Membranes, Dissipative Structures, and Evolution (Advances in Chemical Physics, Vol. 29)

388 Pages·1975·19.206 MB·English

by  Ilya Prigogine, Stuart A. Rice

MEMBRANES, DISSIPATIVE
AND EVOLUTION
STRUCTURES,
ADVANCES IN CHEMICAL PHYSICS
VOLUME
XXIX
ADVANCES IN CHEMICAL PHYSICS
EDITORS
I. Prigogine
Unioersity of Brussels, Brussels, Belgium
S. Rice
Department of Chemistry and The James Franck Institute,
University of Chicago, Chicago, Illinois
EDITORIAL BOARD
THORA . BAK,H . C. Oersted Institute, Copenhagen, Denmark
J. DUCHESNEU,n iversity of Likge, Likge, Belgium
C. LONGUETT-HIGGINDSe,p artment of Machine Intelligence, Uni -
H.
versity of Edinburgh, Edinburgh, Scotland
M. MANDELU, niversity of Leiden, Leiden, Holland
V. MATHOTU, niversitt Libre de Bruxelles, Brussels, Belgium
P. MAZURI, nstitut Lorentz, Leiden, Holland
A. MUNSTERIn, stitut fur theoretische physikalische Chemie, Frankfurt-
am-Main, Germany
S. Institute of Physics, College of General Education, Tokyo,
ONO,
Japan
B. PULLMANIn,s titut de Biologie Physico-Chimique, Universitt de Paris,
Paris, France
J. W. STOUTJ, ames Franck Institute, University of Chicago, Chicago,
Illinois, U.S.A.
G. SZASZ,G eneral Electric Company, Zurich, Switzerland
V. VOLKENSTEINIn, stitute of Macromolecular Chemistry, Leningrad,
M.
U.S.S.R.
B. H. ZIMMS, chool of Science and Engineering, University of California
at San Diego, La Jolla, California, U.S.A.
MEMBRANES,
DISSIPATIVE STRUCTURES,
AND EVOLUTION
Edited by
G. NICOLIS AND R. LEFEVER
FacultP des Sciences
Universite Libre de Bruxelles
Bruxelles, Belgium
Volume XXIX
AN INTERSCIENCE PUBLICATION
@
JOHN WILEY AND SONS
New York London Sydney Toronto
An Interscience Publication
Q
Copyright 0 1975, by John Wiley & Sons, Inc.
All rights TcBeTvcd. Published simultaneously in Canada.
NO part of this book may be reproduced by MYm eans, nor
transmitted, nor translated into a machine language without
the written permission of the publisher.
unwy of canpw catabghg in lwMcah Data:
Membranes, dissipative structures, and evolution.
(Advances in chemical physics; v.
29)
“An Interscience publications.“
R
“Many the published in volume were
of papers this
preeented at an EMBO conference held in Brussels, Novem-
ber 22-24, 1972.”
Includes bibliographical references.
1. Biological systems--Conpre9ses. Bio-
control 2.
logical physics-Chngresses. Biological chemisty-
3.
I. Nicolis, 11. Lcf-
Congresses. G., 1939- cd.
ever, R., 1943- cd. 111. European Molecular Bio-
logy Organization Series.
IV.
vol. S41’.08s
QD453.A27 29 [QH508] [574.8’75]
ISBN
0-471-63792-0 74-23611
Printed in the united states of America
10 1
9 8 7 6 5 4 3 2
PREFACE
I am very pleased to present this special volume devoted to “Mem-
branes, Dissipative Structures and Evolution.” During the last few years
these subjects have made spectacular advances: On the one hand, our
experimental knowledge of membranes and biochemical aspects of
cooperative processes has been rapidly increasing; on the other hand,
new theoretical tools have become available.
From the theoretical point of view the great surprise is certainly the
essential difference that appears between equilibrium and near-
equilibrium situations on one side and far-from-equilibrium situations
on the other. This is the basis of the distinction between equilibrium
structures and dissipative structures. We see now that this distinction
applies as well to fluctuation theory. New elements enter into fluctua-
tion theory whenever we are interested in fluctuations around far-from-
equilibrium situations described by nonlinear equations. In general, we
can really speak of a new physical chemistry corresponding to far-from-
equilibrium situations.
This development leads to a series of fascinating mathematical prob-
lems related to stability theory and bifurcation analysis. Some of these
problems are now amenable to analytical study. Others have led to
fascinating computer simulations.
Many of the papers published in this volume were presented at an
EMBO conference, “Membranes, Dissipative Structures and Evolu-
tion,” held in Brussels, November 22-24, 1972. Other papers have been
added to give a more complete view of the subject.
I believe that this volume presents the first attempt to give a unified
view of such diverse problems of basic interest in physical chemistry
and biology.
I. PRIGOGINE
V
CONTRIBUTORS TO VOLUME
H. BESSERDICH,A kademie der Wissenschaften der DDR, Zentralinstitut fur
Molekularbiologie, 1 115 Berlin-Buch, D.D.R.
A. BOITEUXM, ax-Planck-Institut fur Erhahrungsphysiologie, 46 Dortmund,
Germany
LIANAB OLIS,I nstitute of General Physiology, University of Rome, Italy
JEAN-PIERRBEO ON,F acult6 des Sciences, Universitb Libre de Bruxelles, Bru-
xelles, Belgium
H. BUSSE,M ax-Planck-Institut fur Erhahrungsphysiologie, 46 Dortmund,
Germany
J. CHAW, Laboratoire de Thermodynamique des Milieux Ioniques et Biologi-
ques, Universite Paris VII, Paris, France
J. CHARLEMAGNLaEb,o ratoire de Thermodynamique des Milieux Ioniques et
Biologiques, Universitt Paris VII, Paris, France
M. DELMOTTEL,a boratoire de Thermodynamique des Milieux Ioniques et
Biologiques, Universite Pans VII, Paris, France
J. L. DENEUBOURFGa, cult6 des Sciences, Universitt Libre de Bruxelles, Bru-
xelles, Belgium
G. GERISCHF,r iedrich-Miescher-Laboratorium der Max-Planck Gesellschaft, 74
Tubingen, Germany
B. C. GOODWINS,c hool of Biological Sciences, University of Sussex, Brighton,
Sussex, England
B. HESS, Max-Planck-Institut fur Erhahrungsphysiologie, 46 Dortmund,
Germany
J. JULIENL, aboratoire de Thermodynamique des Milieux Ioniques et Biologi-
ques, Universite Paris VII, Pans, France
E. KAHRIGA, kademie der Wissenschaften der DDR, Zentralinstitut fiir Mo-
lekularbiologie, ll 15 Berlin-Buch, D.D.R.
KAZUOK ITAHARAC,h imie Physique 11, Faculte des Sciences, Universitt Libre
de Bruxelles, Bruxelles, Belgium
KOBATAKEF,a culty of Pharmaceutical Sciences, Hokkaido University,
Y.
Sapporo, Japan
vii
viii VOLUME XXIX
CONTRIBUTORS TO
P. LKUGERD, epartment of Biology, University of Konstanz, Germany
R. LEPEVERF,a cultb des Sciences, Universitb Libre de Bruxelles, Bruxelles,
Belgium
E. MARGOLIASDHe, partment of Biological Sciences, Northwestern University,
Evanston, Illinois
A. M. MONNIERU, niversitb Paris VI-9, Quai St. Bernard, Paris, France
G. NICOLISF, acultd des Sciences, Universitb Libre de Bruxelles, Bruxelles,
Belgium
B. Novm, Department of Pharmacology, Biozentrum der Universitiit Basel,
Klingelbergstrasse 70, Switzerland
ORTOLEVDAe, partment of Chemistry, Massachusetts Institute of Technology,
P.
Cambridge, Massachusetts
1. PRIGOGINEF, acultb des Sciences, Universitb Libre de Bruxelles, Bruxelles,
Belgium
J. Ross, Department of Chemistry, Massachusetts Institute of Technology,
Cambridge, Massachusetts
DANIELTH OMASE, .R.A. n = 338 du C.N.R.S., Universitb de Rouen, France
JACKS . TURNERC, enter for Statistical Mechanics and Thermodynamics, The
University of Texas, Austin, Texas
CHARLEWS ALTERD, epartment of Biomathematics, University of Texas, M.D.
Anderson Hospital, Houston, Texas
WOLPERTD, epartment of Biology Applied to Medicine, The Middlesex
L. as
Hospital Medical School, London, England
CONTENTS
STABILITY AND SELF-ORGANIZATION IN OPEN SYSTEMS 1
By I. Prigogine and R. Lefwer
DISSIPATIVINES TABILITIESS,T RUCTURAEN, D EVOLUTION 29
By G. Nicolis
STUDIEISN DISSIPATIVPHEE NOMENWIAT H BIOLOGICAAL PPLICATIONS 49
By P. Ortoleva and J. Ross
FINITEFL UCTUATIONNOSN, LINEATRH ERMODYNAAMNIDC FSA, RF- ROM-
EQUILIBRIUM TRANSITIOBNEST WEENM ULTIPLES TEADYS TATES 63
By Jack S. Turner
THEH AMILTON-JACOBI-EQAUPAPTRIOOANC HTO FLUCTUATIPOHNEN OMENA 85
By Kazuo Kitahara
FUNCTIONOARLGA NIZATION IN ARTIFICIAELN ZYMEM EMBRANES:
ACCOMPLISHMENANTDS PROSPECTS 1 I3
By Daniel Thomas
THEG LOBASLT ABILITY OF PREY-PREDATOR SYSTEMS WITH SECOND-
ORDERD ISSIPATION 125
By Charles Walter
A SHORTR EMARAKB OUTV ARIOUS DISSIPATISVTREU CTURES 133
By E. Kahrig and H. Besserdich
SPATIOTEMFOROARLG ANIZATIION NC HEMICAANLD CELLULASYRS TEMS 137
By B. Hem, A. Boiteux, H. Busse, and G. Gerisch
THEORETICMAOLD ELSF OR BACTERIALM OTIONA ND CHEMOTAXIS 169
By Jean-Pierre Boon
THEM OLECULAVRA RIATIONSO F CYTOCHROcM AES A FUNCTIOONF
THE EVOLUTIOSNP ECIES 191
By E. Margoliash
THED EVELOPMEPNATT TERNM: ECHANISMBSA SEDO N POSITIONAL
INFORMATION 253
By L. Wolpert
A MEMBRANME ODELF OR POLART RANSPOARNTD GRADIENFOTR MATION2 69
By B. C. Goodwin
PERIODICAL SIGNALS IN THE SPATIAL DIFFERENTIATOIOF PNL ANT CELLS 28 1
By B. Nooak
ix
X CONTENTS
STRUCTURAEND TRANSPORTB IOMEMBRANES 301
IN
By Liana BoIis
ION TRANSPOTRHTR OUGAHR TIFICIALLI PIDM EMBRANES 309
By P. Liiuger
PHYSIOCHEMIPCRAOLB LEMINS EXCITABLMEE MBRANES 3 19
By Y. Kobatake
EXCITABILAIN~D IONIC SELECTXVITYCO, MMON PROPERTIES OF MANY
LIPIDICD ERIVATIVES 34 1
By A. M. Monnier
THERMODYNAMCIOCN SIDERATIOOFN S EXCITABLME ~ R A N E S
THE
BEHAVIOR 343
By M. Delmotte, J. Julien, J. Charlemagne, and J. Chanu
MEMBRANEXEC ITATION 349
By R. Lefeoer and J. L. Deneubourg
AUTHORIN DEX 315
SUBJECITN DEX 385
Advance in Chemical Physics, VolunzeX XIX
Edited by G. Nicolis. R. Lefever
Copyright © 1975, by John Wiley & Sons. Inc.
STABILITY AND
SELF-ORGANIZATION IN OPEN
SYSTEMS
I. PRIGOGINEI AND R. LEFEVER
Universite Libre de Bruxelles, Fact& des Sciences,
Bruxelles, Belgium
CONTENTS
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . 1
. .
11. Definitions Stability, Lyapounov Functions, and Structural Instabilities 3
A. Stabilitoyf in thesenseof LyapounovandOrbital Stability . . . . . . 4
B. Lyapounov Functions . . . . . . . . . . . . . . . . . . 5
C. Linear Stability . . . . . . . . . . . . . . . . . . . . . 5
D. Stability in Respect to “Small Parameters” . . . . . . . . . . . 7
E. StructuralStability . . . . . . , . . . . . . . . . . . . 9
111. Nonequilibrium Thermodynamics-Irreversibility a Symmetry-Breaking
Process.. . . . . . . . . . . . . .a s . . . . . . . . . . 12
IV. . . . . . . . . . . . . . . . . 14
ATh. erSmotadbyinliatmyi CcoSntadbitiiolint yTthheeo Eryq uilibrium State . . . . . . . . . . .
The Linear Range .of . . . . . . . . . . . . . . . . . . . 1I65
CB.. The Nonlinear Range . . . . . . . . . . . . . . . . . . . 17
V. Succession Instabilities. The Martinez Model . . . . . . . . . . . 18
VI. Entropy Proofd uctiqn and Evolutionary Feedback . . . . . . . . . . . 19
A. Simple Linear Chemical Networks . , . . . . . . . . . . . . 22
B. Steady State Entropy Production (s.e.p.) of a Simple Catalytic Model . . 24
VII. Physical Basis of Self-Organization . . . . . . . . . . . . . . . . 25
References . . . . . . . . . . . . . . . . . . . . . . . . 27
I. INTRODUCTION
In several papers included in this volume use is made of stability
theory and of nonequilibrium thermodynamics. It seems appropriate,
therefore, to present a discussion of some general aspects. Very recently
a review dealing with the historical development of nonequilibrium
thermodynamics has been written by Prigogine and Glansdorff.’ Since
the earliest publications on this subject, the idea of nonequilibrium as a
possible source of order has been repeatedly
*Also Center for Statistical Mechanics and Thermodynamics, The University Texas
of
at Austin, Austin, Texas, U.S.A.
1