Mathematics of Nucleic Acids

This tutorial will be divided into two parts. In the first part Wilma Olson will start with an introduction to sequence-dependent information content in known three-dimensional structures of nucleic acids and the implications of this information on larger-scale genetic control.In the second part of the tutorial David Swigon will be present the main concepts, ideas, and results used in the research on DNA topology, elasticity and statistical mechanics. The topics will include, for example, the notion of the linking number, writhe, and twist of closed DNA, the Calugareanu-White theorem, discussions of the elastic rod model, base-pair level model, and worm-like chain model. Emphasis will be placed on the underlying principles that give rise to sequence-dependent fine structure, deformability, and recognition, and how one can use this information in low-resolution modeling of polymeric properties such as ease of spontaneous loop closure or the positioning of nucleosomes. Both lecturers will discuss experimental results that lead to the development of models and the implications of models for the understanding of the behavior of biological systems.