Position-dependent friction in protein folding from a GLE derived with a non-stationary localized projection distribution
Abstract
The Generalized Langevin Equation (GLE) is an integro-differential equation of motion for a general observable of a many-body system and is rigorously derived using the projection operator formalism. In the standard derivation, a stationary canonical phase space distribution is used for the projection. Here, we derive a novel class of GLEs using a non-stationary projection distribution that constrains the initial ensemble to a hypersurface in phase space on which the observable has a fixed value A0. As a result, all GLE parameters, and in particular the memory friction kernel, depend on A0 and can be extracted from short simulations that do not sample the entire phase space. Applying this non-stationary GLE to protein folding trajectories, we find for villin and an α-helical poly-alanine segment that the total friction is higher in the folded state. These results demonstrate that observable-dependent friction effects are non-negligible and can be accounted for using non-stationary GLEs derived by constrained projection schemes.
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BibTeX
@misc{salem2026positiondependent,
title = {{Position-dependent friction in protein folding from a GLE derived with a non-stationary localized projection distribution}},
author = {Salma Salem and Lucas Tepper and Benjamin J. A. Héry and Henrik Kiefer and David D. Girardier and Roland R. Netz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28113},
eprint = {2609.28113},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28113},
}
RIS
TY - UNPB
TI - Position-dependent friction in protein folding from a GLE derived with a non-stationary localized projection distribution
AU - Salma Salem
AU - Lucas Tepper
AU - Benjamin J. A. Héry
AU - Henrik Kiefer
AU - David D. Girardier
AU - Roland R. Netz
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28113
UR - https://arxiv.org/abs/2609.28113
AB - The Generalized Langevin Equation (GLE) is an integro-differential equation of motion for a general observable of a many-body system and is rigorously derived using the projection operator formalism. In the standard derivation, a stationary canonical phase space distribution is used for the projection. Here, we derive a novel class of GLEs using a non-stationary projection distribution that constrains the initial ensemble to a hypersurface in phase space on which the observable has a fixed value A_0. As a result, all GLE parameters, and in particular the memory friction kernel, depend on A_0 and can be extracted from short simulations that do not sample the entire phase space. Applying this non-stationary GLE to protein folding trajectories, we find for villin and an α-helical poly-alanine segment that the total friction is higher in the folded state. These results demonstrate that observable-dependent friction effects are non-negligible and can be accounted for using non-stationary GLEs derived by constrained projection schemes.
ER -