A method for molecular dynamics on curved surfaces

TL;DR

This paper introduces a novel molecular dynamics simulation method for particles constrained on curved surfaces, enabling the study of biological processes with particle interactions on complex geometries.

Contribution

It combines standard constraint algorithms with the velocity Verlet scheme to simulate interacting particles on curved surfaces using Cartesian coordinates.

Findings

Simulated Brownian motion on various curved surfaces.

Analyzed protein diffusion influenced by membrane shape and crowding.

Modeled virus capsid self-assembly on curved geometries.

Abstract

Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in the field of diffusive transport have focussed on solving the diffusion equation on curved surfaces, for which it is not tractable to incorporate particle interactions even though these play a crucial role in crowded systems. We show here that it is possible to combine standard constraint algorithms with the classical velocity Verlet scheme to perform molecular dynamics simulations of particles constrained to an arbitrarily curved surface, in which such interactions can be taken into account. Furthermore, unlike Brownian dynamics schemes in local coordinates, our method is based on Cartesian coordinates allowing for the reuse of many other standard tools without modifications, including parallelisation through domain decomposition. We show that by applying the schemes to the Langevin equation for various surfaces, confined Brownian motion is obtained, which has direct applications to many biological and physical problems. Finally we present two practical examples that highlight the applicability of the method: (i) the influence of crowding and shape on the lateral diffusion of proteins in curved membranes and (ii) the self-assembly of a coarse-grained virus capsid protein model.