Convergence in the QM-only and QM/MM modeling of enzymatic reactions: A case study for acetylene hydratase.

We report systematic quantum mechanics-only (QM-only) and QM/molecular mechanics (MM) calculations on an enzyme-catalyzed reaction to assess the convergence behavior of QM-only and QM/MM energies with respect to the size of the chosen QM region. The QM and MM parts are described by density functional theory (typically B3LYP/def2-SVP) and the CHARMM force field, respectively. Extending our previous work on acetylene hydratase with QM regions up to 157 atoms (Liao and Thiel, J. Chem. Theory Comput. 2012, 8, 3793), we performed QM/MM geometry optimizations with a QM region M4 composed of 408 atoms, as well as further QM/MM single-point calculations with even larger QM regions up to 657 atoms. A charge deletion analysis was conducted for the previously used QM/MM model (M3a, with a QM region of 157 atoms) to identify all MM residues with strong electrostatic contributions to the reaction energetics (typically more than 2 kcal/mol), which were then included in M4. QM/MM calculations with this large QM region M4 lead to the same overall mechanism as the previous QM/MM calculations with M3a, but there are some variations in the relative energies of the stationary points, with a mean absolute deviation (MAD) of 2.7 kcal/mol. The energies of the two relevant transition states are close to each other at all levels applied (typically within 2 kcal/mol), with the first (second) one being rate-limiting in the QM/MM calculations with M3a (M4). QM-only gas-phase calculations give a very similar energy profile for QM region M4 (MAD of 1.7 kcal/mol), contrary to the situation for M3a where we had previously found significant discrepancies between the QM-only and QM/MM results (MAD of 7.9 kcal/mol). Extension of the QM region beyond M4 up to M7 (657 atoms) leads to only rather small variations in the relative energies from single-point QM-only and QM/MM calculations (MAD typically about 1-2 kcal/mol). In the case of acetylene hydratase, a model with 408 QM atoms thus seems sufficient to achieve convergence in the computed relative energies to within 1-2 kcal/mol.