Evidence is presented that the transport of lipid-soluble ions through bilayer membranes occurs in three distinct steps: (1) adsorption to the membranesolution interface; (2) passage over an activation barrier to the opposite interface; and (3) desorption into the aqueous solution. Support for this mechanism comes from a consideration of the potential energy of the ion, which has a minimum in the interface. The formal analysis of the model shows that the rate constants of the individual transport steps can be determined from the relaxation of the electric current after a sudden change in the voltage. Such relaxation experiments have been carried out with dipicrylamine and tetraphenylborate as permeable ions. In both cases the rate-determining step is the jump from the adsorption site into the aqueous phase. Furthermore, it has been found that with increasing ion concentration the membrane conductance goes through a maximum. In accordance with the model recently developed by L. J. Bruner, this behavior is explained by a saturation of the interface, which leads to a blocking of the conductance at high concentrations.

2. External application of l5OnM tetrodotoxin (TTX) and/or l0mMtetra-ethylammonium (TEA) ion reduced the current fluctuations. The difference ofcurrent noise spectra measured inthepresence and absence of TTX (TEA) was not changed by the presence of TEA (TTX) during both measurements, and was taken as the spectrum of the Na (K) current fluctuations.3. Residual current noise during application of both TTX and TEA was, except for some excess noise at the low and high frequency ends of the spectrum, similar to the noise measured from a passive nerve model and could be understood in terms of Nyquist noise of the known resistances and the amplifier noise.4. Na current fluctuation spectra were interpreted as the sum N/f+ SNa(f)whereSNa(f) represents the spectrum expected foraset of equal, independent Na channels with only two conductance states (open or closed) which follow Hodgkin-Huxley kinetics. With values of head Th and m. measured from macroscopic Na currents, the measured spectra were fitted well by optimizing N, SNa(O) and Tm. Values of Tm obtained by this method were in fair agreement with values found from macroscopic currents.

1. Sodium currents (INa) and asymmetrical displacement currents (ID) were measured in the same nerve fibres from Rana esculenta under similar conditions. 2. For exploring possible kinetic and steady state relations between INa and ID the following quantities were compared: (i) the activation of the sodium channels and (ii) the charge displacement of ID. 3. The delay of sodium activation increased after hyperpolarization. A corresponding effect on the displacement of charge was not observed. 4. Upon a small depolarization sodium activation rose slower than the displacement of charge, whereas at large depolarizations sodium activation reached a steady level before the charge displacement. 5. Upon repolarization to various levels between -52 and 12 mV relative to the resting potential, the ratio between the time constants of charge displacement and of sodium tail current varied between 3 and 1. 6. In the steady state the sodium activation was one half at about the same potential as the charge displacement but exhibited a clearly steeper voltage dependence. 7. Blocage of sodium channels with tetrodotoxin did not affect the asymmetrical displacement current. Replacing a part of external Na by tris did not alter the sodijm activation process. 8. The results indicate that the asymmetrical displacement of charge may reflect states of the gating mechanism in sodium channels but cannot be considered as a correlate of the Hodgkin Huxley m variable.

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In this paper the ion transport across a thin lipid membrane is treated using a generalized form of the Nernst-Planck equations. An additional term is introduced into the flux equations to account for the image force acting on the ion. As the membrane thickness is of the same order of magnitude as the range of the image forces, the potential energy of the ion in the membrane is strongly dependent on position. The integration of the flux equations leads to a general expression for the integral membrane conductance lambda as a function of the voltage u. The ratio lambda(u)/lambda(0) (lambda(0) = membrane conductance in the limit u --> 0) depends on the dielectric constant and the thickness of the membrane, but is independent of the ionic radius. When the numerical values of the potential energy function, as calculated by the method of electrical images, are inserted into the expression for lambda(u)/lambda(0), a strongly non-linear current-voltage characteristic is obtained. The theoretical current-voltage curve agrees satisfactorily with the experimental data at a low ionic strength and at low voltages; at higher voltages the observed membrane conductance exceeds the predicted value.