Automated Umbrella Sampling Simulations for the Calculation of Multidimensional Potentials of Mean Force

Abstract

The potential of mean force (PMF) describing the conformational changes of biomolecules is a central quantity that determines the function of biomolecular systems. Calculating a multidimensional PMF (free energy landscape) is a time consuming process. Each additional reaction coordinate drastically increases the required simulation time for conformation sampling, making calculations in four or more dimensions practically impossible. However, in most cases, only a small fraction of such multidimensional space is energetically relevant. PMF calculations in high dimensionality could thus be achieved if one could effectively focus the simulation effort on those region of high interest. We have developed a method based on umbrella sampling (US) that determines, using a feedback mechanism, which regions of the multidimensional space is worth exploring. The first aim of such application is to manage the creation and analysis of sampling windows for the calculation of PMFs involving up to four reaction coordinates. While this approach could in some cases be used to find the minimum free energy pathway underlying large conformational changes, it is not as general as other approaches that were specifically developed in that purpose. However, contrary to most other approaches, our method allows for the simultaneous characterization of several pathways, and not only the most probable one. The current implementation consists in a C++ application with a python interface that manages MD simulations performed with the biomolecular simulation program CHARMM. The feedback mechanism and final PMF calculation involves the unbiasing of simulations using the weighted-histogram analysis methods (WHAM).