Stepping rotation of F(1)-ATPase with one, two, or three altered catalytic sites that bind ATP only slowly.

F(1)-ATPase is an ATP hydrolysis-driven motor in which the gamma subunit rotates in the stator cylinder alpha(3)beta(3). To know the coordination of three catalytic beta subunits during catalysis, hybrid F(1)-ATPases, each containing one, two, or three "slow" mutant beta subunits that bind ATP very slowly, were prepared, and the rotations were observed with a single molecule level. Each hybrid made one, two, or three steps per 360 degrees revolution, respectively, at 5 microm ATP where the wild-type enzyme rotated continuously without step under the same observing conditions. The observed dwell times of the steps are explained by the slow binding rate of ATP. Except for the steps, properties of rotation, such as the torque forces exerted during rotary movement, were not significantly changed from those of the wild-type enzyme. Thus, it appears that the presence of the slow beta subunit(s) does not seriously affect other normal beta subunit(s) in the same F(1)-ATPase molecule and that the order of sequential catalytic events is faithfully maintained even when ATP binding to one or two of the catalytic sites is retarded.

F 1 -ATPase is an ATP hydrolysis-driven motor in which the ␥ subunit rotates in the stator cylinder ␣ 3 ␤ 3 . To know the coordination of three catalytic ␤ subunits during catalysis, hybrid F 1 -ATPases, each containing one, two, or three "slow" mutant ␤ subunits that bind ATP very slowly, were prepared, and the rotations were observed with a single molecule level. Each hybrid made one, two, or three steps per 360°revolution, respectively, at 5 M ATP where the wild-type enzyme rotated continuously without step under the same observing conditions. The observed dwell times of the steps are explained by the slow binding rate of ATP. Except for the steps, properties of rotation, such as the torque forces exerted during rotary movement, were not significantly changed from those of the wild-type enzyme. Thus, it appears that the presence of the slow ␤ subunit(s) does not seriously affect other normal ␤ subunit(s) in the same F 1 -ATPase molecule and that the order of sequential catalytic events is faithfully maintained even when ATP binding to one or two of the catalytic sites is retarded.
The F o F 1 -ATP synthase found in mitochondria, bacteria, and chloroplasts couples proton translocation in the F o portion and ATP synthesis/hydrolysis in the F 1 portion through physical rotation of the central shaft subunits (1)(2)(3)(4)(5). The isolated F 1 portion has ATPase activity, thus often called F 1 -ATPase, and is composed of five different subunits with a stoichiometry of ␣ 3 ␤ 3 ␥␦⑀. The ␣ 3 ␤ 3 ␥ subcomplex is the minimum ATPase-active complex that has catalytic features similar to F 1 -ATPase. In the crystal of the ␣ 3 ␤ 3 ␥ structure, ␣ and ␤ subunits are arranged alternately to form an ␣ 3 ␤ 3 cylinder around the coiledcoil structure of the ␥ subunit (6). Catalytic sites reside mainly on ␤ subunits, whereas some residues of ␣ subunits also contribute.
The isolated F 1 -ATPase by itself is a motor enzyme; the biochemical supporting result of sophisticated subunit-exchange experiments of Escherichia coli F 1 -ATPase (7) was secured by the direct demonstration of ATP hydrolysis-driven rotation of the fluorescent actin filament attached to the ␥ subunit of an ␣ 3 ␤ 3 ␥ subcomplex of thermophilic F 1 -ATPase immobilized on a glass surface (8). At nanomolar ATP concentrations, the ␥ subunit rotates in discrete 120°steps (9). The analysis indicates that the dwell time of the step corresponds to the waiting time for the ATP molecule to occupy the next catalytic site. Further study with a smaller rotation marker and higher time resolution has revealed that a 120°step is split into a 90°substep, triggered by ATP binding, and a 30°substep, probably driven by dissociation of ADP (or phosphate) from the enzyme (10).
The mechanism of how the ATP hydrolysis drives the rotation of F 1 -ATPase is intriguing. The cooperative nature of substrate binding and catalysis of F o F 1 -ATP synthase and F 1 -ATPase has long been recognized and explained by a model, the binding change mechanism proposed by Boyer (11), which assumed the rotational participation of three catalytic sites during catalysis. In support of this model, three ␤ subunits in F 1 -ATPase crystals are in the three different nucleotide binding states: one ␤ subunit with bound AMP-PNP 1 at catalytic site, another with ADP, and the third without nucleotide. The ␤ subunits with bound nucleotides take a "closed" conformation, but the ␤ subunit with an empty catalytic site takes an "open" conformation (6). Thus, it is likely that the rotation of the ␥ subunit is caused by alternative, sequential conformational transition of three ␤ subunits in F 1 -ATPase that is accompanied by each catalytic step in ATP hydrolysis. Then, the mechanism that conducts coordination of three ␤ subunits needs to be clarified. To analyze this, the experimental system may have a great value that enables observation of the role of the individual ␤ subunit during rotation. In this report, we describe a novel method to prepare the hybrid F 1 -ATPase 2 containing one or two copies of mutant ␤ subunit(s) that can bind ATP only slowly. Characteristic rotations of the hybrid F 1 -ATPases were compared with those of wild-type F 1 -ATPase * The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
¶ Supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.

EXPERIMENTAL PROCEDURES
Strains, Plasmids, and Protein Preparation-E. coli strains used were JM109 for preparation of plasmids, CJ236 for generation of uracilcontaining single-stranded plasmids for site-directed mutagenesis, and JM103⌬(uncB-uncD) for expression of the mutant ␣ 3 ␤ 3 ␥ subcomplexes and mutant ␤ subunits of F 1 -ATPase of thermophilic Bacillus strain PS3. Plasmids pUC-␤, which carried genes for the ␤ subunit of thermophilic F 1 -ATPase, and pKAGB1, which carried genes for the ␣, ␤, and ␥ subunits of thermophilic F 1 -ATPase (12), were used for mutagenesis and for gene expression. The plasmid pkk-HC95 (pKAGB1/␣(C193S)/ ␥(S109C/I212C)/␤(His tag at the N terminus)) has been described previously (10). The plasmid pkk-C95 (pKAGB1/␣(C193S)/␥(S109C/I212C)/ ␤), which is a non-His-tagged version of pkk-HC95, was prepared by ligating a 7.4-kb NheI-PmaCI fragment of pkk-HC95 and a 1.3-kb fragment of pKAGB1. The ␣ 3 ␤ 3 ␥ subcomplexes expressed from either pkk-HC95 or pkk-C95 were considered the wild-type F 1 -ATPase in this report. Plasmids pUC-␤ and pUC-␤(I386C/His tag) containing the 1.4-kb MluI-PstI fragment of the ␤ subunit of thermophilic F 1 -ATPase were used for site-directed mutagenesis to introduce "FEFE" mutations (␤(F414E/F420E)) by the Kunkel method (13) with the synthetic oligonucleotide 5Ј-GTA CGA GCC CGG TTG ACC GGT TTC CTG CTC CGC CAC GTG TTC GTT TTG CGA CAA GAA GAA C-3Ј where bold letters are changes made for the mutations Phe to Glu, and italic letters indicate silent mutations that introduce an AgeI site used to identify the mutant. The 1.4-kb MluI-PstI fragment of this plasmid containing the FEFE mutations was ligated with the 7.4-kb MluI-PstI fragment of pkk-HC95 to produce pkk-HC95FEFE and that of pkk-C95 to produce pkk-C95FEFE. The final plasmids used for expression of the mutant products were proved correct by direct nucleotide sequence determination. The expressed ␣ 3 ␤ 3 ␥ subcomplex and ␤ subunits were purified as described previously (12,14) and were stored in 70% ammonium sulfate.
Preparation of Hybrid Complexes-It has been known that the dimer of ␤ subunits is formed in F 1 -ATPase through a disulfide bond between cysteines introduced at the position of ␤-Ile-386 (15). We have adopted this mutation to obtain a ␤ dimer that can reconstitute F 1 -ATPase with other subunits. The outline of the procedures to isolate F 1 (1xFEFE) is as follows (see Fig. 1A). 1) The ␤(I386C/His tag) dimers were generated from monomers and isolated. The ␤(I386C/His tag) subunits in ammonium sulfate suspension were centrifuged and dissolved in 40 mM Tris-HCl, pH 8.0, and 100 mM NaCl. To dimerize ␤ subunits, the solution was treated with 100 M CuCl 2 for 2 h at room temperature. The solution was concentrated to 200 l by ultrafiltration and was subjected to a gel filtration HPLC column Superdex 200HR (Amersham Biosciences) that had been equilibrated with potassium P i buffer (0.1 M potassium phosphate, pH 7.0, 2 mM EDTA). The peak fraction of the ␤(I386C/His tag) dimer was collected and was applied again to the same column. 2) Two cysteines in the ␥ subunit of F 1 (3xFEFE) were labeled with biotin-maleimide. The F 1 -ATPase, containing three ␤(FEFE)s but not His tag, in ammonium sulfate was centrifuged, dissolved in potassium P i buffer, and reduced with 20 mM dithiothreitol for 4 h at room temperature. The solution was subjected to a gel filtration HPLC column (Superdex 200HR, Amersham Biosciences) that had been equilibrated with potassium P i buffer, and the protein peak fraction was treated with a 20-fold molar excess of biotin-PEAC 5 -maleimide for 2 h at room temperature. Unbound reagents were removed with a PD-10 column (Amersham Biosciences). 3) Thus, treated F 1 (3xFEFE) and ␤(I386C/His tag) dimers were mixed and denatured by urea. Biotinylated F 1 -ATPase (0.7 mg) was thus obtained, and a 3-fold molar amount of purified ␤(I386C/His tag) dimers was dissolved in 1 ml of potassium P i buffer. The proteins were denatured by the addition of 120 mg of solid urea and were incubated at 4°C for 1 h. 4) Urea was diluted, and the proteins were concentrated. The solution was diluted with a 50-fold amount of a wash buffer (50 mM imidazole-HCl, pH 8.0, 100 mM NaCl) plus 100 M ATP and 2 mM MgCl 2 and concentrated to 1 ml by ultrafiltration. By these procedures, F 1 (1xFEFE) complexes were assembled from the ␤(FEFE) subunit, biotin-labeled ␥ subunit, and the ␤(I386C/ His tag) dimer. Other molecular species were also present in the solution: assembled F 1 (3xFEFE), free ␤(FEFE) monomer, free ␣ subunit, free ␥ subunit, and free ␤(I386C/His tag) dimer. 5) The former four species without His tag were removed by passing through an Ni-NTA column. The solution was passed through an Ni-NTA Superflow column (1.5-ml bed volume, Qiagen) equilibrated with the wash buffer. The column was washed with 6 ml of the wash buffer and eluted with 6 ml of elution buffer (200 mM imidazole-HCl, pH 8.0, 100 mM NaCl). 6) F 1 (1xFEFE) was isolated from free ␤(I386C/His tag) dimer by gel filtration. The eluate was concentrated to 200 l with ultrafiltration and was subjected to a gel filtration HPLC column (Superdex 200HR, Amersham Biosciences) that had been equilibrated with potassium P i buffer. The hybrid F 1 (1xFEFE) that contained a ␤(I386C/His tag) dimer and a ␤(FEFE) subunit was eluted as an isolated protein peak separated from unassembled ␤(I386C/His tag) dimer. 7) The disulfide crosslink in F 1 (1xFEFE) was reduced just prior to the rotation assay. To reduce the cross-link, the isolated peak fraction of F 1 (1xFEFE) was treated with 100 mM dithiothreitol for 1 h at room temperature and was used for assays within a day. Similarly, F 1 (2xFEFE) was obtained from the ␤(FEFE/I386C/His tag) dimer and the wild-type F 1 -ATPase. F 1 (0xFEFE) was also obtained by reconstitution from the ␤(I386C/His tag) dimer and the wild-type F 1 -ATPase.
Rotation Assay Using Beads-The two cysteines of the ␥ subunit (S109C/I212C) were labeled with biotins (10,16). To visualize the rotation of the ␥ subunit under a microscope, a duplex of streptavidincoated beads (mean diameter: 330 or 530 nm, Bangs Laboratories, Inc.) was attached to the ␥ subunit. An observation flow cell (10 l) was made of two KOH-cleaned or Ni-NTA-coated 3 coverslips (9). Molecules of F 1 -ATPases (10 l, 30 nM) were applied to the flow cell and incubated for 2 min at room temperature to fix them on the glass surface. Unbound molecules of F 1 -ATPase were washed out with 20 l of a BSA buffer (10 mM MOPS, pH 7.0, 50 mM KCl, 2 mM MgCl 2 , and 10 mg/ml bovine serum albumin). The flow cell was infused with 10 l of 0.5 weight percent streptavidin-coated beads in BSA buffer, incubated for 10 min at room temperature, and washed with 20 l of BSA buffer to remove unbound beads. The flow cell was infused with 20 l of 200 M ATP buffer (BSA buffer containing 0.1 mg/ml creatine kinase, 1 mM creatine phosphate, and indicated concentrations of Mg-ATP), and rotation was observed. Then, 40 l of 5 M ATP buffer was infused into the flow cell, and the rotation was observed again. Finally, the solution was exchanged with 40 l of 10 mM ATP buffer, and the rotation was observed again. These procedures of buffer exchange ensured that the stepping rotation was ATP concentration-dependent and not due to an artifact. Movement of beads was observed with a phase contrast microscope (IX70; Olympus). Observed images were collected through a charge-coupled device camera (CCD-300-RC; Dage-MTI) and recorded on a digital video tape at 30 frames/s. Analysis of rotation angle was performed as described previously (8,9).
Measurement of Torque Force-The biotinylated F 1 -ATPases were conjugated with streptavidin and were immobilized on the glass surface of the flow cell (9). The flow cell was infused with 10 l of 1 nM fluorescent actin filament instead of beads, incubated for 10 min at room temperature, washed with 20 l of BSA buffer, and infused with 20 l of 5 mM ATP buffer. The fluorescent actin filament was observed with a fluorescence microscope (IX70; Olympus). Observed images were recorded with an intensified charge-coupled device camera (ICCD-350F; Videoscope) on a digital video tape. Analysis of rotational angle and computation of torque force were preformed as described previously (9).
Assay of ATPase Activity-ATPase activity was measured at 25°C in the presence of an ATP-regenerating system (17) consisting of 300 g/ml pyruvate kinase, 300 g/ml lactate dehydrogenase, 2.5 mM phosphoenolpyruvate, and 0.2 mM NADH and indicated concentrations of Mg-ATP in MOPS buffer (10 mM MOPS-KCl, pH 7.0, 50 mM KCl, 2 mM MgCl 2 ). The initial hydrolysis rate was determined from the slope of absorbance decrease at 340 nm within 5 s after the initiation of the reaction.

RESULTS
FEFE Mutant-To generate mutants that can bind substrate ATP slowly, we replaced two phenylalanine residues of ␤ subunits, Phe-414 and Phe-420, which are located at the "adeninebinding pocket" (6), with glutamic acid residues. These mutations of the ␤ subunit are called FEFE in this report, and according to the number of copies of ␤(FEFE) subunits contained, we designate the mutant F 1 -ATPases as F 1 (0xFEFE), F 1 (1xFEFE), F 1 (2xFEFE), and F 1 (3xFEFE).
Isolation of Hybrid F 1 -ATPases-As has been described under "Experimental Procedures," F 1 (1xFEFE) was isolated by gel filtration HPLC (Fig. 1B). The analysis of the arrowed peak fraction in Fig. 1B with non-reducing SDS-PAGE showed the bands of ␤ dimer and ␤ monomer with consistent band intensities (Fig. 1C, right lane). The ␤ dimer band disappeared and the intensity of the ␤ monomer band increased after dithiothreitol treatment (Fig. 1C, left lane). The disulfide cross-link in F 1 (1xFEFE) was reduced just prior to the rotation assay. F 1 (2xFEFE) and F 1 (0xFEFE) were prepared by similar procedures (see "Experimental Procedures").
Bulk Phase Kinetics of the Mutants-The initial rates of ATP hydrolysis by F 1 (0xFEFE), F 1 (1xFEFE), and F 1 (2xFEFE) were measured and analyzed by non-linear regression analysis as-suming simple Michaelis-Menten kinetics (Table I). For F 1 (3xFEFE), since ATP hydrolysis started with a lag phase, the steady-state rate of ATP hydrolysis, instead of the initial rate, was used for analysis. As expected, FEFE mutations resulted in the dramatic decrease of ATP affinity, and the K m value of F 1 (3xFEFE) was almost 100 times larger than that of F 1 (0xFEFE). The K m values of F 1 (1xFEFE) and F 1 (2xFEFE) are approximately one-third and two-third of the K m value of F 1 (3xFEFE), respectively, reflecting the occurrence of one or two times of slow ATP binding in a catalytic turnover for each mutant. 4 In contrast, the V max values of the mutants remain in the same order with the value of F 1 (1xFEFE) being the smallest. It should be added that the K m value of F 1 (0xFEFE) is similar to that of the wild-type F 1 -ATPase (0.027 mM), whereas the V max value of F 1 (0xFEFE) is about 40% of that of the wild type (162 s Ϫ1 ). The decreased V max value of F 1 (0xFEFE) is 4 Assuming that three catalytic sites have the same k cat and independent, different k on ATP and k off ATP , rate of ATP hydrolysis (V) at steadystate catalysis is calculated as   1. Isolation of hybrid F 1 -ATPase. A, the procedures to isolate hybrid complexes. 1) The His-tagged ␤ dimer, cross-linked between Cys-386 of two ␤ subunits, and F 1 (3xFEFE) were mixed, denatured, renatured, and reassembled. 2) Hybrid F 1 (1xFEFE) was purified with Ni-NTA and gel filtration columns. B, elution profile of the gel filtration HPLC monitored by absorbance at 280 nm. The His-tagged F 1 (1xFEFE) was eluted at 21 min as indicated by an arrow. The peaks at 26 and 43 min correspond to ␤ dimer and ATP, respectively. C, polyacrylamide gel electrophoresis of F 1 (1xFEFE) in the presence of sodium dodecyl sulfate. The purified F 1 (1xFEFE) was incubated at room temperature for 1 h (ϩ) with or (Ϫ) without 100 mM dithiothreitol (DTT) and applied on the 13% gel.
probably due to the presence of two ␤-I386C mutations that differentiate F 1 (0xFEFE) from the wild-type F 1 -ATPase. The turnover rate of F 1 (1xFEFE) is about half the rates of other hybrids. The reason is not known, but possibly the prepared F 1 (1xFEFE) contained more fraction in inhibited states of the enzyme than those of the other hybrids. Taken together, it is safe to conclude that FEFE is a "K m mutation"; the effect of the FEFE mutations is predominantly restricted to the decrease of ATP binding affinity.
Stepping Rotation of Mutant F 1 -ATPases-Rotation of F 1 -ATPase, monitored by beads attached to the ␥ subunit, was observed successively at 200 M ATP at first, at 5 M ATP next, and then at 10 mM ATP. These procedures ensured that the observed stepping motions were not artifacts caused by, for example, surface obstacles. At 5 M ATP, in the case of the wild-type F 1 -ATPase, ATP binding should take place within 10 ms, and rotation of beads (330 or 530 nm diameter) was seen only as smooth rotation by impeding viscous friction ( Fig. 2A,  dashed line) (9). Similar to the wild-type F 1 -ATPase, all of the 27 molecules of F 1 (0xFEFE) that we observed at 5 M ATP showed smooth rotation without steps (data not shown). F 1 (3xFEFE), on the contrary, showed the rotation with three discrete steps per revolution at 5 M ATP ( Fig. 2A, solid line). The positions of the dwells are separated from each other by about 120°, reflecting 3-fold symmetric locations where ATP binding occurs ( Fig. 2A, inset). For F 1 (2xFEFE), more than half of the molecules (11 out of 19) in which we detected rotation showed the rotation with two discrete steps per revolution at 5 M ATP (Fig. 2B). The step positions are separated by about 120°and 240°from each other (Fig. 2B, inset). The rest of the eight molecules rotated like F 1 (1xFEFE). This apparent high percentage of the molecules rotating like F 1 (1xFEFE) is probably due to the unstable nature of F 1 (2xFEFE); a smaller fraction of F 1 (2xFEFE) might survive during the procedures of rotation assay than contaminating F 1 (1xFEFE). In the case of F 1 (1xFEFE), almost all rotating molecules, 34 out of 39, rotated with a single step separated by 360°during revolutions at 5 M ATP (Fig. 2C and inset). The remaining five molecules rotated like F 1 (0xFEFE), that is, without step. The stepping rotations described above are all dependent on ATP concentrations. At 200 M ATP, rotations of all mutants were rather smooth, but a rotation trajectory was slightly rugged by occasional brief steps (Ͻ0.1 s). At 10 mM ATP, all rotations were smooth and fast. It should be worth noting that even during a long dwell time, obvious single backward rotation was not observed throughout the whole experiment.
Rate Constant of ATP Binding-The dwell times at 5 M ATP of all rotating molecules examined for F 1 (3xFEFE) were collected and plotted (Fig. 3, top). The histogram is well fitted by a single exponential curve, suggesting that the dwell time corresponds to the waiting time of the enzyme for the next ATP and that binding of a single ATP drives one 120°rotation (9). The rate constant for ATP binding (k on ATP ) is obtained from the fitting as 1.8 ϫ 10 5 M Ϫ1 s Ϫ1 . Similar analyses were carried out for a two-step rotation of F 1 (2xFEFE) and a single-step rotation of F 1 (1xFEFE) (Fig. 3, middle and bottom), and k on ATP values of 1.6 ϫ 10 5 M Ϫ1 s Ϫ1 and 3.7ϫ 10 5 M Ϫ1 s Ϫ1 , respectively, were obtained. These values of mutants were 2 orders of magnitude smaller than the k on ATP value of the wild type (3 ϫ 10 7 M Ϫ1 s Ϫ1 ) (10). As described, the K m value of F 1 (3xFEFE) is 2 orders of magnitude larger than that of F 1 (0xFEFE) (and the wild-type F 1 -ATPase). Therefore, the increase in K m value of FEFE mutations can be explained solely by the decrease in the k on ATP value.
The fact that k on ATP values of F 1 (1xFEFE), F 1 (2xFEFE), and F 1 (3xFEFE), obtained from the above analysis are similar to each other 5 implies that ATP binding to ␤(FEFE) in F 1 -ATPase occurs at the same rate regardless of how many ␤(FEFE) and normal ␤ subunits are present in the F 1 -ATPase. In F 1 (2xFEFE), for example, the ATP binding to the first ␤(FEFE) during steady-state catalysis is neither decelerated by the presence of the second ␤(FEFE) nor accelerated by the third normal ␤ subunit. It seems that the effect of slow ATP binding to the first ␤(FEFE) is restricted to the corresponding 120°rotation driven by that ATP binding.
Torque Force of Rotation-Instead of beads, an actin filament was attached to the ␥ subunit, and rotation velocities 5 The k on ATP value of F 1 (1xFEFE) is about double of the values of other mutants. However, we do not take this difference seriously at this stage because k on ATP values obtained from dwell time observed for each of rotating molecules varied from one molecule to another. The k on ATP values calculated for F 1 (1xFEFE), F 1 (2xFEFE), and F 1 (3xFEFE) are were measured for F 1 (3xFEFE) at 5 mM ATP. As shown in Fig.  4, the rotational velocities decreased as the length of the actin filament increased. The observed rotations were scattered mostly between two theoretical lines that assumed the constant torque forces, 20 and 40 pN⅐nm. Higher velocities are thought to be more reliable because any obstructions against rotation would reduce the velocity. Therefore, we conclude that F 1 (3xFEFE), similar to the wild-type F 1 -ATPase, exerted constant torque of ϳ40 pN⅐nm (9).

F 1 -ATPase Does Not Easily Confuse the Order of Catalytic
Sequence-This study reports that when one, two, or three ␤ subunits in F 1 -ATPase become slow in binding of substrate ATP, an obvious consequence is the retardation of initiating one, two, or three 120°rotations. During a long period in which one slow ␤ subunit waits for ATP, other ␤ subunits are also just waiting without letting the next catalytic event start. The principle underlying this seemingly natural consequence is the faithfulness of F 1 -ATPase in keeping the order of sequential catalytic events. Also confirmed is the assumption that although three catalytic sites exist in F 1 -ATPase, catalytic events of all three sites are coordinated essentially as a single, linear chain reaction pathway, excluding possibilities of other diverging-converging or parallel reaction pathways. This is another expression of Boyer's binding change mechanism, and this report provides a support for it from the rotation kinetics. Previously, we reported that when one of the ␤ subunits in F 1 -ATPase was replaced with an incompetent ␤ subunit, catalytic turnover of ATP hydrolysis was completely blocked (14). Two other active ␤ subunits cannot exert their catalytic ability until a preceding catalytic event, which is impossible for the incompetent ␤ subunit, finishes.
Probably related to the above contention is the absence of the backward step during prolonged dwell time. Previously, occasional backward steps, about once per 20 forward steps, were observed and were supposed to be caused by the ATP binding to the wrong empty catalytic site (9). If so, under the situation in which the next correct ATP binding site is on the ␤(FEFE) subunit and the wrong binding site is on the normal ␤ subunit, chances for the wrong site to bind ATP (and thus cause a backward step) should have increased drastically because ATP binding to the correct site is retarded about 100 times. However, such frequent backward steps were not observed for F 1 (1xFEFE) and F 1 (2xFEFE), and therefore, ATP binding to the wrong site does not account for the backward steps. The above argument is based on the bi-site catalysis model (18 -20) in which two catalytic sites are empty at the moment just before a new ATP binds to the enzyme. If the tri-site catalysis is assumed (21)(22)(23)(24), only one catalytic site is available for the next ATP binding and wrong ATP binding cannot occur. In this context, faithful order of catalysis of F 1 -ATPase revealed in this study is explained more easily by the tri-site model than the bi-site model.
Energy of ATP Binding and Torque-It has been known that a 120°-step rotation is composed of 90-and 30°-substep rotations (10). The 90°-substep rotation is likely driven by the energy liberated when F 1 -ATPase binds (but not hydrolyzes) ATP, and subsequent 30°-substep rotation occurs in ϳ2 ms. The method employed here did not resolve the substeps, and we observed a 120°-step rotation triggered by ATP binding. The magnitude of energy to be liberated upon ATP binding varies depending on the binding affinity of ATP to F 1 -ATPase. Then k on ATP values of ␤(FEFE) in F 1 -ATPase mutants are 2 orders of magnitude smaller than the wild type, and therefore, the affinity of ATP to the mutants is also very low. Nonetheless, the observed torque force of F 1 (3xFEFE) is not significantly changed from that of the wild-type F 1 -ATPase. In the converse combination of catalytic site and substrate, that is, when wildtype F 1 -ATPase binds GTP or ITP, whose binding affinity was lower than ATP, the observed torque forces were not significantly changed from those observed for ATP (25). These apparent contradictions are explained by the "binding zipper" model proposed by Oster et al. (26,27). In this model, the process of ATP binding to F 1 -ATPase is divided into two subprocesses: the docking of ATP and zipping of hydrogen bonds between phosphate moiety of ATP and residues of the catalytic site. The torque force is not generated at the docking process but during the zipping process. The FEFE mutations contain mutations at the adenine-binding pocket rather than at the phosphate binding residues in F 1 -ATPase. It is plausible that this mutation might reduce the chance for the docking of ATP (or the chance to enter the zipping process), but once the ATP-binding mode can transit into the zipping process by chance, the same torque force is exerted.