Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 114, Issue 31, Pages 8265-8270Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1704803114
Keywords
molecular dynamics; integrative structural biology; maximum entropy; Markov state models; augmented Markov models
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Funding
- Freie Universitat Berlin
- European Commission (Dahlem Research School POINT-Marie Curie COFUND)
- European Research Council (ERC)
- Deutsche Forschungsgemeinschaft [825/2-2, SFB 1114/A4, SFB 1114/C3]
- National Science Foundation [CHE-1265929]
- Welch Foundation [C-1570]
- Direct For Mathematical & Physical Scien
- Division Of Chemistry [1265929] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Physics [GRANTS:13776680, 1427654] Funding Source: National Science Foundation
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Accurate mechanistic description of structural changes in biomolecules is an increasingly important topic in structural and chemical biology. Markov models have emerged as a powerful way to approximate the molecular kinetics of large biomolecules while keeping full structural resolution in a divide-and-conquer fashion. However, the accuracy of these models is limited by that of the force fields used to generate the underlying molecular dynamics (MD) simulation data. Whereas the quality of classical MD force fields has improved significantly in recent years, remaining errors in the Boltzmann weights are still on the order of a few kT, which may lead to significant discrepancies when comparing to experimentally measured rates or state populations. Here we take the view that simulations using a sufficiently good force-field sample conformations that are valid but have inaccurate weights, yet these weights may be made accurate by incorporating experimental data a posteriori. To do so, we propose augmented Markov models (AMMs), an approach that combines concepts from probability theory and information theory to consistently treat systematic force-field error and statistical errors in simulation and experiment. Our results demonstrate that AMMs can reconcile conflicting results for protein mechanisms obtained by different force fields and correct for a wide range of stationary and dynamical observables even when only equilibrium measurements are incorporated into the estimation process. This approach constitutes a unique avenue to combine experiment and computation into integrative models of biomolecular structure and dynamics.
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