Can introduce negative superhelical turns into double-stranded circular DNA. ATP-dependent breakage, passage and rejoining of double-stranded DNA. Binds two Mg(2+) per subunit. The magnesium ions form salt bridges with both the protein and the DNA. Can also accept other divalent metal cations, such as Mn(2+) or Ca(2+). Belongs to the type II topoisomerase family.