Staying in Shape: Molecular Dynamics on Curved Surfaces

bpj_110_6_3c_rThe cover image for the March 29 issue of BJ is a series of snapshots from a simulation of complex particle dynamics constrained to a spherical template by the RATTLE algorithm.. These images were obtained by implementing the algorithm in the molecular dynamics program LAMMPS (http://lammps.sandia.gov/). The acquired data were then further visualized with the Tachyon raytracer in Ovito (http://www.ovito.org/).

Our article describes how standard constraint algorithms can be used in molecular dynamics simulations to study the self-assembly properties of complex particles constrained to curved surfaces.  On the cover, we show how the effective shape and the arising steric effects of capsomeres influence the final shape of a virus capsid. The three snapshots on the cover show three different time steps, from the initial disordered packing of the model capsomeres on a spherical template, through an ordered but “open” capsid structure, to the final icosahedral capsid structure. In the study of virus self-assembly, for example, it is thought that the effective shape of the capsomeres in HIV-1 is far from spherical, and this might lead to different assembly pathways and final assembly products. With the method we describe in the article, the effect of the shape of capsomeres can be taken into account rigorously and systematically.

Another example relates to the crowded diffusion along curved surfaces. This models the lateral diffusion along membranes, a process that is thought to regulate quite a few processes in biological systems, including the regulation of synaptic strength in neurons and the photosynthetic electron transport sites in grana thylakoids. While the examples presented in this paper are in a biophysical context, the computational tool we describe is very generally applicable to anything that can be modelled as particles constrained to a curved surface such as colloids constrained to a liquid-liquid interface or, more theoretically, to study dynamics of the (generalized) Thomson problem. Furthermore, the algorithm as implemented in LAMMPS shows excellent parallel scaling, making it a good tool for studying dynamics of large numbers of particles constrained to curved surfaces.

– Stefan Paquay and Remy Kusters

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