通过显式考虑统计不确定性改进马尔可夫状态模型的粗粒度化
Improved coarse-graining of Markov state models via explicit consideration of statistical uncertainty
摘要：
马尔可夫状态模型（MSMs）--或离散时间主方程模型--是一种强大的方法来模拟分子系统的结构和功能，如蛋白质。不幸的是，具有足够多的状态以与实验建立定量联系的MSM（即使对于小系统，通常也有数万个状态）通常太复杂而难以理解。在这里，我提出了一个贝叶斯凝聚聚类引擎（BACE）粗粒度的马尔可夫模型，从而降低其复杂性，使他们更容易理解。该算法的一个重要特征是它能够明确地解释有限采样引起的模型参数的统计不确定性。这一进展建立在一些最近的工作，强调在MSM的分析中考虑不确定性的重要性，并提供了显着的优势，现有的粗粒度马尔可夫状态模型的方法。我在这里导出的用于确定哪些状态要合并的封闭形式表达式等价于广义詹森-香农散度，广义詹森-香农散度是信息论中与相对熵相关的一个重要度量。因此，该方法在最小化信息损失方面具有吸引人的信息论解释。该算法的自下而上的性质可能使其特别适合于构建中尺度模型。我还提出了一个非常有效的表达贝叶斯模型比较，可以用来确定最有意义的层次结构的模型从BACE。
英文摘要：
Markov state models (MSMs)---or discrete-time master equation models---are a powerful way of modeling the structure and function of molecular systems like proteins. Unfortunately, MSMs with sufficiently many states to make a quantitative connection with experiments (often tens of thousands of states even for small systems) are generally too complicated to understand. Here, I present a Bayesian agglomerative clustering engine (BACE) for coarse-graining such Markov models, thereby reducing their complexity and making them more comprehensible. An important feature of this algorithm is its ability to explicitly account for statistical uncertainty in model parameters that arises from finite sampling. This advance builds on a number of recent works highlighting the importance of accounting for uncertainty in the analysis of MSMs and provides significant advantages over existing methods for coarse-graining Markov state models. The closed-form expression I derive here for determining which states to merge is equivalent to the generalized Jensen-Shannon divergence, an important measure from information theory that is related to the relative entropy. Therefore, the method has an appealing information theoretic interpretation in terms of minimizing information loss. The bottom-up nature of the algorithm likely makes it particularly well suited for constructing mesoscale models. I also present an extremely efficient expression for Bayesian model comparison that can be used to identify the most meaningful levels of the hierarchy of models from BACE.
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