"Non-markovian Dynamic Models for Studying Protein Conformational Changes"
Abstract: Protein’s dynamic transitions between metastable conformational states play an important role in numerous biological processes. Markov State Model (MSM) built from molecular dynamics (MD) simulations provides a useful approach to study these complex dynamic transitions, but it is challenging to build truly Markovian models due to the limited length of lag time (bound by the length of relatively short MD simulations). In this talk, I will introduce our recent work on developing non-Markovian dynamic models based on the Generalized Master Equation (GME) theory that encodes the dynamics in a generally time-dependent memory kernel, whose characteristic decay time scale corresponds to the kernel lifetime. We show that GME methods can greatly improves upon Markovian models by accurately predicting long timescale dynamics using much shorter MD trajectories on complex conformational changes. I will also introduce our Integrative GME (IGME) based on the time integrated memory kernels to avoid huge numerical instability in the memory kernel tensor. In IGME, the analytical solution of GME when the memory kernels have decayed to zero is derived. Based on the analytical solution, the IGME can achieves significantly smaller fluctuations for both memory kernels and long-time dynamics. Finally, I will also present our newly developed algorithm, the Memory Kernel Minimization based Neural Networks (MEMnets), which can accurately identify the slow CVs of biomolecular dynamics. Our MEMnets algorithm is distinct from popular deep-learning approaches, such as VAMPnet and SRVnet, which assume Markovian dynamics. Instead, MEMnets is built on the GME theory. Its key innovation is the development of a novel loss function that corresponds to the integrals of memory kernels. By optimizing this loss function in encoder deep-neural networks, we demonstrate that our MEMnets algorithm can effectively identify the slow CVs involved in the folding of the FIP35 WW-domain with high accuracy. Furthermore, we tested MEMnets on a more complex conformational change, specifically the clamp opening of a bacterial RNA polymerase (a system consisted of over 540K atoms), where the sampling from all-atom MD simulations is limited. We expect that the GME-based methods hold promise to be widely applied to study functional dynamics of proteins.