arXiv subjects

Benjamin J. A. Héry

Publications and source records attributed to Benjamin J. A. Héry.

6 recordsLinked to original sources

arXiv2026

Position-dependent friction in protein folding from a GLE derived with a non-stationary localized projection distribution

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.

cond-mat.soft↗

arXiv2026

Reaction-Coordinate-Dependent Non-Markovian Friction Governs Protein-Folding Dynamics

It is common to project the full atomic-resolution representation of a protein onto a one-dimensionalreaction coordinate (RC) to capture the protein-folding kinetics. As a direct consequence ofthis dimensionality reduction, non-Markovian friction emerges in the framework of the general-ized Langevin equation (GLE). All previous applications of GLEs to protein folding employed anRC-independent friction memory function and therefore did not account for the different frictionin the folded and unfolded states. Using a recently derived GLE with RC-dependent mass andfriction memory function, we introduce a novel method to extract memory functions from timeseries data via a conditional Volterra equation. When applied to molecular dynamics (MD) data ofsix fast-folding proteins, we find strongly RC-dependent memory friction in line with the intuitiveexpectation that friction is higher in the folded than in the unfolded state due to internal proteinfriction. Our numerically efficient method to simulate the GLE confirms the accuracy of the GLEparameter extraction by comparison with the MD data. We show that RC-dependent memoryfriction not only adds physical insight into the folding process but also significantly improves thedescription of protein folding kinetics using low-dimensional RCs.

physics.bio-ph↗

arXiv2026

Comparison of different exact generalized Langevin equations with a non-linear potential of mean force and an observable-dependent mass and friction

The Mori-Zwanzig projection formalism constitutes a powerful and robust framework for deriving equations of motion in terms of generalized Langevin equations (GLEs) for an arbitrary observable using evolution and projection operators. Based on this framework, we analyze the properties of four distinct GLEs for a scalar observable including a Markovian force derived from a generally non-linear potential, a non-Markovian friction force, and an orthogonal force, commonly interpreted as a random force. While all four GLEs are exact, they differ in the memory friction kernel, which may either be dependent or independent of the observable, and by the potential, which may either include or exclude the effective kinetic energy of the observable. Inclusion of the kinetic energy in the potential is advantageous for observables whose velocity satisfies Wick's theorem, since this reproduces the correct distribution of the observable and its velocity even without contributions from the friction force and the orthogonal force.

cond-mat.stat-mech↗

arXiv2026

Non-equilibrium generalized Langevin equation for multi-dimensional observables

The Mori-Zwanzig formalism is a powerful theoretical framework for deriving equations of motion for coarse-grained observables in the form of generalized Langevin equations (GLEs) involving evolution and projection operators. Using a time-dependent many-body Hamiltonian and a multi-dimensional Mori projection operator, we derive a non-equilibrium Mori GLE for a multi-dimensional observable of interest $\vec{A}$ that consists of a Markovian force, a running integral over time of a non-Markovian friction force, and an orthogonal force that is often interpreted as a random force. We study the structure of the derived GLE in three limiting cases: when the components of $\vec{A}$ are uncorrelated, when the Hamiltonian is time-independent and thus the system is at equilibrium, and when both conditions are simultaneously satisfied. We highlight the presence of a contribution to the Markovian force that takes the form of an instantaneous friction force which only vanishes when the components of $\vec{A}$ are uncorrelated. Our non-Markovian framework is an important step towards the systematic modeling of the coupled kinetics of coarse-grained reaction coordinates in biological complex systems, exemplified for the coupled intra- and inter-protein folding during fibril formation of the human islet amyloid polypeptide (IAPP).

cond-mat.stat-mech↗

arXiv2025

Analysis and Simulation of Generalized Langevin Equations with Non-Gaussian Orthogonal Forces

The generalized Langevin equation (GLE) is a useful framework for analyzing and modeling the dynamics of many-body systems in terms of low-dimensional reaction coordinates, with its specific form determined by the choice of projection formalism. We compare parameters derived from different GLE formulations using molecular dynamics simulations of butane's dihedral angle dynamics. Our analysis reveals non-Gaussian contributions of the orthogonal force in different GLEs, being most enhanced for the Mori-GLE, where all non-linearities are relegated to the orthogonal force. We establish a simulation technique that correctly accounts for non-Gaussian orthogonal forces, which is critical for accurately predicting dihedral-angle mean first-passage times. We find that the accuracy of GLE simulations depends significantly on the chosen GLE formalism; the Mori-GLE offers the most numerically robust framework for capturing the statistical observables of the dihedral angle dynamics, provided the correct non-Gaussian orthogonal force distribution is used.

physics.comp-ph↗

arXiv2025

Integrable fishnet circuits and Brownian solitons

We introduce classical many-body dynamics on a one-dimensional lattice comprising local two-body maps arranged on discrete space-time mesh that serve as discretizations of Hamiltonian dynamics with arbitrarily time-varying coupling constants. Time evolution is generated by passing an auxiliary degree of freedom along the lattice, resulting in a `fishnet' circuit structure. We construct integrable circuits consisting of Yang-Baxter maps and demonstrate their general properties, using the Toda and anisotropic Landau-Lifschitz models as examples. Upon stochastically rescaling time, the dynamics is dominated by fluctuations and we observe solitons undergoing Brownian motion.

cond-mat.stat-mech↗