Hi everyone,
Attached to this post is a script to calculate the Potential of Mean Force (PMF) with Forcite using the Weighted Histogram Analysis Method (WHAM, [1]) and/or the Umbrella Integration method [2].
The PMF is calculated for the center of a molecule, between given begin- and end-points. The path is divided into a number of steps (or “windows”). For each window a molecular dynamics simulation is run, in which the molecular center is restrained to a fixed point (anchor) on the path. The restraint acts as an umbrella potential. The histogram of the distance from the anchor point, projected along the reaction coordinate is evaluated for each window.
On completion, the histograms can be analyzed in two ways: in WHAM the histograms are reweighted to construct a histogram that spans the entire reaction coordinate interval. The PMF then follows as the logarithm of the overall histogram. In the Umbrella Integration method, the mean force is evaluated using a Gaussian approximation to each histogram, and the PMF is obtained through integration of the mean force.
Example output is included for aspartame approaching the {1 0 4} face of calcite, in water. This run was performed without analysis; you can run an analysis by setting the analysis flag(s) to TRUE and setting the \\\$doc parameter to the location of the study table. Running the analysis creates additional columns and sheets in the study table, without repeating the umbrella sampling.
You can launch the script as a normal Script job, or as a User Command. To use the latter method, import the provided PotentialOfMeanForce.xml (Tools | Scripting | Library... | User Menu | Import) and point to the script. You can now launch the job via User | PotentialOfMeanForce.
Hope this is of use to someone!
Reinier
[1] Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swendsen, R. H.; and Kollman, P. A., “The weighted histogram analysis method for free‐energy calculations on biomolecules. I. The method”, J. Comput. Chem., 13, 1011-1021 (1992). https://doi.org/10.1002/jcc.540130812 [2] Kästner, J.; Thiel, W., “Bridging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: Umbrella integration", J. Chem. Phys., 123, 144104 (2005). https://doi.org/10.1063/1.2052648
