Thomas Fischer Weiss Cellular Biophysics Volume 1: Transport A Bradford Book The MIT Press Cambridge, Massachusetts London, England
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 printed and bound in the United States of America. 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 To Aurice B, Max, Elisa, and Eric
Contents Preface xix ix Units, Physical Constants, and Symbols xxvii 1 Introduction to Membranes 1 2 Introduction to Transport 49 3 Diffusion 83 4 Solvent Transport 185 5 Concurrent Solute and Solvent Transport 281 6 Carrier-Mediated Transport 333 7 Ion Transport and Resting Potential 449 8 Cellular Homeostasis 571 List of Figures 645 List of Tables 659 Contents of Volume 2 663 Index 669
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 Acknowledgments References xxvi xxiv xxiii Units, Physical Constants, and Symbols Units xxvii xxi xxvii xix 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 xx xxviii
xi X 1 2 Introduction to Membranes 1 1.1 Historical Perspective 1 1.1.1 Fundamental Concepts of Living Organisms 1 1.1.2 Emerging Concepts of Cell Membranes 3 1.2 Survey of Cell Structure 6 1.3 Molecules 9 1.3.1 Atoms, Elements, and Bonds 10 1.3.2 Organic Molecules 16 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 Exercises 44 References 46 Introduction to Transport 49 2.1 Introduction 49 2.2 Cell Requirements 50 2.3 Transport in the Body Illustrated Using a Potato 51 2.3.1 Composition of a Potato 51 2.3.2 Digestion of a Potato 52 2.3.3 Structure of the Small Intestine 54 2.3.4 Structure of Enterocytes 57 2.3.5 Final Stage of Digestion 60 2.3.6 Sugar Transport into and out of Enterocytes 63 2.3.7 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 68 2.4.2 Water Homeostasis 69 2.4.3 Secretion and Absorption 69 2.5 Survey of Transport Mechanisms 70 66.. 3 2.6 Methods for Studying Membrane Transport 73 2.6.1 Physicochemical Methods 73 2.6.2 Preparations 76 2. 7 Summary 79 Exercises 80 References 81 Diffusion 83 3.1 Macroscopic Description 83 3.1.1 Background 83 3.1.2 Diffusion Variables 84 3.1.3 Fick's First Law 86 3.1.4 The Continuity Equation 87 3.1.5 Fick's Second Law: The Diffusion Equation 89 3.1.6 Diffusion with Convection and Chemical Reactions 90 3.1.7 Postscript on Diffusion: The Second Law of Thermodynamics 91 3.2 Microscopic Model 92 3.2.1 Introduction 92 3.2.2 The Microscopic Basis for Fick's First Law 93 3.2.3 The Microscopic Space-Time Evolution of Particle Location: The Binomial Distribution 95 3.2.4 The Macroscopic Space-Time Evolution of Particle Location: The Gaussian Distribution 98 3.2.5 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 3.5 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
xii xiii 4 3.7 Two-Compartment Diffusion 129 3.7.1 Derivation for a Thin Membraneh T1hi3? M mbrane Conditions for the Validity of t e n- e 3.7.2 l 133 Approximation: A Specific Examp e 3.8 Measurements of Diffusion Through Cellular Membranes 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 Appendix 3.2 Moments of the Gaussian Distnbutwn 151 153 Appendix 3.3 Solution of the Homogeneous Diffusion Equation 156 Exercises 158 Problems 162 References 1 79 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 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 4.4.3 Steady-State Solvent Transport 137 4.5 Steady-State Solvent Transport Through Thin Membranes 199 4 5 1 Macroscopic Relations 199. 4.5.2.. 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.. 4.6.2 General Conclusions Concerning the Mechamsm of Osmotic Pressure and of Osmosis 220 5 4.6.3 An Intuitive Explanation of Osmotic Pressure and Osmosis 220 4.7 Primary Responses of Cells to Changes in Osmotic Pressure 222 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 Molecular Mechanisms of Water Transport Through Cellular Membranes 2 3 7 4.8.1 Osmotic and Diffusive Permeability of Membranes 237 4.8.2 Molecular Biology of Water Channels 242 4.8.3 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 References 2 72 Concurrent Solute and Solvent Transport 281 5.1 Introduction 281 5.2 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 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 Derivation of Flux Equations 297 5.4.2 The Linearized Equation of Coupled Flow for an "Indistinguishable" Solute 299
xiv XV 6 5.5 5.6 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 Coupled Solute and Solvent Transport for a Cell 308 5.6.1 Theory 308 5.6.2 Measurements 313 5.7 Conclusions 315 Exercises 316 Problems 320 References 329 carrier-mediated Transport 333 6.1 Introduction 334 6.2 6.1.1 Distinguishing Characteristics 334 6.1.2 The Notion of a Carrier 339 Chemical Reactions: A Macroscopic Description 341 6.2.1 Chemical Reactions of Low Order 342 6.2.2 Reaction Rates 350 6.3 Discrete Diffusion Through Membranes 358 6.4 carrier Models 360 6.4.1 Simple, Symmetric, Four-State Carrier Model with One Solute 360. 6.4. 2 Simple, Symmetric, Six-State Carrier Model With Two Ligands 372 6.4.3 Introduction to Active Transport 385 6.. 4 4 General, Four-State Carrier Model 386 6.4.5 Other Carrier Models 394 6.5 Hexose Transport in Cells 396. 6.5.1 Experimental Measurements and Methods for Estimatmg the Kinetic Parameters 396 6.5.2 Applicability of Carrier Models to Measurements from Cells 400 6.5.3 Conclusions 403. 7 6.6 Regulation of Glucose 404 6.6.1 The Discovery of the Role of Insulin: A Historical Perspective 404 6.6.2 Glucose Absorption, Utilization, Storage, and Control 406 6.6.3 Summary 408 6. 7 Molecular Biology of Glucose Transporters 409 6.7.1 Density of Glucose Transporters 409 6.7.2 Isolation of the Glucose Transporter 409 6.7.3 Structure of Glucose Transporters 410 6.7.4 Exercises Problems Recruitment of Glucose Transporters by Insulin 415 421 414 References 440 Ion Transport and Resting Potential 449 7.1 Introduction 449 7.1.1 The Importance of Ion Transport 449 7.1.2 The Maintained Difference of Potential and Concentration Across Cellular Membranes 450 7.2 Continuum Electrodiffusion 454 7.2.1 Electrodiffusion Equations 454 7.2.2 Electrodiffusive Equilibrium Condition 458 7.2.3 Electroneutrality 461 7.2.4 Steady-State Conditions 466 7.3 The State of Intracellular Ions 470 7.4 Macroscopic Model of Passive Ion Transport 474 7.4.1 Derivation from Microscopic Models 474 7.4.2 Properties of the Macroscopic Model 477 7.5 Resting Potential of Uniform Isolated Cells 483 7.5.1 Modell: A Single Permeant Ion (the Bernstein Model) 483 7.5.2 Dependence of Resting Potential on Ion Concentration 485 7.5.3 Model 2: Multiple Permeant Ions 488 7.5.4 Model 3: Independent Passive Voltage-Gated Ion Channels 493 7.5.5 Molecular Basis of Passive Ion Transport Through Channels 495
xvii xvi 7.6.1 Instability of the Resting Potential 7.6.2 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 Sodium- Potassium 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 Exercises 533 Problems 541 References 562 8 Cellular Homeostasis 571 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 Kinetic Equations 577 8.3.2 Quasi-Equilibrium Equations 578 8.3.3 Solutions of the Equations for Homeostasis 579 8.4 Homeostasis for Simple Cell Models 579 8.4.1 Solute Flux Equations 580 8.4.2 Nonelectrolyte Solutes 582 8.4.3 Ionic Solutes 588 8.4.4 Summary 605 8.5 Inventory of Homeostatic Mechanisms 606 8.5.1 Transport Mechanisms 606 8.5.2 Intracellular Solute-Binding/Release Mechanisms 612 8.5.3 Transporter Regulatory Mechanisms 612 8.6 Transport Mechanisms in Selected Cell Types 613 8.6.1 Uniform Isolated Cells 613 8.6.2 Cells in an Epithelium 616 8.6.3 Electrically Excitable Cells 618 8.6.4 General Comments on the Mechanisms of Volume Regulation 619 Exercises 622 Problems 624 References 635 List of Figures 645 List of Tables 659 Contents of Volume 2 663 Index 669