Mechanism of Inhibition by C-terminal α-Helices of the ϵ Subunit of Escherichia coli FoF1-ATP Synthase*

The ϵ subunit of bacterial FoF1-ATP synthase (FoF1), a rotary motor protein, is known to inhibit the ATP hydrolysis reaction of this enzyme. The inhibitory effect is modulated by the conformation of the C-terminal α-helices of ϵ, and the “extended” but not “hairpin-folded” state is responsible for inhibition. Although the inhibition of ATP hydrolysis by the C-terminal domain of ϵ has been extensively studied, the effect on ATP synthesis is not fully understood. In this study, we generated an Escherichia coli FoF1 (EFoF1) mutant in which the ϵ subunit lacked the C-terminal domain (FoF1ϵΔC), and ATP synthesis driven by acid-base transition (ΔpH) and the K+-valinomycin diffusion potential (ΔΨ) was compared in detail with that of the wild-type enzyme (FoF1ϵWT). The turnover numbers (kcat) of FoF1ϵWT were severalfold lower than those of FoF1ϵΔC. FoF1ϵWT showed higher Michaelis constants (Km). The dependence of the activities of FoF1ϵWT and FoF1ϵΔC on various combinations of ΔpH and ΔΨ was similar, suggesting that the rate-limiting step in ATP synthesis was unaltered by the C-terminal domain of ϵ. Solubilized FoF1ϵWT also showed lower kcat and higher Km values for ATP hydrolysis than the corresponding values of FoF1ϵΔC. These results suggest that the C-terminal domain of the ϵ subunit of EFoF1 slows multiple elementary steps in both the ATP synthesis/hydrolysis reactions by restricting the rotation of the γ subunit.

F o F 1 -ATP synthase (F o F 1 ) 3 is an enzyme that is responsible for ATP synthesis during oxidative phosphorylation and photosynthesis (1)(2)(3). F o F 1 is a complex of two rotary motors F 1 and F o , and the ATP synthesis/hydrolysis reaction that is reversibly catalyzed by F 1 is coupled with proton transport across membrane-embedded F o (4 -6). The subunit composition of bacterial F 1 and F o is ␣ 3 ␤ 3 ␥␦⑀ and ab 2 c 10 -15 , respectively, and the ␥⑀c 10 -15 complex rotates against the ␣ 3 ␤ 3 ␦ab 2 complex in F o F 1 .
Among these subunits, ⑀ is known to be an endogenous inhibitor of the ATP hydrolysis reaction catalyzed by F 1 and F o F 1 (7)(8)(9)(10). The inhibition of ATP hydrolysis by the ⑀ subunit of Escherichia coli F 1 (EF 1 ) and F o F 1 (EF o F 1 ) has been extensively studied. Addition of ⑀ to ⑀-depleted EF 1 showed noncompetitive inhibition of ATP hydrolysis (7). The affinity of MgATP and MgADP to the high affinity site of the three catalytic ␤ subunits of EF 1 was decreased by ⑀ (11). It has been reported that the ⑀ subunit of EF 1 had no effect on the equilibrium between ATP and ADP⅐P i but inhibited product release under unisite catalysis conditions (12). Inhibition of EF o F 1 -mediated ATP hydrolysis by ⑀ was also demonstrated in experiments involving partial digestion by a protease (13). The inhibitory effect of the ⑀ subunit of thermophilic Bacillus PS3 F 1 (TF 1 ) and F o F 1 (TF o F 1 ) has also been studied extensively. Slow binding and hydrolysis of TNP-ATP, a fluorescent ATP analog, under unisite catalysis conditions have been reported (14). However, in contrast to EF 1 , inhibition by the ⑀ subunit of TF 1 was relieved slowly and apparently disappeared at high ATP concentrations ([ATP]). This is not due to the dissociation of ⑀ from the F 1 complex, because disappearance of inhibition at high [ATP] was also reported in TF o F 1 in which ⑀ is indispensable for stable complex formation (15). However, in contrast to ATP hydrolysis, there has been no detailed analysis of the effect of ⑀ on ATP synthesis. The ⑀ subunit has a molecular mass of 14 kDa and a twodomain structure consisting of an N-terminal 10-stranded ␤-sandwich and two C-terminal ␣-helices. Of these two domains, the C-terminal domain is responsible for inhibiting ATP hydrolysis, and the ⑀ subunit in which this domain is absent does not have any inhibitory effect (15,16). Structural studies on isolated ⑀ and its complex with the truncated ␥ subunit have shown that the C-terminal domain of ⑀ adopts two different conformations, the "hairpin-folded" and "extended" states ( Fig. 1) (17)(18)(19)(20). These conformations are also found in the crystal structure of the bovine mitochondrial homolog of F 1 and in the low resolution crystal structure of EF 1 (21,22). Chemical modification of the ⑀ subunit of EF o F 1 indicated that the C-terminal domain is intrinsically flexible (23). Cross-linking and fluorescence resonance energy transfer experiments supported the existence of multiple conformations of the ⑀ subunit of EF o F 1 and TF o F 1 (24 -30). 4 These studies have shown that the extended state inhibits ATP hydrolysis, whereas the hairpin-folded state does not.
In contrast to ATP hydrolysis, the correlation between the conformation of ⑀ and its effect on ATP synthesis has not been fully understood. In both EF o F 1 and TF o F 1 , when ⑀ was fixed in an extended state that inhibits ATP hydrolysis, no change was observed in the ATP synthesis activity driven by the proton motive force (⌬) generated by the respiratory chain in the inverted membrane (26,27). Based on these results, it has been proposed that ⑀ functions as a ratchet that inhibits only ATP hydrolysis. However, Masaike et al. (31) reported that truncation of the C-terminal domain of ⑀ increased the ATP synthesis activity of TF o F 1 , suggesting that the C-terminal domain of ⑀ suppresses the ATP synthesis activity.
In this study, we generated an EF o F 1 mutant with a truncated ⑀ subunit that did not contain the C-terminal ␣-helices (F o F 1 ⑀⌬C ). This mutant was purified and reconstituted into a liposome, and the ATP synthesis rate was measured by the acidbase transition (⌬pH) and K ϩ -valinomycin diffusion potential (⌬⌿) methods. The rate of ATP hydrolysis by solubilized EF o F 1 was also measured. The activities of F o F 1 ⑀⌬C under various conditions were investigated and compared in detail with those of the wild-type enzyme (F o F 1 ⑀WT ). The results indicated that the ATP synthesis and hydrolysis activities of F o F 1 ⑀⌬C were much higher than those of F o F 1 ⑀WT . The inhibitory mechanism of the C-terminal ␣-helices of the ⑀ subunit of EF o F 1 was discussed.

EXPERIMENTAL PROCEDURES
Construction and Expression of the EF o F 1 Mutant-A wildtype EF o F 1 expression vector (pRA100) (32) was provided by Prof. R. A. Capaldi, University of Oregon. Based on this vector, a 1.3 S subunit of Propionibacterium shermanii transcarboxylase (33) was fused to the N terminus of the ␤ subunits, and three histidine residues were introduced at the C terminus of the c subunits. This mutant is referred to as the wild-type (denoted by F o F 1 ⑀WT ) hereafter. F o F 1 lacking the two ␣-helices in the C terminus of the ⑀ subunit (denoted by F o F 1 ⑀⌬C ) was generated by introducing a stop codon at the position of Asp-91.
Preparation of Inverted Membrane Vesicles-The cells were harvested and washed with buffer containing 100 mM HEPES-KOH (pH 7.5) and 50 mM KCl. The pellet was then resuspended in buffer A (100 mM HEPES-KOH (pH 7.5), 1 mM EDTA, 500 mM sucrose, 1 mM dithiothreitol, and 2ϫ protease inhibitor mixture (Complete, Roche Applied Science)). Egg white lysozyme (8 -12 mg, Seikagaku Corp.) was added, and the mixture was incubated at room temperature for 20 min. Subsequently, 1-2 mg of DNase I (Roche Applied Science) and 5 mM MgCl 2 were added, and incubation was carried out at 4°C for 20 min. The spheroplasts were then spun down, resuspended in buffer B (50 mM HEPES-KOH (pH 7.5), 0.5 mM EDTA, 250 mM sucrose, 0.5 mM dithiothreitol, 5 mM MgCl 2 , and 5 mM 4-aminobenzamidine dihydrochloride (PAB)), and sonicated (model CL4, Misonix) on ice. They were then centrifuged at 9000 rpm for 10 min at 4°C to remove the cell debris. The supernatant containing the inverted membrane was transferred to a new tube and centrifuged at 75,000 rpm for 20 min at 4°C. The supernatant was discarded, and the pellet was resuspended in buffer B at 250 mg/ml. The inverted membrane was stored at Ϫ80°C prior to further use.
Purification of EF o F 1 -The membrane suspension (250 mg/ml, wet weight of inverted membrane/volume of buffer) in 0.8% (w/v) n-octyl ␤-D-glucopyranoside (Sigma) was centrifuged at 75,000 rpm for 20 min at 4°C. The supernatant was transferred to a new tube on ice. Buffer C (20 mM HEPES-KOH (pH 7.5), 500 mM NaCl, 5 mM MgCl 2 , 200 M ADP, 50 mM imidazole, 20% (v/v) glycerol, 1ϫ protease inhibitor mixture, and 5 mM PAB) and 2% (w/v) octaethylene glycol mono-n-dodecyl ether (C 12 E 8 , Wako) were added to the pellet, and the mixture was incubated for 15 min on ice. It was then centrifuged, and the supernatant was collected. The collected supernatant was injected into a HisTrap HP column (GE Healthcare) pre-equilibrated with 5 ml of buffer D (20 mM HEPES-KOH (pH 7.5), 500 mM NaCl, 5 mM MgCl 2 , 200 M ADP, 50 mM imidazole, 20% glycerol (v/v), 1ϫ protease inhibitor mixture, 5 mM PAB, 0.3% (w/v) C 12 E 8 , and 0.1% (w/v) E. coli total lipid (Avanti)). The column was washed twice with 5 ml of buffer D. His-tagged EF o F 1 was eluted with 3 ml of buffer E (20 mM HEPES-KOH (pH 7.5), 500 mM NaCl, 5 mM MgCl 2 , 200 M ADP, 500 mM imidazole, 20% glycerol (v/v), 1ϫ protease inhibitor mixture, 5 mM PAB, 0.3% (w/v) C 12 E 8 , and 0.1% (w/v) E. coli total lipid). Six drops of the eluate were collected in each 1.5ml tube containing 1 mM dithiothreitol. The purified EF o F 1 fractions were run on 15% SDS-PAGE to select the purest fractions that contained all the subunits and the least contaminants. The chosen fractions were pooled and passed through a NAP-5 column (GE Healthcare) that had been pre-equilibrated with buffer F (20 mM HEPES-NaOH (pH 7.5), 100 mM NaCl, 2 mM MgCl 2 , 0.1ϫ protease inhibitor mixture, 5 mM PAB, 0.3% (w/v) C 12 E 8 , and 0.1% (w/v) E. coli total lipid). EF o F 1 was eluted with 1 ml of buffer F. The eluate was concentrated and further purified in an Amicon Ultra-4 100,000 centrifugal filter device (Millipore). The protein concentration of the sample was determined by the BCA assay (Pierce) using bovine serum albumin (Sigma) as the standard. Purified EF o F 1 was immediately used for reconstitution into the liposome or to measure the ATP hydrolysis activity.
Liposome Preparation and Reconstitution of EF o F 1 into the Liposome-L-␣-Phosphatidylcholine from soybean (type II-S, Sigma) was suspended in buffer G (10 mM HEPES-NaOH, 5 mM MgSO 4 , and 1 mM KCl (pH 7.5)) by vigorous vortexing. The liposome suspension was then repeatedly freeze-thawed three times. The final concentration of the lipid was 40 mg/ml. Solubilized EF o F 1 was reconstituted into the liposomes using the freeze-thaw method. The EF o F 1 solution (ϳ1 mg/ml, 100 l) was added to the liposome suspension (40 mg/ml, 1 ml), and the mixture was frozen in liquid nitrogen and stored at Ϫ80°C prior to further use. Reconstitution efficiency of EF o F 1 into liposome was assessed by SDS-PAGE of EF o F 1 /liposome suspension and the supernatant after centrifugation of EF o F 1 /liposome at 75,000 rpm for 20 min at 4°C.
Measurement of the ATP Synthesis Activity-The ATP synthesis activity was measured as described previously with slight modifications (35). To acidify the interior of the proteoliposomes, 10 l of the proteoliposome suspension was mixed with 50 l of acidification buffer (300 mM MES-NaOH or HEPES-NaOH) and incubated for 3 min at room temperature. Following incubation, the pH of the acidified liposome suspension was measured by a glass electrode, and this value was regarded as the pH inside the liposome (pH in ). The ATP synthesis reaction was initiated by injecting 60 l of the acidified proteoliposomes into 1 ml of base buffer containing 100 mM Tricine-Na (pH 8.8) or HEPES-NaOH (pH 7.5), 2.5 mM MgSO 4 , 0.1-50 mM phosphate, 2.2 mg of luciferin/luciferase mixture from ATP Bioluminescence Assay Kit CLS II (Roche Applied Science), 0.001-1 mM ADP, 36 nM valinomycin, and 1-300 mM KCl. The amount of ATP generated was measured as the increase in the lumines-cence intensity of the luciferin/luciferase reaction at 550 nm in an FP-6500 spectrofluorometer (Jasco, Japan). The ATP synthesis rate was calculated using the initial slope of the increase in the luminescence intensity. To calibrate the system for measuring the amount of generated ATP, a known amount of ATP was injected into the base buffer after measurement. To measure the dependence of the ATP synthesis rate on the ADP or phosphate concentration, the phosphate and ADP concentrations were fixed at 10 and 1 mM, respectively. The pH of the mixture of acidified proteoliposome suspension and base buffer (pH out ) was directly measured using a glass electrode to determine ⌬pH (ϭ pH out Ϫ pH in ). The ⌬pH and ⌬⌿ dependences were measured by changing the pH and [K ϩ ] of the acidification and base buffers. ⌬⌿ was calculated by the Nernst equation using the difference in [K ϩ ] inside and outside the liposome, i.e.
where k B is the Boltzmann constant, and e is the elementary charge. Measurements were carried out at 24 -25°C.
Measurement of the ATP Hydrolysis Activity-The ATP hydrolysis activity of solubilized EF o F 1 was measured with an ATP regeneration system using a UV-visible spectrophotometer (VP-550, Jasco). Various concentrations of ATP (Sigma) were added to the assay mixture (10 mM HEPES-NaOH (pH 7.5), 5 mM MgSO 4 , 1 mM KCl, 0.3% (w/v) C 12 E 8 , 2.5 mM phosphoenolpyruvate, 0.1 mg/ml pyruvate kinase, 0.1 mg/ml lactate dehydrogenase, and 0.2 mM NADH) at 0 s, and this was followed by the addition of various concentrations of EF o F 1 at 30 s. The NADH absorbance at 340 nm was monitored for 1200 s. The ATP hydrolysis rate was calculated from the time course of the change in [NADH] using a molecular extinction coefficient value of 6220 at 340 nm. Because the ATP hydrolysis activity gradually increased in the initial state after the addition of EF o F 1 , the maximum activity in the steady state at around 1000 -1200 s was used for data analysis. Measurements were carried out at 24 -25°C.    were measured. Several methods have been proposed for reconstituting EF o F 1 into liposomes, including the following: 1) reconstitution by detergent removal from a mixture of solubilized EF o F 1 and liposome using Bio-Beads SM (36); 2) dialysis; and 3) reconstitution by diluting the detergent in solubilized EF o F 1 with an excess amount of liposome and subsequent freeze-thaw. Because the last method resulted in the highest ATP synthesis activity (data not shown), we employed this method throughout this study. The reconstitution efficiencies were very high, and no differences were observed between F o F 1 ⑀WT and F o F 1 ⑀⌬C (Fig. 2B). By using an excess of the liposome suspension, a high lipid/protein molar ratio was obtained (ϳ2 ϫ 10 5 ). The average protein/liposome ratio was less than unity, and most liposomes contained one or zero EF o F 1 molecules. This was estimated by assuming that the liposome diameter is in the range 100 -200 nm (Fig. 3A) (30,35).

ATP
Examples of raw data obtained from the ATP synthesis experiments are shown in Fig. 3B. The amount of generated ATP was determined on the basis of the luminescence observed in the luciferin-luciferase reaction. The luminescence intensity was proportional to the ATP concentration in the reaction mixture under our experimental conditions (data not shown). Addition of ADP to the reaction mixture showed a slight increase in the luminescence intensity because of the ATP contamination in ADP, which was calculated to be ϳ0.05%. Under the "Discussion," we used the initial rate of ATP synthesis. As shown in Fig. 3B, F o F 1 ⑀⌬C exhibited a much higher rate (49 s Ϫ1 , red line) than F o F 1 ⑀WT (11 s Ϫ1 , blue line), as reported earlier for TF o F 1 in an inverted membrane (31). The observed differences were actually due to the removal of C-terminal ␣-helices of the ⑀ subunit and not to variations in concentration determination, purity, and reconstitution efficiency between F o F 1 ⑀WT and F o F 1 ⑀⌬C (Fig. 2). This result indicates that the C-terminal domain of ⑀ suppresses the ATP synthesis activity. As a control, the time course of the liposome without EF o F 1 is also shown (Ͻ1 s Ϫ1 , Fig. 3B, black line), and the results indicate that the ATP was actually generated by EF o F 1 .
Dependence of ATP Synthesis and Hydrolysis Rates on the Substrate Concentration-The ATP synthesis rate was measured at various concentrations of ADP and P i . The [substrate]-velocity plots for ADP and P i showed that the ATP synthesis rates of F o F 1 ⑀WT and F o F 1 ⑀⌬C obeyed Michaelis-Menten kinetics (Fig. 4, A  and B). The values of the turnover number (k cat ) and Michaelis constant (K m ) are summarized in Table 1 (Table 2).  Dependence of the ATP Synthesis Rate on ⌬pH and ⌬⌿-In the chemiosmotic theory first proposed by Mitchell (37), ⌬ consists of ⌬pH and ⌬⌿, i.e. ⌬ ϭ 2.3(k B T/e)⌬pH ϩ ⌬⌿. Several studies on F o F 1 from E. coli, Propionigenium modestum, and the chloroplast have reported that the dependence of the ATP synthesis rate on the amplitude of ⌬pH and ⌬⌿ is kinetically different (38 -40). Previous results have suggested the possibility that elementary steps of the ATP synthesis reaction are affected in different ways by ⌬pH and ⌬⌿, although the mechanism is still unclear. Therefore, we measured the ATP synthesis rates using various combinations of ⌬pH and ⌬⌿. Fig.  5A shows contour plots of the ATP synthesis rate as a function of ⌬pH and ⌬⌿. Although the absolute values of the rates of F o F 1 ⑀WT and F o F 1 ⑀⌬C differed, their dependences on ⌬pH and ⌬⌿ were similar. Applying ⌬pH resulted in a higher ATP synthesis rate than when the same amplitude of ⌬⌿ was applied in both F o F 1 ⑀WT and F o F 1 ⑀⌬C . This result was apparently inconsistent with previous studies reporting that ⌬⌿ was more effective than ⌬pH in driving ATP synthesis by EF o F 1 (38 -40). So far, we have no clear idea why ⌬p⌯ was more effective in our experiment. Because we did not use the dicarboxylic acid such as maleic acid and succinic acid as the acidification buffer, concomitant formation of ⌬⌿ was not plausible (38,40). Other factors such as different compositions of the liposome and the reaction solution might affect the dependence of ⌬pH and ⌬⌿.
Under our experimental conditions, [ADP] and [P i ] were 1 and 10 mM, respectively, and ATP contamination in ADP was ϳ0.05%. By using the standard Gibbs free energy value of 14.9 k B T (37 kJ/mol) (41), this corresponds to Gibbs free energy for ATP hydrolysis of Ϫ11.9 k B T (ϭ Ϫ14.9 k B T ϩ k B T ln(10 Ϫ3 ϫ 10 Ϫ2 /5 ϫ 10 Ϫ7 )) or Ϫ306 mV. Thus, if we assume that 3 ATP molecules are synthesized and 10 protons are transported per turn (42), the potential difference that counteracts single proton translocation, or the value of ⌬ at the ATP synthesis/ hydrolysis equilibrium point, will be 92 mV (ϭ (306 mV ϫ 3)/10). We next plotted the dependence of the ATP synthesis rate on ⌬⌿ and ⌬pH when 2.3 k B T/e ⌬pH and ⌬⌿ were fixed around this equilibrium value (89 and 87 mV, respectively) (Fig.  5B, corresponds to the dashed lines in Fig. 5A). As expected, no ATP synthesis was observed around the equilibrium value. When ⌬pH increased, the ATP synthesis rate increased nonlinearly in the pH in range from 5.5 to 8.5 (Fig. 5B, circles). The ⌬ has a dimension equivalent to energy. Therefore, the nonlinear increase can be explained if we assume that the ATP synthesis rate changes according to the equation that resembles the Arrhenius equation in which the rate increases exponentially as the activation energy decreases.   [ADP] and [P i ] were set at 1 and 10 mM, respectively. Measurements were carried out two to six times (total of two independent preparations) for each data point at 24 -25°C.

DISCUSSION
Correlation between the Conformation of the ⑀ Subunit of EF o F 1 and Catalytic Activity-Truncation of the C-terminal domain of the ⑀ subunit of EF o F 1 (F o F 1 ⑀⌬C ) resulted in increased ATP synthesis and hydrolysis activities ( Fig. 4 and Tables 1 and  2). The enhancement was observed under all conditions studied. This indicates that the C-terminal domain of the ⑀ subunit of EF o F 1 suppresses both ATP synthesis and hydrolysis. As described above, ⑀ can adopt either of two different conformations, hairpin-folded or extended (Fig. 1). The crystal structure of F 1 with the hairpin-folded ⑀ shows that ⑀ does not have any direct interaction with the catalytic ␣ 3 ␤ 3 ring, whereas in the EF 1 crystal structure with the extended ⑀, the C-terminal helix of ⑀ interacts with the ␣ 3 ␤ 3 ring. Therefore, the extended form is thought to be responsible for the inhibitory effect of ⑀. Previous experiments involving the cross-linking of EF o F 1 and TF o F 1 showed that the ATP hydrolysis activity was inhibited when ⑀ was fixed in the extended state (26,27). These results are consistent with the present results. On the other hand in the previous studies, there was no significant change in the ATP synthesis activity when ⑀ was fixed in the extended state. This observation can be explained by assuming that ⑀ mostly adopts the extended form under conditions of ATP synthesis, as suggested earlier (27). Thus, although the apparent inhibitory effect of ⑀ differs during ATP hydrolysis and synthesis, probably as a result of the different ratios of the extended versus hairpinfolded forms, the extended form of ⑀ is the primary inhibitory state under both ATP synthesis and hydrolysis conditions, and the C-terminal domain is responsible for inhibition. With respect to ATP hydrolysis, our result is consistent with that of a previous study in which the decreased affinity of MgATP in the presence of the ⑀ subunit was demonstrated (11). A previous study also reported that the ⑀ subunit of EF 1 had no effect on the equilibrium between ATP and ADP⅐P i but reduced the rate of product release under unisite ATP hydrolysis conditions (12). If this is also the case in multisite catalysis, ⑀ will not affect covalent bond formation/cleavage, and product release will be slowed. In the case of ATP synthesis, a previous study proposed that the energy of ⌬ is mainly used for product release (43), suggesting that the product release step is ratelimiting. This is consistent with the assumption that it is the product release step that is slowed in F o F 1 ⑀WT and not the covalent bond formation/cleavage step. In our study, the dependence of the ATP synthesis rate on various combinations of ⌬pH and ⌬⌿ was similar in both F o F 1 ⑀WT and F o F 1 ⑀⌬C (Fig. 5A). This suggests that the C-terminal domain of ⑀ in the extended state does not change the rate-limiting step of ATP synthesis. Furthermore, it is consistent with the notion that multiple elementary steps of the ATP synthesis reaction are slowed. Thus, during both ATP synthesis and hydrolysis, the rates of substrate binding and product release appear to be suppressed by the C-terminal domain of ⑀.

Mechanism of Inhibition of ATP Synthesis by the C-terminal
However, when the reversibility of the reaction is considered, there is a problem in explaining our results. To examine this, we discuss our results based on our recently proposed model of mechanochemical coupling of F 1 (Fig. 6) (44 -48). During ATP hydrolysis, the lower k cat of value F o F 1 ⑀WT in comparison with that of F o F 1 ⑀⌬C corresponds to a lower rate of product (ADP or P i ) release (Fig. 6, B 3 C or E 3 F)  The green circles, red arrow, and blue circle represent the ␤, ␥, and ⑀ subunits, respectively. In this model, ␥ rotates 120°by single ATP hydrolysis (44), and each 120°step is further divided into 80°and 40°s ubsteps (45). The 80°substep is triggered upon ATP binding, whereas the 40°substep occurs after covalent bond cleavage (45,46). Dwells before the 80°and 40°substeps are termed the binding dwell and catalytic dwell, respectively. ADP release and P i release occur before (or during) the 80°and 40°substeps, respectively (47,48). States in catalytic dwell (D-F) correspond to the crystal structures of F 1 (51). *ATP represents ATP that is tightly bound to the ␤ subunit but is not hydrolyzed. Although the C-terminal domain of ⑀ in the extended state interacts with only ␤ TP in the crystal structure ( Fig. 1 lower ATP release rate (Fig. 6, B 3 A), this result also appears to be inconsistent with the higher K m value of F o F 1 ⑀WT for ATP in comparison with that of F o F 1 ⑀⌬C during ATP hydrolysis. From a structural point of view, there is another problem in explaining our results. As shown in Fig. 6, each ␤ subunit sequentially executes elementary steps of the reaction and is always in a different chemical state from the other subunits (49,50). In the low resolution crystal structure of EF 1 (Fig. 1), the C-terminal domain of ⑀ in the extended state interacts with only one ␤ subunit bound to the ATP analog (Fig. 6, ␤ TP in crystal structure), although there must be some displacement due to steric hindrance in the structural model (22). We recently proved that the crystal structures of F 1 correspond to states D-F in Fig. 6 (states in catalytic dwell), and ␤ TP corresponds to the ␤ subunit immediately after ATP binding (51). Thus, ⑀ would affect only ATP binding and release by direct interaction with ␤ TP . Even if we consider states A to C in Fig. 5 (states in binding dwell), it seems difficult for ⑀ to simultaneously interact with multiple ␤ subunits and to directly suppress other elementary steps of the reaction such as ADP and P i binding/release that occur in other ␤ subunits.
These apparent difficulties can be explained on the basis of the following model in which we assume that the rates of elementary steps of the reaction executed in each ␤ subunit are modulated not by direct interaction with ⑀ but by the rotary angle of ␥ (rotor). The C-terminal domain of ⑀ in the extended state increases the diameter of the rotor (␥ and ⑀) inserted into the ␣ 3 ␤ 3 ring and restricts its rotation. This results in lower rates of multiple elementary steps during both ATP synthesis and hydrolysis in multiple ␤ subunits. Our assumption that the rate of the elementary step is dependent on the rotary angle of ␥ is supported by our previous single-molecule experiments in which we reported that the rate of ADP release from the MgADP-inhibited ␣ 3 ␤ 3 ␥ subcomplex of TF 1 strongly depended on the rotary angle of ␥ (52). This suggests that the rate of ADP release (Fig. 6, B 3 C) in active F 1 is also dependent on the angle of ␥. Furthermore, the rates of ATP binding/release (Fig. 6, A 7 B) are strongly dependent on the rotary angle of ␥ in an actively rotating TF 1 ␣ 3 ␤ 3 ␥ subcomplex. 5 Interestingly, our unpublished results 5 also indicate that the rates of covalent bond formation/cleavage (Fig. 6, D 7 E) are less dependent on the angle of ␥. Taking this into consideration, the results of a previous study in which it was reported that this step was unaffected by ⑀ (12) are consistent with our assumption that ⑀ restricts the rotation of ␥.
Our model predicts that the dwell times before the 80°and 40°substeps will become longer when the rotation of EF 1 is assayed in the presence of ⑀. Previous single molecule observations of EF 1 rotation driven by ATP hydrolysis have shown that ⑀ increases the frequency and duration of the transient pause and results in decreased rotation speed (53). However, in the previous study, the pause angles were not resolved. Detailed analysis of pause angles and dwell times will provide further insights into the mechanism of inhibition by the ⑀ subunit.
Effect of the C-terminal Domain of ⑀ on the Efficiency of the Mechanochemical Coupling during ATP Synthesis-In this study, F o F 1 ⑀⌬C showed a higher rate of ATP synthesis than F o F 1 ⑀WT . However, we could not directly assess the coupling efficiency between the mechanical rotation of ␥ and each elementary step of the reaction. A high ATP synthesis rate does not necessarily indicate high coupling efficiency. As proposed previously (54), we can expect a situation in which the rotation rate is faster but the coupling efficiency of F o F 1 ⑀⌬C is lower than that of F o F 1 ⑀WT during ATP synthesis. We previously reported that reconstitution of ⑀ into the ␣ 3 ␤ 3 ␥ subcomplex of TF 1 improved the coupling efficiency of ATP synthesis when ␥ was forcibly rotated with magnetic tweezers (55,56). The role of the C-terminal domain of ⑀ in the coupling efficiency of ATP synthesis can be directly investigated by single molecule manipulation of F o F 1 ⑀⌬C or the ␣ 3 ␤ 3 ␥ subcomplex of F 1 reconstituted with C-terminal truncated ⑀.