Mathematical modeling, analysis and computation arising in continuum mechanical descriptions of DNA

University Of Texas At Austin, Austin TX

Investigators

Abstract

Gonzalez 0102476 The investigator studies constitutive relations for continuum rod models of DNA and develops new tools for analyzing the supercoiling and packaging of DNA and other material filaments. The main objectives of the project are to apply the theories of statistical mechanics and stochastic differential equations to develop constitutive relations for continuum rod models of DNA that are provably consistent with detailed, sequence-dependent structural information at the base-pair level; to apply the new concept of global curvature to develop a geometrically exact and computationally tractable formulation of the self-contact constraint that plays a central role in the supercoiling and packaging of DNA and other biological filaments; and to develop efficient and provably accurate computational methods for continuum rod models that faithfully respect global geometric constraints as well as qualitative features of the underlying system. Biologists and chemists now believe that the linear sequence of base-pairs along a DNA molecule contains not only a genetic code, but also a structural code that governs the global organization of the molecule and its susceptibility to interactions with other molecules. An understanding of this structural code requires realistic mechanical models of DNA over a wide range of length scales. The research project pursued by the investigator is aimed at the further refinement of medium- to long-scale continuum models. In particular, methods are developed for estimating local, sequence-dependent material parameters and for describing global, finite-thickness effects. Results from this research will be useful in developing a greater understanding of the physical and mechanical properties of DNA, in modeling how DNA may twist, bend and supercoil upon itself, and in studying how DNA and other material filaments may be optimally packed in confined geometries.