Ion selectivity in protein binding sites is of great significance to biological functions. Although additive force fields have been successfully applied to various protein-related studies, it is difficult to well capture the subtle metal-protein interaction for the prediction of ion selectivity, due to the remarkable polarization and charge transfer effect between the metals and the surrounding residues. Quantum mechanics-based methods are well-suited for dealing with these systems, but they are too costly to apply in a direct manner. In this work, the reference-potential method (RPM) was used to measure the selectivity for calcium and magnesium cations in the binding pocket of parvalbumin B protein by calculating the free energy change associated with this substitution reaction at an ab initio quantum mechanics/molecular mechanics (QM/MM) level. The alchemical transformations were performed at the molecular mechanics level, and the relative binding free energy was then corrected to the QM/MM level via thermodynamic perturbation. In this way, the free energy change at the QM/MM level for the substitution reaction was obtained without running the QM/MM simulations, thus remarkably enhancing the efficiency. In the reweighting process, we found that the selection of the QM region greatly affects the accuracy of the QM/MM method. In particular, the charge transfer effect on the free energy change of a reaction cannot be neglected.

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