  Self-assembly is a vital part of the life cycle of certain icosahedral RNA
viruses. Furthermore, the assembly process can be harnessed to make icosahedral
virus-like particles (VLPs) from coat protein and RNA in vitro. Although much
previous work has explored the effects of RNA-protein interactions on the
assembly products, relatively little research has explored the effects of
coat-protein concentration. We mix coat protein and RNA from bacteriophage MS2,
and we use a combination of gel electrophoresis, dynamic light scattering, and
transmission electron microscopy to investigate the assembly products. We show
that with increasing coat-protein concentration, the products transition from
well-formed MS2 VLPs to ``monster'' particles consisting of multiple partial
capsids to RNA-protein condensates consisting of large networks of RNA and
partially assembled capsids. We argue that the transition from well-formed to
monster particles arises because the assembly follows a nucleation-and-growth
pathway in which the nucleation rate depends sensitively on the coat-protein
concentration, such that at high protein concentrations, multiple nuclei can
form on each RNA strand. To understand the formation of the condensates, which
occurs at even higher coat-protein concentrations, we use Monte Carlo
simulations with coarse-grained models of capsomers and RNA. These simulations
suggest that the the formation of condensates occurs by the adsorption of
protein to the RNA followed by the assembly of capsids. Multiple RNA molecules
can become trapped when a capsid grows from capsomers attached to two different
RNA molecules or when excess protein bridges together growing capsids on
different RNA molecules. Our results provide insight into an important
biophysical process and could inform design rules for making VLPs for various
applications.
