Ion transport through biological membranes : an integrated theoretical approach
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書誌事項
Ion transport through biological membranes : an integrated theoretical approach
（Lecture notes in biomathematics, 7）
Springer-Verlag, 1975
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注記
Bibliography: p. [229]-238
内容説明・目次
内容説明
This book illustrates some of the ways physics and mathematics have been, and are being, used to elucidate the underlying mechan isms of passive ion movement through biological membranes in general, and the membranes of excltable cells in particular. I have made no effort to be comprehensive in my introduction of biological material and the reader interested in a brief account of single cell electro physlology from a physically-oriented biologists viewpoint will find the chapters by Woodbury (1965) an excellent introduction. Part I is introductory in nature, exploring the basic electrical properties of inexcitable and excitable cell plasma membranes. Cable theory is utilized to illustrate the function of the non-decrementing action potential as a signaling mechanism for the long range trans mission of information in the nervous system, and to gain some in sight into the gross behaviour of neurons. The detailed analysis of Hodgkin and Huxley on the squid giant axon membrane ionic conductance properties is reviewed briefly, and some facets of membrane behaviour that have been revealed since the appearance of their work are dis cussed. Part II examines the foundations of electrodiffusion theory, and the use of that theory in trying to develop quantitative expla nationsof the observed membrane properties of excitable cells, in particular the squid giant axon. In addition, an ad hoc formulation of electrodiffusion theory including active transport is presented to illustrate the qualitative nature of cellular homeostasis with respect to intracellular ionic concentrations and membrane potential, and cellular responses to prolonged stimUlation.
目次
I. Introduction.- 1. Basic Membrane Structure and Electrical Properties.- A. Some Simple Concepts About Membrane Structure.- B. The General Nature of Membrane Electrical Properties.- 2. Passive Electrical Properties of Axons.- A . Non-Myelinated Fibres.- B. Myelinated Fibres.- 3. Overview of the Gross Properties of Excitable Cells.- A. The Membrane Theory of Excitation and Propagation.- B. Strength-Duration Relation, Accomodation.- C. Refractory States and Firing Frequency.- D. Axonal Characteristics and Action Potential Propagation.- 4. The Hodgkin-Huxley Axon.- A. Voltage Clamping.- B. Ionic Current Flow as Revealed by the Voltage Clamp.- C. Empirical Formulae for the Conductances.- D. Reconstruction of the Action Potential.- 5. Current Levels of Knowledge About the Early and Late Current Flow Pathways.- A. The Action of Tetrodotoxin (TTX).- B. The Action of Tetraethylammonium Ion (TEA).- C. Ionic Strength Effects on the Kinetic Parameters of Excitation.- D. The Effect of Calcium on the Membrane.- E. The Effects of pH Changes.- F. Cation Selective Properties of the Membrane at Rest and During Excitation.- G. Kinetic Behaviour in the K Channel.- H. High Potassium Effects on the K Channel Current-Voltage Curve.- I. The Nature of the Leakage Pathway.- II. Classical Electrodiffusion Theories of Membrane Electrical Properties.- 6. Conservation and Field Equations.- 7. The Steady State Problem: Approximate Solutions.- A . Constant Field Approximation.- B. The Microscopic Electroneutrality Approximation.- 8. Active Transport and the Maintenance of Transmembrane Ionic Distributions.- A. General Characteristics of Active Transport Systems.- B. The Consequences of Including Active Transport of Na+ and K+ in Steady State Electrodiffusion.- C. Active Transport and the Recovery From Excitation.- 9. Admittance Properties of the Electro-Diffusion Equations.- A . Analysis.- B. The Behaviour of the Transformed Membrane Admittance.- C. Quantitative Comparisons with Data.- 10. The Steady State Again: Approximations to Investigate the Role of Membrane Fixed Charge.- A. Volume Charge Considerations.- B. Surface Charge Effects.- III. A Molecular Treatment of Transmembrane Ion Movement.- 11. Mathematical Formulation of the Model.- A. The Concept of the Distribution function.- B. The Relation of Some Macroscopic Quantities to the Distribution function.- C. The Derivation of an Equation of Change for the Distribution function.- D. The Dynamics of a Binary Collision.- E. Evaluation of the Boltzmann Equation Collision Term.- F. Simplification of the Boltzmann Equation.- G. Dependence of the Collision Frequency, V1, on vi.- H. Expressions for Macroscopic Quantities from the Expanded Distribution function.- I. Summary.- 12. Relationship Between the Microscopic and Macroscopic Formulations of Electro-Diffusion Theory.- A . Conservation Equations.- B. Relation to Electrodiffusion.- 13. The Microscopic Model in a Steady State: No Concentration Gradients.- A. Spatial Gradients in a Steady State.- B. Solutions of the Kinetic Equations For a DC Field.- C. Analytic Behaviour of the Current Density as a Function of Electric Field Strength.- D. Computed Behaviour of ? (?) and Gc (?).- E. Estimation of Some Membrane Related Quantities.- 14. The Steady State Microscopic Model with Solution Asymmetry.- A. Solution of the Kinetic Equations.- B. A Generalized Goldman Equation.- C. Computed Properties of the Model.- D. One Way Fluxes and the Independence Principle.- 15. Steady State and Dynamic Properties of the Macroscopic Model.- References.- Appendix 1.- Appendix 2.
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