Langevin dynamics simulation of polymer-assisted virus-like assembly

Abstract

Starting from a coarse grained representation of the building units of the minute virus of mice and a flexible polyelectrolyte molecule, we have explored the mechanism of assembly into icosahedral structures with the help of Langevin dynamics simulations and the parallel tempering technique. Regular icosahedra with appropriate symmetry form only in a narrow range of temperature and polymer length. Within this region of parameters where successful assembly would proceed, we have systematically investigated the growth kinetics. The assembly of icosahedra is found to follow the classical nucleation and growth mechanism in the absence of the polymer, with the three regimes of nucleation, linear growth, and slowing down in the later stage. The calculated average nucleation time obeys the laws expected from the classical nucleation theory. The linear growth rate is found to obey the laws of secondary nucleation as in the case of lamellar growth in polymer crystallization. The same mechanism is seen in the simulations of the assembly of icosahedra in the presence of the polymer as well. The polymer reduces the nucleation barrier significantly by enhancing the local concentration of subunits via adsorbing them on their backbone. The details of growth in the presence of the polymer are also found to be consistent with the classical nucleation theory, despite the smallness of the assembled structures.

50th Anniversary Perspective: A Perspective on Polyelectrolyte Solutions

“…The result of sequence-independent genome packing based only on electrostatics has been observed in experiments as well. 165,172,173 Simulation studies 167,168,170 of the kinetics of virus assembly showed that the process is dominated by electrostatics and ideas from polymer crystallization can be substantively used to understand the simulation and experimental results. 174−176 As one would expect, there are several additional avenues to expand the theoretical approach to address finer details of virus assemblies.…”

Modeling Viral Capsid Assembly

“…Several groups have therefore developed models for subunits which, although highly simplified, retain the most important features. Namely, they have an excluded-volume geometry and orientation-dependent attractions designed such that the lowest energy structure is shell with icosahedral symmetry [76, 105, 106, 112, 128, 172, 188–190, 209–211, 227, 272–274]…”

“…12B). For example, several groups [190, 208, 210] have considered models in which subunits have a trapezoidal shape which is roughly consistent with that of capsid proteins with the beta-barrel architecture [219] or models in which 20 triangular subunits (which could correspond to protein trimers) form icosahedral shells [76, 106, 172, 188, 209, 210]. Extended subunits have also been used to model nanoparticles with a variety of shapes (e.g.…”

Inferring bulk self-assembly properties from simulations of small systems with multiple constituent species and small systems in the grand canonical ensemble

“…[15][16][17] With increased computing power and improved simulation techniques, it has become possible to simulate mesoscale models that reproduce such self-assembling behaviour. In recent years mesoscopic models have been used to assemble micelles, [18][19][20][21][22][23][24][25][26][27][28][29][30][31] vesicles, 29,32,33 hollow shells of specific symmetry analogous to virus capsids [34][35][36][37][38][39][40][41][42] and aggregates of particles which resemble protein clusters. 43 Additionally, reflecting the growth of DNA nanotechnology, 44 many coarse-grained models of DNA assembly have recently been proposed.…”