Dixit Purushottam D, Dill Ken A
Department of Systems Biology, Columbia University , New York, New York 10032, United States.
Laufer Center for Quantitative Biology, Department of Chemistry, and Department of Physics and Astronomy, Stony Brook University , Stony Brook, New York 11790, United States.
J Chem Theory Comput. 2018 Feb 13;14(2):1111-1119. doi: 10.1021/acs.jctc.7b01126. Epub 2018 Jan 26.
Rate processes are often modeled using Markov State Models (MSMs). Suppose you know a prior MSM and then learn that your prediction of some particular observable rate is wrong. What is the best way to correct the whole MSM? For example, molecular dynamics simulations of protein folding may sample many microstates, possibly giving correct pathways through them while also giving the wrong overall folding rate when compared to experiment. Here, we describe Caliber Corrected Markov Modeling (CM), an approach based on the principle of maximum entropy for updating a Markov model by imposing state- and trajectory-based constraints. We show that such corrections are equivalent to asserting position-dependent diffusion coefficients in continuous-time continuous-space Markov processes modeled by a Smoluchowski equation. We derive the functional form of the diffusion coefficient explicitly in terms of the trajectory-based constraints. We illustrate with examples of 2D particle diffusion and an overdamped harmonic oscillator.
速率过程通常使用马尔可夫状态模型（MSM）进行建模。假设你事先知道一个MSM，然后发现你对某个特定可观测速率的预测是错误的。纠正整个MSM的最佳方法是什么？例如，蛋白质折叠的分子动力学模拟可能会对许多微观状态进行采样，可能会给出通过这些状态的正确路径，但与实验相比，同时也会给出错误的整体折叠速率。在这里，我们描述了口径校正马尔可夫建模（CM），这是一种基于最大熵原理的方法，通过施加基于状态和轨迹的约束来更新马尔可夫模型。我们表明，这种校正等同于在由斯莫卢霍夫斯基方程建模的连续时间连续空间马尔可夫过程中断言位置依赖的扩散系数。我们根据基于轨迹的约束明确推导了扩散系数的函数形式。我们用二维粒子扩散和过阻尼谐振子的例子进行说明。
