Comment on "Toward identification of the reaction coordinate directly from the transition state ensemble using the kernel PCA method"

Quantifying the limits of transition state theory in enzymatic catalysis

While being one of the most popular reaction rate theories, the applicability of transition state theory to the study of enzymatic reactions has been often challenged. The complex dynamic nature of the protein environment raised the question about the validity of the nonrecrossing hypothesis, a cornerstone in this theory. We present a computational strategy to quantify the error associated to transition state theory from the number of recrossings observed at the equicommittor, which is the best possible dividing surface. Application of a direct multidimensional transition state optimization to the hydride transfer step in human dihydrofolate reductase shows that both the participation of the protein degrees of freedom in the reaction coordinate and the error associated to the nonrecrossing hypothesis are small. Thus, the use of transition state theory, even with simplified reaction coordinates, provides a good theoretical framework for the study of enzymatic catalysis.

Reaction coordinates, one-dimensional Smoluchowski equations, and a test for dynamical self-consistency

We propose a method for identifying accurate reaction coordinates among a set of trial coordinates. The method applies to special cases where motion along the reaction coordinate follows a one-dimensional Smoluchowski equation. In these cases the reaction coordinate can predict its own short-time dynamical evolution, i.e., the dynamics projected from multiple dimensions onto the reaction coordinate depend only on the reaction coordinate itself. To test whether this property holds, we project an ensemble of short trajectory swarms onto trial coordinates and compare projections of individual swarms to projections of the ensemble of swarms. The comparison, quantified by the Kullback-Leibler divergence, is numerically performed for each isosurface of each trial coordinate. The ensemble of short dynamical trajectories is generated only once by sampling along an initial order parameter. The initial order parameter should separate the reactants and products with a free energy barrier, and distributions on isosurfaces of the initial parameter should be unimodal. The method is illustrated for three model free energy landscapes with anisotropic diffusion. Where exact coordinates can be obtained from Kramers-Langer-Berezhkovskii-Szabo theory, results from the new method agree with the exact results. We also examine characteristics of systems where the proposed method fails. We show how dynamical self-consistency is related (through the Chapman-Kolmogorov equation) to the earlier isocommittor criterion, which is based on longer paths.

Toward the mechanism of ionic dissociation in water

We investigate the solvent effects leading to dissociation of sodium chloride in water. Thermodynamic analysis reveals dissociation to be driven energetically and opposed entropically, with the loss in entropy due to an increasing number of solvent molecules entering the highly coordinated ionic solvation shell. We show through committor analysis that the ion–ion distance is an insufficient reaction coordinate, in agreement with previous findings. By application of committor analysis on various constrained solvent ensembles, we find that the dissociation event is generally sensitive to solvent fluctuations at long ranges, with both sterics and electrostatics of importance. The dynamics of the reaction reveal that solvent rearrangements leading to dissociation occur on time scales from 0.5 to 5 ps or longer, and that, near the transition state, inertial effects enhance the reaction probability of a given trajectory.