Affiliations: [a] Karolinska Institutet, Division of Medical Radiation
Physics, Box 260, SE-171 76 Stockholm, Sweden | [b] University of Tokyo, Nuclear Professional School,
Graduate School of Engineering 2-22 Shirane Shirakata Tokai-mura Naka-gun,
Ibaraki 319-1188, Japan
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.
Keywords: Electrodiffusion, ion channel, membrane potential, polarization relaxation, dissipative admittance
