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. 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. Ile-198 is present instead of the conserved Val which is part of the DDVD box.