Building insightful, memory-enriched models to capture long-time biochemical processes from short-time simulations

Abstract

The ability to predict and understand the complex molecular motions occurring over diverse timescales ranging from picoseconds to seconds and even hours occurring in biological systems remains one of the largest challenges to chemical theory. Markov State Models (MSMs), which provide a memoryless description of the transitions between different states of a biochemical system, have provided numerous important physically transparent insights into biological function. However, constructing these models often necessitates performing extremely long molecular simulations to converge the rates. Here we show that by incorporating memory via the time-convolutionless generalized master equation (TCL-GME) one can build a theoretically transparent and physically intuitive memory-enriched model of biochemical processes with up to a three orders of magnitude reduction in the simulation data required while also providing a higher temporal resolution. We derive the conditions under which the TCL-GME provides a more efficient means to capture slow dynamics than MSMs and rigorously prove when the two provide equally valid and efficient descriptions of the slow configurational dynamics. We further introduce a simple averaging procedure that enables our TCL-GME approach to quickly converge and accurately predict long-time dynamics even when parameterized with noisy reference data arising from short trajectories. We illustrate the advantages of the TCL-GME using alanine dipeptide, the human argonaute complex, and FiP35 WW domain.

Memory unlocks the future of biomolecular dynamics: Transformative tools to uncover physical insights accurately and efficiently

“…37) or both first-and secondorder time derivatives (as in Ref. 87) of the TPMs and we demonstrated that these approaches accurately predict the intermediate-and long-time dynamics of alanine dipeptide, a system small enough to affordably converge the underlying reference dynamics. However, obtaining converged TPMs becomes formidably challenging as we tackle larger biological systems such as FiP35 WW Domain, RNAP, and the human argonaute complex.…”

“…We have recently employed the root mean square error (RMSE) to identify these parameters. 36,37,86,87 Specifically, we define the RMSE between the reference (MD) dynamics E(t) and the predicted dynamics P(t; τ x ) to be…”

“…While the qMSM has already demonstrated the ability to significantly reduce the amount of MD data required to predict the long-time conformational dynamics of systems ranging from alanine dipeptide and the FiP35 WW domain, 37 to the human argonaute complex 86 and RNA polymerase, 36 construction of the memory kernel can be challenging, 87,120 its truncation can be susceptible to statistical noise associated with limited simulation data, and its interpretation eludes the simple states-and-rates framework that renders MSMs conceptually transparent and straightforward. Below we introduce two recently developed methods to address these problems which demonstrate great potential in leveraging memory to capture the long-timescale biomolecular dynamics.…”

Integrative Generalized Master Equation: A Theory to Study Long-timescale Biomolecular Dynamics via the Integrals of Memory Kernels

“…We anticipate that IGME may be numerically more robust than the existing implementation of HMM, because IGME is fitted to several TPMs at lag times longer than 𝜏 " while HMM maximizes the likelihood function defined by entire input trajectories 60 . Recently, the time convolutionless GME (TCL-GME) 61 has been developed and it is shown that the rate matrix (𝑅(𝑡)) becomes time invariant when the lag time is longer than a characteristic time. This is also consistent with our IGME theory.…”

Integrative Generalized Master Equation: A Theory to Study Long-timescale Biomolecular Dynamics via the Integrals of Memory Kernels

“…We anticipate that IGME may be numerically more robust than the existing implementation of HMM, because IGME is fitted to several TPMs at lag times longer than 𝜏 " while HMM maximizes the likelihood function defined by entire input trajectories 57 . Recently, the time convolutionless GME (TCL-GME) 58 has been developed and it is shown that the rate matrix (𝑅(𝑡)) becomes time invariant when the lag time is longer than a characteristic time. This is also consistent with our IGME theory.…”