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)∝exp(−γx), γ>0 and a linear ramp potential U_c(x), is in good agreement with experimental data and it may be shown analytically that if γ is sufficiently large, f_c(t)∝t^−2−ν for intermediate times, where ν=U_c^′∕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.