Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and associated structural changes, and stationary or kinetic experimental observables of complex molecules from large amounts of molecular dynamics simulation data. However, MSMs approximate the true dynamics by assuming a Markov chain on a clusters discretization of the state space. This approximation is difficult to make for high-dimensional biomolecular systems, and the quality and reproducibility of MSMs has, therefore, been limited. Here, we discard the assumption that dynamics are Markovian on the discrete clusters. Instead, we only assume that the full phase-space molecular dynamics is Markovian, and a projection of this full dynamics is observed on the discrete states, leading to the concept of Projected Markov Models (PMMs). Robust estimation methods for PMMs are not yet available, but we derive a practically feasible approximation via Hidden Markov Models (HMMs). It is shown how various molecular observables of interest that are often computed from MSMs can be computed from HMMs/PMMs. The new framework is applicable to both, simulation and single-molecule experimental data. We demonstrate its versatility by applications to educative model systems, a 1 ms Anton MD simulation of the bovine pancreatic trypsin inhibitor protein, and an optical tweezer force probe trajectory of an RNA hairpin.
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14 November 2013
Research Article|
November 13 2013
Projected and hidden Markov models for calculating kinetics and metastable states of complex molecules
Frank Noé;
Department of Mathematics and Computer Science,
FU Berlin
, Arnimallee 6, 14159 Berlin, Germany
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Hao Wu;
Department of Mathematics and Computer Science,
FU Berlin
, Arnimallee 6, 14159 Berlin, Germany
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Jan-Hendrik Prinz;
Department of Mathematics and Computer Science,
FU Berlin
, Arnimallee 6, 14159 Berlin, Germany
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Nuria Plattner
Nuria Plattner
Department of Mathematics and Computer Science,
FU Berlin
, Arnimallee 6, 14159 Berlin, Germany
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a)
Author to whom correspondence should be addressed. Electronic mail: frank.noe@fu-berlin.de
b)
H. Wu and J.-H. Prinz contributed equally to this work.
J. Chem. Phys. 139, 184114 (2013)
Article history
Received:
September 03 2013
Accepted:
October 22 2013
Citation
Frank Noé, Hao Wu, Jan-Hendrik Prinz, Nuria Plattner; Projected and hidden Markov models for calculating kinetics and metastable states of complex molecules. J. Chem. Phys. 14 November 2013; 139 (18): 184114. https://doi.org/10.1063/1.4828816
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