A Method for Molecular Dynamics on Curved Surfaces
#MMPMID27028633
Paquay S
; Kusters R
Biophys J
2016[Mar]; 110
(6
): 1226-33
PMID27028633
show ga
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 focused 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 take such interactions into account by
combining standard constraint algorithms with the classical velocity Verlet
scheme to perform molecular dynamics simulations of particles constrained to an
arbitrarily curved surface. 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
parallelization through domain decomposition. We show that by applying the
schemes to the Langevin equation for various surfaces, we obtain confined
Brownian motion, which has direct applications to many biological and physical
problems. Finally we present two practical examples that highlight the
applicability of the method: 1) the influence of crowding and shape on the
lateral diffusion of proteins in curved membranes; and 2) the self-assembly of a
coarse-grained virus capsid protein model.
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