Hybrid ab Initio Quantum Mechanics/Molecular Mechanics Calculations of Free Energy Surfaces for Enzymatic Reactions:  The Nucleophilic Attack in Subtilisin

An effective approach for ab initio calculations of activation free energies of enzymatic reactions is developed and examined. This approach uses an empirical valence bond (EVB) potential surface as a reference potential for evaluating the free energies of a hybrid ab initio quantum mechanics/molecular mechanics (QM(ai)/MM) potential surface. This procedure involves an automated calibration of the EVB potential using gas-phase ab initio calculations. In addition, strategies for treating the contact region of QM and MM atoms as well as enzyme and solvent environments are developed. Two levels of ab initio calculations are used in studying the QM atoms: the HF/4-31G method, which allows calculations on a large number of points while still giving accurate results, and the MP2/6-31+G* approach. The QM(ai)/MM method is implemented and examined by simulating the nucleophilic attack step in the catalytic reaction of subtilisin. It is found that the use of the EVB potential as a reference allows one to obtain the actual ab initio activation free energies of enzymatic reactions. Possible powerful simplifications such as the use of the ab initio intermolecular electrostatic energy are discussed, and the advantage of focusing on the difference between the reaction in protein and solution is demonstrated.