QM/MM Free-Energy Perturbation Compared to Thermodynamic Integration and Umbrella Sampling: Application to an Enzymatic Reaction

We used the free-energy perturbation (FEP) method in quantum mechanics/molecular mechanics (QM/MM) calculations to compute the free-energy profile of the hydroxylation reaction in the enzyme p-hydroxybenzoate hydroxylase (PHBH). k statistics were employed to analyze the FEP sampling including estimation of the sampling error. Various approximations of the free-energy perturbation method were tested. We find that it is adequate not only to freeze the density of the QM part during the dynamics at frozen QM geometry but also to approximate this density by electrostatic-potential-fitted point charges. It is advisable to include all atoms of a QM/MM link in the perturbation. The results of QM/MM-FEP for PHBH are in good agreement with those of thermodynamic integration and umbrella sampling.