Coupling of intramolecular and intermolecular linkage complexity of two DNAs

The free energy of two interlinked circular DNAs is argued to couple their interlinkage (catenation) to their “internal” double-helix linkages. Changes in internal linkage which drive supercoiling can therefore alter the free-energy cost of intermolecule catenations. This effect is weak for low amounts of supercoiling or catenation, but becomes strong when there is more than one link added per persistence length. DNA supercoiling can therefore increase the free-energy cost of interlinkages, and in living cells can help to direct type-II topoisomerases to remove catenations between DNAs following their replication, a process required for the segregation of the duplicate molecules. The related problem of the interaction of applied tension with catenation and supercoiling is also analyzed.