Accuracy and precision of free-energy calculations via molecular simulation

A quantitative characterization of the methodologies of free-energy perturbation (FEP) calculations is presented, and optimal implementation of the methods for reliable and efficient calculation is addressed. Some common misunderstandings in the FEP calculations are corrected.; The two opposite directions of FEP calculations are uniquely defined as generalized insertion and generalized deletion, according to the entropy change along the perturbation direction. These two calculations are not symmetric; they produce free-energy results differing systematically due to the different capability of each to sample the important phase-space in a finite-length simulation.; The FEP calculation errors are quantified by characterizing the simulation sampling process with the help of probability density functions for the potential energy change. While the random error in the FEP calculation is analyzed with a probabilistic approach, the systematic error is characterized as the most-likely inaccuracy, which is modeled considering the poor sampling of low-probability energy distribution tails. Our analysis shows that the entropy difference between the perturbation systems plays a key role in determining the reliability of FEP results, and the perturbation should be carried out in the insertion direction in order to ensure a good sampling and thus a reliable calculation. Easy-to-use heuristics are developed to estimate the simulation errors, as well as the simulation length that ensures a certain accuracy level of the calculation.; The fundamental understanding obtained is then applied to tackle the problem of multistage FEP optimization. We provide the first principle of optimal staging: For each substage FEP calculation, the higher entropy system should be used as the reference to govern the sampling, i.e., the calculation should be conducted in the generalized insertion direction for each stage of perturbation. To minimize the simulation error, intermediate states should be constructed in such a way that the entropy difference Delta S between the perturbation pairs at each stage is equalized. It is found that the number of stages n leading to the most efficient calculation would satisfy DeltaS/ n = -2, where DeltaS is the total entropy change.