BAR-based optimum adaptive sampling regime for variance minimization in alchemical transformation

The efficiency of alchemical free energy simulations with the staging strategy is improved by adaptively manipulating the significance of each ensemble followed by importance sampling. The OBAR (optimum BAR) method introduced in this work with explicit consideration of the statistical inefficiency in each ensemble outperforms the traditional equal time rule which is used in standard applications of alchemical transformation with the window sampling regime in the sense of minimizing the total variance of the free energy estimate. The Time Derivative of total Variance (TDV) is proposed for the OBAR criterion which is linearly dependent on the variance and is more sensitive to the importance rank than the overlap matrix. The performance of OBAR workflow is demonstrated for solvation of several small molecules and a protein ligand binding system.