Abstract
The mathematic modelling of icosahedral virus assembly has drawn increasing interest because of the symmetric geometry of the outer shell structures. Many models involve equilibrium expressions of subunit binding, with reversible subunit additions forming various intermediate structures. The underlying assumption is that a final lowest energy state drives the equilibrium toward assembly. In their simplest forms, these models have explained why high subunit protein concentrations and strong subunit association constants can result in kinetic traps forming off pathway partial and aberrant structures. However, the cell biology of virus assembly is exceedingly complex. The biochemistry and biology of polyoma and papillomavirus assembly described here illustrates many of these specific issues. Variables include the use of cellular ‘chaperone’ proteins as mediators of assembly fidelity, the coupling of assembly to encapsidation of a specific nucleic acid genome, the use of cellular structures as ‘workbenches’ upon which assembly occurs, and the underlying problem of making a capsid structure that is metastable and capable of rapid disassembly upon infection. Although formidable to model, incorporating these considerations could advance the relevance of mathematical models of virus assembly to the real world.