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Ion Transport through Biological Membranes

An Integrated Theoretical Approach

  • Book
  • © 1975

Overview

Authors:
  1. Michael C. Mackey

    1. Department of Physiology, McGill University, Montreal, Canada

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Part of the book series: Lecture Notes in Biomathematics (LNBM, volume 7)

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Table of contents (15 chapters)

  1. Front Matter

    Pages N2-IX
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  2. Introduction

    1. Front Matter

      Pages 1-3
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    2. Basic Membrane Structure and Electrical Properties

      • Michael C. Mackey
      Pages 5-11

    3. Passive Electrical Properties of Axons

      • Michael C. Mackey
      Pages 12-26

    4. Overview of the Gross Properties of Excitable Cells

      • Michael C. Mackey
      Pages 27-41

    5. The Hodgkin-Huxley Axon

      • Michael C. Mackey
      Pages 42-50

    6. Current Levels of Knowledge About the Early and Late Current Flow Pathways

      • Michael C. Mackey
      Pages 51-62

  3. Classical Electrodiffusion Theories of Membrane Electrical Properties

    1. Front Matter

      Pages 63-63
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    2. Conservation and Field Equations

      • Michael C. Mackey
      Pages 65-71

    3. The Steady State Problem: Approximate Solutions

      • Michael C. Mackey
      Pages 72-83

    4. Active Transport and the Maintenance of Transmembrane Ionic Distributions

      • Michael C. Mackey
      Pages 84-102

    5. Admittance Properties of the Electrodiffusion Equations

      • Michael C. Mackey
      Pages 103-115

    6. The Steady State Again: Approximations to Investigate the Role of Membrane Fixed Charge

      • Michael C. Mackey
      Pages 116-127

  4. A Molecular Treatment of Transmembrane Ion Movement

    1. Front Matter

      Pages 129-131
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    2. Mathematical Formulation of the Model

      • Michael C. Mackey
      Pages 133-160

    3. Relationship Between the Microscopic and Macroscopic Formulations of Electrodiffusion Theory

      • Michael C. Mackey
      Pages 161-167

    4. The Microscopic Model in a Steady State: No Concentration Gradients

      • Michael C. Mackey
      Pages 168-198

    5. The Steady State Microscopic Model with Solution Asymmetry

      • Michael C. Mackey
      Pages 199-216

    6. Steady State and Dynamical Properties of the Macroscopic Model

      • Michael C. Mackey
      Pages 217-228

  5. Back Matter

    Pages 229-242
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Physiology, McGill University, Montreal, Canada

    Michael C. Mackey

Bibliographic Information

  • Book Title: Ion Transport through Biological Membranes

  • Book Subtitle: An Integrated Theoretical Approach

  • Authors: Michael C. Mackey

  • Series Title: Lecture Notes in Biomathematics

  • DOI: https://doi.org/10.1007/978-3-642-81008-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin ยท Heidelberg 1975

  • Softcover ISBN: 978-3-540-07532-5Published: 01 December 1975

  • eBook ISBN: 978-3-642-81008-4Published: 13 March 2013

  • Series ISSN: 0341-633X

  • Series E-ISSN: 2196-9981

  • Edition Number: 1

  • Number of Pages: X, 242

  • Topics: Mathematics, general

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