In a previous paper [Berger et al., PNAS 91 7732, 1994], a theory of virus shell formation was proposed in which shell assembly is directed by local interactions of the coat and scaffolding subunits. This theory requires that the same chemical subunits assume different, stable conformations depending on their position in the shell. During assembly, the conformation of a protein subunit dictates the conformations of its neighboring subunits. It was shown that these local interactions could be designed so as to generate shells that have the same geometric structure as virus capsids. Different sets of local interactions, or local rules, were designed to produce different final shell geometries. In this paper, local rules are given that assemble a T = 7 shell such that a small change in these rules produces a T = 4 shell. This is intriguing since evidence has been accumulating that some T = 7 shells are closely related to T = 4 shells. These local rules also predict that hexamers in the assembled procapsid would have approximate two-fold rotational symmetry. This symmetry is exemplified by the elongation of hexamers observed in many T = 7 viruses. These rules also provide a possible explanation for spiraling and tubular malformations.

A local rule theory is developed which shows that the self-assembly of icosahedral virus shells may depend on only the lower-level interactions of a protein subunit with its neighbors, i.e. local rules, rather than on larger structural building blocks. The local rule theory provides a framework for understanding the assembly of icosahedral viruses. These include both viruses that fall in the quasi-equivalence theory of Caspar and Klug and the polyoma virus structure, which violates quasi-equivalence and has puzzled researchers since it was first observed. Local rules are essentially templates for energetically favorable arrangements. The tolerance margins for these rules are investigated through computer simulations. When these tolerance margins are exceeded in a particular way, the result is a "spiraling" malformation that has been observed in nature.