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  • 1
    Publication Date: 2021-12-23
    Description: Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long-timescale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large lengthscales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time- and lengthscales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B 〈--〉 C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.
    Language: English
    Type: article , doc-type:article
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  • 2
    Publication Date: 2022-12-05
    Description: In this paper, we consider the eigenvalue PDE problem of the infinitesimal generators of metastable diffusion processes. We propose a numerical algorithm based on training artificial neural networks for solving the leading eigenvalues and eigenfunctions of such high-dimensional eigenvalue problem. The algorithm is useful in understanding the dynamical behaviors of metastable processes on large timescales. We demonstrate the capability of our algorithm on a high-dimensional model problem, and on the simple molecular system alanine dipeptide.
    Language: English
    Type: article , doc-type:article
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  • 3
    Publication Date: 2023-11-06
    Description: In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski's equality.
    Language: English
    Type: article , doc-type:article
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