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. In this work, we develop a novel algorithm, the Memory kErnel Minimization based Neural Networks (MEMnets), that accurately identifies the slow CVs of biomolecular dynamics. MEMnets is distinct from popular deep-learning approaches (such as VAMPnets or SRVs) that assume Markovian dynamics. Instead, MEMnets is built on the integrative generalized master equation (IGME) theory, which incorporates non-Markovian dynamics by encoding them in a memory kernel for continuous CVs. The key innovation of MEMnets is to identify optimal CVs by minimizing time-integrated memory kernels. To accomplish this, MEMnets process time sequences of molecular dynamics (MD) conformations by using parallel encoder neural networks that project high-dimensional MD data into a low-dimensional latent space. The time-integrated memory kernels, derived from IGME theory, are then computed in the latent space as the objective function. We demonstrate that our MEMnets algorithm can effectively identify the slow CVs involved in the folding of FIP35 WW-domain with high accuracy, and successfully reveal two parallel folding pathways. Furthermore, we test MEMnets’ on the clamp opening of a bacterial RNA polymerase (RNAP), a much more complex conformational change (a system containing over 540K atoms), where sampling from all-atom MD simulations is limited. Our results demonstrate that MEMnets greatly outperforms SRVs, which is based on Markovian dynamics and may result in disconnected dynamics along the identified CVs. We anticipate that MEMnets holds promise to be widely to study biomolecular conformational changes.