Department of Neurosciences, School of Medicine, Case Western Reserve University, 10900 Euclid Avenue, Ohio 44106-4975, USA.
Phys Rev Lett. 2012 Sep 14;109(11):118101. doi: 10.1103/PhysRevLett.109.118101. Epub 2012 Sep 11.
Markov chains provide realistic models of numerous stochastic processes in nature. We demonstrate that in any Markov chain, the change in occupation number in state A is correlated to the change in occupation number in state B if and only if A and B are directly connected. This implies that if we are only interested in state A, fluctuations in B may be replaced with their mean if state B is not directly connected to A, which shortens computing time considerably. We show the accuracy and efficacy of our approximation theoretically and in simulations of stochastic ion-channel gating in neurons.
马尔可夫链为自然界中许多随机过程提供了现实的模型。我们证明，在任何马尔可夫链中，如果状态 A 和状态 B 直接相连，那么状态 A 中的占据数的变化与状态 B 中的占据数的变化是相关的。这意味着，如果我们只对状态 A 感兴趣，如果状态 B 与状态 A 没有直接连接，那么状态 B 的波动可以用它们的平均值来代替，这大大缩短了计算时间。我们从理论和神经元中随机离子通道门控的模拟两个方面展示了我们的近似方法的准确性和有效性。
