BayesWHAM: A Bayesian approach for free energy estimation, reweighting, and uncertainty quantification in the weighted histogram analysis method

The weighted histogram analysis method (WHAM) is a powerful approach to estimate molecular free energy surfaces (FES) from biased simulation data. Bayesian reformulations of WHAM are valuable in proving statistically optimal use of the data and providing a transparent means to incorporate regularizi...

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Bibliographic Details
Published in:Journal of computational chemistry 2017-07, Vol.38 (18), p.1583-1605
Main Author: Ferguson, Andrew L.
Format: Article
Language:English
Subjects:
Alanine
Bayesian analysis
Bayesian inference
Chemical engineering
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Free energy
free energy surfaces
histogram reweighting
Order parameters
Parameter uncertainty
Sampling
Simulation
umbrella sampling
weighted histogram analysis method
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Summary:The weighted histogram analysis method (WHAM) is a powerful approach to estimate molecular free energy surfaces (FES) from biased simulation data. Bayesian reformulations of WHAM are valuable in proving statistically optimal use of the data and providing a transparent means to incorporate regularizing priors and estimate statistical uncertainties. In this work, we develop a fully Bayesian treatment of WHAM to generate statistically optimal FES estimates in any number of biasing dimensions under arbitrary choices of the Bayes prior. Rigorous uncertainty estimates are generated by Metropolis‐Hastings sampling from the Bayes posterior. We also report a means to project the FES and its uncertainties into arbitrary auxiliary order parameters beyond those in which biased sampling was conducted. We demonstrate the approaches in applications of alanine dipeptide and the unthreading of a synthetic mimic of the astexin‐3 lasso peptide. Open‐source MATLAB and Python implementations of our codes are available for free public download. © 2017 Wiley Periodicals, Inc. The molecular free energy surface (FES) is valuable in understanding and engineering molecular behavior. Biased molecular simulations provide a means to efficiently explore configurational space, and the unbiased FES can be estimated using the weighted histogram analysis method (WHAM). We present a Bayesian reformulation of WHAM to generate statistically optimal FES estimates in any number of arbitrary variables, under arbitrary choices of Bayes priors, and with rigorous uncertainty estimates.
ISSN:0192-8651
1096-987X
DOI:10.1002/jcc.24800