DNA Topology Review

DNA holds the instructions for an organism’s development, reproduction, and, ultimately, death. It encodes much of the information a cell needs to survive and reproduce. It is important for inheritance and coding for proteins, and contains the genetic instruction guide for life and its processes. But also, DNA of an organism has a complex and interesting topology. For information retrieval and cell viability, some geometric and topological features of DNA must be introduced, and others quickly removed. Proteins perform these amazing feats of topology at the molecular level; thus, the description and quantization of these protein actions require the language and computational machinery of topology. The use of tangle algebra to model the biological processes that give rise to knotting in DNA provides an excellent example of the application of topological algebra to biology. The tangle algebra approach to knotting in DNA began with the study of the site-specific recombinase Tn3 resolvase. This chapter is a summary of some basic knot theory and biology. We then describe the tangle model developed by Ernst and Sumners using the Tn3 resolvase as an example. We conclude with applications of the tangle model to other biological problems.