Bacterial enzymes of the DNA TOPOISOMERASES, TYPE II class that catalyze ATP-dependent breakage of both strands of DNA, passage of the unbroken strands through the breaks, and rejoining of the broken strands. These enzymes bring about relaxation of the supercoiled DNA duplex. Bacterial DNA topoisomerases in the Type II class exist as heterotetramers of 2 subunits, such as 2 gyrA and 2 gyrB in DNA GYRASE.