Activation and Stiffness of the Inhibited States of F1-ATPase Probed by Single-molecule Manipulation

F1-ATPase (F1), a soluble portion of FoF1-ATP synthase (FoF1), is an ATP-driven motor in which γϵ subunits rotate in the α3β3 cylinder. Activity of F1 and FoF1 from Bacillus PS3 is attenuated by the ϵ subunit in an inhibitory extended form. In this study we observed ATP-dependent transition of ϵ in single F1 molecules from extended form to hairpin form by fluorescence resonance energy transfer. The results justify the previous bulk experiments and ensure that fraction of F1 with hairpin ϵ directly determines the fraction of active F1 at any ATP concentration. Next, mechanical activation and stiffness of ϵ-inhibited F1 were examined by the forced rotation of magnetic beads attached to γ. Compared with ADP inhibition, which is another manner of inhibition, rotation by a larger angle was required for the activation from ϵ inhibition when the beads were forced to rotate to ATP hydrolysis direction, and more torque was required to reach the same rotation angle when beads were forced to rotate to ATP synthesis direction. The results imply that if FoF1 is resting in the ϵ-inhibited state, Fo motor must transmit to γ a torque larger than expected from thermodynamic equilibrium to initiate ATP synthesis.

F o F 1 -ATP synthase (F o F 1 ) is a ubiquitous enzyme located in bacterial plasma membranes, mitochondrial inner membranes, and chloroplast thylakoid membranes. F o F 1 consists of two major portions, water-soluble F 1 and membrane-embedded F o . In the simplest version of bacterial F o F 1 such as F o F 1 from thermophilic Bacillus PS3 and Escherichia coli, subunit composition of F 1 and F o is ␣ 3 ␤ 3 ␥␦⑀ and ab 2 c 10 , respectively. Downward proton flow across membrane through F o along proton motive force (pmf) 2 drives the rotation of the rotor ring of oligomer c subunits (c-ring) in F o that induces rotation of the rotor shaft of F 1 consisting of the ␥ and ⑀ subunits in the surrounding ␣ 3 ␤ 3 cylinder. This rotation causes cyclic conformational changes in the catalytic sites in ␤ subunits that result in ATP synthesis (1)(2)(3)(4)(5). F o F 1 can catalyze a back reaction, ATP hydrolysis-driven proton pumping, when ATP hydrolysis is thermodynamically more favorable than pmf-driven proton flow. The isolated F 1 has ATPase activity, often called F 1 -ATPase, and is itself an ATP-driven rotary motor (6 -8). Starting from the orientation angle of the ␥ subunit at 0°(ATP-waiting dwell), ATP binding induces the 80°substep rotation of ␥, the ATP previously bound is hydrolyzed (catalytic dwell), and P i -release induces the 40°s ubstep rotation (9 -11). Duration of ATP-waiting dwell is inversely proportional to the concentration of ATP ([ATP]), but that of the catalytic dwell is independent from ATP, always a few milliseconds.
ATPase activity of F 1 as well as F o F 1 is attenuated by several mechanisms. In bacteria, two mechanisms are common; they are inhibition by MgADP (ADP inhibition) and inhibition by ⑀ subunit (⑀ inhibition). ADP inhibition is caused by the persistent occupation of a high affinity catalytic site by MgADP (without P i ) (12)(13)(14)(15)(16)(17)(18). Using Bacillus PS3 F 1 , Hirono-Hara et al. revealed that ADP inhibition accompanied the stall of rotary catalysis at the catalytic dwell angle (19) and that activation required rotation of ␥ by ϳ40°in ATP hydrolysis direction by mechanical manipulation (20) or by thermal fluctuation without manipulation. In the case of ATP synthesis, high pmf can expel the inhibitory ADP from F o F 1 , and once activated, turnover of ATP synthesis is not interrupted by ADP inhibition (for details, see review Ref 21 and references therein). The ⑀ subunit is part of a rotor (22,23) and has been known as an intrinsic inhibitor of ATPase activity (24,25) as well as a subunit that improves coupling efficiency (26,27). The ⑀ subunit consists of two domains (28,29); that is, an N-terminal ␤-sandwich domain, by which ⑀ binds to globular part of ␥ and c-ring, and a C-terminal domain with two ␣-helices, which undergoes conformational transition between hairpin and extended forms (30 -34). ATPase activity is inhibited only when the two ␣-helices are extended. In ⑀ inhibition, rotation is slowed down (35) or paused at the position of the catalytic dwell, the same position as observed for ADP inhibition (36,37), and it has been proposed that ⑀ inhibition involves strengthened ADP inhibition (15,37). The manner of ⑀ inhibition varies among species. In the case of Bacillus PS3 F 1 , the inhibition is observed only at low [ATP] and ATP can bind to and stabilize the non-inhibitory hairpin form of ⑀. ATP synthesis reaction appears to be affected by C-terminal domain of ⑀ as a mutant F o F 1 (⑀ ⌬C ) that lacked this domain had a higher rate of ATP synthesis (38,39).
In this study, a population of hairpin ⑀ in Bacillus PS3 F 1 immobilized on the glass surface was directly estimated at various [ATP] by single-pair fluorescence resonance energy transfer (FRET). The results confirmed the previous bulk FRET experiments and correspondence of the fraction of F 1 contain-ing the hairpin ⑀ to the fraction of active F 1 at any [ATP]. Next, magnetic beads attached to ␥ of ⑀-inhibited and ADP-inhibited F 1 were forced to rotate by a external magnetic field, and mechanical activation and stiffness of the inhibited forms were examined. The results indicate that the ⑀-inhibited F 1 is more resistant against mechanical perturbation than ADP-inhibited F 1 , and more torque is required for activation.
FRET Assay-For reconstitution, F 1 (Ϫ⑀) and ⑀ Cy3,5 were mixed at a molar ratio of 1:3 and incubated for more than 30 min. The mixture was passed through a size exclusion column (Superdex 75, Amersham Biosciences) equilibrated with 50 mM Tris-HCl (pH 7.5), 100 mM KCl, and 0.5 mM EDTA to remove free ⑀ Cy3,5 . The obtained F 1 (F 1 (⑀ Cy3,5 )) at 1 nM was incubated at room temperature in Tris(ATP) buffer (50 mM Tris-HCl (pH 7.5), 100 mM KCl, and 2 mM MgCl 2 , and indicated concentrations of ATP, and an ATP-regenerating system (100 g/ml pyruvate kinase, 2 mM phosphoenolpyruvate)). Incubation time was 30 min in 1 mM ATP and 1 h in other ATP concentrations. F 1 (⑀ Cy3,5 ) was further diluted to ϳ50 pM with Tris(ATP) buffer and infused into an observation chamber constructed from a nickel-nitrilotriacetic acid-coated glass slide and a non-coated slide, separated by ϳ50 m spacers, which had been blocked with 20 mg/ml bovine serum albumin for more than 1 h. After a 30-s incubation, unbound F 1 was washed out with ϳ10 volumes of Tris(ATP) buffer containing the oxygen scavenging system (8 mg/ml D-glucose, 1 mg/ml glucose oxidase, 0.04 mg/ml catalase, and 1% 2-mercaptoethanol).
Single-pair FRET was measured at 25°C under an objective-type total internal reflection fluorescence microscope built on an inverted microscope (IX70, Olympus). Donor dye (Cy3) was excited at 532 nm by laser (MG-532C-500, Spectra-Physics). Fluorescence from the donor and the acceptor were divided and filtered by dichroic mirrors and bandpass filters and captured with an intensified (VS4 -1845D, VideoScope) CCD camera (CCD-300T-RC, Dage-MTI). Due to random labeling, non-FRET signals from ⑀ labeled with only donor dyes were contained in the obtained fluorescent signals. Observation fields were also illuminated at 594 nm (LHYP-0201, Research Electro-Optics) to check the existence of the acceptor, and the non-FRET signals were omitted. Images recorded on a videotape were analyzed on PC with software (Celery, LIBRARY). FRET efficiency was defined as I Cy5 /(I Cy3 ϩ I Cy5 ), where I Cy3 and I Cy5 are the fluorescence intensities from a fluorescent spot after background intensities near the pair were subtracted.
ATPase Assay-Wild-type ⑀, ⑀ Cy3 , and ⑀ Cy3,5 were incubated with F 1 (Ϫ⑀) by mixing at a molar ratio of 2:1, and the ␣ 3 ␤ 3 ␥⑀ complexes (termed as F 1 (⑀), F 1 (⑀ Cy3 ) and F 1 (⑀ Cy3,5 ), respectively) were reconstituted. Excess free ⑀ was not removed. ATPase activity was measured with an NADH-coupled ATPregenerating system at 25°C. The assay mixture consisted of Tris(ATP) buffer supplemented by 0.2 mM NADH and 100 g/ml lactate dehydrogenase. The reaction was initiated by the addition of F 1 to the assay mixture, and changes in absorbance at 340 nm were monitored in a spectrophotometer (V-550, Jasco). ATP hydrolysis rate was taken at 3550 -3600 s (1750 -1800 s in the case of 1 mM ATP) after initiation of the reaction.
Rotation Assay-For the rotation assay, F 1 (Ϫ⑀) was biotinylated as follows. Precipitated sample in 70% ammonium sulfate was dissolved in 100 mM potassium phosphate (pH 7.0), 2 mM EDTA, and 10 mM dithiothreitol and passed through a Superdex 200 HR column equilibrated with 100 mM potassium phosphate (pH 7.0) and 2 mM EDTA. A 5-10 molar excess of biotinmaleimide (Sigma) was added to the elution, and the mixture was incubated for 1.5 h at room temperature. Free reagent was removed by passing through a Superdex 200 column equilibrated with 50 mM Tris-HCl (pH 7.5), 100 mM KCl, and 0.5 mM EDTA. ⑀ Cy3 was added to the biotinylated F 1 (Ϫ⑀) at a molar ratio of 2:1 for reconstitution. The procedure for fixing F 1 to glass slides was almost the same as those for FRET assay. The solution containing magnetic beads (MG-SA, Seradyn) was infused into the flow chamber. After 20 min, free magnetic beads were washed out with 50 mM Tris-HCl (pH 7.5), 100 mM KCl, and 2 mM MgCl 2 containing the desired concentration of ATP. Bright field images of rotating beads were captured with a CCD camera (CCD-300-RC, Dage-MTI) at 30 frames/s. The recorded images were analyzed on a PC with image analysis software (Celery) and a custom-made program (R. Yasuda, Duke University).
Magnetic Tweezers-Magnetic tweezers consisted of two opposing pairs of electromagnets and were positioned ϳ10 mm above the microscope stage (20). Direction and strength of magnetic field were controlled by changing the electric voltage applied to the pairs of electromagnets, which was accomplished with software (Celery) from the PC. Strength of magnetic fields was proportional to the applied voltage, and the maximum magnetic field was ϳ100 gauss at the observation area. The strength of the magnetic tweezers was stable during experimental times and constant during the 360°rotation (data not shown). The formulation and properties of the tweezers are described in the supplemental material.

ATP-dependent Transition of ⑀ in F 1 Probed by Single-pair
FRET-To detect conformational transition, fluorescent dyes Cy3 and Cy5 were introduced into ␤-sandwich portion (E31C) and C terminus (134C) of the isolated ⑀ subunit of F 1 . This double-labeled ⑀ (termed as ⑀ Cy3,5 ) was reconstituted with ␣ 3 ␤ 3 ␥, and the resultant ␣ 3 ␤ 3 ␥⑀ Cy3,5 complex (termed as F 1 (⑀ Cy3,5 )) was purified. After a 1-h incubation of F 1 (⑀ Cy3,5 ) at the indicated [ATP] in the presence of an ATP-regenerating system, F 1 (⑀ Cy3,5 ) molecules were immobilized, and single-pair FRET was observed for the Cy3, Cy5 doubly-labeled molecules that showed fluorescence of both Cy3 and Cy5 when excited individually. Histograms of FRET efficiency distributed in two major peaks, ϳ0.3 (low FRET) and ϳ0.95 (high FRET) (Fig. 1A,  a-g), representing an extended and hairpin form of ⑀ Cy3,5 , respectively. At 0.1 M ATP, most molecules (90%) were included in the low FRET fraction (Fig. 1Aa). Molecules in the high FRET fraction increased as [ATP] increased, and most molecules (81%) were found in the high FRET fraction at 1 mM ATP. ATP-dependent conformational transition of ⑀ was reversible as the histogram of the sample preincubated in 1 mM ATP and transferred in 0.1 M ATP showed the same pattern (Fig. 1Ah) as that of the sample incubated at 0.1 M ATP (Fig. 1Aa).
Fractions of molecules that showed high FRET (FRET efficiency between 0.8 -1.2) in the histograms of Fig. 1A were plotted to [ATP] (Fig. 1B, cyan bars). Simulation of the data by a simple binding function gave the apparent K d of 34 M (Fig. 1B, orange line). The molecules that did not respond to the changes in [ATP] occupied 29% of total Cy3, Cy5 double-labeled molecules, and they were omitted from simulation. Thus, it is clear that partition of the extended and hairpin ⑀ in F 1 is determined by [ATP].
ATPase-active Fraction of F 1 and the Hairpin Fraction of ⑀-We previously reported that ⑀ inhibition was not observed at micromolar ATP (37). In that case, however, ATPase was measured immediately after dilution of F 1 with hairpin ⑀ in high ATP into micromolar ATP. As the transition of ⑀ from hairpin to extended form is very slow (41,42), we actually measured the activity of F 1 with hairpin ⑀ in these experiments. To attain equilibrium between the active and ⑀-inhibited state, ATPase activities of F 1 (⑀), F 1 (⑀ Cy3 ), and F 1 (⑀ Cy3,5 ) were measured after a 1-h incubation at the indicated ATP concentration (Fig. 1C). These ⑀-containing F 1 s exhibited similar activities at all [ATP] ranges, indicating that fluorescent labels Cy3 and Cy5 did not have a significant artifactual effect on the ATPase activity. The activity of the ␣ 3 ␤ 3 ␥ complex (termed as F 1 (Ϫ⑀)) was measured as a control activity free from ⑀ inhibition. Comparison of activities of ⑀-containing F 1 s and F 1 (Ϫ⑀) showed that ⑀ inhibition became weak as [ATP] increased (25,43,44) and finally disappeared at 1 mM ATP. Then, ratios of activities of ⑀-containing F 1 s to those of F 1 (Ϫ⑀) at each ATP were plotted as a function of [ATP] (Fig.  1B). As seen, half of the ⑀-containing F 1 population became active at 20 -40 M ATP. Comparison of these plots with the high FRET fraction of F 1 (⑀ Cy3,5 ) (Fig. 1B) showed clearly that [ATP] in the solution for fluorescence observation infused after fixation was the same as in the incubation buffer except for h. In h the incubation was done in the presence of 1 mM ATP, whereas 0.1 M ATP solution was infused after fixation; observation was started 10 min later. The ATP-regenerating system was present in all experiments. B, shown is the correlation between the fraction of high FRET and the fraction of active F 1 . A FRET efficiency of 0.8 -1.2 was defined as high FRET. Cyan bars represent the fractions of high FRET from the histograms in A, and ATP hydrolysis activities of F 1 (⑀), F 1 (⑀ Cy3 ), and F 1 (⑀ Cy3,5 ) divided by that of F 1 (Ϫ⑀) (taken from C) are plotted as green, red, and blue circles, respectively. The fractions of high FRET were fitted assuming a simple binding reaction after the fraction of the non-FRET pair was omitted (orange line). The apparent K d from the fit was 34 M. C, shown is ATP hydrolysis activity of F 1 (Ϫ⑀),F 1 (⑀), F 1 (⑀ Cy3 ), and F 1 (⑀ Cy3,5 ). ATP hydrolysis rate was measured in the presence of ATP-regenerating system at 25°C. Velocities were taken at 3550 -3600 s (1750 -1800 s in the case of 1 mM ATP) after initiation of the reaction. Values were the average of two measurements. the fraction of ATPase-active population of F 1 varied in parallel with the high FRET fraction. This means that at any given [ATP], F 1 with extended ⑀ has no ATPase activity, whereas F 1 with hairpin ⑀ has full ATPase activity under the experimental conditions used. Concerning this, two comments should be added. We previously reported that E. coli F o F 1 and Bacillus PS3 F o F 1 with ⑀ fixed to an extended form by cross-linking lost ATPase activity but exhibited ATP synthesis activity (34,45). Because experimental conditions, such as temperature, nucleotide, and pmf, to measure ATP synthesis and hydrolysis, were very different, tests under the strictly same conditions with defined ⑀ form have to be done. Another point concerns the site of ATP binding that is responsible for ⑀ transition. The isolated ⑀ (46) in hairpin form (47) can bind ATP with an apparent K d 4.3 M (41), much lower than an apparent K d 34 M for the transition. Therefore, ATP binding to ␤, rather than ⑀, might induce conformational transition of ⑀ in F 1 complex as proposed previously (41,42).
Mechanical Activation of ⑀-Inhibited F 1 and ADP-inhibited F 1 -To know how the native enzyme can escape from ⑀ inhibition, we examined the artificial activation from ⑀-inhibited state by single-molecule manipulation ( Fig. 2A). F 1 (⑀ Cy3 ) molecules that showed active rotation of a magnetic bead attached to ␥ in 1 mM ATP were marked at first, and then the solution containing 0.1 M ATP was infused into the observation chamber. After this exchange of the solution, most of the marked molecules fell into the ⑀ inhibition and stopped rotation. Next, the solution containing 100 M ATP was infused into the chamber. No rotation was observed within several min after the buffer exchange. The magnetic bead was forced to rotate to the desired angle by magnetic tweezers, and then the tweezers were turned off. After this manipulation, F 1 (⑀ Cy3 ) behaved in three ways; (i) it resumed rotation, (ii) it did not resume rotation, and the bead returned to the original inhibitory angle, or (iii) it did not resume rotation, and the bead stayed at the position other than the original inhibitory position. We defined case (i) as "activation." In the case of (iii) (ϳ3% of the total manipulations), the molecules might be broken and were not analyzed further. Most activations observed in this experiment should be caused by the forced rotation but not by spontaneous activation, because the time constant for the spontaneous activation from the ⑀-inhibited state was about 10 min at 100 M ATP (data not shown) (42), much longer than the infusion time (ϳ2 min) and manipulation time (within 20 s). Once F 1 (⑀ Cy3 ) was activated from ⑀ inhibition at 100 M ATP, it hardly fell into ⑀ inhibition again (Fig. 1C). We also tested the mechanical activation of ADP-inhibited F 1 (Ϫ⑀) as a reference. Because F 1 (Ϫ⑀) lapses into ADP inhibition spontaneously at any [ATP] (19), exchange of the solution was not necessary, and [ATP] was fixed to 100 M.
In the mechanical activation experiments, we defined 0°as the angle of ⑀ and ADP inhibitions, "plus" as the ATP hydrolysis direction, and "minus" as the opposite direction. It should be noted that in the following experiments one can compare the observed angle of bead but cannot argue the absolute angle of ␥ rotation, because the bead angle contains torsional movement of elastic components of the system such as His-tag linkers (between glass surface and ␣ 3 ␤ 3 ) and biotin linkers (between ␥ and bead). In a typical experiment of the manipulation of ⑀-in- Retention of ⑀ Cy3 in F 1 complex during experiments was checked by total internal reflection fluorescence microscopy. Simultaneously, rotation of magnetic beads attached to ␥ was observed by bright-field microscopy. B, shown is mechanical activation of ⑀-inhibited F 1 . At time 0 the enzyme was inactive; the initial angular position of the magnetic bead was taken as 0°. Then the bead was rotated by magnets by ϩ120°, Ϫ120°, and Ϫ240°(green points, rotation speed 0.1 Hz). After forced rotation by ϩ120°and by Ϫ120°, the bead returned to its initial position, and the enzyme remained inactive. After the Ϫ240°forced rotation, F 1 resumed rotation. C, shown is angular dependence of mechanical activation probability. Mechanical activation of ⑀-inhibited F 1 (⑀ Cy3 ) (blue) and ADP-inhibited F 1 (Ϫ⑀) (red) were tested in the presence of 100 M ATP. The average trial number for each point was 10.8. hibited F 1 (⑀ Cy3 ) (Fig. 2B), forced rotations (green traces) to ϩ120°and to Ϫ120°did not induce activation (case (ii)), but forced rotation to Ϫ240°resulted in resumption of rotation (case (i)). Similar experiments were repeated at each manipulated angle for ⑀-inhibited F 1 (⑀ Cy3 ) and ADP-inhibited F 1 (Ϫ⑀), and the probability of mechanical activation was obtained (Fig.  2C). As reported (20), the probability of activation from ADP inhibition increased steeply in the plus direction and reached 100% at ϩ80°. On the contrary, ⑀ inhibition resisted strongly against activation; most attempts of forced rotations to ϩ80°a nd ϩ120°failed, and forced rotation as much as ϩ240°was necessary for efficient activation. In minus directions, there was no striking difference between ⑀ inhibition and ADP inhibition; that is, almost no activation was observed up to Ϫ120°, and another Ϫ120°rotation was necessary for full activation. The above observations imply that if the enzyme falls into ⑀ inhibition, a large and, hence, a very rare thermal angular fluctuation of ␥ is necessary for spontaneous activation.
Mechanical Stiffness of ⑀-Inhibited F 1 and ADP-inhibited F 1 -Mechanical stiffness of F 1 in the ⑀-inhibited state and ADP-inhibited state was examined by applying rotary torque by magnetic tweezers. Because magnetic beads in asymmetric shapes were suitable for observation, such magnetic beads made from broken pieces were chosen among the beads attached to F 1 on the glass surface. To know actual trapping force applied to each of beads with different sizes and shapes, the torque of F 1 during ATP-driven rotation at 1 mM ATP was used as a calibration standard. In accordance with theory (see the supplemental text), it was confirmed that the power (stiffness) of the magnetic trap was proportional to the square of the voltage (V) applied to the magnetic tweezers (supplemental Fig. S1) and that the magnetic torque exerted on a bead was proportional to V 2 sin2 (, the angle between long axis of a bead and the applied magnetic field) (supplemental Fig. S3). The minimum clamping voltage (MCV), defined as the voltage necessary to clamp the bead for 3 s on average, was obtained for each bead. In a typical rotation trajectory (Fig. 3A), as voltage increased, the stall time prolonged; a bead spent ϳ2 s on average at each stall position when 1.0 V was applied and ϳ10 s on average when 1.1 V was applied. Therefore, MCV in this case was 1.1 V. As expected from the fact that F 1 exerts nearly constant torque at any angle during rotation at saturating (Ͼ0.5 mM) ATP (48), similar results were obtained at several arbitrarily chosen magnet trapping angles (data not shown).
After the MCV value was obtained, the inhibited state was induced by buffer exchange (⑀ inhibition) or was attained spontaneously (ADP inhibition), and the inhibited molecules were forced to rotate slowly (0.05 Hz) to the minus direction by magnetic tweezers at various voltages (Fig. 3B). As the bead was rotated, the backward resilience torque of the twisted molecule increased. Finally, the beads could no longer follow the rotation FIGURE 3. Stiffness of ⑀-inhibited F 1 and ADP-inhibited F 1 . A, shown is determination of MCV. A magnetic field of a different strength was applied to F 1 , rotating in the presence of 1 mM ATP. An example of rotational trajectories is shown. Small square panels show the magnetic bead centroid position for each voltage tried; gray arrows indicate the direction and the strength of magnetic field. MCV was defined for each individual rotating bead as the voltage that clamped the bead for more than 3 s on average. In the example, MCV was determined as 1.1 V. ⌬Ј ATP indicates angular deviation of beads from the direction of magnetic field when ATP-driven rotation was clamped at MCV. B, stiffness measurement is shown. The inhibited F 1 molecules were rotated at 0.05 Hz by magnetic tweezers at various voltages. In this example, ADP-inhibited F 1 (Ϫ⑀) was rotated at 65, 87, and 109% of MCV (green, red, and blue, respectively). If the stiffness of inhibited F 1 was greater than the trapping stiffness of the magnetic tweezers, beads could not follow the angular movement of the magnetic field and escaped from trapping. The maximum angular deviation from the initial angle (⌬) was measured, and angular deviation of the beads from the direction of the magnetic field (⌬ inhib Ј ϭ angular displacement of the magnetic field Ϫ ⌬) was obtained. Cyan bold and dotted lines indicate the magnetic field angle. C, stiffness of ⑀-inhibited F 1 and ADP-inhibited F 1 is shown. ⌬ values of ⑀ inhibition and ADP inhibition (blue open circle and red filled circle, respectively) were plotted against the square of manipulation voltage, which were normalized by MCV (⑀ inhibition, n ϭ 27, 5 molecules; ADP inhibition, n ϭ 25, 5 molecules). Linear fits for each data set are shown as orange (ADP inhibition) and cyan (⑀ inhibition) lines. The gray dotted line indicates the approximate torque of ATP-driven rotation of F 1 (supplemental text).
of magnetic field and detached from magnet trapping. This maximum angular deviation of beads from the inhibitory position just before detaching was defined as ⌬. It was expected that at the position of ⌬ the resilience torque generated by the twisted F 1 in the inhibited state was equal to the torque applied by magnetic tweezers. Values of ⌬ of ⑀ inhibition (blue open circle) and ADP inhibition (red circle) were plotted against the torque of the trap expressed by square of magnet voltage normalized by MCV (Fig. 3C). The cases where the inhibited molecules were activated during manipulation were excluded from analysis.
As mentioned above, the torque exerted by magnetic tweezers depends on the angle between the bead long axis and the magnetic field direction. In the case of the inhibited F 1 , this angle (⌬ inhib Ј ), measured at the moment when the beads detached from magnetic trap, was ϳ36°(supplemental Fig. S2). In the case of the active F 1 , this angle (⌬ ATP Ј ), measured when the rotation at 1 mM ATP, was blocked by magnetic tweezers at MCV, was ϳ22°(supplemental Fig. S3). From these angles we were able to calculate that the torque of ATP-driven rotation of F 1 corresponded to ϳ0.73 units of the y axis (dotted line) in Fig.  3C (see the supplemental material).
The data points in Fig. 3C were scattered probably because of fluctuation of the magnetic trap system, difference of immobilization tightness of individual molecules, and error of MCV calibration. Nonetheless, the tendency is obvious; ⑀ inhibition is mechanically stiffer than ADP inhibition. Rough fitting lines of ⑀ inhibition (cyan) and ADP inhibition (orange) show that, compared with F 1 in ADP inhibition, about 1.5-fold higher torque is required for F 1 in ⑀ inhibition to twist the same angle in the range Ϫ40°ϳ Ϫ90°.

DISCUSSION
⑀ Inhibition Is More Resistant Than ADP Inhibition to Rotational Displacement-This study reveals that, when ⑀-inhibited F 1 and ADP-inhibited F 1 are activated by forced rotation to the direction of ATP hydrolysis, the former requires larger rotation angles than the latter (Fig. 2C, plus ⌬). The forced rotation to the same angular positions in the direction of ATP synthesis gives apparently the same activation chances to both ⑀-inhibited F 1 and ADP-inhibited F 1 (Fig. 2C, minus ⌬). However, to attain the same rotation angle to ATP synthesis direction, ⑀-inhibited F 1 requires an ϳ1.5-fold larger torque of the magnetic trap than ADP-inhibited F 1 (Fig. 3C). Thus, ⑀-inhibited F 1 is structurally more resistant than ADP-inhibited F 1 against rotational displacement of ␥. Without forced rotation, occasional large rotational displacement of ␥ in F 1 is brought about by thermal angular fluctuation and gives the inhibited F 1 a chance of spontaneous activation. The above contention predicts that spontaneous activation from ⑀ inhibition will take a much longer time compared with ADP inhibition. Indeed, at 100 M ATP, the time constant for activation of ATPase from ⑀ inhibition, ϳ10 min, is 20 times larger than that of ADP inhibition, ϳ30 s (19).
Activation of F o F 1 Resting in the Inhibited State May Need Extra pmf-Similar to F 1 , ⑀ in F o F 1 can adopt either an extended or a hairpin form, and ATPase activity is inhibited when ⑀ is extended (34). Activation of the inhibited F o F 1 in native mem-branes can be achieved by the rotation of ␥ to the ATP synthesis direction that is forced by the torque transmitted from a rotating c-ring, which is powered by pmf-driven proton flow. When F o F 1 synthesizes ATP, the energy of pmf-driven proton flow is converted to the energy of rotation and then to the energy of ATP synthesis. Because pmf-dependent ATP synthesis is highly efficient, as measured under conditions close to equilibrium (49,50), these conversions must also be highly efficient; the energy of rotation (torque ϫ 2) would be close to the energy of proton flow (proton charge ϫ number of transported protons per revolution ϫ pmf). Such a linear pmf-torque relationship was well proved for another proton-driven motor, bacterial flagella (51,52).
Assuming that the pmf-torque relationship abovementioned is the case and that mechanical properties of F 1 are not largely changed by interactions with F o (53), we made a rough estimation of the pmf value necessary for the activation of F o F 1 in ADP-and ⑀-inhibited states from the data in Fig. 3C. The unit of measurement in the y axis in Fig. 3C corresponds to ϳ50 pN⅐nm that is equivalent to the torque generated by flow of 10 protons per one revolution with an ϳ190-mV pmf. The plots suggest that a rotation of ␥ Ͼ Ϫ120°, necessary for activation, requires the torque equivalent to pmf of at least 280 and 400 mV for ADP-inhibited and ⑀-inhibited F 1 , respectively (Figs. 3C and Fig. 4). As pmf for ATP synthesis is usually in the range of 160 -220 mV, the above values are more than ϳ1.3-fold (ADP inhibition) and ϳ1.8-fold (⑀ inhibition) larger than pmf necessary for ATP synthesis. Although these quantitative estimates are rough, it is likely that the pmf required for the activation of  Fig. 3C). It was assumed that the torque generated by magnetic tweezers is equivalent to the pmf-powered torque generated by F o . Bold blue and red lines represent the measured stiffness of ⑀-inhibited and ADP-inhibited F 1 , respectively. Threshold pmf for ATP synthesis (green band) was approximated from likely ranges of chemical potential of ATP synthesis in vivo. Torque necessary for activation (i.e. rotation by 120°) was assumed to be between the maximum measured values and the extrapolated values (marked by arrows between the dotted lines).
⑀-inhibited F o F 1 is significantly higher than the thermodynamic pmf threshold for ATP synthesis (green band in Fig. 4). Activation of ADP-inhibited F o F 1 also seems to require marginal extra pmf. Such a higher pmf requirement for activation was proposed earlier from the experiments with chloroplast F o F 1 (54).
The above contention implies that in experiments where a pulse of pmf is generated to start ATP synthesis by F o F 1 in the inhibited state (e.g. acid-base transition of proteoliposomes or illumination of photosynthetic membranes by flashes), the minimal pmf required for detection of ATP synthesis might reflect the threshold for the activation rather than that for ATP synthesis itself. The role of C-terminal helices of ⑀ in increasing the activation threshold pmf might be responsible for the apparently lowered pmf threshold for ATP synthesis of E. coli F o F 1 (⑀ ⌬C ) (39).
Activation from the inhibited state by pmf was also suggested from the initial ATPase activity of F o F 1 (55,56). In a previous study we found that pmf levels sufficient to activate the mutant Bacillus F o F 1 (⑀ ⌬C ) in the presence of ADP was not sufficient for activation of wild-type F o F 1 (15). This finding also confirms that inhibition by ⑀ elevates the pmf level necessary for the enzyme activation.