Handbook of Computational Neurodegeneration 3319759213, 9783319759210

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Panagiotis Vlamos Ilias S. Kotsireas Ioannis Tarnanas Editors

Handbook of Computational Neurodegeneration

Handbook of Computational Neurodegeneration

Panagiotis Vlamos • Ilias S. Kotsireas • Ioannis Tarnanas Editors

Handbook of Computational Neurodegeneration With 194 Figures and 48 Tables

Editors Panagiotis Vlamos Department of Informatics Ionian University Corfu, Greece

Ilias S. Kotsireas Wilfrid Laurier University Waterloo, ON, Canada

Ioannis Tarnanas Altoida Inc Atlantic Fellow with the Global Brain Health Institute Trinity College Dublin Dublin, Ireland

ISBN 978-3-319-75921-0 ISBN 978-3-319-75922-7 (eBook) https://doi.org/10.1007/978-3-319-75922-7 © Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, 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 publisher, 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 publisher 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 publisher remains 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

With love to my youngest son Aggelos, may he always convey good news, as Herodotus mentioned . . .

Preface

The Handbook of Computational Neurodegeneration provides a comprehensive overview of the field and thus bridges the gap between standard textbooks of research on neurodegeneration and dispersed publications for specialists that have a narrowed focus on computational methods to study this complicated process. The handbook reviews the central issues and methodological approaches related to the field for which the reader pursues a thorough overview. It also conveys more advanced knowledge, thus serving both as an introductory text and as a starting point for an in-depth study of a specific area, as well as a quick reference source for the expert by reflecting the state of the art and future prospects. The book includes topics that are usually missing in standard textbooks and that are only marginally represented in the specific literature. The broad scope of the Handbook of Computational Neurodegeneration is reflected by five major parts (see below) that facilitate the integration of computational concepts, methods, and applications in the study of neurodegeneration. Each part is intended to stand on its own, giving an overview of the topic and the most important problems and approaches, supported by examples, practical applications, and proposed methodologies. The basic concepts and knowledge, standard procedures, and methods are presented, as well as recent advances and new perspectives. Part I: Neurodegenerative Disease Modeling Part II: Information Processing and Visualization Part III: Digital Health and Mixed Realities Part IV: Data Mining, Metaheuristics, High-Performance Computing Part V: Mathematical Modeling Methodologies in Neurodegeneration Corfu, Greece Waterloo, Canada Dublin, Ireland August 2023

Panagiotis Vlamos Ilias. S. Kotsireas Ioannis Tarnanas

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Acknowledgment

We would like to thank Konstantina Skolariki for the help she provided during the editorial process which was fundamental to the completion of this handbook.

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Contents

Part I

Neurodegenerative Disease Modeling . . . . . . . . . . . . . . . . . .

1

1

Neurodegenerative Disease Modeling: An Introduction . . . . . . . . . Antigoni Avramouli and Panagiotis Vlamos

3

2

Computational Modeling of Neural Networks of the Human Brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ludmila Kucikova, Samuel O. Danso, Graciela Muniz-Terrera, and Craig W. Ritchie

11

3

Applications of Nanotechnology in Alzheimer’s Disease . . . . . . . . Maria Chountoulesi, Nikolaos Naziris, Anna Gioran, Aristeidis Papagiannopoulos, Barry R. Steele, Maria Micha-Screttas, Stavros G. Stavrinides, Michael Hanias, Niki Chondrogianni, Stergios Pispas, Cécile Arbez-Gindre, and Costas Demetzos

4

Nanoplatforms as Information Carriers and Thermodynamic Epitopes in Neurodegenerative and Immune Diseases . . . . . . . . . . Costas Demetzos

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Detecting Active Molecular Subpathways Related to Alzheimer’s Disease: A Systems Biology Approach . . . . . . . . . . . . Aristidis G. Vrahatis and Panagiotis Vlamos

91

5

31

6

Neuronal Encoding Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Emmanouil Perakis

111

7

AD Blank Spot Model for Evaluation of Alzheimer’s Disease . . . . Antigoni Avramouli and Panagiotis Vlamos

133

8

Game Theory and Other Unconventional Approaches to Biological Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kalliopi Kastampolidou and Theodore Andronikos

163

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9

Contents

Gene Regulatory Network Reconstruction Using Single-Cell RNA-Sequencing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dimitrios E. Koumadorakis, Georgios N. Dimitrakopoulos, Marios G. Krokidis, and Aristidis G. Vrahatis

181

10

MicroRNAs in Neurodegenerative Diseases . . . . . . . . . . . . . . . . . . Constantinos Stathopoulos, Nikoleta Giarimoglou, Adamantia Kouvela, Argyris Alexiou, and Vassiliki Stamatopoulou

197

11

Role of Buccal Cells in Neurodegeneration . . . . . . . . . . . . . . . . . . . Maria Gonidi, Nafsika Kontara, Aristidis G. Vrahatis, Themis P. Exarchos, and Panagiotis Vlamos

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12

Current Psychological Approaches in Neurodegenerative Diseases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Panagiotis Kormas and Antonia Moutzouri

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13

Neurodegenerative Diseases and Psychosocial Impairment . . . . . . Maria Myrto Kasimati and Konstantina Skolariki

14

Behavioral and Psychological Changes in Alzheimer’s and Other Neurodegenerative Disorders . . . . . . . . . . . . . . . . . . . . . . . . Marios Diamantopoulos

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Emotional and Behavioral Symptoms in Neurodegenerative Diseases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Katsigianni Lamprini

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H2UMANISM: Holistic Healthcare Supply Chain Management for Precision Medicine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vasileios Karyotis, Cleopatra Bardaki, and Panos Kourouthanassis

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Effects of Neuron Axons Degeneration in 2D Networks of Neuronal Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Provata and Panagiotis Vlamos

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15

16

17

18

19

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Amyotrophic Lateral Sclerosis-Related Gene Interactions with Fat Mass and Obesity-Associated Gene . . . . . . . . . . . . . . . . . . . . . Katerina Kadena, Konstantina Skolariki, Dimitrios Vlachakis, and Panagiotis Vlamos Effects of Sleep Deprivation and Experience on Sleep Characteristics and Memory Formation Based on EEG Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Konstantina Skolariki and Julie Seibt Exhaled Breath Analysis in Neurodegenerative Diseases . . . . . . . . Stephanos Patsiris, Anna Karpouza, Themis Exarchos, and Panagiotis Vlamos

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427 441

Contents

21

Implications of Neuroplasticity to the Philosophical Debate of Free Will and Determinism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Panagiotis Kormas, Antonia Moutzouri, and Evangelos D. Protopapadakis

Part II 22

23

24

25

26

27

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Information Processing and Visualization . . . . . . . . . . . . . .

Information Processing and Visualization in the Human Brain: An Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gerasimos Vonitsanos, Foteini Grivokostopoulou, Ioanna Moustaka, and Andreas Kanavos

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473

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Visualizing Neurodegeneration Using Atomic Force Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dionysios Cheirdaris

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Platforms for Analyzing Networks of Neurodegenerative and Psychiatric Diseases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Katerina Kadena and Evgenia Lazarou

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From Raw EEG Signals to Brain Networks: An EEGLAB Tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Georgios N. Dimitrakopoulos

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Protein Fold Recognition Exploited by Computational and Functional Approaches: Recent Insights . . . . . . . . . . . . . . . . . . . . Marios G. Krokidis, Evangelos Efraimidis, Dionysios Cheirdaris, Aristidis G. Vrahatis, and Themis P. Exarchos Neuroscientific Research on Computer-Based Teaching Georgia Tzortsou

Part III

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Digital Health and Mixed Realities . . . . . . . . . . . . . . . . . . .

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Digital Health and Mixed Realities: An Introduction . . . . . . . . . . . Gerasimos Vonitsanos, Foteini Grivokostopoulou, Ioanna Moustaka, and Andreas Kanavos

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E-Health and Neurodegeneration . . . . . . . . . . . . . . . . . . . . . . . . . . George Intas, Charalampos Platis, and Pantelis Stergiannis

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Affective Computing for Brain Health Disorders . . . . . . . . . . . . . . Erin Smith, Eric A. Storch, Helen Lavretsky, Jeffrey L. Cummings, and Harris A. Eyre

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Advanced Technologies in Health and Neurodegenerative Diseases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nikolaos Naziris and Costas Demetzos

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32

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Contents

Assessment and Cognitive Training of Patients with Mild Cognitive Impairment Using Mobile Devices . . . . . . . . . . . . . . . . . Panagiota Giannopoulou and Spyridon Doukakis

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From G-Protein-Coupled Receptors to Designer Receptors Exclusively Activated by Designer Drugs . . . . . . . . . . . . . . . . . . . . Emmanouil Perakis

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Health Informatics Application on Medical Rescue Incidents . . . . Emmanouil Zoulias, Charalampos Platis, and George Intas

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Cybersecurity Threats in the Healthcare Domain and Technical Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Christoforos Ntantogian, Christos Laoudias, Antonio Jesus Diaz Honrubia, Eleni Veroni, and Christos Xenakis

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Heart Rate Variability Components in Electromagnetic Hypersensitive Persons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Styliani A. Geronikolou, George P. Chrousos, and Dennis V. Cokkinos

Part IV Data Mining, Metaheuristics, High-Performance Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

38

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701

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Computational Models in the Prediction of Alzheimer’s Disease and Dementia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Isabella Papageorgiou, Michail Kavvadias, and Themis P. Exarchos

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Early Alzheimer’s Prediction Using Dimensionality Reduction Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Petros Paplomatas and Aristidis G. Vrahatis

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Biomedical Applications of Precision Medicine in Neurodegenerative Diseases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Eleftheria Polychronidou and Panagiotis Vlamos

823

Protein Misfolding and Neurodegenerative Diseases: A Game Theory Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Styliani Adam, Panagiotis Karastathis, Dimitris Kostadimas, Kalliopi Kastampolidou, and Theodore Andronikos Dietary Components as Promoters of Medicinal Activity in Alzheimer’s Disease . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Efstathia G. Kalli Heart Rate Variability Indexes in Schizophrenia . . . . . . . . . . . . . . Paraskevi V. Tsakmaki and Sotiris K. Tasoulis

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875 889

Contents

Part V Mathematical Modeling Methodologies in Neurodegeneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

44

45

46

47

48

49

Mathematical Modeling of Gene Regulatory Networks: An Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mirto M. Gasparinatou Parkinson’s Disease: Bioinspired Optimization Algorithms for Omics Datasets Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . Konstantina Skolariki, Marios G. Krokidis, Aristidis G. Vrahatis, Themis P. Exarchos, and Panagiotis Vlamos

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899

901

909

Omic-Based Biomarkers Discovery in Alzheimer’s Disease: High-Throughput Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . Efstathia G. Kalli

923

Computational Models and Advanced Digital Techniques in Alzheimer’s Disease . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Eleni Stella, Athanasia Maria Tsiampa, and Antonia Stella

941

Antibody Clustering and 3D Modeling for Neurodegenerative Diseases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dimitrios Vlachakis

953

Gene Expression Profiling and Bioinformatics Analysis in Neurodegenerative Diseases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Marios G. Krokidis, Themis P. Exarchos, and Panagiotis Vlamos

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Brain Computational Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1003 Emmanouil Perakis

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1019

About the Editors

Panagiotis Vlamos is a Professor, Chairman of the University Research Center of the Ionian University, and Scientific Director of the Bioinformatics and Human Electrophysiology Laboratory (BiHELab) at the Ionian University. He has won various awards and has authored more than 300 papers in peer-reviewed journals and conference proceedings as well as 16 educational books. The topics of his papers are Mathematical Modelling, Applied and Discrete Mathematics as well as Bioinformatics. His main research interest is to help bridge the translational gap from data to models and from models to drug discovery and personalized therapy by developing quantitative deterministic approaches to biological and clinical problems by utilizing high-performance computing. He is the founder of the series of the World Congresses GeNeDis (“Genetics, Geriatrics and Neurodegenerative Diseases Research”), organized every 2 years starting from 2014. In addition, Prof. Vlamos is Co-Chair of the Hellenic Initiative Against Alzheimer’s (HIAAD). HIAAD is a joint collaboration between Greek researchers from Johns Hopkins University, USA, and scientists from BiHELab who combine their knowledge and expertise in order to cope with the “epidemic” of Alzheimer’s and related disorders in Greece. He also founded the Master’s Program “Bioinformatics & Neuroinformatics” and is the editor of the Handbook of Computational Neurodegeneration that will be published by Springer International Publishing.

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About the Editors

Ilias S. Kotsireas serves as a Computer Science Professor and the Director of the CARGO Lab (http:// www.cargo.wlu.ca) at Wilfrid Laurier University (Waterloo, ON, Canada). He has more than 200 peer-reviewed journal and conference publications as well as chapters in books and had authored and edited books and special issues of journals in the research areas of Computational Algebra, Metaheuristics, High-Performance Computing, Dynamical Systems, and Combinatorial Design Theory. He serves on the Editorial Board of 11 international journals. He serves as the Managing Editor of two Springer journals and as the Editor-in-Chief of a Springer journal and a Birkhauser book series. He has organized a very large number of international conferences in Europe, North America, and Asia, often serving as a Program Committee Chair or General Chair. His research has been funded by NSERC, the European Union, and NSFC. He has received funding for conference organization from Maplesoft, the Fields Institute, and several Wilfrid Laurier University offices. He served as Chair of the ACM Special Interest Group on Symbolic Computation (SIGSAM) on a 4-year term: July 2013 to July 2017. He is a Co-Chair of the Applications of Computer Algebra Working Group (ACA WG), a group of 45 internationally renowned researchers that oversee the organization of the ACA conference series. He has delivered more than 50 invited/plenary talks at conferences and research institutes around the world. Ioannis Tarnanas received his PhD in Neuroscience from Aristotle University of Thessaloniki, Greece. Dr. Tarnanas pioneered virtual and augmented reality environments for everyday function monitoring since 2000. In 2005, he became involved in the first digital biomarker project in the world from Novartis AG, the smart exelon patch, approved by the FDA in 2013. Since then, he has been a Novartis fellow focusing on using new technologies to understand the aging process and to establish prevention methods that decrease the risk of developing dementia or delay the onset of the disease. Currently, Dr. Tarnanas is a Senior Fellow with the Global Brain Health Institute (GBHI), based in Trinity College Dublin. Dr. Tarnanas’s work on novel technologies for assessing and treating age-related cognitive

About the Editors

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function is of central strategic interest to GBHI and together they have the international outreach to scale up scientific, medical, and technological discoveries of proven value through a truly global alumni network. Dr. Tarnanas recently created an accurate predictive tool based on cognitive and non-cognitive biomarkers of early onset dementia. The program, named Altoida’s Neuro Motor Index (NMI), aims to spot the first neurological effects of Alzheimer’s disease with 94% accuracy up to decades before symptoms appear. Currently part of the expert evaluators for the European Institute for Innovation and Technology, Health sector (EIT Health) for Brain and Mental Health and Digital Biomarkers, Dr. Tarnanas will continue to pursue his development of computational biomarkers of Alzheimer’s disease.

Contributors

Styliani Adam Department of Informatics, Ionian University, Corfu, Greece Argyris Alexiou Department of Biochemistry, School of Medicine, University of Patras, Patras, Greece Theodore Andronikos Department of Informatics, Ionian University, Corfu, Greece Cécile Arbez-Gindre Institute of Chemical Biology, National Hellenic Research Foundation, Athens, Greece Antigoni Avramouli Bioinformatics and Human Electrophysiology Laboratory, Department of Informatics, Ionian University, Corfu, Greece Cleopatra Bardaki Department of Informatics and Telematics, Harokopio University of Athens, Athens, Greece Dionysios Cheirdaris Bioinformatics and Human Electrophysiology Laboratory, Department of Informatics, Ionian University, Corfu, Greece Niki Chondrogianni Institute of Chemical Biology, National Hellenic Research Foundation, Athens, Greece Maria Chountoulesi Section of Pharmaceutical Technology, Department of Pharmacy, School of Health Sciences, National and Kapodistrian University of Athens, Athens, Greece George P. Chrousos Clinical, Experimental Surgery, Translational Research Centre, Biomedical Research Foundation of the Academy of Athens, Athens, Greece UNESCO Chair on Adolescent Health Care, Geneva, Switzerland University Research Institute of Maternal and Child Health and Precision Medicine, National and Kapodistrian University of Athens, Athens, Greece Dennis V. Cokkinos Clinical, Experimental Surgery, Translational Research Centre, Biomedical Research Foundation of the Academy of Athens, Athens, Greece

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Contributors

Jeffrey L. Cummings Chambers-Grundy Center for Transformative Neuroscience, Department of Brain Health, School of Integrated Health Sciences, University of Nevada Las Vegas (UNLV), Las Vegas, NV, USA Samuel O. Danso Edinburgh Dementia Prevention and Centre Clinical Brain Sciences, University of Edinburgh Medical School University of Edinburgh, Edinburgh, UK Costas Demetzos School of Health, Department of Pharmacy, Laboratory of Pharmaceutical Technology Section of Pharmaceutical Nanotechnology, National and Kapodistrian University of Athens, Athens, Greece Marios Diamantopoulos Laboratory of Cognitive Neuroscience and Sensorimotor Control, University Mental Health, Neurosciences and Precision Medicine Research Institute “COSTAS STEFANIS”, Athens, Greece Georgios N. Dimitrakopoulos Bioinformatics and Human Electrophysiology Laboratory (BiHELab), Department of Informatics, Ionian University, Corfu, Greece Spyridon Doukakis Department of Informatics, Ionian University, Corfu, Greece Evangelos Efraimidis Hellenic Open University, MSc Program Bioinformatics and Neuroinformatics, Patras, Greece Themis P. Exarchos Bioinformatics and Human Electrophysiology Laboratory, Department of Informatics, Ionian University, Corfu, Greece Harris A. Eyre The PRODEO Institute, San Francisco, CA, USA Organisation for Economic Co-operation and Development (OECD), Paris, France Global Brain Health Institute, University of California, San Francisco, CA, USA Trinity College, Dublin, Ireland Department of Psychiatry and Behavioral Sciences, Baylor College of Medicine, Houston, TX, USA IMPACT, The Institute for Mental and Physical Health and Clinical Translation, Deakin University, Geelong, VIC, Australia Mirto M. Gasparinatou Department of Informatics, Ionian University, Corfu, Greece Styliani A. Geronikolou Clinical, Experimental Surgery, Translational Research Centre, Biomedical Research Foundation of the Academy of Athens, Athens, Greece UNESCO Chair on Adolescent Health Care, Geneva, Switzerland University Research Institute of Maternal and Child Health and Precision Medicine, National and Kapodistrian University of Athens, Athens, Greece Panagiota Giannopoulou Department of Informatics, Ionian University, Corfu, Greece

Contributors

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Nikoleta Giarimoglou Department of Biochemistry, School of Medicine, University of Patras, Patras, Greece Anna Gioran Institute of Chemical Biology, National Hellenic Research Foundation, Athens, Greece Maria Gonidi Bioinformatics and Human Electrophysiology Laboratory, Department of Informatics, Ionian University, Corfu, Greece Foteini Grivokostopoulou Computer Engineering and Informatics Department, University of Patras, Patras, Greece Michael Hanias Physics Department, International Hellenic University, Kavala, Greece Antonio Jesus Diaz Honrubia Computer Languages and Systems, and Software Engineering, Universidad Politécnica de Madrid, Madrid, Spain George Intas General hospital Nikaia “Agios Panteleimon” – G.H.W.A. “Agia Varvara”, Pireas, Greece Katerina Kadena Department of Informatics, Ionian University, Corfu, Greece Efstathia G. Kalli Department of Informatics, Ionian University, Corfu, Greece Andreas Kanavos Department of Informatics, Ionian University, Corfu, Greece Panagiotis Karastathis Department of Informatics, Ionian University, Corfu, Greece Anna Karpouza General Hospital of Corfu, Corfu, Greece Vasileios Karyotis Department of Informatics, Ionian University, Corfu, Greece Maria Myrto Kasimati Imperial College Business School, London, UK Kalliopi Kastampolidou Department of Informatics, Ionian University, Corfu, Greece Michail Kavvadias Department of Informatics, Ionian University, Corfu, Greece Nafsika Kontara Bioinformatics and Human Electrophysiology Laboratory, Department of Informatics, Ionian University, Corfu, Greece Panagiotis Kormas National and Kapodistrian University of Athens, Athens, Greece Dimitris Kostadimas Department of Informatics, Ionian University, Corfu, Greece Dimitrios E. Koumadorakis Bioinformatics and Human Electrophysiology Laboratory, Department of Informatics, Ionian University, Corfu, Greece Panos Kourouthanassis Department of Informatics, Ionian University, Corfu, Greece

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Contributors

Adamantia Kouvela Department of Biochemistry, School of Medicine, University of Patras, Patras, Greece Marios G. Krokidis Bioinformatics and Human Electrophysiology Laboratory, Department of Informatics, Ionian University, Corfu, Greece Ludmila Kucikova Biomedical Sciences, Edinburgh Medical School, University of Edinburgh, Edinburgh, UK Edinburgh Dementia Prevention and Centre Clinical Brain Sciences, University of Edinburgh Medical School University of Edinburgh, Edinburgh, UK Katsigianni Lamprini Ionian University, Aridaia, Greece Christos Laoudias KIOS Research and Innovation Center of Excellence, University of Cyprus, Nicosia, Cyprus Helen Lavretsky Semel Institute for Neuroscience and Human Behavior, University of California, Los Angeles (UCLA), Los Angeles, CA, USA Evgenia Lazarou Department of Informatics, Ionian University, Corfu, Greece Maria Micha-Screttas Institute of Chemical Biology, National Hellenic Research Foundation, Athens, Greece Ioanna Moustaka Department of Informatics, Ionian University, Corfu, Greece Antonia Moutzouri National and Kapodistrian University of Athens, Athens, Greece Graciela Muniz-Terrera Edinburgh Dementia Prevention and Centre Clinical Brain Sciences, University of Edinburgh Medical School University of Edinburgh, Edinburgh, UK Nikolaos Naziris Section of Pharmaceutical Technology, Department of Pharmacy, School of Health Sciences, National and Kapodistrian University of Athens, Athens, Greece Christoforos Ntantogian Department of Informatics, Ionian University, Corfu, Greece Isabella Papageorgiou Department of Informatics, Ionian University, Corfu, Greece Aristeidis Papagiannopoulos Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Athens, Greece Petros Paplomatas Hellenic Open University, Patras, Greece Stephanos Patsiris General Hospital of Corfu, Corfu, Greece Department of Informatics, Ionian University, Corfu, Greece Emmanouil Perakis Department of Informatics, Ionian University, Corfu, Greece

Contributors

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Stergios Pispas Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Athens, Greece Charalampos Platis Scientific Personnel at School of Public Administration and Local Governance, National Centre of Public Administration and Local Governance, Athens, Greece Eleftheria Polychronidou Bioinformatics and Human Electrophysiology Lab, Department of Informatics, Ionian University, Corfu, Greece Evangelos D. Protopapadakis National and Kapodistrian University of Athens, Athens, Greece A. Provata Institute of Nanoscience and Nanotechnology, National Center for Scientific Research “Demokritos”, Athens, Greece Craig W. Ritchie Edinburgh Dementia Prevention and Centre Clinical Brain Sciences, University of Edinburgh Medical School University of Edinburgh, Edinburgh, UK Julie Seibt Surrey Sleep Research Centre, University of Surrey, Guildford, UK Konstantina Skolariki Bioinformatics and Human Electrophysiology Laboratory, Department of Informatics, Ionian University, Corfu, Greece Surrey Sleep Research Centre, University of Surrey, Guildford, UK Erin Smith The PRODEO Institute, San Francisco, CA, USA Organisation for Economic Co-operation and Development (OECD), Paris, France Stanford University, Palo Alto, CA, USA Global Brain Health Institute, University of California, San Francisco, CA, USA Trinity College, Dublin, Ireland Vassiliki Stamatopoulou Department of Biochemistry, School of Medicine, University of Patras, Patras, Greece Constantinos Stathopoulos Department of Biochemistry, School of Medicine, University of Patras, Patras, Greece Stavros G. Stavrinides School of Science and Technology, International Hellenic University, Thessaloniki, Greece Barry R. Steele Institute of Chemical Biology, National Hellenic Research Foundation, Athens, Greece Antonia Stella National and Kapodistrian University of Athens, Athens, Greece Eleni Stella Tilburg University, Tilburg, The Netherlands Pantelis Stergiannis General Oncology Hospital “Agioi Anargiroi”, Kifisia, Greece

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Contributors

Eric A. Storch Department of Psychiatry and Behavioral Sciences, Baylor College of Medicine, Houston, TX, USA Sotiris K. Tasoulis Department of Computer Science and Biomedical Informatics, University of Thessaly, Lamia, Greece Paraskevi V. Tsakmaki Department of Computer Science and Biomedical Informatics, University of Thessaly, Lamia, Greece Athanasia Maria Tsiampa HAU, Hellenic American Union, Athens, Greece Georgia Tzortsou Department of Informatics, Ionian University, Corfu, Greece Eleni Veroni Department of Digital Systems, University of Piraeus, Piraeus, Greece Dimitrios Vlachakis Bioinformatics & Medical Informatics Team, Biomedical Research Foundation, Academy of Athens, Athens, Greece Genetics and Computational Biology Group, Laboratory of Genetics, Department of Biotechnology, Agricultural University of Athens, Athens, Greece Panagiotis Vlamos Department of Informatics, Ionian University, Corfu, Greece Gerasimos Vonitsanos Computer Engineering and Informatics Department, University of Patras, Patras, Greece Aristidis G. Vrahatis Bioinformatics and Human Electrophysiology Laboratory, Department of Informatics, Ionian University, Corfu, Greece Christos Xenakis Department of Digital Systems, University of Piraeus, Piraeus, Greece Emmanouil Zoulias Faculty of Nursing, School of Health Sciences, National and Kapodistrian University of Athens, Athens, Greece

Part I Neurodegenerative Disease Modeling

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Neurodegenerative Disease Modeling: An Introduction Antigoni Avramouli and Panagiotis Vlamos

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Neurodegenerative Cell Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Biology of Neurodegeneration and Associated Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Abstract

Neurodegenerative disorders are a varied group of ailments that are characterized by the progressive malfunction and death of neuronal cells. Tens of millions of individuals all over the world are currently affected by neurodegenerative diseases such as Alzheimer’s disease, Parkinson’s disease, multiple sclerosis, amyotrophic lateral sclerosis, Huntington’s disease, and a wide variety of other conditions related to brain pathology. It is anticipated that the prevalence of a number of these diseases will continue to rise and will have more than quadrupled by the year 2050 as a result of the aging of the world’s population. Because of the rising incidence of these illnesses and the absence of treatments that are proven to be effective, there is a significant need for novel pharmaceuticals. The creation of dependable assays for researching degenerative processes and identifying the primary agents of cause is the most essential step in the development of remedies for these diseases. This is the stage at which the most progress is made. In this chapter, the current status of modeling in the field of neurodegeneration is described as well as debated. Additionally, the gaps between known clinical A. Avramouli (*) Bioinformatics and Human Electrophysiology Laboratory, Department of Informatics, Ionian University, Corfu, Greece e-mail: [email protected] P. Vlamos Department of Informatics, Ionian University, Corfu, Greece © Springer Nature Switzerland AG 2023 P. Vlamos et al. (eds.), Handbook of Computational Neurodegeneration, https://doi.org/10.1007/978-3-319-75922-7_68

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information and the mechanistic understanding of the primary pathogenic mechanisms underlying neurodegenerative diseases are compared objectively. New directions in the field of neurodegeneration are reviewed as well, along with the potential for these new directions to advance treatment methods and strategies. Keywords

Neurodegenerative disorders · Disease modeling · Neurodegenerative cell models · Mathematical models · Computational models

Introduction Neurodegenerative disorders (ND) are complex conditions that are defined by the slow degeneration and loss of nerve cells. Symptoms such as trouble with mobility (ataxias, dyskinesias, and akinesias) along with mental function (dementias) can arise as a result of the degeneration of neurons and get progressively worse over time. These incapacitating diseases cannot be cured and place a significant burden not only on the individuals who are afflicted but also on their families and on society as a whole. In addition, the incidence of these diseases is growing at a rate that is proportional to the increase in life expectancy seen in both industrialized countries and developing countries. As a consequence of this, there is an urgent requirement for the development of novel treatments that are capable of either halting or reversing the progression of these diseases. To this day, a great number of different cellular and molecular processes that play a role in the development of various illnesses have been identified. In spite of the availability of a large amount of data, which includes in vitro as well as animal models, the molecular pathways behind the onset or advancement of neurodegeneration are still not completely known. This is due to the fact that neurodegeneration is a complex and diverse process. In addition, there is an accumulation of evidence indicating that many forms of ND share common faulty phenotypes at multiple levels. The existence of disease-specific misfolded and aggregated peptides and proteins in damaged brain areas has been related to a number of ND, for example. Because it is currently uncertain whether the formation of aggregates is the source or the outcome of neurodegeneration, this raises the question of whether or not it would be beneficial or harmful to inhibit this aggregation through medical treatment. Not only has the clinical diagnosis become more difficult as a result of this widespread identification of clinical and pathological overlap across numerous ND disorders, but also it has hampered the development of drugs that could prevent neuronal loss in people on a broad scale. The dearth of data in the current scientific literature addressing the molecular components and pathways is the biggest obstacle in the way of gaining a systemslevel understanding of these complex diseases. This is made clear by the difficulties encountered in clinical diagnostics and therapeutic development. Systems modeling

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is a strategy that gives a method for combining current information about these mechanisms as a series of events. This method is used to comprehend the complex and dynamic interplay that exists between multiple biological systems. As a result, a method known as systems modeling is currently being applied in order to investigate the cellular and molecular pathways that are responsible for the pathophysiology of complex multietiological illnesses. It is also increasingly being utilized to better characterize, elucidate, and predict new pharmaceutical targets in a quantitative manner. This application of the technology is growing in popularity. In addition, pharmaceutical companies are making significant efforts to implement modelinformed drug discovery and development frameworks for prediction and extrapolation. This is done with the intention of improving the quality of decisions made as well as their efficiency and cost-effectiveness. In light of the vast variety of ND, efforts are currently being made to build a systems-level understanding of the disease by employing various modeling strategies. The currently available models of neurodegeneration, which were developed at a variety of biological sizes, are able to give light on the mechanisms that are responsible for the pathogenicity of many pathways. The mechanisms that have been uncovered from these models, along with our understanding that we have gained from the literature and other resources on the topic of neurodegeneration, are helping to narrow the gap that exists between the clinical or experimental information that is currently available and the mechanistic explanation of the processes that are behind neurodegeneration. Due to this lack of information and mechanistic expertise, we are able to examine poorly defined pathways and so broaden our understanding of ND modeling.

Neurodegenerative Cell Models Decades of research have been committed to understanding the cellular and molecular underpinnings of ND; nonetheless, the fundamental mechanisms remain opaque despite all of this effort. CNS problems are notoriously difficult to examine in compared to other types of diseases, partly due to the fact that living neurons and the human brain cannot be studied either in vivo or in vitro. In addition, research that utilize postmortem tissues almost often represent the disease’s final stage, and these studies almost never give information regarding the development of the disease. The failure of several recent studies aiming at ND has raised issues about how successfully animal models can be adapted to human patients, driving a demand for better research tools in this field. This is in addition to the ethical problems that are created by the use of animals in clinical research. In order to avoid this issue, an initial screening of potential therapeutic pharmaceutical choices for ND can be carried out with the assistance of a number of different cell models. When a chemical is generated, the first time it comes into touch with a complex biological system is during drug screening with immortalized, nondifferentiated cells. It provides the initial results on the toxicity of the chemical as well as its effectiveness

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in cellulo. In order to facilitate further research, the chemical in question ought to exhibit low levels of inherent cytotoxicity while simultaneously exhibiting high levels of cell survival. Immortalized cell lines are readily available for purchase, are simple to work with, continually grow (which makes it possible to conduct more experiments), and are not expensive to maintain. Due to the large number of human cell lines available, the clinical relevance of the findings has been increased. There are several distinct ways in which cells react to cytotoxic substances. Within the cell, the chemical may go through a metabolic shift that renders it less dangerous and has a smaller impact on the cell’s ability to survive. Apoptosis and necrosis are both potential outcomes of metabolic stimulation. Hepatocytes are utilized for the preliminary cytotoxicity assay, and this is the case regardless of the place of action of the drug. HepaRG and HepG2 cells are two types of immortalized human hepatocyte lines now in use (Dubey et al. 2019). However, the central nervous system is the site of action for drugs used to treat ND. As a result, drug cytotoxicity needs to be tested using a simplified brain cell model. Since SH-SY5Y is a frequent immortalized CNS cell line, the human neuroblastoma cell line is used for this evaluation. Another method for producing cell models is using genetically modified cell lines that are immortalized, and lack differentiation. HEK293 cells, 7 W Chinese hamster ovary (7 W CHO), LUHMES (Lund human mesencephalic), and other immortalized cell lines are frequently used in the generation of genetically engineered models. Since differentiated LUHMES cells are dopaminergic, PC-12 cells are similar to sympathetic ganglion neurons, and SH-SY5Y cells have the ability to produce multiple phenotypes, these cell lines are useful for studying tau pathology in Alzheimer’s disease (AD) as well as the effects of α-syn mutations and other PD-associated genes. Cellular modeling of ND has been advanced through the process of reprogramming human somatic cells (such as dermal fibroblasts, blood cells, and hair follicles) into induced pluripotent stem cells (iPSCs) (Pasteuning-Vuhman et al. 2021). Neurons created from human iPSCs perform significantly better than neurodegenerative models derived from immortalized cells. Somatic cells that are required to produce iPSCs can be obtained from patients who are symptomatic and have a ND. In this way, the genetic history of the disease is incorporated into the cell model, presuming that the original somatic cell sample is representative of the patient’s pathology. As is the case with immortalized cell lines, iPSC-derived brain cells that express either AD or Parkinson’s disease (PD) can be used in conjunction with a wide variety of neurotoxins and research approaches to explore the cytotoxic or neuroprotective characteristics of various compounds. By creating basal forebrain cholinergic neurons, which are significantly damaged in AD, HiPSCs can be utilized to imitate the disease and its symptoms. Following one of the many established protocols for hiPSC differentiation and subjecting hiPSCs to a variety of signaling and growth factors at specific time intervals allows for the generation of cholinergic neurons either directly or after the stage of neural progenitor cells. In a similar way, hiPSCs differentiation into midbrain dopaminergic neurons for the purpose of

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simulating PD is made possible by the provision of signaling molecules that induce a gene expression pattern characteristic of the formation of endogenous dopaminergic neurons. This can be achieved through the use of techniques revolving around the mechanical selection of neural rosettes or the induction of floor plates. Patients suffering from AD or PD may benefit from a more individualized therapy option thanks to the use of hiPSCs, in addition to the increased biological research on the pathophysiology of these diseases. Nonneuronal cells and neuroinflammation play a major part in ND (Kwon and Koh 2020). Coculturing neurons with epithelial, endothelial, and glial cells, all of which may be created from hiPSCs, can also increase the complexity of cell models. Growing these cells in three-dimensional cultures using artificial matrices that imitate extracellular matrix makes the model for ND more difficult to understand (e.g., Matrigel). The interaction that occurs between individual neurons and their surroundings is not replicated in 2D cell cultures, but it is captured by these 3D models. The term “organoids” refers to the three-dimensional organ-like structures that are produced from PSCs. They are able to be cultivated in a microfluidic environment, similar to that of an organ-on-a-chip model. Through the use of this platform, brain organoids that mimic natural immature embryonic neurons can be created and allowed to develop. 3D interactions and cell-to-cell and cell-to-extracellular matrix interactions affect cell proliferation, gene and protein expression, and differentiation. In comparison to 2D cell models, the transfer of potentially dangerous misfolded proteins is possible in brain organoids, which boosts the translational utility of these models. iPSC-derived organoids have also the ability to mirror the organization of the human brain. For example, the cerebral cortex can be used to model AD, and the midbrain can be used to investigate nigrostriatal dopaminergic neurons as a model for PD. In a 3D AD cellular model, Aβ oligomers posed a greater threat than they did in a 2D model. This was attributed to hindered diffusion in the 3D model, which gave oligomers more time to coalesce and resembled in vivo settings. Although 3D models may be promising for bridging the gap between artificial in vitro environments and natural in vivo environments, further research and developments are needed to overcome certain limitations. In the process of drug development, there are several distinct types of cellular models of neurodegeneration, each of which plays an important role in facilitating the identification of the most promising clinical candidates. However, the high percentage of failure that is shown in clinical trials is indicative of their low utility in terms of translation, and it highlights the necessity of further refining cellular assays. The utilization of high-quality cell models, on the other hand, has the potential to cut down on the number of experiments conducted on animals and, as a result, the number of ethical issues and financial burdens connected to the preclinical stage of drug development. Consequently, improvements in screening models make phenotypic screens in neurodegeneration more feasible. Only with the development of more accurate models and the acquisition of a deeper knowledge of the molecular processes that precede neuronal death will it be possible to discover treatments for ND that are both efficient and potent.

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Biology of Neurodegeneration and Associated Models Neurodegeneration is a complex disorder, and numerous articles have been written about the molecular processes that are involved in the beginning stages of the disease and its subsequent course. The molecular processes associated with AD and PD are described in complete interaction maps for AD (AlzPathway – http://alzpathway. org) (Mizuno et al. 2012) and PD (PDMap – https://www.fr.uni.lu/lcsb/research/ parkinson_ s_ disease map) (Fujita et al. 2014). The accumulation of disease-specific misfolded proteins in the brains of elderly people is a prevalent trigger of neurodegeneration, which is commonly associated with cell death and inflammatory damage (Knopman et al. 2021). The cleavage, folding, and clearance of proteins are all dysregulated, which leads to this effect. In AD, neurotoxic Aβ aggregation is caused by aberrant cleavage of the amyloid precursor protein (APP). The dynamics of APP cleavage, the clearance of amyloid beta, and the aggregation of amyloid beta have all been investigated and modeled mathematically. Tauopathy, also known as the accumulation of hyperphosphorylated tau proteins, is another important indicator of AD. An abnormally high level of phosphorylation of Tau causes a disruption in the microtubule-mediated transport that occurs within neurons. This ultimately results in the formation of neurofibrillary tangles in the somatodendritic compartment. Tau phosphorylation and aggregation have also been mechanistically investigated in a number of separate studies. The presence of α-synuclein (α-Syn) inclusion bodies is diagnostic of PD. When there is a large concentration of α-Syn, the proteins misfold and produce Lewy bodies. The relationship between oxidative stress and α-Syn kinetics, the failure of α-Syn degradation machinery resulting in the aggregation of α-Syn, α-Syn trafficking in axons under normal and pathological conditions, and other parameters governing α-Syn aggregation in PD have also all been studied with the help of mathematical models. Protein aggregation is a hallmark of several other ND. Pick’s illness is distinguished from other ND by the presence of Pick bodies; Huntington’s disease is distinguished by nuclear aggregates; Creutzfeldt-Jakob disease is distinguished by mutated prion protein; and familial amyotrophic lateral sclerosis (ALS) is distinguished by superoxide dismutase. The antidote for protein aggregates is the utilization of clearance processes such as protein refolding, disintegration, or transit through the blood–brain barrier. It has been stated that the current ND circumstances are making these clearance tasks more difficult. Misfolded aggregates not only are resistant to degradation, but also they interfere with the function of proteasomes. The processes underlying the deregulation of clearance pathways in AD, PD, and other ND have been investigated using many models. Glucose is the primary source of fuel for the brain’s neurons. The death of neurons can be caused by an improperly controlled energy metabolism. According to the findings of a mathematical model of the ketoglutarate dehydrogenase complex in cerebral energy metabolism, this enzyme complex regulates energy metabolism through the synthesis of ATP and reactive oxygen species (ROS) (Berndt et al. 2012). Glycogen breakdown in astrocytes in response to sensory stimulus is just one example of how important energy metabolism and transport systems are to brain

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tissue metabolism, and there are many other models that support this idea. Oxidative stress is a component of neurotoxicity as well. Oxidative stress encourages the buildup of amyloid peptides in neurons. This can lead to ND. Many models also investigate the mechanisms that underlie fundamental mitochondrial functions, such as the metabolism of energy, the formation of free radicals, disease-related protein interactions, and malfunctions that lead to oxidative stress. The apoptotic process, which ultimately results in the death of neurons, is triggered in these cells by oxidative stress and other cellular stressors. In ND, the primary components of the apoptotic machinery have been defined with the help of models. Synaptic transmission and ion homoeostasis both play a role in the regulation of neuron activation. These two processes are impacted by the metabolism of energy. Different approaches have been taken in order to model ND ion homoeostasis and synaptic transmission. Research on the fundamental processes that can lead to aberrant ND suggests that a genetic component may possibly be involved. There is some evidence that genetic variables, like as variations in the ApoE allele, play a part in the development of diseases. In the ApoE4 scenario, a late onset peak of A is associated with localized neuronal death that can be ameliorated by short-term proinflammatory mediators. When microglia are activated, survival-related activities are impaired, which leads to decreased protein synthesis and cellular energy, which in turn has an effect on the concentrations of neurotransmitters and the activity of neurons. In order to create a mathematical model of inflammation, Dunster et al. (2014) conducted research on neutrophils and macrophages. The reduction of inflammation could be achieved through therapeutic alteration of macrophage phagocytosis; however, this may be contingent on neutrophil death. The processes that underlie the aggregation of microglia and chemical buildup in senile plaques have also been researched in order to gain a better understanding of the inflammation-associated pathophysiology of AD. The activation of inflammatory microglia speeds up the process of neurodegeneration. Microglia have been proposed as a prospective target for the prevention and therapy of AD in a number of different mathematical models.

Conclusion Several models of the underlying mechanisms of ND have been developed. In this chapter, whenever possible to do so, challenges and prospects for future study are addressed; new and extended models and creative experiments to inform models could all potentially be of tremendous benefit for the growth of the field. As these tools are developed and enhanced, we urge their use in situations where they will be of the most use, where their advantages and disadvantages are made explicit, and where they are utilized in conjunction with other models. Models are indispensable due to their adaptability, propensity to produce new hypotheses, and ability to test counterfactuals that cannot be investigated under physiological conditions. Models need to be validated through experimentation, preferably in vivo, because discrepancies between the two may lead to key insights.

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Cross-References ▶ AD Blank Spot Model for Evaluation of Alzheimer’s Disease ▶ Computational Modeling of Neural Networks of the Human Brain ▶ Computational Models and Advanced Digital Techniques in Alzheimer’s Disease ▶ Computational Models in the Prediction of Alzheimer’s Disease and Dementia

References Berndt N, Bulik S and Holzhutter HG (2012) Kinetic modeling of the mitochondrial energy metabolism of neuronal cells: the impact of reduced alpha-ketoglutarate dehydrogenase activities on ATP production and generation of reactive oxygen species. Int J Cell Biol 2012:757594 Dubey SK, Ram MS, Krishna KV et al (2019) Recent expansions on cellular models to uncover the scientific barriers towards drug development for Alzheimer’s Disease. Cell Mol Neurobiol 39: 181–209 Dunster JL, Byrne HM, King JR (2014) The resolution of inflammation: a mathematical model of neutrophil and macrophage interactions. Bull Math Biol. 76:1953–1980 Fujita KA et al (2014) Integrating pathways of Parkinson’s disease in a molecular interaction map. Mol Neurobiol. 49:88–102 Knopman DS et al (2021) Alzheimer disease. Nat. Rev. Dis. Prim 7:33 Kwon HS, Koh SH (2020) Neuroinflammation in neurodegenerative disorders: the roles of microglia and astrocytes. Transl. Neurodegener. 9:1–12 Mizuno S et al (2012) AlzPathway: a comprehensive map of signaling pathways of Alzheimer’s disease. BMC Syst Biol. 6:52 Pasteuning-Vuhman S, de Jongh R, Timmers A, Pasterkamp RJ (2021) Towards advanced iPSCbased drug development for neurodegenerative disease. Trends Mol. Med. 27:263–279

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Computational Modeling of Neural Networks of the Human Brain Ludmila Kucikova, Samuel O. Danso, Graciela Muniz-Terrera, and Craig W. Ritchie

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Brain Connectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Functional Brain Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neuroimaging Preprocessing Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computational Approaches to Modeling Resting State Functional Networks . . . . . . . . . . . . . . Applications to Neurodegeneration Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Considerations and Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Study Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computational Approaches and Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Computational modeling of the neural networks of the human brain has numerous applications including research into neurodegeneration diseases, more specifically Alzheimer ‘s disease and mild cognitive impairment. Changes in functional connectivity as a feature of the neural networks of the human brain might precede alterations in structural connections in Alzheimer’s disease, hence the extensive research in the application of computational modeling to understand the alterations in the functional connectivity. Before functional networks and their L. Kucikova (*) Biomedical Sciences, Edinburgh Medical School, University of Edinburgh, Edinburgh, UK Edinburgh Dementia Prevention and Centre Clinical Brain Sciences, University of Edinburgh Medical School University of Edinburgh, Edinburgh, UK e-mail: [email protected] S. O. Danso · G. Muniz-Terrera · C. W. Ritchie Edinburgh Dementia Prevention and Centre Clinical Brain Sciences, University of Edinburgh Medical School University of Edinburgh, Edinburgh, UK e-mail: [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2023 P. Vlamos et al. (eds.), Handbook of Computational Neurodegeneration, https://doi.org/10.1007/978-3-319-75922-7_63

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alterations can be modeled, optimal data preprocessing steps and computational approaches need to be elected. Approaches to data preprocessing and computational modeling including seed-based, data-driven, and graph theory are discussed. The challenges associated with these approaches and their implications to research and applications are also discussed. Keywords

Neural networks · Neurodegeneration · Dementia · Alzheimer’s Disease · Brain connectivity · Functional brain networks · Networks modeling

Introduction Computational modeling can help to understand different types of brain connectivity with respect to Alzheimer’s disease and mild cognitive impairment, for example, by modeling the functional connectivity in resting state networks, focusing on default mode network. In this chapter, an overview of methods of neural network computational modeling using fMRI data will be provided. Different approaches such as seed-based, data-driven, and graph-based analysis will be discussed. Validation, a step of a modeling approach, will be discussed and examples derived from studies will be provided. The discussion will be followed by some recommendations for future research.

Brain Connectivity To better understand models of neural networks, first different types of brain connectivity that describe the interactions between neurons and neuronal ensembles need to be distinguished. Structural connectivity refers to physical connections between brain areas, while functional connectivity refers to communication between neurons regardless of their structural connections. Effective connectivity is a specific type of functional connectivity which refers to causal interactions between neuronal ensembles and their influence on other neuronal ensembles. Enhancing our understanding of the interactions between brain changes on structural and functional levels may allow researchers to better comprehend the mechanisms of neurodegeneration and its progression. Structural magnetic resonance imaging (MRI) has mostly used measurements of hippocampal and entorhinal cortex to distinguish between healthy individuals and Alzheimer’s disease (AD) patients (Jack et al. 2000). As an anatomical computational approach, voxel-based morphometry measures differences in voxel-wise comparison of brain tissue concentrations between two groups of subjects. Applications of voxel-based morphometry to cerebral gray matter measurements might predict the conversion from mild cognitive impairment (MCI) to AD (Whitwell et al.

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2007). Not controlling for gray matter atrophy threatens validity and reliability of a model of functional networks, specifically in neurodegenerative disorders. Axonal degeneration along white matter tracts accompanies cortical atrophy. By using diffusion-weighted MRI, we can estimate the magnitude and orientation of water molecules diffusion alongside white matter fibers. Differences reported from diffusion imaging studies mainly include reduced fractional anisotropy and increased mean diffusivity in MCI and AD patients compared with healthy individuals (see Filippi and Agosta 2011; Sexton et al. 2011, for reviews). Fractional anisotropy refers to the factor that describes the degree of anisotropy in white matter tracts. Mean diffusivity refers to an average value of the total diffusion within a voxel. Variability of reported brain regions with abnormal fractional anisotropy and mean diffusivity values is greater in MCI than in AD patients. This is commonly explained by MCI group consisting of more heterogeneous symptoms with no global defining criteria (Sexton et al. 2011). In addition to patients’ characteristics, imaging acquisition parameters vary among studies. That might result in potential confounds in proposed models (Sexton et al. 2011). As functional brain changes might precede structural atrophy (Fox and Raichle 2007), functional MRI might be a promising technique for studying neurodegeneration levels in the course of AD based on connectivity measurements. Promisingly, functional network models might alter our view of the progress of degeneration in global and regional brain systems and might serve as a novel biomarker of neurodegenerative disorders.

Functional Brain Networks To establish a promising connectivity biomarker, understanding of both global and local network changes is essential. In the notion of anatomy, global brain changes refer to whole-brain changes. That is, changes between regions which are not necessarily in the local neighborhood. Conversely, local changes refer to changes within a particular region and directly neighboring regions. While studying local changes might bring much detailed information, the subdivision of brain into specific networks eliminates a possible analysis of whole-brain network architecture and interactions between various networks. A different understanding of global and local network changes in the notion of graph theory will be covered later in this chapter. Alzheimer’s as a disconnectivity syndrome. “Disconnectivity hypothesis” is a proposed explanation of disrupted functional connectivity in multiple studies with neurophysiological, neuropsychological, and neuroimaging evidence (Delbeuck et al. 2003; Stam et al. 2007; Supekar et al. 2008; Wang et al. 2007). “Disconnection syndrome in AD” refers to a disconnection of one region from a functionally relevant region, compromising a network. However, this hypothesis has not been conclusively validated as there are no distinct AD-specific lesions (Brier et al. 2014). There is currently no consensus on the timing of the occurrence of disconnection events,

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but it is widely assumed that it happens before the onset of AD symptoms (see Brier et al. 2014, for a review). Considering local regional changes, hippocampus is the main area of interest in multiple studies due to its link to memory disturbances in AD and evidence of the correlates of hippocampal atrophy with cognitive decline (Jack et al. 2000). The right hippocampal reduced connectivity to a set of regions including medial prefrontal cortex and dorso-lateral prefrontal cortex suggests asymmetry of hippocampal activity (Wang et al. 2006). The functional connectivity of the hippocampus with other regions seems to be disrupted already in early stages of AD (Delbeuck et al. 2003) and continue decreasing with the disease progression (Allen et al. 2007). Another local region of interest is posterior cingulate cortex which shows decreased metabolic activity in AD (Minoshima et al. 1997). Posterior cingulate cortex shows reduced connectivity with hippocampus (Wang et al. 2006; Zhang et al. 2009; Zhou et al. 2008) and with praecuneus (Zhang et al. 2009). Reduced connectivity between posterior cingulate cortex and left hippocampus was observed in early stages of the disorder (Zhang et al. 2009), which agrees with the findings of asymmetrical glucose hypometabolism and atrophy in early stages of neurodegeneration (Derflinger et al. 2011; Janke et al. 2001; Loewenstein et al. 1989). Resting brain networks. Multiple regions exhibit synchronous patterns of spontaneous brain activity in the low-frequency fluctuations in the blood oxygen level dependent (BOLD) signal. The low-frequency fluctuations are distributed unevenly throughout the brain, which results in a coherent pattern of activity in brain regions that are functionally connected. This coherent activity is in the frequency interval between 0.01 and 0.08 Hz and reflects changes in blood flow and the ratio of oxyhemoglobin to deoxyhemoglobin. As BOLD activity is not characteristic for a specific experimental paradigm, it has been largely viewed as noise. Biswal et al. (1995) were the first to observe this perfectly organized low-frequency activity in the resting brain using fMRI. Shulman et al. (1997) observed changes in brain activity across many goal-directed tasks during the task-free windows. The observation that this synchronous activity consumes most of the brain’s energy (Raichle and Mintun 2006, for a review) prompted an excessive research into spontaneous BOLD activity. Thus, the importance of low-frequency fluctuations research is mostly attributed to their role in metabolic demands of the resting brain (Raichle and Mintun 2006) and to their significance in organizing neuronal activity (Buzsaki and Draguhn 2004). Default mode network (DMN), salience network, attention network, executive network, sensorimotor network, visuospatial, medial temporal lobe, and dorsoparietal networks all belong to the group of other resting state networks commonly studied in neurodegeneration research (Smitha et al. 2017). DMN is the most widely studied intrinsic connectivity network in AD research. Brain regions involved in DMN are spontaneously active and demonstrate temporal correlations when an individual is not focused on any external stimuli. DMN is therefore, characterized as a task-negative network and is anticorrelated with task-positive networks which are active as a result of task-induced stimuli (Fox et al. 2005). Raichle et al. (2001) originally proposed DMN as the brain default network, based

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on the observations from oxygen extraction factor in positron emission tomography study. Oxygen extraction factor was decreased in the DMN areas in goal-directed tasks and increased in a coordinated fashion at resting state. The authors proposed the first default (baseline) state of adult human brain. A noteworthy overlap between DMN areas and the localization of both amyloid depositions and atrophy (Buckner et al. 2005) motivated substantial research in the relationship between DMN and AD. In AD, functional connectivity is overall decreased in DMN with the disruptions already present in MCI (see Yildirim and Buyukiscan 2019, for a review). This review concluded the occurrence of progressive DMN connectivity disturbances in the course of AD across fMRI studies, with specific connectivity patterns in preclinical and prodromal stages, which are linked with AD risk factors and underlying neuropathology. Methods, tools, and techniques used in DMN research will be described later in this chapter. Compensatory mechanisms. Reduced connectivity is not the only change in resting state functional networks occurring in the course of AD. Increased connectivity in some brain areas suggests that the functional connectivity changes in AD follow a complex pattern. Frontal connectivity networks demonstrate increase in their functional connectivity in some studies. That is often referred to as a compensatory mechanism for reduced temporal connectivity (Gould et al. 2006). Findings suggest that regions with enhanced connectivity might form an executive control network and a salience processing network. For instance, executive, ventral salience and frontoparietal network connectivity was altered in AD patients in comparison with both MCI group and healthy controls. MCI did not show any changes in frontal activity in comparison with healthy controls (Agosta et al. 2012). On the other hand, increased frontal connectivity (Bai et al. 2009) and decreased frontal connectivity (Sorg et al. 2007) in MCI in comparison with healthy controls was reported. Inconsistencies in findings in MCI group findings might be explained by both – different design of studies and by the “cognitive reserve hypothesis” (Stern 2006). Increased frontal activity can be an attempt to maintain cognitive efficiency from the so-called cognitive reserve that is bigger in some patients creating an advantage in performance despite comparable underlying pathology.

Neuroimaging Preprocessing Techniques Resting state functional MRI (RS-fMRI) is a powerful, noninvasive, and widely available tool to investigate the BOLD signal and network organization in the resting state condition. This tool allows us to relate brain functions to topography. In RS-fMRI studies, subjects are not required to perform or participate in any cognitive tasks. As such, this technique provides an insight into neural dynamics that are functionally dissociated from any task. Typically, subjects are instructed to close their eyes or to fixate their gaze on a fixed point and not to think about anything specific, while avoid falling asleep. Before statistical analysis and computation modeling can be performed, neuroimaging preprocessing is a required step to ensure that the assumptions of the analysis are met. This includes normalization, spatial

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correction, and smoothing. Not all the steps of preprocessing are always required, and some additional complementary steps might be necessary to ensure the most suitable preprocessing of images and data for a given study. Within-individual and between-individual differences in a form of brain size, shape, and position are accounted for. Similarly, an optimal signal to noise ratio needs to be considered. Any additional confounding signals such as physiological noise and scanner noise needs to be removed before proceeding to main analysis. Spatial realignment and normalization. Analysis assumes that time course represents a value from a single location. Adjusting for a movement-related artifact is the foremost step as subjects’ movement is likely to cause the biggest proportion of variance in a model. There are several ways of correcting movement-related artifacts. For instance, motional adjustment can be performed by Fourier Transform interpolation which aligns each volume to the mean volume. Alternatively, linear regression or ICA might be performed (see Uddin 2017, for a comprehensive spotlight article). Slice acquisition, interpolation artifacts, spin-excitation effects, and magnetic field inhomogeneity are other possible causes of variance which should be accounted for when building a model. Moreover, analysis assumes that time course is uniformly spaced in time. However, as volumes are acquired slice-byslice, this assumption is violated, and each slice has a different delay. Slice timing correction temporarily shifts the time series of each slice to align them to a specific reference time-point. Previous work examined the relationship between slice time correction and RS-fMRI functional connectivity data and demonstrated no significant interaction (Wu et al. 2011). This might be due to very slow low-frequency signals of resting state data. Thus, slice time correction might not be a necessary preprocessing step in functional connectivity research. As brains across a sample of subjects are expected to differ in shapes and sizes, an important step is aligning them based on a common anatomical space to reduce intersubject variability, or in other words spatially normalize them. One way to achieve this alignment is by estimation of warp-field and application of such estimation with resampling. Alternatively, procedure of matching gray matter with gray matter and white matter with white matter across the sample is frequently available in most of software packages for the brain images analysis. Once, brain images respond in shapes and sizes, they can be registered to an anatomical space to ensure one coordinates system for all the data. The two of the most prevalent anatomical spaces are Montréal Neurologic Institute (MNI; Evans et al. 1993) and Talairach and Tournoux (1988). MNI is based on the series of structural MRI scans of healthy population, whereas Talairach atlas is based on the dissected and photographed brain slices. The disparity between MNI and Talairach brains results in the incompatibility of the findings from the studies employing different co-registration spaces on an anatomical level. Despite MNI availability in common software packages, a significant percentage of functional imaging results have been reported in Talairach space (Laird et al. 2010), making it challenging to compare the findings of these studies. Unlike structural networks, functional networks require a co-registration of functional images and their anatomical reference to maximize mutual information

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(e.g., T2*-weighted echo planar imaging sequence and T1-weighted imaging sequence). Slices of T2*-weighted echo planar images might be out of the phase due to their magnetic field inhomogeneity (Penny et al. 2011). Thus, such co-registration might cause distortions if spatial normalization is not performed in advance. Spatial smoothing. Voxels are averaged with their neighboring voxels so that low-frequency signal is enhanced, and high-frequency signal is removed. Spatial smoothing enhances spatial correlation between voxels by convoluting signal with a Gaussian function. A specific width of such function should be greater than the voxel size according to the Gaussian random field theory. Where applicable, smoothing will increase the validity of assumptions based on the parametric tests according to the central limit theorem. Smoothing ensures increase in signal to noise ration by increasing sensitivity. However, it also reduces the spatial resolution of the data especially near the edges of a brain where brain structures meet non-brain structures. Therefore, some researchers opt out spatial smoothing preprocessing step to avoid spurious synchronization between neighboring voxels and to ensure the maximum resolution at the expense of enhanced sensitivity (e.g., Sanz-Arigita et al. 2010). Removal of nonneural signal. The resting state activity is typically below 0.1 Hz and is not related to physiological noises such as cardiac or respiratory noise. Additional confounds of resting state signal include scanner instability or subjects’ movement. To remove physiological signals, there are four main strategies. Physiological and scanner noises can be reduced by regressing out their corresponding signals from the resting state activity signal through linear regression (Rombouts et al. 2003). High sampling rate can be applied to the overall signal after acquisition in a form of a band-pass filter. Such rate separates frequencies of physiological signal with resting state signal (Biswal et al. 1995). The global signal that is common to all voxels and likely represents nonphysiological noise can be regressed out (Fox et al. 2005). Alternatively, regions that are susceptible to higher physiological activity such as white matter can be inspected and the signal from these regions can be regressed out (Fox et al. 2005; Rombouts et al. 2003). Another option is using independent component analysis to project out the components that correspond to noise.

Computational Approaches to Modeling Resting State Functional Networks First, a baseline condition needs to be characterized and identified, against which other conditions of interest are contrasted. The first level of analysis is performed on an individual level. The second level of analysis is performed on a group level. There are two most commonly used approaches to evaluate resting state networks – seedbased approach and data-driven approach. Alternatively, graph theory might be applied to brain functional connectivity analysis to answer different questions regarding detailed networks’ functions. The primary connectivity analysis methods are summarized in Fig. 1. Commonly used software for resting state pre-processing

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Fig. 1 The summary of the primary connectivity analysis methods. (Original figure)

and analysis include SPM (https://www.fil.ion.ucl.ac.uk/spm), FSL-MELODIC (https://www.fmrib.ox.ac.uk), CONN (Whitfield-Gabrieli and Nieto-Castanon 2012), DPARSF (Yan and Zang 2010), GIFT (Rachakonda et al. 2007), REST (Song et al. 2011), GRETNA (Wang et al. 2015), and GraphVar (Kruschwitz et al. 2015). Seed-based approach. Seed-based approach or model-based approach requires a priori selection of regions of interest (RoIs). BOLD time series of activations from RoIs are then correlated with the BOLD time series of activations from all other brain voxels (other brain regions). Only significant correlations are then selected for the main analysis. A functional network is only formed from positive correlations between voxels. On the other hand, negative correlations suggest that two regions are anticorrelated. However, as a brain region is often involved in multiple functional networks, exploring several networks simultaneously is sometimes essential. Due to a priori selection of the regions of interest, this becomes problematic. Therefore, using seed-based approach might be preferred if a strong hypothesis of the functional connectivity between specific regions is formed a priori and exploration of other networks is not necessary for the research. To obtain a connectivity measurement, seed-based approach uses various metrics such as cross-correlation analysis, statistical parametric mapping, and coherence analysis (Li et al. 2009). Cross-correlation analysis was first introduced to brain connectivity studies by Cao and Worsley (1999). Based on this analysis, if there is a correlation between BOLD time courses of two or more regions, these regions are functionally connected. Statistical parametric mapping was originally used to investigate connectivity in task-based fMRI studies; however, it was also implemented by researchers to investigate resting state connectivity of the DMN (Greicius et al. 2003). Greicius and colleagues used this approach to mimic a stimulus based on selected seed area. This is done by using the averaged voxels in a certain seed as a covariate of interest in the first-level SPM analysis (Friston et al. 1994). Coherence

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analysis (Sun et al. 2004) is a spectral measure that estimates the linear timeinvariant relationship between time series, which allows for the assessment of the correlation between two signals in the frequency-domain. Data-driven approach. Data-driven approach is a model-free, unbiased alternative to analyze fMRI data performed either via decomposition technique or via clustering. First introduced in PET data analysis in form of Principal Component Analysis (Friston et al. 1993), decomposition-based methods extract the original fMRI dataset as a linear combination of vectors and statistically independent components. On the other hand, clustering analyses utilize intensity proximity of the time courses as the basis to separate the data into clusters (see Li et al. 2009 for a review of different methods of clustering analysis). Independent component analysis (ICA) as the extension of Principal Component Analysis is the most commonly used computational method for the functional connectivity analyses. ICA generates fixed number of group-level components for the whole sample either based on spatially independent time courses or temporally independent time courses. ICA reveals hidden factors that underlie non-Gaussian signal by assuming that the components are statistically independent from each other. For instance, choosing n-number of independent components leads to repeating group ICA multiple times, while using randomly resampled data each time to ensure the stability of n spatially independent components across the group. Therefore, several resting state networks can be identified simultaneously based on their spatial patterns. It avoids the biases that are introduced by a priori selection of seeds of interests. ICA evaluates different brain regions and forms networks between the regions with high temporal correspondence in their BOLD activation. ICA is largely influenced by the required number of independent components. Too many components are likely to split one functional network into smaller networks, whereas too few components are likely to combine two or more functional networks. Unsupervised machine learning techniques can help identify the optimal number of components. Statistical approaches. Pearson correlation is one of the most popular statistical approaches to map components/regions and their connections in time series data due to its simplicity. Simple Pearson correlation is sufficient to capture most of the dependence between BOLD time series and create an individual whole-brain functional connectivity map (Hlinka et al. 2011). Pearson coefficient r is computed between the time course of one network component and all other independent components/regions of interest, then r is Fisher z transformed. Converting to z-scores allows for a direct comparison of values in each participant’s maps. To assess grouplevel differences, conventional t-tests, ANOVA tests, and ANCOVA tests are commonly used. Alternatively, dual regression might be used to construct individual components maps based on both spatial and temporal information (Filippini et al. 2009). First, large-scale patterns are identified across the sample using seed-based or data-driven approaches. Resting state networks of interest are identified based on their spatial correlations. Subsequently, spatial regression is performed to create matrices of temporal dynamics for each component of a given network. Temporal regression

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is then performed to estimate subject-specific maps. To find between-subject or group differences, nonparametric permutation tests are commonly used. Software tools use General Linear Model to estimate parameters that could explain the spatially continuous data same as discrete data. Additionally, they use Gaussian Random Field to resolve the multiple comparison problems. Bonferroni correction is too conservative as it assumes the independence of the tests that are performed; however, voxels are not spatially independent. Thus, False Discovery Rate is preferred way to solve multiple comparison problems by controlling for the expected proportion of false positives instead of the accurate number of false positives. To assess a causal relationship of effective functional networks, dynamic casual modeling efficiently generates separate neural activity from hemodynamic and estimates the parameters of such networks and direct connections between regions. The observed parameters are further compared via Bayesian observations. Dynamic causal modeling entails a priori selection of the regions of interests within a particular network; hence, such modeling is confirmative rather than exploratory. The analysis can be done at a group level to infer underlying causal relationships. Graph-theoretical approach. Graph theory is a mathematical construct for complex systems analyses that allows for quantifying summary of whole network properties with respect to integration and segregation. Graphs are data structures that model pairwise relations between network components. Using graph theory provides a general language that enables direct comparison of graphs that describe functional connectivity incorporating connectivity information from the whole network. Based on graph theory, a network can express global and local changes. Global connectivity refers to whether there is a connection between two nodes or not. On the other hand, local connectivity refers to the strength of the connection. When applied to resting state fMRI data, different brain regions represent nodes and functional connections represent edges. To show spatial or temporal dynamics of a network, weights can be assigned to edges of a graph. Additionally, information flow is assigned to edges in effective connectivity research to describe the direction of information. A functional network is represented as a graph that might have assigned weights but does not have assigned directionality. Visually, graphs are represented by a circle for every node and a line that connects functionally connected nodes (see Fig. 2). The local connectivity is visually represented by the thickness of the edge, such as the thicker line, the stronger is the connection between two nodes. Alternatively, graphs can be represented as arbitrary NxN matrices, where each row and column represents one network component (Daianu et al. 2014). Graphs can be further described by their properties (see Fig. 3). Network size represents a total number of nodes on a global level (i.e., brain areas). Degree refers to a number of connections per node and can be measure on global or local level. Clustering coefficient is a global or local measurement of the network segregation. It represents the density of connectivity between nodes. Path length is a global or local measurement of network integration. Betweenness centrality is a global or a local centrality measure of the number of shortest paths that run through a node. Deviation of the global clustering coefficient of a network from that of any random network is

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Fig. 2 Visual illustration of basic graphs: (a) A graph consisting of six nodes N1-N6 and eight edges. The thickness of the edges represents their strength. The connection between the nodes N2 and N6 is the strongest, followed by the connection between the nodes N1 and N6. (b) A directional and weighted graph consisting of six nodes and eight edges. The direction represents the direction of the information flow. The weights represent the temporal (sec) or spatial (mm) distance between two nodes. (Original figure)

Fig. 3 Graph properties: (a) Clustering coefficient: Low clustering coefficient with low connections density (left), high clustering coefficient with high connections density (right). (b) Path length: Low path length (left; e.g., shortest path length from the central node 1 to node 7 is 1), high path length (right; e.g., shortest path length from the central node 1 to node 7 is 5). (c) Degree centrality: The number of links a central node has. (d) Betweenness centrality: The number of shortest paths that run through a central node. (e) Assortavity: assortative network (left), disassortative network (right). (Original figure)

quantified by normalized clustering coefficient. Similarly, the deviation of the global path length of a network from that of any random network is quantified by normalized path length. Assortativity is a correlation of the degrees of two neighboring nodes.

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Fig. 4 A visual representation of randomness-regularity: (a) Random network: low clustering coefficient, low path length. (b) Small-world network: high clustering coefficient, low path length. (c) Regular network: high clustering coefficient, high path length. (Original figure)

Small-world property measures the level of integration-segregation of a network and represents the balance between a random and a regular network. That is, a relationship between clustering coefficient and characteristic path length to minimize information processing cost (see Fig. 4). A network with high clustering coefficient and high path length is regular, while a network with low clustering coefficient and low path length is random. A small-world network exhibits high clustering coefficient and low path length. In the graph theory, hubs refer to central nodes of a given network that demonstrate a high degree, a high centrality, and low clustering coefficient. Thus, they are highly connected regions of a network. Resampling methods. To validate the stability of existing models, resampling methods such as permutation tests, bootstrapping, and cross-validations computationally are used (Chaubey 2000). Such validation is a necessary step after modeling a network using one of abovementioned approaches and before finalizing a computational model. For instance, permutation tests test null hypothesis under all possible rearrangements of the data. Bootstrapping resamples data to create many subsamples. Data characteristics are then obtained from averaging estimates from created subsamples. Cross-validation methods can be divided in exhaustive and nonexhaustive methods. Exhaustive cross-validation methods need to train and validate the model for all possible combinations, therefore are only recommended for small to moderately big datasets. For instance, leave-one-out cross-validation leaves one data point out of the original data sample s, s-1 samples are then used to train the model which is then validated on the left-out point. Similarly, leave-p-out crossvalidation leaves p number of data points out of the original data sample s, s-p samples are then used to train the model which is then validated on the p data points. Nonexhaustive cross-validation methods do not need to compute all possible combinations. To better illustrate different validation methods, some practical examples from several studies will be outlined. For instance, Sanz-Arigita et al. (2010) investigated different properties of resting state networks in AD using a seed-based approach. To

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validate their results, the authors randomly repartitioned AD patients and healthy controls over two groups under the permutation distribution. Koch et al. (2015) used pairwise correlations and structural equation modeling to study the link between amyloid pathology and intrinsic functional connectivity in prodromal AD. Bootstrapping was used on ICA to verify the distribution of the network paths. Alternative leave-one-out cross-validation to evaluate the generalization power of the proposed model for MCI network identification was performed by Jie et al. (2013). The authors left one subject out from n number of subjects and used remaining n-1 subjects for training. They repeated the process for each subject.

Applications to Neurodegeneration Research Computational modeling of neural networks in AD significantly contributes to the general understanding of the overall brain activity as well as the downstream changes related to the disorder. Advances in neuroimaging acquisition, data analytic approaches, and statistical methods resulted in a progress of the depiction of the structural, functional, and effective networks on the different stages of AD progression. This provides not only a new direction of clinical applications in comparing different stages of the disorder but also allows for the prognosis of clinical outcomes modeling (Woo et al. 2017). In particular, the data-driven approach is widely applied in large datasets to answer model-free questions about network connectivity. To be applicable into a clinical setting, predictive models need to be valid, reliable, sensitive, and specific to a given disorder (Castellanos et al. 2013). By using datadriven pattern recognition, predictive models incorporate all available data to simulate the best-fitting outcomes (Reddan et al. 2017). On the other hand, seed-based approach might be applied to a given dataset to answer a question about the connectivity between specific regions. The individual regions can be coupled into networks and the connections between these regions can be derived from the data to obtain within-network connectivity. Seed-based methods are applied to AD research mostly to investigate the connectivity between the regions that demonstrate AD pathology (e.g., hippocampus, posterior cingulate cortex, precuneus). Thus, a previous knowledge of the topology of a network is necessary. For instance, the posterior cingulate cortex showed alterations in functional connectivity with several regions including medial prefrontal cortex, dorsolateral prefrontal cortex, and hippocampus (Zhang et al. 2009). Graph analysis can be used to study the global network architecture of brain, or local changes in specific regions and specific networks. In the global network, SanzArigita et al. (2010) demonstrated changes in both clustering coefficient and longdistance connectivity, indicating a loss of a global information integrations. On the other hand, reduced clustering coefficient and unchanged path length was reported in Supekar et al. (2008). Both studies focused on small-worldness – the relationship between clustering coefficient and path length. The inconsistency in findings might be explained by methodological differences between studies. To investigate correlations between components, Supekar et al. used wavelet correlation, whereas

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Table 1 A summary of the application of methodological approaches used in network connectivity research Methodological approach Data-driven

Advantages Unbiased; model-free

Challenges Optimal number of components; separating noise

Seed-based

Straightforward interpretation; hypothesis-driven

Graph theory

Permitting a detailed quantification of summary measures on global and nodal network levels

Simultaneous examination of multiple networks; selection of RoIs Calculations of some properties in weighted and directional networks

Applications In large data sets; when investigating one/multiple networks; when having an open question about network connectivity In smaller data sets; when investigating connectivity between specific regions

When detailed information about the network is needed

Sanz-Arigita et al. used synchronization likelihood. Additionally, Sanz-Arigita and colleagues opted out spatial smoothing preprocessing step which has an impact on sensitivity. Consistently, both studies report disrupted small-worldness in AD in comparison with healthy controls, interpreted as randomness of networks in AD, along with other studies (Achard and Bullmore 2007; de Haan et al. 2009). Due to its characteristics of minimizing information processing cost while maximizing information integration, small-worldness is an attractive property of graph network in neurodegeneration research (Latora and Marchiori 2001). The economic efficiency of small-world network property is already affected in healthy aging to a certain degree (Achard and Bullmore 2007), which is in line with the interpretations that the processes of functional network disruption are accelerated in AD and further decline as the disease progresses (see Brier et al. 2014, for a review). The summary of methodological approaches and their applications in connectivity research can be found in Table 1.

Considerations and Recommendations Study Characteristics The most common methodological weakness of RS-fMRI connectivity studies is the data source. A good data source is necessary to develop a valid computational model of brain networks. This includes bigger, more inclusive, and diverse samples. Too small dataset threatens validity and reliability of a proposed model and subsequently meaningfulness of the results. There is no blanket recommendation for a required

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sample size as it varies depending on the methods used and number of predictors. Similarly, effect size depends on preprocessing strategies as well as methods for computational modeling (e.g., number of components of a network). Tailored power calculations are highly recommended. For instance, Thirion et al. (2007) recommend a minimum of 20 subjects to have sufficient reliability in task-based fMRI studies. As for resting state studies, higher number of participants is recommended to account for a no-block design. A nonparametric significance assessment with cluster-level thresholding is also recommended. Moreover, preprocessing strategies (Shirer et al. 2015) and the effect of scan length (Birn et al. 2013) should be additionally taken into consideration when conducting power calculations. To delineate the determinants of interindividual variation in the functional connectivity, demographic and environmental factors should be considered. Ethnical background, race, age, and age of onset of the disorder, as well as levels of education and work complexity, should be taken into account as possible factors that might not only impact functional connectivity but also influence applicability of findings to low- and middle-income countries. A more inclusive model of a brain network on a global and local level is necessary. Such model should also incorporate other AD-related changes such as amyloid deposition, grey matter atrophy, inflammation, aerobic glycosis, and glucose metabolism as well as genetic influences such as apolipoprotein E4 gene. A more complex model should additionally include medical history, namely mood disorders, psychotic disorder, depression, anxiety, or other cognitive disorders that might have an impact on the level or perseverance of brain connectivity. Multimodal imaging including a relevant pathology allows for a more specific model. Before full onset of symptoms, AD might manifest in biomarker changes. Preclinical and prodromal stages of AD are the most crucial period to investigate functional connectivity as a possible biomarker of AD. Studies should consider classification of groups based on the factors of neurodegeneration rather than based on distinct categories of MCI and AD which are limiting. More longitudinal studies from the same sample are recommended to ensure a valid comparison of neural networks in the progressive nature of the disease.

Computational Approaches and Statistical Analysis To ensure generalizability of a computational model, comparability of approaches and their direct implications on the results are important. Different preprocessing techniques might influence the results (e.g., implementing spatial smoothing in analysis), and thus, should be considered carefully. The ability of ICA to segregate BOLD signal into multiple meaningful components is useful in identifying the boundaries of functional regions that form a network. However, finding an optimal number of components is challenging as too few components are likely to combine multiple separate networks and too many components are likely to split a network into its subnetworks. Using unsupervised learning methods might resolve this challenge. On the other hand,

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simplicity and straightforwardness of the seed-based method make it an easily interpretable approach. However, as it is entirely dependent on the a priori selection of regions of interest and the strength of correlations between them, it is difficult to examine multiple simultaneous interactions of distinct networks. Alternatively, graph theory measures the integration-segregation of the whole-brain network and its topological properties. As all the abovementioned approaches have their advantages and disadvantages when applied to RS-fMRI data, their applications should be considered carefully, depending on a purpose of an analysis. Machine learning as an application of artificial intelligence offers advantages in computational neuroscience research such as the ability to automatically improve based on the data patterns without being directly reprogrammed. However, such overreliance on the data source might cause problems in generalizability of the results (Pellegrini et al. 2018). The authors identified various factors that might constrain transfer to clinical practice. Robustness and consistency of machine learning methods need to be considered in relation to public and clinically relevant datasets before it can be reliably applied to individual patients, especially as a prediction of a neurodegenerative disorder. Moreover, there are challenges with both sides of the spectrum – too homogeneous or too heterogeneous data. For instance, too heterogeneous data should be managed in a structured way, eliminating a possible algorithmic bias and overfitting models. High variance in a model results in overfit. On the other hand, if a dataset is too homogenous, such as a sample without different ethnic backgrounds, results derived from such dataset are likely to not be generalizable to the whole population. Introducing such biases to a model results in less power and underfit. Validation and test-retest reliability are important and highly recommended steps before using a functional network model as a basis for an effective network analysis. Furthermore, comparing connectivity changes of a network of interest betweenindividuals and between-groups should be supported by the findings from a control network, which is unlikely to change as a result of neurodegeneration (e.g., sensorimotor network in Agosta et al. 2012).

Conclusion Computational modeling of neural networks offers a new insight into brain alterations related to different stages of Alzheimer’s disease. In this chapter, we outlined different approaches of computational modeling and their respective advantages and disadvantages. Seed-based approaches offer a straightforward interpretation; however, they introduce biases into a model. On the other hand, data-driven approaches are biased-free alternatives. For more detailed information about the functional networks and their properties, graph theoretical approach can be applied. Implementing other environmental and demographic factors, more information about data source and other pathological and physiological data from progressive stages of neurodegeneration are recommended to obtain a more inclusive, generalizable and comparable model. Subsequently, resampling methods are necessary to

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validate the stability of an existing model. The implementation of more longitudinal studies that entail changes over time from various stages of neurodegeneration is essential for more comprehensive models.

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Applications of Nanotechnology in Alzheimer’s Disease Maria Chountoulesi, Nikolaos Naziris, Anna Gioran, Aristeidis Papagiannopoulos, Barry R. Steele, Maria Micha-Screttas, Stavros G. Stavrinides, Michael Hanias, Niki Chondrogianni, Stergios Pispas, Ce´cile Arbez-Gindre, and Costas Demetzos

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hypotheses of AD Pathogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. elegans Models of AD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aβ Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tau Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . UPS in AD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Blood–Brain Barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polymer-Based Nanostructures in the Regulation and Treatment of AD Pathologies . . . . . . . . . . Nano-delivery of Drugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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M. Chountoulesi · N. Naziris Section of Pharmaceutical Technology, Department of Pharmacy, School of Health Sciences, National and Kapodistrian University of Athens, Athens, Greece e-mail: [email protected]; [email protected] A. Gioran · B. R. Steele · M. Micha-Screttas · N. Chondrogianni (*) · C. Arbez-Gindre (*) Institute of Chemical Biology, National Hellenic Research Foundation, Athens, Greece e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected] A. Papagiannopoulos · S. Pispas (*) Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Athens, Greece e-mail: [email protected]; [email protected] S. G. Stavrinides School of Science and Technology, International Hellenic University, Thessaloniki, Greece e-mail: [email protected] M. Hanias Physics Department, International Hellenic University, Kavala, Greece e-mail: [email protected] C. Demetzos (*) School of Health, Department of Pharmacy, Laboratory of Pharmaceutical Technology Section of Pharmaceutical Nanotechnology, National and Kapodistrian University of Athens, Athens, Greece e-mail: [email protected] © Springer Nature Switzerland AG 2023 P. Vlamos et al. (eds.), Handbook of Computational Neurodegeneration, https://doi.org/10.1007/978-3-319-75922-7_16

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Polymer-Based Nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dendrimer-Based Nanostructures in the Treatment of AD Pathologies . . . . . . . . . . . . . . . . . . . . . . . . . Dendrimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Biomedical Applications of Dendrimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dendrimer-Based Approaches to the Treatment of Alzheimer’s Disease . . . . . . . . . . . . . . . . . . . Lipidic-Based Nanostructures in Treatment of AD Pathologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liposomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Application of Nonlinear Dynamics for Liposome-Based Therapies . . . . . . . . . . . . . . . . . . . . . . . . Solid Lipid Nanoparticles (SLNs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Small-Angle Scattering Methods in Studying Amyloid Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Alzheimer’s disease (AD) is a neurodegenerative disorder, proved by the accumulation of extracellular amyloid (Aβ) plaques, leading to degeneration of vulnerable brain regions. Till today, the available marked approved medicines still focus on controlling the symptoms and slowing down the disease progression, but unfortunately not curing it. The low drug bioavailability, due to low ability of crossing the blood–brain barrier (BBB), hinders the efficacy of the existing therapies. However, nanotechnology has gained great scientific interest, providing alternative approaches to upgrade the AD treatments, such as by increasing the drug penetrating efficacy to BBB and drug bioavailability, by drug delivery nanosystems and minimizing the adverse effects. In the present chapter, the currently suggested theories on AD development and progression are presented, as well as the contribution of C. elegans AD models to understanding the disease’s mechanisms. Subsequently, the recent advances of nanotechnology in the treatment of AD are discussed, focusing on three different main nanosystem categories, namely polymer-based nanostructures, dendrimers, and lipidic nanosystems. Moreover, useful experimental methods towards the evaluation of the nanosystems and the study of amyloid formation are explored, including physicochemical methods as light scattering and nonlinear dynamic methods. Finally, the future perspectives of nanotechnology field to AD and the emerging challenges are highlighted. Keywords

Alzheimer’s disease (AD) · C. elegans · Drug delivery nanosystems · Polymers · Dendrimers · Lipidic nanoparticles

Introduction Alzheimer’s disease (AD) accounts for up to 80% of dementia cases worldwide and its prevalence is still growing partially due to the expansion of the aging population. Currently, no cure for AD exists and the few available treatments, if prescribed timely, can improve the life quality of the patients mainly providing symptomatic benefits but no prevention or deceleration of the disease progression. Direct and

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indirect costs for healthcare related to AD in the United States are currently estimated to reach $500 billion annually (Weller and Budson 2018). Therefore, there is an urgent need to develop treatments against AD, or even better, to discover biomarkers that will allow prevention or prognosis/diagnosis of the disease before severe neurodegeneration occurs. The remaining question is why despite the intensive effort, we still lack a cure against AD. The complexity of the disease is definitely one of the main reasons behind our poor understanding of the underlying molecular mechanisms. Moreover, there are currently no model organisms that recapitulate all the histological and pathological aspects of AD. Since mice do not develop AD, most mouse AD models carry mutated human genes encoding for the amyloid precursor protein (APP), tau, and presenilin 1 (PSEN1), the main genes involved in AD (Esquerda-Canals et al. 2017). Briefly, APP is a transmembrane protein with an incompletely clarified function that undergoes two cleavages (firstly by β-secretase and then by γ-secretase) to form a 42-residue product that comprises Aβ and tends to misfold, forming aggregates. γ-secretase is a complex comprised among others by a PSEN1 subunit (De Strooper 2003). Tau is a microtubuleassociated protein (MAP) and has been proposed to maintain neuronal projections and to affect synaptic function. Tau hyperphospholylation and aggregation have been associated with impaired neuronal plasticity although the underlying mechanisms are not fully understood (Naseri et al. 2019). Although the existing transgenic AD mouse models have been helpful, “forced” overexpression of AD-related genes can lead to false interpretation of the findings. Moreover, genetic mutations in APP and PSEN1 are linked to a rare (99% of AD cases are sporadic being highly affected by the complex genetics-environment interplay, for which we do not currently have available models (Lane et al. 2018). Finally, no model presents Aβ plaques, neurofibrillary tangles, age-dependent neurodegeneration, synaptic and memory deficits concomitantly but they rather manifest a subset of the above as opposed to AD in humans that is characterized by all of these defects at the same time (Puzzo et al. 2014). Considering the above, it is quite apparent that more effort is needed to increase our knowledge around basic molecular mechanisms governing AD that will lead to improved models useful in developing therapeutic strategies. In this chapter, the currently suggested theories on AD development and progression, and how the study of C. elegans AD models has contributed to our understanding of the disease’s mechanisms are reviewed. Moreover, the chapter summarizes the evidence showing that one of the main proteolytic mechanisms of the cell, namely the ubiquitinproteasome system (UPS), might comprise a promising target for the design of therapeutic strategies against AD. Subsequently, the recent advances of nanotechnology in the treatment of AD are discussed, as efforts to upgrade the AD treatments, for example by increasing the drug penetrating efficacy to BBB and drug bioavailability. Furthermore, three different main nanosystem categories, namely polymerbased nanostructures, dendrimers, and lipidic nanosystems are presented, together with the currently used methods towards their development and evaluation. Finally, the future perspectives of nanotechnology field regarding AD and the emerging challenges are highlighted.

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Hypotheses of AD Pathogenesis AD was described for the first time in 1906 by the German psychiatrist Alois Alzheimer who identified and described a case of the disease in one of his patients (Jarvik and Greenson 1987). Its symptoms can be variable but significant alterations are typically observed in multiple cognitive, functional, and behavioral aspects. Symptoms usually include mood changes, increase of anxiety levels, short-term memory loss, depression, apathy, and withdrawal, while the progression of the disease can induce judgment impairs, disorientation, confusion, aggressiveness, and long-term memory deficits (Atri 2019). Regarding its histopathological hallmarks, AD is characterized by the accumulation of extracellular amyloid (Aβ) plaques and hyperphosphorylated tau that forms neurofibrillary tangles (nonbiodegradable filaments). Additionally, tau-positive neuropil threads and dystrophic neurites are present in combination with activated microglia and reactive astrocytes. Hirano bodies (intracellular aggregates of actin and actin-associated proteins), granulovacuolar degeneration, and cerebral amyloid angiopathy can also be found in patient brains. All these lesions can lead to degeneration of the most vulnerable brain regions due to neuronal and synaptic loss that eventually lead to brain atrophy (DeTure and Dickson 2019). The temporal order by which the various disturbances of protein homeostasis occur as well as their causative relationship to neuronal loss during progression are not yet fully understood. Various theories exist on the causes of AD pathogenesis. The most prevalent one is the amyloid cascade hypothesis. According to this, Aβ deposition is the earliest sign of protein dyshomeostasis in AD, and Aβ deposits can be detected even 15 years prior to symptom manifestation in fAD patients. Consequently, it could be the target of putative therapies to prevent further damage while all other histological changes are downstream events (Bateman et al. 2012). Several therapeutic strategies have been designed based on this hypothesis and include passive immunization of AD patients through administration of exogenous monoclonal antibodies against various Aβ epitopes and conformations (Panza et al. 2019). Nevertheless, multiple clinical trials have either failed or yielded confusing results possibly because the antibodies do not target the correct Aβ epitope and/or conformer or they are administered too late in the disease progress (van Dyck 2018). Nevertheless, it is possible that the amyloid cascade theory needs to be further implemented in order to explain all findings regarding Αβ pathogenicity. For instance, Aβ deposition is found in brains of a significant proportion of elderly individuals that die without ever manifesting AD symptoms indicating that the presence of Αβ plaques is not sufficient to cause the disease (Lane et al. 2018). Moreover, the Aβ soluble oligomer:plaque ratio may be higher in patients with AD compared to asymptomatic ones, supporting the idea that Aβ plaques may act protectively by accumulating harmful Aβ oligomers (Lane et al. 2018). The lack of successful immunotherapies against Aβ has caused seeking of alternative theories that may explain better AD pathogenesis and lead to new therapeutic strategies. Consequently, the tau propagation hypothesis states that tau may be spreading from one brain region to another, thereby attributing “propagon”

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properties to tau (Colin et al. 2020). Posttranslational modifications of tau like phosphorylation and acetylation can interfere with the protein’s microtubule binding properties and induce its misfolding leading to the formation of neurofibrillary tangles (Naseri et al. 2019). Phosphatase, kinase, acetylase, and tau-aggregation modifiers have been extensively tested but in most cases rejected due to toxicity and/or lack of efficacy (Congdon and Sigurdsson 2018). Promising data from animal models have prompted testing of tau-directed passive and active immunization in AD patients based on the assumption that like in fAD, also in sporadic AD, Aβ deposition precedes tau misfolding and therefore targeting tau may be more effective when the disease has already progressed (Congdon and Sigurdsson 2018). Several agents targeting tau are currently under evaluation in clinical trials. Several other hypotheses like the neurotransmitter, inflammatory, and the neurovascular hypotheses have led to numerous clinical trials (Liu et al. 2019). So far, trials with compounds that act as modifiers of the aforementioned factors have not yielded promising pharmacological interventions (Liu et al. 2019).

C. elegans Models of AD C. elegans is a free-living, soil-dwelling nematode that was introduced as a model organism by Sydney Brenner in 1963. It is a 1 mm long, transparent roundworm with a short life cycle and life span (3 days and 3 weeks at 20  C, respectively), an invariant cell lineage and cell fate, and a fully mapped nervous system while the completion of its genome sequence revealed that almost 40% of the nematode genes have a human ortholog (Brenner 1974; Shaye and Greenwald 2011). All these characteristics together with the genetic amenability and ease of transgenic C. elegans generation render it an excellent model to study human diseases. Modeling human diseases in an invertebrate such as C. elegans offers the unique advantage of performing experiments that are not possible with mammalian models such as unbiased forward and reverse genetic screens that may lead to the identification of new genes involved in pathological processes (Link 2006). Finally, C. elegans, as a multicellular organism of small size subjected to simple drug administration (through food intake) and a plethora of scorable phenotypes, offers a wealth of advantages as a model for high throughput screens (HTSs) to identify candidate drugs for AD (Lublin and Link 2013).

Aβ Models Although C. elegans carries the apl-1 gene that is a homolog of the human APP, this gene does not contain an Αβ sequence nor does C. elegans have β-secretase activity to produce Aβ (Alexander et al. 2014). Therefore, similarly to mouse models, overexpression of human Αβ transgenes is necessary. In 1995, Christopher Link introduced the first humanized C. elegans AD model that expressed Aβ1–42 human peptide under a muscle-specific promoter and showed that these animals have

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amyloid deposits that are stained by thioflavin S and cause progressive paralysis (Link 1995). Since then, a cascade of studies has introduced numerous C. elegans models overexpressing Aβ1–42 or Aβ3–42 ubiquitously, in all or subsets of neurons and in muscle cells. These models mostly demonstrate paralysis caused by Aβ-induced toxic aggregates in the muscle or loss of chemotaxis and locomotory defects due to neuronal dysfunction (Griffin et al. 2017). To generate models that offer a direct readout for Aβ-mediated neurodegeneration, expression of Aβ was driven in the glutamatergic neurons of C. elegans that degenerate with age progression in response to Aβ accumulation (Treusch et al. 2011). This model has been particularly effective in identifying genetic mediators of AD that may be translated to humans. For example, neuronal degeneration in this model was reduced upon phosphatidylinositol-binding clathrin assembly protein (PICALM) overexpression, a validated AD risk factor in humans (Treusch et al. 2011). The applicability of the findings in Aβ-expressing C. elegans models is highlighted by several studies. Recently, a systems biology approach has compared transcriptome profiles from nematodes, mice, and humans, and revealed that similar pathways are affected by Aβ expression in all three species (Godini et al. 2019). Moreover, it was shown that a mitochondrial stress response is triggered in worms in the presence of Aβ. Upon its genetic or pharmacological enhancement, amyloid aggregation is reduced resulting in increased fitness and life span. Similar results were revealed in cells and mouse models of AD, thus strengthening the value of AD nematode models even further (Sorrentino et al. 2017). Reverse genetic screens have also been applied on C. elegans AD models with promising outcomes. RNA interference (RNAi) in C. elegans is accomplished simply by feeding the nematodes with bacteria that express gene-specific doublestranded RNA. Therefore, large-scale genome-wide screens are feasible. Almost 8000 genes from a C. elegans RNAi library were found to have human orthologs. These RNAis were tested for their ability to reduce Aβ-induced acute paralysis in a C. elegans model. Although none of the positive hits were orthologs with human genes reported by AD genome-wide association studies, further analysis showed that some of the candidates were separated by a single degree from known modifiers of Aβ toxicity (Khabirova et al. 2014). Finally, C. elegans Aβ models have been applied for drug discovery against AD. So far, there are no large scale HTSs based on C. elegans AD models, but these models have been rather used for the validation of candidate compounds found in screens with, e.g., primary neurons or yeast. For example, a study that screened FDA-approved drugs for their protective properties against glucose-induced toxicity in primary cortical neurons yielded 30 candidate compounds, 3 of which were tested in a C. elegans Αβ model and were found to increase the life span of these transgenic worms (Lublin et al. 2011). Similarly, an Aβ yeast model-based screen revealed a small number of compounds able to ameliorate Aβ toxicity. These compounds were tested in C. elegans expressing Aβ in glutamatergic neurons and exhibited neuroprotective properties (Matlack et al. 2014).

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Tau Models C. elegans has one tau homolog encoded by the ptl-1 gene. Although PTL-1 plays a role in neuronal aging and integrity maintenance as well as organismal longevity, there are no reports on PTL-1 aggregation or fibril formation (Link 1995). Thus, several groups have generated transgenic C. elegans overexpressing human tau. The first tau-expressing lines were introduced in 2003 and they carried either a transgene encoding for the normal human tau or a mutated tau allele associated with frontotemporal dementia with Parkinsonism chromosome 17 type (FTDP-17) under a pan-neuronal promoter. Both transgenes caused progressive uncoordinated locomotion, accumulation of phosphorylated insoluble tau, reduced cholinergic neurotransmission, neuronal defects, and eventual neuronal loss (Kraemer et al. 2003). Expression of the same genes in mechanosensory neurons led to decreased responses to light touch that were exacerbated with time, particularly for the FTDP17 allele, while this functional deficit was accompanied by morphological defects of the neurons (Miyasaka et al. 2005). The transgenic nematodes that express tau under a pan-neuronal promoter have been used in a large RNAi screen that included almost 17,000 genes to identify modifiers of the tau-induced uncoordinated phenotype (Kraemer et al. 2006). With this study, novel genes that prevent tau toxicity were revealed as well as genes previously known to be implicated in tau-induced neurodegeneration. Despite the above positive results, overexpression of mutated tau alleles might not be an appropriate model for tau pathology in AD specifically, but rather for frontotemporal dementia and Parkinsonism. A model that might be more representative for tau modifications in AD was introduced in 2009 expressing human tau and pseudohyperphosphorylated (PHP) tau under a pan-neuronal promoter (Brandt et al. 2009). Both transgenic animals showed age-dependent uncoordinated locomotion but only the PHP-tau-expressing animals had neurodevelopmental defects. Importantly, this study showed that C. elegans is capable of highly phosphorylating human tau making its overexpression relevant for AD studies.

UPS in AD Failure of protein homeostasis is a hallmark of aging, one of the major risk factors for the initiation, establishment, and progression of AD (López-Otín et al. 2013). Neurodegenerative disorders (including AD) are indeed characterized by protein dyshomeostasis while the existing link with perturbed proteasome function has been already suggested (Layfield et al. 2003). On top of that, the accumulation of Aβ aggregates and hyperphosphorylated tau in neurofibrillary tangles suggest that Aβ and tau clearance are impaired in AD. The proteasome is a large multi-subunit enzymatic complex that catalyzes the degradation of both normal and abnormal proteins in an ATP-dependent or independent manner (Ciechanover and Stanhill 2014; Davies 2001). It is comprised by the main complex of the proteasome, namely the 20S core. Binding of a regulatory

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multi-subunit complex, namely the 19S particle, is possible either at one (19S:20S, known as 26S proteasome) or at both edges (19S:20S:19S, referred to as 30S proteasome complex) of the main proteasome core (Papaevgeniou and Chondrogianni 2016). In the ATP-dependent branch of degradation, the protein to be degraded is tagged by a small conserved protein, namely ubiquitin, through the coordinated action of three enzymes, namely E1, E2, and E3 ligases (Papaevgeniou and Chondrogianni 2016). Partially unfolded proteins (like the oxidized proteins) and peptides have been reported to be degraded in an ATP- and ubiquitinindependent manner. In total, the UPS plays a key role in proteostasis maintenance and in several crucial cellular processes like cell cycle progression, proliferation, and apoptosis as it finely regulates the turnover of short-lived, misfolded, and damaged proteins (Voges et al. 1999). The proteasome has been initially involved in the pathogenesis of AD once ubiquitin was identified in senile plaques and neurofibrillary tangles in the brain of AD patients (Perry et al. 1987). Testing of proteasome activities in different brain parts of AD patients revealed decreased levels that verified the link between impaired UPS function and AD (Keller et al. 2000). On top of that, proteasome function has been extensively shown to be negatively affected by aging leading to accumulation of misfolded proteins and thereby contributing to the onset and progression of neurodegenerative diseases (Ciechanover and Kwon 2015). Consequently, the ubiquitin-proteasome system (UPS) has been investigated and its targeting has been suggested as an emerging field of potential therapeutic intervention against AD (Papaevgeniou and Chondrogianni 2016; Xin et al. 2018; Boland et al. 2018). A vicious circle between proteasome function and Αβ peptide is established; the proteasome plays a key role in Aβ turnover but at the same time Aβ oligomers inhibit proteasome activity contributing to the age-related pathological accumulation of Aβ (Tseng et al. 2008). More specifically, various ligases have been shown to ubiquitinate Aβ, while the Aβ peptide has been also shown to be a competitive substrate for the chymotrypsin-like activity of the 20S human proteasome (Hong et al. 2014). Consequently, proteasomes seem to play a role in the degradation of both non-ubiquitinated and ubiquitinated Αβ species. On the other hand, elegant mechanistic analyses recently showed that Αβ oligomers inhibit the 20S core through allosteric impairment of the core gate where the substrate is supposed to bind in order to pass into the 20S catalytic sites (Xin et al. 2018). Moreover, enhancement of proteasome function in a mouse model of tauopathy has led to reduced aggregated tau levels with downstream improvements in cognitive performance (Myeku et al. 2016). The tight correlation between Aβ, tau, and the proteasome has led to the hypothesis that the proteasome may be the link between Aβ and tau pathology further supported by a study showing that tau clearance following Aβ immunotherapy is proteasome-dependent in a transgenic AD mouse model (Oddo et al. 2004). C. elegans has been proven to be a very useful tool in the dissection of pathways that regulate UPS function as well as in the discovery of compounds that possess UPS modifying properties (Papaevgeniou and Chondrogianni 2014). Importantly,

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overexpression of proteasome subunits (rpn-6 and pbs-5) in C. elegans has shown that enhanced proteasome activities can extend the life span of the organism and protect from proteotoxic stress and Aβ aggregate-induced toxicity (Vilchez et al. 2012; Chondrogianni et al. 2015). Apart from the enhancement of proteasome function through genetic means, several studies have revealed compounds that can activate the proteasome and lead to reduction of AD-related protein toxicity in C. elegans often with similar implications in mammalian cells and/or whole organisms. For example, two largely studied natural compounds, namely quercetin and resveratrol, have been shown to reduce Aβ aggregation and the consequent paralysis in C. elegans AD models in a proteasome modulation-dependent manner (Regitz et al. 2014, 2016). Resveratrol was also found to reduce Aβ and phosphorylated tau pathology in the hippocampus of a transgenic AD mouse model with an associated increase of proteasome protein levels and activity (Corpas et al. 2019). Finally, 18α-glycyrrhetinic acid, a diet-derived compound that enhanced proteasome function in an Nrf2-dependent manner in human primary fibroblasts (Kapeta et al. 2010), decelerated paralysis and Aβ deposition in C. elegans AD models (Papaevgeniou et al. 2016). In agreement, the same compound conferred similar protective effects in human neuroblastoma and murine primary cortical neurons (Papaevgeniou et al. 2016). Conclusively, C. elegans AD models have been shown to be able to lead the way in the identification of genetic or pharmacological interventions that may ameliorate Aβ and tau toxicity by modifying positively the UPS.

The Blood–Brain Barrier Therapeutic strategies for the treatment of AD require the development of pharmacologically active platforms which combine bioactive compounds and appropriate drug delivery systems which are able to penetrate the blood–brain barrier (BBB) and reach the targeting site (Patel et al. 2009; de la Torre and Ceña 2018). As the primary interface between blood and the extracellular fluid in the central nervous system (CNS), the BBB is a unique, dynamic, and complex structure acting as physical, physiological, and biochemical barrier that drastically limits what can enter the brain, making it difficult to employ normal drug delivery methods such as oral dosing of specific drugs and other materials for CNS disorders (Xu et al. 2019). Consequently, the regulatory aspects of the BBB have a significant impact in the pharmacotherapy of AD as well as other neurodegenerative conditions (Beg et al. 2011). The BBB comprises a microvasculature system (Fig. 1) with an average surface area of between 12 and 15 m2 and capillaries that can exceed 600 km in length in adult humans, although in the degenerative process associated with AD the length of this network is reduced and capillary degeneration drastically reduces not only the transport of nutrients and essential substances but also the clearance of neurotoxins such as Aβ (Wong et al. 2019). The main constituents of the BBB are microvascular endothelial cells (EC) which are surrounded by extravascular components including astrocytes, pericytes, and a

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Fig. 1 Schematic illustration of the blood–brain barrier. (Adapted from Xu et al. (2019). Reuse permitted under CC BY-NC)

noncellular component, the basement membrane with the following specific functions: • Brain microvascular endothelial cells (BMEC) form the walls of the blood vessels and monitor the movement of molecules and ions into the brain and, since these cells are lipophilic, compounds in the hydrophobic environment of blood are impeded from passing through. • Astrocytes are located on the basement membrane and play a very important role in the production of factors to support the BMECs in the maintenance and modulation of the BBB. They can also control the passage of immune cells from blood to brain (Volterra and Meldolesi 2005). • Pericytes are mural cells covering capillaries in the vasculature and help to regulate critical functions by maintaining tight junctions and offering overall protection of the integrity of the BBB (Daneman and Prat 2015). • The basement membrane (BM) is a unique form of the extracellular matrix consisting highly organized protein sheets indispensable for the integrity of BBB (Xu et al. 2019). The BM plays an important role in signaling transduction process by contributing to the control of movement of molecules from blood to brain (Daneman and Prat 2015). Supplemented by various efflux proteins and enzymes (de la Torre and Ceña 2018), the BBB therefore protects the CNS from the influx of toxic substances and is crucial in regulating the flow of nutrients and waste. The BBB regulates the movement of small molecules or macromolecules from blood to the extracellular fluid in the CNS of the brain with great selectivity. On the one hand, the BBB permits selective transport of substances that are essential for

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brain functions such as glucose, oxygen, amino acids, or endogenous hormones, peptides, while, on the other hand, it protects the CNS from exogenous potentially neurotoxic compounds (Wong et al. 2019). The means by which a substance can cross the BBB depend on its physicochemical properties, namely size, liposolubility, and charge (Wong et al. 2019) (Fig. 2). Passive transcellular crossing directly through the endothelial membrane is possible only for small highly lipid soluble molecules with a molecular weight under 400–500 Da (Wong et al. 2013, 2019; Alam et al. 2010; Fong 2015), so that, as a result, about 98% of small active compounds and large molecules are prevented from passing into the brain (de la Torre and Ceña 2018). The passage of other compounds is achieved by active transport means such as: a) Carrier-Mediated Transporters (CMT): In this pathway, compounds are bound to a specific transporter on the membrane surface. This triggers conformational changes that allow passage through the BBB (Chen and Liu 2012). For example, glucose uptake is achieved by means of GLUT1, a glucose-transporter, a recent study showing a correlation between neurodegeneration and GLUT1 reduced brain levels (Winkler et al. 2015). Other transporters localized on luminal and abluminal membranes of BMECs have also been reported for the transport of amino acids such as valine, histidine, alanine, serine, cysteine, etc. b) Absorptive-Mediated Transcytosis (AMT): Endocytosis is initiated by electrostatic interactions of positively charged molecules such as peptides and proteins with negatively charged parts of the membrane which then permit transcytosis (Bickel et al. 2001). This pathway for BBB penetration is characterized by very low specificity but better capacity. c) Receptor-Mediated Transcytosis (RMT): This route is used by a wide range of large molecules such as proteins, hormones, and the majority of drug delivery systems. The mechanism of transportation is based on binding with specific receptors of the endothelial cell membrane. The receptor/large molecule complex that is formed can then cross the endothelial “wall” and the procedure of exocytosis is initiated (Chen and Liu 2012; van Rooy et al. 2011). This is the main pathway employed by drug delivery systems involved in the therapy of AD. The reverse process by which toxic compounds are removed from the brain are dependent on different mechanisms of the BBB. Efflux pumps (P-glycoprotein [P-gp], ATP-binding cassettes, multidrug resistance-associated proteins [MRP]) located on the membrane of BMECs act as strong “clearance” factors for toxic substances, and return unwanted substrates back into circulation (de la Torre and Ceña 2018; Temsamani et al. 2000; Wang et al. 2019). The problem of ensuring drug penetration into the brain has necessitated the development of approaches to circumvent the protection provided by the BBB (Garbayo et al. 2012). Invasive methods, such as ultrasound, radiotherapy, as well as biochemical or osmotic disruption, open up the BBB by disrupting its tight junctions (Patel et al. 2009). However, due to the high risk of damaging the integrity of the brain, such procedures have generally only been applied to treat special

Fig. 2 Pathways for BBB penetration. (Adapted and reproduced with permission from Elsevier Publishers Ltd.: Chen and Liu (2012))

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situations such as cerebral cancer or traumatic injury (Kwon et al. 2016). Therefore, much effort has been focused on the development of noninvasive routes and techniques which facilitate the passage of pharmaceuticals through the BBB and then reach the specific target site in order to have the desired therapeutic effect (Garbayo et al. 2012). Among the methods that have been examined are novel nanotechnological platforms which involve chemical and biological modifications of conventional drugs (Mignani et al. 2017; Naqvi et al. 2020). Liposomal drug delivery, for example, has emerged as an attractive alternative to increase the lipophilicity of drugs and to complement conventional chemical lipidization of small molecules in order to improve the permeability of drugs through the BBB. Likewise, other nanotechnological systems, such as polymeric nanoparticles, solid nanoparticles, micelles, and dendrimers, have been devised which involve adaptations of conventional drugs so as to enhance their transport from blood to brain. These adaptations include (i) cationization for triggering the AMT process and (ii) modifications which mimic either small nutrients (amino acid, hexoses, vitamins) to activate the CMT or endogenous large molecules (transferrin, lactoferrin, neuropeptides, lectins, insulin, insulin-like growth factor) to activate the RMT system (van Rooy et al. 2011). The recent literature contains many diverse examples of the development of promising nanotechnological approaches for the delivery of neuroprotective drugs, and it is often difficult to determine which system is the most suitable (Naqvi et al. 2020). Moreover, nanoparticles can be administrated through various routes apart from the systemic administration, such as the intranasal one, for example, in cases where the nose-to-brain delivery is desired. In the following paragraphs, different literature cases on nanoparticles and AD are being examined, focusing on three different categories of nanoparticles, namely polymer based, dendrimer based, as well as lipid based. In addition, useful experimental methods towards the evaluation of the nanosystems and the study of amyloid formation are explored.

Polymer-Based Nanostructures in the Regulation and Treatment of AD Pathologies Polymers are unique molecules that can create soft and complex nanostructures with multifunctionality and stimuli-responsiveness (Cabane et al. 2012). In aqueous media, they can spontaneously self-assemble into vesicles (Zhu et al. 2017), coreshell micelles (Torchilin 2006), and various other shapes by the exploitation of amphiphilic block copolymer architectures. They can also be used in the form of nanostructured hydrogels (Lee and Kim 2018) or nanogels (Soni et al. 2016) by chemical and/or physical cross-linking. Amphiphilic copolymers take part in drug nanoformulations in order to solubilize hydrophobic drugs and this way increase bioavailability and therapeutic effectiveness of the drugs. Additionally, charged macromolecules (i.e., polyelectrolytes) can interact with proteins and DNA via electrostatic interactions in applications of biomacromolecule transportation, separation from solution, and bio-sensing (Semenyuk and Muronetz 2019). These

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aforementioned realizations of macromolecular nanostructures that are widely used in biomedical and pharmaceutical applications owe their effectiveness on the great variety of both polymer chemical characteristics and architectural and conformational properties. Polymeric structures at the nanoscale have been extensively studied in terms of their individual morphology, dynamic properties, and interactions. Characteristic examples are the investigations of interactions between linear polyelectrolytes, coreshell polyelectrolyte micelles (Papagiannopoulos et al. 2016), and polyelectrolyte interfaces (Becker et al. 2012) with proteins. The broad field of macromolecular chemistry and soft matter physics naturally invites researchers to explore the possibilities in understanding and treatment of brain diseases such as AD (Hadavi and Poot 2016).

Nano-delivery of Drugs Nanoparticles of synthetic or biological macromolecules have traditionally been used in targeted drug delivery against cancer and neurodegenerative disorders (Patra et al. 2018). This includes the treatment and improvement of AD conditions as nanoparticles have the ability to overcome the BBB (Cacciatore et al. 2016). Nanoparticles with sizes below 200 nm sustain drug delivery in time and are capable of transport within the cells (Gamisans et al. 1999; Calvo et al. 2001). Treatment with rivastigmine is widely practiced in order to ameliorate clinical manifestations of AD. These treatments are based on frequent administration either orally or by transdermal patches. Errors in dosing and problems with compliance are related with these routes and may lead to undesired side effects. Formulations of rivastigmine were prepared in phase-sensitive systems using poly(lactic-co-glycolic acid) and poly(lactic acid) dissolved in mixtures of benzyl benzoate and benzyl alcohol which are biocompatible organic solvents (Lipp et al. 2020). The aim was to produce a system that could be administered by a single subcutaneous injection and sustain controlled release for an extended time period. Injection of the aforementioned solutions into aqueous medium creates a gel-like depot with flexible shape as the organic solvent diffuses in water. The release of the hydrophobic therapeutic compound is defined by its diffusion through the polymer phase and the degradation/ hydrolysis of the polymer. Polymer concentration, mass ratio of the two polymers, and concentration and hydrophobicity of the drug are parameters that could be used to tailor the release profiles. The studied rivastigmine formulations prolonged the release for 7 days. This potentially reduces drug level fluctuation in time and improves life quality and compliance of AD patients (Lipp et al. 2020). The neuroprotective ability of the phytopharmaceutical compound piperine has been reported (Elnaggar et al. 2015). However, its effective delivery with oral administration is compromised by its hydrophobicity and pre-systematic metabolism. The targeting of piperine to the brain has been proposed by the formulation of the drug inside chitosan nanoparticles and administration via the intranasal route. The mucoadhesive chitosan nanoparticles were synthesized by cross-linking with

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the aid of tripolyphosphate. Their optimum size, polydispersity index, and zeta potential (indicative of the surface charge) were about 250 nm, 0.24, and 56 mV, respectively, showing charged particles with well-defined size. Sporadic dementia of AD type was induced in Wistar rats that were subsequently tested in terms of behavior and brain biochemical analysis. A dose decrease by 20 times was achieved in comparison to the oral dose. Moreover, a dual mechanism was reported, i.e., inhibition of esterase acetylcholine and antioxidant activity (Elnaggar et al. 2015). Biopolymer nanoparticles based on mango gum were synthesized as potential nanocarriers for drugs targeting the central nervous system. Nanoparticles in size of about 100 nm were produced and they were found to successfully deliver the AD drug donepezil to the brain. The very effective approach for gelation in polysaccharides, ionic gelation, was employed in combination with cross-linking in emulsion (Jakki et al. 2016). In an example of mixed polysaccharides, the widely used complexation between alginate and chitosan has been used to form nanoparticles that could deliver the bone morphogenic protein (BMP) peptide in the form of the small BMP peptide SpBMP-9 (Beauvais et al. 2016). The viability of the human neuroblastoma (SH-SY5Y) cells increased and their differentiation to mature neurons was promoted (Lauzon et al. 2018). PLGA-b-PEG diblock copolymer-based nanoparticles were loaded with the diabetes drug pioglitazone after dissolving in a mixture of organic solvents and injection into the aqueous solution of the diblock copolymer by the aid of the tween 80 surfactant. The drug nanoparticles were shown to penetrate mucosa surfaces and the authors proposed the particular drug delivery system for nasal administration as nasal mucosa is the most convenient route to treat AD (Silva-Abreu et al. 2018). Polymeric nanoparticles for AD treatment studies are customarily based on synthetic polymers such as poly(lactic-co-glycolic acid) (PLGA), poly(glycolic acid) (PGA), and poly(caprolactone) (PCL), and biopolymers such as chitosan and gelatin. The ability of the nanoparticles to cross the BBB is enhanced by the use of surfactants (Wilson 2009). Intranasal administration of PEG-b-PLGA nanoparticles coated with lectin and loaded with a growth factor improved memory and spatial learning in rat AD conditions (Zhang et al. 2014). Growth factors that are administered by the aid of polymeric nanoparticles has shown promising effects on AD animal model pathophysiology (Lauzon et al. 2015). Loading of growth factors on chitosan nanostructures has been achieved both on chitosan in the dissolved state and in nanoparticle formulations. The growth factors BMP-2 (Lai et al. 2013) and fibroblast growth factor (Tang et al. 2010) were successfully loaded on chitosan nanocapsules showing controlled and prolonged release. Brain-derived neurotrophic factor permeation into the brain of rats was greatly facilitated by the aid of chitosan (Vaka et al. 2012). Nanoparticles that are based on poly(lactic-co-glycolic acid) and poly(butylcyanoacrylate) have been used in AD treatment showing that the choice of polymer could be used to tune the release kinetics and encapsulation efficiency of rivastigmine (Joshi et al. 2010). Core-shell nanoparticles of a polystyrene (PS) core and a poly(butyl-2-cyanoacrylate) (PBCA) shell were prepared as vesicles containing the thioflavin T and

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thioflavin S drugs. These nanoparticles attract Aβ fibrils and are controllably biodegradable in the cerebral environment (Siegemund et al. 2006). The size of the nanoparticles was measured by dynamic light scattering and was found between 90 and 100 nm. Fluorescent spectroscopy revealed the significant increase in fluorescence intensity (resulting from the drug) upon encapsulation (Biancalana and Koide 2010). The model drugs were confirmed to target Αβ fibrils after the enzymatic biodegradation of the nanoparticles’ shell after intracerebral injection in APP/PS1 mice with age-dependent β-amyloidosis. These nanosystem offers a promising template for tracing and clearance of Αβ fibrils in the brain (Siegemund et al. 2006).

Polymer-Based Nanostructures Polymers in aqueous media have the ability to interact via electrostatic interactions, hydrophobic interactions, and hydrogen bonding. They therefore may be associated in structures that have sizes in the range of 10–1000 nm and interfere with the selfassociation of other macromolecular (peptide, proteins, etc.) entities in solution. Synthetic and biological polymers have the ability to interact nonspecifically with amyloid peptides in multiple manners based on their size, charge, and hydrophobic content. Electrostatic interactions are the main force that acts between polymers and amyloids, whereas hydrophobic interactions and hydrogen bonding enhance these forces. Amyloidogenic proteins contain amino acids that may be positively charged (e.g., lysine) or negatively charged (e.g., aspartic acid). This way, as in all proteins, the overall charge of the proteins is pH tunable because of the weak acidic or basic character of the charged amino acids. There is a certain pH value for every protein where its overall charge is zero, the so-called isoelectric point (pI). However, positive and negative charges are distributed on the surface of the proteins giving them the ability to interact with both positive and negative compounds (Kayitmazer et al. 2007, 2013) even when their net charge is zero. The aggregation of amyloidogenic proteins is affected by macromolecules as DNA and heparin sulfate (Huang et al. 2014). In more detail, the rate of the formation of amyloid fibrils can be tuned by the size of the polymer and the overall charge of the protein. It has to be mentioned that the protein-polyelectrolyte interaction is more intense when the protein is in the aggregated state (Abraham and Nardin 2018). Poly(amino acids) have been reported to interact with human α-syn (Narkiewicz et al. 2014), whereas nucleic acids interact with Aβ, tau, and prion peptides affecting their association (Ahn et al. 2000). Chitosan has a positive charge at acidic pH and has been reported to decrease the amount of Aβ fibrils (Liu et al. 2015) and poly(ethyleneimine) accelerates aggregation (Assarsson et al. 2014). The inherent hydrophobic and electrostatic characteristics of nanoparticles are widely regarded as critical factors that define the inhibition of fibrillogenesis in Αβ. In a recent study, the effect of the surface charge of nanoparticles with similar hydrophobic content was investigated (Liu et al. 2016). The nanoparticles were prepared with the same percentage of hydrophobic monomer N-tbutylacrylamide

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and varying percentages of charged, acrylic acid, and thermoresponsive, N-isopropylacrylamide, monomers. The system showed overall very good inhibition of the fibrillogenesis of Aβ42 while it reduced its cytotoxicity. Remarkably, an optimum value of negative surface charge density was found and it was concluded that at this value, there is a balance between the hydrophobic attraction that immobilizes the peptides and the electrostatic repulsion that leads to stretching of the peptides. This mechanism effectively hinders β-sheet formation (Wei and Shea 2006) which is a prerequisite for on-pathway fibrillation. In AD pathophysiology, the Αβ prefibrillar oligomers are considered as mediating factors. The compromised synaptic function and neurotoxicity are connected to these oligomeric Αβ aggregates and not with Αβ monomers or plaques (Gunther and Strittmatter 2010). Cellular prion protein (PrPc) interacts with the oligomeric Αβ peptides and facilitates AD and transmissible spongiform encephalopathy. The negatively charged polymer poly[4-styrenesulfonic acid-co-maleic acid] (PSCMA) was found to associate specifically with the cellular prion protein (PrPc), inhibit PrPc/ Αβ aggregation, stop the Aβ peptides from binding to neurons, and cancel the production of scrapie conformation of the prion protein (PrPsc) (Gunther et al. 2019). Electrostatic interactions have been also utilized for the adsorption of Αβ peptides to the positively charged polymer belt of the polymethacrylate-copolymer (PMA) nanodiscs. PMA forms nanodiscs in aqueous media by mixing with lipids (Yasuhara et al. 2017). The association of Aβ with the nanodiscs interferes with Αβ aggregation and regulates its kinetics by trapping intermediate aggregates (Sahoo et al. 2018). The Aβ oligomers that were introduced to SH-SY5Y with PMA-nanodiscs had less toxicity than in the case with no nanodiscs. Nanogels are sub-micrometer scale nanoparticulate hydrogels that combine the enhanced hydration and multifunctionality of hydrogels with the nanocarrier and nanoformulation advantages of nanoparticles. Intense research is being devoted on tuning nanogel properties in drug loading and release and applying on brain diseases including AD (Sabir et al. 2019). Hyaluronic acid has been modified by epigallocatechin-3-gallate (EGCG) and curcumin in a work that aimed at the inhibition of Aβ aggregation (Jiang et al. 2018), thus being a promising means to prevent and treat AD (Jiang et al. 2018). EGCG has a proven anti-amyloid action by non-covalent and nonspecific interactions (Giorgetti et al. 2018). Curcumin has demonstrated the capacity to prevent Aβ and tau oligomerization, and lead to aggregation into nontoxic oligomers (Rane et al. 2017). These two molecules belong to the class of natural polyphenols, and they are safe and nontoxic. They have chemical structures that resemble each other while their aromatic rings interact with the amyloidogenic protein aromatic residues hindering aggregation. Modification with only one of the components leads to dispersed hydrogel phases in the case of EGCG and nanogels in the case of curcumin in aqueous media. The dual modification also leads to nanogels. The synergistic effect of the two components leads to significantly higher inhibitory effect in comparison to the hyaluronic acid structures modified by only one component. The nanogel structure that is induced by the conjugated curcumin provides additional inhibitory effects that are related to the morphology itself. The network allows for an isolation effect that prevents Aβ molecules to interact with each other.

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Additionally, the Aβ peptide conformation is stretched by strong Aβ-Aβ and Αβ-hyaluronic acid electrostatic repulsion when Aβ peptides are immobilized on the nanogels via hydrophobic interaction with curcumin. This change in morphology leads to off-pathway aggregations (Jiang et al. 2018). The irreversible damages that are caused by the early abnormalities in microglia facilitate the development of AD before symptoms emerge. The treatments at late stages of the disease are on the other hand of low effectiveness as they act after pathological symptoms appear. Strategies that attack the loss of the acetic choline neurotransmitter, neuron damaging and protein aggregation, perform on AD only when the disease is already at a late stage (Lu et al. 2019). The immune cells of the brain, microglia, are delicately controlled in number and function by the cerebral environment. In AD conditions, microglia priming is induced, which is a phenotype with unconstrained inflammatory response. A system of polymeric micelles with embedded reactive oxygen species (ROS) has been proposed for the regulation of the cerebral microenvironment in AD by facilitating microglia modulation (Lu et al. 2019). The amphiphilic copolymer poly(ethylene glycol)-b-polylysine (PEG-pLys) was synthesized by a ring-opening reaction. The amine side-groups were conjugated with phenylboronic groups inducing hydrophobic character on the pLys block (now denoted as pLysB). This hydrophobic modification allowed the association/encapsulation of the water-insoluble compound curcumin. The synthesized macromolecules were further designed to have properties of RAGE (receptor for advanced glycation end-products)-targeting, by adding a small peptide termed Ab that has the amino acid sequence of the binding domain of Αβ protein. Introduction of hexynoic acid to the C terminal of the peptide was achieved in order to provide an alkynyl group and perform a click reaction with PEG-LysB. Oxidative stimuli (oxidative stress) trigger the phenylboronic group of the hydrophobic segments and lead to hydrolysis and subsequent release of the ROS-scavenging macromolecular group and curcumin. The micelles are able to target aggregation of Aβ and tau and at the same time cluster around abnormal microglia in an early phase of AD. ROS and loaded active compound act synergistically in order to modulate the microglia function, decrease Aβ aggregation, and have a positive impact on cognitive functions as it has been illustrated on AD model mice (Lu et al. 2019). PEGylated nanoparticles were developed with the purpose to accumulate the Αβ1–42 and eliminate from blood circulation by the so-called “sink effect” and reverse the effect of AD on the memory of transgenic mice. The biodegradable nanostructures were functionalized with a monoclonal anti-Αβ antibody. The strong affinity of the streptavidin-biotin pair (Le Droumaguet et al. 2012) was exploited in order to end-functionalize the PEG chains of the core-shell particles with the antibody (Fig. 3). The nanoparticles were able to reduce the presence of amyloids and protect the memory of the mice with AD (Carradori et al. 2018). A significant improvement of the effectiveness of the approved AD drug memantine, both in increasing its action and reducing its side effects, was achieved by loading to PLGA nanoparticles. The biodegradable nanoparticles were

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Anti-Ab1-42 Ab

SAv

PEG

= Rhodamine B

Vitamin B7

Fig. 3 Multifunctional fluorescent PEGylated nanoparticles decorated with anti-Aβ1–42 monoclonal antibody using the streptavidin-biotin pair. (Adapted with permission from Le Droumaguet et al. (2012). Copyright (2012) American Chemical Society)

synthesized with emulsion methods and they were subsequently PEGylated. Monodisperse nanoparticles in the order of 150 nm in diameter with negative surface charge were obtained. The nanoparticles showed an initial burst drug release and a subsequent slow release of the drug. The controlled release of the second stage was due to the entrapment of the drug in the interior of the nanoparticles. The cell viability in brain endothelial cells and rat astrocytes was higher than 90%. In vitro and in vivo studies proved the ability of the colloidal particles to cross the BBB. The nanoformulations were designed for oral administration, and the distribution of the nanoparticles in the target tissue, i.e., the brain of APPswe/ PS1dE9 mice, was confirmed by labeling with the fluorescent probe rhodamine (Sánchez-López et al. 2018). Phytol-loaded PLGA nanoparticles with size at 180 nm with smooth and nonporous surface have been manufactured and resulted in the controlled release of the pharmaceutical compound. Inhibition of the enzyme cholinesterase was tested as this effectively blocks the hydrolysis of acetylcholine and reverses the cognitive capabilities of patients with AD. Phytol in the encapsulated or free form was successful in the inhibition that reached values higher than 96%. Th-T fluorescence assay and microfluorescence assay with confocal microscopy confirmed the anti-aggregation and disaggregation of amyloids by the action of phytol either free or encapsulated. Neuro2a cell survival was comparable or higher to the one observed in control experiments with donepezil. Therefore the system was proposed as multi-purposed nanoparticles (Sathya et al. 2018).

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Dendrimer-Based Nanostructures in the Treatment of AD Pathologies Dendrimers Dendrimers constitute a class of advanced nanosystems with great potential (Naqvi et al. 2020) due to the wide-ranging possibilities for tuning their physicochemical properties according to their intended application. This makes them of great potential interest in therapeutic approaches to complex conditions such as AD either by functioning as drug delivery systems (DDS) or due to their own intrinsic antiamyloidogenic effects (Zhu et al. 2019; Benseny-Cases et al. 2012). Applications of nanosized compounds in medicine originated with the advent of polymer chemistry and of macromolecular chemistry in general. At the same time, in the beginning of twentieth century, investigations into protein chemistry resulted in the development of the field of biopolymers in parallel with that of the wider area of bioscience (Micha-Screttas and Ringsdorf 2008). Many years later, a number of groups reported studies of new types of macromolecules called dendrimers, a particular kind of hyper-branched polymers which have been considered by many scientists to constitute a fourth class of polymers, after the linear, cross-linked, and branched types of polymer architecture. An initial report from the group of Vögtle at University of Bonn on the preparation of this type of molecule by a cascade synthetic approach appeared in 1978 (Buhleier et al. 1978) and related work was patented by Denkewalter at Allied Corporation soon after (Denkewalter et al. 1981). More systematic studies were reported a few years later by the groups of Tomalia at Dow Chemicals (Tomalia et al. 1985) and Newkome at the University of Louisiana (Newkome et al. 1985), and since then there has been a sustained growth of interest in the field (Malkoch and García Gallego 2020). The term “dendrimer” for this new class of compounds was proposed by Tomalia and originates from the Greek “dendron” meaning “tree” and “meros” meaning “part” due to their tree-like structure. Dendritic structures are not unknown since they appear in nature, mainly where very important functions need to be enhanced (e.g., in trees using their leaves to optimize photosynthesis, in the human CNS many cells have a kind of dendritic structure to maximize the connections between them). Similar structures can also be found in abiotic systems (e.g., lightning patterns, snow crystals). Dendrimers themselves are characterized by their special architecture consisting of a central core from which successive branching units extend in a repetitive manner creating the so-called dendrimer generations (0th, 1st, 2nd, 3rd, etc.) which finally terminate at the outer part which constitutes the periphery. The overall three-dimensional structures are approximately spherical and generally have a size within the area of so-called nanocompounds (10–100 nm) (Fig. 4). Dendrimers are well-defined hyperbranched macromolecules characterized by monodispersity unlike conventional polymers that have a range of molecular weight. This monodispersity is a very important feature for compounds intended for biomedical applications, because it is a significant factor for ensuring reproducible

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Fig. 4 (a) Basic structural components of dendrimers. (b) A G3 polyamidoamine (PAMAM) dendrimer

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pharmacological behavior. Another advantage of dendrimers is that, due to their unique architecture, the interior branching units create cavities where hydrophobic or hydrophilic substances can be enclosed. This ability of dendrimers to enclose different compounds thus provides them with the potential to behave as carriers of bioactive compounds. The outer part of the dendrimer, the surface groups, affords a means of adding more specific features to the molecule. For example, surface groups such as amines(–NH2) or hydroxy(–OH) or carboxylic acid(–COOH) are amenable to a large variety of chemical modifications and thus dendrimers can be tailored for desired properties. This is especially important when considering the design of systems intended to target specific sites of action or for transport and delivery of drugs. Each part of a dendrimer contributes to its physicochemical properties, such as size and shape, solubility, encapsulating ability, etc., all of which determine the suitability for potential applications in the area of nanomedicine. The possibility of manipulating the chemical structure of dendrimers in a variety of ways appropriate to their desired applications attracted research interest very early on, and this interest has been a major factor in the rapid development in the field of dendrimers. Much initial work was focused on the development of suitable synthetic procedures, and two main synthetic routes, the divergent and, later, the convergent routes, were generally followed (Fischer and Vögtle 1999; Grayson and Fréchet 2001). These methods involve relatively simple repetitive chemical procedures but can present some difficulties in the isolation, purification, and large-scale production of final products. These factors can often be of great importance and can add considerably to the preparation times and consequently the overall cost. In addition, these approaches are often not always suitable for the preparation of compounds with specific features and more recent work has seen the development of other alternative synthetic methodologies involving orthogonal coupling, self-assembly, solid-phase synthesis, and so on (Villalonga-Barber et al. 2008; Sandoval-Yañez and Castro Rodriguez 2020). As a result, a large variety of dendrimers have now been reported and many of them are available commercially.

Biomedical Applications of Dendrimers Soon after the first reports, dendrimers were studied for their potential in a wide range of biomedical applications both in diagnosis and therapy, including their use as imaging agents, as tools in biological assays, as drugs, and as DDS. In order to be acceptable for use as therapeutic agent, any compound, nano or otherwise, must be nontoxic, non-immunogenic, and stable during the time of circulation in the biological system, and this has led to the concept of critical nanoscale design parameters which need to be taken into consideration (Kannan et al. 2014). The ready control of these parameters that is often possible for dendrimers has therefore made them attractive candidates for biomedical use. The branches in dendrimers give rise to multiple cavities which can provide a suitable environment for encapsulating drugs which are held by non-covalent

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interactions. By acting as a means of providing solubility, stabilization, and protection of the drug when it is transported into the bloodstream, the dendrimer can thereby offer improved drug bioavailability. In an alternative mode of drug transport, called the nanoconstruct or prodrug formation approach (Beg et al. 2011), the bioactive compound is directly conjugated either covalently or ionically to the multivalent part of the dendrimer surface via functional groups such as –OH, –SH, –NH2, –COOH, azide, allyl, etc. The linkages to these groups are engineered so as to be sensitive to cleavage by stimuli such as changes in pH, redox potential, or enzymatic reaction when they reach their target (Chauhan 2018). The tunable functionalization of the dendrimer allows the multivalent presentation of groups which can facilitate crossing the BBB and this has been an especially active field of research (Beg et al. 2011; Mignani et al. 2017; Chauhan 2018; Kannan et al. 2014; Leiro et al. 2018; Aliev et al. 2019). As an example of this, recent innovations include the conjugation of groups such as carbohydrates, specific ligands or functional groups, or peptides which in the case of groups such as maltose or histidine (Klementieva et al. 2013; Aso et al. 2019) will trigger the CMT mechanism, whereas functionalization with a positively charged amino group (Sharma et al. 2018) can activate the AMT mechanism while anchoring of a ligand such as transferrin (Pérez-Martínez et al. 2011), sialic acid (Patel et al. 2006), or lactoferrin (Gothwal et al. 2019a, b) can invoke the more selective RMT mechanism.

Dendrimer-Based Approaches to the Treatment of Alzheimer’s Disease Dendrimer-based applications have been administered by a variety of routes. Some of these, such as intranasal administration, for example, involve bypassing the BBB (Selvaraj et al. 2017; Bahadur et al. 2020), but dendrimers also have promising potential for noninvasive treatment of neurodegenerative diseases by incorporating features favoring the penetration of the BBB (Zhu et al. 2019). These properties can also be combined with the ability of certain dendrimers to be therapeutically active per se (Mignani et al. 2017; Wen et al. 2017; Aliev et al. 2019), since numerous in vitro and in vivo studies have indeed shown that dendrimers can interact structurally with protein fragments associated with neurodegenerative disorders such as amyotrophic lateral sclerosis, Parkinson’s disease, Huntington’s disease, and AD (McCarthy et al. 2013). Several hypotheses have been put forward to account for the mechanisms involved into AD and these have given rise to corresponding therapeutic approaches. A number of dendrimer systems have been investigated in connection with these hypotheses and the results have demonstrated that this is a field worthy of further study. The amyloid and tau hypotheses form the basis for reports in which dendrimers per se are the bioactive agents. The disruption of the amyloid aggregation process and the inhibition of tau abnormality have been considered as two of the most promising therapeutic approaches to AD In the context of these hypotheses, it has

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been demonstrated that amine-terminated PAMAM dendrimers have the ability to inhibit the formation of amyloid deposits, simultaneously exerting hydrolytic activity on preexisting forms of toxic aggregated proteins in incubated cells (Klajnert et al. 2006). By disrupting preformed amyloid fibrils into non-fibrillar structures, they inhibit amyloid aggregation and remove the existing toxic forms of aggregated proteins (Mignani et al. 2017; Aliev et al. 2019). Other dendrimers, such as the neutrally charged morpholine-G3-acid-triethyleneglycol (GATG) dendrimer (Klajnert et al. 2012), or cationic dendrimers such as G3-PAMAM, G4-polypropyleneimine (PPI), G4-cationic phosphorus dendrimers (CPD) have also been investigated (Mignani et al. 2017). The dendrimers affect the polymerization process either by accelerating the production of the nontoxic fibrils or by inhibiting the initial formation of the toxic oligomers (Benseny-Cases et al. 2012). The aforementioned studies have been carried out in in vitro model systems, and the toxicity of the larger PAMAM or PPI dendrimers in many cell lines used in the amyloid toxicity assay is generally not taken into consideration. Nevertheless, the positively charged surface of these dendrimers at physiological pH makes their use as a drug even more problematic (Jain et al. 2010). The toxicity of cationic amine-terminated dendrimers in vivo is attributed to the strong electrostatic interaction with the negatively charged cell membrane which results in disruption of the membrane. The toxicity is also size dependent, the larger dendrimers being more toxic. Neutral or negatively charged dendrimers, on the other hand, do not demonstrate corresponding toxicity. Consequently, it has been found that modification of the surface groups with oligosaccharides forming glycodendrimers produces systems which are more biocompatible while still allowing for attachment of the dendrimers to appropriate substrates via hydrogen bonds (Benseny-Cases et al. 2012; Klajnert et al. 2008). Thus, maltose-PPI modified glycodendrimers were found to behave in vitro in a similar way to PAMAM or CPD regarding the nuclear-dependent aggregation of Αβ(1–40) (Klementieva et al. 2011). Neutral and cationic PPI glycodendrimers have also been assessed for their effect on Αβ(1–40) aggregation in vitro and on reducing toxicity of Αβ(1–42) and natural Αβ in vivo. Although the dendrimers were able to cross the BBB when administered intranasally to APP/PS1 transgenic mice, no rescue of memory impairment was observed. The cationic PPI dendrimer was seen to pass through the BBB more readily than the neutral one but still displayed toxicity (Klementieva et al. 2013). A subsequent recent report describes a continuation of this work whereby the use of the G4-PPI-His-Mal dendrimer was designed to resolve the issues previously seen. The histidine groups on the surface of this dendrimer enhance its ability to cross the BBB, probably via the CMT mechanism pathway (Aso et al. 2019; Yamakami et al. 1998). Increased bioavailability in vivo and selective ability to penetrate BBB were indeed observed. It was shown that the dendrimer had improved biocompatibility and ability to cross the BBB in vivo. The dendrimer also provided noticeable synapse and memory protection when administered to AD transgenic mice. The histidine groups also potentially provide supplementary neuroprotective activity by forming complexes with copper ions which are implicated in the formation of reactive oxygen species. This dendrimer would therefore appear to be a promising treatment for diseases of the central nervous

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system. Phosphorus-containing dendrimers, initially intended as DDS, have also been found to act as inhibitors of hyperphosphorylated tau proteins (Wasiak et al. 2012). Other approaches using modified dendrimers as anti-amyloidogenic agents may also be mentioned here. Bearing in mind that β-amyloid peptides bind to cells via interaction with surface glycolipids or glycoproteins through sialic acid (SA) residues, and that the removal of SA from cell surface has been shown to attenuate Αβ toxicity (Mignani et al. 2017), it has been shown that the use of SA-conjugated-PAMAM dendrimers to mimic the cell surface reduces plaque toxicity by sequestering Αβ (Leiro et al. 2018; Patel et al. 2007). Dendrimers have also been conjugated with the KLVFF peptide, which has been demonstrated to inhibit the aggregation of Αβ(1–42) into fibrils (Chafekar et al. 2007). It has also been demonstrated that PAMAM-curcumin conjugates retain the well-known ability of curcumin itself to inhibit amyloid aggregation and to dissolve amyloid fibrils (Patel et al. 2007). The cholinergic hypothesis referring to a cholinergic deficit due to reduced choline uptake and acetylcholine hypersecretion associated with memory and cognition impairments in AD (Parihar and Hemnani 2004) has led to the development of acetylcholinesterase (AChE) inhibitors some of which, namely donepezil, galantamine, and rivastigmine, have received approval from the FDA. Likewise, following the excitotoxicity hypothesis where hyper-excitation of NMDA (N-methyl-D-aspartate) receptors initiates a cascade of events which leads to apoptosis (Hynd 2004), approval has also been given to the NMDA antagonist memantine for symptomatic treatment of AD (Robinson and Keating 2006). Proposed therapeutic treatments of AD involve a single agent or a combination of AChE inhibitor and NMDA antagonist although none have so far been clinically successful (Riching et al. 2020). Studies have been carried out with animal models using bio-functionalized PAMAM dendrimers for the delivery of both types of drug (Gothwal et al. 2018, 2019a, b). In one of these studies, a third-generation PAMAM dendrimer, G3-PAMAM, was conjugated with lactoferrin and subsequently loaded with the AChE inhibitor rivastigmine (Gothwal et al. 2018, 2019a). Lactoferrin is a member of the transferrin family of proteins which are recognized by receptors in the BBB and thus their transport is facilitated via the RMT pathway. The G3-PAMAM dendrimer was used due to its proven biocompatibility and because of the known toxicity of higher generation PAMAM dendrimers. Similar studies were also carried out with the NMDA antagonist, memantine (Gothwal et al. 2019b). In both studies it was found it was possible to combine brain targeting and highly efficient drug delivery in both non-induced and AD-induced animal models which was correlated with the improvements of cognitive responses corresponding to motor and memory spatial memory amelioration in AD-induced animals. The correlation between the improvement of overall drug bioavailability and biodistribution in the brain of the animal models has led to similar interventions being proposed for Parkinson’s disease, cerebral palsy, or brain malignancies, as well as drug co-delivery approaches (Gothwal et al. 2019a).

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Higher generation PAMAM dendrimers with either a positively charged amine surface or a negatively charged carboxylic one at physiological pH have also been recently been investigated for the delivery of tacrine (TAC) (Igartúa et al. 2020), a strong hepatotoxic AChE inhibitor, and for the delivery of carbamazepine (CBZ) (Igartúa et al. 2018). Despite having multiple side effects, the latter drug is a potent enhancer of natural autophagy process involved in the disruption of aggregate protein and has been considered for the treatment neurodegenerative diseases. In these studies, the aforementioned ability of PAMAM dendrimers to behave as antiamyloidogenic agents has also been combined. Higher generation amine terminated PAMAM dendrimers have well-known toxicity drawbacks (Florendo et al. 2018), but the negatively charged carboxylate dendrimers used in the CBZ studies were found to reduce the cytotoxicity caused by the free CBZ in cell culture and could be therefore considered as biocompatible drug delivery systems. G4.0 PAMAM was chosen due its known ability to interfere with β-sheet amyloid fibril structure formation (Klajnert et al. 2006), as well as its inhibitory effect on AChE activity (Klajnert et al. 2004; Shcharbin et al. 2006), and, while it has known toxicity issues due to its positively charged periphery, co-administration with the negatively charged G4.5 PAMAM effectively suppressed these and no cytotoxicity was observed. These results are potentially applicable for administration via transdermal and nasal routes that are known to providing a rapid delivery of drug to the brain and bypass the BBB (Selvaraj et al. 2017).

Lipidic-Based Nanostructures in Treatment of AD Pathologies Liposomes Liposomes are biocompatible drug delivery nanosystems, being able to carry many different types of bioactive molecules. Liposomes can incorporate hydrophilic (entrapped in the aqueous core) or hydrophobic compounds (incorporated within the lipid bilayer). Many literature examples mention the great potential of liposomal platforms to contribute to the AD treatment and the enhancement of the already existing treatment, mainly due to their ability of facilitating the passage of the BBB. On one hand, non-targeted liposome have been mentioned, which can transport the compound directly, and on the other hand, “targeted” liposomes which are designed to interact with specific molecular targets relevant to the diagnosis, treatment, or prevention of AD (Dal Magro et al. 2017).

Formulating Liposomes for AD Treatments Regarding the size of the liposomes, in brain delivery treatments, the administrated liposomes should be roughly nano- or microsized and consist of one or more lipid bilayers surrounding an aqueous core. Only certain sizes will allow passage across the BBB in AD treatment and so small vesicles (100 nm and less) are often preferred. On the other hand, larger liposomes from 100 to 140 nm, being also referred in some studies, have certain advantages, such as a longer half-life in blood circulation and

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avoidance of plasma proteins (Fanciullino and Ciccolini 2009). Regarding their charge, due to the fact that Aβ has been shown to insert preferentially into any anionic phospholipids being incorporated into liposomes, they are more preferable. Moreover, they could have a protective effect, by removing toxic Aβ. Moreover, the majority of the literature referred liposomal treatments aimed at AD have used PEGylated 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-PEG 2000 (DSPE) in order to improve circulation time (Alarcón et al. 2006). The transport of liposomes across the BBB can be facilitated by the attachment of appropriate molecules to the lipid surface. For example, glutathione is transported actively across the BBB, via a sodium-dependent glutathione transporter that is highly expressed on the BBB epithelium. Moreover, glucose carrier-mediated transport mechanisms can facilitate the transport of glucose across the BBB, and the incorporation of glucose onto the liposome surface can enhance BBB delivery. Transferrin is the most commonly targeted receptor (TfR), due to its localization on BBB endothelia. The lactoferrin receptor (LfR) is also heavily overexpressed on the BBB, which has led to the development of Lf functionalized liposomes to enhance transport into the brain via receptor-mediated endocytosis. This delivery system has the potential to be particularly efficient, as the expression of the LfR on microvessels and neurons is increased in AD, allowing more effective targeting. Cell-penetrating peptides (CPPs), being positively charged amino acids interacting with the negatively charged membrane, are able to translocate across biological membranes, including the BBB. Among all CPPs, the HIV-1 tat (TAT) protein has been best described and successfully used for delivery of liposome nanoparticles into the brain, while polyarginines (e.g., octa-arginine) and penetration have also shown potential for the delivery of therapeutics directly to the brain (Chen et al. 2010, 2016; Gregori et al. 2017).

Liposome-Based Therapies Against Aβ Plaques Liposomes have been investigated as nanotechnological platforms to carry synthetic or natural compounds with previously reported affinity for Aβ peptides or antibodies against specific Aβ regions. Balducci et al. (2014) designed liposomes targeting the brain and promoting the disaggregation of Aβ assemblies and evaluated their efficiency in reducing the Aβ burden in AD mouse models. Liposomes were bifunctionalized with a peptide derived from the apolipoprotein-E receptor-binding domain for BBB targeting and with phosphatidic acid for Aβ binding. According to the results, the proposed liposomes displayed the unique ability to hinder the formation of, and disaggregate, Aβ assemblies in vitro. Following, the administration of the liposomes to transgenic mice decreased total brain-insoluble Aβ1–42, as was assessed by ELISA, the number and total area of histologically detected plaques and the brain Aβ oligomers. The novel-object recognition test showed that the treatment ameliorated mouse impaired memory. This synergistic effect could be due to simultaneous interaction of the negatively charged phosphatidic acid phosphate group with positively charged amino acid residues on Aβ and of positively charged amino acids on mApoE with negatively charged regions of Aβ. Finally, liposomes reached the brain in an intact form, as determined by confocal microscopy

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experiments with fluorescently labeled liposomes, suggesting that bifunctionalized liposomes destabilize brain Aβ aggregates and promote peptide removal across the blood–brain barrier and its peripheral clearance. This all-in-one multitask therapeutic device can be considered as a candidate for the treatment of AD. In another study, the intraperitoneal injection of small unilamellar vesicles containing phosphatidic acid or cardiolipin significantly reduced the amount of Aβ peptide in the plasma in a rodent model. Brain levels of Aβ were also affected – although to a lesser extent – suggesting that targeting of circulating Aβ may be therapeutically relevant of AD. The reduction of the peripheral levels of amyloid was accompanied by a decrease in the amyloid burden in the brain and the reduction of some phospho-epitopes of tau protein. In these experiments, the APP/PS1 transgenic mouse line, which is one of the most extensively studied mouse models of AD, was utilized. The results indicated that liposomes containing phosphatidic acid or cardiolipin can alter circulating amyloid, and in addition, directly or indirectly, they can modify brain metabolism, serving as an interesting therapeutic agents to reduce Aβ in the peripheral blood, and subsequently, this peripheral reduction in Aβ may modify the final Aβ levels in the brain (Ordóñez-Gutiérrez et al. 2015). Bana et al. (2014) investigated the ability of liposomes bifunctionalized with phosphatidic acid and with a modified ApoE-derived peptide to affect Aβ aggregation/disaggregation features and to cross in vitro and in vivo the BBB. According to the results, the liposomes strongly binded with Aβ, inhibited the peptide aggregation, and triggered the disaggregation of preformed aggregates. The liposomes were found to be able to cross the BBB in vitro and in vivo. Liposomal formulations that are able to restore and maintain physiological membrane properties after the toxicity induced by Aβ have been also reported. For example, hybrid liposomes were found to inhibit the accumulation of Aβ1–40 for SH-SY5Y cells. They prepared liposomes composed by phospholipids having various charged head groups (cationic L-alpha-dimyristoyltrimethyl ammonium propane (DMTAP), anionic L-alpha-dimyristoylphosphatidylserine (DMPS), or zwitterionic L-alpha-dimyristoylphosphatidylcholine (DMPC) and polyoxyethylene(23) dodecyl ether (C(12)(EO)(23)) and found that the cytotoxicity of Aβ (1–42) peptides on the SH-SY5Y cells decreased after the treatment with this formulation of liposomes (Zako et al. 2011). In the other study, unilamellar liposomes were administrated in HEK-APP cells, exhibiting protection from oxidation and effective incorporation of the omega-3 fatty acid docosahexaenoic acid into cell membranes comparing with HEK293 control cells and as a result providing neuroprotection, being able to restore and maintain physiological membrane properties transferring docosanoic acid (Eckert et al. 2011).

Liposome-Based Therapies for Nose-to-Brain Delivery of AD Drug Molecules Liposomes are considered to be promising systems for drug delivery via the nasal route, because of the containing phospholipids exhibit many similarities to the nature of the lipids in the biological membranes, while their other components like PEG can minimize interactions with mucin, increase mucus diffusivity, and favor a close

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contact with the underlying epithelium (Sonvico et al. 2018). Liposomal drug delivery via the nasal route in AD has been investigated in order to enhance the bioavailability and the efficacy of drug molecules in already existing therapies. For example, Azmari et al. (2016) studied the brain bioavailability of the anti-AD drug donepezil, being formulated in a liposomal formulation after its intranasal administration in rats. The pharmacokinetic parameters were measured, and the bioavailability of donepezil in plasma and brain was increased significantly by the intranasal route. Histopathological examination showed that the formulation was safe and nontoxic. The authors attribute the increase bioavailability via nasal route to the enhanced cellular uptake and transport of drugs across the capillary endothelium via receptor-mediated endocytosis and passage through the BBB. Curcumin was formulated in a liposomal form of soya lecithin and cholesterol as a lipid phase and xanthan gum as a mucoadhesive polymer, in order to mucoadhesive properties get achieved via the nasal route. The particle size, entrapment efficiency, and mucoadhesion of the liposomes were evaluated. Ex vivo permeation, histopathological studies, in vitro drug release, and in vivo study for the estimation of drug in brain after intranasal administration were carried out. The results suggested that the xanthan gum coated curcumin liposomes are a promising drug delivery system for brain delivery through the nasal route. The liposomes exhibited higher drug distribution in the brain compared to the drug solution, which could be due to their small particle size, along with any deleterious effect on the nasal mucosa (Samudre et al. 2015). Yang et al. (2013) formulated rivastigmine liposomes and cell-penetrating peptide (CPP) modified liposomes (CPP-Lp), in order to improve rivastigmine distribution in brain by intranasal administration, and simultaneously to decrease the hepatic first pass metabolism and the gastrointestinal adverse effects. According to the in vitro results in a murine brain microvascular endothelial cells model, the liposomes and especially the CPP-Lp ones enhanced the permeability across the BBB by intranasal administration, compared to the IV administration and achieved an adequate retention in CNS regions, especially in hippocampus and cortex, which were the regions most affected by AD. In addition, there was very mild nasal toxicity by liposomal formulations. Studies on morphology of nasal mucosa, movement of cilia and hemolytic effect was not significantly different from that of the physiological saline, indicating that there was no prominently nasal toxicity of rivastigmine formulations.

Application of Nonlinear Dynamics for Liposome-Based Therapies Behaviors in nature appear to demonstrate either stochastic or deterministic chaotic performances. In the latter case, natural systems appear to exhibit adaptability, selfsimilarity (fractal nature), and steady loss of information regarding their state (Fox 1969). Thus, complexity and chaos theory offer a universal frame for studying dynamical systems in an interdisciplinary sense, while an enormous number of applications in various fields have emerged. Within this frame, although precise behavioral predictions of complex systems may not be possible, analysis and

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assessment of patterns provide with a basic idea of the existing order within chaos (Hanias et al. 2015; Volos et al. 2011). Sometimes, information hidden within microscopic behaviors gets unveiled when seen through the lenses of the theoretical frame of complexity and chaos theory. The mechanism of self-assembly is present in natural processes. An important point is the issue of stability in self-assembled (or self-organized) biological nanosystems. It is very important and directly linked to essential features of their nature, functionality, and biological fate. Stability is studied on various levels, including thermodynamics, physical chemistry, biophysics, and mathematics. Nonlinear dynamics offer another domain for studying stability of biological nanosystems. Lipidic nanoparticles, such as liposomes, are one such case. Liposomes are considered as artificial structures mimicking biomembranes or cells and cellular compartments. Their simple composition and structure apparently facilitate the study of various phenomena in the nanoscale, with applications in drug delivery. The dynamical properties of artificial membranes are a crucial and still open issue for drug delivery. A typical exemplary case is liposome systems serving as vesicles for the administration of therapeutic and diagnostic agents, such as drug molecules and vaccines. The membrane behavior, including stability and functionality, depends on its composition and makes it respond dynamically to various external stimuli, while preserving its structural integrity (Bertalanffy 1952; Prigogine and Strengers 1984). In certain cases, phase separation and new domain/raft formation occur. It has been shown that these states are associated with various diseases, like cancer (Naziris and Demetzos 2017). One molecule insertion might produce dynamic effects in particle self-assembly, morphology, and final biophysical behavior, and this effect is a reflection of various phenomena occurring on natural biomembranes (Naziris et al. 2017). Becoming more specific, the colloidal stability of various liposomes is an important factor that needs to be assessed and evaluated in relation to the possible chaotic behavior, in terms of their physicochemical properties, for example, particle size and polydispersity. Such properties, communicating their stability, are of fundamental importance for the behavior and effectiveness of liposomes in vivo. On the other hand, complex behavior evaluation of nanotechnological platforms, such as liposomes, could give rise to new and improved drug and vaccine delivery nanosystems. Chaotic evaluation could serve as a useful prediction tool for various properties like the stability of liposomal nanosystems. Stability in the case of liposomes is of utmost importance for their applications in pharmaceutical and medical applications, including their development and industrial production, as well as the relevant regulatory framework. As a result, established nonlinear dynamics tools may be useful as indicators, reflecting the liposomal nanoparticle innate properties that take place in the nanoscale and aiding the prediction and control of their chaotic behavior, in vivo fate, and final biological effect. It is well-known that liposome stability varies, and we speculate that this instability is associated with the composition and the physicochemical properties. Thus, the question regarding the nature of this instability (stochastic or deterministic chaotic) emerges. Therefore, the need for identifying and assessing any possible chaotic behavior, by applying nonlinear dynamics on the irregular time series of their

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stability over time is imperative, since instability could be associated with enriched chaotic dynamics. There are examples of such studies, where the described chaotic evaluation, instability and loss of information, was identified for liposomal nanosystems. However, despite their order decrease in the same direction, important differentiations have been observed, apparently related to their different composition. Since liposomes are vesicles for administrating drug molecules, nutrients, and cosmetic ingredients, an approach presented in Naziris et al. (2021) is included in the frame of finding analysis tools for potential prediction and control of liposomes, towards a more efficient development and industrial scale-up, as well as to contribute to the regulatory authorities concerning their evaluation and approval, in the light of the emergence of new nanocolloidal dispersion systems. A very important work (which is the first one to this direction) presents the study of the demonstrated chaotic behavior of lipidic nanoparticles in accordance to their physical colloidal stability. Towards this an experiment considering two different types of lipidic nanosystems was designed and developed. The first one was colloidally more stable and the second one was less stable. The less stable system was a simple DPPC dispersion, while the more stable was DPPC:stearylamine (100: 1 weight ratio or 100:2.7 molar ratio) (Fig. 5), both developed in HPLC-grade H2O. The nanosystems were produced by the TFH, followed by extrusion and probe sonication. Physicochemical characterization was subsequently conducted by evaluating measures that were carried out, in order to monitor the lipidic nanoparticle behavior and stability in real-time. These measurements had the form of time series. The registered time series for each of the two liposomal nanosystems, measuring their size and polydispersity, described the system’s behavior and dynamics. The hyper-chaotic dynamics of the two systems were revealed through the analysis of the size and polydispersity as these evolve over time. It was confirmed that both systems were dissipative, while they demonstrated almost the same chaotic dynamics. However, the relevant metrics highlight noteworthy differences, which lead to important conclusions. In specific, the maximal Lyapunov exponent λ1 in the case of the unstable DPPC system, for both the size and the polydispersity, was significantly higher than in DPPC:stearylamine, means that the former is less predictable over time. The positive Kolmogorov entropy for the stable DPPC:stearylamine was

Fig. 5 Chemical structures of DPPC and stearylamine

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half the value of the corresponding Kolmogorov entropy in the case of the unstable DPPC system. Thus, the former displayed significantly higher information loss, while decorrelation between the past and the present state of the system was considerably quicker, compared to the latter. The reconstructed strange attractors showed that the DPPC system evolves in two different directions thus the DPPC system allows for the creation of a divergent entropic pathway is possible that led to evolution in two different particle populations. Extending the above towards utilization of nonlinear dynamics, the case of macroscopic clinical data in the case of AD, combined with microscopic properties of nanoparticles could be studied. It is well-known that brains injured by the development of AD show decreased chaotic electrophysiological behavior. Our goal is to correlate this behavior quantitatively with the formulation of liposomes for AD treatments. For this purpose, AI methods such as machine learning, deep neural networks, knn algorithm would be used. The main idea is to classify the dynamics of human brain in case of AD with nanoparticles properties and transportation. The invariant parameters as correlation and embedding dimension, Kolmogorov entropy and Lyapunov exponent would be classify the formulation of Liposomes in order to characterize the efficiency of nanoparticles interactions and also predict the critical states and the progress of AD. Future work should also expand to the investigation of chaotic synchronization between biosystems and artificial nanosystems. In this perspective, utilization of nonlinear dynamics in the field of nanosystems might provide an enhancement of our research horizon and insight that could further lead to new directions in pharmaceutics and therapeutics.

Solid Lipid Nanoparticles (SLNs) Drug-loaded SLNs are known to have preferential BBB permeation compared with the free drug form. The enhanced BBB permeation of the SLNs can be due to their lipid content, which can enhance transcellular diffusion across the BBB. Moreover, the surfactants of the SLNs can act as absorption enhancers, decrease the nanoparticle clearance by the reticuloendothelial system, and inhibit the efflux system, especially the P-glycoprotein one. The associated surfactants can also increase the brain uptake via the transient opening of the brain endothelial tight junctions. SLNs can also be endocytosed by the BBB endothelial cells and subsequently be transcytosed into the brain (Alam et al. 2010).

SLNs-Based Therapies for Nose-to-Brain Delivery of AD Drug Molecules Donepezil was formulated as a form of SLNs in order to delivery donepezil directly to the brain through the intranasal route. The SLNs were prepared by solvent emulsification diffusion technique, by using glyceryl behenate as lipid and blend of tween 80 and poloxamer 188 as surfactants. The particle size, zeta potential, and drug entrapment efficiency of the SLNs were evaluated, while in vitro drug release, stability, and in vivo studies were also carried out. According to the results,

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donepezil SLNs exhibited a greater release rate compared to IV and IN administrated donepezil solution, which could be attributed to the ability of the formulated SLNs to protect the encapsulated drug from biological and/or chemical degradation and prevent its extracellular transport by P-glycoprotein efflux protein. The tween 80 is also considered to improve the brain delivery of nanoparticles by solubilization of endothelial cell membrane lipids, temporary opening of inulin spaces, endocytosis of nanoparticles, and inhibition of the efflux system, especially the P-glycoprotein one, being present on the intranasal membrane (Yasir et al. 2018). Shah et al. (2015) developed SLNs formulations with the hydrophilic drug rivastigmine, formulated by homogenization and ultrasonication method, by using Compritol 888 ATO, tween 80, and poloxamer 188 as lipid, surfactant, and stabilizer, respectively. The effect of drug:lipid ratio, surfactant concentration, and homogenization time were investigated by using factorial design. The optimized rivastigmine SLN formula showed narrow size distribution, while DSC and XRD studies showed incorporation of rivastigmine into imperfect crystal lattice of Compritol 888 ATO. In comparison to the rivastigmine solution, where there is the crystalline form of the drug, the rivastigmine in SLNs exhibited higher in vitro and ex vivo diffusion, because the SLNs are lipidic in nature. The diffusion followed Higuchi model. According to the histopathology study, there was an intact nasal mucosa after the rivastigmine SLNs administration and no nasociliary damage and/or cell necrosis, indicating safety profile of rivastigmine SLNs and suitable for intranasal administration.

Small-Angle Scattering Methods in Studying Amyloid Formation Small-angle scattering (SAS) methods have been widely used and established in the soft matter research (Wignall and Melnichenko 2005). Macromolecular conformation and polymeric aggregates shape, internal structure and hierarchical morphology in solution are customarily being probed by these methods. Small-angle neutron scattering (SANS) offers the advantages of contrast variation and isotopic labeling as the scattering length of hydrogen is significantly different than the one of deuterium (Papagiannopoulos 2017a). Recently, amyloid peptides Αβ, i.e., Aβ1–40, Aβ1–42, and Aβp3–42, were investigated by SANS in terms of their aggregation state. It is very important to note that in SAS methods, the peptides are investigated in their native unperturbed state (noninvasively), and the morphological parameters are averaged over a vast number of unimers, oligomers, and aggregates, i.e., all scattering particles in the sample (Fig. 6). The morphology and aggregation state in monomers, oligomers, and fibrils were analyzed (Fig. 6) by the use of Beaucage model (Papagiannopoulos 2017b) which allows the description of aggregates in terms of characteristic length scales (radius of gyration) and internal arrangement (fractal dimension) (Festa et al. 2019). The analysis showed that the monomers, oligomers, and fibrils have radii of gyration about 20, 40, and 80 nm, respectively. The values of fractal exponents reveal linear conformation for monomers, compact accumulation for oligomers, and clustercluster aggregation (diffusion-limited) in fibrils (Festa et al. 2019). This is a study

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Fig. 6 SANS data for monomers, oligomers, and fibrils of the Aβ1–40, Aβ1–42, and Aβp3–42 peptides. Color horizontal lines are background values at high Q data. (Reproduced with permission from Festa et al. (2019))

that demonstrates how the Αβ aggregation states can be resolved, which is a very important point for the understanding of AD and other neurodegenerative pathologies. The SANS methodology can be naturally extended to the investigation of Αβ interactions and associations with polymer molecules and polymer nanostructures (or even other types of nanostructures).

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Fibrillation kinetics can be monitored by SAS methods as, for example, in the formation of insulin amyloid fibrils (Chatani et al. 2015) and in amyloid β and α-synuclein aggregation pathways (Ricci et al. 2016). Fibril formation in insulin amyloids was found to begin with pre-fibrillar aggregates with rod shape while in later stages, larger aggregates appear. Small-angle X-ray scattering (SAXS) experiments resolved the kinetics of formation of fibrils as a function of time upon the increase in temperature that triggered the aggregation process (Chatani et al. 2015). The time-dependence of the volume fractions of the individual species had an abrupt change at a certain time (that was higher for higher salt content), where the monomers volume fraction dropped and the one of fibrils increased. SAXS remarkably resolved the shapes of monomers (cylinders) and fibrils (elliptical cylinders). The evolution of the fibril semiminor/major axis and length proved that early stage fibrillation occurs by increasing the length while at later stages by increasing mainly the cross-section of the fibrils (Chatani et al. 2015). Oligomerization state was efficiently resolved by the traditional Kratky plots in Αβ where a stable oligomer is formed at sufficiently high concentrations preventing the fibrillation process (Nick et al. 2018). In a Kratky representation, the product I(q)∙q2 versus q (where q is the scattering wave vector and I(q) the azimuthally integrated scattered intensity) is analyzed. Open and extended conformations can be readily resolved from compact ones as the second ones show a plot with a characteristic maximum. This kind of studies can be used in the investigation of fibril formation in the presence of synthetic polymers in order to see how polymer-amyloid interactions affect fibrillation at the nanoscale.

Conclusion Despite the plethora of already existing data, more effort is needed to increase our knowledge around basic molecular mechanisms governing AD that will lead to improved models useful in developing therapeutic strategies. For example, C. elegans AD models have been shown to be able to lead the way in the identification of genetic or pharmacological interventions that may ameliorate Aβ and tau toxicity by modifying positively the UPS. Regarding the new opportunities in AD treatment, nanotechnology field contributes to this scope. More specifically, several promising DDS are being developed for the targeted delivery of AD drug molecules and the penetration of BBB, in order to increase their therapeutic efficiency and decrease the unwanted side effects that are caused by the high doses. Currently, numerous studies describe the successful administration and the promising results of various nanoparticles, including polymer-based nanostructures, dendrimers, and lipidic nanosystems, in different AD animal models at the preclinical stage. Physicochemical methods present great potential not only in the characterization of the drug delivery nanosystems but also to study the AD pathogenesis. Finally, there is a great potential in nanotechnological formulations, by monitoring their physical characteristics and the functionalization of their biomaterials that continually creates future perspectives for the upgrade of the current AD therapies.

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Nanoplatforms as Information Carriers and Thermodynamic Epitopes in Neurodegenerative and Immune Diseases Costas Demetzos

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Prefix Nano . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Terms Information and Entropy. Thermodynamics in Brief . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Concept, the Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applied Thermodynamics: The Thermodynamic Epitope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

This chapter discusses the idea of producing artificial nanoplatforms that can carry thermodynamic variables. The implementation of this innovative idea requires that new scientific and technological tools are established. Neurodegenerative and immune diseases are among those that need to be given priority in the development of new medicines and the adoption of new therapeutic approaches. Thermodynamics and biophysics are impressive scientific tools that should be incorporated into the scientific framework. Their systematic use in the fight against human diseases should be enhanced and promoted by the scientific community. The term thermodynamic epitope emerges as a new approach that can bridge the gap between basic and applied research and translate the most promising laboratory and preclinical results into clinical proofs. The thermodynamic epitope is the copy of the thermodynamic variables of a biological epitope on a nanoplatform which will, in turn, carry them to the desirable biosite of action. This process will result in a modulation of life functions and the promotion of human health. The concept of thermodynamic epitope relates to a balancing act C. Demetzos (*) School of Health, Department of Pharmacy, Laboratory of Pharmaceutical Technology Section of Pharmaceutical Nanotechnology, National and Kapodistrian University of Athens, Athens, Greece e-mail: [email protected] © Springer Nature Switzerland AG 2023 P. Vlamos et al. (eds.), Handbook of Computational Neurodegeneration, https://doi.org/10.1007/978-3-319-75922-7_59

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between information and entropy. By controlling such balance and by mapping the thermodynamic variables of proteins that modulate the functions of life, we can propose the thermodynamic epitope that exceeds existing knowledge and opens up new avenues to cure human complex diseases such as neurodegenerative and immune diseases. Keywords

Neurodegenerative disease · Immune disease · Metastable phase · Information · Entropy · Nanomedicine · Thermodynamics · Thermodynamic epitope

Introduction The Prefix Nano “It was in the 1980s that the word nano, used as a prefix to a variety of importantsounding words, reached me from various directions. ‘What is this nano thing (. . ..)? It’s the technology of small, dwarfish things. Nano in Greek, means dwarf’, Prof. Gregory Gregoriadis mentioned in the forward section of the monograph entitled ‘Pharmaceutical Nanotechnology. Fundamentals and Practical Applications’,” Springer, 2016 (Demetzos 2016). Nanotechnology is the multidisciplinary scientific field which meets a variety of applications and deals with the manipulation of matter at the nanometer. The term comes from the Greek word νανo (nano) that corresponds to very small objects (1 nm ¼ 109 meter) and from the Greek word τεχνoλoγία (technology). Nanotechnology covers issues from biology (cellular functions), colloid science (interface phenomena and colloidal stability), chemistry (organic chemistry and catalysis), and biochemistry and molecular biology (gene expression), as well as physics, mathematics, and medicine. It refers to the use of principles and methods of mechanics, electronics, material science, physics, and particularly thermodynamics and biophysics with the purpose of producing systems that possess diameter less than one micron (1 micron ¼ 106 meter). The Royal Society in London, UK, proposed the definition that “nanotechnologies are the design, characterization, production and application of structures, devices and systems by controlling shape and size at nanometer scale.” According to the National Nanotechnology Initiative (NNI; http://www.nano.gov/node/1113) “nanotechnology is the understanding and control of matter at dimensions of roughly 1-100 nm, where unique phenomena enable novel applications.” Richard Feynman (Nobel prize in Physics, 1965), gave a lecture in 1959 during the American Physical Society dinner where he announced for the first time the word nanotechnology. The term nanotechnology was first presented by Prof. Norio Tanaguchi in 1974 in his thesis, entitled “On the basic concept of Nano-technology” in which he described materials that have dimensions of a nanometer. Nanotechnology is considered to be a huge and ever-expanding discipline that deals with systems of sizes in the range of about 1–100 nm. On the nanoscale level, the properties of matter are different from the

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ones on the macroscale, providing new and challenging possibilities for producing new and innovative products mainly in the field of health (Demetzos 2016). The description of nanotechnology, however, is not inclusive because of the following argument (formed as a question): What are the experimental protocols and the results that prove the exact dimension of the prefix nano? Protagoras (Fig. 1a) was an important pre-Socratic classical philosopher from Abdera, Thrace, Greece (490 BC – ca 420 BC). According to Protagoras (Fig. 1a), knowledge is everything we perceive, as is depicted by our senses. Protagoras introduced the concept of “anthropocentrism,” with his characteristic statement “Man is the measure of all things.” This statement means that man is the measure of truth and knowledge, and for this reason every subjective view on a given subject is of value. People are the measure of everything and the ones to define the limits of each other’s behavior. Consequentially, a researcher is the measure of truth and knowledge. It follows that different limits can be introduced describing the dimension of the prefix nano, because of the researcher’s subjective approach. That is additionally supported by the quantum phenomena that occur in the nanodimension. Richard P. Feynman (Fig. 1c) pointed out, regarding the quantum phenomena, “I think it is safe to say that no one understands Quantum Mechanics.”

The Terms Information and Entropy. Thermodynamics in Brief Nanodimension Let us now go deeper into the terms nano and information, because of the need to construct a more precise understanding of the prefix nano and consequently of the term nanodimension. It is well understood that the creation of nanostructures is related to their morphology. This means that new forms emerge on the nano scale. The evolution of information creates the “statistical advantage” of new features of nanoparticulate

Fig. 1 (a) Protagoras of Abdera, Thrace, Greece (490 BC – ca 420 BC); (b) Aristotle, Stagira in Northern Greece (384–322 BC); (c) Richard P. Feynman 1918–1988, American theoretical physicist, received the Nobel Prize in Physics in 1965 jointly with J. Schwinger and S. Tomonaga. (Adapted from Wikipedia)

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systems. “Statistical physics” leads to natural laws based on the distribution-variance of the variables around the mean value that all of us perceive. Our brain and the neurons as well as the resulting bionetwork perceive physical reality which functions in a locally Euclidean space – “as sufficient according to the need” (‘óσoν ικανóν πρoς την παρoύσαν χρείαν’ Τoπικά, 153 α 13); according to Aristotle (Fig. 1b) – even if in reality – on microcosmic level – it is not Euclidean. The importance of the concept of locality (topikotita; τoπικóτητα) becomes apparent when one acknowledges the fact that the forces in the interaction between two nanoparticles in a noninteracting distance are the same as if they were in constant interaction. The question that is raised is the following: Which nanosystem is chosen as the most stable and functional promoting the experimentally found dimension? We argue that it is the nanosystem which the researcher recognizes and accepts as the most functional and stable. When looking into the aspect of stability, another question is raised: Is it a system stable for nature, and thus has the highest entropy? Or is it a system stable for us, with minimum entropy, contrary to the precepts of nature. The researcher defines the limits of dimensions of a nanosystem. “Man is the measure of all things,” as Protagoras argued.

Thermodynamics: Biophysics and Complex Diseases We have to mention that thermodynamics and biophysics are key scientific blocks in bringing forward research in health science and particularly in complex diseases such as neurodegenerative and immune diseases and in personalized medicine, beyond existing practices (Singer et al. 1972; Demetzos et al. 2020). According to the JPND European Union joint program- neurodegenerative, “Neurodegenerative disease is an umbrella term for a range of conditions which primarily affect the neurons in the human brain. Neurodegenerative diseases are incurable and debilitating conditions that result in progressive degeneration and/or death of nerve cells. This causes problems with movement (called ataxias), or mental functioning (called dementias)” (JPND Research 2015). Two crucial questions are hereby raised: • Why should biophysics and thermodynamics be applied in the research and development processes of innovative therapeutic products? • Why should these disciplines (i.e., biophysics and thermodynamics) be part of the dossier submitted to the regulatory agencies by stakeholders? (Demetzos and Pippa 2019a, b) It is our firm belief that raising these two questions suggests a new, not straightforwardly obvious, direction in the development process of therapeutic agents. Answering these questions could lead to new achievements in the prevention, diagnosis, and cure of diseases.

Metastable Phases, Silent Functionality, and Irregularities An in-depth knowledge of the laws of physics and of their applications in health sciences is required in order to design and develop new medicines and innovative therapeutic approaches. The changes in natural phenomena and biological processes

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are related to the reduction of free energy, while the thermal transition plays a crucial role in the process of living organisms. Thermodynamics describes the diversity and the polyvalence in the evolution process of living organisms. The adaptation processes of biological objects are internally influenced by the thermodynamic equilibrium processes of the material transitions. The metastable phases play a key role on their functionality by regulating the switching on and of the processes (Demetzos 2015). The metastable phases and the thermal changes are related to the functionality of living organisms while the equilibrium processes are considered as responsible for the life organization and evolution. In the field of pharmaceutics, thermodynamics and biophysics are considered as ultimate scientific tools in order to effectively develop and evaluate innovative therapeutics, diagnostics, and imaging agents. It is of importance to point out that the self-assembly process of matter and of biomaterials is a field that gained special attention by researchers. The spontaneous (ΔG < 0) processes of biomaterials, to minimize their free energy by increasing the attractive molecular interactions, are driven by thermodynamics and biophysics. The intramolecular interactions promote the lower free energy of the system and consequently the spontaneous self-assembly process. The thermodynamics process of self-assembly can be represented by Eq. (1) and is characterized as an equilibrium process. ΔG5ΔH  TΔS

ð1Þ

In a previously published work (Demetzos and Pippa 2019a, b), we claimed that the disclosure of “encrypted natural codes” which exist in nature, in a dynamic process, could provide new insights and tools for effectively studying nanoparticulate systems as nonequilibrium thermodynamic platforms. The equation (Demetzos 2016) may contribute to this approach. The “silent functionality” is encoded in metastable phases that constitute a dynamic multidimensional phenomenon. Therefore, we could say that “the concept of probability in quantum theory should be approached in a different way from the concept of possibility in statistical physics.” Eugene Wigner (1902–1995), Nobel Prize laureate in Physics in 1963, proposed the following: “If Schrödinger’s equation represents a reality, then the encrypted variable, which is decisive for the result of any event, could be consciousness itself.” The encrypted code is synonymous to quantum necessities. The attributes of metastability and of polymorphism, which exist in natural biosystems and bionetworks, could potentially project what we can artificially develop as carriers and transporters of information. These two important terms (i.e., metastability and polymorphism) are considered as the “holy grail” that drives knowledge further beyond. The plethora of metastable phases of self-assembled nanostructures carrying information are the main requirements that nature promotes. The complexity of natural objects is related to the quality of information that they carry. Natural membranes, such as cell membranes and their cellular organelles, display melting transitions that correspond to the functional behavior that fits on their metastability process. By activating the metastability process due to exogenous or even endogenous stimuli, membranes

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facilitate important to life phenomena (i.e., signaling transduction, endocytosis, exocytosis, etc.) that are based on their thermodynamic and biophysical payload. The changes of thermodynamic variables such as enthalpy, entropy, Gibbs free energy, heat capacity, etc., as well as biophysical behavior such as flip-flop and lateral diffusion phenomena, transit from gel to liquid crystalline order membranes and can produce phase separation, giving rise to the production of domains or rafts, well-known as metastable phases. Such metastable phases are responsible for the variability of biosystems’ parameters that cause biophysical and thermodynamic “irregularities.” These “irregularities” can be correlated with the terms “biophysical disease factor” and “thermodynamical disease factor,” which describe biophysical or thermodynamical abnormalities of cells, respectively, corresponding to human diseases (Demetzos 2016). By studying thermodynamic variables and by using nerve pulses as model, we can disclose the beauty of thermodynamics. Such nerve pulses are related to membrane transition and can influence the functions of nerves (Demetzos and Pippa 2019a; Heimburg 2019). A phase transition in small nonextensive systems can be classified by the topological and morphological properties of the entropic surface, (Tsallis 2010) according to the energy and the number of particles. According to the book “Non-extensive entropy. Interdisciplinary applications,” (Gell-Mann and Tsallis 2004) nonextensive statistical mechanics replaces Boltzmann-Gibbs statistical mechanics in systems that are in thermal equilibrium consistent with ergodicity. Nonextensive statistical mechanics could be applied in a variety of open systems in economics, linguistics, biology, and other fields. Phase transition and its consequences, such as the metastable phases in biosystems, are dynamic quantum phenomena and processes. Static (equilibrium) nature is called “phase equilibrium,” i.e., gas, liquid, solid, and triple point of water, given that it is a macroscopic phase transition. The nonextensivity of complex systems, in terms of entropy, is considered as the main pillar in modern physics. We can conclude that the greater the complexity and the structural diversity of nanosystems, the better and the more effective the transportation of information. The prefix nano does not emerge as important in comparison to information context. It is obvious that the study of the nonequilibrium state and process of nanoparticulate systems, and not the study of their dimension, is an emerging and exciting research field that gives rise to new research direction for producing nanoplatforms carrying information based on the selected variables that should be identified and rationally managed. Our effort deals with the promotion of an alternative approach. According to this approach, the thermodynamic variables of particular biological epitopes (i.e., biological macromolecules or cells) will be identified and measured and then copied and located to well-defined nanotechnological platforms. These platforms will be able to carry the variables to the desired biosite of action. This is not an easy and welltolerated behavior due to the lack of scientific and technological tools and due to the lack of precise knowledge. A lot of efforts, much time, and funds should be spent in order to establish acceptable and effective thermodynamic and biophysical protocols. Such efforts should be focused on the identification, mapping, and “isolation” of the most important thermodynamic variables by using customized digital

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approaches, depending on the nature and complexity of a particular biological epitope, in order to copy them on a particular, well-defined, artificial nanoparticulate system. These nanosystems could be defined as “thermodynamic epitopes” that can carry the thermodynamic variables (i.e., information) of a particular biological epitope. This is a particularly complicated task due to the complexity of the interfacial and physicochemical biological phenomena that should also be identified. In this chapter, we will provide the main concept for achieving such goal.

The Concept, the Goal Applied Thermodynamics: The Thermodynamic Epitope The Thermodynamics of a Cell Membrane The pioneers in the field of the structure and morphology of cell membranes, S.J Singer and Garth L. Nicolson, published an impressive article (Singer et al. 1972) whereby they referred to thermodynamics of cell membranes in aqueous environment. They pointed out that by applying thermodynamic principles to cell membranes they recognized that proteins are the predominant biomolecules, among others. This argument, which recognizes the major role of proteins in the functionality of cellular membrane, had initially endorsed the concept that thermodynamic variables could be used for mapping cellular proteins. Biological membranes are the result of thermodynamic equilibrium between hydrophobic and hydrophilic interactions of molecules. Moreover, due to their composition, they exhibit functionality, responding dynamically to external stimuli (i.e., temperature, ionic strength, lateral pressure fluctuations, etc.) while retaining their structural integrity (Singer et al. 1972). These stimuli, as well as compositional alterations in the membrane, e.g., cholesterol content, through integration, might induce phase separation and consequently metastable phase formation. This mechanism might be associated with various diseases, such as cancer (Binder et al. 2003). After more than 40 years, Garth L. Nicolson published an updated article entitled “The fluid-mosaic model of membrane structure: still relevant to understanding the structure, function and dynamics of biological membranes after more than 40 years,” (Nicolson 2014). In this article, the author pointed out the importance of membrane domains such as lipid rafts (i.e., metastable phases). They have their own thermodynamic and biophysical profile that emerges as an attractive field for investigation. One of the outcomes of this article states that “(. . .) future work will likely concentrate on answering additional questions on the thermodynamics and physical explanations concerning the relationships between the structure and functional activities of membrane components (. . .).” Nanothermodynamics and Small Systems The scientific tools that are considered as essential in order to prove the above statement should include the extended Boltzmann-Gibbs theory, which is based on the entropy and the nonextensive statistical mechanics. The theories by Shannon and

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Tsallis should be taken into consideration, with regard to the information and the nanothermodynamical profile of small systems, (Demetzos et al. 2020). Phase transition and its consequences, such as the metastable phases in biosystems, are dynamic quantum phenomena and processes. Nature, in equilibrium, behaves as in “phase equilibrium,” in a macroscopic view, (i.e., gas, liquid, solid, and triple point of water). On the other hand, nature’s internal dynamic processes promote new and functional bioplatforms carrying information (i.e., thermodynamic variables), in a microscopic view. The second law of thermodynamics refers to entropy. Entropy S is referred to as a factor which contributes to the full understanding of the change of Gibbs free energy, which is represented by ΔG. Gibbs free energy (G) constitutes an overall parameter which is incorporated in the change of enthalpy (ΔH). Classical thermodynamics is related to macroscopic observation. On the other hand, statistical thermodynamics refers to a huge number of small systems. The probability for a nanoplatform to reach any given state should be established by measuring all the possible distributions accessible to it. We can summarize that entropy is increased by spontaneous processes while its probability also increases. Statistical thermodynamics is quantitatively related to measuring the changes of the entropy from a less probable to a more probable state (Connors and Mecozzi 2010). It is an excellent approach to understand the dynamic and nonequilibrium way in natural phenomena that promote life evolution and to identify and isolat the thermodynamic variables that correspond to thermodynamic conformations of particular biomacromolecules such as peptides or proteins that have played essential roles in life processes. Such an approach discloses the thermodynamic characteristics and variables of a biomacromolecule (i.e., protein) which are involved in human diseases and which play a role in the balance of human health.

Information, Entropy, and the Thermodynamic Epitope Fig. 2 represents two different, in their polymeric content, biomaterials (dark (I) and dark/gray (II)). The dark (I) one, behaves “normally” due to the simple (i.e., one biopolymer) content, but the dark/gray (II) might produce different conformations due to the different thermodynamic payload because of its higher complexity (i.e.,

Fig. 2 Different in nature biomaterials (dark (I) and dark/gray (II) change their conformations because of their different information/entropy balance due to an external stimulus

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two biopolymers, dark and gray). These different conformational changes, meaning different lyotropism, could be projected on different metastable phases. The importance of this behavior lies in that, by mapping such behavior of a biomolecule (i.e., protein) and by identifying its thermodynamic variables, we could copy them to an artificial nanostructure that would carry such information and release them on demand (i.e., responsiveness to environment stimulus), to the biosite of action. Such artificial nanostructure can transport the thermodynamic variables of a biomolecule to the exact site of action and could behave as thermodynamic epitope that might be used in therapeutics. Such a thermodynamic epitope incorporates thermodynamic characteristics as those identified and isolated from the biological epitope (i.e., protein). The changes of the thermodynamic variables of a biological epitope are affected by metastable phases of cellular membrane. The above argument can help in better understanding the well-known concept regarding the coding process of information and entropy. The following equation shows the relationship between information and entropy: J K1 51023 bits or 1bit51023 JK1 This equation is the consequence of calculation (Sestak 2004). Leon Nicolas Brillouin (Brillouin 1956) studied the relation between entropy and information and proposed the following relation: S5kΒ ln2 ðJ=KÞ This relation shows us that one bit of information leads the system to degradation and to a quantity of entropy with value kΒ ln2 (J/K), where kΒ ¼ 1.38 Χ 1023 (J/K) is Boltzmann’s constant. It is important to mention that the metastable phases are the information carriers and entropy traps that affect the macroscopic behavior of human tissues. This could be correlated with human health and could be seen as a future direction in personalized medicine. Figure 3 presents a plethora of phase separation of artificial lipidic bilayers which correspond to different metastable phases due to the lyotropism effect, which act as the driving force for production of metastable phase (Matsingou et al. 2005). It is important to point out that the self-assembling process occurring in bioorganisms depends on the concentration of the biomaterials used. There is a physicochemical hierarchy which determines which biostructures are predominant and which of the thermodynamic payload will survive. According to the information theory by Shannon (Shannon 1948) and according to the entropic approaches, information is the statistically predominant direction of the organization process of the biosystem based on the hierarchy of which biosystem is considered as necessary for survival. By changing the concentration of biomaterials, the thermodynamic balance is affected, and the information payload changes and consequently the hierarchy is reconsidered.

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Examples of Thermodynamics of the Metastable Phases An important publication by Binder and coworkers, regarding the frame of virus infections, points out that “(. . .) rafts can include or exclude certain transmembrane molecules selectively. For example, it appears that a 200 kDa transmembrane phosphatase protein CD45 is abundant in all cell membranes except within rafts. Surprisingly, the HIV-1 envelope also excludes this molecule, whereas the virus incorporates other membrane proteins that are present at lower levels than CD45. This result has led researchers to suspect that the virus may bud from rafts, and not from the surrounding membrane (. . .).” The term raft can be correlated with a phase separation (i.e., metastable phase) embracing its own thermodynamic variables. The

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article (Binder et al. 2003) presents an impressive finding in the field of virology that HIV-1 prefers to bind rafts/metastable phases in order to interact with proteins with a particular thermodynamic profile, contrary to binding with an abundant transmembrane protein which is highly expressed. This HIV-1 behavior, to bind rafts/metastable phases, could be the key in unlocking the way in which personalized medicine should work, in terms of thermodynamics and biophysics. It might be possible that the thermodynamical and biophysical profile of membranes’ rafts (i.e., metastable phases) and their conformational properties promote effective interaction between HIV-1 with particular protein. It is reasonable to underline that such rafts/metastable phases embrace the encrypted code and the silent functionality that HIV-1 needs for effective interactions. In the same review article, the authors pointed out that “(. . .) Future progress in biology, continuing to address membrane structure, dynamics, and function where domains and rafts play a key role. Even now it can be assumed that new strategies for fighting viral infections, lipid storage disease, cancer, and other persistent illnesses of mankind will arise through the understanding of rafts (. . .) (i.e. metastable phases)” (Binder et al. 2003). This could be a pioneering approach in order to create thermodynamic epitopes that will be able to recognize which kind of protein should be prioritized in terms of their thermodynamic payload, meaning that the more hierarchically effective thermodynamic variables will be the ones modulating the biological effect. The morphology and the functionality as well as the biochemical modulatory behavior of self-assembled structures such as proteins can be recognized as a thermodynamic and concentration-dependent phenomenon that regulates life functions. Figure 4 presents DiOleoylPhasphatidylCholines’ (DOPC) artificial cell lipidic bilayers, both free of PolyAMinoAMiDone (PAMAM) as well as incorporating of

Fig. 4 DOPC incorporating different concentration of PAMAM dendrimer produce phase separation which corresponds to different metastable phases due to changes of their internal thermodynamic variables. (Adapted from Gardikis et al. 2010 with permission from Elsevier)

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PAMAM dendrimer, in different concentrations. The latter promotes phase separation which corresponds to metastable phases that have been identified based on their thermodynamic variables (Gardikis et al. 2010). Thermal analysis techniques and mainly Differential Scanning Calorimetry (DSC) are well-known tools and are considered as useful for studying and evaluating phase separation phenomena and the metastable phases of biological molecules and artificial nanoplatforms, respectively (Demetzos 2008).

Summary Thermodynamics and biophysics should be reconsidered as important scientific tools that can highly contribute to the field of health sciences. This chapter discusses the scenario of producing artificial cellular nanoplatforms that carry thermodynamic variables. These variables will be the ones identified as predominant and can be correlated with the thermodynamic profile of essential proteins. The thermodynamic variables’ mapping process is, beyond any doubts, difficult. This chapter suggests that the thermodynamic variables are measured by using thermal analysis techniques and are located on nanotechnological platforms which are eligible to transport them to the desired biological site of action and behave as thermodynamic epitopes.

Conclusion According to Tsallis statement in his monograph (Tsallis 2010), “(. . .) a scientific theory cannot be considered as such if it is not capable of providing falsifiable predictions. This is to say predictions that can in principle be checked to be true or false. And a successful theory is of course that one which accumulates predictions that have been verified to be correct, and whose basic hypothesis has not been proved to be violated within the restricted domain of conditions for which the theory is thought to be applicable.” It is well understood that the theory suggested in this chapter should be checked experimentally regarding its necessity for developing digitalized therapies based on the already existing thermodynamics principles and variables. The nonextensive approach of Tsallis and his contribution to the entropic payload of the nonextensive nanosystems is a beautiful tool for developing new knowledge and innovative therapeutic approaches that will help us construct the “thermodynamic epitope” theory to be applicable in the field of personalized and digital therapies. Neurodegenerative and immune diseases are characterized by complexity related to the balance between information and entropy. This chapter suggests that by controlling such balance and by mapping the thermodynamic variables of proteins that modulate the functions of neurons or immune cells, we could aim for the production of artificial nanostructures that can carry thermodynamic information and can modulate life function promoting human health. This is a scenario that goes

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beyond existing knowledge and opens new avenues for the cure of human complex diseases, such as the neurodegenerative and immune diseases.

References Binder WH, Barragan V, Menger FM (2003) Domains and rafts in lipid membranes. Angew Chem Ind Ed 42:5802–5827 Brillouin JF (1956) Science and Information Theory.2nd edn. Academic, New York, (1962) Connors KA, Mecozzi S (2010) Thermodynamics of pharmaceutical systems. Willey, Hoboken Demetzos C (2008) Differential Scanning Calorimetry (DSC): a tool to study the thermal behavior of lipid bilayers and liposomal stability. J Liposome Res 18(3):159–173 Demetzos C (2015) Biophysics and thermodynamics: the scientific building blocks of bio-inspired drug delivery nano systems. AAPS PharmSciTech 16(3):491–495. https://doi.org/10.1208/ s12249-015-0321-1 Demetzos C (2016) Pharmaceutical nanotechnology. Fundamentals and practical applications. Springer Science + Business Media, Singapore Demetzos C, Pippa N (eds) (2019a) Thermodynamics and biophysics of biomedical nanosystems. Applications and practical consideration. Springer Nature, Singapore Demetzos C, Pippa N (2019b) Introducing thermodynamics and biophysics in Health Sciences. In: Demetzos C, Pippa N (eds) Thermodynamics and biophysics of biomedical nanosystems. Applications and practical consideration. Springer Nature, Singapore, pp 1–11 Demetzos C, Kavatzikidou P, Pippa N, Startakis E (2020) Nanomedicines and nanosimilars: looking for a new and dynamic regulatory “Astrolabe” inspired system. AAPS PharmSciTech 21(2):65–74 Gardikis K, Hatziantoniou S, Bucos M, Fessas D, Signorelli M, Felekis T, Zervou M, Screttas CG, Steele BR, Ionov M, Micha-Screttas M, Klajnert B, Bryszewska M, Demetzos C (2010) New drug delivery nanosystems combining liposomal and dendrimeric technology (Liposomal Locked-In dendrimers) for cancer therapy. J Pharm Sci 99(8):3561–3571 Gell-Mann M, Tsallis C (eds) (2004) Nonextensive entropy. Interdisciplinary applications. Santa Fe Institute, studies in the science of complexity. Oxford University Press, Oxford Heimburg T (2019) Phase transition in biological membranes. In: Demetzos C, Pippa N (eds) Thermodynamics and biophysics of biomedical nanosystems. Applications and practical consideration. Springer Nature, Singapore, pp 39–61 JPND Research (2015) What is neurodegenerative disease? JPND Research. Retrieved 7 February 2015 Matsingou C, Hatziantoniou S, Georgopoulos A, Dimas K, Terzis A, Demetzos C (2005) Chem Phys Lipids 138:1–11 Nicolson GL (2014) The fluid-mosaic model of membrane structure: still relevant to understanding the structure, function and dynamics of biological membranes after more than 40 years. Biochim Biophys Acta 1838:1451–1466 Sestak J (2004) Heat, thermal analysis and society, Published by Nucleus HK, Divisova 882, CZ50003 Hradec Kralove Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(3):379–423 Singer SJ, Garth L, Nicolson GL (1972) The fluid mosaic model of the structure of cell membranes. Science 175:720–731 Tsallis C (2010) Introduction to nonextensive statistical mechanisms. Approaching a complex world. Springer+Business Media, LLC, New York

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Detecting Active Molecular Subpathways Related to Alzheimer’s Disease: A Systems Biology Approach Aristidis G. Vrahatis and Panagiotis Vlamos

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Biological Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pathway Analysis: Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methodological Steps of Pathway Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selecting a Zero Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pathway Analysis Methods Generations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An Indicative Systems Biology Workflow for Detecting Active Molecular Subpathways . . . . Construction of a Network of Gene Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gene Interaction Network Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subpathway Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subpathway Prioritization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Application to Alzheimer’s Disease Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Pathway analysis is a thriving research area of Systems Biology tools and methodologies which aim to unravel the inherent complexity of high-throughput biological data produced by the advent of Omics technologies. Subpathway-based analysis, the latest evolution of such methods, provides a new level of analytical capabilities to experimentalists and paves the way for Systems Medicine. A. G. Vrahatis (*) Bioinformatics and Human Electrophysiology Laboratory, Department of Informatics, Ionian University, Corfu, Greece P. Vlamos Department of Informatics, Ionian University, Corfu, Greece e-mail: [email protected] © Springer Nature Switzerland AG 2023 P. Vlamos et al. (eds.), Handbook of Computational Neurodegeneration, https://doi.org/10.1007/978-3-319-75922-7_52

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Simultaneously, RNA-seq is gaining ground and has the potential of becoming the predominant technology in transcriptome profiling. A subpathway analysis method for RNA-seq experiments is proposed toward this orientation, which isolates differentially expressed subpathways indicating potentially perturbed biological processes. The method constructs a differentially expressed gene interaction network, extracts, and prioritizes subpathways using a consensus-based linear score. The differential expression status of each gene is negotiated among wellestablished RNA-seq differential expression analysis tools to minimize false discoveries. Also, the efficacy of this method is demonstrated on an Alzheimer’s disease-related dataset and corroborates findings using recent literature. Such methodological pipelines may lead to the identification of several perturbed biological processes known to be associated with Alzheimer’s disease. Keywords

Systems biology · Systems medicine · RNA-seq · Pathway analysis · Subpathway approach · Alzheimer’s disease · Neurodegenerative diseases

Introduction Basic Concepts Systems Biology Systems Biology is the scientific field that its general idea concerns the interpretation of various biological events using system theory, thus giving a new impetus to understanding multiple structures and functions. From the study of individual biomolecules, system biology has shifted its interest in the integrated study of biomolecule groups whose components interact synergistically to execute and integrate biological functions. Essentially, Systems Biology is characterized by the collaboration of scientists from various fields, as the building and verification of each theory require knowledge from the field of biology, mathematics, physics, and computer science, and other subfields (Kitano 2002). Figure 1 depicts an indicative overview of Systems Biology, which highlights its corpus, the trinity of biology, technology, and computation. More specifically, biology offers new biological challenges and technology tries to solve them by creating new technologies or by updating the already existing technological equipment. New technologies such as RNA-seq or single-cell RNA-seq as well as improvements in microarrays technique are part of this field. The greatest challenge that arises from this process is the vast amount of heterogeneous data generated. Their analysis requires substantial computational resources and effective computational software. These data are constantly increasing in the level of heterogeneity, complexity, and dimensionality. Thus, new computational tools are needed to cope with these challenges. After, the computational analysis offers new biological results where the biology is called upon to analyze them and give new knowledge or raise further biological questions. This cycle is unstoppable and is the core of Systems Biology.

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Fig. 1 Schematic overview of Systems Biology. (Source: https://www.systemsbiology.org/)

Systems Biology studies are beyond the limits of the reductionist’s approach and is a holistic approach that has begun to gain ground after completing the Human Genome Project, which made it clear that biology is an information science. It integrates multilevel biological information, from DNA to populations, into models that can describe the underlying biological processes. A general framework of work in Systemic Biology is the following (Ideker et al. 2001): – Build a model that describes the system. Using earlier genetic and biochemical information, an original model of the system is constructed. Such a model can describe the structure of the interaction in the system and predict the data behavior of specific disruptions of its components. – Systemic disorders in system components. These disorders can be genetic (deletion, overexpression, or under-expression of genes) or environmental (temperature change, hormone stimulation, or drugs). The system’s response to each disorder or array of changes is measured at the level of biological information expression (mRNA, protein expression). – Update model with observed disorders. Ideally, the model should extensively describe/predict the observed disorders. The process is repetitive. – Systems Medicine is the extension of Systems Biology, which is applied in clinical data. Through such approaches we understand the mechanisms that are disrupted in disease through a holistic look (zoom-out view) and allows us to observe the organization between “molecular components” (molecular components) (Auffray et al. 2009). Systems Biology has several extensions with the Network Medicine term to have a more significant impact.

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Network Medicine Network medicine represents the “marriage” of network science and Systems Biology and applies to human diseases. It depicts the reality that the (phenotypic) phenotype or disease phenotype is driven by complex interactions between a variety of “molecular mediators.” These interactions are responsible for some pathways that facilitate the (pathological) phenotype (Barabási et al. 2011). The idea behind the term “Network Medicine” is that the biological systems contain several interconnected components in a specific topological structure and have simple principles. This structure can be comprehensively analyzed by representing these biological systems in the form of complex networks. High-Throughput Techniques of Molecular Biology Molecular biology is the branch of biology that studies the structure, synthesis, and function of genetic information (DNA and RNA) at a molecular level, how it interacts with proteins, and studies the activities of different cell systems between them. Each cell in a living organism contains the information inherited in each new cell (Kaiser et al. 2007). The information is contained in genes encoded within DNA molecules in structures called chromosomes. Each DNA molecule consists of two strands, each of which is a long chain of four nucleotide species: adenine (A), guanine (G), thymine (T), and cytosine (C). Each gene is the encoded expression of a protein. Proteins are the active molecules within the cell and are responsible for the following functions: (a) structuring of the cell, (b) treating the obtained chemical signals, (c) catalyzing the reactions are performed in the cell, and (d) multiplying the DNA. Its three-dimensional structure determines the activity of a protein and the environment it belongs to, and it is not easy to predict. The production of a protein from a gene is carried out in two stages. Originally the gene is copied to a form known as mRNA. The mRNA then translates into a protein according to the genetic code. The genetic code is the same for most living organisms. The genome, respectively, consists of the DNA sequences and the set of chromosomes. In genetics, with the term gene expression or gene expression, the process that causes the transfer of encoded information (the gene) to the functional product of the gene (protein or RNA) is characterized. It usually refers to the whole process by which a gene is activated to produce a protein. The first stage of gene expression is transcription, where an RNA molecule is created, using a DNA strand as a template, of which it is complementary (Crick 1970). Its purpose is to transfer genetic information from DNA to ribosomes to make protein synthesis. The translation follows where the mRNA-based polypeptide chain is created, and then the polypeptide chain is folded. However, in each cell, not all proteins are produced at each time point, and the amount of protein to be produced depends on the tissue, the stage of growth of the organism and the physiological or metabolic state of the cell. Therefore, it is necessary to operate a gene expression regulation program that guides the type and

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amount of proteins that must be produced at all times. Gene regulation regulates the cell for structure and function, and is the basis for cell differentiation, morphogenesis, and adaptability of an organism. Over the last 5 years, the blueprint of next generation sequencing has allowed researchers to develop personalized transcript profiles and to clarify the leading genes of various diseases. The RNA-seq technique allows many more processes beyond differential gene expression (Reeb and Steibel 2013). Although microarrays are available for exon and microRNA study, most researchers still are interested in 30 biased differential gene expression. Both microarrays are biased in terms of the content to be placed in the array. On the other hand, the RNA-seq technique does not require detectors or primers, and because of this, the data is less biased. The RNA-seq technique allows for the elucidation of the expression of coding RNA and noncoding RNA, spliced and allelic. Also, the digital form of the data from the aligned “readings” allows increased sensitivity to the detection of rare transcripts. The cost of the technique is competitive with microarrays and enables repeat analyzes to when more information about the total transcript of an organism is available.

Biological Networks Initially, a brief definition of a graph which imprints the networks in the mathematical aspect is presented. The graph in its simplest definition is the visual representation of relationships that develop certain quantities, designed with respect to a set of axes. A graph G is denoted by G ¼ (V, E), where V is the set of vertices (or nodes) and E is a set of edges (or links). The declaration of nodes and edges is also denoted by V ¼ V(G) and E ¼ E(G), respectively. Each edge e  E of a graph G ¼ (V, E) corresponds to two nodes u and v  V of G, and is denoted as e ¼ (u, v) ¼ (v, u). If the edge has a direction that starts from node u and ends at node v, it is denoted as e ¼ (u, v). In molecular biology, there are different types of networks representing biological molecules (genes, proteins, metabolites) in nodes and their mutual relations in edges (interactions). The interactions can be immediate and represent a natural interaction or regulation between the nodes or indirect and represent the joint involvement of the nodes in a process (e.g., participation in the same enzymatic reaction). Generally, these networks consist essentially of two kinds of information, the genes encoding proteins responsible for the structure and function of an organism, and a network of regulatory interactions that determine the expression of the genes. Interactions involve other macromolecules and small molecules, but genes are the reference point. Biological networks have several exciting properties whose discovery has given a particular impetus to the field of Systems Biology (Barabasi and Oltvai 2004).

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Protein Interaction Networks Proteins often form complexes through interactions, which are autonomous functional units. Network nodes are proteins and edges interacting with each other. The edges are nondirected, i.e., if a protein binds to a B protein, then B also binds to A. The interaction may also be transient, that is, a brief interaction that modifies a protein that affects other interactions. These interactions are an active part of the network (Meyers 2009). Metabolic Networks Metabolic networks consist of metabolic pathways that are sequences of biochemical reactions of a cell. These reactions are catalyzed by enzymes, where the product of one reaction is either used in the cell or acts as a substrate for a subsequent reaction. Network nodes are the products of the reactions, while the edges represent the reactions. Gene Regulatory Networks The central mechanism of regulation of levels of gene expression involves the regulation of transcription by proteins called transcription factors. The transcription factor detects and binds to specific short DNA sequences, enhancing or decreasing the concentration of RNA-polymerase responsible for the transcription. A transcriptional factor can regulate one or more genes, and a gene can be regulated by one or more transcription factors. The network consists of nodes that are genes and transcription factors. The edges correspond to interactions between them, they are directed and start with a transcription factor and end up in one of the regulated genes. Signaling Networks It is a complex system of interactions that controls the basic cellular processes. It consists of signaling pathways that indicate the changes that occur due to activation of the cell membrane receptor (receptor) protein. Network nodes are proteins (and, by extension, genes that encode them) that integrate, transport, and route the biological signal through chemical transformations in which they participate. An example of such transformations is posttranslational modifications resulting in the mature protein product, to which a functional group such as a phosphate group (phosphorylation), a methyl group (methylation), an acetyl group (acetylation) or amide, resulting in a change in enzymatic and therefore signaling function. Another example is the formation of stable protein complexes or the removal of a protein from such a dissociation. Nodes can participate and therefore transmit the signal to multiple paths at the same time. Each pathway typically has inputs to the ligands and exits changes in intracellular concentrations of signaling molecules such as calcium or cyclic nucleotides (Meyers 2009). Metabolic and signaling networks show clear similarities, but the purpose of the analysis is completely different. In the first case, a static network of protein interactions is extracted, i.e., a static topology, while the second represents information transmission, which takes into account both the nature of the interaction and its

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direction, the period in which it occurs, and the quantitative effect on the function of the target protein. Molecular processes in a signaling pathway may last for milliseconds (phosphorylation and protein structural changes) up to one minute or more (control of gene expression or transport of receptors from one area of the cell to another). Therefore, the complexity of the information transmitted in time and space complicates the analysis of such networks (Meyers 2009).

Pathway Analysis: Related Works Methodological Steps of Pathway Analysis Biological pathway analysis is a set of Systems Biology techniques that are used to extract knowledge from high-throughput sequencing data by creating a model that attempts to describe the underlying biological processes. Sequence techniques typically output a list of differentially expressed genes between a state of interest (e.g., disease) and a control state (healthy state) that are cut off from the biological context in which they act and which can make sense in their behavior. In this direction, analysis techniques incorporate earlier biological knowledge from biological databases with statistical, mathematical, and computational methods to extract the desired model. High-throughput biological data produced in omics are the input of a method of Systems Biology. The main studies are: (i) genomics, i.e., the study of the structure and function of an organism’s genome; (ii) proteomics, the study of the structure and function of the proteins of an organism; (iii) transcriptomics, the study of the transcription of one or more cells, i.e., all of these RNA molecules; and (iv) metabolomics, the study of the metabolites, i.e., the products of the enzymatic reactions.

Preprocessing The first step of a path analysis technique is the preprocessing of biological data obtained as a result of a high-performance sequencing technique and path-specific data obtained from a base of biological paths. For the first type of data, standard pretreatments are: (i) normalizing the data values for all samples so that expression values from different experiments are comparable, (ii) completing values for absent expression values; (iii) adopting a common nomenclature (e.g., (HGNC, Entrez ID), (iv) deletion of samples having identical identifiers, and (v) finding differentially expressed genes between a control state and the condition under consideration (e.g., disease) (Hung et al. 2011). The choice of bases from which path data will be extracted should be based not only on the relevance of each with the purposes of the analysis but also on the coverage it provides in relation to genes appearing in biological data, basis does not cover all the genes of an organism.

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Selecting a Zero Hypothesis The analysis phase involves finding the paths represented by the biological data and having at the same time the least chance of being represented by random data. The thresholds of statistical significance used are P-value < 0.05 and P-value < 0.001, which show strong evidence against the null hypothesis model (H0 – null hypothesis), which is the denial of correlation between quantities where there is a correlation. The usual options for H_0 are as follows (Ackermann and Strimmer 2009; Goeman and Bühlmann 2007): Q1: The genes belonging to a set (such as a path) are no more related to the phenotype than a competitive null hypothesis. The correlation between the genes in total and the phenotype with the correlation of the genes apart and the phenotype is compared. Therefore, the correlation between the samples and the phenotypes is stable, while the genes are the sampling units. In the context of differential expression, the assumption is that the genes are as much as differentially expressed as the other genes. Q2: The genes belonging to a set are not related to the association null hypothesis. The correlation of the genes in the set and the phenotype is compared with the correlation of the same with random phenotypes. Therefore, the participation of the genes in the set is stable whereas the phenotypes are the sampling units. In the context of differential expression, the hypothesis is that the genes of the whole are not differentially expressed. The hypothesis commonly used is Q2, as Q1 considers the genes as sampling units. In a gene expression experiment, however, the aim is to determine whether differential gene expression changes between different phenotypes, and therefore it is more correct to consider phenotypes as sampling units. Moreover, Q2 has a clear biological meaning because the interpretation of the P-value corresponds to the reproduction of the same experimental process in new subjects. A significant P-value excludes randomness in the results of the experiment and gives confidence that the same associations will occur in a subsequent repetition (Goeman and Bühlmann 2007).

Selection of Statistics at the Gene Level The next step after selecting the model’s zero hypothesis is to find differentially expressed genes. The statistics used are usually one of the following: fold-change, signal-to-noise ratio, t-statistics, correlation coefficient, linear or accounting regression (linear/logistic regression), and log-likelihood ratio. Then, statistics are typically transformed in one of the following ways: absolute value, quadratic value, binary transformation, P-values, Q-values, or posterior Bayesian probabilities (Goeman and Bühlmann 2007).

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Select Genotyping Level Statistics By switching to the level of the gene set, statistics such as the sum, average or average of the transformed gene level statistics, Kolmogorov-Smirnov, max-mean, Wilcoxon rank sum tests, or false discovery rate (FDR) are used. The selected statistic should ultimately be evaluated by calculating the P-value by sampling either genes or phenotypes, depending on the choice of the zero hypothesis (Q1 or Q2). In the first case, a large number of random sets of genes of the same size are selected from all genes and the statistic is calculated for each of these sets. In the second case, the phenotypes of the subjects are disturbed many times, and each time the statistics are recalculated. The P-value is in each case calculated by the fraction of the values of the statistics that exceed the reference value (Goeman and Bühlmann 2007).

Pathway Analysis Methods Generations Methods for the analysis of pathways are classified in four generations chronologically and in terms of the general philosophy of the approach they follow (GarcíaCampos et al. 2015; Khatri et al. 2012).

First Generation: Overrepresentation Analysis The underlying assumption in an overrepresentation analysis (ORA) is that statistically significant pathways can be determined if each pathway displays more differentially expressed genes than those that would occur in a random fashion. Methods based on such an analysis typically follow the general methodology as previously seen. The key advantages over methodologies that are not based on previous biological knowledge are that the physical data is put into a biological framework that helps to extract a model that can describe to some extent the complex processes behind the very same data. These methods are typically quite simple and computationally cheap. However, they have some basic constraints. (i) Due to the fact that the choice of differentially expressed genes is based on a threshold, many potentially interesting genes located near the threshold (e.g., P-value < 0.05) are removed. (ii) They are indifferent to the interactions between the genes and their topology in the path. Analyzing two different paths with the same set of genes would give exactly the same results. (iii) Assume that the paths are independent of one another by ignoring the existence of interactions between them (Barabasi and Oltvai 2004). (iv) Genelevel statistics ignore the size of the fold change and treat each gene, in the same way, ignoring valuable biological information. These limitations have prompted the next generation of path methods. Second Generation: Analysis of Functional Category The basic assumption in a functional class scoring (FCS) is that in addition to the major changes in gene expression, smaller changes are important, and their composition significantly affects the state of the path. Each such method has three steps: (i) Calculation of a statistic at the gene level as well as in the general methodology.

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(ii) Concentration of individual statistics from the genes of each pathway to a pathlevel statistic (equivalent to selecting genotype-level statistics where a set of genes is the members of the pathway). (iii) Statistical evaluation of each pathway according to the null hypothesis adopted (Q1 or Q2 as in the general methodology). The main advantages with respect to ORA methodologies are: (i) They do not need a random threshold to identify some differentially expressed genes, so they do not ignore genes with similar expression values that do not pass through the threshold. (ii) They can detect small changes that have a measurable composite effect. (iii) Consider combined changes in gene expression to identify the interdependencies between the genes of a pathway. However, these have, in turn, some basic limitations: (i) All the genes of a pathway have the same contribution in terms of gene-level statistics, i.e., no prior knowledge of the path is taken into account. (ii) They continue to ignore the topology of the pathway and the interactions between the genes. (iii) Analyze each path separately by ignoring overlaps and interdependencies (Barabasi and Oltvai 2004). In particular, while there may be only one statistically significant pathway, if some of its genes appear on other paths, they may also appear to be significant. These limitations triggered the third generation of path methods.

Third Generation: Pathway Topology Analysis The underlying assumption in a pathway topology-based analysis is that the interactions contained in the topology of the pathway are important for studying the correlation of changes occurring between the parts of a pathway by addressing some of the limitations of the previous methods. The same general methodology follows, except that the whole topology of the pathway and not only its members is used to compute gene-level statistics. The main advantages with regard to ORA and FCS are as follows: (i) Topology of pathways gives information about the nature of the interaction of their members, which allows the assignment of different weights to each gene according to the changes that exist the expression of each one and its effect on the state of the whole path. (ii) Different biological states may correspond to different interactions between the same genes. Knowing the interactions allows the method to distinguish between the two states which, considering only the genes and their expression, would be considered identical. The basic constraints of this generation of methods are: (i) these methods generally do not take into account the links between paths in order to identify interactions between them as the connections between them tend to be weak and (ii) they do not matter at what time one moment of experimentation enriches a path than determining whether or not enrichment exists. Fourth Generation: Subpathway Analysis The basic hypothesis in a subpathway analysis is that certain biological processes can be described not by an entire biological path but by a submodule that can be shared with other paths. Besides, the very structure of a path as it is attributed by a base is not a gene collection, but a collection of submodules or groups of nodes that

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have a specific function. In addition, different subpathways may have the same role in different pathways (Chen et al. 2010). Here, a network-based Systems Biology approach is designed and implemented under the perspective of the fourth generation of pathway analysis, that extracts disease-perturbed subpathways within a pathway network as recorded by RNA-seq experiments.

An Indicative Systems Biology Workflow for Detecting Active Molecular Subpathways Indicative methods for identifying molecular subpathways are focused on the location of differentially expressed submultiples in signal pathways by incorporating gene expression data from RNA-seq experiments. The main biological assumption here is that a subpathway corresponds to a potentially disrupted biological process that has a specific phenotypic correlation. The main points of such methods are the following: (i) The construction of a network of gene interactions which reflects the prior knowledge of the operation of the signaling pathways; (ii) Negotiation of differential gene expression between established differential expression analysis tools in RNA-seq data and overlay in the gene interactions network; (iii) The extraction of differentially expressed genes from the network; and (iv) Classification based on a linear score that takes into account the size and level of certainty of the differential expression of the genes that make up it. In the context of evaluating the performance of the method with respect to the biological significance of the results, an open set of RNA-seq data is utilized (Nativio et al. 2018) related with the dysregulation of the epigenetic landscape of normal aging in Alzheimer’s disease. Initially, the biological significance of subpathways with high positions in the overall classification is presented, confirming the findings through recent literature on Alzheimer’s disease. Then the enrichment of the paths in those subpathways that achieve a good ranking position is examined and the findings through relevant literature is confirmed. In summary, the results largely agree with the original study from which the biological data were used but also with a large number of studies on the aging of hematopoietic stem cells, making it an extremely useful approach.

Construction of a Network of Gene Interactions As a basis for generating gene interaction networks, the KEGG base path maps are stored as KGML (KEGG Markup Language) files. A KGML file is an xml file that stores information about the paths of the pathway (gene products or chemical compounds) as well as about the interactions between gene products or gene product and chemical compound. A metabolic pathway contains information on (i) gene products, i.e., enzymes (or genes encoding them) and orthologous genes (genes belonging to different

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organisms and derived from a common ancestor), (ii) chemical compounds, and (iii) on maps of other paths, which show the transmission of information from one path to the next. The graph will relate to a trail of an organism, so we do not care about the bonds and links and we therefore construct a graph with nodes, genes, and chemical compounds. Edges are created by looking at the reactions of the path. Let be the enzyme involved in the reaction, the substrate, the product, and the type of reaction that can be reversible or irreversible. In a nonreversible interaction, the interactions (s, e) and (e, p) are mapped between substrate-enzyme and productenzyme, respectively. In a reversible interaction, the interactions (e, s) and (p, e) are also mapped (Li et al. 2013). A non-metabolic pathway contains information on (i) gene products, i.e., proteins, genes, and orthologous genes, (ii) chemical compounds, and (iii) links to maps of other pathways. A graph with nodes of proteins, genes, and chemical compounds is constructed. Edges are created by examining pathway interactions involving either two gene products or a gene product and a chemical compound. Here are many types of interactions, which are categorized in interactions (i) gene expression (GErel), (ii) protein-protein (PPrel), and (iii) protein-chemical compound (PCrel). Each type of interaction has its own subclasses such as gene expression, gene suppression, and indirect effect for GErel, and chemical compound, activation, suppression, indirect effect, change state, ligation/association, absent interaction, phosphorylation, dephosphorylation, methylation for PPrel. Each subclass regulates the role of an interaction, as well as the direction of the corresponding edge in the graph. Some subcategories reveal the address in a direct way. For example, the interaction “node A triggers node B” has a clear direction from A to B. On the other hand, interactions such as binding/correlation do not give clear directional information, so we think it is bidirectional. As bidirectional interactions, we consider the subcategories as indirect effect, state change, ligation/correlation, and absent interaction (Li et al. 2015). A node may correspond to more than one gene that either have a common function or belong to the same gene family. In this case, the node can be deployed on multiple nodes while developing the connections with its neighbors. Such knots usually characterize protein complexes and thus maintain the interaction between each part (Li et al. 2013). In addition, some nodes in both metabolic and non-metabolic pathways may account for more than one gene product. These can be either gene families that share common roles (Sales et al. 2013), or they are paralogue, i.e., they come from a common ancestor but have different functions. In any case, a new node is created for each gene and assign the inbound and outbound links of the original node (Li et al. 2013). In order to create the gene interaction network, chemical compounds that belong to the path should be appropriately eliminated without affecting the flow of information on the topology of the path. If a g1 gene is linked to a compound c, which in turn is associated with a g2 gene, the node of the compound is removed and the interaction between the two genes remains (Li et al. 2013).

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Gene Interaction Network Refinement Next, the differential expression of genes is incorporated in a topological context by refining the gene interaction network, namely removing interactions between non-cDEGs. The resulting network contains highly expressed communities of statistically significant differentially expressed genes. In order to ensure strong evidence of differential expression for each cDEG, four well-established methods have been used for differential expression analysis of RNA-seq data: DESeq (Anders and Huber 2010), edgeR (Robinson et al. 2010), baySeq (Hardcastle and Kelly 2010), and voom (Soneson and Delorenzi 2013). These methods have exhibited satisfactory accuracy and good scalability, but lack in precision and exhibit unsatisfactory false discovery rates. As seen in study (Soneson and Delorenzi 2013), voom performs poorly for a small number of samples per condition, which is a frequent occurrence in experimental settings. On the other hand, for a reasonably large number of samples, DESeq exhibits low accuracy, while edgeR suffers from low precision. BaySeq presents high variance in its results, especially for high ratios of upregulated to downregulated genes. To overcome the shortcomings of each method, the FDR adjusted P-value of each gene (Q-value) is obtained by using each method (Soneson and Delorenzi 2013) and consider genes reported as differentially expressed by all methods simultaneously with Q-value < 0.05 as cDEGs. This way, there is strong evidence of differential expression for each cDEG, as will be seen in the corresponding evaluation later on. Finally, the graph is refined by removing interactions between genes which are not cDEGs. The minimization of false discoveries ensures that the signal transduction is preserved locally. The severe penalizing of interactions between genes which do not show any measure of differential expression is a key aspect in identifying biologically significant parts of the network pertaining the condition under study.

Subpathway Extraction Next, the refined network is decomposed to a list of subpathways, using an appropriate method (Chen et al. 2010; Nam and Park 2012; Dimitrakopoulos et al. 2015; Vrahatis et al. 2015; Vrahatis et al. 2016). Linear and nonlinear subpathways are the two main subpathway extraction types. The first type is a linear cascade of gene members representing how an extracellular stimulus produces an activation signal propagated across a signaling pathway. A linear subpathway is defined as an ordered sequence of genes. It starts from a node without incoming links (start node) to a node without outgoing links (end node), while the intermediate genes have one incoming and one outgoing node. The main drawback here is that this process results in hundreds of thousands of solid sub-paths, and the higher the complexity of the gene-gene network, the higher the number of possible sub-paths. Huge length pathways (number of member genes) also occur. Let M be the adjacency matrix denoting the interactions between genes in a pathway network. Element i, j of the k-th power of M, namely Mkij, reveals the number of distinct walks of length k, or paths

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if the graph is acyclic. By allowing subpathways to range from a to b genes, valid startend node pairs are extracted as follows (Vrahatis et al. 2019): n

VP ¼ [ ðsi , di Þ, ðsi , di Þ  VP

b

iff

i¼1

Mksi ,di > 0

ð1Þ

k¼a

Typically, a subpathway can range from a single connection between the start and the end node to cascade of interactions matching the network diameter max dij. ij

Subpathway Prioritization Each DEG method provides evidence of each gene’s differential expression in the form of an FDR-adjusted P-value. As noted previously, each method has variable efficacy under different experimental conditions. Towards this direction, individual measures are consolidated of evidence to a consensus-based global prioritization scheme in order to exploit each method’s strengths. Each linear subpathway is scored according to the weight of evidence of each member-gene (Consensus Score) as follows: CS sub ¼

1 m1

n

T

i¼1

j¼1

n j  r ij

ð2Þ

where Τ is the number of DEG tools used for corroborating differential expression evidence, nj the number of DEGs returned by method j, r ij the rank of gene i in the corresponding ranked list of DEGs produced by method j, and m the number of subpathway members. The scoring process can be viewed as a Borda Count scheme with each linear subpathway’s score normalized using the number of subpathway interactions. Hence, a high-scoring subpathway indicates a cascade of genes with strong evidence concerning their differential expression and thus, a potential biological process activated between the condition under study and the control condition.

Application to Alzheimer’s Disease Data A transcriptomic analysis using expression profiling by high throughput sequencing is applied to the proposed indicative pipeline in previous section. The corresponding study (Nativio et al. 2018) examined the dysregulation of the epigenetic landscape of normal aging in Alzheimer’s disease. The KEGG database is used to obtain the signaling pathway maps, both metabolic and non-metabolic. After the conversion step, the final gene-gene network included more than 5000 unique gene nodes with

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Fig. 2 Visualization of two resulted components based on our methodology related with the pathway maps from neurodegenerative diseases. Node color indicates the type of regulation of genes (upregulation or downregulation with blue and red gradient respectively). Edge color indicates the relation among gene interactions (positive or negative correlated with green and red gradient)

almost 59,000 edges (interaction among genes). Transcriptomics dataset was obtained from NCBI GEO database with accession number GSE104704 (Fig. 2). Next, some indicative subpathways of differential expressed genes which are associated with the dysregulation of normal aging in Alzheimer’s disease are presented. All aforementioned metabolic and non-metabolic pathways were tested for enrichment for each one of the 2240 identified subpathways (Benjaminicorrected Fisher exact P-value < 0.05) by means of gene-annotation enrichment

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Table 1 Pathway terms for the two resulted components based on our methodology related with the pathway maps from neurodegenerative diseases Adjusted P-value 4.70E-33

Combined score 17345.3

Huntington disease

2.81E-23

3256.7

Long-term potentiation

2.96E-14

3314.8

Glutamatergic synapse

3.40E-14

2138.8

Dopaminergic synapse

1.14E-13

1786.0

Endocrine and other factor-regulated calcium reabsorption Human cytomegalovirus infection

1.26E-13

3866.5

3.64E-13

1093.2

Cellular senescence

3.60E-11

1074.5

C-type lectin receptor signaling pathway Alzheimer disease

5.45E-11

1441.1

5.26E-11

983.5

VEGF signaling pathway Kaposi sarcomaassociated herpesvirus infection Renin secretion

5.59E-11

2204.3

9.38E-11

878.8

1.48E-10

1804.9

1.79E-10

1109.4

Term Amyotrophic lateral sclerosis (ALS)

Osteoclast differentiation

Genes TOMM40;MAPK14;GRIN2B;GRIN1; SOD1;MAPK13;MAPK11;PPP3CA; PPP3CB;PPP3R1;PPP3CC;NEFL; NEFH;PRPH;MAP3K5;MAP2K6 HIP1;CLTC;CLTB;ITPR1;HTT;CLTA; AP2A1;AP2B1;GRIN2B;GRIN1;SOD1; REST;PLCB4;DLG4;CLTCL1;PLCB1 PPP3CA;PPP3CB;PPP3R1;PLCB4; PPP3CC;ITPR1;PLCB1;GRIN2B; GRIN1 PPP3CA;PPP3CB;PPP3R1;PLCB4; PPP3CC;DLG4;ITPR1;PLCB1; GRIN2B;GRIN1 MAPK11;PPP3CA;PPP3CB;PLCB4; PPP3CC;ITPR1;MAPK14;PLCB1; GRIN2B;MAPK13 PLCB4;CLTC;CLTCL1;CLTB;CLTA; AP2A1;AP2B1;PLCB1 MAPK11;PPP3CA;PPP3CB;PPP3R1; PLCB4;PPP3CC;ITPR1;MAPK14; PLCB1;MAPK13;MAP2K6 MAPK11;PPP3CA;PPP3CB;PPP3R1; PPP3CC;ITPR1;MAPK14;MAPK13; MAP2K6 MAPK11;PPP3CA;PPP3CB;PPP3R1; PPP3CC;ITPR1;MAPK14;MAPK13 PPP3CA;PPP3CB;PPP3R1;PLCB4; PPP3CC;ITPR1;PLCB1;GRIN2B; GRIN1 MAPK11;PPP3CA;PPP3CB;PPP3R1; PPP3CC;MAPK14;MAPK13 MAPK11;PPP3CA;PPP3CB;PPP3R1; PPP3CC;ITPR1;MAPK14;MAPK13; MAP2K6 PPP3CA;PPP3CB;PPP3R1;PLCB4; PPP3CC;ITPR1;PLCB1 MAPK11;PPP3CA;PPP3CB;PPP3R1; PPP3CC;MAPK14;MAPK13;MAP2K6

The second and the third column represent a modified Fisher Exact P-value and a combined score using the Fisher exact test with the z-score (), respectively

analysis from DAVID-WS (Jiao et al. 2012). Table 1 illustrates the enriched KEGG pathways derived from our methodology. In detail, the significance level was set to 0.05. All exported results were analyzed and evaluated on the basis of enriched pathways and GO terms reported in the original study and recent literature (Fig. 3).

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Fig. 3 Visualization of the top six subpathways of our methodology applied in all available KEGG pathway maps. Node color indicates the type of regulation of genes (upregulation or downregulation with blue and red gradient respectively). Edge color indicates the relation among gene interactions (positive or negative correlated with green and red gradient)

Discussion Systems Biology and Network Medicine are emerging research fields with promising results since they have the potential to elucidate hidden mechanisms for complex biological processes and complex biological diseases. Most genes associated with diseases have minor effects, the conspicuous effect of which can become significant. Therefore, the efficacy of a biomarker based on a gene with a large effect may vary depending on how the effects of genes with lesser effects are transmitted (Gustafsson et al. 2014). Even when there is a way for the magic bullet to find its target, the problem of the drug’s overall toxicity remains. Ultimately, the complexity of biological systems suggests that current definitions of diseases are careful discriminations of a complex phenotypic space. The compromise of the complex nature of the organism with the distinct nature of the disease that affects it makes it necessary to understand how diseases are associated and to obtain an overall picture of how a cure changes the state of the organism (Hidalgo et al. 2009). The inherent properties of Systems Biology and Network Medicine studies can tackle part of the above complex processes. Such approaches aim to solve the problem that a disease is rarely the result of dysfunction of a particular gene product, but it depends on multiple products that interact on a complex network. The fact that strengthens the value of Systems Biology and Network Medicine approaches is that in recent years the cost of DNA sequencing has decreased significantly. The cost per genome after completing the human genome sequencing

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started from $ 95,263,072 in 2001 and ended in July 2015 at $ 1363, tending to the $ 1000 final goal (Wetterstrand 2017). This development will potentially allow the analysis of the genome for each patient, enabling the development of drugs targeted at specific subgroups of the population, which will be determined by genetic and environmental criteria. Therefore, the information of a human’s genome can lead to drug development (provided social and legal conditions for mass-scale mapping) and the choice of the appropriate drug for the patient, depending on the genetic and environmental peculiarities that characterize it.

Conclusion We are in the era of Network Medicine, where we need new computational pipelines, which will contain system-based approaches on biological networks to find new disease-related genes, new drug targets, and network biomarkers for complex diseases. Under this perspective, we have proposed a methodology that identifies differentially expressed pathways associated with a case under study. The method is based on KEGG pathway networks integrating information from omics studies. Our application to AD data offers new biomarkers in the form of subnetworks, almost all with biological meaning.

References Ackermann M, Strimmer K (2009) A general modular framework for gene set enrichment analysis. BMC Bioinformatics 10(1):47 Anders S, Huber W (2010) Differential expression analysis for sequence count data. Genome Biol 11(10):R106 Auffray C, Chen Z, Hood L (2009) Systems medicine: the future of medical genomics and healthcare. Genome Med 1(1):2 Barabasi AL, Oltvai ZN (2004) Network biology: understanding the cell’s functional organization. Nat Rev Genet 5(2):101 Barabási AL, Gulbahce N, Loscalzo J (2011) Network medicine: a network-based approach to human disease. Nat Rev Genet 12(1):56 Chen X et al (2010) A sub-pathway-based approach for identifying drug response principal network. Bioinformatics 27(5):649–654 Crick F (1970) Central dogma of molecular biology. Nature 227(5258):561 Dimitrakopoulos GN, Vrahatis AG, Balomenos P, Sgarbas K, Bezerianos A (2015) Age-related subpathway detection through meta-analysis of multiple gene expression datasets. In: 2015 IEEE international conference on digital signal processing (DSP). IEEE, pp 539–542 García-Campos MA, Espinal-Enríquez J, Hernández-Lemus E (2015) Pathway analysis: state of the art. Front Physiol 6:383 Goeman JJ, Bühlmann P (2007) Analyzing gene expression data in terms of gene sets: methodological issues. Bioinformatics 23(8):980–987 Gustafsson M, Nestor CE, Zhang H, Barabási AL, Baranzini S, Brunak S, . . . Benson M (2014) Modules, networks and systems medicine for understanding disease and aiding diagnosis. Genome medicine 6(10):1–11 Hardcastle TJ, Kelly KA (2010) baySeq: empirical Bayesian methods for identifying differential expression in sequence count data. BMC Bioinformatics 11(1):422

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6

Neuronal Encoding Models Emmanouil Perakis

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Models of Single Neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An Intraneuronal Ionic Concentration Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Hodgkin-Huxley (H-H) Model and Its Two Simplifications . . . . . . . . . . . . . . . . . . . . . . . . . . The Fitz-Hugh-Nagumo (FHN) Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An AP Propagation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Synapse Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electrical Synapses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chemical Synapses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

112 113 113 117 121 123 126 126 127 130 130

Abstract

This review summarizes the basic information about neurons and their mechanisms and it presents a variety of the mathematical models applied in neuroscience research. A description of the models, which can predict and explain biomedical phenomena, is provided. This is also supported by experimental data. The mathematical models concern both single neurons and synapses. In addition, their main simplifications are also presented, which can help reduce their complexity but without losing their validity. Keywords

Neuron · Model · Mathematical · O.d.e · P.d.e

E. Perakis (*) Department of Informatics, Ionian University, Corfu, Greece e-mail: [email protected] © Springer Nature Switzerland AG 2023 P. Vlamos et al. (eds.), Handbook of Computational Neurodegeneration, https://doi.org/10.1007/978-3-319-75922-7_11

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Introduction Neurobiology is a science that basically differs from other sciences, especially from mathematics and mathematical modeling. Based on powerful statistical and other tools, which assist us to the detailed data processing, neuroscience can become more understandable, by using mathematical theory. Mathematical theory and tools can be enhanced by proper scientifical computational applications. Thus, the proofs and conclusions become more powerful. However, neuroscience is still characterized by experimental methods and findings, while mathematical theory is developing; some of the observations and findings during the experiments are most predicted using mathematical modeling. In general, there are two types of models: descriptive and mechanistic. The first ones disregard the biology system physiology and the second ones are interested in the reproduction of the observed behavior and explain in details the physical and biological processes, using advanced applied mathematical tools. Neurons constitute a special type of cells that are composed of three major parts: an axon, the dendrites, which are essentially elongated projections, and a central body (or “soma”). The first major part of the neuron, which are the dendrites, are projections that form “branches.” They are specialized to receive signals from other neurons, which are, in sequence, in direct contact with other neurons at the so-called structures: the synapses. The signals that are transmitted along the length of the neuron can be chemical or electrical. The electrical signals are transmitted over distance, with a relatively high velocity. The neuron, just like all cells, has a membrane, which constitutes a highly important feature and it permits the passage of some major ions, through the so-called ion channels or pores. These ions are mainly: sodium Na+, potassium K+, calcium Ca++, and chlorine Cl
. The flow of the ion channels is regulated by those, which are found in the membrane of the neuron. The transmembrane voltage can be one of the major factors, in combination with different signals, derived from the external and internal environment, which is regulated by the ion flow across these pores. An important ion exchange through the membrane of the neuron is the movement of Na+ and K+, via the Na+
K+ “gate.” Thanks to it, the voltage can have the stable value of
70 mV, known as resting potential (RP). These signals last about 1 msec and take place through the neuronal axon, consisting of consecutive fluctuations in voltage (O(100) (O(n) means generally: “within an approximate order of n.”) mV) (action potentials (AP) or spike). Positive ions create the positive current, which flows out and, on the other hand, negative current flows inside the neuron and hyperpolarizes it, making the membrane voltage more negative and excitating the neuron. So that the result is the positive voltage of the membrane. There are two temporal phases: the first one is called absolute refractory period, in which the neuron does not spike. This happens independently of the fact that the pumps work and coordinate to reestablish the concentration gradient, enabling to spike. This period is followed by the relative refractory period, when the concentration of the cations or anions during this phase is difficult to spike.

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Another characteristic that plays an important role in the regulation of the neuron volume is the neuron membrane, which contains pores or ion channels, through which several ions and molecules pass. Also, it separates the external from the internal environment of the neuron and it prevents uncontrolled passage of water, Na+, K+, and Cl
. Two of the characteristics of the neuron membrane are: the electrical resistance and the capacitance, which alternate by the channel condition. Different ion movement is regulated by different channels. Across the membrane of the neuron, ions and molecules can be transported. This kind of transport and movement is highly important for several facts that take place in the neuron. Specifically, several concentrations of ions can regulate the water crossing. This phenomenon occurs passively and it is so-known as osmosis, which constitutes a passive process. There is the passive process and the active process, which requires energy to take place and it can happen via pumps. Diffusion is another process that assists to the control of the neuron volume. There are two types of synapses: electrical and chemical. Electrical synapses include direct communication of the cytoplasm of two different neurons and they permit depolarizing signals. Also, the production of excitatory and inhibitory postsynaptic potentials can be via (the slower) chemical synapses by the following process: A presynaptic neuron releases a neurotransmitter that is received by the postsynaptic neuron. Multiple EPSPs (excitatory postsynaptic potentials) cause the postsynaptic neuron to spike. IPSPs (inhibitory postsynaptic potentials) drive the voltage down and tend to delay or even to prevent spiking. The behavior of chemical synapses is considered to be more complicated, for they permit the neuronal communication.

Models of Single Neurons An Intraneuronal Ionic Concentration Model We now briefly describe two mathematical models of the concentration of ions inside the neuron (Krinsky and Kokoz 1973), which cover a wide range of cases: the Nernst equation, which solves the potential of an electrochemical cell containing a reversible system with fast kinetics and it is valid only at equilibrium and the Goldman-Hodgkin-Katz (GHK) equation, which describes the ionic flux across a neuron membrane as a function of the transmembrane potential and the concentrations of the ion inside and outside of the cell. Since both the voltage and the concentration gradients influence the movement of ions, this process is a simplified version of electrodiffusion, which is most accurately defined by the Nernst-Planck equation. The GHK flux equation is a solution to the Nernst-Planck equation with some assumptions. Assume a given region of space Ω and let c(x,t) be the concentration of the ion, which we are interested in, as a function of the spatial variable x and time t on Ω. If q denotes the production of concentration c/unit volume, which is defined over the

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E. Perakis !

region Ω, J the vector flow of c, which is defined along the boundary @Ω of Ω and ! n the unit vector perpendicular to the boundary, results in the following conservation law: @ @t

!

¼ qdV


cdV Ω

Ω

!

J  n dA

ð1Þ

@Ω

i.e., the rate of change of c in Ω equals to the difference: production
loss through boundary. Applying the Gauss (divergence) theorem, we have: !

!

!

J  n dA ¼ div J dV

ð2Þ

Ω

@Ω

and, for a fixed region Ω, expression (1) becomes:

Ω

@c dV ¼ @t

!

q
div J

dV

ð3Þ

Ω

This integral conservation law is valid for any stable arbitrary region Ω and, so the integrand must be identically equal to 0. Therefore, there is the following partial differential equation (p.d.e), describing the rate of change of c: ! @c ¼ q
div J @t

ð4Þ

Fick’s law (which is not a natural law) also states, in our case, that ions tend to flow from high concentration areas to low concentration areas. Substituting Fick’s law with a diffusion coefficient D (in cm2/sec) into equation (4), we obtain: @c ! ! ¼ ∇ D∇ ðcÞ þ q @t

ð5Þ

Let also z be the valence of the ion (so, the quantity kzzk ¼1 denotes the sign of !

the charge on the ion). If vector u describes ion’s mobility and φ denotes the electrical potential, Planck’s equation describes the ion flux resulting from such a potential gradient (Ermentrout and Terman 2010): !

!

J ¼u

z ! c∇ ðφÞ kz k

ð6Þ

Thus, there is a concentration gradients flow and a potential gradients flow, each of them is presented by a constant. Each ion is characterized by this constant. Einstein constructed a relation, which relates the diffusion constant D in Fick’s

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!

law to ionic mobility u in Planck’s equation (Ermentrout and Terman 2010). Given that F’96485.3 Cb/mol is the Faraday’s constant, T denotes the absolute temperature (in  K) and R’8.3 J/(Kmol) is the universal ideal gas constant; this reads: !

D¼

u RT kzkF

ð7Þ

Combining the concentration-driven (diffusion) p.d.e (5) with the Planck’s equation flux (6) and applying Einstein’s expression (7) yield the Nernst-Planck equation: !

!

J ¼
D ∇ ðcÞ þ

zF ! c∇ ðφÞ RT

ð8Þ

If there is a specific concentration difference, the potential is equal and stable to ! ! zero flux. Setting the flux J ¼ 0 permits us to solve for the potential difference and the following ordinary differential equation (o.d.e) occurs (the membrane is modeled as one-dimensional x, without spatial variations parallel to the boundary): c 0 ð xÞ þ

c0 ðxÞ zF 0 zF cðxÞφ0 ðxÞ ¼ 0 , φ ð xÞ ¼ 0 þ RT cðxÞ RT

ð9Þ

Integrating o.d.e (9) across the membrane length, with cex and cin denoting the values of the external and internal concentrations, respectively, and φex, φin describing the values of the respective potentials, recognizing the difference Vφin
φex as the membrane potential and exponentiating next yields the Nernst equation: V¼

RT c ln ex zF cin

ð10Þ

which concerns the Nernst potential. According to the equation (10), although there is one species of ions in equilibrium, nonzero currents and currents that change the potential are created. Assuming that a constant electric field takes place across a neuron membrane of thickness L and potential V, the field within the membrane is given by: E ¼
φ0 ðxÞ ¼


V : L

This is then substituted into expression (8) to obtain the o.d.e: c 0 ð xÞ


JFV J c ð xÞ þ ¼ 0 RTL D

ð11Þ

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E. Perakis

which can be solved for c(x). It may be taken J(x)J as constant (since the current remains constant across the membrane), because there is no local charge accumulation. The boundary conditions here are formed as: c(0)cin and c(L)cex and we conclude to the following equation: c ð xÞ ¼

JRTL zVF 1
exp x DzVF RTL

þ cin exp

zVF x RTL

ð12Þ

Moreover, we apply the second boundary condition above, we rename the fraction DL PS: the parameter of the transmittance of the membrane to ion S, we set ISzFJ and we replace JIS: the GHK current for ion S. Here J denotes the flux in moles/(unit area‧unit time), while zF denotes the charge carried/mole of ion S. Thus, IS is the charge/(unit area‧unit time) or the current/unit area: IS ¼ P S V

z2 F2 cin
cex exp
zFV RT RT 1
exp
zFV RT

ð13Þ

which is the GHK current equation (Ermentrout and Terman 2010). For J¼0, the GHK current (13) equals also to 0 at: V¼

RT c ln ex , zF cin

which is the Nernst potential equation (10) (the same result of the previous process). It is now required to determine the potential of the membrane, at which the pure ionic current equals to zero: the resting potential (RP). Obviously, for given concentrations of the inner and outer neuronal environment, each ion has a Nernst potential (10). The (GHK current) equation (13) allows the currents to be added, thus obtaining the required equilibrium. With some ions with valence z¼1 and others with valence z¼
1, zero total current is obtained, if: FV RT þ FV 1
exp
RT

cjin
cjex exp
Pj j ðz¼1Þ

FV RT FV 1
exp RT

cjin
cjex exp Pj j ðz¼
1Þ

¼0

(14)

and, solving for the GHK potential V, we have that the RP: Pj cjin þ V¼

RT ln F

j ðz5-1Þ

Pj cjex j ðz51Þ

Pj cjin þ j ðz51Þ

Pj cjex j ðz5-1Þ

(15)

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Concentrations and permeabilities assist in the representation of the RP of the neuron. The type of neuron, the concentration levels, and other factors define the validity of a given and constant electric field assumption required for the GHK derivation. The RP determined by expression (15) generally will not coincide with any of the Nernst potentials for individual ions, which are given by the equation (10). Thus, a passive ion flux is expected to occur, thus altering the concentration ratios.

The Hodgkin-Huxley (H-H) Model and Its Two Simplifications The Hodgkin-Huxley (H-H) model was developed through ingenious experimental work by Hodgkin, Huxley, Katz, and others, the time period just before and just after World War II (Hodgkin and Huxley 1952a, b; Barlow 1996; Keener and Sneyd 2009; Wilson 1999; Hodgkin and Huxley 1952c), built on earlier work by Cole and Marmont. It is a four o.d.e model that reproduces the action potential and extension to a p.d.e, in order to explain its propagation along the axon (Hodgkin and Huxley 1952a), where n(t),m(t),h(t)  [0,1] are gating time–dependent probability functions: Cm v0 ðtÞ5
gK n4 ðv
vK Þ
gNa m3 hðv
vNa Þ
gL ðv
vL Þ þ Iapp 0

n ðtÞ5αn ðvÞð1
nÞ
nβn ðvÞ 0

a b

m ðtÞ5αm ðvÞð1
mÞ
mβm ðvÞ

c

h0 ðtÞ5αh ðvÞð1
hÞ
hβh ðvÞ

d

ð16Þ

Variable n(t) represents the probability that a K+ channel is open, m(t) the probability that a Na+ channel is open, and h(t) the probability that the Na+ inactivation gate is open. Equation (16a) represents the alternation in membrane potential based on four ion flows: K+ current, Na+ current, a leakage ion current, and an external applied current (according to Kirchhoff’s law). Bars in K+ and Na+ conductances indicate that they now denote constant parameter values that multiply probability functions n, m, and h to form the maximum conductances: g KgKn4 and g NagNam3h of equation (16a). n4 represents the probability that a K+ channel is open: The K+ channel has four independent components, all of which are identical. For the same reason, the probability that the Na+ activation gate is open is m3 and the probability that the Na+ inactivation gate is open is h. The leak conductance gLgCl, primarily due to chloride ions, remains constant. The external current Iapp may derive from synaptic inputs, electrical contacts with other neurons or from an intraneuronal electrode. Writing equations (16) and the expressions (17, 18, 19) below together, we have adopted the usual convention of increasing voltages, leading to an action potential. Channel gating variables m, n, and h correspond to dependence of voltages, associated with the K+ and Na+ ions. These variables evolve under equations (16b–16d), whose coefficients αn and βn depend on voltage, as shown in expressions

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(17–19) below, so that the entire set of equations is coupled. Transmembrane potential takes the reversal potentials vK, vNa, and vL and alternate the directions of the currents. The most important effect of the ions is those of Cl
that is combined by the leakage current, as well as its conductance gL that is considered to remain constant over a relevant voltage range. The forms of the α and β functions are given by: α n ð vÞ ¼

10
v 1 v ,βn ðvÞ ¼ exp
10
v 8 80 100 exp 10
1

ð17Þ

25
v v ,βm ðvÞ ¼ 4 exp
18 10 exp 25
v
1 10

ð18Þ

α m ð vÞ ¼

α h ð vÞ ¼

7 v exp
,β ðvÞ ¼ 10 20 h exp

1 30
v 10

þ1

ð19Þ

Units are of: membrane voltage: mV, currents: μA, capacitance: μF, and conductance: mS(¼10
6/mΩ). The units in equation (16a) are then μA for the neuron as a whole. Neuron size can be removed by expressing membrane capacitance and ion channel conductances as μF/cm2 and mS/cm2, respectively, giving current densities/ unit area in μA/cm2. The gating variables are dimensionless (for m,n,h  [0,1]) and the usual time scale unit is msec. In equations (16c) and (16d), each of the α and β is a voltage function. The resulting six voltage-depending functions have units of msec
1, measured with respect to the RP of the neuron. The constants are: gNa ¼ 120,gK ¼ 36,gL ¼

3 53 ,v ¼ 115,vK ¼
12 and vL ¼ : 10 Na 5

The RP is very close to the K+ Nernst potential vK, compared to the Na+ potential vNa, because the equilibrium conductance is higher for K+ than this for Na+ and it can drive the RP closer to the K+ Nernst potential. A membrane potential was created, when a metallic conductor was inserted inside the neuron, thus the membrane voltage is irrelative to the space. In the experiments it was observed that there was no charge accumulation in the neuronal axon and the applied current was equal to the transmembrane ion currents. Combines with manipulations of the solution on the outer environment of the neuron, this device permitted characterizations of the single ionic currents, leading to the gating functions of expressions (17), (18) and the polynomial fits n4 and m3h for conductance dependence in equation (16a) (Ermentrout and Terman 2010). In their experiments, Hodgkin and Huxley observed that, during a spike, an initial output current followed an input current. According to what they hypothesized, the influx was the current, which entered the neuron and is due to the flow of Na+, while the outflux is due to the K+ ions. The latter had the highest concentration within the neuron. Separating the K+ current, as described above, its conductivity was observed from experimental data to show sigmoidal increase and exponential decrease. This

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was modeled in terms of the fourth power of a new function n(t): the activated K+. The fourth power was the smallest exponent, which showed an acceptable fit to the data. In addition, n(t), elevated to the fourth power, reproduces the sigmoid increase from n¼0 and the exponential decrease from n>0 (Hodgkin and Huxley 1952a). According to the spike initiation dynamics the Na+ conductance is considered more complicated, including two processes. In the first one the Na+ is activated and deactivated. Variables m and h correspond to them respectively. Acceptable adjustments were again made by an exponential law: m3h. This elegant solution models the conductivity of the two underlying processes. The activation is given by the function m(t), where the internal current Na+ starts and function h(t) expresses its deactivation. The so-called upstroke is represented by a sharp increase in membrane potential as the conductivity of Na+ increases rapidly up to the potential Na+ Nernst, which does not last long. The Na+ conductance is lowering as function h(t) decreases, while the Na+ conductance increases as function n(t) increases. Based on the fact that there are no longer time constants, n(t) remains high and h(t) stays low. Therefore, the potential stays also low without any spike again. The recovery phase shows us that functions n(t) and h(t) have returned to the values that allow others to spike. The functions m, n, and h are associated with the pores in the neuron membrane that permit the ions to pass through them. A probability is determined here, which is relied on the voltage and the expression that defines the variable. n defines the fact that one fourth of the K+ channels are open. That is, the percentage of open pores is proportional to n4. Over a large number of ion channels, the probability of a given being open is very close to the percentage of those that are actually open. The percentage of open gates is given by m3h, because the Na+ channel is assumed to have three m gates and one h gate. It is presented now a two-dimensional simplification of the H-H equations, a two-dimensional reduction of H-H model. In examining the behavior of the four H-H state variables, it is important to note that m(t) changes relatively rapidly, 1 because its timescale τm¼ αm þβ is small, relative to τn and τh in the relevant voltage m range (Rall et al. 1967). Therefore, the provisional quantities were ignored in m and _ ’0. So, it turns out that: considered to be approximately balanced, so that m mðtÞ ’ m1 ðvÞ ¼

α m ð vÞ αm ðvÞ þ βm ðvÞ

ð20Þ

from expression (18). The functions n(t) and h(t) are approximately anticorrelated in that, throughout the action potential and the recovery phase, they remain close to a straight line with a slope equal to
1: h¼α
n (Rinzel and Keener 1983). This allowed the elimination of m and h as state variables, dropping equations (16c), (16d) and, replacing m and h in equation (16a) by the function m1(v) and by h¼α
n (Krinsky and Kokoz 1973) gives the value α¼1, but for the “classical” parameters of the H-H model (Hodgkin and Huxley 1952a), α¼0.8 is more appropriate. The H-H system of equations (16) was reduced to the two variables v and n:

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E. Perakis

Cm v0 ðtÞ5
 gK n4 ðv
vK Þ
gNa m31 ðvÞð1
nÞðv
vNa Þ
gL ðv
vL ÞþIapp 0

n ðtÞ5αn ðvÞð1
nÞ
nβn ðvÞ

a b

(21) However, while the n_ ¼0 nullcline: nðvÞ ¼

αn ðvÞ αn ðvÞ þ βn ðvÞ

ð22Þ

the v_ ¼0 nullcline, given by setting the right-hand side of equation (21a), is zeroed and demands solution of a quartic polynomial in n. To show the rich dynamics that a plane system with nonlinear nullclines can exhibit, we have chosen parameter values for which the equations (21) have three fixed points or only one, like the original H-H equations (Rall et al. 1967). The spikes are qualitatively similar to those of the full H-H system of equations (16). Relatively to the applied current Iapp¼0, solutions settle to the stable fixed point at V¼0, but, for the value of Iapp¼15, they approach a stable limit cycle, representing periodic spiking behavior. When the fixed point is located to the left of it, as it is in the case of Iapp¼0, the solutions can spike expressing the perturbations, which push v above the threshold potential vth. Therefore, with absent further perturbations, the state will remain at the stable fixed point. When it gets over vth, it loses stability and solutions repeatedly reach and cross the threshold value, leading to an independent spiking. Wilson (Krinsky and Kokoz 1973) presents an also two-dimensional simplification of Rinzel’s reduction system of equations (21), which also uses cubic and linear functions, but which better captures the spike rate vs applied current characteristic. Models, such as H-H, which produce distinct spikes from fast excitative (Na+) currents, separated by erratic periods, which are controlled by slower overpolarization (K+) currents, were considered. Multiple spikes clusters, followed by a period of inactivity, called bursting, can also occur and can vary (Ermentrout and Terman 2010; Krinsky and Kokoz 1973). Two subsystems interact, separated by their time scales: a faster one, characterized by the K+ and Na+ channels, and a slower, driving the first through its quiescent and oscillatory states, which can be attributed to accumulation of Ca++ ions within the neuron (so-called Ca++ dynamics (Ermentrout and Terman 2010)). Singular perturbative reduction methods (Johnston and Wu 1997) can also provide insights into the dynamics of bursting neurons, which may be written generally as a system of o.d.e.s: ! ! ! u_ 5 f u , c !

c_ 5εg u , c

a b

ð23Þ

6

Neuronal Encoding Models !

121

!

where the vector u 5(v, w)  ℝn, v represents the voltage of neuronal membrane, ! the n-1-dimensional vector w 5(w1,w2,. . .,wn
1)  ℝn-1 denotes a collection of gating variables wj, j  {1,2,. . .,n
1}, and ε1 expresses a small value parameter. The variable c can indicate the concentration of Ca++ or, in general, any very slowly changing quantity, which is responsible for bursting. The set of equations (23a) generally may take the H-H form (16) as follows: _
Iion ðv, w1 , w2 , . . . wn , cÞ þ Iext ðtÞ a Cv5 wj1 ðvÞ
wj , j  f1, 2, . . . , n
1g b w_ j 5 τj ð v Þ

ð24Þ

where the term Iion represents the sum of all ionic currents and the functions wj1(v) and τj(v), j  {1,2,. . .,n
1}, are formed similar to those of the H-H system of equations. Some of the introductory equations (24b) may be so much faster than others that those variables can be considered to be equilibrated, but they are all fast, compared to the slow variable c.

The Fitz-Hugh-Nagumo (FHN) Model Although the Fitz-Hugh-Nagumo (FHN) model predated the H-H reduction (Nagumo et al. 1962; Rinzel and Keener 1983; Rall 1964), it is described now. The FHN equations are mathematically structured similarly to that of Rinzel’s H-H reduction. In addition, apart from the two time schedules, the physiological interpretation and the physical units do not exist, but the basic quality properties remain (Krinsky and Kokoz 1973): 1 v3 v

r þ Iapp τv 3 1 5 3 r_ 5 v
rþ τr 4 2 _ v5

a ð25Þ b

Here with v is still represented the voltage of the membrane, but r is virtually a 1 combined effective gating/recovery variable. Wilson chooses values τv¼ 10 and 5 τr¼ 4 (which are adopted for the calculations to follow), but the time constants are written as parameters to indicate that they may vary (Hodgkin and Huxley 1952a). 1 and the (slow) value 54 have been chosen to reflect the rapid The (fast) value 10 upstroke and downstroke in the action potential and the slower hyperpolarized, subthreshold dynamics, respectively, but the relative durations of the depolarized and hyperpolarized events are approximately equal. The reason for this becomes clear when we examine the nullclines:

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E. Perakis

v_ ¼ 0 ) r_ ¼ 0 Provided that τvτr and

1 10

v3 þ Iapp 3 5 3 r ¼ vþ 4 2 r ¼v


ð26Þ

 54 in this case , the vector field of system of o.

d.e.s (25) is dominated by its large v_ component everywhere, except in an O jττvr j

neighborhood of the v_ ¼0 nullcline. The flow, therefore, moves approximately horizontally and quickly toward this slow manifold and follows it closely in the direction determined by the slower component o.d.e (25b) of the vector field. This leads to the slow climb up the right-hand branch of the cubic v_ ¼0 nullcline and the slow descent of its left-hand branch, punctuated by fast jumps up and down in voltage, when the solutions leave the neigborhood of the attracting branches of the nullcline. O.d.e.s (25) have obviously a single equilibrium point for all values of Iapp, as it is obvious by examining the cubic equation, that results from setting r¼ 32 + 54 v (ensuring r_ ¼0) in v_ ¼0, to obtain: 4v3 þ 3v
12Ιapp þ 18 ¼ 0

ð27Þ

Alternatively, the cubic v_ ¼0 nullcline of system of equations (26) satisfies the o. d.e r0 (v)¼1
v2 and so has maximum (positive) slope equal to 1, while the linear nullcline v_ ¼0 has slope equal to 54 . Therefore, they can only be crossed once. However, as the Iapp changes, the stability of this equilibrium can vary, creating boundary circles in the Hopf bifurcations (Rinzel and Keener 1983). We will now construct the simplified FHN version, a p.d.e of which exhibits a Hopf bifurcation to periodic traveling waves (Jones 1994). Adding the (diffusive) 1 @2 v term pR @x2 to o.d.e (25a) and assuming constant resistance/unit length along the axon, we have the system of p.d.e.s: @v 1 1 @ 2 v v3
r þ Iapp þ v
5 @t τv pR @x2 3

a

@r 1 5 3 v
rþ 5 @t τr 4 2

b

where τvτr. Hence, we define a small parameter ε and space, we let:

τv τr

1. Then, rescaling time

t and x  ε pRx, τr p @ @ @ and @x ε pR @x . Then, the system of p.d.e.s (28) @t

t so that the operators @t@  τ1r becomes:

ð28Þ

6

Neuronal Encoding Models

123

ð29Þ

Assuming the axon is very long, relatively to its diameter, it occurs a high resistance R1, so then the rescaling makes sense. We now seek a uniform traveling wave, with voltage and recovery variable profiles: vðx, tÞ  Vðx
ctÞ : rðx, tÞ  Rðx
ctÞ Proceeding, we obtain the system of o.d.e.s: «2 V00 þ «cV0 þ f ðV, RÞ50

a

cR0 þ gðV, RÞ50

b

ð30Þ

where the operator (. . .)0  @

@ . This is essentially a third-order o.d.e (Bender and ðx
ctÞ Orszag 1978; Johnston and Wu 1997) (although it might make a nice project for the more mathematically inclined). Briefly, since ε1, the waveframe dynamics of o.d.e (30a) is fast compared to that of o.d.e (30b), so that it may be assumed that R remains approximately constant, while V rapidly approaches a point on the nullcline f (V,R)¼0, according to o.d.e (30a). After V equilibrates, R changes slowly according to o.d.e (30b) and the solution moves along close to the nullcline until the bend, where it jumps rapidly to the other attracting branch. Another version is been solved (Ermentrout and Terman 2010), in which the cubic V-dependence in f(V,R) is replaced by a linear function, representing the external branches with negative slope (Fitz Hugh 1960). They have exponential solutions, for there are chosen integration constants, such that to satisfy proper specific conditions and a geometrical approach is also being presented to the nonlinear problem. It is also given a shorter account of this problem (Destexhe et al. 1999).

An AP Propagation Model It will now be presented a model for the transmission of the AP along the axon (seen as one-dimensional continuous medium) (Hodgkin and Huxley 1952a). The o. d.e.s (16) and their simplifications assume a spatially uniform potential difference across the neuron membrane. It is also necessary to construct a spatiotemporal model, because there are neurons with long axon and rapid potential changes. The cable equation gives, based on the potential across the membrane, the spatial description of current Im that passes through the membrane of the neuron:

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E. Perakis

Im ¼

@ 1 @v @x R @x

ð31Þ

where appears the (well known!) diffusion equation. Here, R5Rin+Rex, which may depend on x, denotes the sum of the resistances of the internal and external neuronal environment/unit length (Ermentrout and Terman 2010). This equation may be derived as follows: first let us consider a short infinitesimal segment [x,x+dx] of length dx, having intra- and extraneuronal resistances Rindx, Rexdx, respectively, and denote the intra- and extraneuronal voltages at either end as vin(x), vex(x) and vin(x+dx), vex(x+dx), respectively. Assuming that there is positive current flow from left x to right x+dx and applying Ohm’s law, we have: vin ðx þ dxÞ
vin ðxÞ ¼
Iin ðxÞRin dx and vex ðx þ dxÞ
vex ðxÞ ¼
Iex ðxÞRex dx ð32Þ

where Iin and Iex denote the internal and external currents in the axial direction, respectively. It gives that: Iin ðxÞ ¼


1 @vin 1 @vex and Iex ðxÞ ¼
Rin @x Rex @x

ð33Þ

Balancing the currents of the axon Iin and Iex at x and x+dx, respectively, with the current through the membrane, we appeal to Kirchhoff’s laws. If Im is again the transmembrane current/unit length, this gives: Iex ðx þ dxÞ
Iex ðxÞ ¼ Im dx ¼ Iin ðxÞ
Iin ðx þ dxÞ

ð34Þ

(i.e., what is lost in external current is gained in internal current), which gives: I m ð xÞ ¼

@Iex @I ¼
in @x @x

ð35Þ

Because v¼vin
vex and total axial current Iax¼Iin+Iex is constant, explicit reference is reduced to the internal and external currents and voltages. From expressions (33) we get: ðR þ Rex Þ @vin 1 @vin 1 @ ðvin
vÞ 1 @v ¼
in )
þ @x Rin Rex Rin @x Rex @x Rex @x Rex Iax 1 @vin 1 @v ) ¼
þ Rin @x Rin þ Rex @x Rin þ Rex ð36Þ

Iax ¼ Iin þ Iex ¼


Since @I@xax ¼0 (Iax is constant), this gives: @ 1 @vin @x Rin @x

¼

@ 1 @v @ Rex
Iax @x Rin þ Rex @x @x Rin þ Rex

ð37Þ

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Neuronal Encoding Models

125

If the resistances are stable or, if Rex’0 (e.g., we isolate the axon in a fluid (Hodgkin and Huxley 1952a; Ermentrout and Terman 2010)), the final term is zeroed in and, substituting Iin for @v @x from the first of equations (33) and applying p.d.e (36), we obtain: Im ðxÞ ¼


@Iin @ 1 @v ¼ @x Rin þ Rex @x @x

¼

@ 1 @v @x R @x

ð38Þ

Connecting this with the H-H o.d.e.s (16), the transmembrane current Im is the sum of the capacitive current C @v @t and the ionic and applied currents. Hence: p C

@v þ Iion
Iapp @t

¼

@ 1 @v @x R @x

ð39Þ

Here the left-hand side of the equation multiplied by the perimeter p of the axis to imply that all terms have the same units, vv(x,t) and the currents also depend on the variables t and x. Finally, the sign of Iapp in p.d.e (39) is chosen for consistency with o.d.e.s (16) to which p.d.e (39) reduces if v does not depend on x. Also, it is solved along with the o.d.e.s (16c) and (16d) for the gating variables. Here they are considered one-dimensional axons and, so, the end point voltages must be specified. For x¼0 and x¼L, the boundary conditions become: vð0, tÞ  v0 ,vðL, tÞ  vL

ð40Þ

@v @v ð0, tÞ ¼ ðL, tÞ ¼ 0 @x @x

ð41Þ

@v ð0, tÞ ¼
Rin Iin ð0, tÞ @x

ð42Þ

(voltage clamp),

(insulated ends) or

(current injection at x¼0) and assuming that the axon starts in the resting state is a suitable initial condition, so: vðx, 0Þ  vrest where vrest satisfies the relation: gK ðV
VK Þ þ gNa ðV
VNa Þ þ gCl ðV
VCl Þ ¼ 0, with gK ¼ gK n41 ðvÞ,gNa ¼ gNa n31 ðvÞh1 ðvÞ and Iapp ¼ 0:

ð43Þ

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E. Perakis

There is a brief source, with more information on dendritic trees and spatially distinct models of neurons with multiple compartments (Krinsky and Kokoz 1973). Also, tree structures of dendrites could form incoming signals (Rall 1959; Dayan and Abbott 2001) and it is now known that passive and active, linear and nonlinear effects on dendrites, including the back propagation of APs, can affect neuronal communication (London and Häusser 2005).

Synapse Models Electrical Synapses Electrical synapses, or, otherwise, gap junctions, permit the neurons to contact directly via communications of the cytoplasm of two distinct neurons via channels at which the neurons are only 3.5 nm apart. This sort of channels are specialized protein structures with pores and a pair of hemichannels (or so known as connexons), each one of them is made up of six proteins that are called connexins: proteins that span their respective neuron membranes. The alternating orientation of the connexins results in the closing and opening of the channels, permitting study of the neuronal apparatus. In general, the electrical synapses are excitatory via the transmitted potentials. The fact that the cytoplasms are continuous is not true for all of the cases. High voltages might have as a result the closing of certain channels. Thus, the spikes are able to travel along a single direction. This kind of synapses are so called as rectifying synapses (Dayan and Abbott 2001). Different signs that state that the neurons have undergone damage are the closing of the channels that are found within the synapses. This happens because of low cytoplasmic pH or high Ca++. In the locations that we need a quick response we observe electrical synapses, which permit the communication of large groups of neurons. As a result, the smaller neurons function as a larger network. All neurons are linked in parallel series. So that a small change in input in the neuronal apparatus can lead to change in the voltage in them, but once there is a sufficient input to cause a spike, all neurons spike simultaneously, in so-called “all-or-none” mode. For the current passing from the j-th to the k-th neuron, it is added to the internal ionic currents a term Igap¼+ ggap (vj
vk), where ggap represents the conductance of the junction, the gap junction current term is conventionally shown as +Igap and vj
vk is the potential difference between neuron j and neuron k. For a pair of H-H type model neurons, this implies the system of o.d.e.s: C1 v_ 1 5
I1

ion ð. . .Þ

þ I1

ex

þ ggap ðv2
v1 Þ a

C2 v_ 2 5
I2

ion ð. . .Þ

þ I2

ex

þ ggap ðv1
v2 Þ b

plus equations for the gating variables of each neuron.

ð44Þ

6

Neuronal Encoding Models

127

Chemical Synapses Synaptic clefts separate the neurons of chemical synapses. This is found between the presynaptic terminals or, so-called, boutons and postsynaptic dendritic spines. The first ones are like swellings on the axon. We can use the term exocytosis in order to describe the amplification of the signal. The product of the release of one vesicle corresponds to the size of the synaptic vesicle. Thousands of “quantal” neurotransmitter molecules are able to open many ion channels and, as a result, they can excitate a much larger neuron that is possible with gap junctions (Barlow 1996; Keener and Sneyd 2009). Receptors are activated by the release of the neurotransmitter that diffuses in the synaptic cleft. These receptors exist along the whole surface of the postsynaptic membrane. In the postsynaptic neuron the spanned proteins close or open ion channels, which based on the type of channel can lead to excitatory or inhibitory effects: excitatory postsynaptic potentials (EPSPs) and inhibitory postsynaptic potentials (IPSPs), respectively (Rall et al. 1967). Ionotropic receptors are characterized by the direct passage of quick responses within msecs, based on directly ligand-gated ion channels. The first subtype of the ionotropic receptors together with cys-loop receptor and ionotropic glutamate and adenosine triphosphate subdivides into anionic and cationic groups. In the metabotropic receptors, second messenger act on the postsynaptic ion channels, indirectly. This fact causes effects lasting from several seconds to minutes and it is determined by the cascade properties that mediate the action of the metabotropic receptors. The cascade inside the neuron is mediated by G-proteins and it can be characterized by more complex formation. We can model neurotransmitter arrival as a current source in the postsynaptic neuron (Fitz Hugh 1961; Dayan and Abbott 2001). The variable, that affects the synaptic flow, is the conductivity of the postsynaptic ion channels, which is typically standardized as the result of a maximum conductivity, with Ps the probability of being open. Probability Ps of an open single channel determines the fraction of the channels that are open in the whole group of them. The transmitter unbinds from the receptor and the channels close. We have gs as constant, the dynamics occur in Ps, which can be modeled like the introductory variables in the H-H o.d.e.s (16): P0s ðtÞ ¼ αs ½1
Ps ðtÞ

ð45Þ

where αs and βs, respectively, determine the rates at which channels open and close (Hodgkin et al. 1949; Agmon-Snir et al. 1998). The time constants of the relevant channels can be determined by in vitro experiments with pharmacological exclusion of specific receptors (Prinz et al. 2004). In order to model neurons as single compartments, we gather the properties of presynaptic synapses together in a postsynaptic neuron, so that Ps expresses the fraction of the postsynaptic channels that are open and the resulting synaptic current Ipost syn (t) (to be introduced later, in equation (52)) represents the net effect of all individual EPSPs and IPSPs arriving at time t (Hodgkin and Huxley 1952d).

128

E. Perakis

The opening of the channels is typically faster than the closing, so αsβs. The closing rate βs is generally thought to be constant, but the opening rate αs depends on the concentration of neurotransmitter in the synaptic cleft and can be expressed as constant αs multiplied by a function describing how it depends on the presynaptic voltage v (Hodgkin et al. 1949): α s ð vÞ ¼

fCNT g max 1 þ exp kpre Epre syn
v

 αs GðvÞ

ð46Þ

In this sigmoid function, {CNT}max represents the maximum concentration of the neurotransmitter in the synaptic cleft, kpre symbolizes the “sharpness” of the switch and Epre syn is defined as the voltage at which it opens. Due to the rapid increase of AP, the neurotransmitter fills the slit to its full concentration faster than any other timescale in the model, so it behaves like a momentary switch, which turns on and off as the v goes up and down. It can therefore be simplified by modeling the transmitter concentration with the help of the step function, which assumes a constant value of αs for a constant time T, otherwise it is zeroed, i.e: αs ðtÞ ¼

0,

t 0 or t  T

αðtÞ,

0