BackgroundIn order to replicate within their cellular host, many viruses have developed self-assembly strategies for their capsids which are sufficiently robust as to be reconstituted in vitro. Mathematical models for virus self-assembly usually assume that the bonds leading to cluster formation have constant reactivity over the time course of assembly (direct assembly). In some cases, however, binding sites between the capsomers have been reported to be activated during the self-assembly process (hierarchical assembly).ResultsIn order to study possible advantages of such hierarchical schemes for icosahedral virus capsid assembly, we use Brownian dynamics simulations of a patchy particle model that allows us to switch binding sites on and off during assembly. For T1 viruses, we implement a hierarchical assembly scheme where inter-capsomer bonds become active only if a complete pentamer has been assembled. We find direct assembly to be favorable for reversible bonds allowing for repeated structural reorganizations, while hierarchical assembly is favorable for strong bonds with small dissociation rate, as this situation is less prone to kinetic trapping. However, at the same time it is more vulnerable to monomer starvation during the final phase. Increasing the number of initial monomers does have only a weak effect on these general features. The differences between the two assembly schemes become more pronounced for more complex virus geometries, as shown here for T3 viruses, which assemble through homogeneous pentamers and heterogeneous hexamers in the hierarchical scheme. In order to complement the simulations for this more complicated case, we introduce a master equation approach that agrees well with the simulation results.ConclusionsOur analysis shows for which molecular parameters hierarchical assembly schemes can outperform direct ones and suggests that viruses with high bond stability might prefer hierarchical assembly schemes. These insights increase our physical understanding of an essential biological process, with many interesting potential applications in medicine and materials science.

Assembly of protein complexes like virus shells, the centriole, the nuclear pore complex, or the actin cytoskeleton is strongly determined by their spatial structure. Moreover, it is becoming increasingly clear that the reversible nature of protein assembly is also an essential element for their biological function. Here we introduce a computational approach for the Brownian dynamics of patchy particles with anisotropic assemblies and fully reversible reactions. Different particles stochastically associate and dissociate with microscopic reaction rates depending on their relative spatial positions. The translational and rotational diffusive properties of all protein complexes are evaluated on-the-fly. Because we focus on reversible assembly, we introduce a scheme which ensures detailed balance for patchy particles. We then show how the macroscopic rates follow from the microscopic ones. As an instructive example, we study the assembly of a pentameric ring structure, for which we find excellent agreement between simulation results and a macroscopic kinetic description without any adjustable parameters. This demonstrates that our approach correctly accounts for both the diffusive and reactive processes involved in protein assembly.

Many viruses rely on the self-assembly of their capsids to protect and transport their genomic material. For many viral systems, in particular for human viruses like hepatitis B, adeno or human immunodeficiency virus, that lead to persistent infections, capsomeres are continuously produced in the cytoplasm of the host cell while completed capsids exit the cell for a new round of infection. Here we use coarse-grained Brownian dynamics simulations of a generic patchy particle model to elucidate the role of the dynamic supply of capsomeres for the reversible self-assembly of empty T1 icosahedral virus capsids. We find that for high rates of capsomere influx only a narrow range of bond strengths exists for which a steady state of continuous capsid production is possible. For bond strengths smaller and larger than this optimal value, the reaction volume becomes crowded by small and large intermediates, respectively. For lower rates of capsomere influx a broader range of bond strengths exists for which a steady state of continuous capsid production is established, although now the production rate of capsids is smaller. Thus our simulations suggest that the importance of an optimal bond strength for viral capsid assembly typical for in vitro conditions can be reduced by the dynamic influx of capsomeres in a cellular environment.