UCLA

The statistical physics of complex polymers with branches and circuits is the topic of this dissertation. An important motivation are large, single-stranded (ss) RNA molecules. Such molecules form complex ``secondary" and ``tertiary" structures that can be represented as branched polymers with circuits. Such structures are in part directly determined by the nucleotide sequence and in part subject to thermal fluctuations. The polymer physics literature on molecules in this class has mostly focused on randomly branched polymers without circuits while there has been minimal research on polymers with specific structures and on polymers that contain circuits. The dissertation is composed of three parts: Part I studies branched polymers with thermally fluctuating structure confined to a potential well as a simple model for the encapsidation of viral RNA. Excluded volume interactions were ignored. In Part II, I apply Flory theory to the study of the encapsidation of viral ss RNA molecules with specific branched structures, but without circuits, in the presence of excluded volume interaction. In Part III, I expand on Part II and consider complex polymers with specific structure including both branching and circuits. I introduce a method based on the mathematics of Laplacian matrices that allows me to calculate density profiles for such molecules, which was not possible within Flory theory.