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. These include crystal nucleation, protein folding and many others. When these high-dimensional systems are projected on low-dimensional coordinates often needed for enhanced sampling or analysis of trajectories, one often ends 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. In this work, we develop a formalism that learns a multi-dimensional yet minimally complex reaction coordinate (RC) for generic high-dimensional systems such that all possible kinetically relevant pathways can be demarcated and the true high-dimensional connectivity is maintained. The central idea is to calculate the interconversion times between different pairs of metastable states and monitor how they change by adding additional dimensions to the RC, stopping when the interconversion times do not vary with additional RC components. The interconversion times themselves are constructed by combining the Commute Map formalism of Noé, Banisch and Clementi, J. Chem. Theor. Comp. 2016, with the ``Spectral Gap Optimization of Order Paramaters (SGOOP)", Tiwary and Berne, PNAS 2016. This amounts to inducing a distance metric, which we call ``SGOOP-d" that preserves kinetically truthfulness in the underlying high-dimensional landscape. Our method works on long unbiased simulations as well as biased simulations which are 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.

SGOOP-d: Estimating commute distances and interconversion times for rare event systems

ACS Fall 2021

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