Cells must remove all entanglements between their replicated chromosomal DNAs to segregate them during cell division. Entanglement removal is done by ATP-driven enzymes that pass DNA strands through one another, called type II topoisomerases. In vitro, some type II topoisomerases can reduce entanglements much more than expected, given the assumption that they pass DNA segments through one another in a random way. These type II topoisomerases (of less than 10 nm in diameter) thus use ATP hydrolysis to sense and remove entanglements spread along flexible DNA strands of up to 3,000 nm long. Here we propose a mechanism for this, based on the higher rate of collisions along entangled DNA strands, relative to collision rates on disentangled DNA strands. We show theoretically that if a type II topoisomerase requires an initial 'activating' collision before a second strand-passing collision, the probability of entanglement may be reduced to experimentally observed levels. This proposed two-collision reaction is similar to 'kinetic proofreading' models of molecular recognition.
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