9705016 Coleman The principal investigator will continue his work on the development of the elastic rod model for DNA with the goals of (i) attaining insight into the mode of action of topoisomerases, (ii) finding efficient ways to calculate configurations of DNA segments and plasmids in circumstances in which the forces arising from self-contact are not negligible, and (iii) obtaining mathematical results in the theory of vibrations of elastic rings that are needed to account for the effects of thermal fluctuations on quantities, such as writhe, that depend on the tertiary structure of DNA plasmids. In research in a different area, analytical and numerical methods will be employed to study the morphological changes and instabilities that result from curvature driven mass diffusion within the bounding surfaces of solid bodies. Among the topics to be investigated are (i) the evolution and stability of axisymmetric surfaces and of planar curves in the theory of curvature driven diffusion and (ii) the evolution of pit-like defects in otherwise flat films. Much is yet to be learned about the modes of action of proteins that are known to bind to and induce deformations in DNA. There are cases in which one can discuss the action of DNA bending proteins by treating a DNA molecule as an elastic rod. Recent research has shown that one can use exact solutions of the equations of equilibrium for elastic rods to investigate the nature of the dependence of the configuration of a segment of DNA on conditions imposed at its end points. Several of the problems that are investigated in this way are important for understanding mechanisms of gene regulation. The work on curvature driven mass diffusion within the bounding surfaces of solids is expected to have significant applications in materials science. As the effects of surface diffusion increase in importance as dimensions become small, the theory of such diffusion can be applied to obtain insight and quan titative results in the following research areas: the formation of thermal grooves, i.e., the development of surface indentations at grain boundaries in heated metals; the stability of field-emitter cathodes, of interconnecting elements in microelectronic circuits, and of moving parts in micro-electromechanical devices; fiber spheroidization in metallic composites; and the pitting of thin films at grain boundary vertices.
