This project addresses probing questions in molecular biology by extending methods from the mechanical sciences. For instance, molecular biologists have postulated that DNA must vibrate in order to convert bending strain energy (or "writhe") to torsional strain energy (or "twist") to initiate the biological processes of transcription and replication. This "writhe to twist conversion" occurs in DNA supercoils and over lengths scales spanning nanometers to microns. Similarly, the looping of DNA segments when bound to certain proteins is a dynamical process that serves as a regulatory mechanism for gene expression. Our objective is to understand the fundamental dynamical properties of DNA at work in these processes using both theoretical and experimental methods.
Our theoretical effort will lead to a vibration theory for DNA over long spatial/time scales. We approximate a strand of DNA as a long and nonlinear continuum (an elastic rod) that dynamically bends and twists in response to multi-physical (e.g., thermal, electrostatic, fluid, chemical binding) forces. The resulting nonlinear dynamical theory for DNA strands will be used to explore how DNA supercoils and loops evolve and the vibration properties of these states. Our experimental efforts include ambitious studies on single-molecule DNA that employ optical traps to measure dynamic response. The scientific impact of these novel theoretical and experimental studies include: 1) a vibration theory for DNA supercoils on long length/time scales, 2) the experimental characterization of the spatially extended vibration and relaxation times of supercoils, 3) a nonlinear theory that captures the dynamic transitions between supercoiled states, and 4) direct experimental measurements of nonlinear transitions.
