Nerve and Muscle MEMBRANES, CELLS, AND SYSTEMS

Transcription

1 Nerve and Muscle MEMBRANES, CELLS, AND SYSTEMS

2 Nerve and Muscle MEMBRANES, CEllS, AND SYSTEMS Richard B. Stein University of Alberta Edmonton, Alberta, Canada PLENUM PRESS NEW YORK AND LONDON

3 Stein, Richard B Nerve and muscle. Library of Congress Cataloging in Publication Data Includes index. 1. Electrophysiology. 2. Nerves. 3. Muscle. l. Title. [DNLM: 1. Electrophysiology. 2. Nervous system-physiology. 3. Muscles-Physiology. WLl02 N454] QP341.S78 599'.01'852 8(}'15028 ISBN-13: e-isbn-13: DOl: / First Printing-November 1980 Second Printing - September 1981 Third Printing-July Plenum Press, New York Softcover reprint of the hardcover 1st edition 1980 A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y All righ ts 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

4 Preface There has been a convergence in recent years of people from the physical and biological sciences and from various engineering disciplines who are interested in analyzing the electrical activity of nerve and muscle quantitatively. Various courses have been established at the graduate level or final-year undergraduate level in many universities to teach this subject matter, yet no satisfactory short text has existed. The present book is an attempt to fill this gap, and arises from my experience in teaching this material over the past fifteen years to students on both sides of the Atlantic. Although covering a wide range of biophysical topics from the level of single molecules to that of complex systems, I have attempted to keep the text relatively short by considering only examples of the most general interest. Problems are included whenever possible at the end of each chapter so the reader may test his understanding of the material presented and consider other examples which have not been included in the text. No attempt has been made to write a comprehensive textbook. That would have required a longer book, probably a multi author work by specialists in each area who can weigh the evidence for or against current concepts. Instead, I have tried to start where these books leave off, with the current conceptual picture, and to elaborate the mathematical and physical bases of these concepts. Care has been taken to define both biological and mathematical terms whenever they are introduced, to aid those who are unfamiliar with either field. Standard units and abbreviations according to the Systeme Intemationale (SI) have been used throughout, although with their common American spellings. Many of these will be familiar, such as the meter (m), gram (g), and second (s). Others may need some introduction: the siemen (S) for conductance, rather than the mho, and the newton (N) for force, rather than the kilogram (kg), which is a unit of mass. The two units are related, according to Newton's law (F = rna), by the acceleration of gravity, 9.8 m/s2. The standard prefixes v

5 vi Preface are also used: kilo (k) = 10 3, centi (c) = 10-2, milli (m) = 10-3, micro (p.) = 10-6, nano (n) = 10-9, and pico (P) = Thus, micrometer (p.m) is used rather than micron and nanometer (nm = 10-9 m) rather than Angstrom (A = m). Readers with a modest knowledge of biology or of mathematics should be able to appreciate the major themes of the book. Wherever mathematical notions or proofs are introduced, the essence and implications are carefully explained for the benefit of those with a limited mathematical background. The mathematics required for a full understanding involves calculus, including the use of Laplace and Fourier transforms, and some knowledge of stochastic processes. Interestingly, the same mathematical approaches are useful in describing such diverse pairs of phenomena as (l) the movements of ions through membrane channels and the attachment of bonds between actin and myosin molecules in muscle, (2) the enzyme reactions involved in transport of ions and the conductance changes involved in synaptic transmission, (3) the spread of charge along a nerve and muscle fiber and the transfer function of a sensory receptor, and (4) the quantal release of transmitter and the stochastic pattern of nerve impulses. These few examples suggest that there is a biophysics of nerve and muscle which is not merely a collection of unrelated topics that happened to attract the attention of people from the physical sciences and engineering. These underlying similarities, arising from physical principles and mathematical approaches, have been emphasized, rather than the diversity and complexity of biological systems. This emphasis also requires a book which is short enough to read in its entirety, rather than a more comprehensive reference source. To the extent that I have succeeded in these aims, I am indebted to Professor Walter Rosenblith of the Massachusetts Institute of Technology, who first introduced me to the field of biophysics, and to Doctor Denis Noble and Doctor Peter Matthews of Oxford University, who aroused my interests in the problems of biological membranes and in motor control. These fine teachers, by their enthusiasm and example, produced a lasting effect. This book would not have been possible without their efforts on my behalf in years past. The book also owes much to colleagues at the University of Alberta and to former students such as Parveen Bawa, Robert Wong, and Ted Milner, whose comments and suggestions have improved the text greatly. Fred Loeffler and Ken Burt prepared many of the figures, while Tella White typed numerous drafts of the book. Finally, my wife, Suzanne, and other members of my family have provided the support to bring this work to a successful conclusion. R. B. Stein

6 Contents Chapter 1. Membrane Organization Phospholipids.. Membrane Proteins Myelin..... Chapter 2. Membrane Thermodynamics Equilibrium Thermodynamics. Osmotic Equilibrium... Irreversible Thermodynamics Problems Chapter 3. Carrier Transport Facilitated Transport.. Active Transport... Effects of the Na+ Pump Problems Chapter 4. Membrane Permeability and Voltage Equilibrium (Nemst Equation) Electrical Steady State.. Chemical Steady State.. Ussing's Flux-Ratio Test Constant Field Assumption Problems Chapter 5. Ionic Currents in Nerve and Muscle. Voltage Clamp Technique Assumptions of the Hodgkin-Huxley Equations Form of the Equations. Structure of the Channels Role of Ca + + Ions Cardiac Muscle.. Problems.... vii

7 viii Contents Chapter 6. Cable Theory and Extracellular Recording Assumptions and Definitions. Derivation of the Basic Cable Equation Unmyelinated Fibers. Myelinated Fibers. Comparison with Experimental Data Linear Cables. Extracellular Recording. Problems. Chapter 7. Synaptic and Neuromuscular Transmission. Presynaptic Mechanisms Statistics of Transmitter Release. Facilitation and Depression of Transmitter Release Presynaptic Inhibition Postsynaptic Mechanisms. Synaptic Channels. Modified Interactions between Nerve and Muscle Problems. Chapter 8. Muscular Contraction Muscle Proteins Contraction Cycle and Sliding Filaments Contraction Kinetics. Energetics of Contraction. Excitation-Contraction Coupling Motor Units. Viscoelastic Properties Problems Chapter 9. Sensory Receptors Crustacean Stretch Receptors. Impulse Generation. Input-Output Relations. Classification of Nerve Fibers. Muscle Spindles Frequency-Response Curves. Statistical Properties of Impulse Trains. Transmission of Information Problems. Chapter 10. Control of Movement Reflexes. Size Principle Feedback Systems. Stability and Oscillations: Physiological Tremor Pattern Generation

8 Contents ix What is Controlled? Problems.... Solutions to Problems References Index