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 $R_c$ 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 $D_c(x)=D_c\exp ({\gamma }_{c}x)$ and $D_m(x)=D_m\exp (-{\gamma }_{m}x)$. 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 $D_m\ll D_c$ or the diffusion parameter ${\gamma }_m$ 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.

9 pages, 5 figures

References in corpus (2)

• Fractional diffusion modeling of ion channel gating
• Nonlinear drift-diffusion model of gating in the fast Cl channel

Cited by in corpus (1)

• Voltage dependence of Hodgkin-Huxley rate functions for a multi-stage K channel voltage sensor within a membrane