The mathematical basis of the hypothesis that type-2 topoisomerases recognize and act at specific DNA juxtapositions has been investigated by coarse-grained lattice polymer models, showing that selective segment passages at hooked juxtapositions can result in dramatic reductions in catenane and knot populations. The lattice modeling approach is here extended to account for the narrowing of variance of linking number (Lk) of DNA circles by type-2 topoisomerases. In general, the steady-state variance of Lk resulting from selective segment passages at a specific juxtaposition geometry j is inversely proportional to the average linking number, Lk(j), of circles with the given juxtaposition. Based on this formulation, we demonstrate that selective segment passages at hooked juxtapositions reduce the variance of Lk. The dependence of this effect on model DNA circle size is remarkably similar to that observed experimentally for type-2 topoisomerases, which appear to be less capable in narrowing Lk variance for small DNA circles than for larger DNA circles. This behavior is rationalized by a substantial cancellation of writhe in small circles with hook-like juxtapositions. During our simulations, we uncovered a twisted variation of the hooked juxtaposition that has an even more dramatic effect on Lk variance narrowing than the hooked juxtaposition. For an extended set of juxtapositions, we detected a significant correlation between the Lk narrowing potential and the logarithmic decatenating and unknotting potentials for a given juxtaposition, a trend reminiscent of scaling relations observed with experimental measurements on type-2 topoisomerases from a variety of organisms. The consistent agreement between theory and experiment argues for type-2 topoisomerase action at hooked or twisted-hooked DNA juxtapositions.
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