Improved coarse-graining of Markov state models via explicit consideration of statistical uncertainty

TL;DR

This paper introduces BACE, a Bayesian clustering algorithm for coarse-graining Markov state models that explicitly accounts for statistical uncertainty, improving interpretability and model hierarchy identification.

Contribution

The paper presents a novel Bayesian agglomerative clustering method for MSMs that incorporates uncertainty and offers an information-theoretic interpretation.

Findings

BACE effectively reduces MSM complexity while preserving essential dynamics.

The method explicitly accounts for statistical uncertainty from finite sampling.

An efficient Bayesian model comparison technique identifies optimal model hierarchies.

Abstract

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.