Application of a skein relation to difference topology experiments

Abstract

Difference topology is a technique used to study any protein that can stably bind to DNA. This technique is used to determine the conformation of DNA bound by protein. Motivated by difference topology experiments, we use the skein relation tangle model as a novel technique to study experiments using topoisomerase to study SMC proteins, a family of proteins that stably bind to DNA. The oriented skein relation involves an oriented knot, [Formula: see text], with a distinguished positive crossing; a knot [Formula: see text], obtained by changing the distinguished positive crossing of [Formula: see text] to a negative crossing; a knot, [Formula: see text], resulting from the non-orientation persevering resolution of the distinguished crossing; and a link [Formula: see text], the orientation preserving resolution of the distinguished crossing. We refer to [Formula: see text] as the skein quadruple. Topoisomerases are proteins that break one segment of DNA allowing a DNA segment to pass through before resealing the break. Recombinases are proteins that cut two segments of DNA and recombine them in some manner. They can act on direct repeat or inverted repeat sites, resulting in a link or knot, respectively. Thus, the skein quadruple is now viewed as [Formula: see text] circular DNA substrate, [Formula: see text] product of topoisomerase action, [Formula: see text] product of recombinase action on directed repeat sites, and [Formula: see text] product of recombinase action of inverted repeat sites.