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Biopolymers Under Large External Forces and Mean-field RNA Virus Evolutionary Dynamics



Biopolymers Under Large External Forces

and Mean-field RNA Virus Evolutionary Dynamics


Syed Amir Ahsan

Doctor of Philosophy in Physics

University of California, Los Angeles, 2013

Professor Robijn Bruinsma, Chair

The modeling of the mechanical response of single-molecules of DNA and RNA under large external forces through statistical mechanical methods is central to this thesis with a small portion devoted to modeling the evolutionary dynamics of positive-sense single-stranded RNA viruses. In order to develop and test models of biopolymer mechanics and illuminate the mechanisms underlying biological processes where biopolymers undergo changes in energy on the order of the thermal energy, , entails measuring forces and lengths on the scale of piconewtons (pN) and nanometers (nm), respectively. A capacity achieved in the past two decades at the single-molecule level through the development of micromanipulation techniques such as magnetic and optical tweezers, atomic force microscopy, coupled with advances in micro- and nanofabrication. The statistical mechanical models of biopolymers developed in this dissertation are dependent upon and the outcome of these advancements and resulting experiments.

The dissertation begins in chapter 1 with an introduction to the structure and thermodynamics of DNA and RNA, highlighting the importance and effectiveness of simple, two-state models in their description as a prelude to the emergence of two-state models in the research manuscripts. In chapter 2 the standard models of the elasticity of polymers and of a polymer gel are reviewed, characterizing the continuum and mean-field models, including the scaling behavior of DNA in confined spaces. The research manuscript presented in the last section of chapter 2 (section 2.5), subsequent to a review of a Flory gel and in contrast to it, is a model of the elasticity of RNA as a gel, with viral RNA illustrating an instance of such a network, and shown to exhibit anomalous elastic behavior, a negative Poisson ratio, and capable of facilitating viral RNA encapsidation with further context provided in section 5.1. In chapter 3 the experimental methods and behavior of DNA and RNA under mechanical forces are reviewed culminating with the research manuscript in section 3.4 of the development of the two-state worm-like chain, modeling the overstretching transition of B-DNA to S-DNA. Chapter 4 considers the behavior of DNA in an electric field, first reviewing DNA as a polyelectrolyte and of DNA electrophoresis in free solution and it's polarization and resulting stretched conformation as context for the study of the contrasting behavior of DNA in an AC electric field presented in the research manuscripts of the final two sections of chapter 4. In section 4.3 the collapse of DNA in ac electric fields is investigated with the experimental results and possible models for collapse presented with a scaling analysis of the frequency- and confinement-dependent critical field for collapse presented in section 4.4, contrasting a mean-field Flory-type model and a continuum, wormlike chain model. Chapter 5 investigates viral RNA; reviewing the encapsidation, life cycle and the evolutionary dynamics of single-stranded RNA viruses including the quasispecies model and it's prediction of the information or error catastrophe, providing context for the models developed in the research manuscripts presented in sections 2.5 and 5.3. In section 5.3, a simple ODE model of the evolution of positive-sense single-stranded RNA viruses is developed, adopting the two-state mean-field quasispecies model, to characterize the selection pressure associated with the encapsidation and independently, the degradation by RNAi of the wild-type relative to the mutant population and demonstrate their capacity to induce an information catastrophe and consequently support the evolution of intermediate encapsidation rates and of viral suppressors of RNA silencing, in addition to providing support for antiviral therapeutic pathways.

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