Potential of Mean Force Calculation Using Non-Uniform Sampling Windows for Optimal Computational Efficiency

Free energy calculation in molecular simulation is an computationally expensive process. Umbrella sampling (US) is a go-to method for obtaining the potential of mean force (PMF) along a reaction coordinate. Its computational cost increases drastically as the molecular system gets more complex. For many polymeric and biomolecular systems, adequately sampling all configurational degrees of freedom is computationally prohibitive. Using the adsorption of a short-chain methylcellulose on a cellulose crystalline surface as the test case, we show that the sampling time required for reliable results is much higher than typical choices made in the literature. The accuracy of the PMF profile is strongly affected by sampling inadequacy in a few regions along the reaction coordinate. We propose to use non-uniform windows and sampling parameters to enhance the sampling in difficult regions. Sampling windows that vary with the local PMF steepness are allocated with a new algorithm. Parameters in this algorithm are optimized for best sampling efficiency. We demonstrate that significantly less computer time would be required to achieve the same sampling accuracy if computational resources are optimally distributed along the reaction coordinate.