Mechanism of AAA+ ATPase-mediated RuvAB–Holliday junction branch migration

The Holliday junction is a key intermediate formed during DNA recombination across all kingdoms of life1. In bacteria, the Holliday junction is processed by two homo-hexameric AAA+ ATPase RuvB motors, which assemble together with the RuvA–Holliday junction complex to energize the strand-exchange reaction2. Despite its importance for chromosome maintenance, the structure and mechanism by which this complex facilitates branch migration are unknown. Here, using time-resolved cryo-electron microscopy, we obtained structures of the ATP-hydrolysing RuvAB complex in seven distinct conformational states, captured during assembly and processing of a Holliday junction. Five structures together resolve the complete nucleotide cycle and reveal the spatiotemporal relationship between ATP hydrolysis, nucleotide exchange and context-specific conformational changes in RuvB. Coordinated motions in a converter formed by DNA-disengaged RuvB subunits stimulate hydrolysis and nucleotide exchange. Immobilization of the converter enables RuvB to convert the ATP-contained energy into a lever motion, which generates the pulling force driving the branch migration. We show that RuvB motors rotate together with the DNA substrate, which, together with a progressing nucleotide cycle, forms the mechanistic basis for DNA recombination by continuous branch migration. Together, our data decipher the molecular principles of homologous recombination by the RuvAB complex, elucidate discrete and sequential transition-state intermediates for chemo-mechanical coupling of hexameric AAA+ motors and provide a blueprint for the design of state-specific compounds targeting AAA+ motors.

Homologous recombination is a fundamental cellular process involved in the maintenance of genetic integrity and the generation of genetic diversity across all domains of life. The central and universal element in genetic recombination as well as in double strand break repair and in the process of replication fork rescue is a four-way DNA heteroduplex called the Holliday junction 1,3,4 . In prokaryotes, the two proteins RuvA and RuvB play critical roles in the processing of the Holliday junction by promoting the ATP-dependent unidirectional strand-exchange reaction known as active branch migration 2,[5][6][7][8][9][10][11] . Previous biochemical and structural evidence suggests that branch migration is facilitated by a tripartite complex: RuvA tetramers assemble around the Holliday junction crossover to provide structural guidance for DNA separation and rewinding and are flanked by two hexameric RuvB AAA+ ATPases that together fuel the translocation of the newly emerged recombined DNA [12][13][14][15][16][17][18][19] . Furthermore, these studies demonstrated that domain III of RuvA (RuvA D3 ) binds to the presensor-1 β-hairpin of RuvB, a distinguishing feature of the PS1 insert superclade 20,21 , regulates branch migration and increases ATPase activity of the RuvB motor 22,23 . Moreover, the ability for cross-species hetero-complementation established the existence of a robust and conserved mechanism of the RuvA-and RuvB AAA+-coordinated action at the Holliday junction 24,25 . Despite the large body of knowledge, the structure of the RuvAB-Holliday junction complex (hereafter referred to as RuvAB-HJ) and the molecular mechanisms by which the RuvB AAA+ motors drive the translocation of DNA to facilitate one of the most basic biological processes in living organisms-namely the maintenance and exchange of genetic information 26,27 -remain unknown. To unravel the architecture and decipher the operating principles of the RuvAB machinery, we applied time-resolved cryo-electron microscopy (cryo-EM) and single-particle analyses of in vitro reconstituted RuvAB complexes processing a Holliday junction. Our structural analyses reveal a highly coordinated conformational landscape of an active RuvAB branch migration complex and uncover the dynamic interplay between a completely resolved nucleotide cycle in a rotating RuvB AAA+ motor as well as DNA translocation. Furthermore, we show that RuvB motors translocate the DNA as molecular levers in an ATP-dependent power stroke to convert chemical energy to mechanical force. https://doi.org/10.1038/s41586-022-05121-1

Structure of the RuvAB-HJ complex
Branch migration of Holliday junctions driven by the RuvAB machinery is a fast and highly dynamic process that is essential during DNA recombination 28,29 (Fig. 1a). To visualize this process, we reconstituted RuvAB-HJ complexes in vitro from individually purified components originating from Salmonella typhimurium and Streptococcus thermophilus, respectively, and tested their function in a branch migration assay (Fig. 1b). Both homo-(RuvA and RuvB from S. typhimurium) and hetero-(RuvA from S. typhimurium and RuvB from S. thermophilus) complexes processed the Holliday junction similarly upon addition of ATP, suggesting a highly conserved underlying mechanism, owing to interchangeability of individual components ( Fig. 1b and Extended Data Fig. 1a-h). To capture the catalytic steps of this rapid process, we first slowed down the reaction by replacing ATP with an equimolar mixture of the slowly hydrolysable ATPγS 30 and ADP and incubated the reaction on ice either for 30 min (dataset t1) or for 5 h (dataset t2) to mimic an initiation and an equilibration phase of the RuvAB-HJ complex (Extended Data Fig. 1h). Subsequent vitrification of samples led to aggregates and low numbers of individual particles for homo-complexes, whereas the distribution of hetero-complexes over the grid was largely monodisperse and suitable for single-particle analysis (Extended Data Fig. 1f-j). The cryo-EM structure of the RuvAB-HJ complex resolved to a resolution of 8 Å revealed highly flexible and linearly arranged tripartite assemblies, with eight RuvA molecules symmetrically arranged in two tetramers (3.3 Å resolution) and the four-way Holliday junction flanked by, and flexibly connected to, one or two RuvB hexamers (2.9-4.1 Å resolution) as well as bipartite particles (3.9 Å resolution) (  Table 1). This architecture is consistent with previously proposed models of the RuvAB machinery 14,15,17,22,23,31 . In both particle types, DNA enters and exits the RuvA core as a double helix, with one or two hexameric RuvB motors engaging the minor groove of the rejoined DNA (Fig. 1f). The RuvA core is physically connected to both RuvB motors through RuvA D3 (Fig. 1c). On either side, two RuvA D3 domains are bound to adjacently positioned RuvB subunits, indicating that these domains could cooperate to control the two RuvB AAA+ motors (Fig. 1c,e). Notably, all four RuvB-coordinating RuvA D3 domains localize to the same side of the Holliday junction crossover (Extended Data Fig. 4f), implying that a single RuvA tetramer might be sufficient to operate both RuvB motors simultaneously. These findings are also in agreement with the proposed architecture of the RuvABC resolvasome, in which the Holliday junction is believed to be sandwiched by one RuvA tetramer and a dimer of the resolvase RuvC 32,33 (Extended Data Fig. 4g).
To investigate the flexibility of RuvAB-HJ complexes, we subjected our particles to further three-dimensional classifications. This analysis revealed that, besides the overall flexibility, in about 7% of the bipartite particles and about 6% of the tripartite particles, the position of   (2) particles. Focused classifications on one of the RuvB motors (3) or the central RuvA-HJ core (4) highlight the overall flexibility of tripartite particles. Scale bar, 10 nm. e, RuvB motors bind to one or two RuvA D3 domains (blue). The two RuvA D3 domains bind to adjacent RuvB subunits in the RuvB motors. f, RuvAB-HJ complex in which substratedisengaged RuvB subunits and one RuvA tetramer are removed to visualize the Holliday junction and the interaction of each RuvB motor with its cognate DNA substrate. Arrows show the direction of movement of DNA at the entry to the RuvA core and the exit of the new DNA duplex from the RuvB motors. Dimensions of the complex are indicated. g, Configuration of RuvB hexamers that undergo a rotation by 60° relative to the RuvA core. Focused 3D classes (end-on (upper panel) and side views (lower panel) using a mask enclosing one RuvB motor and the central RuvA core. Interacting RuvA D3 domains as well as conformation-specific RuvB subunits are rotated by 60° with respect to the RuvA-HJ core.

Article
DNA-engaged RuvB with respect to the RuvA-HJ core is rotated by around 60°. This suggests that the RuvB motors are able to rotate and that after completion of a 60° rotation, each RuvB subunit takes the position occupied by its neighbour before the rotation (Fig. 1g, Extended Data Fig. 5a,b and Supplementary Video 1). The rotation is further evidenced by multibody refinement analysis in which it accounts for around 45% of the total flexibility in the particles (Extended Data Fig. 5c-e and Supplementary Video 2). Thus, we reasoned that the reconstituted RuvAB complex is enzymatically active and has therefore been imaged in distinct conformational states. Moreover, our data reveal that the previously described continuous rotation of the DNA substrates 34 is accompanied by a concomitant rotation of the RuvB AAA+ motors themselves.

Conformational landscape of RuvB motors
To understand how rotation of the RuvB motor is linked to branch migration, we applied iterative focused refinement together with rigorous three-dimensional classification to the RuvB hexamers from our t2 dataset. This analysis revealed 9 structurally distinct RuvB motor maps at resolutions ranging between 2.9 and 4.1 Å (Extended Data Figs. 2c,e and 3e-n and Extended Data Table 1). Two of these maps (at 3.9 and 4.1 Å resolution) could not be improved to a resolution that would allow unambiguous assignment of nucleotides and were therefore not considered further. The remaining seven RuvB motors can be grouped according to the number of bound RuvA D3 , with one map lacking RuvA D3 (s0 −A ), two maps containing one RuvA D3 (s0 and s1) and four maps showing two bound RuvA D3 domains (s2, s3, s4 and s5), together suggesting a dynamic interplay between RuvA D3 and the RuvB motors.
All RuvB motors assemble into closed, asymmetric hexamers, featuring an approximately 2 nm-wide central pore that accommodates the DNA (Extended Data Fig. 3e-m). Consistent with previous structural and interaction studies, RuvB oligomerization is driven by the large (RuvB L ) and small (RuvB S ) ATPase domains of adjacent subunits 18,19,35 (Extended Data Fig. 4c-e). Similar to other AAA+ translocases [36][37][38][39] , four RuvB subunits (A, B, C and D) together assemble into a 'spiral staircase'. This generates a continuous interface that primarily binds one of the two DNA strands ( Fig. 2a,b), highlighting that only one strand from each double-stranded DNA entering the RuvA core is held by one RuvB motor (Extended Data Fig. 4h). The two remaining RuvB subunits (E and F) close the spiral staircase, but do not bind the DNA. The DNA-engaged subunits (A, B, C and D) bind the DNA through their C-terminal head domains (RuvB H ). Each RuvB H domain harbours four conserved arginine residues Arg291, Arg310, Arg312 and Arg315, which generate a positively charged binding interface complementary to the negatively charged DNA backbone (Fig. 2c,d).
(To aid comparison with the Escherichia coli RuvAB system, the corresponding residues are listed in Supplementary information Tables 1 and 2). The repeated binding pattern of the arginine residues originating from each of the subunits engages with the DNA separated by the distance of two nucleotides (approximately 7 Å). Moreover, as the RuvB subunits are positioned around 60° apart from each other within the RuvB hexamer, these data further imply that the rotation of the RuvB motors is linked to the events occurring within one translocation step.
To investigate the overall conformational plasticity of the hexamer, we analysed the variability for each Cα atom over all seven distinct motor structures expressed as the standard deviation of the distances to their corresponding centroids (Fig. 2e). This revealed that the RuvB hexamer can be divided into rigid (white), flexible (blue) and intermediate regions. Whereas the rigid area contains the DNA-bound subunits B and C, the DNA-disengaged subunits E and F reside in the flexible part. Notably, the DNA-bound subunits A and D, which connect the two unequal halves at the top and at the bottom of the staircase, respectively, are in intermediate regions, suggesting that the differential flexibility within the hexamer is involved in RuvAB-mediated branch migration. Of note, the extent of the variability is not necessarily confined to an entire RuvB subunit as exemplified for subunits A and D, which show both flexible and rigid areas (Fig. 2e). To further assess the plasticity of individual RuvB subunits, we determined the average root mean squared deviation (r.m.s.d.) between the 42 RuvB subunits, and also between their individual domains: RuvB L (residues 21-181), RuvB S (residues 182-254) and RuvB H (residues 255-330). This analysis revealed a low average r.m.s.d. (r.m.s.d. Ø 1.2 Å, 0.48 Å and 0.453 Å, respectively) for each domain (Extended Data Fig. 6a) showing that the overall structures  of RuvB L , RuvB S and RuvB H remain largely constant, yet their position relative to each other varies ( Fig. 2f and Extended Data Fig. 6a,b). The presence of the DNA substrate within the hexamer further enabled us to determine that RuvB subunits display position-specific, distinct conformations, which hereafter are referred to as clusters (with cluster [A] corresponding to the position of subunit A in RuvB, cluster [B] corresponding to the position of subunit B, and so on) (Fig. 2f). We then quantified the structural plasticity within RuvB clusters from state s1 to s5 by measuring two dihedral angles (d1 between RuvB L and RuvB S , and d2 between RuvB S and RuvB H ) and one triangle angle, which provides a more holistic view on the changes occurring in RuvB (Extended Data Fig. 6c). We found that each of the RuvB clusters ([A] to [F]) is characterized by a unique combination of the three angles, and thus harbours a set of RuvB subunits with more similar conformations (Fig. 3a). RuvB is also subject to deformation within clusters and is most variable in cluster [E], in which the triangle angle covers a dynamic range of 5.6° ( Fig. 3a and Extended Data Fig. 6c). To better characterize the motions in this flexible area of the RuvB hexamer, we aligned the five structures s1 to s5 to the almost invariant subunit C and analysed the movements of all the other subunits (Extended Data  Right, representative cryo-EM densities within the nucleotide-binding pockets and modelled nucleotides for ATPγS, ADP and apo. f, ATP-non-hydrolysing nucleotide-binding pocket. Superposition of the interfaces that form the nucleotide-binding pocket of subunit A (trans) and B (cis) from s1 to s5. The ligand pocket stays largely invariant. g, The ATP-hydrolysing nucleotidebinding pocket: superposition of the interfaces that form the nucleotidebinding pocket between subunit A (cis) and F (trans) from s1 to s5. α-Helices α4 and α5 in subunit F are gradually displaced leading to ATP hydrolysis. h, Magnification highlights unmodelled cryo-EM density (green density) in state s2, which probably corresponds to ordered water molecules initiating the nucleophilic attack on the ATP γ-phosphate. Fig. 6d-f). This approach revealed that sequential conformational changes within cluster [E] can be described along a trajectory with an average length of around 7 Å (range: 6-10 Å), which is directed towards the RuvA-HJ core (Fig. 3b). Notably, the length of the trajectory within cluster [E] corresponds well to the step size of the RuvB staircase of two nucleotides (the distance between nucleotides in DNA is approximately 3.5 Å), suggesting that the five RuvB structures (s1 to s5) could represent consecutive atomic snapshots of an active RuvB motor as it progresses through one translocation step.

Nucleotide cycle and conformational states
To investigate the interdependence between the observed conformational changes in RuvB hexamers and ATP hydrolysis, we first analysed the nucleotide identity and occupancy for all thirty nucleotide-binding pockets (Extended Data Fig. 7a Irrespective of the previous ordering on the basis of conformational changes along a trajectory, the nucleotide cycle of the five states revealed the same sequence of structural states (s1→→s5), and thus independently validates their ordering: the cycle starts with ADP release in subunit D (s1→s2), followed by the catalytic reaction through three states in subunit A (ATP→ADP + Mg 2+ →ADP (s2→s3→s4)) and is completed by ATP uptake in subunit D (s5) (Fig. 3d). These data highlight that ATP hydrolysis and nucleotide exchange occur in opposite clusters located at the top [A] and bottom [D] of the staircase, respectively, and individual steps are spatiotemporally separated (Fig. 3c-e). The need for structural cohesion to cycle between oppositely located subunits and the concomitant conformational changes described above suggests that there is an interlocked signalling chain between the subunits that connects the nucleotide cycle and, ultimately, DNA translocation.
Remarkably, the DNA remains bound to all four staircase subunits (A to D) across all five states and thus the interaction of the DNA substrate with these subunits is independent of the type of nucleotide bound, including at the ATP hydrolysis (subunit A) and at the exchange position (subunit D) (Extended Data Fig. 7c). Consequently, our data reveal that in order to relocate the DNA substrate inside the central RuvB motor pore, RuvB subunits must be subject to additional conformational changes that follow the nucleotide cycle. We therefore reason that the nucleotide cycle in fact functions first to prime the RuvB subunits over five states to then acquire the conformations of their respective neighbouring clusters (Extended Data Fig. 6f). This is also supported by the fact that the nucleotide arrangement in state s5 corresponds to the same configuration as in state s1, but the respective conformations of the six subunits have shifted forward by one to occupy the new successor state (s5→s1′: A(s5) →F(s1′), B(s5) →A(s1′), and so on). When this event occurs, all six RuvB subunits simultaneously transition to the next conformational cluster without any additional changes to the nucleotide arrangement (subunits in s5 and s1′ have the same nucleotide occupancy), resetting the conformation of the entire hexamer to state s1. We therefore refer to this process as a 'cluster switch' (s5→s1′) (Extended Data Fig. 8). It follows that all subsequent processes now take place in the respective adjacent subunit, implying that nucleotide hydrolysis and all other processes operate around the hexameric ring in repeated sequences.

Reorganization of the catalytic centre
To gain structural insights into the events occurring at the nucleotidebinding pockets, we first analysed their common features. Nucleotides bind at the interface of two consecutive subunits (cis and trans), with the nucleoside exclusively clamped between the RuvB S and RuvB L domain of one subunit 35,40 (RuvB in cis) ( Fig. 3f and Extended Data Fig. 9a,b). In all ATP-containing pockets, a conserved Walker-A motif binds the ATPγS-Mg 2+ complex in which previously identified Lys65 interacts with the ATP γ-phosphate 41 , and Thr66 coordinates the Mg 2+ ion (Fig. 3f). Additional contacts are provided by two conserved cis-acting arginine residues: Arg21 and the sensor 2 arginine Arg218 42 . Arg21 is located at the N terminus and binds the ATP α-phosphate, whereas sensor 2 arginine Arg218 is in the small ATPase domain and mediates nucleotide sensing (Fig. 3f). In agreement with previous studies, ATPγS-Mg 2+ trans-sensing is achieved by two elements: a conserved signature motif (Glu127-Asp130), located on α-helix α4, and trans-acting Arg171 on α-helix α5 40,43 (Fig. 3f). Thus, Arg171 represents the canonical arginine finger that is conserved in most AAA+ ATPases and directly coordinates the γ-phosphate 44 . Furthermore, two additional acidic trans-residues, Glu128 and Asp129, sense cis-residues Arg21 and Arg218, respectively, and thus indirectly stabilize nucleotide binding (Fig. 3f).
To understand the molecular mechanism and chemistry of coupling ATP hydrolysis and signal transduction, we followed the fate of ATPγS before (s1), during (s2) and after (s3-s5) hydrolysis in subunit A, whose nucleotide-binding pocket interfaces in trans with DNA-disengaged subunit F. During the transition through the catalytic states (s1→→s5), helices α4 and α5 from subunit F undergo a concerted motion, which enables distinct local rearrangements of trans-residues critical for ATP hydrolysis in subunit A (Fig. 3g). In particular, the intermolecular interaction between trans-Glu128 and cis-Arg21, which is maintained in state s1, is lost in the following states, enabling trans-Glu128 to instead engage with the canonical arginine finger trans-Arg171. Further, in state s2, residue trans-Tyr131 joins cis-Arg21 in coordinating trans-Asp129, an event that coincides with the appearance of continuous density between trans-Asp129 and the ATPγS-Mg 2+ complex ( Fig. 3h and Extended Data Fig. 9c). The connecting density is best described as ordered water molecules, which are required to facilitate the nucleophilic attack on the ATP γ-phosphate. The importance of this signature motif has been highlighted by mutational studies, in which the substitution of trans-Asp129 markedly compromised branch migration activity, and mutation of trans-Glu128 resulted in a bacterial growth defect 45 . As an additional validation of the ATP hydrolysis reaction taking place in subunit A of state s2, connecting density also emerges between the ATP γ-phosphate and the Walker-B motif residue cis-Asp110, which, similar to trans-Asp129, has been shown to be important for ATP hydrolysis 45,46 ( Fig. 3h and Extended Data Fig. 9a).
In the next states, progression of the ATP hydrolysis reaction can be observed, which first results in the release of the γ-phosphate (s2→s3) (Fig. 3h and Extended Data Fig. 9a). As a result, the binding of sensor 2 cis-Arg218 to the nucleotide is released, whereas the coordination of the Mg 2+ ion through cis-Thr66 remains intact ( Fig. 3h and Extended Data Fig. 9a). In the next transition (s3→s4), loss of the Mg 2+ ion liberates cis-Thr66, which now coordinates the ADP β-phosphate. Subsequently, (s4→s5) cis-Arg218 of sensor 2 moves away from its own binding pocket and demarcates subunit A to be primed to undergo a cluster switch.

Information relay through the converter
The fact that we observed specific binding of RuvA D3 to the RuvB hexamer opposite the catalytic centre in subunit A through all states (s1 to s5) at the bottom of the staircase does not explain an increase in ATPase activity in the presence of RuvA 9 . Instead, it suggests that RuvA D3 in such an arrangement elicits a regulatory function onto the nucleotide cycle and directly coordinates branch migration. In particular, we found that a single RuvA D3 is bound to subunit D during all five states, revealing that the RuvA-HJ complex is tethered to both opposing RuvB motors in tripartite particles throughout the entire nucleotide cycle. By contrast, a second RuvA D3 binds exclusively to subunit E in states s2 to s5 (Extended Data Fig. 10a). Both RuvA D3 bind to a previously described hydrophobic composite interface in their respective RuvB subunits, which is composed of RuvB L α-helix α3 and the presensor-1 β-hairpin 15 (Extended Data Fig. 10b), which in other hexameric AAA+ motors of the PS1 insert superclade coordinates with their substrates either directly or indirectly 20,36,47 . Analysing the effect of the RuvA D3 recruitment (s1→s2) to subunit E revealed that the binding event exerts a wedge-like effect on the RuvB hexamer, which drives apart the large domains of subunits E and D. The motion of subunit E suggests that RuvA D3 binding is achieved by an induced-fit mechanism (Fig. 4a, Extended Data Fig. 10c and Supplementary Video 3). The repositioning of subunit E causes a concomitant displacement of the large ATPase domain of subunit D, which then promotes the opening of its nucleotide-binding pocket and thereby enables the escape of the ADP molecule (Fig. 4b, Extended Data Fig. 10d and Supplementary Videos 4 and 5). Thus, our data reveal that RuvA D3 (binding to subunit E) functions as a nucleotide exchange factor by acting on subunit D. Notably, at the same time, repositioning of E causes a motion of the adjacent, DNA-disengaged subunit F, whose trans-acting residues Glu128, Asp129 and Arg171 facilitate the ATP hydrolysis reaction in A as described above (Fig. 3g,h, Extended Data Fig. 10e and Supplementary Videos 4 and 5). On the basis of this observation, we postulate that RuvA D3 also acts through its binding to the presensor-1 β-hairpin on subunit E as an ATPase-activating domain that stimulates ATP hydrolysis in A through forward coordinated, inter-subunit signalling.
Of note, the trans-acting residues in subunit F disconnect from the nucleotide only upon loss of the Mg 2+ ion, which in turn permits a large-scale motion of subunit F (s4→s5) (Extended Data Figs. 6e,f and 9). Releasing subunit F from its association with ADP in RuvB subunit A sets in motion a chain reaction, which also affects the position of DNA-disengaged subunit E. Thus, our data uncover that the dissociation of the Mg 2+ ion triggers retrograde inter-subunit signalling confined within the flexible RuvB subunits (D, E and F) (Fig. 2e and Extended Data Fig. 6e,f)  Article its nucleotide-binding pocket, which in turn causes the entire N terminus to fold away from the pocket (Fig. 4d,e). This prepares subunit E for the release of ADP in the next translocation step, when the cluster switch has occurred and subunit E has transitioned into the conformational cluster [D] where it is finally subject to nucleotide exchange. This is further reflected by a constantly increasing d1 and triangle angles in cluster E (Fig. 3a and Extended Data Fig. 6c), which, on a molecular level, weakens the hydrophobic interaction between N-terminal cis-Leu20 and its cis-binding partners Thr193, Ile196, Phe197 and Asn221. As a result, the destabilization of cis-Leu20 impairs the ability of cis-Arg21 to coordinate the ADP α-phosphate (Extended Data Fig. 10f and Supplementary Video 6). In addition, the retrograde signalling affects subunit D at the bottom of the staircase, which reaches the maximum opening of its binding pocket in state 4, demonstrating that although ADP release is achieved already in s2, nucleotide exchange evolves over four states (s2→→s5) (Fig. 4d,e and Extended Data Fig. 10g). The acquisition of a new ATP molecule (s4→s5) is then accompanied by a concerted motion of subunits E and F together with the large domain of subunit D (hereafter called 'converter': F-E-D L ) (Fig. 4d,e and Extended Data Fig. 10h). As a part of this motion, the coordination of the newly obtained ATP molecule is restored by the N terminus in subunit D (Extended Data Fig. 10i,j). Consequently, the gate-opening (cluster [E]) and gate-closing (cluster [D]) motions of the RuvB N terminus serve as additional proof for the directionality of the nucleotide cycle. Finally, the retrograde signalling causes subunit D (large domain) to become part of the rigid area in the RuvB motor, which marks the completion of the nucleotide cycle (Fig. 4c-e and Supplementary Video 6).
In summary, our findings establish that the conformations of all RuvB subunits are context-dependent within the hexamer and the converter (F-E-D L ) functions as a RuvB motor-operating multi-domain module, which undergoes highly coordinated motions during the nucleotide cycle. The critical position of subunit E in the centre of this module enables the binding of RuvA D3 to pass information through inter-subunit signalling to stimulate ATP hydrolysis in distant subunit A and nucleotide exchange in adjacent subunit D (Fig. 4f and Supplementary Video 7).   c, Schematic of the RuvB motor lever mechanism. Binding of RuvA D3 to substrate-disengaged RuvB subunit E generates a fulcrum, which enables RuvB to convert the energy contained in ATP into a lever action. d, Illustration of the difference between motor lifting (pulling) the DNA substrate accompanied by rotation and motor repositing (walking). e, Structural similarity of the converter between initiation (s0) and processivity states (s1) obtained by time-resolved cryo-EM (t1 and t2) and expressed as per-residue r.m.s.d. between corresponding Cα atoms. The s0 states in both datasets closely resemble each other but differ from the s1 states. Similarly, both s1 states are very similar to each other, but differ from the s0 states. States are aligned to the DNA. f, Model for Holliday junction branch migration through continuous DNA translocation mediated by RuvAB. Initiation states provide a potential entry pathway (s0→s1) into the nucleotide cycle, which starts with state s1. The nucleotide cycle is represented by states s1 to s5, and nucleotide occupancy at subunit interfaces is schematized as coloured circles (red (ATP), green (ADP) and grey (apo). During the nucleotide cycle, the energy contained in ATP is converted into a lever action or power stroke, causing DNA translocation of two base pairs per hydrolysed ATP molecule . This is also indicated by the translocating base pairs (cyan and red) of the Holliday junction crossover. Cluster switches, in which RuvB subunits undergo 'register shifts', cause the repositioning (walking) of the DNA substrate in the central pore and regeneration of state s1. This enables RuvB motors to generate iterative power strokes, and thus provides the mechanistic basis for continuous branch migration.

Lever mechanism
To gain insight into the linkage of conformational changes observed in the converter of the RuvB motor and DNA translocation, we examined the five structures of the nucleotide cycle (s1 to s5) by aligning all states to the centre of the converter (subunit E). The analysis revealed that the sequential movement follows a trajectory that translates into a lifting motion of the RuvB motor, in which the individual areas of the hexamer lift proportionally to their distance from subunit E (Figs. 3b  and 5a). This causes the DNA-binding interface together with its bound DNA to be lifted by around 7.0 Å away from the RuvA-HJ core. Thus, our data provide evidence that RuvB motors act as molecular levers, which convert the energy obtained throughout the nucleotide cycle into a pulling force to physically move the DNA by approximately 7.0 Å-that is, two nucleotides-and thereby achieve branch migration during DNA recombination (Fig. 5b-d and Supplementary Videos 8 and 9). Notably, the subsequent cluster switch only repositions the RuvB hexamer (walking along the DNA substrate) after the nucleotide cycle, but does not exert a direct mechanical force onto the DNA and thus does not actively contribute to strand exchange (branch migration) in the RuvA-HJ core 48 (Fig. 5d and Supplementary Video 10). The largest conformational changes in the converter of the RuvB motor are initiated with the recruitment of the second RuvA D3 (s1→s2), accompanied by the nucleotide exchange reaction of ADP ejection (s1→s2) and ATP uptake (s4→s5), indicating that these two events contribute the most to DNA translocation (Extended Data Fig. 6e,f). Consistently, motions that are associated with nucleotide exchange have recently also been proposed as a force-generating step in the AAA+ ATPase motor of the 26S proteasome 49,50 . On the basis of our findings, we posit that RuvA functions as a fulcrum, which enables RuvB motors to facilitate branch migration by producing a power stroke that pulls the DNA through the RuvA core (Fig. 5c). In summary, the RuvB AAA+ ATPase motor undergoes two consecutive processes (nucleotide cycle and cluster switch) that account for both the maintenance of the unaltered structure of the DNA and the need for its rotation during branch migration.

Time-resolved cryo-EM
In the course of the structural analysis of the t2 dataset we found two additional subsets of particles that exhibit a nucleotide occupancy, which does not line up with the sequential nucleotide cycle described above. The first subpopulation contains particles that lack the centrally localized RuvA oligomer (s0 −A ) (Extended Data Fig. 2e). These clearly show that the four RuvB subunits A to D are occupied by ATPγS and subunits E and F are occupied by ADP (Extended Data Fig. 7a,b). Notably, specific densities are visible at low density thresholds, indicating the partial presence of ATPγS and Mg 2+ , thus determining that an asymmetrically formed RuvB hexamer can carry up to five ATP molecules (Extended Data Fig. 7a,b). The particles of the other subpopulation (s0, RuvA bound) were found to have the same nucleotide configuration as the RuvA-deficient particles (s0 −A ) (Extended Data Figs. 2c,e and 7a,b). Because ATP hydrolysis (s2→s3) precedes the acquisition of a new ATP molecule (s4→s5) in the nucleotide cycle, the simultaneous presence of ATP in subunits A and D suggests that state s0 is not part of the hydrolytic cycle. Moreover, we also noticed that the converter in state s0 assumes a hybrid conformation, which is different from any of the conformations seen in the nucleotide cycle (s1 to s5) ( Fig. 5e and Extended Data Fig. 6b). Therefore, we hypothesized that such a state resembles a RuvB hexamer that has not entered the nucleotide cycle yet and therefore must first undergo ATP hydrolysis or exchange to adopt the position-and conformation-dependent sequence of the nucleotide arrangement as displayed throughout the states s1 to s5. We refer to such a state as the 'initiation state' (s0).
To test this hypothesis, we performed cryo-EM on RuvAB-HJ particles under the same conditions but vitrified the sample shortly after in vitro reconstitution (at 30 min (t1 dataset) instead of 5 h (t2)) (Extended Data Fig. 1h). Only two states (s0 t1 and s1 t1 ) could be recovered at high resolution (3.3 Å) from this dataset (Extended Data Figs. 2d and 3i-n and Extended Data Table 1). In both t1 states, only a single RuvA D3 binds subunit D in the RuvB hexamer (Extended Data Fig. 2d,e), implying that states s2 to s5 observed after a 5 h incubation (t2) are indeed actively generated by a progressing nucleotide cycle. In addition, the finding confirms that the RuvAB-HJ complexes (t2) were vitrified in the process of active branch migration. At the structural level, state s0 t1 is similar to s0 (t2) (Fig. 5e and Extended Data Fig. 10k), yet it contains a fifth ATP molecule in subunit F. This finding corroborates the notion that state s0 (t2) can eventually be generated from s0 t1 through ATP hydrolysis in subunit F (non-processive). Given that ATP levels typically exceed those of ADP in bacterial cells 51 , it appears likely that in vivo RuvB motors first assemble initiation states by preferentially loading ATP stochastically at RuvB subunits (s0 with four or five ATPs), to then enter the processive sequential nucleotide cycle (s0→s1→→s5) to promote branch migration.

An integrated model for branch migration
Our results lead us to propose a model for initiation and processive branch migration that postulates that DNA translocations occur through a lever mechanism executed and controlled by the RuvA-tethered RuvB hexamer combined with DNA rotation 34 (Fig. 5f).
Non-processive initiation phase (stochastic): (1) RuvA tetramers bind to the Holliday junction and their flexible RuvA D3 recruit RuvB subunits to assemble as hexamers arranged in a spiral staircase around the newly formed DNA and in opposite orientations on each side of the RuvA-bound Holliday junction (tripartite RuvAB-HJ complex). (2) The RuvB hexamers are stochastically loaded with nucleotides (ATP or ADP) and initial out-of-register ATP hydrolysis and/or nucleotide exchange take place to adopt a sequential nucleotide arrangement such as represented by state s1 (A-B-C-D-E-F: ATP-ATP-ATP-ADP-ADP-ADP).
Processive translocation phase (sequential): (1) The hexameric RuvB motor works as a unit and undergoes a forward and retrograde signalling wave mediated by the converter and fuelled by the nucleotide cycle: at first ADP is ejected at the bottom of the staircase in subunit D, causing ATP hydrolysis in subunit A at the top of the staircase, followed by ATP uptake in subunit D. (2) Because RuvB is anchored to domain III of RuvA during the nucleotide cycle, rotation of RuvB is accompanied by a pulling of the DNA out of the RuvA core, advancing branch migration by two nucleotides (the power stroke). (3) Following the nucleotide cycle, the RuvB motor is repositioned (cluster switch), whereby RuvB subunits will adopt the conformation of their adjacent neighbours. (4) After the cluster switch and completion of the rotation, RuvA D3 must dissociate owing to physical constraints of the tether and is free to rebind the next advancing RuvB subunits. The motor is now reset by keeping the conformational clusters [E] and [D] confined within reach of RuvA. To go through a full rotation of 360°, the process is repeated six times. Each subunit will go through at least five position-specific conformations and the branch migration complex consumes in total 12 ATP molecules (6 ATP molecules per RuvB motor) and advances the recombined DNA by 12 nucleotides.

Discussion
This work reveals the critical role of substrate-disengaged RuvB subunits, whose highly coordinated motions control the nucleotide cycle in the RuvB hexamer. These subunits are part of a converter through which the binding of RuvA D3 to subunit E can stimulate long-range inter-subunit signalling and which leads to ATP hydrolysis and nucleotide exchange. Substrate-disengaged subunits are a unifying feature across most ring-forming AAA+ motors 20,37,39 , suggesting that variations of the converter probably also operate other AAA+ ATPases. To be able to repeatedly exert their critical function on a rotating RuvB motor,

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RuvA D3 domains need to constantly release from the RuvB hexamer and bind to newly generated binding interfaces that are produced by the nucleotide cycle. Although the driving force behind this rotation remains to be identified, it seems plausible that the energy for this motion is derived from the nucleotide cycle. As the DNA substrate already refolds into a double helix within the confinement of the double-tetrameric RuvA core, we propose that the RuvB motor rotation is powered by the rewinding of the translocating DNA. In this view of the RuvAB machinery, the double RuvA tetramer serves an important function in stabilizing the Holliday junction, ensuring that the two DNA substrates can rewind into a double helix and providing a rationale for the rotation of RuvB motors.
With five distinctive transition-state intermediates (s1 to s5), our data establish structurally that in RuvB motors, the nucleotide cycle progresses around the ring, providing proof of concept for a conserved core mechanistic principle in hexameric AAA+ ATPase translocases 37 . In the context of the RuvAB complex, the sequential nucleotide cycle of the rotating RuvB motor causes the converter to be maintained in the same area with respect to the central RuvA-HJ complex. As a result, a single RuvA tetramer is probably sufficient to control the nucleotide cycle of both RuvB motors. However, in other hexameric AAA+ ATPase motors, sequential ATP hydrolysis events should consequently cause the corresponding substrate-disengaged subunits to progress around the ring. To operate the nucleotide cycle in these motors, putative converter interactors must therefore be able to reach every subunit of the AAA+ ATPase motor. This may provide a rationale for the embedding of ring-shaped AAA+ ATPase motors within multimeric scaffolds, such as in the proteasome or ClpA/X-P 50,52,53 . Alternatively, the regulatory function of RuvA may instead be carried out directly by the substrate.
Further, we show that the nucleotide cycle is a spatiotemporal continuum of conformational changes through which RuvB AAA+ ATPase motors convert the chemical energy retained in ATP to a lever action. The RuvA D3 -bound subunits in the converter are at the heart of this process, as their physical connection to the RuvA core complex generates the fulcrum that is needed to turn the RuvB motor into a molecular lever. Notably, while the DNA is levered, it remains associated with its binding interface; our data thus enable us to decompose the lever action (sequential steps during the nucleotide cycle) from the cluster switch (following the nucleotide cycle). This reveals that the nucleotide cycle serves to promote DNA pulling, while also priming the RuvB hexamer for a cluster switch. This priming event, which is not part of the nucleotide cycle itself, is critical for enabling the propagation of the nucleotide cycle around the ring and, consequently, for continuous DNA translocation ( Fig. 5f and Supplementary Video 11). Notably, hexameric AAA+ ATPases specific for nucleic acid as well as protein translocation share a conserved asymmetric spiral organization around their cognate substrates and are furthermore believed to share a similar translocation rate per hydrolysed ATP molecule 20,38,54 . Similarly, the pulling of DNA, RNA and protein substrates is thought to be powered by a common sequential nucleotide cycle 21,39,44,49,50 . On the basis of their shared geometrical and mechanistic properties, our findings suggest that the majority of ring-shaped AAA+ ATPase translocases may function as molecular levers that efficiently convert a concerted wave of conformational changes associated with their nucleotide cycles into a defined lift-height of their central pores, as a common basic mechanism to facilitate substrate translocation.
Finally, our findings reveal that RuvB motors are most variable in the converter, which changes from a hybrid conformation in the initiation states (s0 and s0 t1 ) to the spatiotemporal continuum observed in the nucleotide cycle (s1-s5). As a functional DNA damage response is essential for intracellular bacterial pathogens to cope with the oxidative environment inside our cells, state-specific targeting of the converter may provide a promising avenue for the inhibition of RuvB motors-and thus homologous recombination-by small molecule interference.

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Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41586-022-05121-1.

Protein engineering, expression and purification
RuvA from S. typhimurium was fused to a C-terminal tetra-histidine tag and cloned into pET-52b(+) expression vector (Novagen), using the NcoI and SacI restriction sites. Recombinant protein expression was performed in E. coli strain BL21(DE3). Bacterial cells were grown at 37 °C in LB medium supplemented with 100 µg ml −1 ampicillin to an absorbance at 600 nm of about 0.6. Expression of RuvA was induced by the addition of 1 mM isopropyl β-d-1-thiogalactopyranoside (IPTG) and cultures were further incubated at 37 °C for 3 h. Cells were then pelleted at 4,250g for 10 min at 4 °C, washed in 20 mM NaCl, 1 mM EDTA, 20 mM Tris-HCl pH 8 buffer (buffer 1), resuspended in 100 mM NaCl, 5% glycerol, 100 mM Tris-HCl pH 8 buffer (buffer 2) and stored at −80 °C. For protein purification, the cell suspension was thawed, supplemented with a complete protease inhibitor cocktail (Sigma Aldrich), lysed by sonication and the resulting cell lysate was cleared by centrifugation (Beckman JA-25.50, 17,500 rpm, 1 h, 4 °C). The supernatant was applied onto a 5 ml HisTrap column (GE Healthcare) equilibrated with buffer 2 and immobilized proteins were recovered by gradient elution using buffer 2 supplemented with 500 mM imidazole. Peak fractions were pooled, dialysed against buffer 2 and loaded onto a Superdex 200 10/300GL size exclusion column (GE Healthcare) equilibrated in 100 mM NaCl, 1 mM EDTA, 0.5 mM DTT, 5% glycerol, 100 mM Tris-HCl pH 8 buffer (buffer 3). The peak fraction containing RuvA was collected, and aliquots were frozen in liquid nitrogen and stored at −80 °C. N-terminally truncated RuvB (16-333) from S. thermophilus was C-terminally fused to a tobacco etch virus (TEV) protease cleavage site, followed by a linker and a HA tag, and cloned into the pProEX HTB expression vector (Thermo Fisher Scientific), using the NcoI and HindIII restriction sites. Protein expression and purification were performed as described for RuvA from S. typhimurium. The TEV cleavage was performed during the dialysis step. The purity of recombinant RuvA and RuvB proteins was assessed by SDS-PAGE, followed by staining with Coomassie R-250 and was estimated to be higher than 95% (Extended Data Fig. 1a,b, Supplementary information Table 3).

DNA substrates
Holliday junctions with mobile (HJ-X26) 55 and immobile (HJ-Y2Ap, modified from Y2A 17 ) cores were prepared by annealing synthetic oligonucleotides (Sigma Aldrich) provided in Supplementary information Table 3, following a previously published protocol 56 . In brief, the oligonucleotides were purified by native 6% PAGE (TAE buffer) and mixed in appropriate ratios in annealing buffer (buffer 4) (25 mM NaCl, 10 mM Tris-HCl pH 8). The annealing reaction was performed in a 0.2 ml tube and covered with a thin layer of mineral oil to prevent water evaporation. The mixture was heated to 95 °C for 10 min, and the temperature was subsequently decrease in 10 °C temperature steps every 10 min. To obtain homogenous four-way Holliday junction preparations, the annealing reaction was supplemented with a DNA sample buffer (New England Biolabs) and separated by native 6% PAGE (TAE buffer). Bands corresponding to four-way Holliday junctions were cut out from the gel and eluted by incubation in 5 mM Tris-HCl pH 8. For DNA-binding assays (electro mobility shift assay (EMSA)), one oligonucleotide strand was labelled with radioactive 32 P (3,000 Ci mmol −1 ) at the 5′ end prior to annealing. For the branch migration activity assays, one oligonucleotide strand was fluorescently labelled with ATTO 647N.

RuvAB-HJ in vitro reconstitution
RuvAB-HJ particles were reconstituted as described 17 , with minor modifications. Purified Holliday junction and RuvA were mixed and supplemented with 5 mM MgCl 2 . The mixture was incubated at 37 °C for 30 min and applied to size exclusion chromatography on a Superdex 200 10/300GL column equilibrated with 100 mM NaCl and 5 mM MgCl 2 , 5 mM Tris-HCl pH 8 buffer (buffer 5). The peak fraction containing RuvA-HJ complexes was mixed with purified RuvB in the presence of 10 mM MgCl 2 and an equimolar ratio of ATPγS and ADP (1 mM). To form RuvAB-HJ complexes, the mixture was incubated at 37 °C for 10 min and then cooled to 4 °C. Prior to vitrification, all samples were analysed for RuvAB-HJ complex formation by negative-stain electron microscopy.

Branch migration activity assay
Branch migration activity was measured as described 57 . Briefly, the branch migration reaction (20 µl) contained 20 nM of purified and fluorescently labelled synthetic HJ-X26 and varying amounts of purified RuvA and RuvB proteins in buffer 6 (15 mM MgCl 2 , 1 mM DTT, 50 µg ml −1 BSA, 2 mM ATP, Tris-HCl pH 8). Following an incubation at 37 °C for the indicated time, RuvA and RuvB proteins were digested by proteinase K treatment (2 mg ml −1 ) and 0.5 % SDS at 37 °C for 10 min. Glycerol was added to the reaction (30% final concentration) and branch migration was assayed by electrophoresis (135 V for 35 min, TAE buffer) in a 6% polyacrylamide gel. Bands corresponding to Holliday junction and Holliday junction derivatives were visualized by ChemoStar Touch ECL and fluorescence images (INTAS Science Imaging).

Electro mobility shift gel assay
Varying amounts of purified RuvA protein were incubated with 5′-32 P-labelled synthetic Holliday junction (HJ-Y2Ap) for 30 min at 37 °C in 5 mM EDTA, 1 mM DTT, 100 µg ml −1 BSA, 30 mM Tris-HCl 8 buffer (buffer 7). DNA sample buffer (New England Biolabs) was added to the reaction and the complex formation was assayed by electrophoresis in a 6% polyacrylamide gel (1× TAE). Electrophoresis was carried out at 4 °C at 150 V for 1.5 h in a 0.5× TAE buffer. Gels were dried, and DNA bands were visualized by autoradiography.

Grid preparation for cryo-EM
Amorphous carbon (1-1.5 nm) was deposited (Leica ACE60 carbon coater) on freshly cut mica sheets and baked for 0.5 h at 120 °C. Quantifoil grids were cleaned by dipping into chloroform for 60 s and dried for 30 min. Continuous carbon grids were made by floating always freshly prepared amorphous carbon on a water surface onto cleaned and strongly glow discharged (3 min at 25 mA) Quantifoil grids. Grids were dried for 1 h followed by 30 min of baking at 120 °C and stored under controlled vacuum for maximum 2 weeks.

Negative-staining electron microscopy
Before sample application, grids were positively glow discharged for 30 s at 25 mA using a GloQube Plus Glow Discharge System (Electron Microscopy Sciences). Four microlitres of freshly prepared RuvAB-HJ complexes were applied to carbon-coated copper grids and incubated for 30 s. The sample was blotted off, and then stained with 4 µl of the staining solution (2% uranyl acetate) for 30 s. Excess stain was blotted off and the grids were air-dried for at least 2 min. Grids were imaged using a Thermo Fisher Scientific Talos L120C TEM with a 4K Ceta CEMOS camera.

Cryo-EM sample preparation and data collection
Freshly in vitro reconstituted RuvAB-HJ complexes were incubated on ice for 30 min (dataset t1) or approximately 5 h (dataset t2) prior to vitrification. N-Dodecyl-β-maltoside (DDM) was added to a concentration of ~0.005% prior to application of the protein sample to the grid. Four microlitres of the final RuvAB-HJ sample was applied twice onto glow discharged (30 s, 25 mA) gold Quantifoil grids (2/2 300 mesh), containing a thin layer (1-1.5 nm) of amorphous carbon (made in-house). In brief, after the first sample application at 4 °C for 1 min in a horizontal position, the liquid was blotted off from the side. The procedure was repeated, and the sample was plunge-frozen into a propane:ethane (63:37) mixture using a Vitrobot Mark V (Thermo Fisher Scientific) set to 100% humidity and 4 °C. Blotting times ranged from 4-7 s. Vitrified samples were imaged on a Thermo Fisher Scientific Titan Krios TEM operating at 300 kV, equipped with a field emission gun (XFEG) and a Gatan Bioquantum energy filter with a slit of 10 eV and a Gatan K3 electron detector. During data acquisition, the slit was re-centred every 6 h. For the t1 dataset, a total of 10,057 micrographs were recorded in electron-counting mode at ×81,000 nominal magnification (1.1 Å per pixel at the specimen level) consisting of 33 frames over 3 s (total electron exposure of of 53 e − Å −2 , corresponding to 1.6 e − Å −2 per frame) using Thermo Fisher Scientific EPU data collection software. The defocus range was set between −0.3 and 3 µm. For the t2 dataset, 30,053 micrographs at ×130,000 nominal magnification (1.09 Å per pixel at the specimen level) consisting of 20 or 25 frames, respectively, were recorded with a Gatan K2 Summit direct electron detector operated in electron-counting mode and Gatan energy filter with slit of 10 eV. The accumulated electron exposure was 30.7 e − Å −2 (corresponding to 1.24 or 1.55 e − Å −2 per frame) during a 5 s exposure at − 0.3 to 4 µm defocus range (Extended Data Table 1).

Cryo-EM image processing and atomic model building
Single-particle analyses were performed using Relion (v3.0b and v3.1) 58,59 . Micrograph frames (movies) were motion-corrected using MOTIONCOR2 (implemented in Relion) 60 , dose-weighted (using 1.24 or 1.55 e − Å −2 per frame for t2 and 1.55 e − Å −2 per frame for t1) and the contrast transfer function (CTF) parameters were estimated with CTFFIND4 (v4.1.14) 61 . Particles were automatically picked from the motion-corrected micrographs either using CrYOLO (v1.4) 62 , Gautomatch (v0.56) 63 or Relion Autopick trained with a subset of manually picked particles. In the t1 dataset, approximately four million coordinates were picked. Particle images were extracted with a box size of 80 pixels (bin = 4) and subjected to multiple rounds of 2D classifications. Only particles present in homogeneous classes were kept, amounting to 948,812 particles (after duplicate removal). Focused classifications were performed by re-extracting particles with a box size of 360 pixels, centred around the RuvB rings (1,881,624 particles) and the central RuvA-HJ (948,812 particles) part. Subsequently, three rounds of refinement, per-particle CTF and Bayesian polishing were performed. Additionally, for the RuvA-HJ reconstruction, signals emerging for the RuvB rings were subtracted. For the t2 dataset, approximately 9 million coordinates were used for particle extraction, which were subsequently subjected to 4 times binning and multiple rounds of 2D classifications, leading to a total of 1,786,669 particles. From these, three groups of particles were identified, and three particle subsets were generated: (1) tripartite RuvAB-HJ particles (717,780) containing two RuvB motors, (2) bipartite RuvAB-HJ particles containing one RuvB motor (549,364 particles), and (3) RuvB-HJ complexes lacking RuvA (519,525 particles). For the reconstruction of the tripartite RuvA-RuvB-HJ complex, only particles from group 1 were used. At first, an ab initio model was created in Relion using a smaller subset of particles (n = 50,000). Subsequent classifications and refinements led to a consensus reconstruction yielding a resolution of ~8 Å. Particles from group 2 were used to reconstruct the bipartite RuvAB-HJ structure (~3.9 Å). Particles from the group 1 after subtraction of the signal corresponding to one RuvB motor were used to generate pseudo-bipartite particles. Focused reconstruction procedures were performed as described for the t1 dataset, which resulted in 3D reconstructions of the RuvB motor and the central RuvA-HJ subcomplexes, respectively. The RuvA-HJ subcomplex was reconstructed using particles from the combined particle stack (groups 1 and 2). For the RuvB structures, a total of approximately 2.3 million RuvB motors were extracted (from all three groups), centred, 3D classified, and subsets were independently refined. Subsequently, per-particle CTF, Bayesian polishing, and 3D refinements were performed twice. Applying this procedure resulted in 9 distinctive RuvB motor structures, ranging from 2.9 to 4.1 Å in resolution. Local resolution estimates, gold-standard resolution (Fourier shell correlation = 0.143) and sharpened maps (B-factor range: 30-80 per focused refinements) and multibody refinements were calculated using Relion 3 .1 64 .

Reporting summary
Further information on research design is available in the Nature Research Reporting Summary linked to this article. All other data are available from the corresponding authors upon reasonable request. Fig. 4 | Structure of RuvA and RuvB subunits and their oligomeric organisation within the RuvAB-HJ branch migration complex. a-c, RuvA consists of three domains. Domains I and II are responsible for binding the HJ and the oligomerisation into tetramers, whereas domain III (N-terminal) extends from the RuvA core (domain I, and II) and binds to the RuvB motor. b, Top and side view of the double-tetrameric organization of the RuvA within the context of the fully assembled RuvAB-HJ complex. Magnifications highlight the individual RuvA subunits constituting the central core by different colours. c, RuvB consists of three domains. A large (RuvB L ) and a small (RuvB S ) ATPase subdomain, together forming the ATP-binding domain, and a C-terminal "head" domain (RuvB H ) binding the DNA substrate via a winged-helix motif. The presensor-1 β-hairpin of RuvB, a distinguishing feature of the PS1 insert superclade, is part of the RuvB L but shown in blue colour. d, Hexameric assembly of the RuvB motor, using the domain colour code in c. Akin to other hexameric AAA+ ATPase translocases, the nucleotide binding pocket is located between adjacent subunits to enable nucleotide-dependent inter-subunit signalling. e, RuvB (S. typhimurium) amino acid sequence with the visualization of secondary structure elements. f, 3D reconstruction of the entire tripartite RuvAB-HJ (low resolution), cut-away view and the composite map. The four RuvA D3 domains localize to the same side of the HJ crossover. The magnification highlights the two adjacently located binding interfaces of RuvA D3 to subunit D, E of RuvB. g, Putative location of RuvC dimer within the the RuvABC-HJ resolvasome. One RuvA tetramer (in green) binds the HJ crossover and operates both RuvB motors simultaneously. The second RuvA tetramer is replaced by a dimer of the RuvC resolvase. h, Spiral staircase organization of the DNA binding interface in RuvB motors. Charge distribution representation of the RuvB H domains in the RuvB motor staircase. Together, the RuvB H domains of RuvB subunits A, B, C, D form a positively charged pit to stably accommodate one strand of the double-stranded DNA substrate. One strand of each maternal DNA substrate (pink/yellow) is processed by one RuvB motor. Fig. 5 | Rotation of the RuvB motor. a, 3D-classification of the bipartite RuvAB-HJ particles. Repeated classifications revealed that in approx. ~7 % of the particles the RuvB motor is rotated by 60° with respect to the RuvA-HJ core complex. b, 3D-classification of the tripartite (pseudo-bipartite) RuvAB-HJ particles. Repeated classifications revealed that in approx. ~6 % of the particles the RuvB motor is rotated by 60° with respect to the RuvA-HJ core complex. c, Multibody refinement of RuvAB-HJ particles. Maps corresponding to the seven most abundant eigenvectors after principal component analysis are shown in top and side views. Repositioning of the reconstructed body densities along the individual eigenvectors (grey and red colour correspond to the start and end point of the movement). Body 1 and 2 indicate body definitions for multibody refinement in RELION. d, Contribution of each of the twelve eigenvectors to the overall variance (in %). The first 7 eigenvectors cover ~95 % of all movements. The rotational motions of eigenvectors 1 and 2, together, cover ~45 % of the variance. A wobbling motion of the RuvB motor with respect to the RuvA core is represented by eigenvectors 3-6 and amount to ~47.5 % of the variance. The motion increasing the gap size (bouncing) between the two bodies (eigenvector 7) covers ~2.5 % of the observed variance. e, Illustration of the directionalities corresponding to the three predominant trajectories: rotation (45 %), wobbling (47.5 %) and bouncing (2.5 %).