SGOOP-d: Estimating kinetic distances and reaction coordinate dimensionality for rare event systems from biased/unbiased simulations

TL;DR

This paper introduces SGOOP-d, a method to accurately identify low-dimensional reaction coordinates that preserve kinetic connectivity in high-dimensional systems, applicable to both biased and unbiased simulations, improving understanding of rare event dynamics.

Contribution

The work develops a formalism for learning multi-dimensional reaction coordinates that maintain kinetic connectivity, extending previous spectral gap optimization methods to biased and unbiased simulations.

Findings

Successfully applied to model systems including a small peptide.

Captured kinetics for 23 out of 28 state transitions in peptide.

Demonstrated effectiveness in preserving kinetic pathways in low-dimensional projections.

Abstract

Understanding kinetics including reaction pathways and associated transition rates is an important yet difficult problem in numerous chemical and biological systems especially in situations with multiple competing pathways. When these high-dimensional systems are projected on low-dimensional coordinates, which are often needed for enhanced sampling or for interpretation of simulations and experiments, one can end up losing the kinetic connectivity of the underlying high-dimensional landscape. Thus in the low-dimensional projection metastable states might appear closer or further than they actually are. To deal with this issue, in this work we develop a formalism that learns a multi-dimensional yet minimally complex reaction coordinate (RC) for generic high-dimensional systems. When projected along this RC, all possible kinetically relevant pathways can be demarcated and the true high-dimensional connectivity is maintained. One of the defining attributes of our method lies in that it can work on long unbiased simulations as well as biased simulations often needed for rare event systems. We demonstrate the utility of the method by studying a range of model systems including conformational transitions in a small peptide Ace-Ala$_3$-Nme, where we show how two-dimensional and three-dimensional reaction coordinate found by our previously published spectral gap optimization method "SGOOP" [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. 113, 2839 (2016)] can capture the kinetics for 23 and all 28 out of the 28 dominant state-to-state transitions respectively.