  While small single stranded viral shells encapsidate their genome
spontaneously, many large viruses, such as the Herpes virus or Infectious
Bursal Disease Virus (IBDV), typically require a template, consisting of either
scaffolding proteins or inner core. Despite the proliferation of large viruses
in nature, the mechanisms by which hundreds or thousands of proteins assemble
to form structures with icosahedral order (IO) is completely unknown. Using
continuum elasticity theory, we study the growth of large viral shells
(capsids) and show that a non-specific template not only selects the radius of
the capsid, but leads to the error-free assembly of protein subunits into
capsids with universal IO. We prove that as a spherical cap grows, there is a
deep potential well at the locations of disclinations that later in the
assembly process will become the vertices of an icosahedron. Furthermore, we
introduce a minimal model and simulate the assembly of viral shell around a
template under non-equilibrium conditions and find a perfect match between the
results of continuum elasticity theory and the numerical simulations. Besides
explaining available experimental results, we provide a number of new
predictions. Implications for other problems in spherical crystals are also
discussed.
