Multidimensional Potentials of Mean Force from Biased Experiments along a Single Coordinate

Abstract

External biasing forces are often applied to enhance sampling in regions of phase space which would otherwise be rarely observed. While the typical goal of these experiments is to calculate the potential of mean force (PMF) along the biasing coordinate, here I present a method to construct PMFs in multiple dimensions and along arbitary alternative degrees of freedom. A protocol for multidimensional PMF reconstruction from nonequilibrium single-molecule pulling experiments is introduced and tested on a series of two-dimensional potential surfaces with varying levels of correlation. Reconstruction accuracy and convergence from several methods--this new protocol, equilibrium umbrella sampling, and free diffusion--are compared, and nonequilibrium pulling is found to be the most efficient. To facilitate the use of this method, the source code for this analysis is made freely available.