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 fc(t) derived from the Fokker-Planck equation with a nonlinear diffusion coefficient D(x)∝exp(−γx), γ>0 and a linear ramp potential Uc(x), is in good agreement with experimental data and it may be shown analytically that if γ is sufficiently large, fc(t)∝t−2−ν for intermediate times, where ν=Uc′∕γ≈−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.