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  Convergence and error estimation in free energy calculations using the weighted histogram analysis method

Zhu, F., & Hummer, G. (2012). Convergence and error estimation in free energy calculations using the weighted histogram analysis method. Journal of Computational Chemistry, 33(4), 453-465. doi:10.1002/jcc.21989.

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 Creators:
Zhu, Fangqiang1, Author
Hummer, Gerhard1, Author                 
Affiliations:
1Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, USA, ou_persistent22              

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Free keywords: Algorithms, Computer Simulation, Models, Biological, Models, Statistical, Sodium, Sodium Channels, Thermodynamics
 Abstract: The weighted histogram analysis method (WHAM) has become the standard technique for the analysis of umbrella sampling simulations. In this article, we address the challenges (1) of obtaining fast and accurate solutions of the coupled nonlinear WHAM equations, (2) of quantifying the statistical errors of the resulting free energies, (3) of diagnosing possible systematic errors, and (4) of optimally allocating of the computational resources. Traditionally, the WHAM equations are solved by a fixed-point direct iteration method, despite poor convergence and possible numerical inaccuracies in the solutions. Here, we instead solve the mathematically equivalent problem of maximizing a target likelihood function, by using superlinear numerical optimization algorithms with a significantly faster convergence rate. To estimate the statistical errors in one-dimensional free energy profiles obtained from WHAM, we note that for densely spaced umbrella windows with harmonic biasing potentials, the WHAM free energy profile can be approximated by a coarse-grained free energy obtained by integrating the mean restraining forces. The statistical errors of the coarse-grained free energies can be estimated straightforwardly and then used for the WHAM results. A generalization to multidimensional WHAM is described. We also propose two simple statistical criteria to test the consistency between the histograms of adjacent umbrella windows, which help identify inadequate sampling and hysteresis in the degrees of freedom orthogonal to the reaction coordinate. Together, the estimates of the statistical errors and the diagnostics of inconsistencies in the potentials of mean force provide a basis for the efficient allocation of computational resources in free energy simulations.

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Language(s): eng - English
 Dates: 2011-08-252011-06-162011-10-082011-11-232012-02-05
 Publication Status: Issued
 Pages: 13
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1002/jcc.21989
BibTex Citekey: zhu_convergence_2012
 Degree: -

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Title: Journal of Computational Chemistry
  Abbreviation : J. Comput. Chem.
Source Genre: Journal
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Publ. Info: New York : Wiley
Pages: - Volume / Issue: 33 (4) Sequence Number: - Start / End Page: 453 - 465 Identifier: ISSN: 0192-8651
CoNE: https://pure.mpg.de/cone/journals/resource/954925489848