Kinetics and the Folding of RNA and Other PolymersZhou, GuangyaocreatorGeman, StuartAdvisorLawrence, CharlesReaderMenon, GovindReaderBrown University. Department of Applied Mathematicssponsor2019, None p.born digitalThesis (Ph. D.)--Brown University, 2019thesesIn this thesis, we study kinetics and the folding of RNAs and other polymers. In the first part, we study the problem from a statistical perspective. Thinking kinetically, we introduce quantitative measures of ``ambiguity" and demonstrate their statistical relationships to native secondary structure and to qualitative distinctions between RNA families. In the second part, we focus on entropic barriers in molecular dynamics simulations. Entropic barriers, while ubiquitous and important in molecular dynamics, received relatively little attention in the literature, and their theoretical characterization and understanding are severely lacking. Here, using a simple toy model with a golf-course energy landscape and two targets, we look at entropic barriers from the perspective of hitting probabilities of the targets. We present rigorous theoretical results to establish global, approximately constant hitting probabilities as an essential feature of entropic barriers, and connect the global hitting probabilities to local information around the targets (in the form of capacities of local sets around the targets) to facilitate the understanding of entropic barriers. Inspired by the theoretical results, a method called Capacity Hopping (CHop for short), based on an efficient capacity estimation algorithm, is proposed for overcoming entropic barriers in molecular dynamics simulations. Extensive numerical experiments on a concrete 5-dimensional version of the toy model show that CHop is highly effective: it can be nearly as accurate as naive simulations in terms of estimating hitting probabilities, but 750 times faster.RNAProtein foldingMolecular dynamicsentropic barriersEnglishRPB2019060310.26300/gn9j-5d68In CopyrightCollection is open for research.dissertations