Abstract
An analysis is given in the article for the study of ion channel behavior in time-varying fields based on the generalized Poisson-Nernst-Planck theory, in which possible effects of the polarization relaxation and the effects of coupling among ion species, their diffusive fluxes and polarization in the mixture of ions can be evaluated. Analytical expressions for ion currents and voltages of the ion channel across a membrane are derived for the one-dimensional configuration both in time-independent steady state and in time-varying fields. While the results recover the classical Goldman-Hodgkin-Katz current and voltage equations in the time-independent steady state, it is shown that in time-varying fields, both the ionic current and the displacement current contribute to the total current in the ion channel, which depends not only on the equilibrium susceptibility of the mixture of the ions, but also on the dissipative polarization relaxation as well as the effect of coupling between the polarization and diffusive fluxes of the ions in the mixture. At the linear approximation, dissipative admittances that may characterize effectively the frequency responses of the ion channel in time-harmonic fields are also derived analytically for the one-dimensional case.