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Learning from molecular dynamics trajectory ensembles

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Molecular dynamics (MD) is a powerful computational tool with applications ranging from chemical reactions, to phase transitions, to biomolecular conformational changes. However, in practice, MD is far from fulfilling this promise due to exceedingly long simulation times caused by high free energy barriers, also known as the rare event problem. One can overcome this problem using enhanced sampling. This requires knowledge of the reaction coordinate (RC): the principal collective variable or feature that determines the progress along an activated or reactive process. A good RC is crucial for generating sufficient statistics with enhanced sampling. Moreover, the RC provides invaluable atomistic insight in the process under study. The optimal RC is the committor, which can be computed with brute force MD, or more efficiently by e.g. Transition Path Sampling (TPS). Novel schemes for TPS using reinforcement learning can now effectively map the committor function. The interpretability of the committor, being a high dimensional function, remains very low. Applying dimensionality reduction can reveal the RC in terms of low-dimensional human understandable molecular collective variables (CVs) or order parameters. Here, I discuss several methods to perform this dimensionality reduction [1]. In the second part, I focus on a general framework of imposing known rate constants as constraints in molecular dynamics simulations, based on a combination of the maximum-entropy (MaxEnt) and maximum-caliber principles (MaxCal). Starting from an existing ensemble of (rare event) dynamical trajectories or paths, e.g. obtained from TPS , each path is reweighted in order to match the calculated and experimental interconversion rates of a molecular transition of interest, while minimally perturbing the prior path distribution [2]. This kinetically corrected ensemble of trajectories leads to improved structure, kinetics and thermodynamics. One also learns mechanistic insight that may not be readily evident directly from the experiments. This method does not alter the Hamiltonian directly, and therefore we recently proposed a novel MaxCal-based path-reweighting technique to optimize parameters in the molecular model itself, while constraining kinetic observables [3]. This opens up the possibility to design molecular models that lead to desired kinetic behaviour.

[1] M. Frassek, A. Arjun, and P. G. Bolhuis, J. Chem. Phys. 155, 064103 (2021). [2] Z. F. Brotzakis, M. Vendruscolo, and P. G. Bolhuis, Proc. Natl. Acad. Sci. 118, (2021). [3] P. G. Bolhuis, Z. F. Brotzakis, and B. G. Keller, J. Chem. Phys. 159, 074102 (2023) .

This talk is part of the Theory - Chemistry Research Interest Group series.

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