A theoretical analysis of rate constants and kinetic isotope effects corresponding to different reactant valleys in lactate dehydrogenase

In some enzymatic systems large conformational changes are coupled to the chemical step, in such a way that dispersion of rate constants can be observed in single-molecule experiments, each corresponding to the reaction from a different reactant valley. Under this perspective here we present a computational study of pyruvate to lactate transformation catalyzed by lactate dehydrogenase. The reaction consists of a hydride transfer and a proton transfer that seem to take place concertedly. The degree of asynchronicity and the energy barrier depend on the particular starting reactant valley. In order to estimate rate constants we used a free energy perturbation technique adapted to follow the intrinsic reaction coordinate for several possible reaction paths. Tunneling effects are also obtained with a slightly modified version of the ensemble-averaged variational transition state theory with multidimensional tunneling contributions. According to our results the closure of the active site by means of a flexible loop can lead to the formation of different reactant complexes displaying different features in the disposition of some key residues (such as Arg109), interactions with the substrate and number of water molecules in the active site. The chemical step of the reaction takes place with a different reaction rate from each of these complexes. Finally, primary kinetic isotope effects for replacement of the transferring hydrogen of the cofactor with a deuteride are in good agreement with experimental observations, thus validating our methodology.