Stochastic dynamics of virus capsid formation: direct versus hierarchical self-assembly

TL;DR

This study compares direct and hierarchical self-assembly mechanisms of virus capsids using simulations and master equations, revealing conditions favoring each scheme and their vulnerabilities, especially in complex virus geometries.

Contribution

It introduces a Brownian dynamics simulation framework with switchable binding sites and a master equation model to analyze virus capsid assembly schemes.

Findings

Direct assembly favors reversible bonds and structural reorganization.

Hierarchical assembly benefits from strong bonds with low dissociation rates.

Differences between schemes are amplified in complex virus geometries.

Abstract

In 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). In 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.