F1-ATPase of Escherichia coli

Background: Bacterial ATP synthases are autoinhibited by the subunit ϵ C-terminal domain. Results: Nucleotide hydrolysis is required to form the ϵ-inhibited state, which also responds dynamically to different ligand conditions. Conclusion: ϵ inhibition initiates at the catalytic dwell angle, but reversible rotation over ∼40° is probably involved in nucleotide effects on the inhibitory state of ϵ. Significance: ϵ inhibition may provide a new target for antimicrobial discovery. F1-ATPase is the catalytic complex of rotary nanomotor ATP synthases. Bacterial ATP synthases can be autoinhibited by the C-terminal domain of subunit ϵ, which partially inserts into the enzyme's central rotor cavity to block functional subunit rotation. Using a kinetic, optical assay of F1·ϵ binding and dissociation, we show that formation of the extended, inhibitory conformation of ϵ (ϵX) initiates after ATP hydrolysis at the catalytic dwell step. Prehydrolysis conditions prevent formation of the ϵX state, and post-hydrolysis conditions stabilize it. We also show that ϵ inhibition and ADP inhibition are distinct, competing processes that can follow the catalytic dwell. We show that the N-terminal domain of ϵ is responsible for initial binding to F1 and provides most of the binding energy. Without the C-terminal domain, partial inhibition by the ϵ N-terminal domain is due to enhanced ADP inhibition. The rapid effects of catalytic site ligands on conformational changes of F1-bound ϵ suggest dynamic conformational and rotational mobility in F1 that is paused near the catalytic dwell position.

F 1 -ATPase is the catalytic complex of rotary nanomotor ATP synthases. Bacterial ATP synthases can be autoinhibited by the C-terminal domain of subunit ⑀, which partially inserts into the enzyme's central rotor cavity to block functional subunit rotation. Using a kinetic, optical assay of F 1 ⅐⑀ binding and dissociation, we show that formation of the extended, inhibitory conformation of ⑀ (⑀ X ) initiates after ATP hydrolysis at the catalytic dwell step. Prehydrolysis conditions prevent formation of the ⑀ X state, and post-hydrolysis conditions stabilize it. We also show that ⑀ inhibition and ADP inhibition are distinct, competing processes that can follow the catalytic dwell. We show that the N-terminal domain of ⑀ is responsible for initial binding to F 1 and provides most of the binding energy. Without the C-terminal domain, partial inhibition by the ⑀ N-terminal domain is due to enhanced ADP inhibition. The rapid effects of catalytic site ligands on conformational changes of F 1 -bound ⑀ suggest dynamic conformational and rotational mobility in F 1 that is paused near the catalytic dwell position.
ATP synthases play a key role in energy metabolism in most living organisms and achieve energy coupling as dual engine rotary nanomotors (1)(2)(3). The F-type ATP synthase of Escherichia coli (Fig. 1), a bacterial prototype, is composed of core subunits that all have homologs in the ATP synthases of mitochondria and chloroplasts (4). The membrane-embedded F O complex (ab 2 c 10 ) acts like a turbine to transport protons across the membrane, and the external F 1 complex (␣ 3 ␤ 3 ␥␦⑀) contains three cooperative catalytic sites for ATP synthesis or hydrolysis. The ring of c-subunits, with the critical proton transport sites, is the rotor complex of F O and connects to the central rotor stalk of F 1 , composed of ␥ and the N-terminal domain (NTD) 2 of ⑀. The three catalytic ␤ subunits alternate with three ␣ subunits to surround the upper half of the asymmetric rotor stalk of ␥, and the ␦-b 2 connection forms a peripheral stator stalk anchoring ␣ 3 ␤ 3 to the other stator subunit of F O , a. In vitro, F 1 from eukaryotes and bacteria can be dissociated from F O as a soluble, rotary motor ATPase, and these F 1 -ATPases have been useful for both mechanistic studies and the determination of high resolution structures.
Despite general conservation between bacterial and mitochondrial ATP synthases, it has been demonstrated that bacterial ATP synthase can be an effective target for antibacterial treatment. It is the target of a novel class of compounds that are bactericidal for actively replicating and dormant mycobacteria (5,6) and that show promising effects against multidrug-resistant tuberculosis in phase II clinical trials (7). However, the lead compound is only effective against a narrow spectrum of mycobacteria, and, because it targets the H ϩ -transporting sites of F O , adapting this scaffold to target other pathogenic bacteria introduces a significant risk of cross-reaction with mitochondrial ATP synthase. Recently, our group determined the first crystal structure of a bacterial F 1 -ATPase that is in an autoinhibited state mediated by the C-terminal domain (CTD) of its ⑀ subunit (8). Inhibition by ⑀ may serve regulatory roles in ATP synthases of bacteria (2,9) and chloroplasts (10) but does not occur in mitochondrial ATP synthase, which has a distinct inhibitor protein (11). Recent studies confirmed that the bacterial ⑀CTD inhibits ATP synthesis as well as hydrolysis (12,13), indicating that ⑀ inhibition may provide a new target for future development of antimicrobial drugs selective for bacteria. With that in mind, the current study focuses on improving our biochemical understanding of how the catalytic F 1 complex of E. coli ATP synthase is inhibited by ⑀. * This work was supported, in whole or in part, by National Institutes of Health As shown in Fig. 1, the ⑀ subunit has two domains. The ⑀NTD, essential for the F 1 rotor connection to the c-ring in F O (2,9), is a ␤-sandwich fold and exhibits a similar conformation and association with ␥ in several structures of bacterial F 1 (8,14) and mitochondrial F 1 (MF 1 ) (15,16); essentially the same ⑀NTD structure is also seen for isolated bacterial ⑀ (17)(18)(19). However, the ␣-helical ⑀CTD has been observed in dramatically different conformations (Fig. 1). A compact conformation (the ⑀ C state) has a coiled-coil between its two ␣-helices, and the second helix packs against the ⑀NTD. The ⑀ C state has been observed for isolated bacterial ⑀ (17)(18)(19) and in one bacterial F 1 structure (14). In structures of MF 1 (15) and MF 1 ⅐c-ring (20), the homolog of ⑀ appears to be locked in the ⑀ C state by a mitochondria-specific subunit. E. coli ATP synthase can synthesize and hydrolyze ATP when ⑀ is restricted to the ⑀ C state (21), in which the ⑀CTD does not contact any F 1 subunits (Fig. 1, left). In contrast, in the recently determined structure of E. coli F 1 (Fig. 1) (8), an extended conformation of the ⑀CTD (⑀ X state) contacts five other subunits, and its terminal half is inserted into the central cavity of F 1 . The position and subunit contacts of the ⑀CTD within the E. coli F 1 structure correlate well with many biochemical studies of ⑀ inhibition and interaction with other F 1 subunits (reviewed in Refs. 2 and 9). The extensive buried surface of the ⑀CTD within the F 1 structure and its inter-actions with two catalytic ␤ subunits suggest that this form of the enzyme represents an inactive state. This correlates with results of "single-molecule" (SM) studies of F 1 from E. coli (22) and other bacteria (23)(24)(25)(26), showing that ⑀ can induce or extend long "pauses" (seconds) during which ␥ does not rotate in the presence of substrate MgATP. Some SM studies concluded that ⑀ inhibits by stabilizing or extending an ADP-induced inhibitory pause that occurs at the catalytic dwell (22,24,27), whereas another recently concluded that ADP-and ⑀-induced inhibitions are separate processes for cyanobacterial F 1 (25). Some studies also concluded that ⑀ inhibition includes or is dominated by changes to one or more intrinsic kinetic steps along the catalytic pathway (12,22,28,29). In the current study, we adapt an optical assay to directly measure the kinetics of binding and dissociation for E. coli F 1 ⅐⑀ and correlate these with inhibitory effects for wild type (WT) and mutant forms of ⑀. Our biochemical evidence confirms that inhibition by the CTD of ⑀ initiates at the catalytic dwell but also shows that ⑀ inhibition competes with formation of the ADP-inhibited state. Further, whereas ⑀ inhibition initiates at the catalytic dwell, we also show that the balance between active and ⑀-inhibited states responds dynamically to changing nucleotide conditions. The smaller image (bottom left) depicts the E. coli ATP synthase, with F O subunits spanning the membrane bilayer (shaded box); the arrow across the bilayer indicates the direction of proton (H ϩ ) transport during net ATP synthesis. F O subunits (ribbons, a (dark red), b 2 (gray), and c 10 (green)) and F 1 subunit ␦ (orange ribbon) are from a homology-modeled assembly (67). All other F 1 subunits are from determined structures and are surface-rendered in the F O F 1 model but displayed as ribbons in the magnified view of E. coli F 1 (3␣ (green), 3␤ (shades of blue), ␥ (yellow), ⑀NTD(1-87) (light pink), and ⑀CTD(88 -138) (dark pink)). The F O F 1 model shows ⑀ in the ⑀ C or compact conformation (Protein Data Bank entry 1BSN), docked to ␥ of EF 1 -␦ (Protein Data Bank entry 3OAA). The magnified ribbon diagram shows the ⑀-inhibited F 1 -␦ structure (Protein Data Bank entry 3OAA) and omits the foremost ␣ subunit to reveal the extended conformation of ⑀ (⑀ X ); for comparison, a ribbon model of the ⑀ C state is shown offset to the right. The ribbon diagram of each ⑀ conformation shows space-filling side-chain atoms (colored by element) predicted in silico for mutations ⑀A101C/L121C. Space-filling atoms are also shown for ADP and SO 4 2Ϫ on the one occupied catalytic ␤ subunit (chain D). The molecular graphics were prepared with Chimera (81).

EXPERIMENTAL PROCEDURES
Plasmid Constructs for Affinity-tagged E. coli ⑀ Subunit-A plasmid described previously (30) (noted here as pH 6 ⑀) encodes a His 6 -tagged ⑀ (H 6 -⑀), with a tobacco etch virus protease cleavage site following the N-terminal His 6 tag. Site-directed mutagenesis was used to create the following mutations in H 6 -⑀. A pair of Cys mutations, ⑀A101C/L121C, was created on pH 6 ⑀ using the QuikChange Multi site-directed mutagenesis kit (Stratagene) with primers 5Ј-CATGGAAGCGA-AACGT-AAGTGTGAAGAGCACATTAGGAG-3Ј (⑀A101C) and 5Ј-GCTCAGGCGTCTGCGG-AATGCGCCAAAGCGATC-3Ј (⑀L121C). H 6 -⑀ that expresses only the ⑀NTD (H 6 -⑀88stop; see Ref. 31) was created with the QuikChange-II XL kit (Stratagene) (forward primer, 5Ј-CAATTCGCGGCCAGTAAGTC-GACGAAGCG-3Ј). Plasmid pBKH2 was created to add a biotin acceptor peptide (Bap) before the N-terminal His 6 tag on H 6 -⑀. This BapH 6 -⑀ has 49 residues before the native initial Met of ⑀, and tobacco etch virus cleavage would yield ⑀ with three extra N-terminal residues (GAM). It was created with pH 6 ⑀ as a template, using PCR to generate a 514-bp amplicon with restriction sites added before (XhoI) and after (BamHI) the gene for H 6 -⑀ (primers, 5Ј-CGACTCGAGCATGTCGTACTA-CCATCACC-3Ј and 5Ј-CTCGGATCCTTACATCGCTTTTTTGGTCAAC-3Ј). Following cleavage with XhoI and BamHI, this amplicon was cloned into the same sites of pDW363 (32), replacing the malE gene, to create pBKH2. BirA (E. coli biotin holoenzyme synthetase) is co-expressed from pBKH2, allowing in vivo biotinylation of the biotin acceptor peptide on BapH 6 -⑀ (32). BapH 6 -⑀ expressed with ⑀88stop or ⑀A101C/L121C had poor protein yields, so ⑀ was also expressed as a fusion protein following an N-terminal maltose-binding protein (MBP), a cleavage site for PreScission protease (GE Healthcare), and the Bap tag. This MBP-Bap-⑀ has a 31-residue segment between MBP and the initial Met of ⑀, and after cleavage by PreScission protease, Bap-⑀ would retain a 25-residue N-terminal Bap tag. The vector for this construct, pMal-PPase, was derived from pMAL-c2e (New England Biolabs), with a PreScission protease cleavage sequence after malE (33), and an NdeI site was removed by cleavage and polymerase fill-in. The sequence encoding the Bap tag was PCR-amplified from pDW363, with flanking restriction sites before (StyI) and after (NdeI and BamHI) the Bap sequence (primers, 5Ј-CATCCCAAGGCTGGAGGCCTGAA-CGATATTTTC-3Ј and 5Ј-CTCGGATCCCATATGGCCAC-CAGTGTCCTCGTG-3Ј). After cleavage with StyI and BamHI, this amplicon was inserted into StyI-BamHI sites of pMal-PPase to generate pMAL-PP-Bap. The atpC gene for WT ⑀ was extracted from p3U (34) as a 625-bp NdeI-XbaI fragment and ligated into the same sites of pMAL-PP-Bap to create pBKH8, encoding a fusion protein of MBP-Bap-⑀. Plasmids encoding MBP-Bap-⑀ with mutation ⑀88stop (pBKH9) or ⑀A101C/ L121C (pBKH10) were produced in the same way, but the NdeI-XbaI inserts were 799 bp (extra sequence downstream of atpC) because those mutant atpC genes had been passed through an intermediate vector.
To express biotinylated MBP-Bap-⑀ mutants, E. coli strain DH5␣ was co-transformed with pBirAcm (which expresses BirA; Avidity (Aurora, CO)) and either pBKH9 (MBP-Bap-⑀88stop) or pBKH10 (MBP-Bap-⑀A101C/L121C). Each strain was grown overnight at 37°C in LB with ampicillin (100 g/ml) and chloramphenicol (25 g/ml). Overnight cultures were used to inoculate 2 liters of the same medium plus 0.4% glucose and 0.1 mM biotin. Cells were grown at 37°C to A 595 ϳ0.5, 0.4 mM isopropyl 1-thio-␤-D-galactopyranoside was added to induce expression of MBP-Bap-⑀ and BirA, and growth continued for ϳ3.5 h at 37°C. Cells were harvested by centrifugation and washed once with column buffer (20 mM Tris-HCl, pH 7.5, 200 mM NaCl, 1 mM EDTA). Cells were lysed by sonication and centrifuged at 11,290 ϫ g for 30 min, and the supernatant was passed through a 0.45-m filter. This sample was mixed with 5 ml of amylose-agarose resin (New England Biolabs; pre-equilibrated with column buffer) and incubated at 4°C, with rocking, for 2 h. The amylose resin was then sedimented (1000 ϫ g, 3 min), the supernatant was discarded, and the resin was washed five times by centrifugation with 40 ml of column buffer ϩ 5 mM ␤ME. For the ⑀A101C/L121C mutant, 5 mM ␤ME was present throughout purification. The resin was incubated with 0.1 mg of PreScission Protease (4°C, 3 h, in 15 ml of column buffer ϩ 5 mM ␤ME) to release Bap-⑀, which was collected in the supernatant and in a subsequent wash of the resin with 10 ml of column buffer ϩ 5 mM ␤ME. Ultrafiltration (Vivaspin-20, 5000 molecular weight cut-off) was used to concentrate the Bap-⑀ from 25 to 1 ml and exchange it into ⑀ buffer ϩ 10% glycerol, including 1 mM ␤ME for Bap-⑀A101C/L121C. Concentrated Bap-⑀ was frozen in liquid N 2 and stored at Ϫ80°C. For some experiments, His 6 -or Baptagged ⑀A101C/L121C was treated with 5,5Ј-dithiobis(2-nitrobenzoate) (DTNB) to induce disulfide bonding between closely approaching cysteines (38). The sample was first passed through a Biogel P6 centrifuge column (39) (pre-equilibrated with 20 mM MOPS-Tris, 50 mM KCl, pH 8 (MTK8)) to remove ␤ME. Tagged ⑀A101C/L121C (ϳ30 M) was then incubated with 50 M DTNB for 15 min or less at room temperature and passed through a second centrifuge column to remove excess DTNB.
ATPase Assays-A coupled enzyme assay (40) was used for continuous monitoring of ATP hydrolysis, and assays were done at 30°C. Decrease in NADH concentration was monitored at 340 nm in a Hewlett-Packard 8453 spectrophotometer. The standard assay buffer was MTK8 supplemented with 1 mM phosphoenolpyruvate and 0.3 mM NADH. MgATP substrate was added from stock solutions of Mg acetate and Na 2 ATP; concentrations and ratios of Mg 2ϩ /ATP are noted for specific experiments. Pyruvate kinase (rabbit muscle, Roche Applied Science catalog number 109045) and lactate dehydrogenase (Porcine heart, Calbiochem catalog number 427211) were each present at 0.1 mg/ml in assays with excess Mg 2ϩ versus ATP; for assays with excess ATP versus Mg 2ϩ , pyruvate kinase was 0.2 mg/ml. In some assays, hydrolysis of GTP was measured rather than ATP. For assays measuring inhibition by ⑀, BSA (fatty-acid free) was added at 0.5 mg/ml, EDTA was added to 0.1 mM, and F 1 (Ϫ␦⑀), ⑀, and ATP were added to final concentrations and preincubated at 30°C for 10 min; the assay was initiated by adding magnesium acetate from a concentrated stock and mixing. Hydrolysis rates were measured at steady state, typically 12-15 min after adding Mg 2ϩ . For each data set varying ⑀ concentration, a fixed concentration of F 1 (Ϫ␦⑀) was used (F T ϭ 0.6 or 1.2 nM), and hydrolysis rates were fit by nonlinear regression (Prism, GraphPad, Inc.) to the following equation, where A 0 is the rate measured for F 1 (Ϫ␦⑀) alone, A i is the rate measured at each ⑀ concentration, ⑀ i , A e is the rate fitted for ⑀-saturated F 1 (Ϫ␦⑀), and K I is the apparent dissociation constant fitted for F 1 ⅐⑀ binding. For assays of inhibition by azide, magnesium acetate, ATP, sodium azide, and ⑀ (if any) were added first, and the assay was initiated by adding F 1 (Ϫ␦⑀) from a concentrated stock; steady-state rates were measured as above.
Kinetic Assays of Binding and Dissociation between F 1 (Ϫ␦⑀) and Biotinylated ⑀, Using Biolayer Interferometry (BLI)-An Octet-RED system and streptavidin-coated sensors (FortéBio, SA biosensors, catalog number 18-5019) were used to monitor BLI kinetics of protein-protein binding and dissociation, analogous to surface plasmon resonance techniques (41). MTK8 buffer included 0.5 mg/ml BSA to minimize nonspecific binding of proteins to the sensors and as carrier protein for nanomolar dilutions of F 1 (Ϫ␦⑀) or ⑀. All steps were done at 30°C, with each sensor stirred in 0.2 ml of sample at 1000 rpm and a standard measurement rate of 5 s Ϫ1 . Wild-type or mutant forms of biotinylated ⑀ (BapH 6 -⑀, or Bap-⑀ after cleavage from MBP-Bap-⑀) were immobilized on SA biosensors. Levels of in vivo biotinylation varied between ⑀ samples, so preliminary BLI titrations were done for each biotinylated ⑀ to determine the Bap-⑀ concentration and loading time needed for optimal BLI kinetic responses in subsequent binding of F 1 (Ϫ␦⑀) to the ⑀-loaded sensors. Minimal loading of ⑀ was found to be favorable for kinetic responses to F 1 (Ϫ␦⑀) binding, so most subsequent experiments loaded biotinylated ⑀ to yield 0.2-0.4 nm of BLI signal per sensor. Use of reference sensors with immobilized biotinylated ⑀ but without added F 1 (Ϫ␦⑀) confirmed that added ligands (nucleotides, Mg 2ϩ , EDTA, and azide) did not alter the BLI signal for immobilized ⑀. To correct for BLI baseline drift and minimal nonspecific binding of F 1 (Ϫ␦⑀) to sensors, all BLI experiments included one or more reference sensors in parallel for which biotinylated ⑀ was omitted from the ⑀-loading step, but F 1 (Ϫ␦⑀) was included in the association step, usually at the highest concentration of F 1 (Ϫ␦⑀) used for each experiment. FortéBio's analysis software (version 6.4) was used for reference subtraction, Savitsky-Golay filtering, and global fitting of kinetic rates for F 1 ⅐⑀ binding and dissociation.

RESULTS
Inhibition of E. coli F 1 by ⑀ with and without the ⑀CTD-Upon in vitro dissociation of E. coli F 1 from the membrane, ⑀ becomes more inhibitory but can dissociate upon dilution of F 1 , relieving inhibition of F 1 -ATPase activity (2). For most experiments in this study, we used F 1 that was depleted of ␦ and ⑀ subunits, or F 1 (Ϫ␦⑀). The stator subunit ␦ does not significantly affect F 1 -ATPase activity (42) but was removed because its dissociation from F 1 could interfere with assays below for F 1 ⅐⑀ binding and dissociation. Fig. 2 compares inhibition of F 1 (-␦⑀) by WT and mutant forms of H 6 -⑀, and Table 1 summarizes the inhibition parameters from regression curves of Fig. 2 and an additional data set. As noted before (30), the N-terminal His 6 tag on WT ⑀ did not significantly alter inhibition compared with WT ⑀ that had the tag removed (Table 1). Also, inhibition was not altered by the N-terminal Bap tag added to ⑀ (WT and mutants) for kinetic assays of F 1 ⅐⑀ binding and dissociation (not shown). For WT ⑀, values for the inhibitory constant K I and residual activity of ⑀-saturated F 1 agree with earlier estimates (29,43).
We obtained nearly the same parameters for ⑀ inhibition in assays with ATP Ͻ K m (not shown), consistent with noncompetitive inhibition by ⑀ versus ATP (29,44). We also show that the Ͼ90% inhibition by saturating WT ⑀ was unaffected by excess Mg 2ϩ ( Fig. 2A), although F 1 (Ϫ␦⑀) alone was inhibited Ͼ50% by 1 mM excess Mg 2ϩ (Table 1).
To test for inhibition by ⑀ lacking its CTD, we used ⑀88stop, one of the largest C-terminal deletions that still allows assembly of F O F 1 that is functionally coupled, both in vivo and in vitro (31). In Fig. 1, both conformations of ⑀ are colored darker for the C-terminal region that is absent in ⑀88stop. As shown in Fig.  2A, H 6 -⑀88stop caused much less inhibition than WT H 6 -⑀ and had a Ͼ15-fold larger K I , confirming that the ⑀CTD is responsible for the majority of inhibition. However, unlike WT H 6 -⑀, the maximal extent of inhibition by H 6 -⑀88stop almost doubled to ϳ45% in the presence of excess free Mg 2ϩ . Inhibitory effects of free Mg 2ϩ are linked to inhibitory MgADP bound at a catalytic site on F 1 from E. coli (45,46), from other bacteria (47), from mitochondria (48,49) and chloroplasts (50,51), and hydrolysis of GTP is less sensitive to this type of inhibition (45,48,52). For example, with 1 mM excess Mg 2ϩ , GTPase turnover by F 1 (Ϫ␦⑀) is ϳ2.5-fold faster than ATPase (Table 1). We show that WT H 6 -⑀ exhibits similar high affinity inhibition for GTPase and ATPase ( Fig. 2A and Table 1). However, H 6 -⑀88stop inhibited GTPase much less, ϳ16% maximal, both with excess free Mg 2ϩ present ( Fig. 2A) and without it (not shown). Thus, observed partial inhibition of ATPase by the ⑀NTD is largely due to increased MgADP inhibition in the absence of the ⑀CTD. This can also explain why ⑀ truncated after ⑀94 (with only about half of the first helix remaining) inhibited E. coli F 1 ϳ50% because the assays contained 2 mM excess free Mg 2ϩ (53). The effects of the ⑀NTD are distinct from the Ͼ90% inhibition caused by the ⑀CTD of intact WT ⑀, which is not sensitive to the effects of excess Mg 2ϩ .
As an alternative to removing the ⑀CTD, we also used the ⑀A101C/L121C mutant (21). 3 This cysteine pair can form a disulfide bond in nearly 100% yield (Fig. 3) that cross-links the two ␣-helices of the ⑀CTD in the ⑀ C conformation, preventing ⑀ 3 The original study with ⑀A101C/L121C (21) showed that an ⑀A101C-L121C disulfide bond could be formed in membrane-bound F O F 1 but did not appear to alter ATPase activity. We tested membranes expressing F O F 1 with ⑀A101C/L121C and showed that removing DTT from the sample activated ATPase 2-fold; this is the same activation seen originally (21) after inducing a disulfide between the ⑀CTD and ⑀NTD (⑀M49C-A126C). We believe that their ATPase assays did not include reductant for the nonoxidized sample of F O F 1 ϩ ⑀A101C/L121C and that the disulfide formed quickly and spontaneously, as we have observed (Fig. 3). Thus, they would not have observed activation of ATPase by oxidation of ⑀A101C-L121C if the disulfide had also formed in the non-oxidized sample.  Table 1. from switching to the ⑀ X conformation (see Fig. 1). As shown in Fig. 2B, this disulfide linkage prevented high affinity inhibition of F 1 (Ϫ␦⑀) as effectively as removing the ⑀CTD. However, the partial inhibition observed was less sensitive to excess free Mg 2ϩ than with H 6 -⑀88stop; this suggests that ⑀CTD/⑀NTD interactions in the ⑀ C state can influence interactions of ⑀NTD with ␥ that alter catalytic behavior. With DTT present to prevent the disulfide bond, H 6 -⑀A101C/L121C could access the ⑀ X state and showed high affinity inhibition (K I ϳ1 nM), similar to that with WT H 6 -⑀ (K I ϳ0.5 nM). However, the activity of F 1 saturated with reduced H 6 -⑀A101C/L121C was 4-fold greater than with WT H 6 -⑀. In the structure of ⑀-inhibited F 1 (8), ⑀Leu-121 is in a coiled-coil interface with the ␥ N-terminal helix, and the ⑀L121C mutation probably perturbs this interface, favoring more F 1 complexes in the active state on average. This supports the concept that, with ⑀-saturated F 1 , the residual ATPase activity (7-8% with WT ⑀) is due to the time-averaged fraction of F 1 complexes in which ⑀ is not in the inhibitory ⑀ X conformation.
Kinetics of F 1 ⅐⑀ Binding and Dissociation, Assayed by BLI-In preliminary assays, H 6 -⑀ was loaded on BLI sensors coated with Ni 2ϩ -nitrilotriacetic acid, but slow dissociation of WT H 6 -⑀ from the sensors prevented accurate measures of the slow dissociation rate of F 1 from WT H 6 -⑀. To achieve more stable and specific attachment of ⑀ to the sensor surface, ⑀ was engineered with an N-terminal Bap tag, so that a specific lysine could be biotinylated in vivo (32). Biotinylated Bap-⑀ could be stably bound to streptavidin-coated sensors (supplemental Fig. S1), and BLI was then used to measure binding and dissociation kinetics of F 1 (Ϫ␦⑀). For each Bap-⑀ variant, 4 -7 sensors were used in parallel, with F 1 (Ϫ␦⑀) concentrations varied Ն10-fold in the association samples, and association/dissociation kinetics were fit globally to determine the rate constants (Table 2). K D values derived from the rate constants correlate well with inhibitory K I values (Table 1) for WT ⑀, ⑀88stop, and disulfidebonded ⑀A101C/L121C. Representative kinetics for binding/ dissociation of F 1 (Ϫ␦⑀) with sensors containing WT ⑀ or ⑀88stop are shown in Fig. 4. The ⑀CTD did not significantly alter the association rate, indicating that only ⑀NTD/␥ interactions are involved in initial F 1 ⅐⑀ binding. In contrast, removing the ⑀CTD (Fig. 4) or preventing it from adopting the ⑀ X state (disulfide-bonded ⑀A101C/L121C) increased the dissociation rate by Ն80-fold (Table 2). For sensors loaded with biotinylated WT BapH 6 -⑀, only a small fraction of bound F 1 (Ϫ␦⑀) could be observed to dissociate in buffer only (Fig. 4), but results presented below show that essentially all F 1 (Ϫ␦⑀) on the sensor is reversibly bound. Additional assays (not shown) included excess, non-biotinylated WT H 6 -⑀ in the dissociation phase and confirmed that the observed, slow dissociation rate was not due to rebinding of F 1 (Ϫ␦⑀) to the sensor. Thus, the much slower dissociation of F 1 (Ϫ␦⑀)/WT-⑀ is probably due to strong bias of bound WT ⑀ to reside in the ⑀ X state, with the ⑀CTD buried within F 1 . However, from the K D values ( Table 2), note that the ⑀CTD contributes only ϳ20% to the net free energy for F 1 ⅐⑀ binding (⌬⌬G, Ϫ10 or Ϫ12 kJ/mol for WT ⑀ versus ⑀88stop or disulfide-bonded ⑀A101C-L121C, respectively). This does not mean the ⑀ X state of ⑀CTD has only weak interactions with other F 1 subunits; rather, the small contribution to net binding energy is probably due to the loss of favorable interactions between ␥ and ␣ 3 ␤ 3 that are blocked by insertion of the ⑀CTD.
Effects of F 1 Ligands (Mg 2ϩ , Nucleotides, P i ) on Conformational Bias of Bound, Full-length ⑀-From the crystal structure of ⑀-inhibited F 1 (8), the extensive surface area of ⑀CTD that is buried within the central cavity of F 1 suggests that the ⑀ X state of ⑀ does not directly dissociate from F 1 ; the slow dissociation observed in Fig. 4 probably occurs due to dynamic transition of ⑀ between ⑀ X and conformations like ⑀ C in which the ⑀CTD is outside of the central rotor cavity. Thus, factors that influence the fraction of F 1 complexes with ⑀ in the ⑀ X state should alter the kinetics of F 1 ⅐⑀ dissociation. To show that the conformation of ⑀ on E. coli F 1 and F O F 1 can be influenced by nucleotides and other ligands that interact with catalytic sites, early studies used static assays, such as the capacity to form a ␤-⑀ cross-link; crosslinking of ␤-⑀ was minimized by non-hydrolysis conditions, such as ATP/EDTA or MgAMPPNP but maximized by posthydrolysis conditions (MgADP/P i ) (54,55). The ␤-⑀ cross-linking residues (56) are within hydrogen-bonding distance in the structure of ⑀-inhibited F 1 but should be at least 35 Å apart with ⑀ in the ⑀ C state (8). Here, we use the BLI assay for F 1 ⅐⑀ binding/ dissociation for more dynamic analyses of how different ligands  may shift the conformation of F 1 -bound ⑀ between the ⑀ X state and other conformations of the ⑀CTD that allow faster F 1 ⅐⑀ dissociation. In control assays (not shown), the various ligands tested did not alter the rate at which F 1 (-␦⑀) dissociated from biotinylated ⑀88stop, confirming that the ligand effects are specific to the ⑀CTD of WT ⑀. F 1 (Ϫ␦⑀) was bound in parallel to multiple sensors with biotinylated WT ⑀, and Fig. 5 shows dissociation of F 1 (Ϫ␦⑀) when sensors were exposed to different ligands. For Fig. 5A, F 1 (Ϫ␦⑀) was bound to all sensors in MTK8 buffer ϩ BSA, and dissociation in this buffer was slow (Fig. 5A, curve 4, ϳ5.4 ϫ 10 Ϫ5 s Ϫ1 Ϯ 0.2%). This is consistent with access to the ⑀ X state when F 1 is in a post-hydrolysis conformation because isolated F 1 (Ϫ␦⑀) retained ϳ1.5 ADP (mol/mol) but negligible ATP at catalytic sites (see "Experimental Procedures"). Added MgADP/P i (Fig. 5A, curve 5) appeared to stabilize the ⑀ X state, consistent with prior ␤-⑀ cross-linking results (55). However, a similar effect was achieved by adding only Mg 2ϩ and P i (Fig. 5A, curve 6), suggesting that the endogenous ADP in isolated F 1 (Ϫ␦⑀) was sufficient to stabilize the ⑀ X state upon the addition of Mg 2ϩ and P i . The importance of P i in stabilizing this state (55) was also observed here because MgADP alone (Fig. 5A, curve 2) allowed a significant fraction of F 1 to dissociate faster. In contrast to slow F 1 ⅐⑀ dissociation under post-hydrolysis conditions, the addition of 1 mM ATP/EDTA caused ϳ94% of F 1 ⅐⑀ to dissociate ϳ80-fold faster (Fig. 5A, curve 1, 4.2 ϫ 10 Ϫ3 s Ϫ1 Ϯ 0.1%) and with Ͻ3-s transition to faster dissociation (Fig.  5C). This effect is due to ATP because EDTA alone had a minimal effect on F 1 dissociation from immobilized WT ⑀ (not shown). Further, by including 1 mM ATP/EDTA during association and dissociation phases, global analysis of F 1 ⅐⑀ binding/ dissociation shows that ATP/EDTA did not alter the F 1 ⅐⑀ binding rate but gave a dissociation rate and K D similar to values for ⑀88stop ( Table 2). The presence of nonhydrolyzable MgAMPPNP (2:1 mM) during the dissociation phase (not shown) also accelerated F 1 ⅐⑀ dissociation, indicating that nucleotide binding alone is sufficient to shift F 1 to a conformation that does not allow the ⑀CTD to insert into F 1 and form the ⑀ X state. Also, the ability of MgADP/P i to stabilize the inhibitory state of ⑀ was readily reversible; even when F 1 (-␦⑀) was bound to  Table 2. WT ⑀/sensors for 45 min with MgADP/P i present, switching the sensors to buffer with MgAMPPNP immediately caused Ͼ90% of F 1 (Ϫ␦⑀) to dissociate at the faster rate (not shown; 3.7 ϫ 10 Ϫ3 s Ϫ1 Ϯ 0.1%).
For the experiment in Fig. 5B, F 1 (Ϫ␦⑀) was bound to immobilized WT ⑀ in the presence of 1 mM ATP/EDTA, so that most F 1 ⅐⑀ complexes would not have ⑀ in the slowly dissociating ⑀ X state at the time the sensors were moved to dissociation wells. As expected, F 1 dissociation was fast with ATP/EDTA present (Fig. 5B, curve 1). With buffer only (Fig. 5B, curve 4), most F 1 still dissociated fast. This could indicate that ATP bound during the F 1 ⅐⑀ association phase dissociated slowly or that endogenous ADP had dissociated from F 1 during the association phase due to the ATP/EDTA present. MgADP alone (Fig. 5B, curve 2) slowed dissociation of most F 1 , but MgADP/P i (Fig. 5B, curve 5) or Mg 2ϩ /P i (Fig. 5B, curve 6) effectively reversed the ATP/ EDTA effect so that almost all F 1 dissociated very slowly. Mg 2ϩ was essential for this effect; without it, F 1 dissociation in the presence of 1 mM P i (not shown) was nearly identical to that in buffer alone (Fig. 5B, curve 4). The effect of Mg 2ϩ was enhanced by submillimolar P i (not shown, K1 ⁄ 2 ϳ0.2 mM P i ), similar to how P i enhanced MgADP protection of F 1 -bound ⑀ from trypsin (55).
With Mg 2ϩ /P i , there was no apparent lag in reverting F 1 ⅐⑀ to slow dissociation (Fig. 5D, curve 6). This suggested that, after F 1 ⅐⑀ association with ATP/EDTA present, rapid reversion by Mg 2ϩ /P i to slow F 1 ⅐⑀ dissociation required hydrolysis of ATP that remained bound at a catalytic site. In the dissociation step, added Mg 2ϩ could complex with the bound ATP, and hydrolysis would return F 1 to the catalytic dwell step, at which insertion of the ⑀CTD into the central cavity appears to occur. The bound MgADP/P i present would then stabilize F 1 with ⑀ in the ⑀ X state. The experiment shown in Fig. 6 tested this possibility. With non-hydrolyzable MgAMPPNP present during F 1 ⅐⑀ association, dissociation of most F 1 ⅐⑀ was fast in the presence of MgAMPPNP (Fig. 6, curve 1) or in buffer alone (Fig. 6, curve 2), similar to the effects of ATP/EDTA in Fig. 5B. However, with MgAMPPNP present during association, inclusion of Mg 2ϩ /P i during dissociation failed to prevent fast dissociation of most F 1 (Fig. 6, curve 3), in contrast to the parallel control with ATP/ EDTA in association (Fig. 6, curve 4). These results indicate that, with catalytic nucleotide bound in a prehydrolysis state, the rotary conformation of F 1 does not allow insertion of the ⑀CTD into the central rotor cavity, but hydrolysis at the catalytic dwell allows the ⑀CTD access to insert and form the ⑀ X state.
In the experiments of Fig. 4, hydrolysis conditions had complex effects on F 1 ⅐⑀ dissociation. With or without ATP/EDTA during F 1 ⅐⑀ binding, MgATP in the dissociation phase (curve 3) induced a small or negligible rate of F 1 ⅐⑀ dissociation during the initial 60 s (Fig. 5, C and D). Comparable with conditions for Fig.  5B, assays for ⑀ inhibition of F 1 -ATPase (Fig. 2) included an ATP/EDTA preincubation, and ⑀-saturated F 1 had initial ATPase activity (1-2 min, not shown) that was ϳ85% of the steady-state, inhibited rate. Thus, compared with fast F 1 dissociation in the continued presence of ATP/EDTA, hydrolysis of MgATP initially reverted F 1 ⅐⑀ complexes to slow dissociation, rapidly re-establishing the bias toward the inhibitory ⑀ X state (Fig. 5D, curves 1 and 3). This is consistent with noncompetitive inhibition of ⑀ versus MgATP and, combined with other results above, indicates that ⑀ accesses the inhibitory ⑀ X state following hydrolysis at the catalytic dwell step. On the longer time scale of Fig. 5 (A and B), hydrolysis conditions increased the dissociation rate for a fraction of F 1 ⅐⑀ complexes. As indicated by other experiments below, this slow effect on F 1 ⅐⑀ dissociation is probably due to gradual competitive transition of some active complexes to the ADP-inhibited state, which favors faster dissociation of ⑀. The fast dissociating fraction was substantially smaller for F 1 ⅐⑀ complexes formed in the presence of ATP/EDTA (Fig.  5B), probably because the ATP/EDTA preincubation minimizes initial inhibition (not shown) due to ADP-inhibited complexes.
Inhibition of F 1 (Ϫ␦⑀) by Azide and the ⑀CTD Are Competing Processes-The above results support prior SM mechanics studies (22)(23)(24)26) that concluded that ⑀ inhibition pauses rotation at the catalytic dwell position. In the absence of ⑀, long pauses at the catalytic dwell have been documented and attributed to inhibitory MgADP (57,58). However, there have been conflicting conclusions about the relationship between inhibitory MgADP and ⑀ inhibition for F 1 of different bacterial species (22,24,25,27). We investigated this by testing interactions between ⑀ inhibition and inhibition by sodium azide, which acts by stabilizing the MgADP-inhibited state (45, 59 -61). We first tested inhibition of F 1 (Ϫ␦⑀) by azide, with or without excess WT or mutant forms of H 6 -⑀ present. Inhibition of F 1 (Ϫ␦⑀) alone showed a K I of ϳ5 M azide, whether assays were done with 2:1 mM Mg/ATP (Fig. 7) or with 1:2 mM Mg/ATP (not shown). Thus, for E. coli F 1 , azide inhibition is separated from the step that confers sensitivity to inhibition by excess free Mg 2ϩ . The K I for azide was not altered by bound H 6 -⑀ mutants that could not access the ⑀ X state due to truncation (⑀88stop) or disulfide bonding (⑀A101C-L121C). The presence of 100 nM WT ⑀ reduced the activity of F 1 (Ϫ␦⑀) ϳ10-fold, but the residual activity was still inhibited by excess azide. However, bound WT H 6 -⑀ increased the K I for azide ϳ5-fold (Fig. 7). Also, saturating F 1 (-␦⑀) with reduced H 6 -⑀A101C/L121C, which was less inhibitory than WT H 6 -⑀, yielded an intermediate K I value for azide inhibition. These results indicate that forming the inhibitory ⑀ X state competes with azide's capacity to inhibit F 1 -ATPase. To test whether azide also competed with formation of the ⑀-inhibited state, F 1 (Ϫ␦⑀) was bound to immobilized WT BapH 6 -⑀ in buffer alone, and F 1 ⅐⑀ dissociation was measured under hydrolysis conditions with varied concentrations of azide (Fig.  8A). Increasing azide concentrations caused greater fractions of F 1 ⅐⑀ to dissociate at a faster rate, and the hyperbolic dependence on azide (Fig. 8B) yielded a K1 ⁄ 2 of ϳ14 M, comparable with the mid-range of K I values for azide inhibition with or without WT H 6 -⑀ (Fig. 6). Taken together, the results of Figs. 7 and 8 show competition between (i) the ability of the ⑀CTD to insert, forming the inhibitory ⑀ X state, and (ii) the ability of azide to bind to and stabilize the MgADP-inhibited state of F 1 .

DISCUSSION
Correlating Results with Functional and Rotational States of the Enzyme-Hydrolysis by the three alternating catalytic sites of F 1 drives a full 360°rotation of the ␥ central rotary shaft, so hydrolysis of each ATP molecule involves a 120°rotation of ␥ relative to ␣ 3 ␤ 3 . As depicted schematically in Fig. 9, SM microscopy studies of bacterial F 1 -ATPases (reviewed in Refs. 62 and 63) have shown that each 120°rotation is comprised of two observable rotary substeps (solid arrows); MgATP binding at one alternating catalytic site drives an ϳ80°rotation of ␥ to the catalytic dwell angle, whereas the subsequent ϳ40°rotation is limited by the intrinsic rates of hydrolysis and P i dissociation at the other alternating catalytic sites. At 120°, Mg 2ϩ and ADP dissociate from one site before or in concert with binding of MgATP at another site to drive the next 80°substep. Fig. 9 also includes bars along the rotational arc that depict the observed angular position of ␥ (relative to ␣ 3 ␤ 3 ) in crystal structures of F 1 or F 1 ⅐c-ring complexes. This is based on alignment of structures by a structurally conserved, apparently stiff core of the ␥ subunit that we identified previously (8). A recent analysis of MF 1 structures concluded that the position of ␥ could not be correlated with rotational angle during the catalytic cycle, arguing that the part of ␥ protruding below ␣ 3 ␤ 3 is variably displaced by lattice contacts in different crystals (64). However, biophysical characterization of the stiffness of ␥ indicates that only the lowest portion of ␥, near its interface with the c-ring of F O , is extremely pliable (65). Also, the 99 residues of ␥ that we identified as a structurally conserved "␥-core" include (i) most of the ␥ coiled-coil that is inside ␣ 3 ␤ 3 , (ii) the first ϳ15 residues of the ␥ C-terminal helix that protrude below ␣ 3 ␤ 3 , and (iii) 41 residues of the ␥ Rossmann fold domain that pack beside the protruding part of the ␥ C-terminal helix (see supplemental Figs. 4 and 5 of Ref. 8). We have updated our analysis of the rotational angle of ␥ to include 34 F 1 or F 1 ⅐c-ring structures and find that all ␥ subunits superimpose well with the ␥-core (supplemental Table S-I). Thus, the distribution of F 1 structures along the rotary arc of ␥ in Fig. 9 should be useful for comparing structural states with functional and rotational data.
Although there is no current consensus for correlating the rotary position of ␥ in known structures with the dwell states observed in SM assays after 80 and 40°substeps (63,66,67), we  assign ␥ to be at 80°for one MF 1 structure, with all three catalytic sites filled with nucleotide (Protein Data Bank entry 1H8E), because structural considerations (68) and molecular dynamics simulations (69) suggest that it is closest to the catalytic dwell state. Most MF 1 structures have no nucleotide in the ␤ E site due to an open conformation that distorts the nucleotide-binding pocket, but 1H8E has a "half-closed" conformation of ␤ E with bound MgADP and SO 4 2Ϫ (thought to mimic P i binding). Another recent MF 1 structure (Protein Data Bank entry 4ASU) also has a nucleotide in all three catalytic sites, but its ␤ E is much closer to the open conformation and has ADP but no bound SO 4 2Ϫ (or P i ) or Mg 2ϩ (64). The 4ASU structure was proposed to represent the catalytic intermediate from which final products Mg 2ϩ and ADP dissociate, and its rotary position at ϳ123° (Fig. 9) correlates with SM studies indicating that ADP dissociates after ϳ40°rotation to one of the 120°dwell positions (70 -72). The structural indication that Mg 2ϩ dissociates before ADP (64) suggests that the inhibitory effect of free Mg 2ϩ occurs at the 120°position. This can explain results showing that excess free Mg 2ϩ does not affect inhibitory transitions that occur at the catalytic dwell step at 80°; free Mg 2ϩ does not affect the rate at which actively rotating E. coli F 1 (Ϫ⑀) switches to the ADP-inhibited (paused) state (22), and, as shown here, free Mg 2ϩ does not alter inhibition of E. coli F 1 by ⑀CTD or azide.
Although our results indicate that ADP and ⑀ inhibition begin as competing processes after hydrolysis at the catalytic dwell, F 1 structures of these inhibited states have ␥ positioned at angles that are distinct from the catalytic dwell; in Fig. 9, azide-inhibited MF 1 (61) has ␥ at 93°, and ⑀-inhibited E. coli F 1 (8) has ␥ rotated much further to 123°(checkered bar). In contrast, SM studies concluded that both ADP and ⑀ inhibition cause long paused/inactive states at the catalytic dwell at 80° (22)(23)(24)57). With a bead attached to ␥ or ⑀, it is possible that SM microscopy could have overlooked dynamic oscillations between 80 and 120°because those assays can exhibit broad angular distributions of events. For example, during long paused periods (up to 1-2 s) without net rotation, a ␥-attached bead on E. coli F 1 (Ϫ⑀) showed rapid, ongoing angular fluctuations spanning at least Ϯ30° (Fig. 3A in Ref. 22). This could represent dynamic rotational oscillations in E. coli F 1 or could be a technical limitation because the bead was attached to ␥ by a single cysteine, allowing for significant flexibility in the linkage. On the other hand, there is prior evidence that functional rotation is needed for transition to and from the ⑀-inhibited state; with E. coli F O F 1 in liposomes, a chemical treatment that blocks rotation of F O also prevented nucleotide-dependent changes in the conformation of ⑀ (54). With F 1 exposed to MgADP/P i , conditions that stabilize the ⑀-inhibited state (Fig.  5), cryoelectron microscopy of E. coli F 1 showed a unique, ⑀-dependent position of ␥ and a unique position of ⑀ relative to ␣ 3 ␤ 3 (73). Also, with F O F 1 -liposomes, SM fluorescence assays showed a shift in the position of the ⑀ NTD relative to the F O stator for active versus inactive complexes (74). Thus, we propose that the ⑀CTD begins inserting into bacterial F 1 near the catalytic dwell (80°) but then induces partial rotation to ϳ120°t o achieve the final ⑀-inhibited state, with the last half of the ⑀CTD buried in the central cavity of F 1 (8). This is similar to a proposal that insertion of the mitochondrial inhibitor protein (IF 1 ) into MF 1 involves rotational steps (75), and IF 1 -inhibited MF 1 has ␥ rotated ϳ27°past the catalytic dwell in Fig. 9. The transitions of azide-inhibited MF 1 and ⑀-inhibited E. coli F 1 to distinct rotary angles may help explain the competition between these inhibitory paths. Azide-inhibited MF 1 has azide bound with MgADP in the closed, high affinity ␤ D site, but azide inhibition is unlikely to occur in the ⑀-inhibited state of E. coli F 1 because insertion of the ⑀CTD and rotation of ␥ shift ␤ D to a distinct "half-closed" conformation. Conversely, if E. coli F 1 first shifted to the ADP-inhibited state, azide would probably stabilize the closed ␤ D state and so prevent opening of the ␣ E ␤ D interface with ␥ that is necessary to allow insertion of the ⑀CTD. In Fig. 9, the broken lines below the arc indicate the proposed rotational paths leading to and from ADP-or ⑀-inhibited states. In SM tests of forced rotation, TF 1 was preferentially activated from the ADP-inhibited state (paused at ϳ93°; Fig. 9) by Ͼ40°rotation forward, and, consistent with proposed release of ADP near 120° (Fig. 9), added ADP suppressed or reversed rotational activation (76). In contrast, forced rotation of up to 120°in either direction failed to reactivate ⑀-paused TF 1 (26). Based on the asymmetric insertion of ⑀CTD within F 1 (8), we suspect that reactivation from the ⑀ X -inhibited state (Fig. 9, near 120°) occurs with the lowest activation barrier by reverse rotation of ␥/⑀NTD toward the catalytic dwell angle at 80° (Fig.  9, dashed arrow). Such reactivation by rotation in the direction of ATP synthesis may be indicated by a study with E. coli F O F 1liposomes; with MgADP and P i present, prior exposure to pro-  Table S-I). Bars are spaced every 5°, and the height represents the number of F 1 structures aligned near each angle Ϯ 2.5°; shortest bar, one structure; longest bar, 12 structures. Bars are shaded for structures of bovine F 1 (black), yeast F 1 (gray), and E. coli F 1 (checkered). The dotted arrows below the bars indicate the proposed paths to and from the ADPinhibited state, as stabilized by azide at ϳ95° (61). The dashed arrow shows the ϳ40°rotary shift proposed to occur during transition into (counterclockwise) or out of (clockwise) the ⑀-inhibited state. The two F 1 aligned past 120°a re also shown near 0°because this position should be the starting point for the next 120°turn. ton motive force activated the initial rate of subsequent ATPase activity up to 9-fold (77).
Dynamics of ⑀ Conformational Changes and the Influence of Nucleotides/Ligands-Under conditions for ATP hydrolysis, SM assays with a 60-nm gold bead attached to ␥ showed that E. coli F 1 complexes switch back and forth between actively rotating and paused states every few seconds, with or without ⑀ bound to F 1 (22). Our results on F 1 ⅐⑀ dissociation kinetics are consistent with such rapid exchange between active and inactive states. As shown in Fig. 5 (C and D), there were no more than a few seconds lag in ligand-dependent switching between the slowest and fastest modes of F 1 ⅐⑀ dissociation. Exposure to saturating nucleotide without hydrolysis (ATP/EDTA or MgAMPPNP) induced the fastest and essentially monophasic F 1 ⅐⑀ dissociation (Figs. 5 and 6), indicating that few F 1 ⅐⑀ complexes remained in or could regain access to the ⑀ X -inhibited state. However, most F 1 ⅐⑀ complexes still dissociated slowly upon exposure to hydrolysis conditions (Fig. 5), consistent with noncompetitive inhibition by ⑀ versus ATP for E. coli F 1 (29,44). Also, the K I for ⑀ inhibition of steady-state hydrolysis ( Table 1, ϳ0.5 nM) is similar to the K D for F 1 ⅐⑀ binding ( Table 2, 0.24 nM), which was measured without added nucleotides. Thus, it is unlikely that catalytic binding of ATP or MgAMPPNP directly increases the rate at which the ⑀ X -paused state returns to an active form. Rather, we propose that the intrinsic rates to and from the ⑀ X -inhibited state are fast enough (seconds or less) to allow ligands to influence subsequent conformational changes once F 1 exits from the ⑀-inhibited state. Once the ⑀CTD escapes from the central cavity of F 1 near 80°, F 1 would be most likely to rotate forward, completing an active 40°step (Fig. 9, solid arrow). At that point, binding of nucleotide would drive an ϳ80°step toward the next catalytic dwell but, without hydrolysis, would trap F 1 in a conformation and rotary position that would not allow the ⑀CTD to reinsert; thus, F 1 ⅐⑀ complexes would dissociate at the faster rate observed with only ␥/⑀NTD interactions. With hydrolysis conditions, each return to a catalytic dwell step would provide the same low probability for insertion of the ⑀CTD, and, as indicated by SM studies (22), the long durations of the paused/inhibited states (1 to 3.5 s) relative to the limiting catalytic steps (1-2 ms) would result in a large fraction of inhibited complexes during steady-state hydrolysis.
In an SM study with E. coli F 1 (22), the presence of ⑀ did not alter the duration time of active complexes (0.5-1 s), but ⑀-paused states had longer duration times (up to 3.5 s) than ADP-paused states (ϳ1 s). This is consistent with other indications that ⑀ inhibition predominates over ADP inhibition. Oxyanions, which are thought to activate F 1 by promoting release of inhibitory ADP (78), activate E. coli F 1 more if ⑀ is absent (28), and recently it was shown that the oxyanion selenite optimally activates ⑀-depleted E. coli F 1 ϳ10-fold 4 with excess free Mg 2ϩ present but only activates ⑀-saturated F 1 2-2.5-fold (79). Also, because our results show that inhibition by the ⑀CTD is distinct from the ADP-inhibited transition, the unaffected duration of the active state (22) suggests that a prior common step is ratelimiting for transitions to either ADP-or ⑀-inhibited states. This common step is probably the end of hydrolysis that precedes P i release because ⑀ reduces the rate of P i release ϳ15-fold following "unisite" hydrolysis (28). P i stabilizes F 1 with ⑀ in the ⑀ X state, which could mean that P i rebinds to ␤ D (with bound MgADP) and delays an active 40°rotation, allowing more time for a possible transition to the ⑀ X -inhibited state. However, we cannot rule out that the P i effect could be due in part to binding to other ␤(s), which show SO 4 3Ϫ bound at the "P-loop" in ⑀-inhibited F 1 (8).
Conclusions-This study sheds further light on how the CTD of subunit ⑀ inhibits the catalytic F 1 complex of a bacterial ATP synthase. Most significantly, results reveal that ATP hydrolysis is required for insertion of the inhibitory ⑀CTD into F 1 at the catalytic dwell step and that ⑀ inhibition competes with conversion to an ADP-inhibited state of the enzyme. With insertion of the ⑀CTD starting at the catalytic dwell (ϳ80°), the dynamic response of the conformation of ⑀ to catalytic site ligands and the structurally observed ␥ angle of ϳ123°in ⑀-inhibited F 1 suggest dynamic, reversible rotation over the 40°substep. Our results also show that the ⑀CTD has a small energetic contribution to net binding of ⑀ to F 1 . Thus, there is potential for antibiotic development by discovering or designing compounds that enhance or mimic ⑀ inhibition of bacterial ATP synthases. The BLI assays established here for kinetics of F 1 ⅐⑀ binding and dissociation should be valuable in further analyzing which ⑀CTD residues and interactions are critical for ⑀ inhibition in F 1 -ATPase from E. coli and other bacteria. Of course, the BLI assay cannot be used to study ⑀ inhibition in membrane-bound ATP synthase because ⑀ does not dissociate from intact F O F 1 . The extent of ⑀ inhibition can vary widely for membranes isolated from different bacteria. For example, E. coli membranes exhibit substantial ATPase activity, whereas mycobacterial membranes are devoid of ATPase activity but can be activated by treatment that probably damages the ⑀ subunit (80). Thus, additional approaches will be needed to determine what other factors influence ⑀ inhibition in ATP synthases of different bacterial species.