A protocol to obtain multidimensional quantum tunneling corrections derived from QM(DFT)/MM calculations for an enzyme reaction

Abstract

The significance of tunneling contributions to the rate constants of enzymatic reactions has been described at length using experimental evidence as well as theoretical computations. Within the frame of variational transition state theory (VTST), tunneling corrections are included using the so-called ground-state tunneling transmission coefficient. For the calculation of those enzymatic rate constants using the ensemble-averaged extension of VTST on QM/MM potential energy surfaces, the transmission coefficient at a given temperature is averaged over a set of coefficient values, each one obtained from an individual minimum energy path (MEP). However, the calculation of accurate QM/MM MEPs for tunneling calculations, also using a reliable QM method like DFT, is highly costly in enzyme models. For this reason, more affordable methodologies have been used. In this paper, we validate a feasible computational strategy to compute multidimensional tunneling corrections that describes better than cheaper alternatives the physics of the hydrogen abstraction from linoleic acid catalyzed by the enzyme 15-rLOX-1. Our recommendations to obtain better values of kinetic isotope effects and, especially, of rate constants are based on multidimensional small-curvature tunneling (SCT) coefficients derived from electrostatic embedding QM(DFT)/MM MEPs. The MEPs used must be calculated with a small enough step-size. Also, the number of gradients and Hessians along the reaction path must be checked to cover the whole tunneling region and to obtain converged adiabatic potential energy profiles. Distinguished reaction coordinates (DCPs) that are commonly used to describe enzyme reaction mechanisms are not adequate for tunneling calculations in such biological systems.