title: Random state transitions of knots: a first step towards modeling unknotting by type II topoisomerases.
abstract: Type II topoisomerases are enzymes that change the topology of DNA by performing strand-passage. In particular, they unknot knotted DNA very efficiently. Motivated by this experimental observation, we investigate transition probabilities between knots. We use the BFACF algorithm to generate ensembles of polygons in Z(3) of fixed knot type. We introduce a novel strand-passage algorithm which generates a Markov chain in knot space. The entries of the corresponding transition probability matrix determine state-transitions in knot space and can track the evolution of different knots after repeated strand-passage events. We outline future applications of this work to DNA unknotting.
authors.affiliation: Mathematics Department, The University of Hong Kong, Hong Kong.
authors.forename: Xia
authors.initials: X
authors.lastname: Hua
authors.forename: Diana
authors.initials: D
authors.lastname: Nguyen
authors.forename: Barath
authors.initials: B
authors.lastname: Raghavan
authors.forename: Javier
authors.initials: J
authors.lastname: Arsuaga
authors.forename: Mariel
authors.initials: M
authors.lastname: Vazquez