The coat proteins of many viruses spontaneously form icosahedral capsids around nucleic acids or other polymers. Elucidating the role of the packaged polymer in capsid formation could promote biomedical efforts to block viral replication and enable use of capsids in nanomaterials applications. To this end, we perform Brownian dynamics on a coarse-grained model that describes the dynamics of icosahedral capsid assembly around a flexible polymer. We identify several mechanisms by which the polymer plays an active role in its encapsulation, including cooperative polymer-protein motions. These mechanisms are related to experimentally controllable parameters such as polymer length, protein concentration, and solution conditions. Furthermore, the simulations demonstrate that assembly mechanisms are correlated to encapsulation efficiency, and we present a phase diagram that predicts assembly outcomes as a function of experimental parameters. We anticipate that our simulation results will provide a framework for designing in vitro assembly experiments on single-stranded RNA virus capsids.

The kinetics for the assembly of viral proteins into a population of capsids can be measured in vitro with size exclusion chromatography or dynamic light scattering, but extracting mechanistic information from these studies is challenging. For example, it is not straightforward to determine the critical nucleus size or the elongation time (the time required for a nucleus to grow to completion). In this work, we study theoretical and computational models for capsid assembly to show that the critical nucleus size can be determined from the concentration dependence of the assembly half-life and that the elongation time is revealed by the length of the lag phase. Furthermore, we find that the system becomes kinetically trapped when nucleation becomes fast compared to elongation. Implications of this constraint for determining elongation mechanisms from experimental assembly data are discussed.

In self-assembly processes, kinetic trapping effects often hinder the formation of thermodynamically stable ordered states. In a model of viral capsid assembly and in the phase transformation of a lattice gas, we show how simulations in a self-assembling steady state can be used to identify two distinct mechanisms of kinetic trapping. We argue that one of these mechanisms can be adequately captured by kinetic rate equations, while the other involves a breakdown of theories that rely on cluster size as a reaction coordinate. We discuss how these observations might be useful in designing and optimising self-assembly reactions.

We simulate the assembly dynamics of icosahedral capsids from subunits that interconvert between different conformations (or quasi-equivalent states). The simulations identify mechanisms by which subunits form empty capsids with only one morphology, but adaptively assemble into different icosahedral morphologies around nanoparticle cargoes with varying sizes, as seen in recent experiments with brome mosaic virus (BMV) capsid proteins. Adaptive cargo encapsidation requires moderate cargo-subunit interaction strengths; stronger interactions frustrate assembly by stabilizing intermediates with incommensurate curvature. We compare simulation results to experiments with cowpea chlorotic mottle virus empty capsids and BMV capsids assembled on functionalized nanoparticles, and suggest new cargo encapsidation experiments. Finally, we find that both empty and templated capsids maintain the precise spatial ordering of subunit conformations seen in the crystal structure even if interactions that preserve this arrangement are favored by as little as the thermal energy, consistent with experimental observations that different subunit conformations are highly similar.

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