Ion Transport through Biological Membranes: An Integrated Theoretical Approach

✍ Scribed by Dr. Michael C. Mackey (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1975
• Tongue: English
• Leaves: 247
• Series: Lecture Notes in Biomathematics 7
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages N2-IX
Front Matter....Pages 1-3
Basic Membrane Structure and Electrical Properties....Pages 5-11
Passive Electrical Properties of Axons....Pages 12-26
Overview of the Gross Properties of Excitable Cells....Pages 27-41
The Hodgkin-Huxley Axon....Pages 42-50
Current Levels of Knowledge About the Early and Late Current Flow Pathways....Pages 51-62
Front Matter....Pages 63-63
Conservation and Field Equations....Pages 65-71
The Steady State Problem: Approximate Solutions....Pages 72-83
Active Transport and the Maintenance of Transmembrane Ionic Distributions....Pages 84-102
Admittance Properties of the Electrodiffusion Equations....Pages 103-115
The Steady State Again: Approximations to Investigate the Role of Membrane Fixed Charge....Pages 116-127
Front Matter....Pages 129-131
Mathematical Formulation of the Model....Pages 133-160
Relationship Between the Microscopic and Macroscopic Formulations of Electrodiffusion Theory....Pages 161-167
The Microscopic Model in a Steady State: No Concentration Gradients....Pages 168-198
The Steady State Microscopic Model with Solution Asymmetry....Pages 199-216
Steady State and Dynamical Properties of the Macroscopic Model....Pages 217-228
Back Matter....Pages 229-242

✦ Subjects

Mathematics, general