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

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 $D(x) \propto \exp(-\gamma x)$,$\gamma > 0$andalinearramppotential$U_c(x)$, 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 $\nu =U_c^{\mathrm{\prime }}\mathrm{/}\gamma \approx -0.3$ 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.