, The absorbance was monitored at 340 nm over 600 s at 37°C with a Shimadzu 1700 spectrophotometer. Reactions were recorded in triplicates with 50-100 nM of GyrA 2 B 2 and 16 nM linear DNA (pCR-blunt) in 500 µl of a buffer containing 50 mM Tris HCl pH 7.5, 150 mM potassium acetate, 8 mM magnesium acetate, 7 mM BME, 100 µg/mg of BSA, ATPase activity assay. ATP hydrolysis is measured by following the oxidation of NADH mediated by pyruvate kinase (PK) and lactate dehydrogenase (LDH)

, Multiple alignment and evolutionary conservation of residues. GyrB ATPase/ Transducer protein sequences from 30 species

L. A0a3a2t2c3_lismn and . Monocytogenes,

, Agrobacterium tumefasciens; Q83FD5_COXBU, Coxiella burnetii, pp.8-12

E. Gyrb_ecoli and . Coli,

N. Gyrb_neigo and . Gonorrhoeae,

S. Gyrb_salty, P. Q7v9n3_proma, ;. Gyrb_strr6, S. , ;. Gyrb_mycpn et al.,

P. Gyrb_pseae, . Aeruginosa, C. Q18c89_pepd6, and . Difficile,

R. Gyrb_ricfe and . Felis,

Y. Q8czg1_yerpe, ;. Gyrb_borbu;-borrelia-burgdorferi, and ;. Gyr-b_entfa, Enterococcus faecalis; Q8YEQ5_BRUME, Brucella melitensis; GYRB_-STAAU

H. Gyrb_haein and . Influenzae,

M. Gyrb_myctu, . Tuberculosis, T. Gyrb_thema, and . Maritima, , vol.8, pp.Thermus ther- mophilus

, Bacillus subtilis

H. Gyrb_helpy and . Pylori,

C. Gyrb_chltr and . Trachomatis,

V. Gyrb_vibch and . Cholerae,

T. Gyrb_theaq and . Aquaticus,

, Aquifex aeolicus) were aligned using the Clustal Omega server (EMBL-EBI). The subsequent alignment was used to plot the amino acids evolutionary conservation on the ATPase/transducer structure, PDB ID 1EI1) using the ConSurf server

, Model coordinates and density maps are available in the Protein Data Bank (PDB ID 6RKS, p.6

, The source data underlying Figs. 1a, 4c, d and Supplementary Fig, p.4914

J. C. Wang, Cellular roles of DNA topoisomerases: a molecular perspective, Nat. Rev. Mol. Cell Biol, vol.3, pp.430-440, 2002.

S. M. Vos, E. M. Tretter, B. H. Schmidt, and J. M. Berger, All tangled up: how cells direct, manage and exploit topoisomerase function, Nat. Rev. Mol. Cell Biol, vol.12, pp.827-841, 2011.

A. J. Schoeffler and J. M. Berger, DNA topoisomerases: harnessing and constraining energy to govern chromosome topology, Q Rev. Biophys, vol.41, pp.41-101, 2008.

N. G. Bush, K. Evans-roberts, A. Maxwell, and . Topoisomerases, EcoSal Plus, vol.6, 2015.

M. Gellert, K. Mizuuchi, M. H. O'dea, and H. A. Nash, DNA gyrase: an enzyme that introduces superhelical turns into DNA, Proc. Natl Acad. Sci. USA, vol.73, pp.3872-3876, 1976.

J. Roca and J. C. Wang, DNA transport by a type II DNA topoisomerase: evidence in favor of a two-gate mechanism, Cell, vol.77, pp.609-616, 1994.

J. Roca, J. M. Berger, S. C. Harrison, and J. C. Wang, DNA transport by a type II topoisomerase: direct evidence for a two-gate mechanism, Proc. Natl Acad. Sci. USA, vol.93, pp.4057-4062, 1996.

D. B. Wigley, G. J. Davies, E. J. Dodson, A. Maxwell, and G. Dodson, Crystal structure of an N-terminal fragment of the DNA gyrase B protein, Nature, vol.351, pp.624-629, 1991.

J. H. Morais-cabral, Crystal structure of the breakage-reunion domain of DNA gyrase, Nature, vol.388, pp.903-906, 1997.

A. J. Ruthenburg, D. M. Graybosch, J. C. Huetsch, and G. L. Verdine, A superhelical spiral in the Escherichia coli DNA gyrase A C-terminal domain imparts unidirectional supercoiling bias, J. Biol. Chem, vol.280, pp.26177-26184, 2005.

K. M. Soczek, T. Grant, P. B. Rosenthal, and A. Mondragon, CryoEM structures of open dimers of gyrase A in complex with DNA illuminate mechanism of strand passage, vol.7, p.41215, 2018.

J. Papillon, Structural insight into negative DNA supercoiling by DNA gyrase, a bacterial type 2A DNA topoisomerase, Nucleic Acids Res, vol.41, pp.7815-7827, 2013.

A. Basu, Dynamic coupling between conformations and nucleotide states in DNA gyrase, Nat. Chem. Biol, vol.14, pp.565-574, 2018.

A. Basu, A. C. Parente, and Z. Bryant, Structural dynamics and mechanochemical coupling in DNA Gyrase, J. Mol. Biol, vol.428, pp.1833-1845, 2016.

A. Gubaev and D. Klostermeier, The mechanism of negative DNA supercoiling: a cascade of DNA-induced conformational changes prepares gyrase for strand passage, DNA Repair (Amst.), vol.16, pp.23-34, 2014.

J. T. Stelljes, D. Weidlich, A. Gubaev, and D. Klostermeier, Gyrase containing a single C-terminal domain catalyzes negative supercoiling of DNA by decreasing the linking number in steps of two, Nucleic Acids Res, vol.46, pp.6773-6784, 2018.

A. J. Schoeffler, A. P. May, and J. M. Berger, A domain insertion in Escherichia coli GyrB adopts a novel fold that plays a critical role in gyrase function, Nucleic Acids Res, vol.38, pp.7830-7844, 2010.

F. Collin, S. Karkare, and A. Maxwell, Exploiting bacterial DNA gyrase as a drug target: current state and perspectives, Appl. Microbiol. Biotechnol, vol.92, pp.479-497, 2011.

L. Heide, New aminocoumarin antibiotics as gyrase inhibitors, Int. J. Med. Microbiol, vol.304, pp.31-36, 2014.

J. L. Delgado, C. M. Hsieh, N. L. Chan, and H. Hiasa, Topoisomerases as anticancer targets, Biochem. J, vol.475, pp.373-398, 2018.

A. Vanden-broeck, A. G. Mcewen, Y. Chebaro, N. Potier, and V. Lamour, Structural basis for DNA Gyrase interaction with coumermycin A1, J. Med Chem, vol.62, pp.4225-4231, 2019.

B. D. Bax, Type IIA topoisomerase inhibition by a new class of antibacterial agents, Nature, vol.466, pp.935-940, 2010.

D. J. Biedenbach, In vitro activity of gepotidacin, a novel triazaacenaphthylene bacterial topoisomerase inhibitor, against a broad spectrum of bacterial pathogens, Antimicrob. Agents Chemother, vol.60, pp.1918-1923, 2016.

N. E. Scangarella-oman, Microbiological analysis from a phase 2 randomized study in adults evaluating single oral doses of gepotidacin in the treatment of uncomplicated urogenital gonorrhea caused by Neisseria gonorrhoeae, Antimicrob. Agents Chemother, vol.62, pp.1221-1239, 2018.

E. G. Gibson, B. Bax, P. F. Chan, and N. Osheroff, Mechanistic and structural basis for the actions of the antibacterial gepotidacin against Staphylococcus aureus Gyrase, ACS Infect. Dis, vol.5, pp.570-581, 2019.

Y. Pommier, Drugging topoisomerases: lessons and challenges, ACS Chem. Biol, vol.8, pp.82-95, 2013.

R. Danev and W. Baumeister, Cryo-EM single particle analysis with the Volta phase plate, Elife, vol.5, p.13046, 2016.

M. Khoshouei, M. Radjainia, W. Baumeister, and R. Danev, Cryo-EM structure of haemoglobin at 3.2 A determined with the Volta phase plate, Nat. Commun, vol.8, p.16099, 2017.

D. Kimanius, B. O. Forsberg, S. H. Scheres, and E. Lindahl, Accelerated cryo-EM structure determination with parallelisation using GPUs in RELION-2, vol.5, p.18722, 2016.

S. H. Scheres, RELION: implementation of a Bayesian approach to cryo-EM structure determination, J. Struct. Biol, vol.180, pp.519-530, 2012.

A. Punjani, J. L. Rubinstein, D. J. Fleet, and M. A. Brubaker, cryoSPARC: algorithms for rapid unsupervised cryo-EM structure determination, Nat. Methods, vol.14, pp.290-296, 2017.

L. Brino, Dimerization of Escherichia coli DNA-gyrase B provides a structural mechanism for activating the ATPase catalytic center, J. Biol. Chem, vol.275, pp.9468-9475, 2000.

S. Petrella, Overall structures of Mycobacterium tuberculosis DNA Gyrase reveal the role of a corynebacteriales GyrB-specific insert in ATPase activity, Structure, vol.27, p.5, 2019.

K. C. Dong and J. M. Berger, Structural basis for gate-DNA recognition and bending by type IIA topoisomerases, Nature, vol.450, pp.1201-1205, 2007.

B. H. Schmidt, N. Osheroff, and J. Berger, Structure of a topoisomerase II-DNA-nucleotide complex reveals a new control mechanism for ATPase activity, Nat. Struct. Mol. Biol, vol.19, pp.1147-1154, 2012.

F. V. Stanger, C. Dehio, and T. Schirmer, Structure of the N-terminal Gyrase B fragment in complex with ADPPi reveals rigid-body motion induced by ATP hydrolysis, PLoS ONE, vol.9, p.107289, 2014.

A. P. Tingey and A. Maxwell, Probing the role of the ATP-operated clamp in the strand-passage reaction of DNA gyrase, Nucleic Acids Res, vol.24, pp.4868-4873, 1996.

V. Lamour, L. Hoermann, J. M. Jeltsch, P. Oudet, and D. Moras, An open conformation of the Thermus thermophilus gyrase B ATP-binding domain, J. Biol. Chem, vol.277, pp.18947-18953, 2002.

S. F. Chen, Structural insights into the gating of DNA passage by the topoisomerase II DNA-gate, Nat. Commun, vol.9, p.3085, 2018.

P. F. Chan, Thiophene antibacterials that allosterically stabilize DNAcleavage complexes with DNA gyrase, Proc. Natl Acad. Sci. USA, vol.114, pp.4492-4500, 2017.

T. J. Miles, Novel tricyclics (e.g., GSK945237) as potent inhibitors of bacterial type IIA topoisomerases, Bioorg. Med. Chem. Lett, vol.26, pp.2464-2469, 2016.

J. Wang and P. B. Moore, On the interpretation of electron microscopic maps of biological macromolecules, Protein Sci, vol.26, pp.122-129, 2017.

E. M. Tretter and J. M. Berger, Mechanisms for defining supercoiling set point of DNA gyrase orthologs: I. A nonconserved acidic C-terminal tail modulates Escherichia coli gyrase activity, J. Biol. Chem, vol.287, pp.18636-18644, 2012.

T. J. Wendorff, B. H. Schmidt, P. Heslop, C. A. Austin, and J. M. Berger, The structure of DNA-bound human topoisomerase II alpha: conformational mechanisms for coordinating inter-subunit interactions with DNA cleavage, J. Mol. Biol, vol.424, pp.109-124, 2012.

M. G. Rudolph and D. Klostermeier, Mapping the spectrum of conformational states of the DNA-and C-gates in Bacillus subtilis gyrase, J. Mol. Biol, vol.425, pp.2632-2640, 2013.

I. Laponogov, Trapping of the transport-segment DNA by the ATPase domains of a type II topoisomerase, Nat. Commun, vol.9, p.2579, 2018.

K. D. Corbett, R. K. Shultzaberger, and J. M. Berger, The C-terminal domain of DNA gyrase A adopts a DNA-bending beta-pinwheel fold, Proc. Natl Acad. Sci. USA, vol.101, pp.7293-7298, 2004.

D. Ward and A. Newton, Requirement of topoisomerase IV parC and parE genes for cell cycle progression and developmental regulation in Caulobacter crescentus, Mol. Microbiol, vol.26, pp.897-910, 1997.

V. M. Kramlinger, H. Hiasa, and . The, GyrA-box" is required for the ability of DNA gyrase to wrap DNA and catalyze the supercoiling reaction, J. Biol. Chem, vol.281, pp.3738-3742, 2006.

L. Costenaro, J. G. Grossmann, C. Ebel, and A. Maxwell, Small-angle X-ray scattering reveals the solution structure of the full-length DNA gyrase a subunit, Structure, vol.13, pp.287-296, 2005.

M. A. Lanz and D. Klostermeier, The GyrA-box determines the geometry of DNA bound to gyrase and couples DNA binding to the nucleotide cycle, Nucleic Acids Res, vol.40, pp.10893-10903, 2012.

M. A. Lanz, M. Farhat, and D. Klostermeier, The acidic C-terminal tail of the GyrA subunit moderates the DNA supercoiling activity of Bacillus subtilis gyrase, J. Biol. Chem, vol.289, pp.12275-12285, 2014.

D. N. Mastronarde, Automated electron microscope tomography using robust prediction of specimen movements, J. Struct. Biol, vol.152, pp.36-51, 2005.

D. N. Mastronarde and S. R. Held, Automated tilt series alignment and tomographic reconstruction in IMOD, J. Struct. Biol, vol.197, pp.102-113, 2017.

S. Q. Zheng, MotionCor2: anisotropic correction of beam-induced motion for improved cryo-electron microscopy, Nat. Methods, vol.14, pp.331-332, 2017.

K. Zhang and . Gctf, Real-time CTF determination and correction, J. Struct. Biol, vol.193, pp.1-12, 2016.

S. H. Scheres and S. Chen, Prevention of overfitting in cryo-EM structure determination, Nat. Methods, vol.9, pp.853-854, 2012.

S. Chen, High-resolution noise substitution to measure overfitting and validate resolution in 3D structure determination by single particle electron cryomicroscopy, Ultramicroscopy, vol.135, pp.24-35, 2013.

P. B. Rosenthal and R. Henderson, Optimal determination of particle orientation, absolute hand, and contrast loss in single-particle electron cryomicroscopy, J. Mol. Biol, vol.333, pp.721-745, 2003.

J. B. Heymann and D. M. Belnap, Bsoft: image processing and molecular modeling for electron microscopy, J. Struct. Biol, vol.157, pp.3-18, 2007.

E. F. Pettersen, UCSF Chimera-a visualization system for exploratory research and analysis, J. Comput Chem, vol.25, pp.1605-1612, 2004.

P. D. Adams, PHENIX: a comprehensive Python-based system for macromolecular structure solution, Acta Crystallogr. D. Biol. Crystallogr, vol.66, pp.213-221, 2010.

P. Emsley, B. Lohkamp, W. G. Scott, and K. Cowtan, Features and development of Coot, Acta Crystallogr. D. Biol. Crystallogr, vol.66, pp.486-501, 2010.

L. A. Kelley, S. Mezulis, C. M. Yates, M. N. Wass, and M. J. Sternberg, The Phyre2 web portal for protein modeling, prediction and analysis, Nat. Protoc, vol.10, pp.845-858, 2015.

T. D. Goddard, UCSF ChimeraX: Meeting modern challenges in visualization and analysis, Protein Sci, vol.27, pp.14-25, 2018.