Optimal Dimensionality Reduction of Multistate Kinetic and Markov-State Models.
Optimal Dimensionality Reduction of Multistate Kinetic and Markov-State Models.
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DOI：
10.1021/jp508375q
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发表时间：
2015-07-23
期刊：
影响因子：
--
通讯作者：
Szabo A
中科院分区：
文献类型：
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作者：
Hummer G;Szabo A
我们开发了一个系统的程序，以获得率和过渡矩阵，最佳地描述了动态的聚合超相结合（集群或集总）微观状态。这些简化的动力学模型是通过匹配满态和聚集态中超态随时间变化的占据数相关函数来构造的。通过使用投影算子形式主义得到相同的结果。减少的动态模型是准确的所有时间在其完整的非马尔可夫制定。在近似的马尔可夫极限，我们推导出简单的解析表达式的减少率或马尔可夫转移矩阵，导致准确的自动和交叉松弛时间。这些减少的马尔可夫模型在短期和长期的动态匹配之间取得了最佳平衡。我们还讨论了如何使用这种方法可以在一个层次的过程中构建最佳的superstates通过聚合的微观状态。一般简化矩阵理论的结果示出与应用程序简单的模型系统和一个更复杂的主方程模型的肽折叠来自原子分子动力学模拟。我们发现，减少模型忠实地捕捉到整个系统的动态，产生了显着的改进，共同的局部平衡近似。
We develop a systematic procedure for obtaining rate and transition matrices that optimally describe the dynamics of aggregated superstates formed by combining (clustering or lumping) microstates. These reduced dynamical models are constructed by matching the time-dependent occupancy-number correlation functions of the superstates in the full and aggregated systems. Identical results are obtained by using a projection operator formalism. The reduced dynamic models are exact for all times in their full non-Markovian formulation. In the approximate Markovian limit, we derive simple analytic expressions for the reduced rate or Markov transition matrices that lead to exact auto- and cross-relaxation times. These reduced Markovian models strike an optimal balance between matching the dynamics at short and long times. We also discuss how this approach can be used in a hierarchical procedure of constructing optimal superstates through aggregation of microstates. The results of the general reduced-matrix theory are illustrated with applications to simple model systems and a more complex master-equation model of peptide folding derived previously from atomistic molecular dynamics simulations. We find that the reduced models faithfully capture the dynamics of the full systems, producing substantial improvements over the common local-equilibrium approximation.