  We study the self-assembly behaviour of patchy particles with `protein-like'
interactions that can be considered as a minimal model for the assembly of
viral capsids and other shell-like protein complexes. We thoroughly explore the
thermodynamics and dynamics of self assembly as a function of the parameters of
the model and find robust assembly of all target structures considered. Optimal
assembly occurs in the region of parameter space where a free energy barrier
regulates the rate of nucleation, thus preventing the premature exhaustion of
the supply of monomers that can lead to the formation of incomplete shells. The
interactions also need to be specific enough to prevent the assembly of
malformed shells, but whilst maintaining kinetic accessibility. Free-energy
landscapes computed for our model have a funnel-like topography guiding the
system to form the target structure, and show that the torsional component of
the interparticle interactions prevents the formation of disordered aggregates
that would otherwise act as kinetic traps.
