Thomas Fischer Weiss
Cellular Biophysics
Volume 1: Transport
A Bradford Book
The MIT Press
Cambridge, Massachusetts
London, England
To Aurice B, Max, Elisa, and Eric
© 1996 Massachusetts Institute of Technology
All rights reserved. No part of this publication may be reproduced in any form by
any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from. the publisher.
This book was set in Lucida Bright by Windfall Software using ZzT£X and was
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library of Congress Cataloging-in-Publication Data
Weiss, Thomas Fischer
Cellular biophysics I Thomas Fischer Weiss
v. <1- > ; em.
Includes bibliographical references and index.
Contents: v. 1. Transport- v. 2. Electrical properties.
ISBN 0-262-23183-2 (v. 1).- ISBN 0-262-23184-0 (v. 2)
1. Cell physiology. 2. Biophysics. 3. Biological transport.
4. Electrophysiology. I. Title.
QH63l.W44 1995
574.87'6041-dcZO
RS WEI
HD H791
95-9801
CIP
Contents
Contents in Detail
Preface
ix
xix
Units, Physical Constants, and Symbols
xxvii
1
Introduction to Membranes
2
Introduction to Transport
3
Diffusion
4
Solvent Transport
5
Concurrent Solute and Solvent Transport
6
Carrier-Mediated Transport
7
Ion Transport and Resting Potential
8
Cellular Homeostasis
List of Figures
List of Tables
669
49
83
185
645
659
Contents of Volume 2
Index
1
663
571
333
449
281
Contents in Detail
Preface
xix
Subject and Orientation of the Book
Expected Background of the Reader
A Note to the Instructor xx
Preparation of the Manuscript
Personal Perspective xxiii
Acknowledgments
References xxvi
xx
xxi
xxiv
Units, Physical Constants, and Symbols
Units
xix
xxvii
xxvii
Base SI Units xxvii
Derived SI Units xxvii
Decimal Multiples and Submultiples of SI Units
Commonly Used Non-SI Units and Conversion
Factors xxviii
Physical Constants xxix
Fundamental Physical Constants xxix
Physical Properties of Water xxix
Atomic Numbers and Weights xxx
Symbols xxxii
References xxxv
xxviii
xi
Contents in Detail
Contents in Detail
X
2.6 Methods for Studying Membrane Transport
Introduction to Membranes 1
1.1 Historical Perspective 1
1.1.1 Fundamental Concepts of Living Organisms
1.1.2 Emerging Concepts of Cell Membranes 3
1
1.2 Survey of Cell Structure
2.6.1
2.6.2
2. 7 Summary
1
Exercises
References
3
10
3.1.1
3.1.2
3.1.3
3.1.4
3.1.5
3.1.6
3.1.7
Exercises 44
References 46
80
81
3.2.1
3.2.2
3.2.3
49
3.2.4
51
2.3.1
2.3.2
2.3.3
2.3.4
2.3.5
2.3.6
2.3.7
Composition of a Potato 51
Digestion of a Potato 52
Structure of the Small Intestine 54
Structure of Enterocytes 57
Final Stage of Digestion 60
Sugar Transport into and out of Enterocytes 63
Sugar Transport into and out of the Circulatory
System 65
2.3.8 Sugar Transport into Cells and Utilization of Sugars
2.4 Cellular Transport Functions 68
2.4.1 Maintenance of Intracellular Composition
2.4.2 Water Homeostasis 69
2.4.3 Secretion and Absorption 69
Survey of Transport Mechanisms
70
68
3.2.5
83
Background 83
Diffusion Variables 84
Fick's First Law 86
The Continuity Equation 87
Fick's Second Law: The Diffusion Equation 89
Diffusion with Convection and Chemical Reactions
Postscript on Diffusion: The Second Law of
Thermodynamics 91
3.2 Microscopic Model
2.1 Introduction 49
2.2 Cell Requirements 50
2.3 Transport in the Body Illustrated Using a Potato
2.5
79
Diffusion 83
3.1 Macroscopic Description
1.4 Cell Membrane Structure 36
1.4.1 Contents of Membranes-Lipids, Proteins, and
Carbohydrates 3 7
1.4.2 The Ubiquitous Phospholipid Bilayer 38
1.4.3 Membrane Fluidity 40
1.4.4 Disposition of Membrane Proteins 40
Introduction to Transport
73
6
1.3 Molecules 9
1.3.1 Atoms, Elements, and Bonds
1.3.2 Organic Molecules 16
2
Physicochemical Methods
Preparations 76
73
92
Introduction 92
The Microscopic Basis for Fick's First Law 93
The Microscopic Space-Time Evolution of Particle Location:
The Binomial Distribution 95
The Macroscopic Space-Time Evolution of Particle Location:
The Gaussian Distribution 98
Concentration as a Statistical Average of the Number of
Particles per Unit Volume 102
3.3 The Diffusion Coefficient
102
3.3.1 Solute in a Simple Fluid 103
3.3.2 Solute in a Polymer 107
3.4 Equivalent Diffusion "Force" · 108
66
3.5
..
90
Diffusion Processes 109
3.5.1 Time-Invariant Diffusion Processes 110
3.5.2 Time-Varying Diffusion Processes 111
3.6 Membrane Diffusion 119
3.6.1 Homogeneous Membranes 119
3.6.2 Porous Membranes 124
Contents in Detail
xii
Contents in Detail
xiii
3.7 Two-Compartment Diffusion
129
4.6.3
3.7.1
3.7.2
Derivation for a Thin Membraneh T1hi3? M mbrane
n- e
Conditions for the Validity of t e
l
133
Approximation: A Specific Examp e
3.8 Measurements of Diffusion Through Cellular Membranes 137
3.8.1 Overton's Rules 137
3.8.2 Methods 138
3.8.3 A Seminal Study 143
144
3.8.4 The Dissolve-Diffuse Mechanism 150
3.8 .5 The Water Channel Hypothesis
Appendix 3.1 Moments of the Binomial Distri~uti.on 151
Appendix 3.2 Moments of the Gaussian Distnbutwn 153
4.7 Primary Responses of Cells to Changes in Osmotic Pressure
4.7.1 Osmotic Equilibrium of Cells 223
4.7.2 Kinetics of Volume Changes of Cells in Response to
Osmotic Pressure Changes 229
4.7.3 The Complexity of Cellular Volume Control 236
4.8 .1
4.8.2
4.8.3
158
Solvent Transport 185
4.1 Introduction 185
4.2 Hydraulic Pressure 186
4.3 Osmotic Pressure 188
4.3.1 Historical Perspective 188
4.3.2 The Van't Hoff Law of Osmotic Pressure
References
5
237
2 72
Concurrent Solute and Solvent Transport
5.1 Introduction 281
5.2
192
4.4 Osmotic and Hydraulic Flow in Porous Media 197
4 ..
4 1 Differential Laws of Solvent Transport 197
4.4.2 Conservation of Mass 198
199
.4.
Steady-State
Solvent
Transport
4 3
4.5 Steady-State Solvent Transport Through Thin Membranes
281
Concurrent, Uncoupled Transport of Solute and Solvent 284
5.2.1 Derivation of Equations 284
5.2.2 Solutions for a Cell with Constant Surface Area 286
5.2.3 Measurements 292
5.3
199
.
Macroscopic Relations 199
Microscopic Mechanisms of Water Transport for Simple
Membrane Models 202
4.6 The Physical Basis of Osmotic Pressure and Osmosis 216
.
.
1 Some Proposed Mechanisms 216
4.6.
4.6.2 General Conclusions Concerning the Mechamsm of Osmotic
Pressure and of Osmosis 220
451
. .
4.5.2
Osmotic and Diffusive Permeability of Membranes
Molecular Biology of Water Channels 242
Summary of Water Transport Mechanisms in Cell
Membranes 247
Appendix 4.1 Thermodynamic Relations for an Ideal, Dilute
Solution 248
Appendix 4.2 Poiseuille's Law 251
Exercises 253
Problems 258
Problems 162
References 1 79
4
222
4.8 Molecular Mechanisms of Water Transport Through Cellular
Membranes 2 3 7
Appendix 3.3 Solution of the Homogeneous Diffusion
Equation 156
Exercises
An Intuitive Explanation of Osmotic Pressure and
Osmosis 220
Inadequacies of Uncoupled Flow Equations 293
5.3.1 Conceptual Problems 293
5.3.2 The Distinction Between Uncoupled and Coupled
Transport 295
5.3.3 Indistinguishable and Impermeant Solutes 296
5.4 Diffusion and Convection Through a Porous Membrane:
Indistinguishable Solute 297
5.4.1
5.4.2
Derivation of Flux Equations 297
The Linearized Equation of Coupled Flow for an
"Indistinguishable" Solute 299
Contents in Detail
Contents in Detail
xiv
5.5
Coupled Solute and Solvent Transport for a Cell
5.6.1 Theory 308
313
5.6.2 Measurements
315
5.7 Conclusions
Exercises 316
Problems 320
References 329
6
6.6
The Kedem-Katchalsky Equations for Linear, Coupled Flow Through
a Membrane 300
1 Macroscopic Laws of Transport 300
5.5.
Microscopic Mechanisms of Transport of Water and a
5.5.2 Permeant Solute in Simple Membrane Models
305
5.6
carrier-Mediated Transport
6.6.2
6.6.3
6.7.1
6.7.2
6.7.3
6.7.4
Exercises
Problems
References
7
7.2
6.5.3
409
Density of Glucose Transporters 409
Isolation of the Glucose Transporter 409
Structure of Glucose Transporters 410
Recruitment of Glucose Transporters by Insulin
415
421
414
440
449
The Importance of Ion Transport 449
The Maintained Difference of Potential and Concentration
Across Cellular Membranes 450
Continuum Electrodiffusion 454
Electrodiffusion Equations 454
Electrodiffusive Equilibrium Condition
Electroneutrality 461
Steady-State Conditions 466
7.3 The State of Intracellular Ions
470
7.2.1
7.2.2
7.2.3
7.2.4
7.4
7.5
.•
458
Macroscopic Model of Passive Ion Transport 474
7.4.1 Derivation from Microscopic Models
474
7.4.2 Properties of the Macroscopic Model 477
Resting Potential of Uniform Isolated Cells 483
7.5.1
7.5.2
6 . 5 Hexose Transport in Cells
6.5.2
406
7.1.1
7.1.2
carrier Models 360
6.4.1 Simple, Symmetric, Four-State Carrier Model with One
Solute 360
.
Simple,
Symmetric,
Six-State
Carrier
Model
With
Two
2
6.4.
Ligands 372
38 5
6 .4. 3 Introduction to Active Transport
386
6 ..
4 4 General, Four-State Carrier Model
394
6 .4.5 Other Carrier Models
6.5.1
The Discovery of the Role of Insulin: A Historical
Perspective 404
Glucose Absorption, Utilization, Storage, and Control
Summary 408
Ion Transport and Resting Potential
7.1 Introduction 449
341
396
.
Experimental Measurements and Methods for Estimatmg
the Kinetic Parameters 396
Applicability of Carrier Models to Measurements from
Cells 400
Conclusions 403
404
6. 7 Molecular Biology of Glucose Transporters
308
6.1
6.4
Regulation of Glucose
6.6.1
333
Introduction 334
334
6 .1. 1 Distinguishing Characteristics
.1.
The
Notion
of
a
Carrier
339
6 2
6.2 Chemical Reactions: A Macroscopic Description
342
6.2.1 Chemical Reactions of Low Order
6.2.2 Reaction Rates
350
6.3 Discrete Diffusion Through Membranes
358
XV
7.5.3
7.5.4
7.5.5
Modell: A Single Permeant Ion (the Bernstein Model)
Dependence of Resting Potential on Ion
Concentration 485
Model 2: Multiple Permeant Ions 488
Model 3: Independent Passive Voltage-Gated Ion
Channels 493
Molecular Basis of Passive Ion Transport Through
Channels 495
483
Contents in Detail
Contents in Detail
xvii
xvi
8.5
7.6.1
7.6.2
8.5.1
8.5.2
8.5.3
Instability of the Resting Potential
Instability of the Cell Volume 499
7.7 Active Ion Transport 499
7.7.1 Model 4: Model of Resting Potential, Including Both Active
and Passive Transport 500
7.7.2 Properties of Active Transport of Ions by the SodiumPotassium Pump 503
7.7.3 (Na+ - K+)-ATPase 524
7.8 Comparison of Active and Passive Transport 527
Appendix 7.1 The Goldman Constant Field Model 528
Derivation of the Voltage-Current Characteristic 529
Properties of the Voltage-Current Characteristic
530
The Unidirectional Flux Ratio 531
The Goldman Equation for the Resting Potential
532
Cellular Homeostasis
Transport Mechanisms 606
Intracellular Solute-Binding/Release Mechanisms
Transporter Regulatory Mechanisms 612
Index
Kinetic Equations 577
Quasi-Equilibrium Equations 578
Solutions of the Equations for Homeostasis
Solute Flux Equations
Nonelectrolyte Solutes
Ionic Solutes 588
Summary 605
580
582
579
579
669
613
Uniform Isolated Cells 613
Cells in an Epithelium 616
Electrically Excitable Cells 618
General Comments on the Mechanisms of Volume
Regulation 619
622
624
635
645
659
Contents of Volume 2
8.4 Homeostasis for Simple Cell Models
8.4.1
8.4.2
8.4.3
8.4.4
Exercises
Problems
List of Tables
8.1 Introduction 571
8.2 Volume Regulation 572
8.2.1 Background 572
8.2.2 Volume Regulatory Responses 575
8.2.3 Conclusions 576
8.3 General Equations for Homeostasis 576
8.3.1
8.3.2
8.3.3
8.6.1
8.6.2
8.6.3
8.6.4
List of Figures
571
606
8.6 Transport Mechanisms in Selected Cell Types
References
Exercises 533
Problems 541
References 562
8
Inventory of Homeostatic Mechanisms
663
612