Proton Transfer at Metal Sites in Proteins Studied by Quantum Mechanical Free-Energy Perturbations

Catalytic metal sites in enzymes frequently have second-sphere carboxylate groups that neutralize the charge of the site and share protons with first-sphere ligands. This gives rise to an ambiguity concerning the position of this proton, which has turned out to be hard to settle with experimental, as well as theoretical, methods. We study three such proton-transfer reactions in two proteins and show that, in [Ni,Fe] hydrogenase, the bridging Cys-546 ligand is deprotonated by His-79, whereas in oxidized copper nitrite reductase, the His-100 ligand is neutral and the copper-bound water molecule is deprotonated by Asp-98. We show that these reactions strongly depend on the electrostatic interactions with the surrounding protein and solvent, because there is a large change in the dipole moment of the active site (2-6 D). Neither vacuum quantum mechanical (QM) calculations with large models, a continuum solvent, or a Poisson-Boltzmann treatment of the surroundings, nor combined QM and molecular mechanics (QM/MM) optimizations give reliable estimates of the proton-transfer energies (mean absolute deviations of over 20 kJ/mol). Instead, QM/MM free-energy perturbations are needed to obtain reliable estimates of the reaction energies. These calculations also indicate what interactions and residues are important for the energy, showing how the quantum system may be systematically enlarged. With such a procedure, results with an uncertainty of ∼10 kJ/mol can be obtained, provided that a proper QM method is used.