Dynamic effects on reaction rates in a Michael addition catalyzed by chalcone isomerase. Beyond the frozen environment approach.

We present a detailed microscopic study of the dynamics of the Michael addition reaction leading from 6'-deoxychalcone to the corresponding flavanone. The reaction dynamics are analyzed for both the uncatalyzed reaction in aqueous solution and the reaction catalyzed by Chalcone Isomerase. By means of rare event simulations of trajectories started at the transition state, we have computed the transmission coefficients, obtaining 0.76 +/- 0.04 and 0.87 +/- 0.03, in water and in the enzyme, respectively. According to these simulations, the Michael addition can be seen as a formation of a new intramolecular carbon-oxygen bond accompanied by a charge transfer essentially taking place from the nucleophilic oxygen to the carbon atom adjacent to the carbonyl group (C (alpha)). As for intermolecular interactions, we find a very significant difference in the evolving solvation pattern of the nucleophilic oxygen in water and in the enzyme. While in the former medium this atom suffers an important desolvation, the enzyme provides, through variations in the distances with some residues and water molecules, an essentially constant electric field on this atom along the reaction progress. Grote-Hynes (GH) theory provides a useful framework to systematically analyze all the couplings between the reaction coordinate and the remaining degrees of freedom. This theory provides transmission coefficients in excellent agreement with the Molecular Dynamics estimations. In contrast, neither the frozen environment approach nor Kramers theory gives results of similar quality, especially in the latter case, where the transmission coefficients are severely underestimated. The (unusual) failure of the frozen environment approach signals the importance of some dynamical motions. Within the context of GH theory, analysis of the friction spectrum obtained in the enzymatic environment, together with normal-mode analysis, is used to identify those motions, of both the substrate and the environment, strongly coupled to the reaction coordinate and to classify them as dynamically active or inactive.