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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7 May 2011
Research Article|
May 04 2011
Markov models of molecular kinetics: Generation and validation
Jan-Hendrik Prinz;
Jan-Hendrik Prinz
1
FU Berlin
, Arnimallee 6, 14195 Berlin, Germany
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Hao Wu;
Hao Wu
1
FU Berlin
, Arnimallee 6, 14195 Berlin, Germany
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Marco Sarich;
Marco Sarich
1
FU Berlin
, Arnimallee 6, 14195 Berlin, Germany
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Bettina Keller;
Bettina Keller
1
FU Berlin
, Arnimallee 6, 14195 Berlin, Germany
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Martin Senne;
Martin Senne
1
FU Berlin
, Arnimallee 6, 14195 Berlin, Germany
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Martin Held;
Martin Held
1
FU Berlin
, Arnimallee 6, 14195 Berlin, Germany
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John D. Chodera;
John D. Chodera
2California Institute of Quantitative Biosciences (QB3),
University of California
, Berkeley, 260J Stanley Hall, Berkeley, California 94720, USA
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Christof Schütte;
Christof Schütte
1
FU Berlin
, Arnimallee 6, 14195 Berlin, Germany
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a)
Author to whom correspondence should be addressed. Electronic mail: frank.noe@fu-berlin.de.
J. Chem. Phys. 134, 174105 (2011)
Article history
Received:
August 04 2010
Accepted:
February 22 2011
Citation
Jan-Hendrik Prinz, Hao Wu, Marco Sarich, Bettina Keller, Martin Senne, Martin Held, John D. Chodera, Christof Schütte, Frank Noé; Markov models of molecular kinetics: Generation and validation. J. Chem. Phys. 7 May 2011; 134 (17): 174105. https://doi.org/10.1063/1.3565032
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