Br?nsted-Evans-Polanyi relationships for C–C bond forming and C–C bond breaking reactions in thiamine-catalyzed decarboxylation of 2-keto acids using density functional theory

The concept of generalized enzyme reactions suggests that a wide variety of substrates can undergo enzymatic transformations, including those whose biotransformation has not yet been realized. The use of quantum chemistry to evaluate kinetic feasibility is an attractive approach to identify enzymes for the proposed transformation. However, the sheer number of novel transformations that can be generated makes this impractical as a screening approach. Therefore, it is essential to develop structure/activity relationships based on quantities that are more efficient to calculate. In this work, we propose a structure/activity relationship based on the free energy of binding or reaction of non-native substrates to evaluate the catalysis relative to that of native substrates. While Br?nsted-Evans-Polanyi (BEP) relationships such as that proposed here have found broad application in heterogeneous catalysis, their extension to enzymatic catalysis is limited. We report here on density functional theory (DFT) studies for C–C bond formation and C–C bond cleavage associated with the decarboxylation of six 2-keto acids by a thiamine-containing enzyme (EC 1.2.7.1) and demonstrate a linear relationship between the free energy of reaction and the activation barrier. We then applied this relationship to predict the activation barriers of 17 chemically similar novel reactions. These calculations reveal that there is a clear correlation between the free energy of formation of the transition state and the free energy of the reaction, suggesting that this method can be further extended to predict the kinetics of novel reactions through our computational framework for discovery of novel biochemical transformations.