Memory kernel minimization-based neural networks for discovering slow collective variables of biomolecular dynamics

Identifying collective variables (CVs) that accurately capture the slowest timescales of protein conformational changes is crucial to comprehend numerous biological processes. Here we introduce memory kernel minimization-based neural networks (MEMnets), a deep learning framework that accurately identifies the slow CVs of biomolecular dynamics. Unlike popular CV-identification methods, which typically assume Markovian dynamics, MEMnets is built on the integrative generalized master equation theory, which incorporates non-Markovian dynamics by encoding them in a memory kernel for continuous CVs. The key innovation of MEMnets is the identification of optimal CVs by minimizing the upper bound for the time-integrated memory kernels through parallel encoder networks. We demonstrate that MEMnets effectively identifies slow CVs involved in the folding of the FIP35 WW domain, revealing two parallel folding pathways. In addition, we illustrate MEMnets' robust numerical stability in identifying meaningful CVs in large biomolecular dynamic systems with limited sampling by applying it to the clamp opening of bacterial RNA polymerase, a much more complex conformational change.