UCLA

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 Pruefer sequence. The calculation was performed numerically and shown to be far more efficient (memory-wise) than typical calculations of the 3D size.