Finite-temperature effects in enzymatic reactions — Insights from QM/MM free-energy simulations

Abstract

We report potential-energy and free-energy data for three enzymatic reactions: carbon–halogen bond formation in fluorinase, hydrogen abstraction from camphor in cytochrome P450cam, and chorismate-to-prephenate Claisen rearrangement in chorismate mutase. The results were obtained by combined quantum mechanics/molecular mechanics (QM/MM) optimizations and two types of QM/MM free-energy simulations (free-energy perturbation and umbrella sampling) using semi-empirical or density-functional QM methods. Based on these results and our previously published free-energy data on electrophilic substitution in para-hydroxybenzoate hydroxylase, we discuss the importance of finite-temperature effects in the chemical step of enzyme reactions. We find that the entropic contribution to the activation barrier is generally rather small, usually of the order of 5 kJ mol–1 or less, consistent with the notion that enzymes bind and pre-organize the reactants in the active site. A somewhat larger entropic contribution is encountered in the case of chorismate mutase where the pericyclic transition state is intrinsically more rigid than the chorismate reactant (also in the enzyme). The present results suggest that barriers from QM/MM geometry optimization may often be close to free-energy barriers for the chemical step in enzymatic reactions.

A Theoretical Study of the Benzoylformate Decarboxylase Reaction Mechanism

“…The constraints that are imposed in the model introduce small imaginary frequencies in the calculations, all of them under 50 i cm −1 . Although it has been demonstrated that entropy only has a small effect on the energies of the chemical step of enzyme reactions (Senn et al, 2005 , 2009 ; Hu and Zhang, 2006 ; Lonsdale et al, 2012 ; Kazemi et al, 2016 ; Mulholland, 2016 ), its contribution must be considered in the case of a release of a gas molecule, which is relevant for the CO 2 release considered in the current study. In line with previous studies (Blomberg and Siegbahn, 2012 ; Lind and Himo, 2014 ; Sheng et al, 2015 , 2017 ), the entropy gain can be estimated as the translational entropy for the gas molecule (calculated to 11.3 kcal/mol), which is added at all steps after the transition state of CO 2 formation.…”

Computational Understanding of the Selectivities in Metalloenzymes

“…As a compromise, a relatively smaller QM region and cheaper method, such as the semi-empirical methods and DFT functionals with double-zeta quality basis sets, are commonly used. Importantly, Senn et al have shown that the differences between QM/MM electronic energy and free energy profiles are quite small in the study of local chemical events (Senn et al, 2009).…”

Stepwise Synthesis of Siloxane‐Substituted Oligoarsanes and Structural Investigation of Alkaline Earth Metal Derivatives

“…Localized reactions that do not involve large‐scale rearrangements of the whole protein, such as the ones discussed here, are well‐suited for the approach of reducing the number of degrees of freedom in the geometry optimization by freezing a large part of the model. These typically also show only a negligible contribution of the entropy to the chemical step 46. However, other cases like the ribosome discussed previously24 require much larger active regions.…”