Comparison of two approaches to potential of mean force calculations of hydrophobic association: particle insertion and weighted histogram analysis methods

We investigated the convergence behaviour of potential of mean force (PMF) calculations using the particle insertion method (PI) and the umbrella sampling with weighted histogram analysis method (WHAM). For PI, two approaches were tested: insertion of two particles at various separations into pure water, and insertion of a second particle into a heterogeneous system consisting of a first particle and water. The comparison of these methods is illustrated by a study of the PMF between two neon atoms and two methane molecules embedded in a periodic box of water. Two water models, TIP3P and TIP4P, were used in the two series of simulations. The choice of the method employed to estimate the PMF affects the efficiency of the calculation and, in turn, the amount of sampling necessary to attain proper convergence. For small particles, with radii similar to that of the neon atom, PI converges faster than WHAM calculations. For larger particles, umbrella sampling with WHAM converges faster, and the size of the methane molecule seems to be close to the practical limit of convergence of the PI method. The umbrella sampling/WHAM approach cannot provide the absolute value of the PMF, and depends on an estimation of the baseline at large distances; however, the PMF curves for two neon atoms in water, for which both the particle-insertion and the umbrella sampling/WHAM approaches give results of comparable quality, converge at large distances, which justifies the assumption that the two- and multi-body contribution to the PMF of clusters of hydrophobic solutes tends to zero at distances beyond the solvent-separated minimum.