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The influence of multi-dimensionality and off-diagonal non-Markovian friction coupling on coarse-grained dynamics

Henrik Kiefer,Cihan Ayaz,Benjamin A. Dalton,R. R. Netz

Published 2025 in New Journal of Physics

ABSTRACT

Coarse-graining complex molecular systems to lower-dimensional reaction coordinates is a powerful approach for capturing their effective dynamics. The generalized Langevin equation (GLE) provides an exact framework for modeling coarse-grained dynamics, and is particularly useful when non-Markovian effects are significant. While one-dimensional GLE models are commonly used, many systems require multi-dimensional reaction coordinates to account for coupled dynamics. Here, we study the GLE formalism for multi-dimensional reaction coordinates, incorporating a memory matrix to quantify non-Markovian frictional coupling between coordinates, and a multi-dimensional potential. Using the GLE model, in conjunction with a multi-dimensional Markovian embedding scheme, we investigate different systems that are characterized by two-dimensional reaction coordinates, namely the dihedral dynamics of pentane and alanine dipeptide, obtained from molecular dynamics simulations in explicit water. We identify significant off-diagonal friction couplings arising from intramolecular and hydrodynamic interactions. In extension of previous studies of multi-dimensional GLEs, we investigate the critical role of different terms in the multi-dimensional GLE for accurately capturing key dynamical properties, including mean first-passage times and mean-squared displacements.

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