Supercoiled DNA is more compact. With circular DNA, a superhelix is not simply the circular DNA strand in twisted conformation. The superhelix is a topoisomer of the circular DNA where all base pairs are in place. Topoisomers are topological isomers, molecules with the same chemical formula but different topologies. Topoisomers can only be interconverted by breaking and reforming bonds. Topoisomerases are enzymes that carry out this interconversion. Imagine trying to untangle a phone cord if it were a complete circle. You couldn't do it without cutting it. DNA gyrase is a topoisomerase that moves in the other direction. It consumes ATP to impart the free energy of supercoiling to DNA. DNA gyrase and topoisomerase 1 are antagonists.
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