Extension to the weighted histogram analysis method: combining umbrella sampling with free energy calculations

Abstract

The Weighted Histogram Analysis Method (WHAM) of Kumar et al. (J. Comput. Chem. 13 (1992) 1011), is used to combine free energy perturbations with umbrella sampling calculations. The formulation is general and allows optimal calculation of the free energies from a set of molecular dynamics simulations generated in the presence of arbitrary biasing umbrella sampling window potentials. The method yields the free energy associated with a given simulation as well as the probability distribution of the molecular system configurations by extracting the information contained in all the biased simulations (the windows) in an optimal way. The method presents some advantages compared to the standard free energy perturbation (FEP) and thermodynamic integration (TI) methods, because the window potential can be used for restricting the conformational space to specific regions during free energy calculations.