Releases the supercoiling and torsional tension of DNA, which is introduced during the DNA replication and transcription, by transiently cleaving and rejoining one strand of the DNA duplex. Introduces a single-strand break via transesterification at a target site in duplex DNA. The scissile phosphodiester is attacked by the catalytic tyrosine of the enzyme, resulting in the formation of a DNA-(5'-phosphotyrosyl)-enzyme intermediate and the expulsion of a 3'-OH DNA strand. The free DNA strand then undergoes passage around the unbroken strand, thus removing DNA supercoils. Finally, in the religation step, the DNA 3'-OH attacks the covalent intermediate to expel the active-site tyrosine and restore the DNA phosphodiester backbone. ATP-independent breakage of single-stranded DNA, followed by passage and rejoining. Binds two Mg(2+) ions 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+). Monomer. Transcription is increased specifically in response to 2,4,6-trinitrotoluene (TNT) and its indicator compounds 1,3-DNB, 2,4-DNT, and 2,6-DNT. Has been used to construct a 2,4,6-trinitrotoluene (TNT) biosensor strain. Belongs to the type IA topoisomerase family.