Impedance and potential measurements have been made on a number of artificial membranes. Impedance changes were determined as functions of current and of the composition of the environmental solutions. It was shown that rectification is present in asymmetrical systems and that it increases with the membrane potential. The behavior in pairs of solutions of the same salt at different concentrations has formed the basis for the studies although a few experiments with different salts at the same concentrations gave results consistent with the conclusions drawn. A theoretical picture has been presented based on the use of the general kinetic equations for ion motion under the influence of diffusion and electrical forces and on a consideration of possible membrane structures. The equations have been solved for two very simple cases; one based on the assumption of microscopic electroneutrality, and the other on the assumption of a constant electric field. The latter was found to give better results than the former in interpreting the data on potentials and rectification, showing agreement, however, of the right order of magnitude only. Although the indications are that a careful treatment of boundary conditions may result in better agreement with experiment, no attempt has been made to carry this through since the data now available are not sufficiently complete or reproducible. Applications of the second theoretical case to the squid giant axon have been made showing qualitative agreement with the rectification properties and very good agreement with the membrane potential data.

ABSTP.ACT Calcium appears to be an essential participant in axon excitation processes. Many other polyvalent metal ions have calcium-like actions on axons. We have used the voltage-clamped lobster giant axon to test the effect of several of these cations on the position of the peak inidal (sodium) and steadystate (potassium) conductance vs. voltage curves on the voltage axis as well as on the rate parameters for excitation processes. Among the alkaline earth metals, Mg +9 is a very poor substitute for Ca +s, while Ba +a behaves like "high calcium" when substituted for Ca +~ on a mole-for-mole basis. The transition metal ions, Ni +~, Co +s, and Cd +~ also act like high calcium when substituted mole-for-mole. Among the trivalent ions, La +8 is a very effective Ca +~ replacement. AI +a and Fe +8 are extremely active and seem to have some similar effects. A1 +8 is effective at concentrations as low as 10 -5 u. The data suggest that many of these ions may interact with the same cation-binding sites on the axon m e mbrane, and that the relative effects on the membrane conductance and rate parameters depend on the relative binding constants of the ions. The total amount of Na + transferred during a large depolarizing transient is nearly independent of the kind or amount of polyvalent ion applied. I N T R O D U C T I O NEvidence has long been available that calcium ions are intimately associated with the m e c h a n i s m of axon conduction (see Brink, 1954). Studies such as those of H 6 b e r (1920), and of G u t t m a n (1940) showed that the resting potential a n d excitability of axons can be effectively m a i n t a i n e d w h e n certain other divalent cations, particularly those of the alkaline earth series, are substituted for calcium. T h e effects of alkali metal ions on nerve excitability have been reviewed by Narahashi (1966). F r a n k e n h a e u s e r and H o d g k i n (I 957) studied the effects of calcium on the m e m b r a n e ionic conductances of voltagec l a m p e d squid axons. R e c e n t studies by D o d g e (1961) and by T a k a t a et al. (1966 b) demonstrate that nickel a n d l a n t h a n u m have certain effects on the electrical properties of voltage-clamped axons which are qualitatively similar 279

A structural model is suggested for axon membranes consisting of a double layer of lipid and phospholipid molecules in which the polar ends of certain phospholipids change their orientation and combining properties under the influence of an electric field. The phosphate groups act as ion exchange "gates" for the control of ion flow through the membrane. Expressions are developed for the calculation of membrane current components as functions of time, potential, and ionic environment. Approximate solutions show fairly good agreement with existing experimental data in a number of different respects such as steady-state current-voltage relations, the effect of calcium on steady-state current, potassium tracer flux ratios, initial current and rate of change of current, and the dependence of the time constants of current change on membrane potential.

The sucrose-gap method introduced by St/impfli provides a means for the application of a voltage clamp to the lobster giant axon, which responds to a variety of different experimental procedures in ways quite similar to those reported for the squid axon and frog node. This is particularly true for the behavior of the peak initial current. However, the steady state current shows some differences. It has a variable slope conductance less than that of the peak initial current. The magnitude of the steady state slope conductance is related to the length of the repolarization phase of the action potential, which does not have an undershoot in the lobster. The steady state outward current is maintained for as long as 100 msec.; this is in contrast to a decline of about 50 per cent in the squid axon. Lowering the external calcium concentration produces shifts in the current-voltage relations qualitatively similar to those obtained from the squid axon. On the basis of the data available, there is no reason to doubt that the Hodgkin and Huxley analysis for the squid giant axon in sea water can be applied to the lobster giant axon. I N T R O D U C T I O NCole (1949) first showed that when the potential difference across the membrane was under control and varied in a stepwise fashion, the membrane current density of a squid giant axon varied continuously. Later, Hodgkin, Huxley, and Katz (1952) refined the technique and coined the name "voltage clamp; " and Hodgkin and Huxley (1952 a, b, ¢, d) interpreted a series of experiments now regarded as major contributions to the understanding of electrically excitable cells. Further, the use of the voltage clamp technique on the frog node by Dodge and Frankenhaeuser (1958) has given results similar to those obtained from the squid.