The Biophysical Approach to Excitable Systems

On July 10, 1980, Kenneth S. Cole became 80 years old. In order to celebrate this landmark, a symposium in the form of a series of Monday evening lectures was held in his honor at the Marine Biological Labora­ tory throughout the summer of 1980. The selection of speakers was made from among those investigators who had been either his students or co-workers. One intent of the symposium was to examine the current status of knowledge of those areas of interest in excitable membrane structure and function that owe their initiation or encouragement to Kacy Cole. The papers assembled in this volume represent a large majority of the presentations given during the 1980 Cole Symposium. It seems clear on examination of these papers that Kacy's interests in membrane impedance, ion channel conductances, channel fluctuation phenomena, excitation, and the development of membrane biophysical methodology are all being actively pursued. It is also clear that many of his suggestions have borne fruit. Of these, his invention of the voltage v vi Preface clamp method has been most productive. It is hoped that these papers will provide new directions for investigations into the nature of excitable membrane phenomena. The organizers of the symposium and the editors of this volume wish to express their thanks to the Marine Biological Laboratory for making available the facilities for the symposium. They also wish to thank Dr.

I. Electrical Characteristics of Membranes.- 1. Electrical Properties of Cells: Principles, Some Recent Results, and Some Unresolved Problems.- Low-Frequency Relaxation Mechanisms.- The State of Tissue Water.- References.- 2. Nonlinear Sinusoidal Currents in the Hodgkin-Huxley Model.- Hodgkin-Huxley Equations.- References.- 3. Second-Order Admittance in Squid Axon.- Linear and Nonlinear Properties of Nerve Membrane.- Properties of Linear Systems.- Theoretical Admittance of Squid Axon Membrane.- Experimental Test of Linearity.- Data Analysis.- Preparation and Electronics.- Standard Measurement of Membrane Admittance.- Linearity and Nonlinearity in the Time Domain.- Linearity and Nonlinearity in the Frequency Domain.- Dependence of Frequency Components of Membrane Current on Stimulus Amplitude.- Dependence of First- and Second-Order Currents on Stimulus Frequency and Membrane Voltage.- Dependence of First- and Second-Order Currents on Na Current.- Experimental and Theoretical Nonlinearity Compared.- Discrepancies between Theory and Experiment.- The Frequency Components of the Higher-Order Currents.- Summary.- References.- 4. Squid Axon K Conduction: Admittance and Noise during Short- versus Long-Duration Step Clamps.- Inductive Reactance in the Impedance of Squid Axon: The Frequency Domain Manifestation of Linearized Ion-Conduction Kinetics.- Advances in the Speed and Resolution of Impedance or Admittance Measurements.- Potassium Conduction Kinetics from a Comparison of Admittance and Noise Data.- Steady-State Linear Analysis of Conduction via Admittance.- Preparation and Low-Noise Voltage Clamp Technique.- Fourier Synthesized Pseudorandom Signal (FSPS).- A Method of Coherence Elimination.- The Measurement System.- The Amplitude Range for a Linear Response.- Potassium Conduction in the Calculated Admittance of Squid Axon.- Comparison of Potassium Conduction Kinetics from Admittance and Noise Data.- The Admittance and Noise of Potassium Conduction during Short- versus Long-Duration Step Clamps.- References.- 5. Squid Axon Membrane Low-Frequency Dielectric Properties.- Small Signal Electrical Equivalent of Squid Giant Axon Membrane.- On the Measurement of Membrane Capacitance and Conductance.- Membrane Capacitance and Conductance.- Complex Capacitance and Membrane Structure.- References.- II. Membrane Channels.- 6. Single-Channel Conductances and Models of Transport.- Channels in Lipid Bilayers.- Observing the Channel Conductance Fluctuations in Cell Membranes.- Direct Observation of Single-Channel Currents.- What do the Measured ? Values Tell About Transport through Open Channels?.- References.- 7. Gating Kinetics of Stochastic Single K Channels.- Chord Conductance and the Probability that a Single Channel is Open.- Instantaneous Conductance and the Driving Force for Ion Flux.- Special Cases of the Function f(E).- Rate Constants for the Gating Kinetics of Stochastic Single K Channels.- The Steady-State Probabilities for an Open K Channel.- References.- III. Membrane Transport.- 8. Calculation of the Electrogenicity of the Sodium Pump System of the Squid Giant Axon.- Method of Calculation.- Procedural Details.- Results of the Calculations.- Conclusions.- References.- 9. Depolarization and Calcium Entry.- Calcium Entry with Stimulation.- Calcium Entry with Steady Depolarization.- Calcium Entry by Na-Ca Exchange.- References.- 10. A Quantitative Expression of the Electrogenic Pump and Its Possible Role in the Excitation of Chara Internodes.- Conductances and Electromotive Forces during the Process of Inhibition of the Electrogenic Pump with 2 ?M Triphenyltin Chloride (TPC).- Internal ATP Level during TPC Poisoning.- The pH Dependence of Conductances and Electromotive Forces.- A Model for the Mechanism of Electrogenic Pump.- The pH Dependence of Pump Current.- References.- IV. Stimuli and Drugs.- 11. Increases in Membrane Conductance Caused by Electrical, Chemical, and Mechanical Stimuli.- The Role of Membrane Conductance Changes.- Ionic Channels in Membranes.- Mechanically Stimulated Changes in Membrane Conductance.- References.- 12. Continuous Stimulation and Threshold of Axons: The Other Legacy of Kenneth Cole.- From Whence We Came—How Kacy Cole and Colleagues Mapped the Geometry of Excitability Space.- Where We Are—New Results on Accommodation and Repetitive Firing.- Whither We Go—What Might “Reverse Accommodation” Mean for Neural Coding?.- References.- 13. A Model of Drug-Channel Interaction in Squid Axon Membrane.- Modified Kinetic Model.- Yohimbine.- QX-314.- Discussion.- Summary.- References.