutational Studies 383 Myosin assembly 357 Negative feed back inhibition 196 Nernst Planck Equation 469 NMR in biomedical research 314 NMR in protein structure determination 315 non-competitive inhibition 193 Non-enzymatic sensing of glucose 271 Non-equilibrium thermodynamics in microbiology 44 Nucleic acid chromophores 368 Oligosaccharides 70 Osmotic effects 37 Oxygen Evolving Complex 332 Passive transport 17 Phase transitions of phospholipids 392 Phenomenological coefficients 53 Phospholipid Bilayer 22 Polysaccharides 72 Potentiometric sensors 272 Pressure Jump Relaxation 355 Prokaryotic cells 8 Protein ladder sequencing 445 Protein structure determination using solid state NMR 323 Purification of Adenovirus 426

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Reaction of horse radish peroxidase with H2 O2 212 Reactions of Amino Acids 120 Reactions of the TCA cycle 253 Redox potential data on water soluble B-Vitamins 227 Relation between Co-enzymes and Vitamins 220 Ribosomes 9 Separation of Membrane Phospholipids 426 spectrophotometry 346 Step gradient elution method 293 Surface Plasmon Resonance 279 Symport 25 Target DNA Binding 464 Temperature jump 345 Thermal denaturation of proteins 390 Thermochemistry of Carbohydrates 74 Transport across cell membrane 17 Turn Over Rates 208 Unimolecular Reactions 337 Vitamin B-6 group 232 Voltammetric biosensors 272 Water soluble vitamins 221 Waxes 105 X-ray Diffractometer 451 Zeta potential data 241