Free energy change estimation: The Divide and Conquer MBAR method

In the present study, the Divide and Conquer MBAR (DC-MBAR) method is proposed to predict the free energies based on the data sampled by multi-states simulations. For DC-MBAR method, the overlap between any two alchemical states is calculated first and those with sufficient overlap are defined as the adjacent states. Unlike the traditional MBAR method, which calculates the free energy of each state using all the data at once, DC-MBAR focuses on predicting the free energy changes between adjacent states. To estimate the free energy changes accurately, the other states with overlaps with the two adjacent states bigger than the defined threshold are included in the MBAR equation. At a specific threshold, the free energies predicted by DC-MBAR are very close to those calculated by the traditional MABR method. Furthermore, DC-MBAR scheme can reduce both the computation and memory cost. One important characteristic of DC-MBAR method is linear scaling, which means the CPU time with the change of the number of states is a straight-line relation. As the pair-based calculations are mutually independent and parallelizable, all accessible CPU cores on the HPC cluster could be utilized, which makes DC-MBAR strategy more efficient.