Nonlinear drift-diffusion model of gating in the fast Cl channel

Abstract

The dynamics of the open or closed state region of an ion channel may be described by a probability density $p(x,t)$ which satisfies a Fokker-Planck equation. The closed state dwell-time distribution $f_c(t)$ derived from the Fokker-Planck equation with a nonlinear diffusion coefficient $D(x) \propto \exp(-\gamma x)$, $\gamma > 0$ and a linear ramp potential $U_c(x)$, is in good agreement with experimental data and it may be shown analytically that if $\gamma$ is sufficiently large, $f_c(t) \propto t^{-2 - \nu}$ for intermediate times, where $\nu = U_c^{\prime}/\gamma \approx -0.3$ for a fast Cl channel. The solution of a master equation which approximates the Fokker-Planck equation exhibits an oscillation superimposed on the power law trend and can account for an empirical rate-amplitude correlation that applies to several ion channels.