Encapsulation of fragmented cargo by virus coat proteins

The co-assembly of multiple nanoparticles ("fragmented cargo") and virus coat proteins is very sensitive both to the size of the nanocolloids and the stoichiometric ratio of nanoparticles to coat proteins, as recent experiments demonstrate. In addition, in a head-to-head competition, larger nanoparticles turn out to be preferentially encapsulated. In order to rationalize these findings, we investigate a simple mass-action model in which we allow for the co-existence of free nanoparticles and coat proteins, complexes consisting of a nanocolloid bound to a coat protein, and fully formed capsids consisting of a fixed number of coat proteins and a variable number of nanoparticles. In qualitative agreement with the experimental findings, we find (i) that there is a relatively narrow range of concentrations of nanocolloids that allows for the formation of appreciable numbers of partially filled capsids, and (ii) that the number of nanocolloids adsorbed on the inner wall of the capsid shell is typically well below the maximum number that fits on the wall facing the lumen. We attribute this to the impact of entropy that offsets the increase in binding free energy gain, which for smaller particles tends to be weaker.