The potential of mean force (PMF) is by construction the potential that reproduces the mean force when calculating the negative gradient.
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General description
The PMF can be obtained in Monte Carlo or Molecular Dynamics simulations which examines how a system's energy changes as a function of some specific reaction coordinate parameter. For example, it may examine how the system's energy changes as a function of the distance between two residues, or as a protein is pulled through a lipid bilayer. It can be a geometrical coordinate or a more general energetic (solvent) coordinate. Often PMF simulations are used in conjunction with umbrella sampling because typically the PMF simulation will fail to adequately sample the system space as it proceeds.
Mathematical description
The Potential of Mean Force of a system with N particles is by construction the potential that gives the average force over all the configurations of all the n+1...N particles acting on a particle j at any fixed configuration keeping fixed a set of particles 1...n
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Application
The potential of mean force