Changes within the central stalk of E. coli F1Fo ATP synthase observed after addition of ATP

F1Fo ATP synthase functions as a biological generator and makes a major contribution to cellular energy production. Proton flow generates rotation in the Fo motor that is transferred to the F1 motor to catalyze ATP production, with flexible F1/Fo coupling required for efficient catalysis. F1Fo ATP synthase can also operate in reverse, hydrolyzing ATP and pumping protons, and in bacteria this function can be regulated by an inhibitory ε subunit. Here we present cryo-EM data showing E. coli F1Fo ATP synthase in different rotational and inhibited sub-states, observed following incubation with 10 mM MgATP. Our structures demonstrate how structural transitions within the inhibitory ε subunit induce torsional movement in the central stalk, thereby enabling its rotation within the Fο motor. This highlights the importance of the central rotor for flexible coupling of the F1 and Fo motors and provides further insight into the regulatory mechanism mediated by subunit ε.

A key component in the generation of cellular energy is the F 1 F o ATP synthase, a biological rotary motor that converts proton motive force (pmf) to adenosine triphosphate (ATP) in both oxidative phosphorylation and photophosphorylation [1][2][3][4] . The enzyme is based on two rotary motors, termed F 1 and F o , that are coupled together by two stalks: a central rotor stalk and a peripheral stator stalk (Fig. 1a). The central stalk is comprised of subunits ε and γ and rotates during the enzyme's catalytic cycle. The peripheral stalk is a homodimer comprised of b subunits, and connects the non-rotating components together. During ATP synthesis, the membrane-bound F o motor converts the pmf into rotation of the F o rotor ring, this rotation is transferred to the F 1 motor via the central rotor which in turn induces conformational changes in the catalytic subunits. These conformational changes alter the chemical environment in the catalytic sites within F 1 so that ATP is synthesized from ADP and inorganic phosphate (P i ) 5,6 . The F 1 motor has pseudo threefold symmetry 5,7 with six dwell positions 8 , but the symmetry of the F o varies across species with the Escherichia coli enzyme having tenfold rotational symmetry (10 c subunits in the rotor ring 9 ). Because of the symmetry mismatch between the F 1 and F o motors, it has been hypothesized that they need to be flexibly coupled for efficient function 10 , with the peripheral and/or central stalks flexing to alleviate the symmetry mismatch between them 11,12 . F 1 F o ATP synthase can operate in reverse, hydrolyzing ATP and pumping protons. However, cells have evolved inhibitory mechanisms to avoid wasteful hydrolysis of ATP that could occur under certain physiological conditions. Bacterial ATP synthases appear to utilize a range of different mechanisms for inhibition, with nucleotides, ions and conformational changes making contributions [13][14][15] . E. coli and other related bacteria exploit an internal subunit, termed ε, that can sense the environment and inhibit the enzyme under certain conditions 13 . In E. coli, subunit ε can be divided into N-terminal (εNTD) and C-terminal (εCTD) domains. The εNTD is a β-sandwich with two five-stranded sheets whereas the εCTD is formed from two short helices, residues 87-102 and 110-136 (referred to as εCTH1 and εCTH2 respectively), connected by a linker (Fig. 1b). It has been hypothesized that the εCTD is able to inhibit the F 1 motor by extending up and blocking rotation under certain conditions 16,17 . Multiple structural studies examining E. coli F 1 or F 1 F o ATP synthase either in the absence of nucleotide 18 or in the presence of AMPPNP 16 or MgADP 19 , have shown the εCTD oriented in an extended up position (Fig. 1b), whereas the isolated ε subunit has also been crystallized in a condensed down position 20 (Fig. 1c). Previously, we reported~5 Å resolution structure of E. coli F 1 F o ATP synthase following incubation with 10 mM MgATP 21 , which confirmed that the εCTD transitions to a condensed down conformation via a half-up intermediate.
To define the transitions of the εCTD in greater detail and understand how it regulates function, we have used cryo-EM to examine detergent-solubilized E. coli F 1 F o ATP synthase 22 following a 45 s incubation with 10 mM MgATP. These conditions allow the enzyme to be observed operating in the hydrolysis direction, and are similar to the concentrations found in E. coli undergoing aerobic respiration 23 (though with much lower Pi concentration 24 ). Strikingly, the improved detail in this study shows that the transition of the εCTD to a down sub-state is associated with a substantial torsional flexing of the central stalk, as evident by rotation of the εNTD about the γ subunit. This flexing, in combination with bending in the peripheral stalk, mediates rotation in the F o motor. Our work provides a structural framework for role of the central stalk in flexible coupling within F 1 F o ATP synthases and suggests a hypothesis of how pmf could modulate the enzyme's structure and function.

Results
Cryo-EM analysis of F 1 F o ATP synthase following incubation with MgATP. Cryo-EM maps of E. coli F 1 F o ATP synthase in the presence of 10 mM MgATP were obtained using methods similar to those in previous studies 18,19,21,25 (Supplementary Figs. 1 and 2) and provided superior structural information than was observed previously 21 . Previous work 18 had identified three major conformational states of the enzyme in which the central stalk is rotated by~120°relative to peripheral stalk. These states are termed State 1, State 2 and State 3, with the order referring to the enzyme operating in ATP hydrolysis direction ( Supplementary  Fig. 2). An overall resolution of 2.7-3.0 Å was achieved for the three rotational states, which enabled bound nucleotides to be identified and modeled (Fig. 2a). The three catalytic β subunits in the present study were identified as containing β1 (β DP ); MgADP, β2 (β E ); ADP and β3 (β TP ); MgATP (Fig. 2a). Compared to the same enzyme imaged in the presence of 10 mM MgADP 19 , the central stalk had rotated as a rigid body by~10°counterclockwise, when viewed from the membrane ( Fig. 2b and Supplementary  Fig. 3), the εCTH2 has dissociated from the central stalk, and the β1 (β DP ) subunit has closed to contact the γ subunit (Fig. 2c) and bind MgADP. Comparison of the relative position of the rotor axel between known structures 8,16,19,[26][27][28] , highlighted that the F 1 -ATPase was in a similar rotary position to that of observed of Geobacillus stearothermophilus (also termed Bacillus PS3) in the catalytic dwell 8 ( Supplementary Fig. 3), indicating that this enzyme was in a similar state. In the maps of these three states, the details of the F o region remained ambiguous and hence further data processing was performed to verify the location of the εCTD and cring, as described in the following section.
Masked 3D classification focusing on the central rotor highlighted sub-states in which the εCTD adopted either a condensed down conformation or an extended half-up conformation ( Fig. 3 and Supplementary Fig. 2). The maps generated for each of these sub-states showed the position of the εCTD, with local resolution estimates of 4-5 Å (Supplementary Fig. 4). However, due to the likely high flexibility of this sample, it was still difficult to unequivocally assign the position of the membrane domain subunits (a, b, and c subunits) in the maps. To obtain clearer information in this region, a refinement that focused on the F o motor was performed ( Supplementary Fig. 2) and produced maps of sufficient detail to enable fitting of the membrane region. These maps were combined (using Phenix 29 ; maps and models provided as Supplementary Data 1-4) with the maps obtained without focused refinement to visualize overall changes between sub-states.
Subunit ε stabilizes the conformation of the central stalk. In this study we observed the εCTD in two conformations, a half-up and a down sub-state. Although the resolution of the maps was not atomic (Fig. 3 and Supplementary Fig. 4) they contained clear detail (4-5 Å resolution) that showed the position of the α-helices and enabled the docking and fitting of known crystal 20 and cryo-EM 19 models ( Supplementary Fig. 5), providing a clear picture of the molecular arrangement in this system. In the half up substates, no density for εCTH2 was observed, however εCTH1 remained attached to subunit γ (Fig. 3b). In the down sub-state, both the εCTH1 and εCTH2 were folded on to each other as seen in the isolated E. coli ε subunit crystal structure 20 (Fig. 3c). The sub-states of State 2 showed the best detail for the two εCTD conformations ( Fig. 3 and Supplementary Fig. 4) and allowed the c subunits to be assigned to F o rotational sub-states based on their interaction with the εNTD (Supplementary Fig. 6), assuming that the c-ring remains bound during rotation, which is likely because the interface between the ring and central rotor has a buried surface of~1200 Å 230, . Nucleotide occupancy and conformational changes in the F 1 motor following incubation with MgATP. a Horizontal section of the State 2 E. coli F 1 F o ATP synthase cryo-EM map and details of the β subunit catalytic site occupancies (with equivalent mitochondrial F 1 nomenclature: 5 β1 = β DP , β2 = β E , β3 = β TP , as named for the E. coli enzyme 16 ). β1 contains MgADP, β2 contains ADP, and β3 contains MgATP. Section of map contoured to 0.028 in ChimeraX 62 and mesh for nucleotides contoured to isolevel 10 in PyMol (Schrödinger). b, c Comparison of the F 1 motor after incubation with MgATP (this study; γ in blue, ε in green and β in yellow) or MgADP (PDB:6oqv 19 ; subunits shown as outline). b The central stalk (subunits γ and ε) is rotated~10°clockwise when viewed from the membrane (structures are aligned to the F 1 β barrel crown). c β1 closes inwards from a half-open to closed conformation. When the State 2 εCTD half-up and down structures were compared ( Fig. 4) additional clear differences beyond the εCTD up and down conformation were observed. When aligned on the stator a subunit (Fig. 4b), the F o ring rotates the equivalent of two c subunits in a clockwise direction when viewed from the membrane (akin to the synthesis direction). This rotation of the F o motor was facilitated mainly by a twisting of the central stalk (~50°), but also by flexing of the peripheral stalk (~15°) (Fig. 5), with the remainder facilitated by small rearrangements within the complex. The twisting of the central stalk involves the εNTD rotating about the γ subunit ( Fig. 4c) and this is mediated by a~10°bending at the foot of the N-terminal γ subunit helix (defined by residues γ39-57) (Figs. 3c and 4d). When the εCTD is half-up, εCTH1 provides an additional link between the εNTD and subunit γ, stabilizing the conformation of the central stalk together (Figs. 3b and 6). When the εCTD is in the down conformation, the central stalk is no longer stabilized by the εCTH1:γ interaction, likely increasing its torsional freedom, and the εNTD rotates relative to the γ subunit. The rotational movement of the εNTD observed between the half-up and down sub-states increases the distance between the εNTD and εCTH1 binding site on subunit γ (Fig. 6), reducing the likelihood of the εCTH1:γ interaction.
εCTD helix mutants alter enzyme function. To further investigate the role of each of the εCTD helices on enzyme function and the impact the half-up sub-state has on ATP hydrolysis, two ε subunit truncation mutants were generated. An εΔCTH2 mutant (lacking residues ε105-124; Fig. 7a) would lack the ability to form the classical autoinhibited up sub-state 16 or the uninhibited down sub-state, but would retain the ability to form the half-up substate and stabilize the central stalk conformation. An εΔCTH1 + 2 mutant (lacking residues ε82-124; Fig. 7b) lacking both εCTD helices would mimic the uninhibited down sub-state and prevent the up or half-up conformations, freeing the central stalk from the bridge made by the εCTH1.
First, to confirm that the εΔCTH2 truncation was still able to form the half-up sub-state, we obtained cryo-EM maps of the εΔCTH2 truncation in the presence of 10 mM MgATP ( Fig. 7c and Supplementary Fig. 7). Although processing and masking methods similar to those used on the wild-type enzyme were performed on these data, only a single conformation of the εΔCTH2 subunit was observed. The maps of this sample showed the εCTH1 was bound to the γ subunit in a manner analogous to that observed in the wild-type half-up sub-state. ATP regeneration assays performed on wild-type and truncation mutants showed different turnover rates (Fig. 7d, e). As expected, εΔCTH1 + 2 showed the highest turnover of ATP because it is unable to form either the up or half-up inhibited sub-states. However, εΔCTH2 showed a higher turnover than wild-type enzyme but lower turnover than εΔCTH1 + 2, indicating that the half-up position of εCTH1and its interaction with γ subunit somehow modulates the enzyme turnover. When superposed on subunit a (orange), the c-ring rotates two c subunits in the F o motor (one c subunit colored black with black arrow-relative rotation of c subunits identified using the interaction between εNTD and c subunit; Supplementary Fig. 6). c When superposed on the β barrel crown of the α and β subunits, the εNTD rotates~50°about the γ subunit and the peripheral stalk flexes~15°. d When superposed on N-terminus of subunit γ, the foot helix (residues γ39-57) bends and twists to accommodate the movement of the εNTD.

Discussion
The cryo-EM and functional studies presented here provide information on how F 1 F o ATP synthase changes conformation after addition of 10 mM MgATP. The central stalk not only transitions to a down state, but also twists, allowing rotation in the F o motor. This twisting, in combination with flexing in the peripheral stalk, may facilitate flexible coupling between the F 1 and F o motors and suggests a hypothesis of how subunit ε can modulate E. coli F 1 F o ATP synthase function.
Although the enzyme is likely rotating and hydrolyzing ATP during the freezing process 21 , we did not observe sub steps (e.g., the binding dwell) in the enzyme beyond the three catalytic dwells and ε/c-ring sub rotation. This is likely due to the limited time the enzyme would spend outside the catalytic dwell under these imagining conditions, with single molecule studies needing external load, in the form of increased medium, to observe substates 9 . Assuming that the F 1 F o enzyme has similar turnover to the F 1 -ATPase, single molecule studies suggest that the enzyme would be in the catalytic dwell~97% of the time 31 , and hence too small number of particles for efficient sorting. Further to this, the relative number of particles between each state differed substantially and the proportional differences were different than that observed for the same enzyme incubated with MgADP 19 . Other work using single molecule methods has suggested that the 3:10 symmetry mismatch between the F 1 and F o motors would cause asymmetry in the c-ring rotation [32][33][34] , and the structural data of E. coli F 1 F o incubated with either MgADP 19 or MgATP certainly corroborates this.
Flexible coupling between the F 1 and F o motors is necessary to facilitate efficient enzyme function, however whether this flexibility originates from the peripheral or central stalk has been controversial [35][36][37][38][39][40] . To date, structural studies have only shown flexibility within the peripheral stalk 12 , with the central stalk remaining rigid in all rotational sub-steps observed 19,[41][42][43][44][45][46] . Previously we have shown that, in E. coli, the peripheral stalk can flexibly couple the F 1 and F o motors, facilitating a single c subunit step in the F o motor without flexing of the central stalk 19 . In the present study we observe that the F o motor rotates two c subunit steps in the clockwise direction (when viewed from the membrane, i.e. the synthesis direction) when the εCTD transitions from the half-up to the down conformation (Figs. 4b and  8a). Torsional flexing of the central stalk facilitates the majority of this F o rotation, while the peripheral stalk flexes to accommodate the remainder (Fig. 5). In this experiment MgATP was added prior to grid freezing (similar but not identical conditions to that seen in E. coli undergoing aerobic respiration) and therefore the enzyme would be rotating in the counterclockwise direction (when viewed from the membrane, i.e. the hydrolysis direction). Hence, the rotation we observe in F o when the εCTD transitions from the half-up to down conformation is in the opposite direction to that in which F o is being driven during ATP hydrolysis. The counter rotation we observe here could be due to several factors. Single molecule studies 33,47 have identified rotation in F o motor of a similar magnitude and direction, suggesting this could be indicative of sub stepping in the synthesis direction. Another possibility could be that that the drag, that would be experienced at the stator/lipid/detergent interfaces, results in the delay of the F o ring during rotation that we observe here (Fig. 8a).
Although single molecule 36,47,48 and molecular dynamics studies 35 have indicated that the central rotor can be flexible, the present work provides a better understanding of how this flexibility is both conferred and modulated by the εCTD. When the εCTD is in the up or half-up conformation, the εCTH1 binds to the γ subunit, clamping the central rotor together (Figs. 8 and 9). This clamping would stabilize the central stalk in a closed position, increasing the stiffness of the rotor which, in turn, has the potential to impede enzyme turnover by decreasing the flexibility of the intact enzyme. When the εCTD subunit is in the down conformation, εCTH1 can no longer bridge between the εNTD and the γ subunit, thereby enabling the complex to open up to an unclamped conformation and allow a greater degree of flexible coupling between the F 1 and F o motors (Figs. 6, 8 and 9). The ATPase assays presented here suggest that, when the enzyme is in half-up conformation (εΔCTH2), although the turnover is reduced compared to a fully active enzyme (εΔCTH1 + 2), it remains greater than for an enzyme that is able to be fully autoinhibited (WT) (Fig. 7). Together these data indicate that the εCTD is able to modulate central rotor flexibility in addition to inserting into the F 1 -ATPase to physically block rotation. An indepth study on yeast F 1 F o ATP synthase 46 , using similar methods to those in this study and which presented the enzyme after incubation with 10 mM ATP, revealed the enzyme in many rotary states. In all structures the rotor was in the same conformation and showed none of the torsional flexing that we observed in the present study, suggesting that the torsional flexing we observe may be limited to the bacterial or E. coli enzyme, and may not always be seen with other species.
The precise function of ATP in regulating the ε subunit of F 1 F o ATP synthase appears to vary between bacterial species. For example, the εCTD of Bacillus PS3 F 1 F o ATP synthase forms a single helix 49 that does not bridge the γ subunit in the same manner as the E. coli εCTD (Supplementary Fig. 9). Furthermore, the isolated Bacillus PS3 ε subunit has been shown to bind ATP 50-52 with micromolar binding affinity (Kd = 4.3 μM 53 ) and a FRET sensor based on this subunit has been used to visualize ATP levels inside living cells 54 . Hence, in Bacillus PS3, cellular Fig. 6 Rotation of the εNTD increases the distance to the εCTH1 binding site. To highlight the relative rotation of the ε subunit between the half-up and down sub-states, the State 2 half-up ε subunit was superposed onto the State 2 down εNTD (shown in yellow). After the εNTD rotates about the γ subunit, the distance between εCTH1 and its binding site on γ is increased in the down sub-state and is less likely to attach to the central stalk.
ATP concentrations are likely to regulate the εCTD conformation and the single εCTD helix is unable to clamp the central stalk in the manner we observe in E. coli ATP synthase. The ATP binding affinity for the isolated E. coli subunit ε has been shown to be much weaker than Bacillus PS3, with little discrimination between ATP and ADP (Kd of~20 mM for both ATP and ADP 13,52 ). The crystal structure of the isolated ε subunit from E. coli also demonstrates that the εCTD can form the down conformation in the absence of ATP 20 . Further to this, studies on Caldalaklibacillus thermarum F 1 -ATPase have also shown that removal of the ε subunit ATP binding site has little effect on activity or conformation of the εCTD 55 . Hence, other mechanisms in addition to ATP binding could potentially control the conformation of the εCTD in E. coli and other related bacteria. ElaB. e ATP regeneration assays of WT (containing full length subunit ε), εΔCTH2 (ε1-104) and εΔCTH1 + 2 (ε1-81). All data points and mean are shown (raw traces are in Supplementary Fig. 8 and values in Supplementary Data 6). Removal of εCTH2 results in higher ATP turnover than WT. Removal of both εCTH1 and εCTH2 shows higher ATP turnover than removal of only εCTH2. The cryo-EM maps generated in this study suggest another mechanism whereby the conformation of subunit ε could be controlled by the pmf. When F 1 F o ATP synthase is operating in synthesis mode with high pmf, torque generated in the F o motor would drive the F o ring clockwise (Fig. 8b). This torque would pull the εNTD clockwise and increase the distance between it and the εCTH1 binding site on subunit γ, reducing the likelihood of εCTH1 binding and favoring the εCTD down conformation (Figs. 6 and 8b). If the pmf were to be reversed, the torque in F o would rotate the εNTD anticlockwise and decrease the distance to the εCTH1 binding site on subunit γ, increasing the likelihood of εCTH1 binding and consequently the εCTD up conformation (Figs. 6 and 8c). In this way, the function of E. coli F 1 F o ATP synthase could be modulated by a combination of the cellular ATP concentration and the pmf (i.e., the torque in the F o motor). Hence, the εCTD would act as a ratchet, inhibiting F 1 F o ATP synthase when the pmf is insufficient to drive ATP synthesis, allowing the bacterium to grow and quickly adapt to unfavorable conditions. A recent in vivo crosslinking study investigating the physiological relevance of subunit ε demonstrated that the εCTD down state would be most prevalent in conditions that produce high pmf 56 , suggesting that the ε subunit does change conformation in response to pmf in addition to ATP concentration. Hence, the data presented here illustrates both flexible coupling in the central stalk and a potential mechanism whereby this torsional flexing could impact the regulation of F 1 F o ATP synthase.

Methods
Cloning and protein purification. Mutant constructs were made by overlap extension PCR and using the following primers: εΔCTH2: Forward primer 5'-aagcgaaacgtaaggctgaagagcactaacaccggcttgaaaagca caaa-3' Reverse primer 5'-tggcttttgtgcttttcaagccggtgttagtgctcttcagccttacgttt-3' εΔCTH1 + 2: Forward primer 5'-aacgtgaccgttctggccgactaacaccggcttgaaaagcaca aa-3' Reverse primer 5'-ggcttttgtgcttttcaagccggtgttagtcggccagaacggtcacgtt-3' E. coli F 1 F o ATP synthase protein was prepared as described in Sobti et al. 21,25 . Cysteine-free E. coli ATP synthase (all cysteine residues substituted with alanine and a His-tag introduced on the β subunit) was expressed in E. coli DK8 strain 22 . Cells were grown at 37°C in LB medium supplemented with 100 μg/ml ampicillin for 5 h. The cells were harvested by centrifugation at 5000 × g, providing~1.25 g cells per liter of culture. Cells were resuspended in lysis buffer containing 50 mM Tris/Cl pH 8.0, 100 mM NaCl, 5 mM MgCl 2 , 0.1 mM EDTA, 2.5% glycerol and 1 μg/ml DNase I, and processed with three freeze thaw cycles followed by one pass through a continuous flow cell disruptor at 20 kPSI. Cellular debris was removed by centrifuging at 7700 × g for 15 min, and the membranes collected by ultracentrifugation at 100,000 × g for 1 h. The ATP synthase complex was extracted from membranes at 4°C for 1 h by resuspending the pellet in extraction buffer consisting of 20 mM Tris/Cl, pH 8.0, 300 mM NaCl, 2 mM MgCl 2 , 100 mM sucrose, 20 mM imidazole, 10% glycerol, 4 mM digitonin and EDTA-free protease inhibitor tablets (Roche). Insoluble material was removed by ultracentrifugation at 100,000 × g for 30 min. The complex was then purified by binding on Talon resin (Clontech) and eluted in 150 mM imidazole, and further purified with size exclusion chromatography on a 16/60 Superose 6 column equilibrated in a buffer containing 20 mM Tris/Cl pH 8.0, 100 mM NaCl, 1 mM digitonin, and 2 mM MgCl 2 . The purified WT protein was then concentrated to 11 μM (6 mg/ml), and snap frozen and stored for grid preparation while the εΔCTH2 and εΔCTH1 + 2 mutants were concentrated and frozen at 9 μM (5 mg/ml) Cryo-EM grid preparation. One μl of 100 mM ATP/100 mM MgCl 2 (pH 8.0) was added to an aliquot of 9 μl of purified cysteine-free E. coli F 1 F o ATP synthase (WT at 11 μM and εΔCTH2 mutant at 9 μM) and the sample was incubated at 22°C for 30 s, before 3.5 μl was placed on glow-discharged holey gold grid (UltrAufoils R1.2/ 1.3, 200 Mesh). Grids were blotted for 4 s at 22°C, 100% humidity and flash-frozen in liquid ethane using a FEI Vitrobot Mark IV (total time for sample application, blotting, and freezing was 45 s).
WT cryo-EM data collection and data processing. Grids were transferred to a Thermo Fisher Talos Arctica transmission electron microscope (TEM) operating at 200 kV and screened for ice thickness and particle density. Suitable grids were subsequently transferred to a Thermo Fisher Titan Krios TEM operating at 300 kV equipped with a Gatan BioQuantum energy filter and K3 Camera at the Pacific Northwest Centre for Cryo-EM at OHSU. Images were recorded automatically using SerialEM v3.7 at ×81,000 magnification yielding a pixel size of 0.54 Å (K3 operating in super resolution mode). A total dose of 48 electrons per Å 2 was used spread over 77 frames, with a total exposure time of 3.5 s. In all, 8620 movie micrographs were collected (Supplementary Fig. 1). MotionCorr2 57 was used to correct local beam-induced motion and to align resulting frames, with 9 × 9 patches and binning by a factor of two. Defocus and astigmatism values were estimated using Gctf 37 and 8215 micrographs were selected after exclusion based on ice contamination, drift, astigmatism. Approximately 1000 particles were manually picked and subjected to 2D classification to generate templates for template picking in cryoSPARC 58 , yielding 869,147 particles. These particles were binned by a factor of four and subjected to 2D classification generating a final dataset of 429,638 particles. The locations of these particles were then imported into Relion 59 , reextracted at full resolution, and further classified into 3D classes using a low pass filtered cryo-EM model generated from a previous study 18 , yielding the three main states related by a rotation of the central stalk (State 1, State 2, and State 3 with 100,831, 215,003, and 113,804 particles, respectively). Focused classification, using a mask comprising the lower half of the central rotor, was implemented without performing image alignment in Relion 3.0, yielding the half-up and the down subclasses in each of the three main states. A further F o focused classification without image shifts was performed on each of the half-up and down sub-classes to elucidate the position of F o subunits in the respective sub-states. See Supplementary  Fig. 2 for a flowchart describing this classification.
εΔCTH2 mutant cryo-EM data collection and data processing. Grids were transferred to a Thermo Fisher Talos Arctica transmission electron microscope (TEM) operating at 200 kV and screened for ice thickness and particle density. Suitable grids were subsequently transferred to a Thermo Fisher Titan Krios TEM operating at 300 kV equipped with a Gatan BioQuantum energy filter and K2 Camera at the Molecular Horizons, University of Wollongong. Images were recorded automatically using EPUv2.7 at ×120,000 magnification yielding a pixel size of 1.13 Å. A total dose of 55 electrons per Å 2 was used spread over 50 frames, 3680 movie micrographs were collected. All the processing was subsequently performed in cryoSPARC 58 . Initial particles were picked using the blob protocol which were 2D classified to create templates to the pick the entire dataset. Extracted particles were subjected to multiple rounds of 2D classification, ab initio reconstruction, heterogenous refinement to sort the particles into discreet structures. See Supplementary Fig. 7 for a flowchart describing this classification. Additional processing was performed using masks and focused refinement but did not yield any maps showing alternate conformations, so are not included in the flow chart. Supplementary Table 1 contains a summary of data collection/processing statistics and Supplementary Fig. 10 for FSC curves.
Model building. Models were built and refined in Coot 60 , PHENIX 29 , and ISOLDE 61 using pdbs 6OQT, 6OQV, 6OQW 19 (E. coli ATP synthase incubated with MgADP), and 1AQT 20 (isolated E. coli ATP synthase subunit ε) as guides. See Supplementary Table 1 for a summary of refinement and validation statistics.
ATP regeneration assays. ATP regeneration assays were performed as in Sobti et al. 25 . Five μg of detergent solubilized protein was added to 100 mM KCl, 50 mM MOPS pH 7.4, 1 mM MgCl 2 , 1 mM ATP, 2 mM PEP, 2.5 units/ml pyruvate kinase, 2.5 units/ml lactate dehydrogenase and 0.2 mM NADH and monitored for OD at 340 nm at for up to 20 min (Supplementary Fig. 8).
Statistics and reproducibility. The cryo-EM analyses were performed on single protein preparations. We have performed similar experiments on similar protein preparations (more than ten times using a range of microscopes) with similar outcomes 18,19,21,25 . Detailed statistics for the sample size, data collection and analysis of cryo-EM data are provided in Supplementary Table 1, and Fourier shell correlation curves are provided in Supplementary Fig. 10. The activity assays were performed in technical triplicate, with only means provided as the raw data Fig. 9 Schematic of clamping by εCTH1. When the εCTH1 is in the half-up state and bound to subunit γ, the central stalk is clamped and increases the stiffness of the rotor. When εCTH1 is in the down state, the central stalk is no longer clamped and has increased flexibility. Fig. 8 and Data 6) could be plotted and interpreted without error bars (Fig. 7e).

(Supplementary
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