Table Of ContentTHE BIOPHYSICAL APPROACH
TO EXCITABLE SYSTEMS
Kenneth S. Cole
THE BIOPHYSICAL APPROACH
TO EXCITABLE SYSTEMS
A Volume in Honor of Kenneth S. Cole
on His 80th Birthday
Edited by
William J. Adelman, Jr.
and
David E. Goldman
Laboratory of Biophysics, NINCDS
National Institutes of Health
At the Marine Biological Laboratory
Woods Hole, Massachusetts
PLENUM PRESS • NEW YORK AND LONDON
Library of Congress Cataloging in Publication Data
Main entry under title:
The biophysical approach to excitable systems.
Bibliography: p.
Includes index.
I. Excitation (Physiology) - Addresses, essays, lectures. 2. Neural conduction - Ad
dresses, essays, lectures. 3. Biological transport, Active - Addresses, essays, lectures. 4.
Biophysics-Addresses, essays, lectures. 5. Cole, Kenneth Stewart, 1900- . I. Cole,
Kenneth Stewart. 1900- . II. Adelman, William 1.,1928- . III. Goldman, David
Eliot, 1910-
QP363.B56 574.19'12 81-15759
ISBN-13: 978-1-4613-3299-2 e-ISBN-13: 978-1-4613-3297-8 AACR2
001: 10.1007/978-1-4613-3297-8
© 1981 Plenum Press, New York
Softcover reprint of the hardcover 1st edition 1981
A Division of Plenum Publishing Corporation
233 Spring Street, New York, N. Y. 10013
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted
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Preface
On July 10, 1980, Kenneth S. Cole became 80 years old. In order to
celebrate this landmark, a symposium in the form of a series of Monday
evening lectures was held in his honor at the Marine Biological Labora
tory throughout the summer of 1980. The selection of speakers was made
from among those investigators who had been either his students or
co-workers.
One intent of the symposium was to examine the current status of
knowledge of those areas of interest in excitable membrane structure and
function that owe their initiation or encouragement to Kacy Cole. The
papers assembled in this volume represent a large majority of the
presentations given during the 1980 Cole Symposium.
It seems clear on examination of these papers that Kacy's interests
in membrane impedance, ion channel conductances, channel fluctuation
phenomena, excitation, and the development of membrane biophysical
methodology are all being actively pursued. It is also clear that many of
his suggestions have borne fruit. Of these, his invention of the voltage
v
vi Preface
clamp method has been most productive. It is hoped that these papers
will provide new directions for investigations into the nature of excitable
membrane phenomena.
The organizers of the symposium and the editors of this volume wish
to express their thanks to the Marine Biological Laboratory for making
available the facilities for the symposium. They also wish to thank Dr.
Harry Grundfest for his cooperation and for having founded the Monday
evening "Electrobiology" seminars at the MBL which were the forum for
Kacy's 80th birthday symposium.
We thank also Ms. Dorothy Leonard for her unflagging assistance in
preparing this book for publication, and Mr. Robert Golder for his
artistic portrait of Dr. Cole, which is the frontispiece of this book.
Lastly, we the authors and editors of this volume wish to express our
profound gratitude to Kacy for the influence he has had on our investiga
tions. We hope that he has many more birthdays and that he can
continue "membrane watching," as we believe this will continue to be
both interesting and informative.
Marine Biological Laboratory William 1. Adelman, Jr.
Woods Hole, Massachusetts David E. Goldman
Contents
PART I. ELECTRICAL CHARACTERISTICS OF MEMBRANES
1. Electrical Properties of Cells: Principles, Some Recent
Results, and Some Unresolved Problems ................ 3
H. P. Schwan
Low-Frequency Relaxation Mechanisms ....................... 8
The State of Tissue Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2. Nonlinear Sinusoidal Currents in the Hodgkin-Huxley
Model .......................................... 25
Richard FitzHugh
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 25
Hodgkin-Huxley Equations .............................. 27
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34
vII
vIII Contents
3. Second-Order Admittance in Squid Axon ............... 37
L. J. DeFelice, W. J. Adelman, Jr., D. E. Clapman,
and A. Mauro
Linear and Nonlinear Properties of Nerve Membrane ............. 37
Properties of Linear Systems .............................. 39
Theoretical Admittance of Squid Axon Membrane ............... 40
Experimental Test of Linearity ............................. 41
Data Analysis ........................................ 43
Preparation and Electronics ............................... 43
Standard Measurement of Membrane Admittance ............... 44
Linearity and Nonlinearity in the Time Domain ................ .46
Linearity and Nonlinearity in the Frequency Domain ............ .48
Dependence of Frequency Components of Membrane
Current on Stimulus Amplitude .......................... 49
Dependence of First- and Second-Order Currents on Stimulus
Frequency and Membrane Voltage ........................ 50
Dependence of First-and Second-Order Currents on Na Current .... 53
Experimental and Theoretical Nonlinearity Compared ............ 55
Discrepancies between Theory and Experiment ................. 59
The Frequency Components of the Higher-Order Currents ......... 60
Summary ............................................ 62
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4. Squid Axon K Conduction: Admittance and Noise during
Short-versus Long-Duration Step Clamps .............. 65
H. M. Fishman, L. E. Moore, and D. Poussart
Inductive Reactance in the Impedance of Squid Axon: The
Frequency Domain Manifestation of Linearized Ion-Conduction
Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Advances in the Speed and Resolution of Impedance or
Admittance Measurements .............................. 66
Potassium Conduction Kinetics from a Comparison of
Admittance and Noise Data ............................. 68
Steady-State Linear Analysis of Conduction via Admittance ........ 69
Preparation and Low-Noise Voltage Clamp Technique ............ 75
Fourier Synthesized Pseudorandom Signal (FSPS) ............... 75
k Method of Coherence Elimination ......................... 78
The Measurement System ................................ 81
The Amplitude Range for a Linear Response ................... 84
Potassium Conduction in the Calculated Admittance of Squid
Axon ............................................. 86
Comparison of Potassium Conduction Kinetics from Admittance
and Noise Data ...................................... 88
The Admittance and Noise of Potassium Conduction during
Short-versus Long-Duration Step Clamps ................... 91
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Contents ix
5. Squid Axon Membrane Low-Frequency Dielectric
Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 97
Robert E. Taylor, Julio M. Fernandez,
and Francisco Bezanilla
Small Signal Electrical Equivalent of Squid Giant Axon Membrane ... 97
On the Measurement of Membrane Capacitance and Conductance ... 98
Membrane Capacitance and Conductance .................... 100
Complex Capacitance and Membrane Structure ................ 103
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
PART II. MEMBRANE CHANNELS
6. Single-Channel Conductances and Models of Transport .. . 109
Harold Lecar
Channels in Lipid Bilayers ............................... 110
Observing the Channel Conductance Fluctuations in
Cell Membranes .................................... III
Direct Observation of Single-Channel Currents ................ 115
What do the Measured y Values Tell About Transport
through Open Channels? .............................. 115
References .......................................... 120
7. Gating Kinetics of Stochastic Single K Channels ......... 123
Jorgen F. Fohlmeister and William J. Adelman, Jr.
Introduction ......................................... 123
Chord Conductance and the Probability that a Single Channel is
Open ............................................ 124
Instantaneous Conductance and the Driving Force for Ion Flux ..... 125
Special Cases of the Functionf(E) ......................... 126
Rate Constants for the Gating Kinetics of Stochastic Single K
Channels ......................................... 128
The Steady-State Probabilities for an Open K Channel ........... 130
References .......................................... 132
PART III. MEMBRANE TRANSPORT
8. Calculation of the Electrogenicity of the Sodium Pump
System of the Squid Giant Axon ..................... 135
David E. Goldman
Method of Calculation .................................. 137
Procedural Details ..................................... 138
Results of the Calculations ............................... 140
x Contents
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
9. Depolarization and Calcium Entry . . . . . . . . . . . . . . . . . . . 151
L. J. Mullins
Calcium Entry with Stimulation ........................... 153
Calcium Entry with Steady Depolarization ................... 156
Calcium Entry by Na-Ca Exchange ........................ 157
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
10. A Quantitative Expression of the Electrogenic Pump and
Its Possible Role in the Excitation of Chara Internodes .... 165
Uichiro Kishimoto, Nobunori Kami-ike, and YUko Takeuchi
Conductances and Electromotive Forces during the Process
of Inhibition of the Electrogenic Pump with 2 p,M Triphenyltin
Chloride (TPC) ..................................... 168
Internal ATP Level during TPC Poisoning .................... 173
The pH Dependence of Conductances and Electromotive Forces .... 173
A Model for the Mechanism of Electrogenic Pump .............. 175
The pH Dependence of Pump Current ....................... 177
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
PART IV. STIMULI AND DRUGS
11. Increases in Membrane Conductance Caused by
Electrical, Chemical, and Mechanical Stimuli ........... 185
Gerald Ehrenstein and Gideon Ganot
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
The Role of Membrane Conductance Changes ................. 186
Ionic Channels in Membranes ............................ 188
Mechanically Stimulated Changes in Membrane Conductance ...... 190
References .......................................... 195
12. Continuous Stimulation and Threshold ofAxons: The
Other Legacy of Kenneth Cole ...................... 197
Eric Jakobsson and Rita Guttman
From Whence We Came-How Kacy Cole and Colleagues
Mapped the Geometry of Excitability Space ................. 197
Where We Are-New Results on Accommodation and Repetitive
Firing .......................................... 201
Whither We Go-What Might "Reverse Accommodation" Mean
for Neural Coding? ................................ 208
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
