Table Of ContentSpringer Series in Synergetics
Editor: Hermann Haken
Synergetics, an interdisciplinary field of research, is concerned with the cooper
ation of individual parts of a system that produces macroscopic spatial, temporal
or functional structures. It deals with deterministic as well as stochastic processes.
1 Synergetics An Introduction 3rd Edition 23 Synergetics of the Brain
By H. Haken Editors: E. Ba§ar. H. Flohr, H. Haken,
2 Synergetics A Workshop A.J. Mandell
Editor: H. Haken 24 Chaos and Statistical Methods
3 Synergetics Far from Equilibrium Editor: Y. Kuramoto
Editors: A. Pacault, C. Vidal 25 Dynamics of Hierarchical Systems
4 Structural Stability in Physics An Evolutionary Approach By 1.S. Nicolis
Editors: W. Guttinger, H. Eikemeier 26 Self-Organization and Management of
5 Pattern Formation by Dynamic Systems and Social Systems
Pattern Recognition Editors: H. Ulrich, G.l.B. Probst
Editor: H. Haken
27 Non-Equilibrium Dynamics in Chemical
6 Dynamics of Synergetic Systems Systems Editors: C. Vidal, A. Pacault
Editor: H. Haken
28 Self-Organization Autowaves and Structures
7 Problems of Biological Physics Far from Equilibrium
By L. A. Blumenfeld Editor: V. I. Krinsky
8 Stochastic Nonlinear Systems
29 Temporal Order
in Physics, Chemistry, and Biology
Editors: L. Rensing, N.1. Jaeger
Editors: L. Arnold, R. Lefever
30 Dynamical Problems in Soliton Systems
9 Numerical Methods in the Study of Critical
Editor: S. Takeno
Phenomena
Editors: J. Della Dora, J. Demongeot, 31 Complex Systems - Operational Approaches
B. Lacolle in Neurobiology, Physics, and Computers
Editor: H. Haken
10 The Kinetic Theory of Electromagnetic
Processes By Yu. L. Klimontovich 32 Dimensions and Entropies in Chaotic Systems
11 Chaos and Order in Nature Quantification of Complex Behavior
Editor: H. Haken Editor: G. Mayer-Kress
12 Nonlinear Phenomena in Chemical Dynamics 33 Selforganization by Nonlinear Irreversible
Editors: C. Vidal, A. Pacault Processes
Editors: W. Ebeling, H. Ulbricht
13 Handbook of Stochastic Methods
for Physics, Chemistry, and the Natural Sciences 34 Instabilities and Chaos in Quantum Optics
2nd Edition By C. W. Gardiner Editors: F. T. Arecchi, R. G. Harrison
14 Concepts and Models of a Quantitative 35 Nonequilibrium Phase Transitions in
Sociology The Dynamics of Interacting Semiconductors Self-Organization Induced by
Populations By W. Weidlich, G. Haag Generation and Recombination Processes
15 Noise-Induced Transitions Theory and By E. Scholl
Applications in Physics, Chemistry, and Biology 36 Temporal Disorder in Human
By W. Horsthemke, R. Lefever Oscillatory Systems
16 Physics of Bioenergetic Processes Editors: L. Rensing, U. an der Heiden,
By L. A. Blumenfeld M.C. Mackey
17 Evolution of Order and Chaos in Physics, 37 The Physics of Structure Formation
Chemistry, and Biology Editor H. Haken Theory and Simulation
18 The Fokker-Planck Equation Editors: W. Guttinger and G. Dangelmayr
By H. Risken 38 Computational Systems - Natural and
19 Chemical Oscillations, Waves, and Turbulence Artificial
By Y. Kuramoto Editor: H. Haken
20 Advanced Synergetics 2nd Edition 39 From Chemical to Biological Organization
By H. Haken Editors: M. Markus, S.c. Muller, and
21 Stochastic Phenomena and Chaotic Behaviour G. Nicolis
in Complex Systems Editor: P. Schuster 40 Information and Self-Organization
22 Synergetics - From Microscopic to Macroscopic Macroscopic Approach to Complex Systems
Order Editor: E. Frehland By H. Haken
M. Markus S. C. Muller
G. Nicolis (Eds.)
From Chemical
to Biological Organization
With 202 Figures
Springer-Verlag Berlin Heidelberg New York
London Paris Tokyo
Dr. Mario Markus
Dr. Stefan C. Muller
Max-Planck-Institut fUr Erniihrungsphysiologie. Rheinlanddamm 201,
D-4600 Dortmund, Fed. Rep. of Germany
Professor Dr. Gregoire Nicolis
Faculte des Sciences, Universite Libre de Bruxelles,
Campus Plaine, c.P. 231, Boulevard du Triomphe, B-1050 Bruxelles, Belgium
Series Editor:
Professor Dr. Dr. h. c. mult. Hermann Haken
Institut fur Theoretische Physik und Synergetik der Universitiit Stuttgart, Pfaffenwaldring 57!IV,
D-7000 Stuttgart 80, Fed. Rep. of Germany and
Center for Complex Systems, Florida Atlantic University,
Boca Raton, FL 33431, USA
ISBN-13: 978-3-642-73690-2 e-ISBN-13: 978-3-642-73688-9
DOT: 10.1007/978-3-642-73688-9
This work is subject to copyright. All rights are reserved, 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 other ways, and storage in data banks. Duplication of this publication or parts thereof is only
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1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German
Copyright Law.
© Springer-Verlag Berlin Heidelberg 1988
Softcover reprint of the hardcover 1st edition 1988
The use of registered names, trademarks, 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.
2153/3150-543210
Preface
Open nonlinear systems are capable of self-or~anization in time and space.
This realization constitutes a major breakthrou~h of modern science, and is
currently at the ori~in of explosive developments in chemistry, physics and
biolo~.
Observations and numerical computations of nonlinear systems surprise us
by their inexhaustible and sometimes nonintuitive variety of structures with
different shapes and functions. However, in addition to this variety one finds
upon closer inspection that nonlinear phenomena share universal aspects: (1)
kinetic and thermodynamic principles; (2) ~lobal behaviour, for instance the
routes to chaos; and (3) novel experimental approaches, for example methods
to determine dimensions of attractors reconstructed from time series.
The universal aspects shared by a variety of nonlinear phenomena in time
and space make it possible to brid~e the ~ap between inanimate and livin~
matter at various levels of complexity, both in theory and experiment. It is
our hope that the present book, which contains a wide ran~e of examples
from very diverse areas of scientific research, provides convincin~ evidence of
the emer~ence of nonlinearity as a new scientific paradi~m.
Benno Hess, head of the Max-Planck-Institut fiir Ernahrun~sphysiolo~ie,
and truly a pioneer in the investi~ation of nonlinear phenomena in chemistry
and biolo~, celebrated his 65th birthday on February 22, 1987. On this
occasion, Ilya Pri~o~ine presented a colloquium in Dortmund on the foun
dations of irreversibility and sent us a manuscript (in collaboration with E.
Kestemont and M. Mareschal) which is included in the present volume. This
anniversary was followed by a meetin~ which ~athered 150 scientists from 16
nations at the Ma.'{-Planck-Institut in Dortmund, March 16-19, 1987. The
meetin~ was devoted to re~ulation in bioener~etics and to nonlinear phenom
ena in the biosciences. The most impressive feature of this event was that
chemists, biolo~ists, ecolo~ists, physicists, mathematicians and medical doc
tors found. themselves speal(in~ the same lan~ua~e - and talkin~ with each
other. One could realize that nonlinear phenomena are currently abolishin~
the scientific Tower of Babel. Inspired by this excitin~ atmosphere, we made
plans to edit this book and invited several participants to send us contribu
tions from their area of research. Subsequently, we asked other scientists to
write articles that would further stren~then this feelin~ of universality within
the phenomenal variety of self-or~anizin~ systems in chemistry and biolo~y.
With this volume, we also intend to express our ~ratitude to Professor Hess
for the stimulation that he has ~iven to so many of us. We are ~rateful to
V
scientists of highest distinction who took the time to prepare a contribution,
honouring him with their work.
Spontaneous emergence of order does not apply to international confer
ences. Without Theo Plesser's efficient organization the conference would
never have been realized in such a successful manner. We wish to thank
him for his deep involvement. We also acknowledge the financial support of
the Instituts Internationaux de Physique et de Chimie, fondes par E. Solvay,
Brussels, for the preparation of this boole Special thanks are due to Ms.
Helga Wagner for her assistance before, during and after the conference, as
well as to Ms. Bettina Plettenberg, Ms. Angelika Rohde, Ms. Christine
Riemer and Ms. Ina Wilms for typing most of the manuscripts. Finally, we
thank Dr. H. Lotsch, Ms. D. Hollis and Ms. J. Meyer of Springer-Verlag for
their patience and publishing efficiency.
Dortmund, Brussels 1\-1. l\Jarkus
February, 1988 S. C. l\Jiiller
G. Nicolis
VI
Contents
Part I General Concepts
From Chemical to Biological Organization: A Snapshot
By E. Katchalski-Katzir ................................ 3
Pattern Formation: Thermodynamics or Kinetics?
By H. Haken (With 3 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Spatiotemporal Organization in Biological and Chemical Systems:
Historical Review. By J.J. Tyson and M.L. Kagan ............. 14
Velocity Correlations and Irreversibility: A Molecular Dynamics
Approach
By I. Prigogine, E. Kestemont, and M. Mareschal (With 3 Figures) 22
Nonlinear Dynamics, Self-Organization and the Symbolic
Representation of Complexity. By G. Nicolis (With 2 Figures) 27
Spectral Kinetics and the Efficiency of (Bio ) Chemical Reactions
By J. Ross, S. Pugh, and M. Schell (With 14 Figures) .. . . . . . . . . . 34
Part II Chemical Organization
Distinction Between Amplified Noise and Deterministic Chaos by the
Correlation Dimension
By A. Freund, Th.-M. Kruel, and F.W. Schneider (With 9 Figures) 49
Exotic Chemical Reactions with Cu(II) Catalyst
By M. Orban (With 7 Figures) ........................... 61
Bifurcation, Periodicity and Chaos by Thermal Effects in
Heterogeneous Catalysis
By E. Wicke and H.U. Onken (With 12 Figures) .............. 68
Spatial Patterns in (Bio ) Chemical Reactions
By S.C. MUller (With 14 Figures) ......................... 83
Experimental Study of the Target Patterns of the BZ Reaction Using
Digital Picture Analysis
By P. Hanusse, C. Vidal, and A. Pagola (With 8 Figures) ........ 99
VII
Dispersion Curves and Pulse Wave Propagation in Excitable Systems
By M. Marek and H. SevCikova (With 7 Figures) ........ :..... 103
Chemical Structures and Convection
By P. Borckmans and G. Dewel ........................... 114
The Path to Hydrodynamic Instability During Reactions at Liquid
Interfaces: Comparison of Experimental Image Analysis Results and
Simulations
By M.L. Kagan, R. Kosloff, and D. Avnir (With 8 Figures) ... . . .. 122
Cellular Automata Simulating the Evolution of Structure Through the
Synchronization of Oscillators
By A.W.M. Dress, M. Gerhardt, and H. Schuster (With 10 Figures) 134
Part III Biochemical Organization
Potential Functions and Molecular Evolution
By P. Schuster (With 5 Figures) .......................... 149
Stochastic and Chaotic Processes in Biochemical Systems
By W. Ebeling, H. Herzel, and 1. Schimansky-Geier (With 8 Figures) 166
Protein Complexity. By H. F'rauenfelder . . . . . . . . . . . . . . . . . . . .. 177
Chemical Turnover and the Rate of Heat Production in Complex
Reaction Systems
By Th. Plesser and 1. Lamprecht (With 7 Figures) ............. 182
Pattern Formation by Coupled Oscillations: The Pigmentation
Patterns on the Shells of Molluscs
By H. Meinhardt and M. Klingler (With 9 Figures) ............ 193
Nonlinear Polymerization of Fibrinogen
By R. Rigler, U. Larsson, and B. Blombii.ck (With 5 Figures) ..... 203
Part IV Cellular and Intercellular Organization
Dynamic Phenomena in Molecular and Cellular Biology
By L.A. Segel ........................................ 211
Thermodynamics of Energy Conversion in the Cell
By J.W. Stucki (With 5 Figures) .......................... 216
Cell Lineage and Segmentation in Development
By G.s. Stent (With 2 Figures) ........................... 226
Models of Cytoplasmic Motion
By W. Alt (With 9 Figures) ............................. 235
VIII
Developmental Control of a Biological Rhythm: The Onset of Cyclic
AMP Oscillations in Dictyostelium Cells
By A. Goldbeter and J.-L. Martiel (With 2 Figures) ............ 248
Periodic Cell Communication in Dictyostelium discoideum
By B. Wurster (With 3 Figures) .......................... 255
Part V From Complex Cellular Networks to the Brain
Memory and Paralysis Phenomena in the Immune Response:
Interpretation in Terms of Multiple Steady State Transitions
By M. Kaufman (With 7 Figures) ......................... 263
Spatiotemporal Patterns of Block in an Ionic Model of Cardiac
Purkinje Fibre. By M.R. Guevara (With 3 Figures) ............ 273
Perturbations of Next-Period Functions: Applications to Circadian
Rhythms. By H. Degn (With 7 Figures) .................... 282
Brain Development and Self-Organization
By W. Singer and Chr. v.d. Malsburg ...................... 288
Do Coherent Patterns of the Strange Attractor EEG Reflect
Deterministic Sensory-Cognitive States of the Brain?
By E. B8.§ar, C. B8.§ar-Eroglu, and J. Roschke (With 7 Figures) 297
The Creutzfeld-Jakob Disease in the Hierarchy of Chaotic Attractors
By A. Babloyantz and A. Destexhe (With 6 Figures) ........... 307
Part VI Ecological, Epidemiological and Economical Organization
Ecosystems Under Varying Ambient Conditions
By J. Rossler, M. Kiwi, and M. Markus (With 8 Figures) 319
Periodic and Chaotic Dynamics in Childhood Infections
By W.M. Schaffer, L.F. Olsen, G.L. Truty, S.L. Fulmer,
and D.J. Graser (With 8 Figures) ......................... 331
Analysis of Life Processes and Economic Systems by Methods of
Thermodynamics
By H.G. Busse and B. Havsteen (With 4 Figures) . . . . . . . . . . . . .. 348
Index of Contributors . . . . . . . . . . . . . . . . 358
IX
Part I
General Concepts
