Adapting the nudged elastic band method for determining minimum-energy paths of chemical reactions in enzymes

Abstract

Optimization of reaction paths for enzymatic systems is a challenging problem because such systems have a very large number of degrees of freedom and many of these degrees are flexible. To meet this challenge, an efficient, robust and general approach is presented based on the well-known nudged elastic band reaction path optimization method with the following extensions: (1) soft spectator degrees of freedom are excluded from path definitions by using only inter-atomic distances corresponding to forming/breaking bonds in a reaction; (2) a general transformation of the distances is defined to treat multistep reactions without knowing the partitioning of steps in advance; (3) a multistage strategy, in which path optimizations are carried out for reference systems with gradually decreasing rigidity, is developed to maximize the opportunity of obtaining continuously changing environments along the path. We demonstrate the applicability of the approach using the acylation reaction of type A beta-lactamase as an example. The reaction mechanism investigated involves four elementary reaction steps, eight forming/breaking bonds. We obtained a continuous minimum energy path without any assumption on reaction coordinates, or on the possible sequence or the concertedness of chemical events. We expect our approach to have general applicability in the modeling of enzymatic reactions with quantum mechanical/molecular mechanical models.

Exploring chemical reaction mechanisms through harmonic Fourier beads path optimization

“…2 could disrupt continuity of the path and of the energy profile. 57,62,63 The combined CG-HFB method performed well with respect to the soft degrees of freedom. The only problem that we found due to the soft degrees of freedom was the occasional excursions of the path to sample the methyl rotations in the early stages of path optimization (see supplementary material 64 ).…”

“…This issue was addressed by imposing positional restraints on the soft degrees of freedom. 57 During the path optimization, the force constants of the restraints were gradually reduced while keeping their anchoring positions unchanged.…”

Free Energies of Chemical Reactions in Solution and in Enzymes with Ab Initio Quantum Mechanics/Molecular Mechanics Methods

“…As an alternative, a quadratic string method (QSM) was developed in our laboratory which has been shown to yield better performance than the NEB method [75]. It has also been found that for large systems it is often important to select a small subset of coordinates as the chemical metric to define the path length for properly positioning the states along the reaction path [76].…”

Sampling reactive pathways with random walks in chemical space: Applications to molecular dissociation and catalysis

“…This wide variety of reaction-path-finding methods has been employed to model a similarly wide variety of chemical processes; representative examples include rearrangements in molecular clusters, 37 metal-catalyzed hydroformylation reactions, 47 protein folding problems, 40,48 and enzyme-catalyzed reactions. 49 Furthermore, these examples demonstrate that such approaches are readily applied to model chemical reaction paths in both gaseous and (implicit or explicit) condensed-phase systems.…”