Crossing-sign discrimination and knot-reduction for a lattice model of strand passage

Abstract

By performing strand-passages on DNA, type II topoisomerases are known to resolve topological constraints that impede normal cellular functions. The full details of this enzyme-DNA interaction mechanism are, however, not completely understood. To better understand this mechanism, researchers have proposed and studied a variety of random polygon models of enzyme-induced strand-passage. In the present article, we review results from one such model having the feature that it is amenable to combinatorial and asymptotic analysis (as polygon length goes to infinity). The polygons studied, called Θ-SAPs, are on the simple-cubic lattice and contain a specific strand-passage structure, called Θ, at a fixed site. Another feature of this model is the availability of Monte Carlo methods that facilitate the estimation of crossing-sign-dependent knot-transition probabilities. From such estimates, it has been possible to investigate how knot-reduction depends on the crossing-sign and the local juxtaposition geometry at the strand-passage site. A strong relationship between knot-reduction and a crossing-sign-dependent crossing-angle has been observed for this model. In the present article, we review these results and present heuristic geometrical arguments to explain this crossing-sign and angle-dependence. Finally, we discuss potential implications for other models of type II topoisomerase action on DNA.

Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology

“…The effects of twisted hooked juxtapositions on simplification of knots [ (28); see also (29)] can be addressed by observing the consequences of passages within a tight "diagonal row" of juxtapositions resembling a plectoneme in supercoiled DNA. To study the effects of the juxtaposition angle considered earlier [ (30,31); see also (32)], one may observe the consequences of passages in most tight juxtapositions, which are not immediately followed by next tight juxtapositions, as such juxtapositions in a 3D situation naturally predispose the contacting segments to be perpendicular to each other. On the other hand, the hooked juxtapositions with a large area of the rectangle enclosed by the interleaving strands would correspond in a 3D situation to junctions with a larger angular freedom of the juxtaposition.…”

Statics and dynamics of DNA knotting

“…Given two knot types, K 1 and K 2 , one can ask how many crossing reversals are (minimally) needed to go, say, from K 1 to K 2 . This gives a sort of 'topological' distance D(K 1 , K 2 ), that partitions the space of knots [50] according to the numbers D. These numbers, once related to the conversion probability between neighbouring knots in models of knotted rings, can be useful in understanding the action of topoisomerases in simplifying the DNA topology [51,80,263].…”

Topological Aspects of DNA Function and Protein Folding

“…Characterization of these knots has allowed researchers to dissect the mechanistic details of various site-specific recombinases. Christine Soteros and Michael Szafron [5] address the interesting question of topoisomerase-mediated preferential unknotting and show, using a modelling approach, that if DNA topoisomerases were able to select DNA-DNA juxtapositions of a specific geometry, this would result in preferential unknotting. Isabel Darcy and Mariel Vazquez [3] describe so-called difference topology experiments that characterize DNA knots in order to deduce the architecture of the recombination protein-DNA complexes responsible for their formation.…”