Flow Matching for Optimal Reaction Coordinates of Biomolecular System

TL;DR

This paper introduces flow matching for reaction coordinates (FMRC), a deep learning method that identifies optimal low-dimensional reaction coordinates for biomolecular dynamics, improving MSM construction and enhanced sampling.

Contribution

FMRC reformulates lumpability and decomposability into a probabilistic framework, enabling efficient data-driven identification of reaction coordinates without explicitly learning transfer operators.

Findings

FMRC outperforms state-of-the-art algorithms in complex biomolecular systems.

FMRC effectively encodes leading eigenfunctions of transfer operators.

FMRC enhances sampling efficiency in simple model systems.

Abstract

We present flow matching for reaction coordinates (FMRC), a novel deep learning algorithm designed to identify optimal reaction coordinates (RC) in biomolecular reversible dynamics. FMRC is based on the mathematical principles of lumpability and decomposability, which we reformulate into a conditional probability framework for efficient data-driven optimization using deep generative models. While FMRC does not explicitly learn the well-established transfer operator or its eigenfunctions, it can effectively encode the dynamics of leading eigenfunctions of the system transfer operator into its low-dimensional RC space. We further quantitatively compare its performance with several state-of-the-art algorithms by evaluating the quality of Markov state models (MSM) constructed in their respective RC spaces, demonstrating the superiority of FMRC in three increasingly complex biomolecular systems. In addition, we successfully demonstrated the efficacy of FMRC for bias deposition in the enhanced sampling of a simple model system. Finally, we discuss its potential applications in downstream applications such as enhanced sampling methods and MSM construction.