Position-dependent stochastic diffusion model of ion channel gating

TL;DR

This paper introduces a position-dependent stochastic diffusion model for ion channel gating, accounting for spatial variations in diffusion coefficients and deriving empirical rate equations from the underlying stochastic dynamics.

Contribution

It develops a novel position-dependent diffusion model with analytical solutions for ion channel gating, incorporating spatially varying diffusion coefficients and transition dynamics.

Findings

Analytical approximation of gating transition rates.

Model captures spatial variation in ion channel dynamics.

Provides a basis for empirical rate equations from stochastic models.

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.