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Nervous System Theory. An Introductory Study PDF

288 Pages·1972·9.868 MB·English
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N E R V O US S Y S T EM T H E O RY An Introductory Study K. N. LEIBOVIC CENTER FOR THEORETICAL BIOLOGY AND DEPARTMENT OF BIOPHYSICS STATE UNIVERSITY OF NEW YORK AT BUFFALO AMHERST, NEW YORK ACADEMIC PRESS New York and London 1972 COPYRIGHT © 1972, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER. ACADEMIC PRESS, INC. Ill Fifth Avenue, New York, New York 10003 United Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON) LTD. 24/28 Oval Road. London NWl LIBRARY OF CONGRESS CATALOG CARD NUMBER: 72-77354 PRINTED IN THE UNITED STATES OF AMERICA PREFACE As a science, nervous system theory must be based on experimental data and must relate to the actual characteristics of structure, function, and mode of operation of the nervous sytem. But it must be more that a mere collection of observations. It must be concerned with the responses of single cells and the interactions of groups of cells and how these may form the basis of per­ ceptual and motor functions. It must be concerned with the principles of operation of the vast and intricate cell assemblies which form a nervous system. As scientific theory, it should be a distillation of a body of observations of precisely formulated data from which one can make logical inferences. But often such data are not available in the form or to the extent required by such a theory. This is due not only to the experimental difliiculties of ob­ taining the data but even more to the rudimentary form of our understanding: in fact, data abound in this as in other fields of biology, but the question is what to look for. In such a situation it is essential to attempt to develop theoretical formulations. The balance between the appropriate amount of speculation and the earthy digest of experimental records is a delicate one and can only be based on individual judgement. One mix may appeal to some and not to others. In this volume the stress is on the means for understanding the nature of the bio­ logical system rather than on the elaboration of mathematical theories. An attempt has been made to stay close to the experimental data but also to con­ sider speculative models which are judged to be valid in the sense that they may provide insight into the relationships between structure and function, into the principles of operation, and into the neural bases of behavioral phen­ omena. Naturally, only a beginning can be made in this respect. This book is not intended to be a complete account of nervous system theory or even an ix χ Preface exhaustive treatment of the topics considered. It contains not only my per­ sonal work but includes that of many others. On the other hand, in regard to theories, I have given preference to those I have fathered together with my collaborators. In the pages which follow, single-cell responses are treated first. This is followed by a discussion of sensory information processing which leads into models of perceptual processes and their possible neural bases. Much of the material here refers to the visual pathway, since experimentally this has been studied more than any other sensory pathway and is thus the most accessible for theoretical investigations. In the last part of the book some general prin­ ciples are considered. Thus, we proceed from the units that make up a nervous system, through a sensory pathway, to central structures. Since the peripheral stimuli can be described accurately, we may hope to understand something about the operations of the brain by following the flow of informa­ tion through it. But the brain is not there simply to receive sensory infor­ mation. One of its most important functions is concerned with motorsensory integration. This is briefly considered in the last part of the book. In addition, there are larger problems of a more philosophical nature that I have dis­ cussed elsewhere and have not included in this volume. ACKNOWLEDGMENTS The material of this book is based on graduate courses of lectures in bio­ physics and theoretical biology which I have given for several years at the State University of New York at Buffalo and at the University of California at Berkeley during the summer of 1969, the latter sponsored by the Division of Medical Physics. My thanks are due to Drs. J. F. Danielli and F. M. Snell at Buffalo for their support on several occasions, and to Dr. Cornelius Tobias for extending his hospitality and making my stay at the Donner Laboratories in Berkeley such a stimulating experience. Thanks are also due to my students at Berkeley and Buffalo for their lively responses which helped to improve the presentation of this material and to my colleagues and collaborators without whose help and enthusiasm much of the work reported here would not have been done. Last, but not least, I have pleasure in expressing my appreciation to Drs. Nassir Sabah and Richard Srebro for reading and commenting on portions of the manuscript. It goes without saying that any errors or shortcoming remain entirely my own. The help and expertise of the staff of Academic Press in producing this volume and of Mrs. Kathryn Ward, who has done most of the typing, have been of great value. Mrs Evelyn Wood drew some of the figures, and Mrs. Ruth Harvey also typed some portions of the manuscript. The latter were supported by Grant NASA NGR 33015002, while some of our work referred to in the text was done in part with support from Grants NIH NB 06682 and NASA NGR 33015002. XI Chapter 1 INTRODUCTION The nerve cell is distinguished from other cells by having a number of long, fibrous processes emanating from the cell body and by its ability to generate and transmit signals. Of these the axonal signals are of constant amplitude and variable frequency, whereas the dendritic ones, as a rule, decay in amplitude as they spread along the fiber. In both cases the signals are in the form of changes of membrane potential. In the resting state the potential inside the cell is some 50-90 mV below that outside the cell. This potential difference is regulated by differences of ionic concentration. The cell membrane is 50-100 A thick and separates two aqueous solutions of which the one outside is rather more electroconductive than the one inside. The sodium and chloride ion concentrations in the external medium are about 10 times as high as those inside the cell, whereas the potassium ion concentra­ tion inside the cell is about 30 times that outside. The permeabiUty of the cell membrane is low but the K"^ and CI" ions move through it much more readily than the Na"^ ions, whose normal leakage into the cell is counteracted by the metabolically driven "sodium pump." If the ionic permeabilities of the membrane are fixed, then a change of polarization produced at some point on a fiber will spread and decay as it is conducted " electrotonically," as in a passive, leaky cable. In an active fiber, on the other hand, the ionic permeabilities depend on the state of polarization of the membrane, and a pulse of depolarization can be regenerated as it is conducted along the fiber. Thus, in an axon, when the resting potential of the initial segment is raised above a certain threshold value, the depolarization is rapidly amplified, producing a "spike," or action potential, which travels along the axon with constant amplitude. This is based on the following mechanism (Hodgkin and Huxley, 1952). The depolarization of the membrane 4 Part One: Single Cell Responses increases Na"^ permeability, whereupon external Na^ ions rapidly enter the cell and amplify the initial depolarization. With only a brief delay, however, the K"^ permeability is increased and K"^ flows out of the cell, while the Na"^ permeability is reduced to its former value, returning the membrane potential toward the resting level. As the spike develops, the membrane immediately ahead is depolarized and the process is repeated along the length of the ñber, ensuring the propagation of the action potential. The process can be com pared to conduction along a leaky cable with repetitive boosting. But during and shortly after the action potential, the fiber goes through a refractory period in which the generation of new impulses is suppressed. In nonmy elinated axons the action potential travels continuously along the fiber. Myelinated axons are surrounded by insulating sheaths with periodic inter ruptions, the so-called nodes of Ranvier, and the action potential jumps from node to node and conduction is more rapid. Some neuron characteristics are illustrated quantitatively by the following typical figures. The internal resistivity is of the same order of magnitude as, though up to three times higher than, the external resistivity, both being within the range of a few tens to a few hundreds of ohm centimeters. The axonal membrane resistance is of the order of a few thousand ohms per square centimeter and membrane capacitance is typically 1 //F/cm^. During the nerve impulse in a squid giant axon, some 3-4 χ 10" mole of Na"^ ions may be taken up, and the same amount of K"^ ions may be lost, per square centimeter of fiber. This represents only a small fraction of the ionic content of the squid axon—in the case of K"^ it is of the order of 10"^—and the original concentrations are restored quickly by metabolic activity. Although the system consisting of membrane, external medium, and internal medium is electrically neutral on the macroscopic scale, the inside of the cell membrane carries a slight negative charge which is balanced by an equal positive charge on the outside. This capacitative charge is of the order of 6 X 10" ® C/cm^, corresponding to a capacitance of 1 μ¥ and a potential difference of, say, 60 mV. From this it can be seen that relatively large changes of potential can arise from quite small charge displacements. For example, a 20% change of potential would involve a change of 1.2 χ 10"® C/cm^, corresponding to a displacement of some 7.5 χ 10^^ univalent ions. Although the foregoing figures are fairly representative, it should be remembered that the properties of neurons vary widely. For example, fiber lengths may vary between several microns and a meter or more, fiber diam­ eters between a micron or less and as much as a millimeter. In general, the larger the diameter, the higher the conduction velocity and the shorter the spike duration and refractory period. The variables are, however, inter­ related in a complex fashion. Conduction velocity, for example, depends among other factors on the rate at which Na"^ permeability increases and Chapter 1: Introduction 5 then decreases, the rate and timing with respect to Na"^ of the K"^ perme­ ability changes, and the spike amplitude and the ionic mobilities within the fiber. The axon represents the output line of the neuron. It usually ends in a number of branches making contact with the dendrites or cell body of other neurons. The dendrites represent input lines, and the numerous signals impinging on them are integrated within the dendritic tree and the cell soma. Although dendrite responses are not as well understood as the axonal potential, they clearly form a very important part of neuron function. The extent and the ramifications of a dendritic tree are often most impressive in relation to the rest of the cell. In many dendrites there may only be electro- tonic conduction, but in others spikes are generated, and clearly involve an active membrane. Communication between neurons can take place through chemical transmitters at synaptic junctions, through direct electrical transmission at tight junctions, or through changes in the ionic composition of the inter­ cellular space produced by activity of neighboring cells. The chemical trans­ mitter is stored in synaptic vesicles and released across the synaptic gap in quantal fashion. The ionic permeabilities of the postsynaptic membrane are altered selectively, depending on the transmitter and the membrane properties. As a result, the postsynaptic membrane may be either depolarized or hyper- polarized. Properties of nerve cells have been described extensively as, for example, in the following publications, where additional references can be found: Cole (1968); Eccles (1964); Hodgkin and Huxley (1952); Katz (1966); Lorente de No (1947); Mountcastle (1968); Quarton et al. (1967); Ruch et ai (1965). The topics mentioned in this introduction will be taken up in more detail in the following chapters, starting with the resting potential, going on to the transmission of signals in axons and dendrites, and concluding with synaptic communication and some reduced models of neuron function. It will be found that different problems necessitate the formulation of different models. For example, in the treatment of the resting potential the ionic flows are divided into components due to diffusion and the electric potential, whereas in the treatment of the cable properties of a nerve fiber all the flows are considered as electric current dependent on conductance, capacitance, and potential. Again in the treatment of active membranes the ionic flows are separated into species components, each with its own conductance and driving force expressed in terms of potentials. Clearly there is a connection between different formu­ lations, but the moral of all this is that it is necessary to maintain some flexibility in formulating a model. This is dictated by convenience of the mathematical treatment of experimental results, and it is developed further in the final chapters of this part of the book. Part One: Single Cell Responses REFERENCES COLE, K. S. (1968). *' Membranes, Ions and Impulses." Univ. of California Press, Berkeley, California. EccLES, J. C. (1964). "The Physiology of Synapses." Springer-Verlag, New York. HODGKIN, A. L., and HUXLEY, A. F. (1952). J. Physiol. 116, 449-506; 117, 500-544. KATZ, B. (1966). "Nerve, Muscle and Synapse." McGraw-Hill, New York. LoRENTE DE NO, R. (1947). A Study of Nerve Physiology, Stud, Rockefeller Inst. Med. Res. 131, 132. MouNTCASTLE, V. B. (Ed.) (1968). "Medical Physiology," Vol. II. Mosby, St. Louis, Missouri. QuARTON, G. C, MELNECHUK, R., and SCHMITT, F. O. (Eds.) (1967). "The Neurosciences." Rockefeller Univ. Press, New York. RUCH, T C, PATTON, H. D., WOODBURY, J. W., and TOWE, A. L. (1965). "Neurophysi­ ology." Saunders, Philadelphia, Pennsylvania. Chapter 2 THE RESTING POTENTIAL As already mentioned, the resting potential of the nerve cell is due to the differences of ionic concentration which are maintained on the two sides of the membrane by metabolic processes. If undisturbed, the system remains in a steady state, but it is not in thermodynamic equilibrium. Nevertheless, the following argument gives reasonable agreement with experimental data, for the departure from equilibrium is not too great. In addition, it is worth comparing the equilibrium treatment with the subsequent one, which takes into account ionic exchanges across the membrane. When a molecule is dissociated into ions in a solution, and the latter is divided by a semipermeable membrane into two compartments with unequal ionic concentrations, then an electric potential difference exists between the compartments. The relationship between potential and concentration differ­ ences at equilibrium can be derived as follows (Moelwyn-Hughes, 1966). Consider two compartments 1 and 2 at different electric potentials ΦkΛ = 1,2. Suppose a small quantity of material δη moles carrying an electric charge önzF is transferred reversibly from compartment 2 to compartment 1 at constant temperature Τ and pressure p. F is the Faraday constant and ζ is the valence of the material. In general, the internal energy U, entropy S, and volume Κ per mole of the substance will be different in the two compartments. The change of internal energy δη AU of the transferred material will be due to a change of heat energy δηΤΑΞ, a change of work energy -δηρ A{pV), and a change of electric energy —δηζΓΑφ, where AX=X2 — is the difference of a quantity X between the two compartments. Thus, δηΑυ = δηΤΑΞ - δη A(pV) - δηζΓ Αφ that is, O = Δ(/ + A{pV) - TAS + ζΓΑφ, O = AG + zFΑφ (2.1)

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