Table Of ContentMembrane Transport in Biology - Volume I
Membrane Transport
in Biology
Edited by
G. Giebisch . D. C. Tosteson H. H. Ussing
Associate Editor
M. T. Tosteson
Volume I
Concepts and Models
Contributors
0. S. Andersen J. E. Hall D. J. Hanahan U. V. Lassen
P. K. Lauf R. J. Lefkowitz E. Racker B. E. Rasmussen
S. A. Rudolph F. A. Sauer C. W. Slayman G. Stark
O. Sten-Knudsen H. H. Ussing
Editor
D. C. Tosteson
With 108 Figures and 36 Tables
Springer-Verlag Berlin' Heidelberg' New York 1978
Professor Dr. Gerhard Giebisch
Yale University, School of Medicine, Department of Physiology
333 Cedar Street, New Haven, Conn. 06510/ USA
Professor Dr. Daniel C. Tosteson, Dean
Harvard Medical School
25 Shattuck Street, Boston, Mass. 02115 / USA
Professor Dr. Hans H. Ussing
University of Copenhagen, Institute of Biological Chemistry A
13 Universitetsparken, DK - 2100 Copenhagen
Dr. Magdalena T. Tosteson
Harvard Medical School, Department of Physiology
25 Shattuck Street, Boston, Mass. 02115 / USA
ISBN-13: 978-3-642-46372-3 e-ISBN-13: 978-3-642-46370-9
DOl: 10.1007/978-3-642-46370-9
Library of Congress Cataloging in Publication Data: Main entry under title: Membrane transport in
biology. 1. Biological transport. 2. Membranes (Biology). I. Giebisch, G., 1927-; II. Tosteson,
D. C, 1925-; III. Ussing, Hans H., 1911-. [DNLM: 1. Biological transport. 2. Cell membrane -
Physiology. QH 509 M 533] QH 509-M44. 574.8'75. 78-17669.
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Preface
This Volume forms the cornerstone of this series of four books on Membrane
Transport in Biology. It includes chapters that address i) the theoretical basis of
investigations of transport processes across biological membranes, ii) some of
the experimental operations often used by scientists in this field, iii) chemical
and biological properties common to most biological membranes, and iv) planar
thin lipid bilayers as models for biological membranes. The themes developed in
these chapters recur frequently throughout the entire series.
Transport of molecules across biological membranes is a special case of diffu
sion and convection in liquids. The conceptual frame of reference used by
investigators in this field derives, in large part, from theories of such processes in
homogeneous phases. Examples of the application of such theories to transport
across biological membranes are found in Chapters 2 and 4 of this Volume. In
Chapter 2, Sten-Knudsen emphasizes a statistical and molecular approach
while, in Chapter 4 Sauer makes heavy use of the thermodynamics of irreversi
ble processes. Taken together, these contributions introduce the reader to the
two sets of ideas which have dominated the thinking of scientists working in this
field. Theoretical consideration of a more special character are also included in
several other Chapters in Volume I. For example, Ussing (Chapter 3) re-works
the flux ratio equation which he introduced into the field of transport across
biological membranes in 1949. Andersen (Chapter 11) discusses some of the
physico-chemical properties of bilayers which place constraints on the applica
bility of the theory of transport processes in homogeneous systems to these extrem
ely thin and highly organized structures. Stark (Chapter 12) treats quite thor
oughly the theory of carrier mediated ion transport across bilayers. These essays
describe many of the concepts now available to and used by investigators of
membrane transport in biology.
Measurements of the rates of transport of substances across membranes in
volve certain common experimental operations. In Chapter 3, Ussing reviews
conceptual and technical aspects of isotopic tracers as non-perturbing probes of
transport processes. He was one of the first scientists to use these techniques
when radioactive isotopes became available in the 1940's and has continued to
observe and participate in the gathering of information with these tools since
that time. Through the use of isotopic tracers, the operational description of net
transport processes as the resultant of oppositely directed unidirectional fluxes
VI Preface
became possible for the first time, thus deepening our grasp of the kinetic
mechanisms underlying these phenomena. For example, measurements of fluxes
with tracers permitted Ussing to recognize exchange diffusion as an important
and hitherto unsuspected pathway for the mixing of molecules separated by
membranes. Electrical methods have also been usefully employed to character
ize the transport of ions across membranes. Lassen and Rasmussen review the
advantages and pitfalls of these techniques when applied to cell membranes in
Chapter 5. They point out that the introduction of microelectrodes into small
cells may seriously perturb the system under investigation. Several applications
of electrical methods to detect ion movements within and across membranes are
included in the three last chapters on bilayers.
Biological membranes share certain molecular properties which influence all
transport processes. These shared characteristics form the substance of several
papers in this Volume. Hanahan introduces these with a thoughtful review of
the chemical composition of red cell membranes. Racker contributes a brilliant
analysis of membrane enzymes with special emphasis on ATPases (Chapter 8).
Slayman reviews the genetic determination of membrane transport systems in
Chapter 7. Lauf explores the relation between immunological reactions and
transport phenomena. Rudolph and Lefkowitz provide an introduction to the
rapidly growing contemporary literature on membrane receptors which modu
late and regulate transport. These Chapters are both distinctive expressions of
important dimensions of membrane transport in biology and also useful summa
ries of material which will be helpful to readers of subsequent Volumes in this
series.
The ingenious work of Mueller and Rudin in the early 60's began a new stage
of research on transport across biological membranes. Before that time, the
minds of most scientists in the field were animated by concepts derived from the
analysis of bulk systems of membranes with dimension and physical properties
that are markedly different from the structures which surround cells and organ
elles. Their development of relatively stable thin lipid bilayers made available
for the first time a model with chemical composition and thickness comparable
to the membranes found in living cells. The planar character of Mueller-Rudin
membranes permitted simultaneous electrical and chemical transport measure
ments. The large number of productive insights into membrane transport which
have resulted from studies of these structures are summarized in the last three
chapters of this Volume. Andersen describes the features of unmodified bilay
ers, Stark considers carriers and Hall discusses channels. The relatively simple
and defined character of these systems permits quantitative analysis of many
concepts which are valuable in thinking about transport across more complicat
ed biological membranes
New Haven, Boston, Copenhagen G. Giebisch
D. C. Tosteson
H. H. Ussing
Contents
List of Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XIX
Chapter 1 - Membrane Transport in Biology
(H. H. Ussing) ............... . 1
Chapter 2 - Passive Transport Processes
(0. Sten-Knudsen) 5
A. Introduction . . . . . . 5
B. Fundamental Definitions 5
I. Flux ....... . 5
II. Types of Passive Transport 6
1. Diffusion 6
2. Migration . 7
3. Convection 7
III. Flux Equations 7
1. Migration Flux 7
2. Convection Flux 9
3. Diffusion Flux 9
a) Fick's Law . 10
b) The Driving Force behind the Diffusion Process 11
4. Diffusion and Migration Proceeding Concurrently 12
5. Convection with Superimposed Diffusion 13
C. Diffusion Processes: Macroscopic Treatment 13
I. The Diffusion Equation ........ 14
1. Classification of Diffusion Processes 15
II. Stationary Processes in One Dimension 15
1. Steady-State Diffusion in a Plate 16
2. The Permeability Coefficient 17
3. Stationary Diffusion through Two Different Media 19
III. Time-Dependent Processes ............. 20
1. Kinetics of Exchange between Two Phases Separated by a Membrane. 21
a) One of the Phases is Infinitely Large .............. 21
(i) Outer Concentration Zero ................. 21
(ii) Outer Concentration Finite, Inner Concentration Initially
Zero ............................ 22
VIII Contents
b) Both Phases Comparable in Size ..... 23
c) Unidirectional Fluxes ..... ..... 26
2. Instantaneous Point Source (Green's Function) 27
a) Solutions of Diffusion Problems by Means of Green's Function 29
(i) Initial Uniform Distribution in the One Half-Space 30
(ii) The One Half-Space is Separated by an Impermeable Wall 30
(iii) The Presence of an Absorbing Barrier 31
(iv) Variable Flux into the Half-Space 31
3. Diffusion Out of a Plate. . . . . . . . . . . . 32
a) Concentration Profiles .......... 32
b) The Time Constant for the Exchange of the Mean Concentration 35
4. Establishing the Stationary Concentration Profile 37
D. Diffusion Processes: Microscopic Aspects 40
I. Brownian Movements . . . . . . . 40
II. Smoluchowski's Treatment 41
1. Statistical Interpretation of the Diffusion Equation 41
2. Random Walk in One Dimension . . . 42
3. The Einstein-Smoluchowski Equation 45
III. Random Walk and Fick's Law (Einstein) 46
IV. The Smoluchowski Equation 48
V. Kramers' Equation ....... 51
VI. Diffusion Coefficient and Mobility 51
1. Einstein's Relation ... 52
2. Einstein-Stokes'Relation . . . 53
E. Diffusion and Superimposed Convection 53
I. The Equation of Motion . , . . . . 54
II. Steady-State Concentration Profile 55
1. Stationary Transport through a Membrane 55
a) Determination of the Flux . . . . . . 55
b) Unidirectional Fluxes and Flux Ratio 56
c) The Concentration Profile 57
F. Electrodiffusion . . . . . . . . . . 58
I. Conductance......... 59
II. The Nemst-Planck Equations 61
1. Various Equivalent Forms 61
2. The Poisson Equation . 63
a) Electroneutrality 64
b) The Constant Field 65
III. Membrane Equilibrium . 65
1. Nonosmotic Equilibrium 65
a) The Nemst Equation 65
b) Equivalent Electrical Circuit for the Ion-Selective Membrane 67
2. Donnan Equilibrium ..................... 68
a) Thermodynamic Treatment . . . . . . . . . . . . . . . . 68
b) Concentration and Potential Profiles between the Phases
(The Poisson-Boltzmann Equation) . 73
IV. Diffusion Potentials ............ 80
1. Charging Time and Redistribution Time 82
2. The Henderson Regime . . . . . . . . . 84
Contents IX
3. The Planck Regime . . . . . . . . . . . . . . . . . . . . . 85
a) Planck's General Relations . . . . . . . . . . . . 86
b) The Electrical Equivalent Circuit for the Planck Regime 87
c) Planck's Expression for the Diffusional Potential 90
V. Electrodiffusion through Membranes 91
1. Single Salt . . . . . . . . 91
a) Diffusion Potential 91
b) Membrane Resistance . . . 92
c) Equivalent Electrical Circuit 94
d) Electroneutrality ..... 95
2. Ion-Selective Membrane ... 96
3. Membrane Separating Electrolytes Having a Common Ion 98
a) Aux Ratio . . . . . . . . . . . . . . . . . . . . . . . 98
b) The Goldman Regime . . . . . . . . . . . . . . . . . 99
(i) The Separate Ionic Currents and the Diffusion Potential 100
(ii) Total Membrane Current and Membrane Potential 102
(iii) Concentration Profiles and Membrane Potential 104
(iv) Ionic Conductances and Membrane Potential 106
c) Equivalent Electrical Circuits 109
Acknowledgements 110
List of Symbols 110
References 112
Chapter 3 - Interpretation of Tracer Fluxes
(H. H. Ussing) ..... . 115
A. Introduction . . . . . . . . . . 115
B. Fundamental Concepts 115
C. Tracer Permeability Coefficients 116
I. Measurement of Tracer Permeability Coefficients 116
II. Multicompartment Systems .......... . 117
D. The Concept of Unidirectional Aux 118
I. Unidirectional Auxes 118
II. Isotope Effects ....... . 118
III. Associated Unidirectional Auxes 119
IV. The Relation of Tracer Auxes to Active and Passive Transport 119
V. Effects of Membrane Potentials on Ionic Auxes 120
VI. Exchange Diffusion ............ . 120
VII. Limitations for Integration of Aux Equations 121
E. Aux Ratio Analysis ........... . 122
I. The Aux Ratio Equation ..... . 122
II. Derivation of the Aux Ratio Equation 123
III. Estimation of Electrochemical Potential Differences 126
IV. The Short-Circuiting Method ....... . 127
V. Aux Ratio with Solvent Drag ....... . 127
VI. Solvent Drag on Non-Electrolytes and Water 130
VII. Solute-Solute Interactions . . . . . . . . . . 131
VIII. Meaning of the Term "Interaction" ..... 131
IX. Interpretation of Deviations from the Aux Ratio Equation 132
X Contents
F. Examples ............ 133
I. The Short-Circuited Frog Skin 133
II. Single-File Diffusion 137
III. Solvent Drag Effects 138
G. Concluding Remarks 139
References 139
Chapter 4 - Nonequilibrium Thermodynamics of Isotope
Flow through Membranes
(F. A. Sauer) .. 141
A. Introduction . . . . . . . 141
B. The System: Definitions and Mathematical Techniques 141
C. Nonthermodynamic Considerations of Isotope Flow 148
D. The Nonequilibrium Thermodynamic Approach 156
E. Applications to Model Systems 162
F. Summary 166
Acknowledgements 167
List of Symbols 167
References 168
Chapter 5 - Use of Microelectrodes for Measurement of
Membrane Potentials
(D. V. Lassen and B. E. Rasmussen) 169
A. Introduction . . . . . . . . . . . 169
B. Principles of Bioelectric Recording 170
I. Electrode Chains and Junction Potentials 171
II. Comments on Electronic Equipment 175
C. The Glass Capillary Microelecirode . . . . . . 178
I. The Suspension Effect . . . . . . . . . . 181
II. Diffusion Regime of the Microelectrode Tip 183
D. Potential Recording with Microelectrodes . . . . 190
I. Penetration of the Cell Membrane . . . . . 190
II. Microelectrodes and Leaks in the Membrane 194
E. Epilogue . . . . . 201
Acknowledgements 202
References 202
Chapter 6 - Chemical Composition of Membranes
(D. J. Hanahan) . 205
A. Introduction . . . . . . . . . . . . . . . . . . . . . . .205
