  Electrostatic interactions play a central role in the assembly of
single-stranded RNA viruses. Under physiological conditions of salinity and
acidity, virus capsid assembly requires the presence of genomic material that
is oppositely charged to the core proteins. In this paper we apply basic
polymer physics and statistical mechanics methods to the self-assembly of a
synthetic virus encapsidating generic polyelectrolyte molecules. We find that
(i) the mean concentration of the encapsidated polyelectrolyte material depends
on the surface charge density, the radius of the capsid, and the linear charge
density of the polymer but neither on the salt concentration or the Kuhn
length, (ii) the total charge of the capsid interior is equal but opposite to
that of the empty capsid, a form of charge reversal. Unlike natural viruses,
synthetic viruses are predicted not to be under an osmotic swelling pressure.
The design condition that self-assembly only produces filled capsids is shown
to coincide with the condition that the capsid surface charge exceeds the
desorption threshold of polymer surface adsorption. We compare our results with
studies on the self-assembly of both synthetic and natural viruses.
