Calculation of collective variable-based PMF by combining WHAM with umbrella sampling

Potential of mean force (PMF) with respect to localized reaction coordinates (RCs) such as distance is often applied to evaluate the free energy profile along the reaction pathway for complex molecular systems. However, calculation of PMF as a function of global RCs is still a challenging and important problem in computational biology. We examine the combined use of the weighted histogram analysis method and the umbrella sampling method for the calculation of PMF as a function of a global RC from the coarse-grained Langevin dynamics simulations for a model protein. The method yields the folding free energy profile projected onto a global RC, which is in accord with benchmark results. With this method rare global events would be sufficiently sampled because the biased potential can be used for restricting the global conformation to specific regions during free energy calculations. The strategy presented can also be utilized in calculating the global intra- and intermolecular PMF at more detailed levels.