MIT{LCS Technical Memo #TM-527 Local Rule Switching Mechanism for Viral Shell Geometry

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 sca olding subunits. This theory requires that the same chemical subunits assume di erent, 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. Di erent sets of local interactions, or local rules, were designed to produce di erent nal 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 exempli ed by the elongation of hexamers observed in many T = 7 viruses. These rules also provide a possible explanation for spiraling and tubular malformations. Mathematics Department and Laboratory for Computer Science, MIT. AT&T Bell Laboratories, Murray Hill, NJ.