Julius B. Lucks/PhD Thesis/Abstract

This thesis encompasses four detailed investigations in theoretical biophysics on polynucleotide unzipping, codon usage in viral genomes, and crystalline defects on curved surfaces. Chapter One provides an introduction to these investigations, as well as a basic introduction into virus biology, which provides a useful framework for considering the biological context of these studies.

Chapter Two describes a theoretical analysis of the dynamics of unzipping double-stranded DNA at a constant force. The central theoretical tool is the free energy landscape for unzipping DNA, which combines the DNA base sequence, experimentally determined base pairing and stacking energies, and the applied force to describe the change in free energy as successive base pairs are unzipped. We show how simulated dynamics on these landscapes recover the experimentally observed pattern of long pauses followed by rapid jumps. Chapter Three applies the same type of analysis to the related problem of translocating a single-stranded RNA molecule through a nanopore, with the aim of addressing the differences between RNA translocation and DNA unzipping.

In Chapter Four, we discuss codon usage patterns in viral genomes. Given the large degeneracy in the genetic code, the protein amino acid sequences encoded by the genome of a virus can have many equivalent forms. Viruses are special in that they require a host to express these proteins, and we study how codon usage patterns of viral genomes can reflect this necessity. We find that the codon usage of viral genes reflects the host-preferred codons for those viral genes that need to be expressed in high copy numbers.

Chapter Five of this thesis turns to a fundamental study in the materials science of two-dimensional surfaces with varying curvature. Using a Gaussian bump as a model surface, we study the geometric potential felt by dislocations, interstitials and vacancies embedded in a two-dimensional crystalline surface with frozen topography. For dislocations, we show that above a critical aspect ratio, it is energetically favorable to introduce two dislocations of opposite orientation into the crystalline medium in order to relieve some of the strain in the crystal due to the geometric frustration caused by the bump.