Structure and Energetics of DNA and RNA In and Out of Viral Capsids: Theory and Simulations

From a physical point of view, double-stranded (ds) DNA is a stiff (semiflexible) linear polymer. Single-stranded (ss) RNA, on the other hand, is a relatively flexible polymer that partially folds on itself with secondary structure giving rise to an effectively branched polymer. Long dsDNA and ssRNA molecules serve as viral genomes and thus need to be efficiently packaged into the small confines of the viral protein shells. The packaged dsDNA is generally extremely densely packed, exerting very high pressure (reaching ~100 atm) on the capsid walls. Although ssRNA is less tightly packed, there is also a limit to its packaged length, and experiments reveal clear correlations between viral RNA length and capsid size (and charge). I will describe some of the basic physical properties of dsDNA in solution and inside viral capsids, outlining and comparing theoretical and simulation studies of the force required to load it into the capsid, and its resulting structure, energy and pressure. Representing the branched ssRNA polymers as tree graphs, we show that viral RNAs are more compact than non-viral ones, and that random-sequence RNAs are more compact than randomly-branched polymers involving equal numbers of monomers. Further, neglecting self-interaction, their 3D size varies with the 1/3 power of their length, in contrast to the 1/4 power that holds for randomly-branched polymers. If time permits I will also outline the Prüfer shuffling procedure used to arrive at these conclusions.