A Note on Genome Organisation in RNA Viruses with Icosahedral Symmetry

The structural organisation of the viral genome within its protein container, called the viral capsid, is an important aspect of virus architecture. Many single-stranded (ss) RNA viruses organise a significant part of their genome in a dodecahedral cage as a RNA duplex structure that mirrors the symmetry of the capsid. Bruinsma and Rudnick have suggested a model for the structural organisation of the RNA in these cages. It is the purpose of this paper to further develop their approach based on results from the areas of graph theory and DNA network engineering. We start by suggesting a scenario for pariacoto virus, a representative of this class of viruses, that is energetically more favorable than those derived previously. We then show that it is a representative of a whole family of cage structures that abide to the same construction principle, and then derive the energetically optimal configuration for a second family of cage structures along similar lines. Finally, we give reasons for the conjecture that these two families are more likely to occur in nature than other scenarios.