Noel Perkins and Edgar Meyhofer Mechanical Engineering University of Michigan Ann Arbor, MI 48109-2125
Our proposed research employs methods of nonlinear dynamical systems to explore the fundamental biological functions of DNA. Critical biological functions such as replication and transcription are influenced by the shape or "structure" of DNA. This very long molecule (length is thousand times longer than diameter) is extraordinarily flexible, and it can undergo nonlinear motions that can regulate (i.e. control) gene expression. For example, proteins can force segments of DNA into loops that prevent transcription. In addition, thermal energy excites vibrations of DNA and resulting changes in supercoiled states can promote transcription.
The motions described above occur over very long length scales (hundreds to tens of thousands of nanometers) and on very long time scales (microsecond to millisecond) relative to atomic dimensions (angstrom) and molecular dynamic rates (picosecond and smaller). It is the long-term objective of our research program to understand these dynamical processes through novel theories and experiments on DNA structural dynamics. A promising dynamical theory for long length/time scales follows from treating the long chain molecule as a dynamic continuum rod. The first step in our research plan is to develop a nonlinear computational rod model for DNA supercoils and loops. Major challenges to be considered include 1) the nonlinear deformation, 2) spatial non-uniformity and anisotropy (e.g., "sequence-dependent" stiffness and "intrinsic" curvature and twist), 3) self-contact/electrostatics and interwinding, 4) dissipation, and 5) efficient numerical algorithms. We will then employ our computational model in two strategic case studies. The first case study focuses on the dynamic evolution of supercoils for strands subjected to controlled end rotation as observed in recent single molecule experiments. The second case study explores the looping of DNA when subjected to a bound protein known as the lac repressor. Our interdisciplinary research team, which possesses the requisite background in dynamical systems and molecular biology, is well-positioned to make these fundamental investigations of DNA dynamics by advancing methods from the engineering sciences.
