  We develop equilibrium and kinetic theories that describe the assembly of
viral capsid proteins on a charged central core, as seen in recent experiments
in which brome mosaic virus (BMV) capsids assemble around nanoparticles
functionalized with polyelectrolyte. We model interactions between capsid
proteins and nanoparticle surfaces as the interaction of polyelectrolyte
brushes with opposite charge, using the nonlinear Poisson Boltzmann equation.
The models predict that there is a threshold density of functionalized charge,
above which capsids efficiently assemble around nanoparticles, and that light
scatter intensity increases rapidly at early times, without the lag phase
characteristic of empty capsid assembly. These predictions are consistent with,
and enable interpretation of, preliminary experimental data. However, the
models predict a stronger dependence of nanoparticle incorporation efficiency
on functionalized charge density than measured in experiments, and do not
completely capture a logarithmic growth phase seen in experimental light
scatter. These discrepancies may suggest the presence of metastable disordered
states in the experimental system. In addition to discussing future experiments
for nanoparticle-capsid systems, we discuss broader implications for
understanding assembly around charged cores such as nucleic acids.
