Position-dependent stochastic diffusion model of ion channel gating

A position-dependent stochastic diffusion model of gating in ion channels is developed by considering the spatial variation of the diffusion coefficient between the closed and open states. It is assumed that a sensor which regulates the opening of the ion channel experiences Brownian motion in a closed region R_c and a transition region R_m, where the dynamics is described by probability densities p_c(x,t) and p_m(x,t) which satisfy interacting Fokker-Planck equations with diffusion coefficient D_c(x)=D_c exp(γ_cx) and D_m(x)=D_m exp(−γ_mx). The analytical solution of the coupled equations may be approximated by the lowest frequency relaxation, a short time after the application of a depolarizing voltage clamp, when D_m⪡D_c or the diffusion parameter γ_m is sufficiently large. Thus, an empirical rate equation that describes gating transitions may be derived from a stochastic diffusion model if there is a large diffusion (or potential) barrier between open and closed states.