Neural Modeling: Electrical Signal Processing in the Nervous System

412 Pages·1977·14.832 MB·English

by  Ronald J. MacGregor, Edwin R. Lewis (auth.)

NEURAL
MODELING
Electrical Signal Processing in the Nervous System
NEURAL
MODELING
Electrical Signal Processing in the Nervous System
Ronald J. MacGregor
University of Colorado, Boulder
and Edwin R. Lewis
University of California, Berkeley
PLENUM PRESS • NEW YORK AND LONDON
Library of Congress Cataloging in Publication Data
MacGregor, Ronald J
Neural modeling.
Bibliography: p.
Includes index.
1. Nervous system-Mathematical models. 2. Electrophysiology-Mathematical
models. 3. Biomedical engineering. I. Lewis, Edwin R 1934- joint
author. II. Title.
QP363.M18 612'.81'0184 77-8122
ISBN-13: 978-1-4684-2192-7 e-ISBN-13: 978-1-4684-2190-3
001: 10.1007/978-1-4684-2190-3
© 1977 Plenum Press, New York
Softcover reprint of the hardcover 15t edition 1977
A Division of Plenum Publishing Corporation
227 West 17th Street, New York, N.Y. 10011
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted,
in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording, or otherwise, without written permission from the Publisher
To our parents
Ronald E. and Vergene Y. MacGregor
and
Edwin M. and Sally R. Lewis
Preface
The purpose of this book is to introduce and survey the various quantitative
methods which have been proposed for describing, simulating, embodying,
or characterizing the processing of electrical signals in nervous systems. We
believe that electrical signal processing is a vital determinant of the
functional organization of the brain, and that in unraveling the inherent
complexities of this processing it will be essential to utilize the methods of
quantification and modeling which have led to crowning successes in the
physical and engineering sciences. In comprehensive terms, we conceive
neural modeling to be the attempt to relate, in nervous systems, function to
structure on the basis of operation. Sufficient knowledge and appropriate
tools are at hand to maintain a serious and thorough study in the area.
However, work in the area has yet to be satisfactorily integrated within
contemporary brain research. Moreover, there exists a good deal of
inefficiency within the area resulting from an overall lack of direction,
critical self-evaluation, and cohesion. Such theoretical and modeling studies
as have appeared exist largely as fragmented islands in the literature or as
sparsely attended sessions at neuroscience conferences.
In writing this book, we were guided by three main immediate
objectives. Our first objective is to introduce the area to the upcoming
generation of students of both the hard sciences and psychological and
biological sciences in the hope that they might eventually help bring about
the contributions it promises. In other words, we introduce the area as
much for its potential value as for its accomplishments. Our second
objective is to make the studies more easily available to our biologically and
psychologically trained colleagues so as to integrate the area more effec
tively within the mainstream of ongoing brain research. Finally, our third
objective is to introduce some cohesiveness (although not consolidation) in
the area in the sense of encouraging more communication, more critical
vii
viii Preface
self-evaluation, and a sense of direction to higher levels of accomplishment
than we have seen thus far.
Recently, several other admirable books which are related more or less
directly to our area of interest have appeared. We have proceeded to write
our book nonetheless, not because we think these books are inadequate, but
simply because it seemed the natural and appropriate thing to do given our
professional and research interests and activities. We hope only that this
work might provide some contribution to our field along with those works
of our colleagues who have been similarly motivated.
R. J. MacGregor
E. R. Lewis
Acknowledgments
Many people have contributed to the substance of this book or supported
us in various critical ways during its creation. First, we express heartfelt
thanks to our wives, Betsy and Millie, and our children, Ned, Sarah,
Ronnie, Terri, and Felicia, for bearing so well the absenteeism required by
this effort. We express thanks as well to many colleagues whose ideas and
discussions have influenced our thinking, including most particularly P. S.
Lykoudis, L. D. Harmon, S. K. Sharpless, T. H. Bullock, D. H. Perkel, R.
F. Reiss, P. M. Groves, H. J. Hamilton, R. M. Oliver, T. E. Posch, and P.
Vogelhut. Robert S. Zucker deserves particular thanks for his suggestions
concerning Part II. Many other colleagues, too numerous to name, of the
EECS, Biophysics, and Neurobiology faculties at Berkeley, and the EDEE,
Chemical Engineering, and Psychology departments at Boulder, have
contributed ideas to the material contained herein. We also thank various
students of EECS 181 and IDS 201 at Berkeley and EDEE 571 and EDEE
572 at Boulder for many exciting discussions and suggestions concerning
the material of the book. We are indebted to many of our graduate students
who have worked often tirelessly and with great insight on various aspects
of material described here, and welcome this opportunity to express
admiration and thanks. In this regard we thank in particular M. J. Murray,
M. Hassul, J. S. Charlton, E. Mayeri, Y. Y. Zeevi, R. Plantz, Y. Hazeyama,
K. L. Lee, C. W. Li, 1. Weeks, R. Prieto-Diaz, R. Spurlock, C. Radcliffe, R.
Palasek, T. McMullen, B. Sherman, T. Bundy, R. Adams, D. Glover, Eric
Berg, and T. Detman. In very large part the book has grown from these
courses and theses work. We are also grateful to the National Science
Foundation (Grants GG 31427, GK 42054, and GB 33687) and to the
Preface ix
National Institute of Neurological and Communicative Disorders and
Stroke (Grants 5ROINSl2359 and lROINSlO781-01) for support of much
of our own original work discussed here.
We express particular thanks to the secretaries of the EECS depart
ment at Berkeley and to Mrs. Virginia ("Ginny") Birkey and Mrs. Marie
Hornbostel of the EDEE department at Boulder for painstaking care and
limitless patience in the essential task of typing the several drafts of the
manuscript. Finally, we express appreciation to Seymour Weingarten,
Evelyn Grossberg, and Betty Bruhns, of Plenum Press, who have shown
great patience in tolerating delay after delay in the preparation of the book,
and whose expert editorial guidance has enhanced the readability of the
manuscript.
Finally, we should like to thank the following individuals and publish
ing companies for permission to use quotations from previously published
materials: Dr. Ter Andersen, Dr. Jack Cowan, Sir John Eccles, Dr. Karl
Lashley (deceased), Dr. David Marr, Dr. Wilfrid Rail, The Association for
Research in Nervous and Mental Disease, Inc., Cambridge University
Press, The Royal Society of London, and Springer-Verlag Company.
The substantive deficiencies of the book remain our own responsibility.
Contents
PART I. INTRODUCTION
1 Signal Processing in Nervous Systems ........................ 3
1.1. Neurons ................................................................. 3
1.2. Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10
2 The Idealized "Standard Neuron" .............................. 19
2.1. The Idealized "Standard Neuron" ................................ 21
PART II. NEURAL MODELING:
MODELS OF EXCITA TlON AND CONDUCTION
3 Models of Passive Membrane ..................................... 35
3.1. The Nernst-Planck Model ........................................ 35
3.2. The Einstein Relation .............................................. 37
3.3. The Nernst Equation and Ionic Reversal Potentials .......... 37
3.4. Space-Charge Neutrality ........................................... 40
3.5. Nernst-Planck Membranes with Space-Charge
Neutrality and Obeying the Einstein Relation ................ 42
xi
Contents
xii
3.6. Space-Charge Neutrality in a Homogeneous
Nernst-Planck Membrane ........................................ 51
3.7. Sources of Permanent Potential Differences across
Membranes .......................................................... 52
3.8. Impedance to Ion Flow at Donnan Jumps .................... 57
3.9. Ion-Concentration and Electrical Potential Profiles
for Various Membrane Models ................................... 60
3.10. Summary: A Quantitative Model of Neuronal
Membrane ............................................................ 62
4 Equivalent Circuits for Passive Membrane .................. 65
4.1. The Basic Equivalent Circuit for a Patch of
Membrane .......................................................... " 65
4.2. Small-Signal Equivalent Circuits ................................. 75
4.3. Equivalent Circuits for Large Signals ........................... 78
4.4. The Frankenhaeuser-Hodgkin Space ........................... 81
4.5. Summary ............................................................. 83
5 Models of Signal Generation in Neural Elements .......... 85
5.1. Some General Considerations .................................... 86
5.2. The Eccles Model of Chemical Synapse ...................... 89
5.3. Bullock's Degrees of Freedom for a Chemical
Synapse ............................................................... 94
5.4. The Quantum Model of Transmitter Release .................. 99
5.5. Discrete Inputs to Other Receptors ............................ 102
5.6. Reliable Detection of Weak Signals in the
Presence of Noise .................................................. 105
5.7. The Fuortes-Hodgkin Model. ................................... III
5.8. Spontaneous Activity in Neurons ............................... 120
6 Models of Distributed Passive Membrane .................. 123
6.1. The Basic Model.. ................................................. 124
6.2. Dipole Annihilation and Redistribution ....................... 126
6.3. Continuous Model for Response Spread over
Neuronal Fibers .................................................... 129
6.4. Continuous Analysis of the Uniform, Passively
Conducting Fiber with Time-Invariant Parameters ......... 132
6.5. Continuous Analysis of Branching Dendritic
Trees: RaIl's Equivalent Cylinder Model. ..................... 139
Contents xiii
6.6. Spatially Discrete Analysis of Passively
Conducting Fibers and Fiber Trees ............................ 143
6.7. Shapes of Passively Conducted Signals ........................ 150
6.8. Conduction of Signals to Very Remote Sites ................. 150
7 Models of Spike Generation and Conduction ............ 153
7.1. The Iron Wire (or Heathcote-Lillie) Model .................. 153
7.2. Threshold and Accommodation (or the Hill-
Rashevsky-Monnier Model) ..................................... 159
7.3. The Hodgkin-Huxley Model .................................... 169
7.4. Abstractions of the Hodgkin-Huxley Model ................. 179
7.5. Conduction of Spikes ............................................. 187
7.8. Concluding Remarks ............... , .............................. 191
PART III. NEURAL CODING:
MODELS OF ELECTRICAL SIGNAL PROCESSING
8 Neuromimes .......................................................... 195
9 Stochastic Models of Neuron Activity ....................... 225
9.1. Gerstein's Model ................................................... 225
9.2. More General Models ............................................. 229
10 Statistical Analysis of Neuronal Spike Trains ............. 233
10.1. Statistical Measures for Single Trains .......................... 234
10.2. Statistical Measures for Simultaneously Recorded
Trains ............................... ". ............................... 242
10 .3. Applications of Neuronal Spike Train Analysis .............. 250
11 Models of Neuron Pools .......................................... 271
12 Models of Large Networks: Analytic Approaches ........ 297