Markov state models (MSMs)---or discrete-time master equation models---are a powerful way of understanding the structure and function of proteins and other molecular systems . However, they are typically too complicated to understand. Here, I present a Bayesian agglomerative clustering engine (BACE) for coarse-graining Markov chains---as well as a more general class of probabilistic models---making them more comprehensible while remaining as faithful as possible to the original kinetics by accounting for model uncertainty . 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  . 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.
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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understanding
modeling
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proteins and other molecular systems . However, they are typically
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
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Markov chains---as well as a more general class of probabilistic models---making
such Markov models, thereby reducing their complexity and making
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while remaining as faithful as possible to the original kinetics by accounting for model uncertainty
. 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
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in terms of minimizing information loss. The bottom-up nature of the algorithm likely makes it particularly well suited for constructing mesoscale models