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J Chem Theory Comput. 2007 Jan;3(1):26-41. doi: 10.1021/ct0502864.

Use of the Weighted Histogram Analysis Method for the Analysis of Simulated and Parallel Tempering Simulations.

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Graduate Group in Biophysics and Department of Pharmaceutical Chemistry, University of California at San Francisco, San Francisco, California 94143, IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, and Department of Chemistry, College of Natural Sciences, Seoul National University, Gwanak-gu, Shillim-dong, san 56-1 Seoul 151-747, Republic of Korea.


The growing adoption of generalized-ensemble algorithms for biomolecular simulation has resulted in a resurgence in the use of the weighted histogram analysis method (WHAM) to make use of all data generated by these simulations. Unfortunately, the original presentation of WHAM by Kumar et al. is not directly applicable to data generated by these methods. WHAM was originally formulated to combine data from independent samplings of the canonical ensemble, whereas many generalized-ensemble algorithms sample from mixtures of canonical ensembles at different temperatures. Sorting configurations generated from a parallel tempering simulation by temperature obscures the temporal correlation in the data and results in an improper treatment of the statistical uncertainties used in constructing the estimate of the density of states. Here we present variants of WHAM, STWHAM and PTWHAM, derived with the same set of assumptions, that can be directly applied to several generalized ensemble algorithms, including simulated tempering, parallel tempering (better known as replica-exchange among temperatures), and replica-exchange simulated tempering. We present methods that explicitly capture the considerable temporal correlation in sequentially generated configurations using autocorrelation analysis. This allows estimation of the statistical uncertainty in WHAM estimates of expectations for the canonical ensemble. We test the method with a one-dimensional model system and then apply it to the estimation of potentials of mean force from parallel tempering simulations of the alanine dipeptide in both implicit and explicit solvent.


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