Concepts and Models

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.

1 ― Membrane Transport in Biology.- 2 ― Passive Transport Processes.- A. Introduction.- B. Fundamental Definitions.- I. Flux.- II. Types of Passive Transport.- 1. Diffusion.- 2. Migration.- 3. Convection.- III. Flux Equations.- 1. Migration Flux.- 2. Convection Flux.- 3. Diffusion Flux.- a) Fick’s Law.- b) The Driving Force behind the Diffusion Process.- 4. Diffusion and Migration Proceeding Concurrently.- 5. Convection with Superimposed Diffusion.- C. Diffusion Processes: Macroscopic Treatment.- I. The Diffusion Equation.- 1. Classification of Diffusion Processes.- II. Stationary Processes in One Dimension.- 1. Steady-State Diffusion in a Plate.- 2. The Permeability Coefficient.- 3. Stationary Diffusion through Two Different Media.- III. Time-Dependent Processes.- 1. Kinetics of Exchange between Two Phases Separated by a Membrane.- a) One of the Phases is Infinitely Large.- (i) Outer Concentration Zero.- (ii) Outer Concentration Finite, Inner Concentration Initially Zero.- b) Both Phases Comparable in Size.- c) Unidirectional Fluxes.- 2. Instantaneous Point Source (Green’s Function).- a) Solutions of Diffusion Problems by Means of Green’s Function.- (i) Initial Uniform Distribution in the One Half-Space.- (ii) The One Half-Space is Separated by an Impermeable Wall.- (iii) The Presence of an Absorbing Barrier.- (iv) Variable Flux into the Half-Space.- 3. Diffusion Out of a Plate.- a) Concentration Profiles.- b) The Time Constant for the Exchange of the Mean Concentration.- 4. Establishing the Stationary Concentration Profile.- D. Diffusion Processes: Microscopic Aspects.- I. Brownian Movements.- II. Smoluchowski’s Treatment.- 1. Statistical Interpretation of the Diffusion Equation.- 2. Random Walk in One Dimension.- 3. The Einstein-Smoluchowski Equation.- III. Random Walk and Fick’s Law (Einstein).- IV. The Smoluchowski Equation.- V. Kramers’Equation.- VI. Diffusion Coefficient and Mobility.- 1. Einstein’s Relation.- 2. Einstein-Stokes’ Relation.- E. Diffusion and Superimposed Convection.- I. The Equation of Motion.- II. Steady-State Concentration Profile.- 1. Stationary Transport through a Membrane.- a) Determination of the Flux.- b) Unidirectional Fluxes and Flux Ratio.- c) The Concentration Profile.- F. Electrodiffusion.- I. Conductance.- II. The Nernst-Planck Equations.- 1. Various Equivalent Forms.- 2. The Poisson Equation.- a) Electroneutrality.- b) The Constant Field.- III. Membrane Equilibrium.- 1. Nonosmotic Equilibrium.- a) The Nernst Equation.- b) Equivalent Electrical Circuit for the Ion-Selective Membrane.- 2. Donnan Equilibrium.- a) Thermodynamic Treatment.- b) Concentration and Potential Profiles between the Phases (The Poisson-Boltzmann Equation).- IV. Diffusion Potentials.- 1. Charging Time and Redistribution Time.- 2. The Henderson Regime.- 3. The Planck Regime.- a) Planck’s General Relations.- b) The Electrical Equivalent Circuit for the Planck Regime.- c) Planck’s Expression for the Diffusional Potential.- V. Electrodiffusion through Membranes.- 1. Single Salt.- a) Diffusion Potential.- b) Membrane Resistance.- c) Equivalent Electrical Circuit.- d) Electroneutrality.- 2. Ion-Selective Membrane.- 3. Membrane Separating Electrolytes Having a Common Ion.- a) Flux Ratio.- b) The Goldman Regime.- (i) The Separate Ionic Currents and the Diffusion Potential.- (ii) Total Membrane Current and Membrane Potential.- (iii) Concentration Profiles and Membrane Potential.- (iv) Ionic Conductances and Membrane Potential.- c) Equivalent Electrical Circuits.- Acknowledgements.- List of Symbols.- References.- 3 ― Interpretation of Tracer Fluxes.- A. Introduction.- B. Fundamental Concepts.- C. Tracer Permeability Coefficients.- I. Measurement of Tracer Permeability Coefficients.- II. Multicompartment Systems.- D. The Concept of Unidirectional Flux.- I. Unidirectional Fluxes.- II. Isotope Effects.- III. Associated Unidirectional Fluxes.- IV. The Relation of Tracer Fluxes to Active and Passive Transport.- V. Effects of Membrane Potentials on Ionic Fluxes.- VI. Exchange Diffusion.- VII. Limitations for Integration of Flux Equations.- E. Flux Ratio Analysis.- I. The Flux Ratio Equation.- II. Derivation of the Flux Ratio Equation.- III. Estimation of Electrochemical Potential Differences.- IV. The Short-Circuiting Method.- V. Flux Ratio with Solvent Drag.- VI. Solvent Drag on Non-Electrolytes and Water.- VII. Solute-Solute Interactions.- VIII. Meaning of the Term “Interaction”.- IX. Interpretation of Deviations from the Flux Ratio Equation.- F. Examples.- I. The Short-Circuited Frog Skin.- II. Single-File Diffusion.- III. Solvent Drag Effects.- G. Concluding Remarks.- References.- 4 ― Nonequilibrium Thermodynamics of Isotope Flow through Membranes.- A. Introduction.- B. The System: Definitions and Mathematical Techniques.- C. Nonthermodynamic Considerations of Isotope Flow.- D. The Nonequilibrium Thermodynamic Approach.- E. Applications to Model Systems.- F. Summary.- Acknowledgements.- List of Symbols.- References.- 5 ― Use of Microelectrodes for Measurement of Membrane Potentials.- A. Introduction.- B. Principles of Bioelectric Recording.- I. Electrode Chains and Junction Potentials.- II. Comments on Electronic Equipment.- C. The Glass Capillary Microelectrode.- I. The Suspension Effect.- II. Diffusion Regime of the Microelectrode Tip.- D. Potential Recording with Microelectrodes.- I. Penetration of the Cell Membrane.- II. Microelectrodes and Leaks in the Membrane.- E. Epilogue.- Acknowledgements.- References.- 6 ― Chemical Composition of Membranes.- A. Introduction.- B. Some General Observations on Erythrocyte Composition.- I. General Composition.- II. Ion Composition.- III. Age-Related Patterns.- 1. Intact Mixed-Age Erythrocytes.- 2. Age (density)-Separated Erythrocytes.- C. Comments on Major Components of the Erythrocyte Membrane.- I. Lipid: an Appraisal of Composition and Orientation or Localization.- 1. Some Structural Features of the Erythrocyte Lipids.- a) Neutral Lipid.- b) Phospholipids.- c) Sphingoglycolipids.- 2. Observations on Types of Phospholipids Present in Human, Cow, and Pig Erythrocyte.- a) Fatty Acid Composition.- b) Positioning of Fatty Acids.- c) Importance of Fatty Acid Composition.- 3. Localization of Lipids in Membranes: A Compositional Study of a Different Type.- a) Some General Observations.- b) Use of Enzymes as Probes for Location of Lipids in Membranes.- 4. Summary of Observations on Phospholipase Action on Erythrocytes.- a) Phospholipase A2.- b) Phospholipase C.- c) Sphingomyelinase.- d) Combined Activity of Phospholipase C and Sphingomyelinase.- 5. Development of the Concept of Asymmetric Location of Phospholipids in Membranes.- 6. On the Validity of the Lipid Asymmetry Proposal.- 7. Summary Statement.- II. Protein Composition.- 1. General Comments.- 2. Nature of Polypeptide Patterns on SDS-PAGE.- a) Specific Protein Components Revealed by SDS Gel Electrophoresis.- b) Studies on “Spectrin” of the Human Erythrocyte Membrane.- c) Observations on the Ox (Bovine) Erythrocyte Polypeptide Heterogeneity.- 3. Summary Statement.- References.- 7 ― Genetic Determination of Membrane Transport.- A. Introduction.- B. Microorganisms.- I. Isolation of Transport Mutants.- II. Kinds of Genetic Analysis.- III. Examples of the Use of Genetic Analysis.- C. Higher Organisms.- I. Cystinuria.- II. HK/LK Erythrocytes.- D. Cultured Somatic Cells.- I. Methods for Selecting Transport Mutants.- II. The Kinds of Genetic Information that can be Obtained.- III. Ouabain-Resistant Mutants.- E. Conclusions.- References.- 8 ― Mechanisms of Ion Transport and ATP Formation.- A. Translocation of Protons by the Oxidation Chain of Mitochondria and Chloroplasts.- I. The Chemiosmotic Mechanism of Mitchell.- II. Asymmetry of Oxidation Chain of Mitochondria and Chloroplasts.- III. The Coenzyme Q Cycle.- B. The Translocation of Protons by Bacteriorhodopsin.- I. Proton Movements and ATP Formation.- II. Mechanism of Proton Translacotion.- C. The Translocation of Protons by the Oligomycin- or Dicyclohexylcarbodiimide-Sensitive ATPase of Mitochondria, Chloroplasts and Bacteria.- I. Proton Movements and ATP Formation.- II. Properties of the Isolated Oligomycin-Sensitive ATPase Complex.- 1. The Water-Soluble ATPase.- 2. The Oligomycin-Sensitivity Conferral Protein (OSCP).- 3. The Heat-Stable Coupling Factor F6(Fc2).- 4. Coupling Factor 2 (F2).- III. Model of the Proton Pump and its Mode of Action.- 1. The Mitchell Hypothesis.- 2. The Phosphoenzyme Intermediate Hypothesis.- 3. The Boyer-Slater Hypothesis.- D. Translocation of Calcium by the ATPase Complex of Sarcoplasmic Reticulum.- I. Properties of the Pump.- II. Properties of the Ca++-ATPase Complex.- 1. Latency of the Ca++-ATPase.- 2. Structural Properties of the Ca++-ATPase Complex.- 3. Catalytic Properties of the Ca++-ATPase Complex.- II. The Reconstituted Pump and its Mechanism of Action.- E. Translocation of Sodium and Potassium Ions by the ATPase Complex of the Plasma Membrane.- I. Properties of the Pump.- II. Properties of the Na+-K+-ATPase Complex.- 1. Latency of the ATPase.- 2. Structural Properties of the Enzyme Complex.- 3. Catalytic Properties of the Enzyme Complex.- III. The Reconstituted Pump.- F. Concluding Remarks.- Acknowledgement.- Abbreviations.- Addendum.- References.- 9 ― Membrane Immunological Reactions and Transport.- A. Introduction: The Concept.- B. Immunological Reactions and Membrane Transport Proteins.- I. Introduction.- II. Antibodies Against the Na+-K+-ATPase.- 1. Properties of Antigens and Antibodies.- 2. Sidedness of Binding and Immunological Effects on the Na+-K+-ATPase and its Partial Reactions.- a) Sidedness of Binding.- b) Immunological Effects on the Na+-K+-ATPase Activity.- c) Effects of Partial Reactions of the Na+-K+-ATPase.- 3. Immunological Alteration of Cation Fluxes in Resealed Ghosts.- 4. Species and Organ Specificities of Immunological Reactions Involving the Na+-K+-ATPase.- III. Antibodies Against Ca++-ATPase of Sarcoplasmic Reticulum.- IV. Conclusion.- C. Immunological Reactions at the Outer Membrane Surface and Cation Transport in Erythrocytes.- I. Introduction.- II. Sheep Red Cells.- 1. Cation Transport, Genetics and Immunological Parameters.- a) Cellular Cations and Genetics.- b) Membrane Antigens and Genetics.- c) Active and Passive Cation Transport.- d) Ouabain Binding.- e) Na+-K+-ATPase.- 2. The Effect of Antibodies on Cation Transport.- a) Modification of Cation Pump and Leak Fluxes.- b) Activation of the Na+-K+-ATPase.- c) Correlation between Antigenic Sites and Na+-K+ Pumps.- 3. Properties of the ML Surface Antigens and Antibodies.- a) Antigens.- b) Antibodies.- 4. Developmental Aspects of Transport and Antigens.- a) Red Cells of Newborn Sheep.- b) Stress-Induced Erythrocyte Regeneration.- III. Cation Transport Polymorphism and Antigenic Parameters in Red Cells of Ruminants Other than Sheep.- 1. Goat Red Cells.- a) Cations and Antigens.- b) Cation Transport and its Modification by Antibody.- 2. Cattle Red Cells.- IV. Human Red Cells.- 1. The Rhesus Antigen Complex and Cation Transport.- 2. The En(a)-Negative Red Cell as Physiological Model.- V. Conclusion.- D. Membrane Immunological Reactions and Cation Transport in Lymphocytes and Other Cells.- I. Lymphocytes.- 1. Introduction..- 2. Cellular Differentiation and Membrane Surface Receptors of Lymphocytes.- 3. Cellular and Membrane Morphological and Biochemical Changes Induced by Immunological Reactions in Lymphocytes.- 4. Modification of Monovalent Cation Transport.- a) General Aspect of the Effect of Immunological Reactions.- b) Cation Transport in the Absence of Immunological Reactions.- c) Cation Transport Changes Induced by Immunological Reactions.- 5. Requirement of Bivalent Cations for Lymphocyte Stimulation by Immunological Reactions.- II. Tumor Cells.- 1. Introduction.- 2. Passive Permeability Changes Induced by Lectins.- III. Conclusion.- E. Summary and Prospectus.- Acknowledgement.- References.- 10 ― Membrane Receptors, Cyclic Nucleotides, and Transport.- A. Introduction.- B. Beta-Adrenergic-Receptor Binding in Avian and Amphibian Erythrocytes.- C. Beta-Adrenergic-Mediated Transport Processes in Avian and Amphibian Erythrocytes.- D. The Amphibian Bladder.- E. Cholera Enterotoxin.- F. The Superior Cervical Ganglion.- G. Nicotinic Cholinergic Receptors.- H. The Heart.- J. General Comments and Conclusions.- References.- 11 ― Permeability Properties of Unmodified Lipid Bilayer Membranes.- A. Introduction.- B. Lipid Bilayer Membranes.- I. Capacitance.- II. Composition.- C. Transport Model and the Potential Energy Barrier.- I. The Transport Model.- II. Unstirred Layers.- 1. Stationary Fluxes.- 2. Transient Fluxes.- 3. The Membrane-Solution Interface.- 4. Chemical Reaction in Unstirred Layers.- III. Potential Energy of Ions Within Lipid Bilayers.- 1. The Born Energy.- 2. The “Image” Force.- 3. Diffusion or Distortion?.- IV. Potential Energy of Dipolar Molecules Within Lipid Bilayers.- V. Interfacial Potentials.- 1. Diffuse Double-Layer Potentials.- 2. Dipole Potentials.- VI. Hydrophobic Interactions.- VII. The Potential Energy Barrier.- D. Permeability to Neutral Solutes.- I. Partition Coefficients.- 1. Nonpolar Solutes.- 2. Polar Solutes.- II. Mobility.- 1. Indirect Measurements.- a) Microviscosity.- b) Walden’s Rule.- 2. Direct Estimates.- 3. Variation through the Membrane.- III. Permeability.- 1. H2O.- 2. Organic Solutes.- IV. The Rate-Limiting Barrier for Solute Movement.- E. Ion Permeability.- I. Tracer Flux Measurements.- II. Anion Permeability.- 1. Stationary Conductance Changes.- 2. Translocation through the Membrane Interior.- a) The Transport Model.- b) Kinetics of Charge Translocation.- c) Temperature-Dependence.- d) Ion Translocation as a Function of Membrane Composition.- III. Positive Ions.- IV. Interactions Among Ions Absorbed into Lipid Membranes.- 1. Space Charge-Limited Conductance.- 2. Blocking Phenomena.- 3. The Three-Capacitor Model.- a) Charge Adsorption.- b) Charge Translocation.- 4. Discrete Charge Effects?.- Acknowledgements.- References.- 12 ― Carrier-Mediated Ion Transport Across Thin Lipid Membranes.- A. Introduction.- I. Carriers and Pores.- II. A Survey of Suggested Ion Carriers.- B. Carriers of Hydrogen Ions.- C. Macrocyclic Carriers.- I. Neutral Carriers.- II. Charged Carriers.- D. The Iodide-Iodine System.- E. The Carrier-Transport Model.- I. Kinetic Analysis of the Carrier Model.- II. Valinomycin and Trinactin.- F. Biological Implications.- References.- 13 ― Channels in Black Lipid Films.- A. Introduction.- B. Basic Experiments.- I. Demonstration of Conductance by Pore.- II. Basic Conductance Characteristics.- 1. Steady-State Current-Voltage Curves.- 2. Conductance and Antibiotic Concentration.- 3. Kinetics of Conductance Development: Response to a Voltage Pulse.- C. Advanced Experiments.- I. Introduction.- II. Single-Step Experiments.- 1. The Probability Distribution.- 2. EIM and Hemocyanin: The Unit Event Explains High-Level Conductance.- 3. Noise Measurements and the Unit Conductance.- 4. Noise Measurements on Alamethicin.- 5. Noise Measurements on Monazomycin.- 6. Compounds with Unknown Unit Events: Summary.- III. Conductance and Ion Selectivity of Unit Channels.- 1. Introduction.- 2. Conductance and Selectivity of the Gramicidin Unit Event.- 3. Conductance and Selectivity of the Unit Events of EIM and Hemocyanin.- 4. Conductance and Selectivity of the Alamethicin Unit Event Levels.- IV. Time Course of the Unit Event.- V. Alteration of the Molecule and the Membrane.- 1. Effects of Membrane Composition.- 2. Alteration of the Pore Forming Molecule.- D. Possible Molecular Mechanisms of Pore Formation.- Acknowledgements.- References.