从布朗动力学到马尔可夫链：一个离子通道的例子
From Brownian Dynamics to Markov Chain: an Ion Channel Example
摘要：
提出了一般多离子通道的离散速率理论，其中离子扩散的连续动力学被简化为马尔可夫离散状态之间的跃迁。在开放通道中，离子渗透过程涉及三种类型的事件：离子进入通道、离子从通道逸出或离子在通道中的不同能量最小值之间跳跃。连续的动态导致一个层次的福克-普朗克方程，索引通道占用。由此可以计算出平均逃逸时间和分裂概率（表示离子从哪一侧逃逸）。通过将这些与马尔可夫模型的相应表达式相等，可以确定马尔可夫转移率。该理论说明了一个双离子单阱通道。并与布朗动力学模拟和Fokker-Planck方程的稳态概率进行了比较。还研究了通道的电导率，并计算了最大化离子通量的最佳几何形状。
英文摘要：
A discrete rate theory for general multi-ion channels is presented, in which the continuous dynamics of ion diffusion is reduced to transitions between Markovian discrete states. In an open channel, the ion permeation process involves three types of events: an ion entering the channel, an ion escaping from the channel, or an ion hopping between different energy minima in the channel. The continuous dynamics leads to a hierarchy of Fokker-Planck equations, indexed by channel occupancy. From these the mean escape times and splitting probabilities (denoting from which side an ion has escaped) can be calculated. By equating these with the corresponding expressions from the Markov model the Markovian transition rates can be determined. The theory is illustrated with a two-ion one-well channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical Fokker-Planck equations. The conductivity of the channel is also studied, and the optimal geometry maximizing ion flux is computed.
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