An improved short-DNA elasticity theory and a model of the dynamics of biological signaling networks

This thesis mainly focuses on three topics in mathematical biology. (1) A DNA elasticity theory for relatively short molecules. Single-molecule experiments rely on a model of the polymer force-extension behavior to calibrate the experiments. The worm-like chain (WLC) theory agrees well with experiments for long molecules. Recent single-molecule experiments use shorter molecules for which the WLC does not agree well. The finite worm-like chain (FWLC) theory takes into account boundary conditions and bead rotational fluctuations, which are important for relatively short molecules. (2) DNA entropic elasticity with a bend. Single-molecule experiments have studied the elasticity of DNA with helix-deforming proteins, including proteins that bend DNA. Previous theoretical work on bent DNA has examined a long DNA molecule with many non-specifically binding proteins. Recent experiments used relatively short DNA molecules with a single, well-defined bend site. This work predicts how the DNA force-extension relation changes due to the formation of a single permanent bend. (3) Dynamics of regulatory and signaling networks. Biological networks are generally robust to changes in genotype and environment. This work on networks addresses how network topology affects the network dynamics. Using a simple model of genes/proteins which interact with and regulate each other, this project addresses how network properties such as connection density and topology affect the ability of the network to show signaling dynamics.