Kinetic properties of electrostatic pores with orientable dipoles, for Na+ and K+ transport through biological membranes.

The model, used previously to account for the transport of K+ ions through squid axon membranes under steady-state conditions, is extended to the description of the kinetic behavior of Na+ and K+ currents, for sudden variations of the applied potential. Theoretical curves are obtained by numerical integration of the electrodiffusion equation for ions within pores, with variable boundary conditions resulting from a progressive reorientation of dipoles at the pore surface. The pores are supposed to be selective and the dipole parameters are allowed to be different for Na+ and K+ pores. The K+ current varies with time, in agreement with the K+ dipole parameters deduced from the steady-state results of Gilbert and Ehrenstein (1969). The dipole parameters for Na+ current are deduced from the steady-state results of Armstrong, Bezanilla & Rojas (1973), where the inactivation phase of the Na+ current is suppressed by introducing pronase in the inside solution. The dipole reorientation is relavent to explain the sigmoid shape of the activation phase of the Na+ current, while the inactivation phase seems to resort to another physical mechanism. The predictions based on this model agree with the experimental results for the steady-state negative resistance and the gating current, associated both with a reorientation of surface dipoles, as well as the activation phase of the Na+ current using a consistent set of parameters for all these comparisons.

The role of proteins in a dipole model for steady-state ionic transport through biological membranes.

The steady-state current-voltage characteristics of biological membranes are analyzed for means of an application of the electrodiffusion theory to the passage of ions through "dielectric pores", with orientable dipoles at the pore-water interfaces. A detailed evaluation of the electrostatic potential barrier shows, indeed, that the ions have practically no chance to penetrate into the phospholipid bilayer, but that they can cross the membrane through local protein inclusions, of high dielectric constant. A "gating mechanism" can be provided, moreover, by a change of the potential barrier, resulting from a dipole reorientation at the pore-water interface. Dipole-dipole interactions are opposed to the orienting effect of an applied field, but they can be neglected when the separation between the dipoles exceeds a certain critical value. The high polarizability of the pore material leads to an amplification of the effect of an applied field on the orientable dipoles. It is therefore possible to achieve a satisfactory agreement with the experimental results of Gilbert and Ehrenstein (Biophys. J., 9: 447, 1969) for the squid axon, and, in particular, to account for the width of the negative resistance regions with a relatively small value for the length of the orientable dipoles.