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Cited by 76Protein Structure and DynamicsAdvanced Physical and Chemical Molecular InteractionsGene Regulatory Network Analysis

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

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Bowman, Gregory R.·2012·The Journal of Chemical Physics
DOI 10.1063/1.4755751PMC PMC3477182
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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.

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  • Recent methods such as Bayesian agglomerative clustering, hierarchical Nystrom, flux PCCA+, and HMM-based coarse-graining have proposed clustering methods to address statistical reliability.

    “Recent methods such as the Bayesian agglomerative clustering (BACE) method [33], a hierarchical Nystrom method [34], flux PCCA+ [35] and HMM-based coarse-graining [3] have proposed clustering methods to address this statistical reliability issue.”

    From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [33]

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Research works printed but not linked: 2

  1. X. Huang et al., Pac. Symp. Biocomput. 15, 228 (2010).
  2. J. G. Kemeny and J. L. Shell, Finite Markov Chains (Springer, Berlin, 1976).

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Authors
Bowman, G. R.
Affiliations
University of California, Berkeley (US)
Corresponding author
Bowman, Gregory R.
ORCID
Bowman, Gregory R.
Venue
The Journal of Chemical Physics
Publisher
AIP Publishing
Published
2012-10-05
Volume
137
Issue
13
Pages
134111-134111
ISSN
  • 0021-9606 (ISSN-L)
  • 1089-7690
DOI
10.1063/1.4755751
PMC
PMC3477182
OpenAlex
W2077947928
Cited by
76
References
32
Citations by year
2026: 1 · 2025: 1 · 2024: 1 · 2023: 4 · 2022: 7 · 2021: 7 · 2020: 3 · 2019: 3 · 2018: 7 · 2017: 6 · 2016: 10 · 2015: 10 · 2014: 8 · 2013: 8
FWCI
3.35
Type
journal article
Language
en
Open access
Locations
  • The Journal of Chemical Physics (publishedVersion)
  • Europe PMC (PubMed Central) (publishedVersion)
  • PubMed Central (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
National Institutes of Health (R01-GM050945)
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
  • Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
Keywords
Markov state models, coarse-graining, state merging, statistical uncertainty, finite sampling, Jensen-Shannon divergence, Kullback-Leibler divergence, information loss, Bayesian model selection, mesoscale model, protein conformational dynamics
MeSH terms
Algorithms, Kinetics, Markov Chains, Proteins, Thermodynamics, Uncertainty

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