Efficient Bayesian estimation of Markov model transition matrices with given stationary distribution
Open accessAbstract
Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the convergence of expectation values of equilibrium probabilities and expectation values of stationary quantities significantly. Unfortunately the convergence of dynamic observables such as correlation functions or timescales of conformational transitions relies on direct equilibrium simulations. Markov state models are well suited to describe both stationary properties and properties of slow dynamical processes of a molecular system, in terms of a transition matrix for a jump process on a suitable discretization of continuous conformation space. Here, we introduce statistical estimation methods that allow a priori knowledge of equilibrium probabilities to be incorporated into the estimation of dynamical observables. Both maximum likelihood methods and an improved Monte Carlo sampling method for reversible transition matrices with fixed stationary distribution are given. The sampling approach is applied to a toy example as well as to simulations of the MR121-GSGS-W peptide, and is demonstrated to converge much more rapidly than a previous approach of Noé [J. Chem. Phys. 128, 244103 (2008)].
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Knowledge of the stationary distribution can be used to further constrain the space of transition matrices.
“A recent publication has shown how knowledge of the stationary distribution (from, say, a long parallel tempering simulation) can be used to further constrain the space of transition matrices [28].”
From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [28]
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Cited by
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Markov state models of biomolecular conformational dynamics
Chodera, J. D., & Noé, F. (2014) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2014.04.002 · Cited by 776 · see citing works
Self-citation
- Authors
- Trendelkamp-Schroer, B., & Noé, F.
- Affiliations
- Freie Universität Berlin (DE)
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 2013-04-24
- Volume
- 138
- Issue
- 16
- Pages
- 164113-164113
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W2035096678
- Cited by
- 39
- References
- 60
- Citations by year
- 2026: 4 · 2025: 4 · 2024: 1 · 2022: 3 · 2021: 3 · 2020: 6 · 2019: 4 · 2018: 3 · 2017: 4 · 2015: 4 · 2014: 3
- FWCI
- 1.04
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Journal of Chemical Physics (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Refubium (Universitätsbibliothek der Freien Universität Berlin) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Deutsche Forschungsgemeinschaft (825/3)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Keywords
- Markov state models, transition matrix, stationary distribution, Bayesian estimation, maximum likelihood estimation, reversible Markov chains, enhanced sampling, conformational dynamics, metastability, peptide dynamics, Monte Carlo sampling
- MeSH terms
- Algorithms, Monte Carlo Method, Peptides, Temperature, Molecular Dynamics Simulation
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