Identification of simple reaction coordinates from complex dynamics

TL;DR

This paper proposes a method to identify simple, interpretable reaction coordinates from complex molecular dynamics by using dominant eigenfunctions of an integral operator, validated on small molecules and proteins.

Contribution

It introduces a new definition of natural reaction coordinates and a sparse estimator to find these coordinates from complex ensemble dynamics.

Findings

Successfully identifies reaction coordinates in molecular systems

Filters noise to extract meaningful reaction pathways

Applicable to both small molecules and proteins

Abstract

Reaction coordinates are widely used throughout chemical physics to model and understand complex chemical transformations. We introduce a definition of the natural reaction coordinate, suitable for condensed phase and biomolecular systems, as a maximally predictive one-dimensional projection. We then show this criterion is uniquely satisfied by a dominant eigenfunction of an integral operator associated with the ensemble dynamics. We present a new sparse estimator for these eigenfunctions which can search through a large candidate pool of structural order parameters and build simple, interpretable approximations that employ only a small number of these order parameters. Example applications with a small molecule's rotational dynamics and simulations of protein conformational change and folding show that this approach can filter through statistical noise to identify simple reaction coordinates from complex dynamics.