Modifies the topological state of DNA by introducing positive supercoils in an ATP-dependent process. It cleaves transiently a single DNA strand and remains covalently bound to the 5' DNA end through a tyrosine residue. May be involved in rewinding the DNA strands in the regions of the chromosome that have opened up to allow transcription or replication (By similarity). Its activity is inhibited by the DNA-binding protein 7d (Sso7d), suggesting that the Sso7d activity might counteract the overwinding effect of reverse gyrase. ATP + H2O = ADP + H(+) + phosphate ATP-dependent breakage, passage and rejoining of double-stranded DNA. Binds two Mg(2+) per subunit. Monomer. Both the DNA unwinding and positive supercoiling activities require the cooperation of both domains. The cooperative action between the helicase-like and the topoisomerase domains is specific. The helicase-like domain probably does not directly unwind DNA but acts more likely by driving ATP-dependent conformational changes within the whole enzyme, functioning more like a protein motor. The 'latch' region of the N-terminal domain plays a regulatory role in the enzyme, repressing topoisomerase activity in the absence of ATP and therefore preventing the enzyme from acting as an ATP-independent relaxing enzyme; it also helps to coordinate nucleotide hydrolysis by the ATPase domain with the supercoiling activity of the topoisomerase domain. This enzyme is the only unique feature of hyperthermophilic bacteria/archaea discovered so far. It appears to be essential for adaptation to life at high temperatures. In the N-terminal section; belongs to the DEAD box helicase family. DDVD subfamily. In the C-terminal section; belongs to the prokaryotic type I/III topoisomerase family.