Computation of kinetic isotope effects for enzymatic reactions.

We describe a computational approach, incorporating quantum mechanics into enzyme kinetics modeling with a special emphasis on computation of kinetic isotope effects. Two aspects are highlighted: (1) the potential energy surface is represented by a combined quantum mechanical and molecular mechanical (QM/MM) potential in which the bond forming and breaking processes are modeled by electronic structure theory, and (2) a free energy perturbation method in path integral simulation is used to determine both kinetic isotope effects (KIEs). In this approach, which is called the PI-FEP/UM method, a light (heavy) isotope is mutated into a heavy (light) counterpart in centroid path integral simulations. The method is illustrated in the study of primary and secondary KIEs in two enzyme systems. In the case of nitroalkane oxidase, the enzymatic reaction exhibits enhanced quantum tunneling over that of the uncatalyzed process in water. In the dopa delarboxylase reaction, there appears to be distinguishable primary carbon-13 and secondary deuterium KIEs when the internal proton tautomerism is in the N-protonated or in the O-protonated positions. These examples show that the incorporation of quantum mechanical effects in enzyme kinetics modeling offers an opportunity to accurately and reliably model the mechanisms and free energies of enzymatic reactions.