Thermodynamic and kinetic aspects of polymorphism in core controlled assembly of virus-like particles*

Motivated by recent experiments we investigate the phenomenon of polymorphism in core- controlled self-assembly of virus-like particles, where identical nanoparticles are encapsulated in capsids with different sizes. Our goal is to understand how protein concentration, stoichiometry and preferred curvature of capsids influence the prevalence of one shell size over another one. Using the equilibrium statistical physics and classical nucleation theory, we study how kinetic traps modify the state diagrams. We find that the free energy penalty associated with the rim proteins that have fewer favorable contacts with other proteins plays an important role in determining the capsid size. We show that in and out of equilibrium phase diagrams differ significantly and that kinetics favors the co-existence of capsids with different sizes at large stoichiometric ratios and/or protein concentration.