The effect of juxtaposition angle on knot reduction in a lattice polygon model of strand passage

Abstract

A model of local strand passage in self-avoiding polygons (SAPs) on the simple cubic lattice is investigated numerically. The polygons studied, called Θ-SAPs, contain a specific strand-passage structure, called Θ, at a fixed strand-passage site. After-strand-passage knot probabilities are estimated from a Monte Carlo study of unknotted and trefoil Θ-SAPs and the estimates are used here to investigate how knot reduction depends on the local juxtaposition structure at the strand-passage site. In particular, we observe a correlation between knot reduction and the angle of the crossing at the strand-passage site; this same angle has been shown experimentally by Neuman et al (2009 Proc. Natl Acad. Sci. USA 106 6986–91) to be important in explaining topoisomerase action on DNA. The angle of the crossing is crossing sign dependent, and, from our observations, so is knot reduction; this can be used to understand experimentally observed knot-type chirality biases.