This book illustrates some of the ways physics and mathematics have been, and are being, used to elucidate the underlying mechanยญ 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 electroยญ 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 transยญ mission of information in the nervous system, and to gain some inยญ 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 disยญ cussed. Part II examines the foundations of electrodiffusion theory, and the use of that theory in trying to develop quantitative explaยญ 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
CONTENT
I. Introduction -- 1. Basic Membrane Structure and Electrical Properties -- 2. Passive Electrical Properties of Axons -- 3. Overview of the Gross Properties of Excitable Cells -- 4. The Hodgkin-Huxley Axon -- 5. Current Levels of Knowledge About the Early and Late Current Flow Pathways -- II. Classical Electrodiffusion Theories of Membrane Electrical Properties -- 6. Conservation and Field Equations -- 7. The Steady State Problem: Approximate Solutions -- 8. Active Transport and the Maintenance of Transmembrane Ionic Distributions -- 9. Admittance Properties of the Electro-Diffusion Equations -- 10. The Steady State Again: Approximations to Investigate the Role of Membrane Fixed Charge -- III. A Molecular Treatment of Transmembrane Ion Movement -- 11. Mathematical Formulation of the Model -- 12. Relationship Between the Microscopic and Macroscopic Formulations of Electro-Diffusion Theory -- 13. The Microscopic Model in a Steady State: No Concentration Gradients -- 14. The Steady State Microscopic Model with Solution Asymmetry -- 15. Steady State and Dynamic Properties of the Macroscopic Model -- References -- Appendix 1 -- Appendix 2
