离子通道门控的位置相关随机扩散模型
Position-dependent stochastic diffusion model of ion channel gating
摘要：
通过考虑离子通道中扩散系数的空间变化，建立了离子通道门控的位置相关随机扩散模型。假设调节离子通道的打开的传感器在封闭区域$R_{c}$和过渡区域$R_{m}$中经历布朗运动，其中动力学由满足具有扩散系数$D_{c}(x)=D_{c}\exp(γ_{c}x)$和$D_{m}(x)=D_{m} \exp(-γ_{m}x)$的相互作用的福克-普朗克方程的概率密度$p_{c}(x,t)$和$p_{m}(x,t)$描述。当$D_{m} \ll D_{c}$或扩散参数$γ_{m}$足够大时，在应用去极化电压箝位后的短时间内，耦合方程的解析解可近似为最低频率弛豫。因此，如果在打开状态和关闭状态之间存在大的扩散（或电势）势垒，则可以从随机扩散模型导出描述门控转变的经验速率方程。
英文摘要：
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 $D_{c}(x)=D_{c}\exp(γ_{c}x)$ and $D_{m}(x)=D_{m} \exp(-γ_{m}x)$. 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 $γ_{m}$ 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.
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