Consistent rationalization of type-2 topoisomerases' unknotting, decatenating, supercoil-relaxing actions and their scaling relation.

How type-2 topoisomerases discern global topology from local properties of DNA is not known precisely but the hypothesis that the enzymes selectively pass double-helix strands at hook-like juxtapositions is promising. Building upon an investigation of unknotting and decatenating using an improved wormlike DNA model, here we focus primarily on the enzymes' action in narrowing the distribution of linking number (Lk) in supercoiled DNA. Consistent with experiments, with selective passage at a hooked juxtaposition, the simulated narrowing factor RLk diminishes with decreasing DNA circle size but approaches an asymptotic RLk ≈ 1.7-1.8 for circle size ≳3.5 kb. For the larger DNA circles, we found that (RLk - 1) ≈ 0.42log10RK ≈ 0.68log10RL and thus RK ≈ (RL)(1.6) holds for the computed RLk and knot and catenane reduction factors RK and RL attained by selective passage at different juxtaposition geometries. Remarkably, this general scaling relation is essentially identical to that observed experimentally for several type-2 topoisomerases from a variety of organisms, indicating that the different disentangling powers of the topoisomerases likely arise from variations in the hooked geometries they select. Taken together, our results suggest strongly that type-2 topoisomerases recognize not only the curvature of the G-segment but also that of the T-segment.