Markov state models (MSMs) are a powerful means of understanding the structure and function of biomolecules by describing their free energy landscapes as a set of local minima (a.k.a. states) and the probabilities of transitioning between them. Unfortunately, it can be difficult to gain an intuition for an MSM because they typically must have tens of thousands of sates to quantitatively describe the rugged landscapes of most biomolecules . Here, I derive a Bayesian agglomerative clustering engine (BACE) for coarse-graining MSMs, making them suitable for extracting human understanding. BACE considerably outperforms existing methods by iteratively lumping together the most kinetically similar states while taking into account model uncertainty. 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. Code for both methods is available on the web URL
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. 
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are a powerful means
---or discrete-time master equation models---are a powerful way
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biomolecules by describing their free energy landscapes as a set of local minima (a.k.a. states) and the probabilities of transitioning between them. Unfortunately, it can be difficult to gain an intuition for an MSM because they typically must have tens of thousands of sates to quantitatively describe the rugged landscapes of most biomolecules
proteins and other molecular systems. However, they are typically too complicated to understand
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derive
present
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MSMs, making them suitable for extracting human understanding. BACE considerably outperforms existing methods by iteratively lumping together the most kinetically similar states while taking into account
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
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I
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
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Code for both methods is available on the web URL