DNA topoisomerases are able to modify the termtiary structure of circular DNA. Prokaryotic enzymes do not require ATP, as do eukaryotic topoisomerases.

DNA topoisomerases have been classified into two types:

Type I DNA topoisomerases: catalyse several reactions, usually in the absence of any high energy cofactor. They remove negative and sometimes positive supercoils from circular DNAs, linkg the single-stranded rings of complementary DNAs, transform single-stranded circles into knotted ones. 

The functions of topoisomerases I are not so well established, alhtough they have been implication in the regulation of transcription and in the transpoisition process (Riou, Eur. J. Biochem, 134, 479-484 (1983). 

Type II DNA topoisomerases: catalyse the reations of relaxation, actenation/decatentation and knotting/uknotting. They are thought to play an important role in repliaction, transcription, recombination and repair processes.