Reactions mediated by topoisomerases and other enzymes: Modelling localised DNA transformations

Many proteins cleave and reseal DNA molecules in precisely orchestrated ways. Modelling these reactions has often relied on the axis of the DNA double helix being circular, so these cut-and-seal mechanisms can be tracked by corresponding changes in the knot type of the DNA axis. However, when the DNA molecule is linear, or the protein action does not manifest itself as a change in knot type, or the knot types are not 4-plats, these knot-theoretic models are less germane. We thus give a taxonomy of local DNA axis configurations. More precisely, we characterise all rational tangles obtained from a given rational tangle via a rational subtangle replacement. This classification is then endowed biologically with a distance that determines how many enzyme-mediated reactions of a particular type are needed to proceed from one local DNA conformation to another, or indeed if it is even possible.We conclude by discussing a variety of biological applications of this categorisation, including reactions mediated by type II topoisomerase, site-specific recombinase and transposase.

Duke Scholars

Author Dorothy Buck Mathematics