Computational modeling of filaments with applications to DNA packing and sedimentation

University Of Texas At Austin, Austin TX

Investigators

Abstract

Proposal: DMS-0405955 PI: Oscar Gonzalez Institution: University of Texas at Austin Title: Computational Modeling of Filaments with Applications to DNA Packing and Sedimentation ABSTRACT The investigator will carry out two projects aimed at developing a deeper understanding of the geometrical and physical properties of material filaments. The first project deals with the numerical analysis of optimal packing problems for curves with thickness. The objective is to exploit the concept of global curvature to develop numerical methods for optimizing the energy of a curve in three-dimensional space (or a framed curved if twist is important) subject to an excluded-volume constraint in which the curve is the centerline of a flexible, solid tube of prescribed radius. The second project deals with the relation between shape and speed in the sedimentation dynamics of thin, rigid (or nearly rigid) filaments. The objective is to characterize how features of geometry (such as length, curvature, tubular neighborhood size) and topology (knot type) affect the possible speeds at which a filament can sediment in a viscous (Stokes) fluid. An understanding of how material filaments may be optimally packed in confined geometries and how they may supercoil or wrap around themselves is of great interest in the study of macromolecules such as DNA and other systems in chemistry and biology. While recent modeling advances have led to concise mathematical formulations of such problems, numerical techniques for studying them have received relatively little attention. The first research project pursued by the investigator is focused on the development of provably convergent numerical methods for studying these and other related packing problems. Sedimentation and gel electrophoresis are common laboratory techniques for analyzing DNA and other polymers. These methods exploit the observation that small, relatively stiff polymer fragments of different shape typically travel at different speeds when forced through a viscous fluid or through a gel. However, the general relation between shape and speed is at present not well understood. The second research project pursued by the investigator is focused on the characterization of the shape-speed relation for sedimentation. Results from this research may lead to improved laboratory techniques, and may enable more detailed structural information about polymers to be deduced from sedimentation data.