Kinetic proofreading can explain the supression of supercoiling of circular DNA molecules by type-II topoisomerases

The enzymes that pass DNA through DNA so as to remove entanglements, adenosine-triphosphate-hydrolyzing type-II topoisomerases, are able to suppress the probability of self-entanglements (knots) and mutual entanglements (links) between $\sim 10\hspace{0.5em}\mathrm{kb}$ plasmids, well below the levels expected, given the assumption that the topoisomerases pass DNA segments at random by thermal motion. This implies that a 10-nm type-II topoisomerase can somehow sense the topology of a large DNA. We previously introduced a “kinetic proofreading” model which supposes the enzyme to require two successive collisions in order to allow exchange of DNA segments, and we showed how it could quantitatively explain the reduction in knotting and linking complexity. Here we show how the same model quantitatively explains the reduced variance of the double-helix linking number (supercoiling) distribution observed experimentally.