Position-dependent stochastic diffusion model of ion channel gating

Abstract

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 Rc and a transition region Rm, where the dynamics is described by probability densities pc(x,t) and pm(x,t) which satisfy interacting Fokker-Planck equations with diffusion coefficient Dc(x)=Dc exp(γcx) and Dm(x)=Dm exp(−γmx). 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 Dm⪡Dc or the diffusion parameter γm 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.