Mechanisms and free energies of enzymatic reactions.

Most enzymatic reactions have very large and remarkably similar apparent second-order rate constants, kcat/KM, at mean values of about 107 M−1 s−1 with kcat in the range of 10–1000 s−1.1–3 In fact, many reactions approach the diffusional encounter rate at the limited enzyme concentration (<10−5 M) in the cell.4 Wolfenden illustrated the catalytic power of enzymes by comparing the rate constant of the catalyzed reaction with that of the same reaction in the absence of the enzyme in aqueous solution, kaq.2,5 Evidently, the most proficient enzymes are those catalyzing the slowest spontaneous reactions, such as the hydrolysis of glycosides and phosphate esters and the decarboxylation reactions of amino acids and of orotidine 5′-monophosphate (OMP), as catalyzed by OMP decarboxylase (ODC).2 In the latter case, the unimolecular rate constant of the spontaneous decarboxylation of OMP is accelerated (kcat/kaq) by 17 orders of magnitude in the active site of ODC.5,6 This reaction also has the distinction of being among the most proficient enzymes in catalyzing reactions without the involvement of cofactors. Significantly, Wolfenden’s experimental approach has been followed and paralleled in computational studies.7 The experiments, along with computational results that we review in this article, provide abundant evidence that the very large observed reductions of the free energy of activation can be achieved through the strong synergism of enzyme and substrate interactions “using ordinary noncovalent forces of attraction”,8 although in other cases enzyme catalysis may involve covalent intermediates9 or a change in reaction mechanism as compared to aqueous solution. Noncovalent attractive forces are mainly electrostatic in nature; they include ion pair interactions, hydrogen bonding, and electronic polarization. The competition between solvent–solvent and solvent–solute interactions contributes to hydrophobic effects (where the “solute” is the substrate or any part of the protein or a coenzyme that participates in the reaction coordinate and the “solvent” is water, spectator residues of the enzyme in the active site, and faraway parts of the protein or protein complex). These interactions all contribute to catalysis. It has been argued insightfully that electrostatic preorganization effects are a key source of enzyme catalysis,10 but the questions remain of what other factors contribute and how preorganization is arranged such that the transition state is stabilized preferentially to the reactant state. To understand enzyme catalysis and mechanism, it is necessary, and often challenging, to elucidate the unique ways in which each enzyme exerts electrostatic and other forces on the substrate and the transition state. In the past 10 years, many computational studies of enzymatic reactions have been carried out, combining quantum mechanical, classical mechanical, and statistical mechanical techniques, coupled with advances in protein structure determination, site-directed mutagenesis, and fast computers and algorithms. All computational studies of atomic scale dynamics must begin with a potential energy surface, and the most promising approach to calculating this surface is to treat the enzyme active site by electronic structure methods11–19 that include the electronic polarization of the reactive species by the dynamical fluctuations of the enzyme–solvent environment through effective sampling of the enzyme conformational space. Although a review necessarily involves only a very limited selection of the reactions that enzymes catalyze in the cell, we can nevertheless conclude7 that each enzyme has its unique characteristics, and enzymes use all possible means to achieve the ultimate objective of reducing the free energy of activation. In addition to providing an enormous rate acceleration, enzymes exercise precise control over the regio- and stereochemistry of the reactions that they catalyze, an aspect of enzyme catalysis that has received relatively little attention in computations (recent studies of triosephosphate isomerase and glyoxal synthase provide a noteworthy exception20). This control is perhaps best illustrated by the reactions catalyzed by terpenoid synthases,21 a large group of enzymes that transform a limited number of linear substrates such as geranyl diphosphate (C10), farnesyl diphosphate (C15), and geranylgeranyl diphosphate (C20) to tens of thousands natural products with a variety of rings and stereocenters, presumably by prefolding the same substrate to a “proper” conformation in the unique binding pocket of each enzyme and subsequently preventing the highly reactive carbocation intermediates from undergoing side reactions and preventing premature terminations of the catalyzed reaction sequences. Both experimental and computational studies appear to point to an important role for the balance of thermodynamic and kinetic factors along the cyclization cascade.22,23 Thus, it is of great interest not only to understand the origin of the enormous catalytic power of enzymes that they achieve by lowering the free energy of activation but also to characterize the detailed mechanism of enzyme actions that control each reaction step and provide the desired regio- and stereospecificity. In this review, we summarize computational studies of the mechanisms and free energies of selected enzymatic reactions. We first highlight computational approaches for enzymatic reactions, with special emphasis on two key elements that affect the computational accuracy, namely, the potential energy function and statistical mechanical sampling of the enzyme system. The potential energy functions may be based on quantum mechanical models, or they may be based on molecular mechanics force fields. In either case, to achieve the required accuracy to understand catalysis, it is essential to parametrize and validate the potential energy functions (or, equivalently, the methods used to calculate them) against model reactions and specific hydrogen bonding interactions in the gas phase. Only when the performance of the potential functions on the intrinsic reactivity of the chemical reactions has been justified can one begin to address the key questions of solvent effects and enzyme catalysis through molecular dynamics and free energy simulations. We then discuss a third element, namely, the choice of the reaction coordinate for determining the free energy of activation to characterize the mechanism of enzymatic processes. Then, we illustrate a variety of factors that have been found to contribute to catalysis in specific enzymatic reactions by lowering the free energy of activation relative to that for the uncatalyzed process in aqueous solution. Finally, we provide a summary of the major conclusions.