DNA, Knots and Tangles

Abstract

The DNA of all organisms has a complex and essential topology. Each cell has a family of naturally occurring enzymes that manipulate cellular DNA in topologically interesting and non-trivial ways in order to mediate the vital cellular life processes of replication, transcription and recombination. In order to assay enzyme binding and mechanism, molecular biologists developed the topological approach to enzymology, an experimental protocol in which one reacts small artificial circular DNA substrate molecules with purified enzyme in vitro (in the test tube). The enzyme acts on the DNA substrate, causing changes in the geometry (supercoiling) and/or topology (knotting and linking) of the DNA molecules. Once change in topology of the DNA is known, mathematical analysis can be employed to tease out the structure of the active DNA-protein complex and the changes in that structure due to enzyme mechanism. This paper will describe the tangle model and apply it to the case of site-specific DNA recombination.