The objective of this research is to understand the structure and dynamics of supercoiled DNA. Emphasis will be on the determination of the three-dimensional structure of supercoiled DNA as a function of linking number; upon the prediction of interaction of local segments that are separated by a considerable distance along the contour length of the DNA; and upon the elucidation of the effects on DNA structure of wrapping on a protein surface. The specific aims are divided into three categories. (1) Description of the tertiary structure of supercoiled DNA using the finite element method. The finite element method from nonlinear structural mechanics will be applied to the analysis of closed DNA structure. Energy minimization criteria will be used to predict the most stable configuration at each linking number. The writhe and twist will be calculated and the results used to predict the hydrodynamic behavior of closed DNA as well as the equilibrium distribution of topoisomers. (2) Description of the generalized helical periodicity of supercoiled DNA. The generalized winding number and generalized helical repeat will be defined for supercoiled DNA and a formula for the linking number of the DNA developed in terms of this winding number. These results will be applied to various experiments involving nuclease digestion and chemical probes in vitro and phasing in vivo. (3) Determination of the writhe, the surface twist and the surface linking number for DNA wrapped on piecewise smooth surfaces. Writhe and the surface twist will be calculated for closed circular DNA wrapped on a connected series of proteins of various geometric shapes. The writhe will be analyzed into its piecewise components and into the contributions due to pairwise interactions, including those between the protein complexes, between the linker regions, and between the protein complexes and the linker regions.
