Weighted Histogram Analysis Research Articles

The calculation of the potential of mean force using computer simulations

The problem of unbiasing and combining the results of umbrella sampling calculations is reviewed. The weighted histogram analysis method (WHAM) of S. Kumar et al. (J. Comp. Chem. 13 (1992) 1011) is described and compared with other approaches. The method is illustrated with molecular dynamics simulations of the alanine dipeptide for one-and two-dimensional free energy surfaces. The results show that the WHAM approach simplifies considerably the task of recombining the various windows in complex systems.

Constant-temperature free energy surfaces for physical and chemical processes

A comparison between two methods for combining data from molecular simulations to generate free energy surfaces for physical and chemical processes is presented. The conventional «splicing» method is compared with a recently introduced histogram-based technique for the calculation of the free energy surface for folding a short peptide in vacuo. We present an extension of the weighted histogram analysis method, described recently by Kumar et al. (J. Comput. Chem. 1992, 13, 1101-1021), which is specialized to the case of constant-temperature simulations and generalized to multiple dimensions. Our data indicate that both methods produce identical results, at the qualitative level, for the folding free energy surface

THE weighted histogram analysis method for free‐energy calculations on biomolecules. I. The method

AbstractThe Weighted Histogram Analysis Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomolecular Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free‐energy and Potential of Mean Force calculations. This algorithm possesses the following advantages over methods that are currently employed: (1) It provides a built‐in estimate of sampling errors thereby yielding objective estimates of the optimal location and length of additional simulations needed to achieve a desired level of precision; (2) it yields the “best” value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addition to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better estimates of the free‐energy differences. By recasting the Ferrenberg–Swendsen Multiple Histogram equations in a form suitable for molecular mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine. © 1992 by John Wiley & Sons, Inc.