Applications of knot theory: Using knot theory to unravel biochemistry mysteries

Abstract

Although knots have been used since the dawn of humanity, the mathematical study of knots is only a little over 100 years old. Not only has knot theory grown theoretically, the fields of physics, chemistry, and molecular biology have provided many applications of mathematical knots. In this expository paper, we provide an overview of some connections between knot theory and DNA–protein interaction, outlining specifics of the biological mechanisms of DNA replication while providing an overview of related knot invariants. This work is based on an oral presentation given by the author at the Association of Women Mathematicians Research Symposium April 11, 2015.