DNA is an essential molecule that enables the storage and retrieval of genetic information. Since the discovery of its structure (double helix), the relationship between the molecule's structure and function has been studied extensively. Here we extend beyond the static structure and consider how the mechanical properties and dynamics influence its function. To do so, we exercise an elasto-dynamic rod model for DNA. By exercising this model, we study two biologically relevant systems. First, we study DNA looping by Lac repressor. Although this is a classic gene regulatory system, the mechanics of the DNA loop remain largely unknown. Therefore, we compute the effects of inter-operator length, intrinsic curvature, and protein flexibility on the energetics and topology these loops. We calculate that anti-parallel loops are energetically preferred, the elastic energy of a family of intrinsically curved DNA loops spans 5-12 kT, and identify the sensitivity of elastic energy to protein flexibility. Our computations compare favorably with published experimental data and motivate experimental work in the Kahn lab at the University of Maryland. Furthermore, we contribute an efficient method to analyze a large family of intrinsically curved DNA molecules and a method to account for Lac repressor flexibility in our rod model. In addition, we analyze cryo-EM images (obtained by the Stasiak lab at the Université de Lausanne) of DNA minicircles with similar lengths to the Lac repressor DNA loops. Second, we study the relaxation of DNA supercoils by topoisomerase. In doing so, we make advancements to the rod model and perform the first multi-scale model of supercoil relaxation by topoisomerase. Specifically, we contribute an efficient method to account for self contact and electrostatics in our elastic rod model. In our multi-scale simulation we couple our rod model with recent data (from MD simulations by the Andricioaei lab at the University of California - Irvine) that characterizes the the mechanics of topoisomerase. In doing so we gain insight into the dynamics of supercoil relaxation and make a first prediction of the relaxation time (0.1-1.0 μs).Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/75861/1/tlillian_1.pd
