| We have developed coarse-grained models of RNA bound by capsid protein (CP) in response to recent in vitro studies on the self-assembly of viral RNA by capsid protein. Under typical in vitro self-assembly conditions and in particular for the case of many ssRNA viruses whose CP have cationic N-termini, the adsorption of CP onto the (anionic) RNA is non-specific because the CP concentration exceeds the Largest dissociation constant for CP-RNA binding. Following an introductory chapter, which recounts the history and physics of the in vitro self-assembly experiments, Chapters 2-4 of this dissertation explore simple lattice models of single-stranded (ss) RNA in the presence of interacting bound particles.;In Chapter 2 our investigation opens with a simple model to account for the measured yield of packaged RNA (nucleocapsids) by CP. We treat the RNA as a 1D lattice, whose sites represent CP binding sites, to calculate the yield of RNA packaged as a function of the CP:RNA mol ratio. The measured yield of in vitro assembled nucleocapsids agrees exceptionally well with our simple 1D model.;In Chapters 3 and 4 we extend our 1D model to 2D to better account for the branched nature of RNA. Our theoretical work provides the statistical-thermodynamic grounding for understanding the in vitro "competition" experiments. In these experiments two RNAs compete for a limited amount of CP. The exchange of CP between the RNAs was found to be reversible at pH 7 and, separately, it was found that long RNAs were able to strip CPs from shorter ones. Our Monte Carlo simulations demonstrate that, for a given RNA mass, the sequence with the highest affinity for protein is the one with the most compact secondary structure arising from self-complementarity; similarly, a long RNA steals protein from an equal mass of shorter ones because of the energetic preference of forming one large cluster of CPs over forming two smaller clusters.;Finally, in chapter 5 we turn our attention away from the self-assembly experiments to focus on branched polymers. We show there that the 3D size of a branched polymer with N monomers can be directly calculated from a sequence of N -- 2 integers, known as the Prufer sequence. The calculation was performed numerically and shown to be far more efficient (memory-wise) than typical calculations of the 3D size. |
