Combine Umbrella Sampling with Integrated Tempering Method for Efficient and Accurate Calculation of Free Energy Changes of Complex Energy Surface

Umbrella sampling is an efficient method for the calculation of free energy changes of a system along well-defined reaction coordinates. However, when multiple parallel channels along the reaction coordinate or hidden barriers in directions perpendicular to the reaction coordinate exist, it is difficult for conventional umbrella sampling methods to generate sufficient sampling within limited simulation time. Here we propose an efficient approach to combine umbrella sampling with the integrated tempering sampling method. The umbrella sampling method is applied to conformational degrees of freedom which possess significant barriers and are chemically more relevant. The integrated tempering sampling method is employed to facilitate the sampling of other degrees of freedom in which statistically non-negligible barriers may exist. The combined method is applied to two model systems and show significantly improved sampling efficiencies as compared to standalone conventional umbrella sampling or integrated tempering sampling approaches. Therefore, the combined approach will become a very efficient method in the simulation of biomolecular processes which often involve sampling of complex rugged energy landscapes.