Electrophoresis ‘81: Advanced methods, biochemical and clinical applications. Proceedings of the Third International Conference on Electrophoresis, Charleston, SC, April 7–10, 1981. [held in conjunction with the first annual meeting of the Electrophoresis Society] 9783111519012, 9783110081558

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Electrophoresis '81 Advanced Methods Biochemical and Clinical Applications

Electrophoresis '81 Advanced Methods Biochemical and Clinical Applications Proceedings of the Third International Conference on Electrophoresis Charleston, SC, April 7-10, 1981 Editors R. C. Allen • P. Arnaud

W G DE

Walter de Gruyter • Berlin • New York 1981

Editors: Robert C. Allen, Ph. D. Professor of Biochemistry Department of Laboratory Animal Medicine and Pathology Medical University of South Carolina 171 Ashley Avenue Charleston, South Carolina 29403, USA Philippe Arnaud, Ph. D.; M. D. Professor of Biochemistry Department of Basic and Clinical Immunology and Microbiology Medical University of South Carolina 171 Ashley Avenue Charleston, South Carolina 29403, USA

CIP-Kurztitelaufnahme

der Deutschen

Bibliothek

Electrophoresis... : advanced methods, biochem. and clin. applications ; proceedings of the Internat. Conference on Electrophoresis. - Berlin ; New York : de Gruyter 3. 1981. Charleston, SC, April 7 - 1 0 , 1981. - 1981. ISBN 3-11-008155-5 NE: International Conference on Electrophoresis

Library of Congress Cataloging in Publication Data

International Conference on Electrophoresis (3rd : 1981 : Charleston, S.C.) Electrophoresis '81. Includes bibliographical references and indexes. 1. Electrophoresis-Congresses. 2. Biological chemistryTechnique-Congresses. 3. Chemistry, Clinical-Technique-Congresses. I. Allen, R. C. (Robert Chadbourne), 1924. II. Arnaud, P. (Philippe) III. Title. QP519.9.E43I57 1981 574.19'283 81-5456 ISBN 3-11-008155-5 AACR2

Copyright © 1981 by Walter de Gruyter & Co., Berlin 30. All rights reserved, including those of translation into foreign languages. No part of this book may be reproduced in any form - by photoprint, microfilm, or any other means - nor transmitted nor translated into a machine language without written permission from the publisher. Printing: Karl Gerike, Berlin. - Binding: Luderitz & Bauer, Buchgewerbe GmbH. Printed in Germany.

PREFACE The International Congress Electrophoresis *81 was held at the Sheraton Charleston Hotel in Charleston, South Carolina from April 6-10, 1981.

It was the third of a projected series of

international meetings organized with the objective of stimulating information exchange and advancement of knowledge and techniques in all areas of electrophoresis. This Congress was held in conjunction with the first annual meeting of the Electrophoresis Society and in future, these Congresses will be held as part of the annual meeting of the Electrophoresis Society. This Congress was attended by over 300 participants which represented almost 75 per cent of the society membership. Also, due in large measure to the generous support of NASA, a complete session devoted to free flow electrophoresis was able to be included. The format of the meeting was in part experimental and based on suggestions of many of the members. Thus, a greater emphasis was placed on posters and following round tables discussions. This format, with all of the attendees staying in a single location, proved to have the desired effect of producing a lively exchange of ideas and views among the participants, well on into the evening. The added atmosphere of a society meeting certainly aided in the success of the participation in the Congress . This volume contains over 100 of the presentations made either as oral reports or posters at "Electrophoresis *81". The manuscripts have been compiled into four sections entitled (I) Theory and Methods, (II) High Resolution Two-Dimensional Electrophoresis, (III) Biomedical and Biological Applications and (IV) Isotachophoresis and Free Flow Electrophoresis. Not every manuscript fits precisely in a given section, but the most

VI appropriate has been attempted in order to provide continuity of subject material. Production of this proceedings has been made possible only by cooperation of the authors who turned their manuscripts in on time and of which only a minority required serious editing. We wish to thank all of the contributors for their splendid efforts to which the many users of this technique are indebted. We also appreciate, in no small way, the efforts of the staff of Walter de Gruyter, Berlin, which led to the rapid publication of this volume. Charleston, South Carolina

Robert C. Allen Philippe Arnaud

We would like to acknowledge the outstanding help from Mrs. Susan Haskill, Mr. Michael Lack, Mr. Peter Brady of the Department of Pathology and our wives, Mrs. Carol Allen and Mrs. Marie-Laure Arnaud, in the organization and running of this meeting and Congress. We also wish to acknowledge the valiant secretarial efforts of Ms. Brenda Altman for preparation of the abstracts and proceedings. Financial aid for the Congress was provided by NASA, Beckman Instruments, Beta Analytical, Biorad, Bio Products, Brinkman Instruments-Desaga, DAKO, de Gruyter Publishers, E C Apparatus Corporation, Gelman Sciences, Helena Laboratories, Isolab, LKB Instruments, Marine Colloid FMC Corporation, Pharmacia Fine Chemicals, Serva Feinbiochemicals, Shandon Company, Upjohn Diagnostics and Verlag-Chemie Publishers.

VII CONTENTS

SECTION I, THEORY AND METHODS ON THE PORE SIZE AND SHAPE OF HYDROPHILLIC GELS FOR ELECTROPHORETIC ANALYSIS P.G. Righetti

3

GENERALIZATION OF THE DEBYE-HUCKEL THEORY TO MACROION SOLUTIONS OF FINITE SIZE AND CONCENTRATION AS APPLIED TO THEIR ELECTROPHORETIC MOBILITY AND TRANSLATIONAL DIFFUSION COEFFICIENT E.N. Serralach and R. Schor

17

CALCULATION OF THE THERMODYNAMIC CONSTANTS OF CONCANAVALIN A - CARBOHYDRATE INTERACTIONS BY MEANS OF AFFINITY ELECTROPHORESIS K. Takeo, M. Fujimoto, A. Kuwahara, R. Suzuno and K. Nakamura

33

HIGH RESOLUTION ELECTROPHORESIS OF PROTEINS IN SDS POLYACRYLAMIDE GELS D. Anderson and C. Peterson

41

CONVENIENT PROCEDURES FOR SDS AND CONVENTIONAL DISC ELECTROPHORESIS J.L. Neff, N. Munez, J.L. Colbourn and A.F. deCastro

49

THE DESIGN AND APPLICATIONS OF A UNIVERSAL GEL ELECTROPHORESIS APPARATUS G. Bambeck and J. Black

65

A SIMPLE METHOD FOR CASTING POLYACRYLAMIDE GELS OF VARIOUS THICKNESS AND SIZE FOR FLAT-BED ISOELECTRIC FOCUSING A. Esen

73

ISOELECTRIC FOCUSING ON CELLULOSIC MEMBRANES B. Janik and R.G. Dane

77

Vili A METHOD FOR PHENOTYPING OF ALPHA-1-ANTITRYPSIN VARIANTS USING SEPARATOR ISOELECTRIC FOCUSING ON AGAROSE R.A. Qureshi and H.H. Punnett

83

QUANTIFICATION OF PROTEINS WITH ZONE IMMUNOELECTROPHORESIS ASSAY (ZIA) 0. Vesterberg

89

SPECIFIC AND EFFICIENT PROCEDURES FOR QUANTIFICATION OF PROTEINS SEPARATED IN GEL ELECTROPHORETIC METHODS USING ZONE IMMUNOELECTROPHORETIC ASSAY (ZIA) 0. Vesterberg and U. Breig

103

A SIMPLIFIED POLYACRYLAMIDE DENSITY GRADIENT GEL ELECTROPHORESIS WITH A NEW STAINING METHOD, ELECTROSTAINING T. Hoshino, S. Jitsukawa, M. Tahara, G. Yamada and K. Sakakibara

117

ENHANCEMENT METHODS IN THE LOCALIZATION OF PROTEINS FOLLOWING ELECTROPHORESIS OR ISOELECTRIC FOCUSING A.M. Johnson

127

ONE AND TWO-DIMENSIONAL MICROELECTROPHORESIS AND STAINING OF PROTEINS WITH A SILVER METHOD H.M. Poehling and V. Neuhoff

133

"COLD FOCUS" ISOELECTRIC FOCUSING OF SMALL SAMPLES OF CEREBROSPINAL FLUID L.L. Lorincz

149

A UNIQUE SILVER STAINING PROCEDURE FOR COLOUR CHARACTERIZSATION OF POLYPEPTIDES L.D. Adams and D.W. Sammons 155 AFFINITY-IMMUNODELETION (AID) ISOELECTRIC FOCUSING ON ULTRATHIN GELS APPLIED TO THE IDENTIFICATION OF SWEAT, SALIVA AND BLOOD PROTEINS USING SILVER-DIAMINE STAINING R.C. Allen, P. Arnaud and S.S. Spicer

167

IX ULTRATHIN LAYER ISOELECTRIC FOCUSING IN 20-50 um POLYACRYLAMIDE GELS: COMPARISON OF CONVENTIONAL AND MINIATURE SYSTEMS B.J. Radola, A. Kinzkofer and M. Frey

181

ULTRATHIN LAYER PAGIF: A COST BENEFIT ANALYSIS OF THE FOCUSING DISTANCE T. LSSs and I. Olsson

191

ISOELECTRIC FOCUSING IN AGAROSE GELS D.L. Harper

205

SEAPREPTM 15/45.. A NEW AGAROSE WITH LOW GELLING AND REMELTING PROPERTIES FOR PREPARATIVE ELECTROPHORESIS S. Nochumson

213

AGAROSE GEL ELECTROENDOSMOSIS: ITS ENHANCEMENT, REDUCTION AND PRACTICAL RAMIFICATIONS R.B. Cook ,

219

ENHANCEMENT OF COMPLEX PATTERNS IN ISOELECTRIC FOCUSING WITH IMPROVED ISOGEL PERFORMANCE S.E. Coulson

229

THE SIEVING OF VIRUSES AND VIRAL CAPSIDS DURING AGAROSE GEL ELECTROPHORESIS P. Serwer

237

NEW ELECTROPHORETIC TECHNIQUES FOR THE SEPARATION AND CHARACTERIZATION OF POLIO VIRUS PROTEINS R. Dernick, K.J. Wiegers, J. Heukeshoven

245

SECTION II, HIGH RESOLUTION TWO-DIMENSIONAL ELECTROPHORESIS SDS-GEL GRADIENT ELECTROPHORESIS, ISOELECTRIC FOCUSING AND HIGH-RESOLUTION TWO-DIMENSIONAL ELECTROPHORESIS IN HORIZONTAL, ULTRATHIN-LAYER POLYACRYLAMIDE GELS A. Görg, W. Postel, R. Westermeier, E. Gianazza and P.G. Righetti

257

X

TWO-DIMENSIONAL ELECTROPHORESIS ON CELLULOSE ACETATE MEMBRANES T. Toda, T. Fujita and M. Ohashi

271

ISOELECTRIC FOCUSING, SDS GEL GRADIENT ELECTROPHORESIS AND TWO-DIMENSIONAL ELECTROPHORESIS OF TROPICAL AND EUROPEAN LEGUME PROTEINS IN ULTRATHIN POLYACRYLAMIDE LAYERS R. Westermeier, W. Postel, A. Görg and L. Telek

281

HIGH RESOLUTION POLYPEPTIDE MAPPING OF HUMAN HAIR ROOTS FROM HEALTHY INDIVIDUALS AND PATIENTS WITH GENETIC DEFECTS S. Singh, I. Willers, H.W. Goedde and J. Klose

289

ANALYSIS OF CULTURED SKIN FIBROBLASTS FROM PATIENTS WITH DUCHENNE MUSCULAR DYSTROPHY USING ELECTROPHORETIC TECHNIQUES A.H.M. Burghes, M.J. Dunn, H.E. Statham and V. Dubowitz

295

STUDIES OF GENE EXPRESSION IN HUMAN LYMPHOCYTES USING HIGH-RESOLUTION TWO-DIMENSIONAL ELECTROPHORESIS N.L. Anderson

309

ISOELECTRIC FOCUSING AND TWO DIMENSIONAL MAPS OF NORMAL AND CYSTIC FIBROSIS SALIVA S.E. Bustos and L. Fung

317

ANALYSIS OF HUMAN AMNIOTIC FLUID PROTEINS BY TWODIMENSIONAL ELECTROPHORESIS P. Burdett, J. Lizana, P. Eneroth and K. Bremme

329

QUANTITATIVE TWO-DIMENSIONAL ELECTROPHORESIS AS A SCREEN FOR GENETIC DISEASE MARKERS C.R. Merril, D. Goldman and M. Ebert

343

A QUANTITATIVE TWO-DIMENSIONAL ELECTROPHORETIC SURVEY OF PROTEINS AFFECTED BY CHROMOSOME 21 M.L. Van Keuren, D. Goldman and C.R. Merril

355

XI MULTISPECTRAL DIGITAL IMAGE ANALYSIS OF COLOR TWODIMENSIONAL ELECTROPHORETOGRAMS R.K. Vincent, J. Hartman, A.S. Barrett and D.W. Sammons

371

A COMPUTERIZED SYSTEM FOR MATCHING AND STRETCHING TWO-DIMENSIONAL GEL PATTERNS REPRESENTED BY PARAMETER LISTS J. Taylor, N.L. Anderson and N.G. Anderson

3 83

GELLAB: MULTIPLE 2D ELECTROPHORETIC GEL ANALYSIS P.F. Lemkin and L.E. Lipkin

401

IMPLICIT MODELING OF SPOTS FOR THE EVALUATION OF TWO-DIMENSIONAL ELECTROPHORETOGRAMS H. Kronberg, H-G. Zimmer and V. Neuhoff

413

SECTION III, BIOMEDICAL AND BIOLOGICAL APPLICATIONS EVALUATION OF IMMUNOGLOBULIN DIVERSITY K. Felgenhauer and H. Mohrmann

427

STUDIES OF ANTIBODY CLONOTYPE PATTERNS IN RABBIT ANTIMICROCOCCAL SERA BY ANALYTICAL ISOELECTRIC FOCUSING IN AGAROSE GELS S. Binion and L.S. Rodkey

433

MONOCLONAL GAMMOPATHY WITH FREE LIGHT CHAINS T. Sun and Y.Y. Lien

439

ISOELECTRIC FOCUSING OF IMMUNOGLOBULINS IN ULTRATHIN LAYERS OF AGAROSE B.L. Schmidt and.G. Pfeifer

443

ELECTROPHORETIC ABNORMALITIES OF HIGH DENSITY LIPOPROTEINS IN LIVER DISEASES K. Taketa, S. Ikeda and M. Watanabe

447

SDS-PAGE OF URINARY PROTEINS: CORRELATION OF DIFFERENT PROTEINS TO RENAL CLEARANCE AND TO RENAL AND EXTRARENAL DISEASES W. Boeskin

453

XII HEPATIC IMPLICATIONS IN THE METABOLISM OF HUMAN SALIVARY AMYLASE ISOENZYME A. Murata, M. Ogawa, K. Fujimoto, T. Kitahara, Y. Matsuda, and G. Kosaki

463

POSTTRANSLATIONAL MODIFICATION OF PANCREATIC AMYLASE IN ACUTE PANCREATITIS: POSSIBLE ROLE OF PANCREATIC DEAMIDASE K. Fujimoto, G. Kosaki, M. Masuike, N. Minamiura, A. Murata, M. Ogawa, N. Saito and T. Yamamoto

4 71

EFFECTS OF DIALYZABLE LEUKOCYTE EXTRACTS WITH TRANSFER FACTOR ACTIVITY ON LEUKOCYTE MIGRATION IN VITRO: VI. STUDIES ON THE PRIMARY STRUCTURE OF TRANSFER FACTOR G.V. Paddock, G.B. Wilson, F-K. Lin, N. O'Leary and H.H. Fudenberg

4 79

CHARACTERIZATION OF HORSE PLASMA PROTEINS BY SPECTROPHOTOMETRY AND ISOELECTRIC FOCUSING C.F. Pelzer, L.D. Aronson and N.E. Robinson

487

ALPHA-1-ANTITRYPSIN DEFICIENCY AND DISEASE P. Arnaud and R.C. Allen

495

RARE TYPES OF ALPHA-1-ANTITRYPSIN ASSOCIATED WITH DEFICIENCY D.W. Cox, G.D. Billingsley, S. Smyth

505

ISOLATION AND CHARACTERIZATION OF AN ALPHA-1"ANTITRYPSIN -RELATED GLYCOPROTEIN FROM HUMAN LIVER R.H. Glew, J.L. Zidian, J. P. Chiao, T. Kuhlenschmidt, R.M. Iammarino and K.P. Brooks

511

CK-MB BY AN IMPROVED ELECTROPHORESIS METHOD H.L. Kincaid

523

DETECTION AND CHARACTERIZATION OF CYSTIC FIBROSIS PROTEIN EMPLOYING ISOELECTRIC FOCUSING AND IMMUNOELECTROPHORETIC TECHNIQUES G.B. Wilson and E. Floyd

529

IMMUNOFIXATION-AGAROSE ISOELECTRIC FOCUSING TECHNIQUES FOR SCREENING GLIAL TUMOR CELL CULTURES FOR GLIAL MARKERS E.A. Quindlen, P.E. McKeever and P.L. Kornblith AGAROSE ISOELECTRIC FOCUSING AND RELATED IMMUNOCHEMICAL TECHNIQUES IN THE ANALYSIS OF SERUM GC-GLOBULIN J. Lizana, A. Savill and I. Olsson ISOELECTRIC FOCUSING IN FORENSIC SEROLOGY P. Kühnl ISOELECTRIC FOCUSING OF THE COMMON TRANSFERRIN0 ALLELE SUBTYPES P. Kühnl, J. Constans, M. Viau and W. Spielmann ISOELECTRIC FOCUSING OF HAIR PROTEINS B. Budowle, R.C.A. Go and R.T. Acton ISOENZYME TYPING OF DRIED BLOODSTAINS USING MYLAR BACKED CELLULOSE ACETATE MEMBRANES R. Briner, R. Longwell, Y. Moll, R. Matthews, A. Abbot and R. Webster CHANGES IN THE ELECTROPHORETIC PATTERNS OF STRUCTURAL PROTEINS AND ENZYMES OF HALIBUT (HIPPOGLOSSUS HIPPOGLOSSUS L.) MUSCLE AFTER PROLONGED (TWENTY-FIVE YEARS" FROZEN STORAGE C. Annand and P. Odense ELECTROPHORETIC BEHAVIOR OF CROSSLINKED DNA E.W. Wunder ELECTROPHORETIC MIGRATION OF FORM IV-DNA AND TOPOISOMERASE MONITORING E.W. Wunder and U. Burghardt PROPERTIES OF NUCLEIC ACIDS PURIFIED FROM AGAROSE J. Locker

XIV FRACTIONATION OF CONCATEMERIC DNA OF BACTERIOPHAGE T7 BY AGAROSE GEL ELECTROPHORESIS P. Serwer and F.A. Greenhaw

627

DNA SEQUENCING ON VERY THIN (0,2mm) GELS W. Ansorge and H. Garoff

635

THE DETECTION OF HUMAN INTRACELLULAR DEXOXYRIBONUCLEASE ACTIVITIES USING ONE DIMENSIONAL POLYNUCLEOTIDE— POLYACRYLAMIDE GEL ELECTROPHORESIS T. Karpetsky, G.E. Brown, E. McFarland, A. Rahman, K. Rictor, W. Roth, M.B. Haroth, A. Ansher, P. Duffey and C. Levy 64 7 RECENT DEVELOPMENTS IN TITRATION CURVES OF PROTEINS BY ISOELECTRIC FOCUSING-ELECTROPHORESIS P.G. Righetti and E. Gianazza

655

A STUDY OF THE STRUCTURAL CONVERSIONS OF TWO CARBOXYL PROTEINASES EMPLOYING ELECTROPHORESIS ACROSS A pH GRADIENT R. Rüchel and M. Trost

667

ELASTASE DETECTION IN ELECTROPHORETOGRAMS OF COMPLEX ANTIGEN MIXTURES J. Westergaard and R.C. Roberts

677

POSITIVE PERIODIC ACID-SCHIFF STAINING OF PROTEOLYTIC ENZYMES FOLLOWING ZONE ELECTROPHORESIS IN POLYACRYLAMIDE GEL J.J. Baumstark

685

ELECTROPHORETIC AND STAIN METHOD FOR PYRUVATE KINASE ISOENZYME PATTERNS E. Melendez-Hevia, J. COrzo and J. Perez

693

ISOENZYMES OF SUPEROXIDE DISMUTASE IN SERRATIA MARCESCENS Z. Gonzalez-Lama, O.E. Santana and P. Betancor

699

ISOENZYMES OF SUPEROXIDE DISMUTASE IN LIVER FROM LACERTA STEHLINII Z. Gonzalez-Lama, A. deArmas, P. Betancor and E. Melendez-Hevia

703

XV ELECTROPHORETIC MULTIPLICITIES OF y-GLUTAMYLTRANSFERASES IN HUMAN SERUM AND THEIR CHARACTERIZATION BY AFFINITY CHROMATOGRAPHY M. Izumi and K. Taketa 709 ISOAMYLASE BY ISOELECTRIC FOCUSING ON MODIFIED CELLULOSE ACETATE R.L. Gilman 715 MULTIPLE FORMS OF TREHALASE FROM AGING SOROCARPS OF THE CELLULAR SLIME MOLD, DICTYOSTELIUM DISCOIDEUM K.A. Killick 721 PURIFICATION OF GRANULOCYTE COLONY STIMULATING FACTOR MONITORED BY ULTRATHIN LAYER ISOELECTRIC FOCUSING R. Neumeier and H.R. Maurer 72 9 PROTEOLYTIC DIGESTION OF THE M PROTEIN OF INFLUENZA A VIRUSES AND ISOELECTRIC FOCUSING OF ITS PEPTIDES A. Darveau, M. Lambert and J. LeComte 735 SECTION IV, ISOTACHOPHORESIS AND FREE FLOW ELECTROPHORESIS QUANTITATIVE ANALYSIS IN ISOTACHOPHORESIS F. Everaerts, N. Groot, F. Mikkers

743

THE ANALYSIS OF HUMAN SERUM PROTEINS BY CAPILLARY ISOTACHOPHORESIS C.J. Holloway and W. Heil

753

ISOTACHOPHORETIC ASSESSMENT OF ENZYME IMMUNOGLOBULIN CONJUGATES USED IN ENZYME IMMUNOASSAY S. Linpisarn, P.M.S. Clark, L.J. Kricka and T. P. Whitehead

767

ANALYTICAL CAPILLARY ISOTACHOPHORESIS APPLIED TO THE STUDY OF NUCLEOTIDE-DEPENDENT ENZYMATIC PROCESSES E. Anhalt, C.J. Holloway, S.Husmann-Holloway and J. Lüstorff CONDITIONS FOR THE SEPARATION OF ADENINE NUCLEOTIDES AND THEIR 3 ^-PHOSPHATE DERIVATIVES IN ANALYTICAL CAPILLARY ISOTACHOPHORESIS J. Lüstorff and C.J. Holloway

781

797

XVI ISOTACHOPHORETIC ANALYSIS OF HIGH DENSITY LIPOPROTEINS M. Bojanovski and C.J. Holloway

809

CAPILLARY ISOTACHOPHORESIS AS AN ANALYTICAL MONITOR DURING THE SYNTHESIS OF THE C-TERMINAL PENTAPEPTIDE OF BOMBININ C.J. Holloway and K. Friedel

821

AN ALTERNATIVE OUTLOOK ON ELECTROKINETIC CELL SEPARATIONS A. Kolin

827

CHARACTERIZATION OF THE SURFACE PHENOTYPE OF ELECTROPHORECTICALLY FRACTIONATED MOUSE LYMPHOCYTES BY FLOW MICROFLUOREMETRY ANALYSIS F. Dumont, R. Habbersett and A. Ahmed

831

EVALUATION OF THE ELECTROPHORETIC SEPARABILITY OF TRYPANOSOMA CRUZI PARASITE STAGES R.C. Boltz, Jr., D.M. Schmatz and P. K. Murray

841

SEPARATION AND CHARACTERIZATION OF HUMAN BONE MARROW CELLS BY DENSITY GRADIENT ELECTROPHORESIS C.D. Platsoukas, N. Kapoor, J.D. Beck, R.A. Good and S. Gupta

851

FREE FLOW ELECTROPHORESIS IN MALARIA RESEARCH H.-G. Heidrich

859

LIBERATION OF INTRAERYTHROCYTIC PARASITES (PLASMODIUM VINCKEI, PLASMODIUM BERGHEI) FROM ERYTHROCYTES AND ELECTROPHORETIC SEPARATION OF FREE PARASITES FROM HOST CELL CONSTITUENTS H.-G. Heidrich, A. Jung, L. Russmann, B. Bayer

860

FREE-FLOW ELECTROPHORESIS SEPARATIONS OF FREE PARASITES (PLASMODIUM FALCIPARUM)ACCORDING TO STAGES H.-G. Heidrich, J.E.K. Mrema, P. Reyes, D.V. Jagt, and K.H. Rieckmann

862

FREE-FLOW ELECTROPHORESIS ISOLATION OF WHOLE BODY PLASMODIUM BERGHEI SPOROZOITES H.-G. Heidrich, H.D. Danforth and R.L. Beaudoin

866

XVII SEPARATION OF FUNCTIONING MAMMALIAN CELLS BY DENSITYGRADIENT ELECTROPHORESIS P. Todd, W.C. Hymer, L.D. Plank, G.M. Marks M.E. Kunze, V. Giranda and J. N. Mehrishi

871

REVIEW OF THE NASA ELECTROPHORESIS PROGRAM R.S. Snyder

883

NUMERICAL ANALYSIS OF CONTINUOUS FLOW ELECTROPHORESIS P.H. Rhodes and R.S. Snyder

899

HIGH-RESOLUTION CONTINUOUS-FLOW ELECTROPHORESIS IN THE REDUCED GRAVITY ENVIRONMENT P.H. Rhodes

919

APPLICATION OF THE AUTOMATED ELECTROPHORESIS MICROSCOPE SYSTEM TO VARIOUS BIOLOGICAL TESTS G.B. Olson, M. McFadden and P.H. Bartels 933 OPERATIONAL PARAMETERS FOR CONTINUOUS FLOW ELECTROPHORESIS OF CELLS J.K. McGuire and R.S. Snyder

947

REDUCTION OF DROPLET FORMATION AND SEDIMENTATION OF FIXED ERYTHROCYTES IN STATIONARY AND FLOWING SYSTEMS S.N. Omenyi, R.S. Snyder, C.J. van Oss, D.R. Absolom and A.W. Neumann

961

DESIGN CONSIDERATIONS OF A THERMALLY STABILIZED CONTINUOUS FLOW ELECTROPHORESIS CHAMBER P.H. Rhodes, T.Y. Miller and R.S. Snyder

971

THE SHEEP ERYTHROCYTES ELECTROPHORETIC MOBILITY: EFFECT OF SUPERNATANTS OF LYMPHOCYTES STIMULATED WITH VARIOUS IMMUNOPOTENTIATORS N. Hashimoto, M. Ageshio, S. Nose, S. Horita, T. Kobayashi and M. Abe

9 83

ELECTRICAL INSULATION OF ELECTROPHORETIC FLOWS AND A "RAIN BOX" J.O.N. Hinckley

995

XVIII

Author Index

1005

Subject Index

1009

SECTION I Theory and Methods

ON THE PORE SIZE AND SHAPE OF HYDROPHILIC GELS FOR ELECTROPHORETIC ANALYSIS Pier Giorgio

Righetti

Department of B i o c h e m i s t r y , U n i v e r s i t y of Milano, Via C e l o r i a 2 , 2 0 1 3 3 , I t a l y and NASA, M a r s h a l l S p a c e F l i g h t C e n t e r , H u n t s v i l l e , Alabama 3 5 8 1 2 , USA

Separation Processes

Milano

Branch,

Introduction S i n c e the i n t r o d u c t i o n of s t a r c h g e l s matrices

for electrophoretic

for gel f i l t r a t i o n ,

(1), polyacrylamide

separations,

and a g a r o s e

(2,

and of c r o s s - l i n k e d d e x t r a n s

c o n s i d e r a b l e i n t e r e s t h a s f o c u s e d on the s t r u c t u r e

t h e s e h y d r o p h i l i c s u p p o r t m e d i a . Fundamental e q u a t i o n s have been l i n k i n g the p a r t i t i o n

coefficient

( K a v or a ) i n t h e l a t t e r

3)

(4) of

described

or t h e m o b i l i t y

(m) i n t h e f o r m e r t e c h n i q u e t o t h e m o l e c u l a r w e i g h t o f t h e f r a c t i o n a t e d macromolecule.'Indeed, resis

between m o b i l i t y , dius.

a u n i f i e d theory f o r gel f i l t r a t i o n

has been proposed

( 5 ) , which p r o v i d e s

partition

coefficient,

equations

Kremmer and B o r o s s

(9),

Fischer exists

( 1 0 ) and Determann

(6,

7 ) , Rodbard

( 1 1 ) . However,

(13,

centration.

I n the

14) w i t h v a r i a t i o n s

from extremely s m a l l

o f a s much a s 6 0 - 7 0 f o l d

I s h a l l attempt here to review t h i s

field,

(12)

to

latter

the n e c e s s a r y ground work f o r f u t u r e s e p a r a t i o n s

gi-

extremely

f o r a given gel

con-

a l s o a t the l i g h t

some r e c e n t d a t a o b t a i n e d i n c o l l a b o r a t i o n b e t w e e n my l a b o r a t o r y as

considera-

t h e r e s e a r c h g r o u p s who h a v e a t t e m p t e d t o m e a s u r e p o r e s i z e s h a v e

ven a l l p o s s i b l e r a n g e s o f v a l u e s , large

ra-

(8),

a s t o t h e a c t u a l p o r e g e o m e t r y and t o t h e ma-

ximum p o r e s i z e which can be o b t a i n e d w i t h h y d r o p h i l i c g e l s . case,

electropho-

inter-relationships

g e l c o n c e n t r a t i o n and m o l e c u l a r

E x t e n s i v e r e v i e w s h a v e been p u b l i s h e d by A c k e r s

ble disagreement s t i l l

and g e l

for

of

and NASA,

in m i c r o g r a v i t y

(15).

Results 1) P o r e

shape

The s e r i e s

of models proposed to d e s c r i b e p o r e s

s e r v a t i o n s by F l o d i n

in g e l s

s t e m from e a r l y

( 1 6 ) , who h a s c o n s i d e r e d t h e p a r t i t i o n

c u l e between t h e g e l and t h e l i q u i d t o be e n t i r e l y g o v e r n e d by s t e r i c tors.

The g e l m a t r i x c h a i n s

form a n e t w o r k of v a r y i n g d e n s i t y .

© 1981 Walter de Gruyter &. Co., Berlin • New York Electrophoresis '81

ob-

of a m a c r o m o l e fac-

Large molecu-

A

B

0

C

Mmm mmsk m^m

E

F

F i g . 1. Geometric p o r e s h a p e s i n g e l s a s s u g g e s t e d by O r n s t e i n ( A ) ( 2 1 ) , Por a t h (B) ( 1 7 ) , C a s a s s a (C, D, F) (20) , Ackers (D, E ) ( 1 4 ) and S q u i r e (B, D, F) (19). l e s can only p e n e t r a t e i n t o r e g i o n s where the meshes i n the n e t a r e l a r g e . On the o t h e r h a n d , s m a l l m o l e c u l e s f i n d t h e i r way i n t o more t i g h t l y k n i t

regions

of the n e t w o r k , c l o s e r t o the c r o s s

thus,

links.

The p a r t i t i o n c o e f f i c i e n t ,

c o r r e s p o n d s t o the p a r t of the whole s p a c e t h a t i s " p e r m i t t e d " t o a g i v e n mac r o m o l e c u l e . The l a t e r t h e o r i e s have been l a r g e l y concerned with d i f f e r e n t models o f the g e l s t r u c t u r e which c o u l d e x p l a i n the mesh width g i v i n g the p r o p o r t i o n s of p e r m i t t e d volume found e m p i r i c a l l y . of models can be d e s c r i b e d :

a) geometric; b) s t a t i s t i c a l

distribution Three groups

and c )

thermodyna-

mic m o d e l s .

a)

Geometric

models.

i n the l i t e r a t u r e .

Fig.

1 groups the most common p o r e g e o m e t r i e s

The e a r l i e s t g e o m e t r i c a l model f o r c a l i b r a t i o n of g e l s

s u a l i z e d the p e n e t r a b l e v o i d s w i t h i n the m a t r i x a s a c o l l e c t i o n o f 1/3 pores

(17)(Fig.

described

I B ) . A c c o r d i n g t o t h i s g e o m e t r y , a p l o t of a

vi-

conical _l

a g a i n s t M^

s h o u l d r e s u l t i n a s t r a i g h t l i n e . T h i s seems t o h o l d f o r randomly c o i l e d macromolecules

( 1 7 ) and even f o r compact g l o b u l a r p r o t e i n s

(18). Squire

(19)

h a s u s e d a b r o a d e r c o l l e c t i o n of c o n s t r a i n i n g s h a p e s , by a s s u m i n g t h a t the p o r e s i z e d i s t r i b u t i o n c o r r e s p o n d s t o t h a t p r o d u c e d by e q u a l amounts of n e s , hollow c y l i n d e r s

(Fig.

ID) and c r e v i c e s .

T h i s l a s t p o r e model c o u l d be

seen a s " c r a c k s on the w a l l " and c o u l d be e x e m p l i f i e d a s p a r a l l e l (Fig.

IF).

co-

C y l i n d r i c a l p o r e s have a l s o been assumed by Ackers

planes

( 1 4 ) , who h a s

5 also regarded them as circular and lying in a plane perpendicular to the direction of movement of the molecules (Fig. IE). The distribution probability of flexible macromolecules within voids represented as spherical cavities (Fig. 1C), cylindrical pores and slab-shaped cavities has been calculated by Casassa (20) using random-flight statistics. Ornstein (21) has assumed that the chains in

a polyacrylamide gel follow the edges of cubes in a cubical

matrix (Fig. 1A). Actually, one of the oldest models is the "random meshwork of fibers" of Ogston (22), who has calculated the fraction of space available to a sphere with radius r g if straight cylindrical rods with radius r are distributed in the space in a random fashion with an average density of L length units of rods per volume unit of space. Laurent and Killander (23) have extended this model by assuming that the molecule is a sphere of a given radius, while the network is described as infinitely long straight rods that are randomly located in space. Among the "random" models, Giddings et at.

(24) have also hypothesized a gel structure consisting of an isotropic

network of random planes in which all plane orientations are equally represented . We will discuss further on critically the various models, but at the moment we can ask ourselves how would a macromolecule fare within the different geometries. We can here distinguish between two limiting particle shapes, spherical molecules and thin rods. Fig. 2 shows how K (and therefore m in eav . lectrophoresis) varies as a function of particle size in the two cases. Spheres move with extreme difficulties in parallel planes, and most easily within random planes. Thin rods don't wander well through spherical structures but, above a critical length, move with the same difficulty within several geometries (parallel and random planes and rectangular shapes). Interestingly, as the sphere diameter (L^) or the cylinder length (L^) become small, all the curves tend to converge and approach unity along a common curve. In other words, as the macromolecule becomes sufficiently small, as compared to the gel pore size (less than 10% of this value), wall curvature and corners boceme unimportant: the molecule is so small that nearly all elements of surface appear to it as plane areas. b) Statistical

models.

In order to circumvent the necessity of postulating

specific geometric shapes for the pores within gel partitioning systems, statistical calibrating functions, which relate the molecular size of the ma-

6

1.0

0.8

K

0.6 0.4 0.2

0

0

1.0

3.0

2.0

4.0

1.0

5.0

SL0(=SL~)

5.0

4.0

0.3

2.0

^-(zSlT)

F i g . 2 . P a r t i t i o n c o e f f i c i e n t (K) of s p h e r e s and t h i n r o d s , a s a f u n c t i o n o f d i a m e t e r ( L 0 ) or l e n g t h ( L ^ ) , r e s p e c t i v e l y , w i t h i n p o r e s o f d i f f e r e n t g e o (24). m e t r i e s (From G i d d i n g s et at.) c r o m o l e c u l e t o the volume a v a i l a b l e t o i t , have been p r o p o s e d . Hohn and P o l lman (25) assumed t h a t K stribution, ckers

i s r e l a t e d t o m o l e c u l a r w e i g h t by a Boltzmann d i -

and found t h i s r e l a t i o n s h i p t o f i t w e l l f o r o l i g o n u c l e o t i d e s .

A-

(26) assumed t h a t the volume o f the domains in the g e l , where m o l e c u -

l e s of a c e r t a i n r a d i u s c o u l d j u s t r e a c h , c o u l d be d e s c r i b e d by a normal ( g a u s s i a n ) d i s t r i b u t i o n . A c k e r ' s " g a u s s i a n p o r e d i s t r i b u t i o n " model h a s

pro-

ven t o be q u i t e s a t i s f a c t o r y f o r many p u r p o s e s b u t , a s p o i n t e d o u t by Rodb a r d ( 8 ) i t has one minor t e c h n i c a l f l a w :

the g a u s s i a n d i s t r i b u t i o n

ranges

from minus i n f i n i t y t o p l u s i n f i n i t y , which means t h a t a s m a l l f r a c t i o n of the p o r e s would be n e g a t i v e .

In o r d e r t o a v o i d t h i s p a r a d o x , Rodbard (8) h a s

s u g g e s t e d t h a t the p o r e s i z e s f o l l o w a " l o g - n o r m a l " d i s t r i b u t i o n ,

i.e.

it

is

the logaritmm of the p o r e s i z e t h a t obeys a g a u s s i a n c u r v e . In t h i s way, no n e g a t i v e pore s i z e s

can o c c u r ; m o r e o v e r ,

the " l o g - n o r m a l " s t a t i s t i c s

de a more s a t i s f a c t o r y f i t f o r the d a t a of F a w c e t t and M o r r i s

provi-

( 2 7 ) on p o r e

r a d i u s d i s t r i b u t i o n i n p o l y a c r y l a m i d e g e l s . As a f u r t h e r r e f i n e m e n t of m o d e l , Rodbard ( 8 ) has p r o p o s e d a " l o g i s t i c " d i s t r i b u t i o n ,

since i t

s i m p l e e q u a t i o n s which can b e f i t t e d more e a s i l y t o s m a l l d e s k - t o p tors,

or drawn d i r e c t l y on l o g i t - l o g

o) Thermodynamic

models.

to apply c l a s s i c a l

calcula-

paper.

Another way t o a v o i d s p e c i f i c p o r e g e o m e t r i e s ,

thermodynamic t h e o r i e s

between two p h a s e s . T h u s , A l b e r t s s o n

this

provides

is

to the p a r t i t i o n i n g o f a s o l u t e

( 2 8 ) h a s p r o p o s e d a thermodynamic r e -

l a t i o n s h i p of the B r o n s t e d - t y p e t o the p a r t i t i o n i n g of c e l l s between two non m i s c i b l e l i q u i d p h a s e s . T h i s approach h a s been e x t e n d e d by F i s c h e r

( 2 9 ) who

7 STRUCTURAL

ELEMENTS OF

WITH DI FUNCTIONAL

SYSTEMS

CROSS-LINKS

UNCNOSSLINKED CHAIN o o «INÛLET (S) FWEE-ENO CHAIN (f ) O VOID (UNSATURATED) FUNCTIONALITY (V)

LOOP ( I )

A

B

F i g . 3. A: s t r u c t u r a l elements in a g e l with a b i f u n c t i o n a l c r o s s - l i n k ( e . g . B i s ) . B: g e l f o r m a t i o n by i n t e r s e c t i o n of long c h a i n s with a b i f u n c t i o n a l c r o s s - l i n k . N o t i c e how s i n g l e t s l a r g e l y p r e d o m i n a t e , forming a r e g u l a r n e t work of c h a i n s (from Z i a b i c k i ) ( 3 2 ) . has c a l c u l a t e d thermodynamic p a r a m e t e r s f o r s o l u t e t r a n s f e r between bulk

li-

quid and g e l p h a s e . In another l i n e of t h i n k i n g , Bode (20) has e x p l a i n e d mol e c u l a r s i e v i n g in p o l y a c r y l a m i d e g e l s as stemming from the p r o p e r t i e s of a h y p o t h e t i c a l " v i s c o s i t y - e m u l s i o n " composed of two i n t e r l a c i n g f l u i d

compartm-

e n t s endowed w i t h d i f f e r e n t f r i c t i o n a l c o e f f i c i e n t s . In t h i s model, the g e l i s imagined as a v i s c o - e l a s t i c m a t r i x composed of l a y e r s of p a r a l l e l

sheets

each of which comprises f l u c t u a t i n g polymer chains i n s e r t e d i n t o an u n s p e c i f i e d backbone. F l u c t u a t i o n s due to thermal a g i t a t i o n a r e c e n t r e d s y m m e t r i c a l ly around the median p l a n e of each s h e e t . The motions of the polymer c h a i n s g i v e r a i s e t o e l a s t i c f o r c e s d i r e c t e d towards any compact o b j e c t which tends to invade the volume o t h e r w i s e a v a i l a b l e t o the polymers f o r m o l e c u l a r

reo-

rientation. 2) Pore shape What i s the b i g g e s t pore s i z e t h a t can be o b t a i n e d with h y d r o p h i l i c g e l s

at

1 g g r a v i t y ? I w i l l narrow my d i s c u s s i o n to two types of g e l s , which have p r o ven over the y e a r s t o be the most p o p u l a r : p o l y a c r y l a m i d e and a g a r o s e

a) Polyacrylamide

gels.

gels.

So much has been w r i t t e n about them t h a t we can con-

f i d e n t l y s t a t e t h a t we know very l i t t l e on t h e i r p r o p e r t i e s . B e f o r e

discus-

8

-t

f "

f" ^

"f-

UNENTANGLED

ENTANGLED

F i g . 4. F o r m a t i o n of e n t a n g l e d c h a i n s d u r i n g p o l y m e r i z a t i o n of de g e l s ( f r o m Z i a b i c k i ) ( 3 2 ) . sing polyacrylamide pore s i z e ,

polyacrylami-

a few words s h o u l d be s p e n t on t h e i r

topolo-

g i c a l s t r u c t u r e . When a g e l i s formed w i t h a b i f u n c t i o n a l c r o s s - l i n k bisacrylamide, to i t

B i s ) we can d i s t i n g u i s h s e v e r a l s t r u c t u r a l e l e m e n t s

( F i g . 3A): u n c r o s s l i n k e d c h a i n s

( s t r i c t l y speaking,

n o t f o r m p a r t of t h e c r o s s - l i n k e d s y s t e m ) ; s i n g l e t s

jnctions, cross-link

(v); doublets

and l o o p s (31,

(1), i . e .

chains

connec-

free-end chains

c h a i n s c o n n e c t e d w i t h one end t o one j u n c t i o n o n l y ; v o i d

functionalities

attached

t h o u g h , t h e y do

(s), i . e .

t e d w i t h t h e i r two e n d s t o two d i f f e r e n t c r o s s - l i n k s ; i.e.

(e.g.

(f),

(unsaturated)

c h a i n s c o n n e c t i n g t h e same p a i r

(d), i . e .

of

c h a i n s c o n n e c t e d w i t h b o t h e n d s t o t h e same

3 2 ) . F i g . 3B shows how a g e l i s formed by i n t e r s e c t i o n

long chains w i t h b i f u n c t i o n a l b r i d g e s .

I t i s assumed h e r e t h a t a t t h e

a n t of i n t r o d u c i n g a c r o s s - l i n k , m a c r o m o l e c u l e s e x h i b i t e q u i l i b r i u m m a t i o n s , so t h a t t h e r e s u l t i n g d i s t r i b u t i o n

of c r o s s - l i n k s

of inst-

confor-

corresponds

to

t h e e q u i l i b r i u m d i s t r i b u t i o n of t e m p o r a r y c o n t a c t s b e t w e e n m a c r o m o l e c u l e s . The s i t u a t i o n i s f u r t h e r c o m p l i c a t e d by t h e f a c t t h a t ,

in f l e x i b l e - c h a i n

, e n t a n g l e m e n t s i n t h e f i b e r s can r e s u l t , which a r e " f r o z e n " i n t h e g e l t u r e by t h e c r o s s - l i n k s

(Fig.

gels struc-

4 ) . I t h a s b e e n c a l c u l a t e d t h a t t h e t o t a l sum

of s t r u c t u r a l e l e m e n t s i n a g e l c o u l d add up t o a f a n t a s t i c number: f o r a 3 . 3 5 m a c r o s c o p i c sample of 1 cm v o l u m e , t h i s number c o u l d be as h i g h as 10 43 . . 10 . A town l i k e M i l a n o (2 m i l l i o n i n h a b i t a n t s ) can p r o b a b l y be d e s c r i b e d by n o more t h a n 10^ t o p o l o g i c a l f e a t u r e s end s t r e e t s ) . re

( i n c l u d i n g s m a l l one-way and d e a d -

S o , a t i n y 1 ml g e l volume i s j u s t as c o m p l i c a t e d a s our

enti-

galaxy.

N o t w i t h s t a n d i n g t h e "random" models p r o p o s e d i n t h e p a s t

(22-24) i t i s

temp-

t i n g , h o w e v e r , t o r e p r e s e n t a g e l s t r u c t u r e as a r a t h e r " r e g u l a r a r r a y " of

9

2

1 LIQUID LINEAR POLYACRYLAMIDE

MODERATELY CROSS L I N K E D GEL

3 HIGHLY LINKED

CROSS GEL

4 PURE C R O S S LINK GEL

Fig. 5. Proposed variations of gel structure from an un-cross-linked gel to a pure cross-link gel. Structure 1 is not a gel, of course, but a highly viscous solution. Notice the shortening and thickening of gel fibers and the growth of beads in going from structures 1 to 4. chains (Fig. 3B) which, indeed, has a much reduced complexity since, by far, singlets predominate and "irregularities" in the gel structure (d, 1 and f topologies) are rather scarce. A regular lattice of this kind, however, cannot be made highly-porous

(by that I mean any gel structure with an average

pore diameter, p, greater than 100 nm) also because the matrix chains are not rigid and tend to fluctuate and collapse. One way to increase pore size in polyacrylamide gels is to progressively decrease the total content of solids (%T), the lowest concentration being 2%T, with a total amount of crosslinker (%C) of 2.2% (33). However, even in these highly diluted gels, it is doubtful that any pore diameter greater than 50 nm can be reached, and indeed much lower values have been given (27). Another way to increase pore size, though, is to progressively increase the percent of cross-linker, at fixed amounts of solids

(%T) (21, 34). We have in fact recently demonstra-

ted that, in highly cross-linked gels (3%T, 50%C B ^ g ) the pore diameter is as high as 500 nm, much higher, thus, than the highly diluted, low %C, gel series. How can we increase so considerably the pore size in high %C gels? I am proposing here the model depicted in Fig. 5. In going from a pure monofunctional monomer gel (un-cross-linked polyacrylamide) to a pure bifunctional monomer gel (pure cross-link gel) the gel matrix keeps changing its structure. Indeed, at one extreme, no gel is formed, but a highly viscous solution of liquid linear polyacrylamide

(a visco-elastic continuum, a la

Bode, but with no gel formation!). As cross-links are introduced, a regular array of chains, tied up by junctions (knots or cross-links), is formed which, at 5%C, has maximum sieving properties, i.e. minimum pore size, within a family of gels of equal %T. Now, as %C is increased above 10%, we a-

10 p= Kd/\^C

(RAYMOND

P - «'d C

(TOMBS,

k"

poc l / ^ C

(RODBARD

and

NAKAMICHI,

1962 )

1965 ) and

CHRAMBACH

p= 1 4 0 . 7 * C ~ ° ' 7 ( R I G H E T T I , B R O S T

, 1970 )

SNYDER,

1981)

F i g . 6. Proposed equations l i n k i n g the mean pore s i z e (p) to the g e l concent r a t i o n (C). The f i r s t three equations have been derived for polyacrylamide g e l s , the fourth f o r agarose matrices (see r e f s . 40, 39, 5 and 15, r e s p e c t i vely) . re diminishing the population of s i n g l e t s ( s ) in favor of the " i r r e g u l a r i t i e s " in the g e l , namely doublets (d) and loops ( 1 ) . As d and 1 i n c r e a s e , two phenomena occur simultaneously: the l i n e a r chains grow shorter and t h i cker, and the knots grow l a r g e r . This automatically drives the system t o wards b i g g e r pore s i z e s ( F i g . 5, 3 ) . As the system approaches a composition of pure c r o s s - l i n k , the chains tend to disappear and the predominant topolog i c a l elements l e f t are l o o p s , or b e t t e r highly-concatenated loops which grow i n t o beads or s p h e r e s . There i s ample evidence in the l i t e r a t u r e f o r the e x i s t e n c e of concatenated chains in l i v i n g and s y n t h e t i c polymers (35) and there i s now a l s o morphological evidence to the e x i s t e n c e of such beads or spheres in pure c r o s s - l i n k g e l s (26, 3 7 ) . This e x p l a i n s the enormous p o r o s i t y of very high %C g e l s . In r e g u l a r l y linked g e l s , the macromolecules have to move through

cross-

the g e l network, through

pores within the chain framework; in highly or pure c r o s s - l i n k g e l s , the macromolecule w i l l move around the g e l g r a i n s (or b e a d s ) , in the void volume in between the gel spheres. Thus, p a r a d o x i c a l l y , h i g h l y - c r o s s - l i n k e d g e l s resemble gel f i l t r a t i o n media. This, in a way, could have been p r e d i c t e d : as shown in F i g . 6, among the four current equations linking the mean pore d i a meter (p) to gel concentration (C), two of them suggest that t h i s can simply be achieved by i n c r e a s i n g the diameter (d) of the g e l f i b e r s . I t i s j u s t too bad that highly c r o s s - l i n k e d g e l s do not work properly f o r e l e c t r o p h o r e t i c s e p a r a t i o n s (38) .

bJ Agarose

gets.

With the new, almost c h a r g e - f r e e agaroses today a v a i l a b l e

on the market, t h i s polymer has become again very popular f o r e l e c t r o p h o r e t i c s e p a r a t i o n s , including i s o e l e c t r i c f o c u s i n g . We have r e c e n t l y

"titrated"

11

PORE DIAMETER |im)

F i g . 7. P l o t of l i m i t i n g pore s i z e vs. % a g a r o s e . The e x p e r i m e n t a l p o i n t s have been obtained by moving e l e c t r o p h o r e t i c a l l y l a t e x p a r t i c l e s through a garose g e l s ranging from 0.16% up to 1%. In the lower box, the e x p e r i m e n t a l p o i n t s have been r e - p l o t t e d according to p = or to p a C"®'^ (from R i g h e t t i et at. ) (15) . the l i m i t i n g pore s i z e of t h i s m a t r i x , as a f u n c t i o n of % s o l i d s in the g e l , by moving e l e c t r o p h o r e t i c a l l y p o l y s t y r e n e p a r t i c l e s through i t . re summarized in F i g .

The data a -

7. I t can be seen t h a t , a t the lowest % agarose

compatible with g e l f o r m a t i o n , a maximum pore diameter of 500 nm i s We have t r i e d t o f i t our d a t a to p = C _ 1 (39) o i t o p « C ~ ° ' 5

(0.16%)

reached.

(AO) ( F i g .

7,

lower c a s e ) but with l i m i t e d s u c c e s s . Our values seem to f i t b e s t the proportionality p = C

( 1 5 ) . This maximum pore s i z e obtained (500 nm) i n agaro-

se i s q u i t e remarkable, s i n c e no o t h e r h y d r o p h i l i c g e l can reach such a porosity

(indeed, high %C polyacrylamides reach t h i s s i z e ,

t o o , but they are

u s e l e s s f o r any p r a c t i c a l p u r p o s e ) . How can agarose p r e s e n t such an open por e s t r u c t u r e ? I t has been demonstrated (41) t h a t t h i s p o l y s a c c h a r i d e in s o l u t i o n e x i s t s as a double h e l i x ( F i g . 8 , l e f t ) and t h e r e f o r e i t i s

conside-

r a b l y more r i g i d than a polyaery1amide s t r a n d . Moreover, 7 to 11 such h e l i ces form bundles which extend as long rods ( F i g . 8 , r i g h t )

thus

further

s t r e n g t h e n i n g the a r c h i t e c t u r a l framework of the g e l . I b e l i e v e i t w i l l be

12

AGAROSE

(«>

AGAROSE

F i g . 8 . L e f t : the agarose double h e l i x viewed p e r p e n d i c u l a r to the h e l i x a x i s . The hydroxymethyl groups are l o c a t e d along the h e l i x p e r i m e t e r . R i g h t : a schematic r e p r e s e n t a t i o n of the agarose g e l network ( f a r r i g h t ) , in comp a r i s o n with a network such as Sephadex, formed from f r e e chains a t s i m i l a r polymer c o n c e n t r a t i o n . Note the l a t e r a l a g g r e g a t i o n of double h e l i c e s in a garose g e l s , which s t r e n g t h e n s the supporting g e l s t r u c t u r e s (from Arnott et al.) (41). 10' (A) (8) (C) (D) IE)

0-7 13, 0 0

j i 0 -5

10' 1

l'oie diameter (A) 103

10-

POROUS 6 L A S S "1700 A " POROUS GLASS " 260 A " POROUS G L A S S " I 7 0 A " CERAMIC BODY CERAMIC BODY

«

5 0-4

(A)

(8)

T(C)

| 0-3 "33 ^ 'o o

r-i

(0)

' (E)

01

00 10*

10'

10»

10"

Pressure (atm.)

F i g . 9 . Pore diameters in t h r e e types of porous g l a s s e s (A-C) and two d i f f e r e n t ceramic bodies (D, E ) . Notice t h a t a pore s i z e o f c a . 2 ym i s only obt a i n e d i n ceramic body E. The pore s i z e i s o b t a i n e d by mercury i n t r u s i o n (from H a l l e r ) ( 4 3 ) . quite d i f f i c u l t

to be able to device new h y d r o p h i l i c g e l s with a p o r o s i t y

much g r e a t e r than the l i m i t i n g value of 500 nm we have found. Even i f i t were p o s s i b l e ,

the s t r u c t u r e w i l l c o l l a p s e ,

crashed by the 1 g g r a v i t y on e a r t h .

13 Whether gels with pore sizes of 1 pm or more can be cast in microgravity, in the space shuttle, remains to be seen. At the moment, here on earth, the only way to make porous bodies (p > 1 ym) appears to be linked to ceramics (Fig. 9) and this belongs more to the art of pottery-making than to the art of biochemistry.

Discussion 1)

Gel

structure.

Whether the gel pores are seen as cones, or cubes, or sphe-

res, or circular holes, or according to any other geometry, at least one model, the "random meshwork of fibers" of Ogston (22) seems to break down. Even though the Gidding's theory (Fig. 2) seems to support this model (whether they are spheres or thin rods, macromolecules seem to wander about most freely within random planes and to experience strong hindrance within an ordered structure of parallel planes or other geometrical shapes) I have an opposite point of view. I think this theory can be developed by people who live in non-seismic areas, but they could hardly survive in the earthquake-prone mediterranean basin. As people who have been buried in a collapsed building during an earthquake well know, it is extremely difficult to move around , even to crawl, within this "random meshwork of rubble". The pore sizes we have measured in polyacrylamide and agarose gels, and the mobilities exhibited by proteins in these matrices are not consistent with a "random meshwork of fibers" model, but rather with a sort of regular structural lattice. Evidence to this fine structure and gel organization has been given by electron microscopy 2) Pore

size.

(36, 37).

Our data show that the upper pore limit which can be obtained

with any hydrophilic gel is around 0.5 pm. The only way to achieve that is to strengthen the beams supporting the ge] cavities, and this is nicely accomplished in agarose since the pillar (a double helix) is already rigid and is further hardened by lateral aggregation of 7 to 11 helices. Assuming a diameter of 1 nm for a double helix, then the supporting column should have a thickness of at least 10 nm, which would give a ratio beam:hole diameter of 1:50. Architecturally, this is quite an achievement, and should be confronted with examples of some of the finest gothic architecture (Fig. 10): in the nave and in the transept, very rarely the ratio column:surrounding cavity exceeds 1:10. In regularly cross-linked acrylamides (5%C) much smaller pore diameters are obtained, because the fiber is very long and thin

14

•"CU

IT" O -^Ttfi rfflrn '1 r 1 ^ iT

fe ]

L* J •

mm

Fig. 10. Plan of Westminster Abbey (London, G.B.). Excerpta: 4: north aisle; 5: nave; 6: south aisle; 7: organ loft; 9: choir; 12: north transept; 33: south transept; 36: chapter house; 39: cloisters; 42: Jericho Parlour; 43: Jerusalem Chamber (sorry, 42 & 43 not open to public) (courtesy of C.A. Fox, sub-dean of Westminster and of Pitkin Pictorials Ptd.). Notice how the ratio pillar:surrounding cavity does not exceed 1:10. (ca. 0.5 nm) is not rigid and therefore keeps fluctuating and vibrating in the space between the cross-links. But as the %C is increased, the fiber grows thicker and shorter, probably also more rigid, and the pores progressively open up. The limit to this structure is the fact that the fibers grow into big boulders, which weaken the gel consistency. The matrix becomes hydrophobic, and exudes water, probably not only due to the increased hydrophobicity of Bis, but also due to the fact that the boulders are tightly annealed into loops, into which the water "icebergs" cannot any longer penetrate (42).

Acknowledgements Supported in part by grants from Consiglio Nazionale delle Ricerche

(CNR),

Ministero della Pubblica Istruzione (MPI, Roma) and NASA (Huntsville, Ala.). I thank J. Biochem. Biophys. Methods for allowing reproduction of Fig. 7 before publication.

References 1.

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2.

Raymond, S., Weintraub, L.: Science 130, 711-713 (1959)

15 3.

Hjerten, S., Jersted, S., Tiselius, A.: Anal. Biochem. 27, 108-115 (19 (1969)

4.

Porath, J.K., Flodin, P.: Nature 183, 1657-1658 (1959)

5.

Rodbard, D. , Chrambach, A.: Proc. Natl. Acad. Sei. 65, 970-977 (1970)

6.

Ackers, G.K.: in Anfinsen, C.B., Edsall, J.T., Richards, F.M. (eds.) Advances in Protein Chemistry, vol. 24, pp. 343-446, Academic Press, New York, 1970

7.

Ackers, G.K.: in Neurath, H., Hill, R.L. (eds.) The Proteins, pp. 194, Academic Press, New York, 1975

8.

Rodbard, D.: in Catsimpoolas, N. (ed.) Methods of Protein Separation, vol. 2, pp. 145-179, Plenum Press, New York, 1976

9.

Kremmer, T., Boross, L.: Gel Chromatography, John Wiley & sons, Chichester, 1979

10.

Fischer, L. : An Introduction to Gel Chromatography, North Holland Publ. Co., Amsterdam, 1969

11.

Determann, H.: Gel Chromatography, Springer Verlag, Berlin, 1967

12.

White, M.L.: J. Phys. Chem. 64, 1563-1565 (1960)

13.

Ackers, G.K., Steere, R.L.: Biochim. Biophys. Acta 59, 137-149 (1962)

14.

Ackers, G.K.: Biochemistry 3, 723-730 (1964)

15.

Righetti, P.G., Brost, B.C.W., Snyder, R.S.: J. Biochim. Biophys. Methods (1981) in press

16.

Flodin, P.: J. Chromatogr. 5, 103-111 (1961)

17.

Porath, J.: J. Applied. Chem. 6, 233-236 (1963)

18.

Andrews, P.: Biochem. J. 91, 222-230 (1964)

19.

Squire, P.G.: Arch. Biochem. Biophys. 107, 471-480 (1964)

20.

Casassa, E.F.: J. Polymer Sei. B5, 773-780 (1967)

21.

Ornstein, L. : Ann. N. Y. Acad. Sei. 121, 321-349 (1964)

22.

Ogston, A.G.: Trans. Faraday Soc. 54, 1754-1756 (1958)

23.

Laurent, T.C., Killander, J.: J. Chromatogr. 14, 317-325 (1964)

24.

Giddings, J.C., Kucera, E., Russell, C.P., Myers, M.N.: J. Phys. Chem. 72, 4397-4408 (1968)

25.

Hohn, T., Pollmann, W.: Z. Naturforsch. 18B, 919-925

26.

Ackers, G.K.: J. Biol. Chem. 242, 3237-3241 (1967)

(1963)

27.

Fawcett, J.C., Morris, C.J.O.R.: Separ. Sei. 1, 9-20 (1966)

28.

Albertsson, P.A.: The Partitioning of Cell Particles and Macromolecules, Academic Press, New York, 1960

29.

Fischer, L. : in ref. 10, pp. 338-351

30.

Bode, H.J.: in Radola, B.J. (ed.) Electrophoresis '79, pp. 39-52, de Gruyter, Berlin, 1980

31.

Ziabicki, A., Walasek, J.: Macromolecules 11, 471-476 (1978)

16 32.

Ziabicki, A.: Polymer 20, 1373-1381 (1979)

33.

Shaaya, E.: Anal. Biochem. 75, 325-328 (1976)

34.

Rodbard, D., Levitov, C., Chrambach, A.: Separ. Sci. 7, 705-723 (1972)

35.

Lehninger, A.L.: Biochemistry, pp. 859-890, Worth Pubi., New York, 1975

36.

Rüche1, R., Brager, M.D.: Anal. Biochem. 68, 415-425 (1975)

37.

Rüche1, R.; Steere, R.L., Erbe, E.F.: J. Chromatogr. 166, 563-575 (1978)

38.

Bianchi Bosisio, A., Loeherlein, C., Snyder, R.S., Righetti, P.G.: J. Chromatogr. 189, 317-330 (1980)

39.

Tombs, M.P.: Anal. Biochem. 13, 121-132 (1965)

40.

Raymonds, S., Nakamichi, M. : Anal. Biochem. 3, 23-32 (1962)

41.

Arnott, S., Fulmer, A., Scott, W.E., Dea, I.C.M., Moorhouse, R., Rees, D.A.: J. Mol. Biol. 90, 269-284 (1974)

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GENERALIZATION OF THE DEBYE-HUCKEL THEORY TO MACROION SOLUTIONS OF FINITE SIZE AND CONCENTRATION AS APPLIED TO THEIR ELECTROPHORETIC MOBILITY AND T RAN S LATIONAL DIFFUSION COEFFICIENT

Eugene N. Serrallach Naval Blood Research Laboratory, Boston University School of Medicine, 615 Albany St., Boston, Mass. 02118, U.S.A. Robert Schor Physics Department and Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06268, U.S.A.

Introduction The quantitative treatment of the Coulombic interactions among salt ions and macroions in aqueous solutions has been a fundamental field of concern for many decades in physico-chemistry (1,2). Several reports (3-13) have summarized and discussed the large amount of experimental and theoretical work done in this field particularly with reference to colloidal particles and biological macromolecules. In addition to the interactions which arise from the molecular dimensions of the macroions (excluded volume), the inter- and intramolecular interactions arising from the electrical charge on the surface of the macroions, also contribute to the free energy of the solution and thus alter the chemical potential (10) given by R T In a = - R T V t ° c 2 ( l / M w + B c 2

+ C

c|

+

...

)

a )

where is the chemical potential of the macromolecular solution, pj the standard chemical potential, R the universal gas constant, T the Kelvin temperature, a the activity coefficient of the macroions, V£ the molar volume of the water, c^ the concentration of the macroions and M their molecular

© 1981 Walter de Gruyter &. Co., Berlin • New York Electrophoresis '81

18 weight.

B and C represent the second and third virial coeffi-

cients respectively, which are expressible in terms of the intermolecular potential.

All the physico-chemical properties

of the macroions in solution such as electrophoretic mobility U, electric conductance A, translational diffusion coefficient D t (K)

(K being the scattering vector), structure factor S(K),

activity coefficient a, osmotic pressure TT , transmembrane potential E^, Donnan effect, solubility S, electroviscosity 7)ej , critical temperature T c of the sol - gel transition and titration curves will depend upon the steric and electrostatic interactions. The Debye-Hiickel (DH) theory

(1) was developed in 1923 for

strong electrolytes such as Na + and CI

and is ordinarily ap-

plied to solutions of ionized salts, where the central ion is one of many similar ions in dimension and charge. ly, the identical formalism was applied

Subsequent-

(3,6) to the field of

colloidal particles and proteins in salt solutions. The theory was used under the implicit assumption of infinite macroion dilution, or equivalently, the absence of any macroionmacroion interactions.

Since then, the DH-theory has become

one of the key elements in the computation and analysis of the physico-chemical quantities mentioned above. Many experiments, however, have been conducted in solutions of finite macroion concentration, where macroion interactions were definitely present.

Under these conditions, the agree-

ment between the experimental and the predicted values is in general semi-quantitative.

For example, the ratio between the

electrokinetic and the titration charge was reported

(4,8,10,

13) to be in the range ofs0.6 to «0.8 for a variety of different globular proteins such as Ovalbumin B-Lactoglobulin

(14), Albumin

(16), Trypsin (17), Aldolose

(15),

(18), and Lyso-

zyme (19), over the entire range of pH's on both sides of the isoelectric point.

Also, the electric conductance measured on

salt free albuminates (20) yielded, when compared to the theoretical values, a ratio between 0.8 and 0.9 for a wide range

19 of protein charge and concentration.

In addition, the coeffi-

cient w, which accounts for the electrostatic intraparticle interactions of the charged groups in the LinderstrjzSm-Lang theory, is about 0.8 of the calculated value for several proteins such as Ovalbumin and Ribonuclease (9). We (21) have previously treated the problem of predicting the translational diffusion coefficient

D^

of uniformly charged

spherical macroions in solution and discusse'd the values of the calculations in the case of bovine serum albumin (BSA) in aqueous solution with added NaOH - minimum salt point - as well as at higher values of the ionic strength.

By intro-

ducing the hard sphere approximation for the radial distribution function

G(r)

of the macroions, which includes only the

excluded volume due to the dimension of the particle, into the Phillies theory (22), we were able to reproduce the predictions of the Doherty-Benedek-Stephen theory (23,24). The ratio BSA between the experimental and the calculated values of D T is between 0.13 and 0.27 for 18, 10 and 7 elementary charges at the minimum salt point. In order to take into account correlations in the positions of the macroions, due to the electrostatic interactions, we then introduced the more realistic dilute gas approximation for G(r) into the Phillies theory. Significantly better agreement with the experimental data was obtained.

The predicted values of D T , however, were system-

atically higher than the experimental values, the ratio being about 0.34. In our opinion, an important reason for the discrepancy between the theoretical and experimental values of the different physico-chemical coefficients is that the DH-theory does not include the contribution of the charged macroions to the charge density J ) ( r ) and therefore to the screening length 1/K of the solution.

In fact, to the best of our knowledge no one has yet

adequately accounted for this effect.

20 Theory In order to take into account the effects of the finite size and concentration of the charged macroions, we have generalized the usual III region Debye-Hiickel (DH 111 ) model (Figure 1) to include IV regions (DHIV) (Figure 2). Region I represents the central macroion of radius R, region II the water layer of thickness 8, region III from r=a to r=2a contains coions and counterions in solution but does not include the macroions. This region results from the excluded volume of two hard spheres. The new feature of the model is the introduction of region IV from r=2a to r=°° which encompasses the macroions in addition to the coions, counterions and water. In order to obtain the electrical potential ^(r) around the uniformly charged central macroion, Laplace's equation must be solved in regions I and II since no ions can penetrate into these regions. The Poisson-Boltzmann equation holds in regions III and IV. The usual boundary conditions for the continuity of the potential and the discontinuity of the normal derivative of the potential must be applied at r=R. In addition, the potential and its normal derivative -must be continuous at r=a and r=2a. Also If(r) must be finite everywhere and in particular at r=0 and r=°°. As has already been mentioned, the charge density p(r) is zero in regions I and II and Laplace's equation is satisfied: V2^(rj- 0

(o< r < R ) and (R < r < aj

(2)

The assumption that the surface of the macroions are spherical and uniformly charged implies a spherically symmetric potential function "^(r) . The appropriate spherically symmetric solutions to Laplace's equation are: = A

l

(0