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Markov models of molecular kinetics: Generation and validation

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Prinz, Jan-Hendrik, Wu, Hao, Sarich, Marco, Keller, Bettina, Senne, Martin, Held, Martin, Chodera, John D., Schütte, Christof +1 more·2011·The Journal of Chemical Physics
DOI 10.1063/1.3565032
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Abstract

Markov state models of molecular kinetics (MSMs), in which the long-time statistical dynamics of a molecule is approximated by a Markov chain on a discrete partition of configuration space, have seen widespread use in recent years. This approach has many appealing characteristics compared to straightforward molecular dynamics simulation and analysis, including the potential to mitigate the sampling problem by extracting long-time kinetic information from short trajectories and the ability to straightforwardly calculate expectation values and statistical uncertainties of various stationary and dynamical molecular observables. In this paper, we summarize the current state of the art in generation and validation of MSMs and give some important new results. We describe an upper bound for the approximation error made by modeling molecular dynamics with a MSM and we show that this error can be made arbitrarily small with surprisingly little effort. In contrast to previous practice, it becomes clear that the best MSM is not obtained by the most metastable discretization, but the MSM can be much improved if non-metastable states are introduced near the transition states. Moreover, we show that it is not necessary to resolve all slow processes by the state space partitioning, but individual dynamical processes of interest can be resolved separately. We also present an efficient estimator for reversible transition matrices and a robust test to validate that a MSM reproduces the kinetics of the molecular dynamics data.

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  • A number of literature reviews and overview articles cover the fundamentals of Markov state models.

    “While a number of literature reviews and overview articles cover the fundamentals of Markov state models [6, 7], the present review focuses on theoretical advances and applications that have been published since these reviews were written.”

    From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [7]

  • Introducing additional partitions near the transition state reduces discrete state lifetimes but increases approximation accuracy by allowing better approximation of the slow eigenspace of the Markov operator.

    “Introducing additional partitions near the transition state will reduce the discrete state lifetimes but actually increase the approximation accuracy of the model by allowing it to better approximate the slow eigenspace of the Markov operator [7].”

    From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [7]

  • Recent theoretical work has shown it is more useful to consider an MSM as a discrete approximation to the dynamics of the Markov operator in the full state space of positions and velocities.

    “Recent theoretical work has shown it is more useful to instead consider the MSM as a discrete approximation to the dynamics of the Markov operator (transfer operator or dynamical propagator) in the full state space of positions and velocities [8, 7, 5].”

    From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [7]

  • The transition matrix is commonly estimated only over the largest connected subset of states and proceeds via an iterative maximum likelihood estimator that respects detailed balance.

    “Commonly, the transition matrix is only estimated over the largest connected subset of states [24, 25] and proceeds via an iterative maximum likelihood estimator that respects detailed balance [26, 7].”

    From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [7]

  • Good MSMs accurately approximate long-time molecular kinetics because their eigenvectors closely approximate the corresponding eigenfunctions of the Markov operator associated with large eigenvalues.

    “A key finding is that good MSMs are able to accurately approximate long-time molecular kinetics because their eigenvectors closely approximate the corresponding eigenfunctions of the Markov operator associated with large eigenvalues [8, 7, 5].”

    From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [7]

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Cited by

Sorted by citations

Authors
Prinz, J.-H., Wu, H., Sarich, M., Keller, B., Senne, M., Held, M., Chodera, J. D., Schütte, C., & Noé, F.
Affiliations
  • Freie Universität Berlin (DE)
  • QB3 (US)
ORCID
Venue
The Journal of Chemical Physics
Publisher
AIP Publishing
Published
2011-05-04
Volume
134
Issue
17
Pages
174105-174105
ISSN
  • 0021-9606 (ISSN-L)
  • 1089-7690
DOI
10.1063/1.3565032
OpenAlex
W2085213650
Cited by
1,275
References
4
Citations by year
2026: 99 · 2025: 105 · 2024: 97 · 2023: 98 · 2022: 107 · 2021: 109 · 2020: 102 · 2019: 84 · 2018: 95 · 2017: 85 · 2016: 76 · 2015: 67 · 2014: 52 · 2013: 54 · 2012: 30
FWCI
19.50
Type
journal article
Language
en
Open access
Locations
  • The Journal of Chemical Physics (publishedVersion)
  • PubMed (publishedVersion)
  • Refubium (Universitätsbibliothek der Freien Universität Berlin) (submittedVersion)
  • Universitätsbibliothek der FU Berlin Hochschulschriftenstelle u. Dokumentenserver
Funders
  • California Institute for Quantitative Biosciences
  • Deutsche Forschungsgemeinschaft (825/2, SFB740)
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
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Model Reduction and Neural Networks
Keywords
Markov state models, molecular kinetics, model validation, approximation error bounds, state space partitioning, metastable states, transition state, sampling efficiency
MeSH terms
Algorithms, Computer Simulation, Kinetics, Markov Chains, Models, Molecular, Peptides, Models, Statistical

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