  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.
