Polymorphism in Core-Controlled Virus Self-Assembly: Thermodynamics vs Kinetics

Abstract

Motivated by recent experimental studies we investigate theoretically the phenomenon of poly- morphism in core-controlled self-assembly of virus-like particles, where identical nanoparticles are encapsulated in differently sized shells formed by virus coat proteins. Our purpose is to understand how protein concentration, stoichiometry and preferred curvature of the protein shells (“capsids”) influence the prevalence of differently sized nanoparticle-protein complexes. We invoke equilibrium statistical theory and classical nucleation theory to study how kinetic trapping influences diagrams of state. Key ingredient is the spherical cap model describing the free energy penalty associated with the rim proteins that have fewer neighbours and hence fewer favourable contacts with other proteins in a shell. We find that the state diagrams that we calculate in and out of equilibrium differ significantly, and that kinetics favours the co-existence of polymorphs at large stoichiometric ratios and/or protein concentration.