Origin of icosahedral symmetry in large viruses.

Most spherical viruses adopt structures with icosahedral symmetry. While small single stranded RNA viruses assemble spontaneously from a solution containing the protein subunits and genome molecules, the large icosahedral viruses, such as Bacteriophage P22, Infectious Bursal Disease viruses and Bluetongue viruses need scaffolding proteins or an inner core to form fully infectious particles. We model the inner core as a hard sphere and study the growth of viral shells built from identical protein subunits. We show that the attractive subunit-core interaction modifies the preferred curvature of the shell and has a key role in the formation of large icosahedral shells. Continuum elasticity theories of virial shells are used to rationalize the simulation results.