Torque Generation and Utilization in Motor Enzyme F0F1-ATP Synthase

Background: ATP synthase (F0F1) is a rotary motor enzyme. Results: F1 with a short-sized helix-1 in β subunit rotates with half of the normal torque and supports reduced ATP synthesis activity. Conclusion: Helix-1 acts as a “pushrod” to generate torque, and torque-reduced F0F1 retains the catalytic ability of ATP synthesis. Significance: Generation and utilization of the torque are crucial for motor enzymes. ATP synthase (F0F1) is made of two motors, a proton-driven motor (F0) and an ATP-driven motor (F1), connected by a common rotary shaft, and catalyzes proton flow-driven ATP synthesis and ATP-driven proton pumping. In F1, the central γ subunit rotates inside the α3β3 ring. Here we report structural features of F1 responsible for torque generation and the catalytic ability of the low-torque F0F1. (i) Deletion of one or two turns in the α-helix in the C-terminal domain of catalytic β subunit at the rotor/stator contact region generates mutant F1s, termed F1(1/2)s, that rotate with about half of the normal torque. This helix would support the helix-loop-helix structure acting as a solid “pushrod” to push the rotor γ subunit, but the short helix in F1(1/2)s would fail to accomplish this task. (ii) Three different half-torque F0F1(1/2)s were purified and reconstituted into proteoliposomes. They carry out ATP-driven proton pumping and build up the same small transmembrane ΔpH, indicating that the final ΔpH is directly related to the amount of torque. (iii) The half-torque F0F1(1/2)s can catalyze ATP synthesis, although slowly. The rate of synthesis varies widely among the three F0F1(1/2)s, which suggests that the rate reflects subtle conformational variations of individual mutants.

F 0 F 1 -ATP synthase (F 0 F 1 ) catalyzes synthesis of ATP in mitochondria, chloroplasts, and bacteria in oxidative and photo-phosphorylation, using the energy of proton translocation caused by the proton motive force (pmf) 2 across membranes. Proton translocation through membrane-embedded F 0 portion drives ATP synthesis in membrane-protruding F 1 portion and, in the reverse reaction, ATP hydrolysis in F 1 can drive pumping back protons through F 0 . These two reactions, the inward/outward proton translocation in F 0 and synthesis/hydrolysis in F 1 , are coupled by mechanical rotation (1)(2)(3)(4)(5)(6)(7)(8)(9)(10). Both F 0 and F 1 are rotary motors; F 0 motor is driven by downhill proton translocation, F 1 motor is driven by ATP hydrolysis, and the two motors share a common rotary shaft. When pmf is high, F 0 drives rotation of the shaft that results in ATP synthesis in F 1 . When the chemical potential of ATP hydrolysis exceeds pmf, F 1 rotates the shaft and F 0 is forced to pump protons. Indeed, isolated F 1 rotates when it hydrolyzes ATP (11), and the reverse rotation by an external force results in ATP synthesis (12,13).
ATP-driven rotation of the isolated F 1 has been extensively studied by using a minimum motor complex consisting of ␣ 3 ␤ 3 ␥ subunits from thermophilic Bacillus PS3 (14 -16), which we also refer to as F 1 in this study unless otherwise indicated. The ␥ subunit is a rotor subunit. Its N-and C-terminal helices form a coiled-coil and are deeply inserted into the cavity of the stator ␣ 3 ␤ 3 ring. The globular domain of ␥ subunit resides outside of the cavity of the ␣ 3 ␤ 3 ring (see Fig. 1, left panel). To visualize rotation, the ␣ 3 ␤ 3 ring is immobilized on the glass surface, and a bead (or bead duplex) is attached to the globular domain of the ␥ subunit. A single cycle rotates the ␥ subunit 120°, consuming one ATP, meaning that F 1 carries out three reaction cycles per revolution. The 120°cycle begins with a pause at 0°, then an ϳ80°-step rotation is followed by another pause, and lastly, an ϳ40°-step rotation occurs. F 1 waits for a substrate ATP during the pause at 0°("ATP-waiting dwell") and rotates ϳ80°upon ATP binding. A pause at ϳ80°("catalytic dwell") is ϳ2 ms, independent of ATP concentration, representing the period required for hydrolytic cleavage of ATP and release of P i from the catalytic site.
The torque of ATP-driven F 1 motor estimated from rotation speed, bead radius, rotation radius, and viscosity of aqueous medium amounts to ϳ40 pN⅐nm (17). The energy required for a 120°rotation (ϳ40 pN⅐nm ϫ 2/3 radians) is roughly equal to the free energy liberated from hydrolysis of an ATP molecule (ϳ90 pN⅐nm) under physiological conditions and, therefore, energy conversion by F 1 motor is very efficient. The torque of F 1 is generated from sequential interactions between a rotor ␥ subunit and three catalytic ␤ subunits in the stator ␣ 3 ␤ 3 ring (18). According to the crystal structures (19,20), ␤ subunits can interact directly with the ␥ subunit at the two positions, the "sleeve" and the "orifice" regions (see Fig. 1, left panel). A mutant F 1 , whose ␥ subunit is truncated at the C terminus and loses interactions with the ␣ 3 ␤ 3 ring at the sleeve region, rotates with half of the normal torque (21). Inversely, F 1 devoid of the entire N-terminal helix, which preserves the sleeve interactions but loses many interactions at the orifice, also rotates with half of the normal torque (22). Therefore, the orifice interactions alone can produce half of the total torque, and the sleeve interactions, probably with the assistance of some of the orifice interactions, produce another half.
At the orifice region, the helix-1-loop-helix-2 structure in the C-terminal domain of the ␤ subunit makes contact with the ␥ subunit (19). The loop in the structure contains a well conserved DELSDED acidic cluster sequence, but its acidic nature is not essential for torque generation (23). Recently, it was shown that deletion of three or four residues in the loop does not impair ATP synthesis activity of F 0 F 1 (24). If neither acidic residues in the loop nor the full-length loop itself are essential for rotation, what structural features of the orifice region are responsible for torque generation? Here, we report isolation of mutant F 1 s that exert half of the normal torque, indicating that the full-length helix-1 acts as a "pushrod" for the ␥ subunit to generate half of the total torque. Then, we addressed the next question. If the F 1 portion of F 0 F 1 wastes a large fraction of the energy transferred from the F 0 motor, can it synthesize ATP? The results show that it can, although slowly.

EXPERIMENTAL PROCEDURES
Strains, Plasmids, and Proteins-Escherichia coli strain JM109 was used for the genetic manipulation, and JM103 ⌬(uncB-uncD), which does not express E. coli F 0 F 1 , was used for the expression of F 1 and F 0 F 1 from thermophilic Bacillus PS3. Mutations of Bacillus PS3 F 1 were introduced into the plasmid pKAGB1/HC95, which expresses the ␣(C193S) 3 ␤(His 10 tag at N terminus) 3 ␥(S107C/I210C) complex of F 1 . Wild-type and mutant F 1 were expressed and purified as described (25) except for two procedures. Heat treatment to precipitate heat-labile E. coli proteins was carried out at 64°C for 20 min for wild-type F 1 but at 60°C for 10 min for the mutants. The procedure to remove endogenously bound nucleotides was omitted for the mutants because mutants with-out bound nucleotides tend to dissociate. The purified F 1 was stored in 70% ammonium sulfate suspension containing 2 mM DTT at 4°C. Mutations of F 0 F 1 were introduced into the plasmid pTR19-ASDS-⑀⌬c in which the F 1 -coding region is the same as pKAGB1/HC95 and the C-terminal domain of the ⑀ subunit is deleted (26). F 0 F 1 was expressed and purified as described (27,28). The purified F 0 F 1 preparation was frozen by liquid N 2 and stored at Ϫ80°C until use. The yields of purified mutant F 1 s and F 0 F 1 s were 20 -50% of that of the wild type. The purity of the isolated preparations, exemplified by the three mutants that are the main focus of this study, is shown (supplemental Fig. S1). The concentrations of F 1 and F 0 F 1 were determined from the absorbance with the molar extinction coefficient at 280 nm of 154,000 and 253,000 M Ϫ1 cm Ϫ1 and with the molecular mass as 356 and 530 kDa, respectively (25,29).
Observation and Analysis of Rotation-Rotation was observed on the stage of an inverted microscope (IX70, Olympus) at 25°C as described (21). A mercury lamp was used to observe rotation of 209-, 291-, and 350-nm polystyrene beads, and a 532-nm laser was used to observe rotation of 40-nm gold beads. Images of beads were captured with a CCD camera (ICL-B0620M-KC, IMPERX and GX-8, nac Image Technology Inc.) with 250 frames/s (fps) for polystyrene beads and with 4,000 fps for gold beads. The glass chamber was made of the nickel-nitrilotriacetic acid-coated bottom coverslip (21) and an uncoated top coverslip. The bottom coverslip and the top coverslip were separated by two strips of double-faced tape. F 1 was biotinylated by incubation with biotin-PEAC5-maleimide for 90 min. The biotinylated F 1 (10 nM) in 50 mM MOPS/KOH, pH 7.0, containing 50 mM KCl and 10 mg/ml bovine serum albumin was applied into the chamber, and overflowing solution was blotted with paper. After 2 min, the chamber was washed by 50 mM MOPS/KOH containing 50 mM KCl, and beads were suspended in 50 mM MOPS/KOH, 50 mM KCl, and 10 mg/ml bovine serum albumin were applied into the chamber. After waiting for 15 min and washing, the rotation buffer (50 mM MOPS/KOH, pH 7.0, 50 mM KCl, 2 mM MgCl 2 , 1 mM phosphoenolpyruvate (Sigma), 200 g/ml pyruvate kinase (Roche Applied Science), and indicated concentration of ATP) was applied into the chamber. As commonly experienced for single molecule observations of this kind, only a few percentages, at most, of beads showed clear rotation due to surface denaturation, improper bead attachment, and other unknown reasons. Numbers of rotating beads of mutant F 1 molecules were slightly fewer than that of wild-type F 1 . Rotating beads rotated at various speeds. In general, fast rotating beads always rotated quickly, whereas sluggish ones almost never showed fast rotation. The rotations at the fastest speed were analyzed because slower rotation can be explained by surface obstructions.
Torque of rotation was defined as where and are the rotation speed (radians/second) and viscous load, respectively. The value of of duplex beads is given as where is the viscosity of a medium ( ϭ 0.93 ϫ 10 Ϫ9 pN/nm 2 ) and R and x i (i ϭ 1, 2) are the radius and rotation radius of each bead, respectively (30). The beads rotating with about the same rotation radius were selected and analyzed. Torque was also estimated from fluctuation analysis (31) and defined as , ⌬t is 4 ms, and P(⌬) is the probability distribution of ⌬. One can estimate N from this equation without the value of . ATP-driven Proton Pumping and ATP Synthesis-Purified F 0 F 1 was reconstituted into proteoliposomes by using BioBeads as described (28). Proteoliposome suspension (20 l) was mixed with 1.2 ml of 10 mM HEPES/KOH, pH 7.5, 5 mM MgCl 2 , 100 mM KCl, and 0.3 g/ml 9-amino-6-chloro-2-methoxyacridine (ACMA). The reaction was started by the addition of 12 l of 100 mM ATP, and formation of a transmembrane pH gradient (⌬pH) was monitored with quenching of ACMA fluorescence (excitation 410 nm, emission 480 nm) at 25°C. Final concentrations of F 0 F 1 were 11.4 nM. At the end of measurement, nigericin (2 M) was added to eliminate ⌬pH. ATP synthesis was measured as described (27,28) except for a long (6-h) incubation of proteoliposome with the acidic mixture (35 mM MES, 10 mM NaH 2 PO 4 , 2.5 mM MgCl 2 , 0.68 mM KCl, 340 mM sucrose, 0.5 mM ADP, 0.2 M valinomycin, pH 6.05). A basic mixture was prepared by mixing 21 l of the luciferin/luciferase mixture (2ϫ concentration, CLS II ATP bioluminescence assay kit, Roche Applied Science), 870 l of the basic buffer (300 mM HEPES, 10 mM NaH 2 PO 4 , 2.5 mM MgCl 2 , 240 mM KOH, pH adjusted with NaOH to 8.05), and 9 l of 50 mM ADP and was incubated for 5 min at 30°C. The acidic mixture containing proteoliposome (100 l) was added into 900 l of the basic mixture, and emission of luciferin was monitored. The calculated size of the imposed pmf was 260 mV (⌬pH ϭ 2, ⌬ ϭ 140 mV). The final concentrations of F 0 F 1 , ADP, and P i were 11.4 nM, 0.5 mM, and 10 mM, respectively. The final pH of the solution outside the proteoliposomes was 8.05. At the end of mea-surements, 10 l of 10 M ATP was added three times for calibration (28).

RESULTS
Torque Mutants of F 1 -F 1 with decreased torque is expected to rotate beads slowly when compared with the wild-type F 1 . For the search for structural features responsible for the torque generation, various mutants of Bacillus PS3 F 1 were expressed in E. coli. They are, in most cases, expressed in smaller amounts and are less heat-stable than the wild-type but purified without difficulty. The purified F 1 was immobilized onto the nickelnitrilotriacetic acid-coated glass surface through His-tagged ␤ subunits and, 291-nm polystyrene beads were attached on the ␥ subunit as a rotation probe. We observed the rotation of duplex beads in 2 mM ATP under the microscopic field with a camera (250 fps). Under these experimental conditions, ATP-waiting dwell and catalytic dwell are too short to be observed, and continuous rotations with occasional pauses by ADP-Mg inhibition or for other reasons were observed. Among beads rotating at various speeds, the rotations at the fastest speed were taken to be the unobstructed rotation of native molecules.
We at first focused on amino acid residues that are located at the rotor/stator interface narrower than 3.5 Å at the orifice region. Except for the residues in the 390 DELSDED 396 sequence of the ␤ subunit that were already demonstrated not to be critical for torque generation, we replaced these residues with alanine and made F 1 variants containing mutations ␣G398A/ S399A/D400A, ␣D400A/L401A/D402A, ␥D83A/R84A/G85A, ␥G85A/L86A, ␥G88A, ␥Y90A/N91A, or ␥N91A/S92A/N93A. We found that these mutants rotated beads at speeds similar to the wild-type F 1 , ϳ20 revolutions/s (data not shown), indicating that specific interactions between side chains of these residues do not significantly contribute to torque generation. Next, we made two mutant F 1 s, ␤⌬ 388 GMDE 391 and ␤⌬ 392 LSD 394 , that have a deletion in the 388 GMDELSDED 396 sequence of the ␤ subunit (Fig. 1, right panel), but again, they showed rotation at a normal speed (Fig. 2, upper panels). Then, we deleted one or two turns of the helix-1 that precedes the 390 DELSDED 396 sequence, and ␤⌬ 380 LQDI 383 , ␤⌬ 376 RYKE 379 , and ␤⌬ 377 YKELQDI 383 were made (Fig. 1, right panel) (superscripts are abbreviated hereafter). These three mutant F 1 s rotated more slowly than the wild-type F 1 (Fig. 2, lower panels), and we focused on these mutants.
Half-torque F 1 -Torque of the three mutants relative to that of wild-type F 1 was estimated from three different analyses. First, continuous rotation of 209-, 291-, and 350-nm duplex beads in 2 mM ATP was analyzed. The rotation speed of each mutant F 1 was obtained from the consecutive, smooth 10 revolutions taken from the five fastest-rotating molecules. As the size of bead increases, viscous load increases and rotation slows down (Fig. 3A). With beads of the same size, viscous load is constant, and torque is obtained from the equation (torque ϭ viscous load ϫ rotation speed) (Fig. 3B). The averaged torque with three different sizes of beads is 46 pN⅐nm (wild-type), 29 pN⅐nm (␤⌬RYKE), 26 pN⅐nm (␤⌬LQDI), and 22 pN⅐nm (␤⌬YKELQDI). Second, rotation of 291-nm duplex beads in 200 nM ATP was observed. At this low ATP concentration, F 1 repeats a pause of ATP-waiting dwell and a 120°-step rotation. The consecutive 10 120°-step rotations were overlaid and averaged (Fig. 3C). Torque was estimated from the rotation speed of the middle part of the averaged 120°-step rotation trajectory. As seen (Fig. 3D), torques of mutants obtained by this analysis are slightly larger than those obtained from continuous rotation. Third, bead fluctuation during rotational motion was analyzed by the recently developed fluctuation theorem (Fig. 3E). By this analysis, the magnitude of torque is directly obtained from fluctuation of rotating beads without knowledge of the values of viscous load and rotation speed. This is advantageous because the estimation of viscous load needs information of exact size of individual beads, rotational radius, and viscosity of the medium near the surface of glass and may contain errors (32). The averaged torque with three different sizes of beads is 47 pN⅐nm (wild type), 22 pN⅐nm (␤⌬RYKE), 23 pN⅐nm (␤⌬LQDI), and 22 pN⅐nm(␤⌬YKELQDI). Altogether, three independent methods give similar torque values for all three mutant F 1 s, that is, about half of the normal torques of wild-type F 1 . Thus, shortening of the helix-1 results in the loss of half of the torque. Out of the energy supplied by hydrolysis of one ATP molecule for 120°r otation, these mutant F 1 s can utilize only ϳ45 pN⅐nm (ϭtorque ϫ 2/3), whereas wild-type F 1 can utilize ϳ90 pN⅐nm.
Kinetic Constants of Half-torque F 1 s-Kinetic characteristics of half-torque F 1 , termed F 1 (1/2) hereafter, were examined by analysis of rotation. First, durations of ATP-waiting dwell in rotation in 200 nM ATP were collected and plotted as histograms (Fig. 4A). The histograms are fitted by an exponential function that contains the rate of ATP binding (k on ) to the catalytic site. The k on values that give the best fit are 2.0 ϫ 10 7 M Ϫ1 s Ϫ1 (wild-type), 1.6 ϫ 10 7 M Ϫ1 s Ϫ1 (␤⌬RYKE), 0.7 ϫ 10 7 M Ϫ1 s Ϫ1 (␤⌬LQDI), and 1.3 ϫ 10 7 M Ϫ1 s Ϫ1 (␤⌬YKELQDI). Taking into account that the values of ␤⌬LQDI and ␤⌬YKELQDI might be underestimated because fitting curves are dragged to the right by the presence of dwells longer than 2 s of unknown origin, it appears that k on values of F 1 (1/2)s are not significantly changed from that of wild-type F 1 .
Next, rotation of a 40-nm single gold bead attached to the ␥ subunit was observed in 2 mM ATP with a high speed camera (4,000 fps). Under these conditions, viscous load of bead rotation is negligible, ATP-waiting dwell is not observed, and only catalytic dwell is observed at each 120°interval. The histogram of durations of the catalytic dwells is fitted by a double exponential function defined by two time constants (Fig. 4B). Previous studies assigned two time constants to the two sequential catalytic events on the enzyme, ATP hydrolysis and P i release (16). Two of the F 1 (1/2)s have time constants (␤⌬RYKE, 0.5 and 1.2 ms; ␤⌬YKELQD, 0.5 and 1.1 ms) that are very similar to those of the wild-type F 1 (0.4 and 1.4 ms). The ␤⌬LQDI mutant has slightly longer time constants (0.8 and 1.3 ms). Enzyme turnover rates calculated from the above values are 560 s Ϫ1 (wild-type), 590 s Ϫ1 (␤⌬RYKE), 480 s Ϫ1 (␤⌬LQDI), and 630 s Ϫ1 (␤⌬YKELQDI). ATP hydrolysis activities measured in the bulk solution containing 2 mM ATP are 330 s Ϫ1 (wild-type), 270 s Ϫ1 (␤⌬RYKE), 110 s Ϫ1 (␤⌬LQDI), and 330 s Ϫ1 (␤⌬YKELQDI) in the presence of lauryldimethylamine-N-oxide, which is thought to relieve ADP-Mg inhibition. Taking into account that purified F 1 s may contain some fraction of inactive molecules, these values are compatible with values obtained from rotation. To summarize the above results, enzyme kinetics of F 1 (1/2)s are not changed much from those of wild-type F 1 .
Proton Pumping and ATP Synthesis-Bacillus PS3 F 0 F 1 containing F 1 (1/2) was expressed in E. coli and purified. The purified mutant F 0 F 1 s are as stable as the wild type. To avoid complexity caused by regulatory function of the ⑀ subunit, the C-terminal domain of the ⑀ subunit (⑀⌬C) was deleted and will be termed wild-type F 0 F 1 hereafter (26,33,34). The purified F 0 F 1 was reconstituted into proteoliposomes, and ATP-driven proton pumping was monitored with the quenching of ACMA fluorescence that reflects pH gradient across membranes (⌬pH). Upon the addition of ATP, quenching started with a short lag, progressed at a maximum rate, and leveled off at the stationary phase (Fig. 5A). The established ⌬pH was completely abolished by the addition of nigericin, an H ϩ -K ϩ antiporter that can dissipate ⌬pH. In general, quenching time courses of the three F 0 F 1 (1/2)s are very similar to each other. The fastest quenching progress rates of F 0 F 1 (1/2)s are about 40% of that of wild-type F 0 F 1 , and the maximum quenching level at the sta-tionary phase with F 0 F 1 (1/2)s was ϳ60% of that of wild-type F 0 F 1 . Thus, F 0 F 1 (1/2)s can pump protons, but the final ⌬pH built up is much smaller than that of wild-type F 0 F 1 .
Using the same proteoliposomes, we observed ATP synthesis driven by acid-base transition and valinomycin-induced K ϩ diffusion potential (Fig. 5B). The reaction was started by the addition of acidified proteoliposome mixture into the basic mixture, and generation of ATP was monitored by luciferin/ luciferase. In the presence of nigericin, which acts as an uncoupler in combination with valinomycin, ATP synthesis did not occur. In contrast to proton pumping, activities of ATP synthesis of the F 0 F 1 (1/2)s are different from each other, and initial rates of synthesis are 28% (␤⌬RYKE), 20% (␤⌬LQDI), and 11% (␤⌬YKELQDI) of that of wild-type F 0 F 1 .

Short-sized Helix-1 Impairs Energy Conversion but Not
Chemical Catalysis-Properties of the half-torque mutants are summarized in Table 1. As seen, when the mutant enzymes hydrolyze ATP without the burden of the viscous load, their enzymatic kinetics are not very different from those of the wildtype enzyme. However, once they have to do work such as rotating large beads and pumping protons, their defects become obvious. Thus, shortening of helix-1 does not impair chemical catalysis but does impair mechanochemical energy conversion.
Torque Generation in F 1 (1/2)-The half-torque mutants we reported here retain the sleeve interactions. In addition, they do not lose all orifice interactions but retain the interactions at the conical entrance of the orifice of ␣ 3 ␤ 3 ring that touches the globular portion of the ␥ subunit (Fig. 1). F 1 with the truncated ␥ subunit, which apparently has only the interactions with the conical entrance region of the ␣ 3 ␤ 3 ring, can generate a small torque that barely supports unidirectional slow rotation of a load-negligible gold bead (35). It appears, therefore, that the Ϫ exp(Ϫ(1/ 2 ) ϫ t). 1 and 2 represent the time constants of two successive reactions, ATP hydrolysis and P i release, that occur in the catalytic dwell (16). Experimental details are described under "Experimental Procedures." FIGURE 5. Activities of F 0 F 1 (1/2)s. A, ATP-driven proton pump. Acidification of the inside lumen of F 0 F 1 (1/2)-containing proteoliposomes by proton pumping was monitored with fluorescence quenching of ACMA. The reaction was started by the addition of 1 mM ATP. B, ATP synthesis activity. The F 0 F 1 (1/ 2)-containing proteoliposomes were pre-equilibrated with the low K ϩ , acidic mixture and then injected into a 10-fold volume of the high K ϩ basic mixture. The acidic mixture contained ADP, P i , and valinomycin. The basic mixture contained ADP, P i , and luciferin/luciferase. Final concentrations of F 0 F 1 , ADP, and P i were 11.4 nM, 0.5 mM, and 10 mM, respectively. ATP produced was monitored with emission of luciferin, and the initial slope of exponential fitting curve between 0 and 6 s was taken to be ATP synthesis activity as shown in the right side of the figure. Experimental details are described under "Experimental Procedures."  Fig. 4). c Typical values of ACMA fluorescence quenching (Fig. 5). sleeve interactions coordinated with the interactions at the conical entrance would be responsible for the generation of torque in F 1 (1/2)s.
Helix-1 with Sufficient Length Is Necessary for Torque Generation, Acting as Pushrod-The orifice interactions by themselves produce at least half of the torque of the ATP-driven F 1 motor (21,35). Given that the interactions at the conical entrance region contribute only a small fraction of the torque, the majority of the torque produced at the orifice is attributed to the interactions of the helix-1-loop-helix-2 with the convex coiled-coil region of the ␥ subunit. Concerning the central loop, the conserved DELSDED sequence is not necessary for the torque generation (23). Even the mutants with the shortened loop can synthesize ATP (24) and produce normal torque (Fig.  2). Instead, this work reveals a critical role of full-length helix-1 in the generation of torque. When helix-1 is shortened by one helical turn (5.4 Å) by deletion of either the RYKE or the LQDI segments, torque is reduced by half. When the segment RYKELQDI, which forms two turns (10.8 Å) in helix-1, is truncated, torque is again reduced by no more than half. It is clear from these results that the physical length, rather than residuespecific interactions, of helix-1 is important for torque generation. In addition, the fact that deletion of one turn and of two turns gives the same result implies the presence of a critical length for helix-1 function. Crystal structure (36), single molecule study (37), and rapid scan atomic force microscopy (38) show that C-terminal domains of three ␤ subunits in F 1 undergo bending motion sequentially and alternately during the catalytic cycle. The helix-1-loop-helix-2 is a protruding body of the C-terminal domain toward the ␥ subunit (Fig. 1), and it can protrude more toward the ␥ subunit by a bending motion (36). It appears that a protruding solid body of the helix-1-loop-helix-2 physically pushes the convex part of the coiledcoil of the ␥ subunit and assists the ␥ subunit to rotate (39). To transmit the force, helix-1, and probably helix-2 as well, must play the role of pushrod with sufficient length and stiffness.
Critical Length of Helix-1-Very recently, more research on the helix-1-loop-helix-2 structure was published by Mnatsakanyan et al. (40). They found that a mutant of Bacillus PS3 F 0 F 1 , ⌬7 (␤⌬(LQDIϩLSD)), can catalyze ATP synthesis, although slowly, but ⌬10 (␤⌬(QDIIAILϩLSD)) cannot. From the difference between ⌬7 and ⌬10, Mnatsakanyan et al. (40) concluded that the critical length of the helix-1-loop-helix-2 structure is around ϳ10 Å shorter than the native length. Our results clearly show that shortening one turn (ϳ5 Å) of helix-1 (␤⌬LQDI and ␤⌬RYKE) is enough to abolish half of the torque. Therefore, we agree on the presence of a critical length but propose that the critical length of the helix as a solid body is ϳ5 Å shorter than the native length. Most likely, ⌬10 is also a half-torque mutant and has the catalytic ability of ATP synthesis, although it might have been very weak and escaped the assay employed in Ref. 40. Actually, ⌬10 retains proton-pumping activity, although weak (40), which should not happen without torque.
Low-torque F 0 F 1 Builds Up a Small ⌬pH-Given that F 1 (1/2) can use only a fraction of the energy of ATP hydrolysis for driving the motor, it is reasonable to assume that F 0 F 1 (1/2) can also use only a fraction of the energy for proton pumping. Indeed, the final ⌬pH built up by the proton-pumping action of F 0 F 1 (1/2) is significantly smaller than ⌬pH built up by wild-type F 0 F 1 . Final ⌬pH could be determined by equilibrium between proton-pumping activity and back pressure of pmf and/or equilibrium between proton-pumping activity and passive leakage of protons through membranes. In any case, however, the fact that three kinds of F 0 F 1 (1/2)s build up the same final ⌬pH indicates that the final ⌬pH is directly determined by the magnitude of the torque, that is, by the energy conversion yield. This agrees with the thermodynamic prediction that ⌬pH is directly related to the torque (n ϫ Z⌬pH ϭ torque ϫ 2/3; where n is the number of transported protons per ATP, and Z is a constant).
Low-torque F 0 F 1 Can Synthesize ATP Slowly under Thermodynamically Favorable Conditions-If the same inefficient energy conversion occurs in the ATP synthesis reaction of F 0 F 1 (1/2), the F 1 (1/2) portion of F 0 F 1 (1/2) can use only a fraction (ϳ45 pN⅐nm per 120°rotation) of the total energy provided by the F 0 portion. Despite this defect, F 0 F 1 (1/2) can synthesize ATP (Fig. 5B). This might be because of the small free energy required for ATP synthesis under actual experimental conditions. The reaction mixtures contained 0.5 mM ADP and 10 mM P i . The ADP we used contained about 0.05% ATP as measured by luciferase assay, and the free energy required for ATP synthesis would amount to ϳ40 pN⅐nm, which the F 1 (1/2) portion of F 0 F 1 (1/2) can manage to exert. Therefore, low-torque F 0 F 1 has catalytic ability and can synthesize ATP under optimum thermodynamic situations.
Because the free energy defines the direction and equilibrium but not the rate of the reaction, it is not surprising that each of the three F 0 F 1 (1/2)s catalyzes ATP synthesis at a different rate. Subtle variations in the enzyme can affect the rate, and the reason for the slow ATP synthesis rate of F 0 F 1 (1/2)s cannot be explained with certainty. During the ATP synthesis reaction, the F 0 portion provides energy to the F 1 portion via rotation of the ␥ subunit. The F 1 portion uses this energy to induce the otherwise thermodynamically unfavorable conformational changes to ␤ subunits that lead to ATP synthesis. We speculate that with insufficient ability to utilize energy, F 0 F 1 (1/2) would fail frequently and take a long time to induce such changes, or even make uncoupled rotations frequently without inducing such changes. We observed that the F 0 F 1 (1/2)s have larger uncoupled ATP hydrolysis activity than wild-type F 0 F 1 , which is probed by resistance to inactivation by dicyclohexylcarbodiimide, a reagent that prevents proton translocation and hence rotation of F 0 . This observation favors the scenario of the uncoupled rotation but does not exclude other interpretations.
Finally, it should be noted that although F 0 F 1 (1/2) can synthesize ATP, the synthesis reaction reaches equilibrium when ATP concentration is 4 or 5 orders of magnitude lower than in the case of wild-type F 0 F 1 . This means that cellular ATP concentration supported by F 0 F 1 (1/2) would be very low and could hardly sustain normal cell activities. Thus, natural selection would not allow field organisms to have a low-torque version of F 0 F 1, even if it had the catalytic ability of ATP synthesis.
Acknowledgment-We thank Daniel Xu for critically reading and polishing the manuscript.