Direct identification of the rotary angle of ATP cleavage in F₁-ATPase from Bacillus PS3

Abstract

F₁-ATPase is the world’s smallest biological rotary motor driven by ATP hydrolysis at three catalytic β subunits. The 120° rotational step of the central shaft γ consists of 80° substep driven by ATP binding and a subsequent 40° substep. In order to correlate timing of ATP cleavage at a specific catalytic site with a rotary angle, we designed a new F₁-ATPase (F₁) from thermophilic Bacillus PS3 carrying β(E190D/F414E/F420E) mutations, which cause extremely slow rates of both ATP cleavage and ATP binding. We produced an F₁ molecule that consists of one mutant β and two wild-type βs (hybrid F₁). As a result, the new hybrid F₁ showed two pausing angles that are separated by 200°. They are attributable to two slowed reaction steps in the mutated β, thus providing the direct evidence that ATP cleavage occurs at 200° rather than 80° subsequent to ATP binding at 0°. This scenario resolves the long-standing unclarified issue in the chemomechanical coupling scheme and gives insights into the mechanism of driving unidirectional rotation.

Graphical abstract

Significance

Chemomechanical coupling is a central question in the mechanism of force generation by motor proteins. In the case of a rotary motor F₁, most rotational steps of the central shaft γ are known to be coupled with elementary chemical steps of ATP hydrolysis in the catalytic subunit β. Nevertheless, distinguishing between chemical states of three catalytic sites in a molecule was a challenge even with the single-molecule observation techniques. Previous studies were found to include contradictory interpretations when a temperature-sensitive dwell of F₁ was discovered. Here, using a hybrid F₁ containing one new mutant β, we present convincing results on the timing of ATP-cleavage event occurring in a single catalytic site, thus providing clear evidence of chemomechanical coupling.

Introduction

Chemomechanical coupling is an indispensable aspect for studies on molecular mechanisms of ATP-hydrolyzing motor proteins (1,2,3). In the case of a rotary molecular motor F₁-ATPase, correlation of each rotational step with a chemical reaction step such as ATP binding, its cleavage, and product release events has been identified to understand the causal relationship between chemical and rotational events (4,5,6).

Single-molecule rotation assay of α₃β₃γ subunits (denoted F₁) from thermophilic Bacillus PS3 has uncovered such details. First, 120°-rotational steps reflecting three-fold symmetry of catalytic β subunits in the presence of ATP at different concentrations revealed that binding of ATP drives rotation (7). Next, the 120° unitary step was resolved into 90° and 30° substeps using a smaller probe with reduced viscous frictional load (8). Subsequently, pauses at 80° (catalytic dwell) during the 120° step were clearly identified by introduction of β(E190D) mutation into F₁ (9). Furthermore, chemical events that occur at the catalytic dwell while waiting for the next 40° substep were shown to be ATP cleavage and release of product inorganic phosphate (P_i) (9,10).

Nevertheless, we should note that a single ATPase cycle at a certain catalytic site does not necessarily complete within a single 120° step. It would rather continue across further rotational steps, and the chemical events would be carried over beyond 120°. Therefore, definition of rotational angle of the shaft on 360° basis rather than 120° basis should be adopted to describe the ATPase cycle, from the starting angle upon binding of ATP at 0° (ATP-waiting dwell) until the full completion of the entire turnover at 360°. Applying this rule, three catalytic dwells of 80° are each defined 80°, 200°, and 320°.

With the above terminology, the scheme that correlates chemical steps with key mechanical events has been long awaited because the timing of other chemical events such as release of P_i had been estimated from the hypothesized cleavage angle. On the 360° basis, possible candidates for ATP cleavage are the angle-80° and angle-200°. The angle-320° is unlikely because hydrolysis of ATP must occur before ADP release occurring in the range from angle-240° to angle-320° (11). We, therefore, address only two possibilities, the angle-80° or angle-200°.

Some studies presented partial answers to the question of ATP-cleavage angle (10,11,12,13,14). Concurrently with these studies, βE190D mutant (9), that indicates the ATP cleavage angle through a long reference pause, came to be widely utilized in rotation assays (15,16,17,18). Nevertheless, the pause of this mutant at angle-0° (200° before cleavage) was found to contain temperature-sensitive dwell, and it complicated interpretation of 0° dwell (18). Without firmly establishing ATP-waiting dwell, we cannot decisively conclude that ATP cleavage occurs at 200°.

To bring the argument on the ATP-cleavage angle to an end, we designed a new experimental setup that enables distinction between chemical events in a single β subunit. Our approach was to introduce two types of mutation, one having a slow ATP-binding rate (F414E/F420E) (denoted FEFE hereafter) (19) and the other exhibiting slow cleavage of ATP (E190D) (9) to the catalytic β subunits. As shown in the Results section, the resultant α₃β₃γ subcomplex has characteristics similar to both of the original mutants, and thus it exhibited two long ATP-waiting and catalytic dwells alternately (Figs. 1 A and 6 A). Furthermore, in the case of the hybrid F₁ in which only one β is mutated and the others remained wild-type, only two pauses out of six (a pair of an ATP-waiting dwell and a catalytic dwell) emerged as prolonged pauses as expected (Figs. 1 B and 6 C). With the genuine ATP-waiting dwell as a standard angle (0°), we uniquely determined the cleavage angle to be 200°. Employing this angle-200° as the origin, all the discussion dependent on the reaction scheme such as the timing of P_i release can now be clarified on the 360° basis. Taken together, the chemomechanical coupling scheme of F₁ is now convincingly understood.

Figure 1.

Combination of β subunits in F₁-ATPase (top left) and their expected rotational steps of the central shaft (arrows in the bottom). (A) F₁-ATPase consisting of three βs with two sets of mutation β(E190D) and β(FEFE). As rates of both binding of ATP and its cleavage slow down, two pauses, an ATP-waiting dwell (solid circle) and a catalytic dwell (open square), are expected to appear in each 120° step even in the video rate rotation assay. (B) Hybrid F₁-ATPase that consists of two wild-type βs and one mutant β(E190D/FEFE). Based on the prolonged ATP-waiting dwell of the mutated β at 0°, the coupled pause that waits for the ATP cleavage could be identified as another prolonged pause. Two possible hypotheses, 80° or 200°, are shown. The case of 320° is excluded as the product ADP is known to be released at 240° (10,11,14). To see this figure in color, go online.

Figure 6.

Dwells and their time constants in stepwise rotation of 3×, 2×, and 1×β(E190D/FEFE). (A–C) Summary of pauses in rotation of hybrid and nonhybrid F₁ revealed by the present study (bottom) and corresponding combinations of β (top). Solid circles and open squares represent ATP-waiting dwells and catalytic dwells, respectively (bottom). (A) nonhybrid 3×β(E190D/FEFE). Cf., Fig. 3B,C. (B) 2×β(E190D/FEFE) hybrid. Cf., Figs. 4A–C, S1, and S2. (C) 1×β(E190D/FEFE) hybrid. Cf., Figs. 5A–F, S3B, and D–F. ATP cleavage at the catalytic site of one β subunit occurs at 200°of γ (with reference to the ATP-waiting angle 0°). (D) Time constants of ATP-waiting dwells (solid circles) and catalytic dwells (open squares) derived from single-molecule rotation assays in the case of a nonhybrid 3×β(E190D/FEFE) and two hybrids, 2×β(E190D/FEFE) and 1×β(E190D/FEFE), at different ATP concentrations. The molecules included in this analysis were those showing clearest rotational steps: four, six, seven, and four molecules under 0.1, 0.2, 0.4, and 2 mM ATP conditions respectively for nonhybrid 3×β(E190D/FEFE); four molecules each under 0.2 and 2 mM ATP conditions for 2×β(E190D/FEFE) hybrids, and seven molecules each under 0.1 and 1 mM ATP conditions for 1×β(E190D/FEFE) hybrids (see Figs. S4 and S5 for details of exponential fits). Observations were made with small metal probes except that 1×β(E190D/FEFE) was observed also with φ = 0.28 μm duplex beads probes. The rotations of 3× and 2×β(E190D/FEFE) were recorded at 30 frames per second. The 1×β(E190D/FEFE) rotation was recorded at 250 or 1000 frames per second.

Materials and Methods

Preparation of F₁

The plasmid pkkαγβHC95 (8,19) was used for preparation of the pseudo-wild-type α₃β₃γ carrying the minimum mutations required for rotation assays (named “HC95” and denoted “wild-type” F₁ in this manuscript). Isolated β subunits containing three mutations were prepared as follows: plasmids pucβ-His-tag(E190D) (16) and pucβ-His-tag(F414E/F420E) (19) were treated with restriction enzymes Mlu I and Mun I. Mlu I-Mun I fragment of pucβ-His-tag(E190D) (16) and fragment lacking MluI-MunI of pucβ-His-tag(F414E/F420E) were ligated to produce a new plasmid containing triple mutations, pucβ-His-tag(E190D/F414E/F420E). Next, the plasmid pkkαγβHC95(E190D/F414E/F420E) was produced in a similar manner using restriction enzymes Mlu I and Pst I for pkkαγβHC95 and pucβHis-tag(E190D/F414E/F420E). This expression system of F₁ containing homogenously mutated three βs was designed to determine rotation kinetics of F₁ with β(E190D/F414E/F420E) mutations without hybridization process (named nonhybrid 3×β(E190D/FEFE)).

Expression, purification, and hybridization of β and α₃β₃γ were performed as described previously (16,19).

Hybridization of F₁-ATPase

We prepared hybrid F₁ by reconstitution based on the original method (19) with the following modifications (16). Isolated βHis-tag (E190D/F414E/F420E) was mixed with the wild-type F₁ at a molar ratio of 10–18 to 1. This process enables stochastic introduction of one or two mutant β subunits per F₁ molecule. Notation of the hybrids are as follows; the F₁ comprised of two wild-type β and one β(E190D/F414E/F420E)s is denoted 1×β(E190D/FEFE) hybrid. The F₁ comprised of one wild-type β and two β(E190D/F414E/F420E)s is denoted 2×β(E190D/FEFE) hybrid hereafter.

For partial disassembly of F₁, 1 M potassium chloride was added to the mixture, and the solution was subsequently incubated on ice overnight. Next, the sample was ultrafiltrated with Amicon Ultra (10 k cut; Millipore) for dilution of potassium chloride down to 0.2 M. The resultant partially desalted mixture was incubated at 37°C for 1 h to reconstitute F₁. Finally, we purified hybrid F₁ by gel filtration (a Superdex 200 10/300 column connected to AKTA Explorer, GE Healthcare) and concentrated the solution by ultrafiltration (100 k cut; Microcon YM100 or Amicon Ultra, Millipore).

Measurements of ATPase activity

Steady-state ATPase activity was measured at 24°C in the presence of an ATP-regenerating system consisting of 150 μg per ml pyruvate kinase (Roche), 150 μg per ml lactate dehydrogenase (Roche), 2 mM phosphoenolpyruvate (Roche), 0.15 mg per ml NADH (Roche), 0.1% N,N-dimethyldodecylamine N-oxide (LDAO, Fluka), and indicated concentrations of Mg-ATP in F₁ buffer (10 mM MOPS-KOH, pH 7.0, 5 mM KCl, 2 mM MgCl₂). The ATP hydrolysis rate was determined from the slope of the decrease in absorbance at 340 nm in the final steady-state phase of the time course measured using a spectrophotometer (V-650, JASCO). The baseline slopes were measured in the same manner except that F₁ buffer without F₁ was injected into the assay mixture at the start of the measurements. The slopes in the same time range as the ATPase measurements were subtracted from those measured with F₁ to calculate the net slope. Measured time course of ATPase activity was evaluated by Michaelis-Menten kinetics using a data analysis software Igor Pro.

Rotation assay at the video rate

Streptavidin-conjugated magnetic beads (Sera-Mag Magnetic Streptavidin, nominal diameter 0.8 μm, Seradyn) were used as markers of F₁ rotation for recording at 30 fps. Particles > ∼0.5 μm were removed by centrifugation as described previously (10) (denoted metal beads hereafter).

Flow chambers were made as reported previously (14) except that spacers were double-faced tapes (Nicetac, Nichiban) of ∼90 μm thickness. We infused one chamber volume (∼10 μL) of 1 nM biotinylated F₁ in F₁ buffer, let it stand for 2 min, and washed with 20 μL of F₁ buffer. Next, we infused 20 μL of 5 mg per ml bovine serum albumin in F₁ buffer. We then infused 20 μL of metal beads, and unbound beads were washed with F₁ buffer after incubation for 15 min. Finally, we introduced the assay mixture (F₁ buffer with Mg-ATP of desired concentrations) under the ATP-regenerating system (0.02 mg per ml creatine kinase and 0.08 mg per ml creatine phosphate) into the flow chamber.

High-speed imaging of rotating F₁

To clarify trajectories between pauses of F₁ rotation, high-speed recording was made initially at 1000 Hz with large marker polystyrene beads of a nominal diameter 0.833 μm. The observations were made as reported previously (20). A flow chamber was constructed with two coverslips, a Ni-NTA coated bottom (24 × 32 mm², Matsunami) and an uncoated top (18 × 18 mm², Matsunami), which were separated by 50-μm spacers. We infused one chamber volume (∼10 μL) of 1 nM biotinylated F₁ in 100 mM MOPS-KOH (pH 7.0), let it stand for 10 min, and washed five times with 10 μL of 100 mM MOPS-KOH (pH 7.0). Next, we infused 10 μL of BSA buffer (5 mg per ml bovine serum albumin in 50 mM MOPS-KOH pH 7.0, 50 mM K₂SO₄, 4 mM MgSO₄) five times. We then infused 10 μL of streptavidin-conjugated beads (Power-Bind Streptavidin, nominal diameter 0.833 μm, Seradyn) twice. After 30 min, unbound beads were washed five times with 10 μL of BSA buffer, and 100 μL (10 μL × 10 times) of the assay mixture (BSA buffer with Mg-ATP of desired concentrations) containing an ATP-regenerating system (0.409 mg per ml creatine kinase and 0.1 mg per ml creatine phosphate) was infused.

As high-speed imaging was found to be effective in observation of circular trajectories, 250 Hz recording was applied to small metal bead probes (∼200 nm) or duplex of small polystyrene beads (Power-Bind Streptavidin, nominal diameter 276 nm) in rotation assays of β(E190D/FEFE) hybrids under 100 μM and 1 mM ATP conditions. Rotation assays were made as described previously (21,22) using a modified F₁ buffer: 50 mM MOPS-KOH (pH 7.0), 50 mM KCl, 2 mM MgCl₂ with two types of ATP-regenerating systems (the one described above in the “Rotation assay at the video rate” section or 2.5 mM phosphoenol pyruvate and 0.1 mg per mL pyruvate kinase). In some cases, 5.0 mg per mL bovine serum albumin in the modified F₁ buffer was infused into the flow chamber before infusion of F₁ to prevent nonspecific binding of F₁ to the Ni-NTA glass surface.

Microscopy

Rotation of beads attached to the central shaft γ of F₁ fixed on the glass surface of the flow chambers was visualized by a brightfield microscopy or a center-stop dark-field microscopy (16) with an inverted microscope (IX-71, IX83 Olympus or TE2000, Nikon Instruments) with an objective lens (×60 Plan Apo, NA 1.45 Olympus, or ×100 U Apo NA 1.49 Olympus, or ×100 Plan Apo NA 0.5–1.3 Nikon Instruments), a center stop (circular reticle with φ = 0.1 μm, LINOS), a halogen lamp and with a charge-coupled device camera (CCD-300, Dage-MTI or LRH1540N, Digimo) or an sCMOS camera (Zyla 4.2, Andor) or a CMOS camera (FASTCAM NOVA S16, Photron). Recording rates were 30, 250, or 1000 Hz. Observations were made at 23°C ± 3°C.

Note that, in a conventional dark-field microscope equipped with an objective lens having a high numerical aperture, the oil-type condenser lens is directly attached to the top cover glass of flow chambers, which frequently causes drifting motion of the observation field. To avoid this problem, we adopted a dry-type condenser and applied a center stop (16) to mask the light illuminated only from a low numerical aperture (Fig. 3 A, left).

Figure 3.

Rotation assay of nonhybrid 3×β(E190D/FEFE) F₁s. (A) Left, schematic drawing showing the dark-field microscope with a center stop (16). The actual center stop is located at the equivalent back-focal plane (BFP) conjugated by a set of lenses between the camera port of the microscope and a camera. Right, schematic drawing of the experimental setup of rotation assay. Not to scale. (B) Time course of rotation at [ATP] = 2 mM recorded at 30 frames per second. Grids indicate 80° and 40° rotational substeps. Pauses waiting for ATP cleavage (catalytic dwell) were highlighted by open arrowheads. Pauses at the ATP-waiting angle (solid arrowheads) were shorter at this high ATP concentration. Inset, trace of a single metal bead rotation in 2000 consecutive frames. Scale bar, 100 nm. (C) Rotation at [ATP] = 0.2 mM. Pauses at ATP-waiting angles (solid arrowheads) became evident at the near-K_m ATP concentration. Inset, rotation in 2,000 consecutive frames. Scale bar, 100 nm. Time zero indicates the moment when observations were started.

Analyses

In the cases of nonhybrid 3×β(E190D/FEFE) exhibiting six-step rotation and 2×β(E190D/FEFE) hybrid exhibiting four-pause rotation of small metal beads captured at the video rate, the center derived from 2D Gaussian fits to the bead images was defined as positions of beads using a custom-made macro Procedure_iGaussDual3D for Igor Pro (WaveMetrics). In the cases of two-step rotation of large polystyrene beads captured at 1000 Hz, centroid positions were determined by Center 5 for Image J (NIH). Additionally, in the case of two-step rotation of small metal beads under the 1 mM or 100 μM ATP conditions, positions were determined by center(centroid) option of Procedure_iGaussDual3D. Custom-made macros Procedure_iTraceViewer or Procedure_iTraceViewer_rtG3 for Igor Pro was used for conversion of Cartesian coordinates to rotational angles. After these analyses, molecules that made clean rotational steps were selected for estimation of stepping angles (large beads) and duration of pauses (small beads) using custom-made Igor macros Procedure_iDwell or Procedure_iDwell9. The histograms of pausing time were fitted by a single-exponential function constant·exp(-kt) where k is the rate constant (the inverse of the dwell time) and t is the time. For dwell time analyses, rotation of molecules that displayed distinguishable steps were selected for analyses. In the case of 1× and 2× β(E190D/FEFE) hybrids, the molecules whose average pausing time of catalytic dwells was less than 1 s were judged to be WT F₁ having artifact pauses due to for example contacts to obstacles on the glass surface. These molecules were not used for further analyses.

Results

ATPase activity of mutant F₁

We prepared and purified the new mutant nonhybrid 3×β(E190D/FEFE), as described in the materials and methods section. The mutant is expected to show both characteristics observed in F₁β(E190D) and F₁β(FEFE), i.e., slow ATP-cleavage rate (9) and slow ATP-binding rate (19) compared with those of the wild-type. To investigate this point, the ATPase activity of the new mutant was measured with an ATP-regenerating system under a spectrophotometer.

The steady-state ATPase activity of the mutant in the presence of 0.1% LDAO basically followed typical Michaelis-Menten kinetics having a single set of K_m and V_max (Fig. 2), V = V_max[ATP]/(K_m + [ATP]). V_max was estimated to be 0.15 ± 0.01 s⁻¹ (coefficient value ± 1 SD), which is ∼10³ times slower than that of the wild-type (247/0.15, Table 1 and in Yasuda et al. and Masaike et al. (8,16)). The large decrease in V_max of ATPase is convincing because V_max values of F₁β(E190D) and F₁β(FEFE) are 10² times (247/2.4, see Shimabukuro et al. (9)) and 4.0 times (247/62, see Ariga et al. (19)) smaller than that of the wild-type, respectively. Assuming that the effect of ADP inhibition is relieved by LDAO, the low V_max of steady-state ATPase activity is attributable to slow cleavage of ATP. In terms of K_m, the mutant nonhybrid 3×β(E190D/FEFE) exhibits (2.1 ± 0.4) × 10² μM (coefficient value ± one SD), which is in between the values 19 or 32 μM for the wild-type (8,16) and 1.55 × 10³ μM for F₁β(FEFE) (19). The k_on estimated using V_max/K_m is 7.1 × 10² M⁻¹s⁻¹, which is ∼10⁴ times smaller than that of the wild-type ((7.8 × 10⁶)/(7.1 × 10²) (16)). Therefore, the new mutant β has features of both mutations F₁β(E190D) and F₁β(FEFE) in terms of extremely slow ATP-cleavage and ATP-binding rate constants.

Figure 2.

Steady-state ATPase activity of nonhybrid α₃β(E190D/FEFE)₃γ subcomplex of F₁-ATPase from thermophilic Bacillus PS3 (nonhybrid 3×β(E190D/FEFE)) measured in the bulk-phase in the presence of 0.1% LDAO. The subcomplex was overexpressed in E. coli and purified in the intact form without a hybridization process. The curve shows a fit to the average ATPase activity from each ATP concentration with Michaelis-Menten kinetics; V = V_max[ATP]/(K_m + [ATP]), where V_max is 0.15 ± 0.01 s⁻¹ and K_m is (2.1 ± 0.4)×10² μM (coefficient values ± 1 SD).

Table 1.

ATPase activity of mutant α₃β₃γ subcomplexes of F₁-ATPase

Mutant description	Bulk-phase steady-state ATPase activity measured by the ATP-regenerating system
	Vmax (s−1)	Km (μM)	kon ∼ Vmax/Km (M−1 s−1)
β(E190D/F414E/F420E)  Present study (Fig. 2)	0.15 ± 0.01 (w/LDAO)	(2.1 ± 0.4) ×102 (w/LDAO)	7.1×102
HC95a (8)	247 ± 9 (w/LDAO)	19 ± 1 (w/LDAO)	1.3×107
HC95a (16)	248 ± 4 (w/LDAO)	32 ± 1 (w/LDAO)	7.8×106
β(E190D) (9)	2.4 ± 0.0 (w/LDAO)	1.4 ± 0.1 (w/LDAO)	1.7×106
β(F414E/F420E) (19)	62	1.55×103	4.0×104

Steady-state ATPase activity was measured in bulk phase at different ATP concentrations using an ATP-regenerating system. Accumulation of an ADP-inhibited fraction of F₁ during turnover of ATP hydrolysis causes gradual decrease in net bulk-phase ATPase activity. Note that most of the molecules are active at the starting point of ATPase measurements. Therefore, initial rate of ATPase generally corresponds to rotational steps of active single molecules. Nevertheless, in the cases where the initial phase of ATPase is a lag phase, ATPase activity is measured with LDAO to relieve ADP inhibition. In these cases, steady-state ATPase activity is compared with rotation. In the case of β(FEFE), the lag was rather heavier in the presence of LDAO, and therefore the ATPase was measured without LDAO (19).

^aHC95 represents pseudo-wild-type α₃β₃γ containing minimum mutations required for a rotation assay (8,19).

Rotation of nonhybrid 3×β(E190D/FEFE)

We initiated single-molecule rotation assay with nonhybrid 3×β(E190D/FEFE) under several ATP concentrations in the range from 100 μM to 2 mM with recording at the video rate.

At [ATP] = 2 mM, a single metal bead attached to the central shaft (Fig. 3 A right) typically showed continuous stepwise rotation at a rotation rate 0.046 ± 0.019 rps (n = 8, mean ± SD), which is roughly one third of the bulk-phase V_max value of ATPase (0.15 s⁻¹, Table 1), being consistent with the three-fold symmetry of the catalytic subunits. These comparable values support the idea that the rotation speed was determined mostly by the ATP-independent rate-limiting step at this high ATP concentration. The traces at 2 mM ATP showed three sets of short and long pauses arranged alternately with 80° and 40° intervals per revolution (inset in Fig. 3 B). Each long pause before 40° step (open arrowheads in Fig. 3 B) was expected to be the catalytic dwell in analogy to the rotation patterns of F₁(βE190D) mutant (9).

To investigate it, we made dwell time analyses of the long pause. The single-exponential fits to the histograms of pausing duration (Fig. S4 right) revealed an almost unchanged time constant of 5–6 s independent from ATP concentration down to 100 μM ATP condition (open magenta squares in Fig. 6 D). In addition, it was consistent with the V_max estimated from bulk-phase ATPase (Table 1 and Fig. 2, 1/0.15 s⁻¹ = 6.7 s). Therefore, this pause is most likely the catalytic dwell. Specifically, it corresponds to the ATP-cleavage event because E190D mutation is known to slow down this process by 100-fold compared to that of the wild-type, whereas the effect on the Pi release event is one order smaller (9).

The other short pauses before 80° substep (solid arrowheads in Fig. 3 B) supposedly correspond to ATP-waiting dwell because duration of these pauses was clearly dependent on ATP concentration (solid magenta circles in Fig. 6 D). In the case of 2 mM ATP, the ATP-waiting dwell estimated from single-molecule dwell time analyses (Fig. S4 left) was 0.6 s (Fig. 6 D), which was in good agreement with 0.7 s, the inverse of {0.15 s⁻¹/(210 × 10⁻⁶ M)}× (2 × 10⁻³ M), calculated with k_on from bulk-phase measurements. Note here that, unlike the wild-type F₁, ATP-waiting dwells are still detectable at 2 mM ATP even under the time resolution of 33 ms, albeit less evident than ATP-cleavage dwells.

In the case of 0.2 mM ATP, ATP-waiting dwells (solid arrowheads) were much more apparent (Fig. 3 C) and became comparable to the catalytic dwells (open arrowheads). The time constant of ATP-waiting dwell was estimated to be 2.9 s at 0.2 mM ATP according to the rotation assay (Fig. 6 D). Meanwhile, it was 7.0 s, the inverse of {0.15 s⁻¹/(210 × 10⁻⁶ M)} × (200 × 10⁻⁶ M), according to the bulk-phase ATPase measurements (Fig. 2 and Table 1), being longer but roughly comparable to the single-molecule result (Fig. 6 D). Similarly in the previous studies, dwell times calculated from bulk-phase measurements sometimes tend to be slightly longer than those from the single-molecule assays (8). This tendency possibly arises from the following reasons under low ATP concentration conditions: increased chances of inactivation of the enzyme due to ADP inhibition even with LDAO, and a matter of precision due to inevitable small slopes of absorbance observed in the time course of ATP-regenerating system.

In summary, the new mutant β that we here designed successfully enabled detection of binding and cleavage events of ATP even at the video rate (30 frames per second) because both elementary chemical steps were distinctively slowed down by the combination of the β(FEFE) and β(E190D) mutations.

Rotation of 1× and 2× β(E190D/FEFE) hybrids

Next, we prepared hybrid F₁s, in which one or two out of three βs of the wild-type F₁ was replaced by β(E190D/FEFE). In line with the strategy argued in the Introduction section and Fig. 1 B, we tried to designate the ATP-cleavage angle through stepping trajectories of markers. Observed rotations were mostly with two pauses indicating 1×β(E190D/FEFE) hybrid (exemplified by Fig. 5 A–C and D–F) and, in rare cases, four pauses indicating 2×β(E190D/FEFE) hybrid (exemplified by Fig. 4 A–C).

Figure 5.

Rotation of hybrid 1×β(E190D/FEFE) F₁s.

For a Figure360 author presentation of Figure 5, see https://doi.org/10.1016/j.bpj.2022.12.027.

Solid and open arrowheads represent ATP-waiting dwells and catalytic dwells, respectively, in each graph. (A–C) Rotation of 1×β(E190D/FEFE) hybrid at 1 mM ATP. (D–F) Rotation of 1×β(E190D/FEFE) hybrid at 0.1 mM ATP. (A, B, and D, E) Time courses of rotation of metal bead probes. (B) and (E) are enlarged graphs from (A) and (D) respectively. Grids indicate 80° and 40°. The insets in (A) and (D) are corresponding traces of centroid positions. Scale bars, 100 nm. (C and F) Histograms of angle distributions. Fits to these traces with multiple Gaussian function gave angle differences between dwells: 192° and 196° for 1 mM ATP (C) and 0.1 mM ATP (F), respectively.

Figure 4.

Rotation of a hybrid 2×β(E190D/FEFE) F₁ at 0.2 mM ATP. Solid and open arrowheads represent ATP-waiting dwells and catalytic dwells, respectively. Combinations of dwells were distinguished by different colors (blue and green). (A, B) Time courses of rotation of metal bead probes. (B) is an enlarged graph from (A). Grids indicate 80° and 40°. The inset in (A) is the trace of Gaussian center of bead images. Scale bar, 100 nm. (C) Histogram of angle distribution. A fit with multiple Gaussian function gave angle differences between dwells: 70°, 122°, 39°, and 129° from the blue arrowhead.

In the four-pause cases, the center of rotation was clearly identified even by eye because the circle that suffices four points is unique (a green dotted circle in the inset in Fig. 4 A). The angle of four pauses in this example roughly corresponded to 0°, 80°, 200°, and 240° (measuring from the solid blue arrowheads in Fig. 4 A–C), which were equivalent to the combinations of 0°(solid green arrowhead) with 200°(open green arrowhead) and 120°(solid blue arrowhead) with 320°(open blue arrowhead) (Fig. 4 A–C). Our interpretation of this kind of rotation trajectories (also exemplified in Figs. S1 and S2) is that the observed F₁ is a 2×β(E190D/FEFE) hybrid (Fig. 6 B). The above combinations directly indicated that each mutant β is responsible for two pauses that are 200° apart (two pairs of open and solid arrowheads in blue or green, Fig. 4 A–C), and two pairs are arranged with 120° shift (Fig. 6 B), being consistent with three-fold symmetry of β. These 2×β(E190D/FEFE) hybrids were rare cases probably due to a smaller chance of incorporating two mutant βs simultaneously into a molecule. Therefore, the number of dwells applied to the dwell time analyses from each molecule was smaller than that of nonhybrid 3×β(E190D/FEFE) (see the legend of Fig. S5 A for details). Still, the tendency of having long (>3 s) and short dwell times was similar to nonhybrid 3×β(E190D/FEFE), and dependence of the short dwell on ATP concentration is consistent with that of nonhybrid 3×β(E190D/FEFE) (Fig. 6 D).

In the two-pause cases, we noticed that determination of rotation center requires additional geometric information (Fig. S3 B). It was met by recording with a high-speed camera (250 or 1000 frames per second), which facilitated tracking of beads with larger numbers of data points (inset in Fig. 5 A and D). As a result, points during steps showed circular trajectories, and two pauses (long and short) remained highlighted as dense dots (see also Fig. S3 D for the case of large beads).

Being consistent with the four-pause cases (Fig. 4 C), the two pausing angles were 200° apart (from solid to open blue arrowheads across 360° line in Fig. 5 C and F). (For precise determination of angles, see Fig. S3.) It indicated that only one β(E190D/FEFE) was introduced into these molecules. We also made dwell time analyses. The time constants of the 0° dwell showed clear ATP dependence, and they were 2.0 ± 0.1 s at 100 μM ATP and 0.64 ± 0.03 s at 1 mM ATP (coefficient values ± 1 SD, solid blue circles in Fig. 6 D). This is a strong piece of evidence that these angles are assigned to the ATP-waiting dwell. The other dwell at 200° showed comparable time constants 4.0 ± 0.0 s and 3.7 ± 0.1 s for 100 μM and 1 mM ATP, respectively (coefficient values ± 1 SD, open blue squares in Fig. 6 D). These values were close to ATP-independent dwell times of the catalytic dwell (∼5 s) observed in the case of nonhybrid 3×β(E190D/FEFE) (open magenta squares, Fig. 6 D). From these analyses, the ATP cleavage in the mutant β indeed occurs at 200° subsequent to binding of ATP at 0°

Taken together, from the results of four-pause and two-pause rotation of hybrid F₁s, we conclude that the shaft angle at which ATP cleavage occurs in the case of F₁ from thermophilic Bacillus PS3 is angle 200°. This conclusion is consequently consistent with previous suggestions (11,12,13) and other models of the rotation mechanism dependent on β(E190D) hybrid assays (13,16,18,23).

Discussion

In our previous study using fluorescently labeled ATP in rotation assays (11), we have suggested the catalytic angle of the shaft is “angle 200°,” based on the reference angle 0° where the same β is empty. The mutant, F₁(βG181A/T165S), exhibited three-step rotations at a low concentration of ATP as in the case of the wild-type under the time resolution of 33 ms. However, unexpectedly, the mutant rotated with six pauses when 2′-O-Cy3-EDA-ATP (labeled ATP) was the substrate. Through simultaneous visualization of rotational substeps and 2′-O-Cy3-EDA-ATP kinetics at the single molecular level, we deduced that the additional pause corresponds to “angle 200°.” The origin of the pause is indirectly assumed to be the dwell that waits for the cleavage of labeled ATP due to the following three reasons: 1) “Angle 0°” is the position of the dwell that waits for the binding of ATP (8,11). 2) The release of labeled ADP occurs at “angle 240°” (Figs. 2, 3, and S4 in Nishizaka et al. (11)). 3) The release rate of inorganic phosphate is expected to be unaltered regardless of the adenosine moiety of the nucleotide (unlabeled or labeled ATP). Note that candidates of the chemical reaction step that cause pauses of rotation are limited to only four elements: ATP binding, ATP cleavage, ADP release, and P_i release. As three of them are excluded by the above arguments, the only reaction that may govern “angle 200°” is the cleavage, if we accept the premise that the fluorophore attached to the ribose does not affect the release of P_i.

In later studies, the 200°-cleavage model was further supported by different experiments. In terms of 2), high-speed imaging and slow forced rotation with magnetic tweezers revealed release of 2′-O-Cy3-EDA-ADP at 240° (10,14). In addition, the release of unlabeled ADP was detected in between angle 285° and 300° in the case of another bacterium, E. coli (24). In terms of 3), Pi release tend to occur at 320° rather than 200° (25,26,27). Even though these results were consistent with the above logic, the cleavage angle was still indicated only indirectly by a method of elimination.

Another contribution had sought for the cleavage angle of unlabeled ATP by rather introducing mutations into F₁ (13). A β(E190D) subunit was introduced into the wild-type F₁ by subunit exchange, and multiple pauses during rotation were found for the resultant hybrid F₁. The dwell time of one of the pauses was 300 ms, which was consistent with that of the catalytic dwell for previous β(E190D) (9). In addition, the rate constant of ATP binding to the catalytic site of β(E190D) had been judged to be 10 times smaller than that of the wild-type, being consistent with previous bulk-phase ATPase measurements (9) and another contribution (28). The angle difference of these two prolonged dwells was 200°. Thus the angle of ATP cleavage was judged to be 200° (13). However, later it was found that F₁(βE190D) has a temperature-sensitive dwell (TS dwell) (18) that is about 100 ms in the case of β(E190D) at 24°C (calculation based on Enoki et al. (18)). If we take this observation into account, the major component of the long pause (80 ms) at 0° under 2 μM condition in Ariga et al. (13) can be interpreted as an unintentionally included TS dwell (18) rather than ATP-waiting dwell. A similar discussion was made for the indistinguishable TS dwell included in pre-P_i release dwell (26). Furthermore, other single-molecule studies using hybrid F₁s left the possibility that E190D mutation does not slow down the ATP-binding rate under specific conditions (Fig. 3 in Okuno et al. (23) and Masaike et al. (16)). With these contradictions, “0° dwell” of β(E190D) cannot convincingly serve as a solid signature for the ATP-waiting angle. Therefore, neither the strategy of mutating the enzyme nor labeling the substrate could successfully provide a decisive answer to the question of ATP-cleavage angle.

In this study, we inherited the idea of identifying pausing angles (13) by introducing mutations to the enzyme. Combination of FEFE mutation with β(E190D) in the 1×β(E190D/FEFE) hybrid caused two long pauses clearly detected at different angles. The chemical states of these dwells were identified by dwell time analyses of pauses. The ATP-independent pause was in good agreement with the V_max from bulk-phase measurements, thus suggesting that this dwell corresponds to ATP cleavage. The other pause corresponds to ATP binding because duration of this pause is clearly dependent on ATP concentration. We noticed that the dependence was not precisely an inverse proportion to ATP concentration. It may result from contribution of a minor fraction of an ATP-independent dwell such as TS dwell mixed into this pause. Even if it is likely to be the case, clear ATP dependence guarantees ATP binding at this angle, and the conclusion drawn from this study is solid. Thus, the ATP-cleavage angle was finally determined to be 200° on the 360° basis.

It is noteworthy that k_on of the 1×β(E190D/FEFE) hybrid tends to be higher than that of the nonhybrid 3×(βE190D/FEFE) (Fig. 6 D). We may be able to hypothesize that the mutant β recovered affinity to ATP to some extent due to positive cooperativity arising from the other two wild-type βs. This hypothesis can explain the discrepancy found among k_ons of hybrid and nonhybrid 3×(βE190D) F₁s in some of the previous studies (9,16,23). It should be investigated elsewhere in future studies because intramolecular cooperativity of ATP binding as well as acceleration of turnover (29,30,31) between β subunits is an important question deeply involved in the binding change mechanism (32).

Structural studies also provided important insights into the chemomechanical coupling of F₁ from thermophilic Bacillus PS3. Recently determined structures of β(E190D) mutant in both catalytic and TS dwells by cryo-electron microscopy provided snapshots of chemical and conformational states of β in relation to direction of γ (27). In this model, the nucleotide bound to β_200° is ATP but not ADP. On the contrary, subsequent β_240° contains ADP and P_i. It suggests that the cleavage event occurs at 200° or later, and it is completed before 240°. These sequential chemical states deduced from structural studies are consistent with the results of the present single-molecule observation of rotating F₁ and thus support our conclusion.

In recent years, chemomechanical coupling schemes of F₁-ATPase from other species (Escherichia coli, human, yeast, bovine, and Paracoccus denitrificans) have also been studied albeit using nonhybrid F₁s on 120° basis rather than 360° basis (22,33,34,35,36). Based on the discussion complemented by crystal structures, they mostly support ∼200°-cleavage scheme. They seem to indicate that the timing of this event is fairly conserved among species. Nevertheless, single-molecule studies of Paracoccus denitrificans F₁ were an exception and found to have no substeps (36). This new finding indicated that the ATP cleavage at an interim catalytic dwell separated from ATP-waiting dwell is not a strict requirement for the rotation of F₁. Depending on the species, the ATP cleavage event in fact can occur at an ATP-waiting dwell of a different catalytic site.

V₁-ATPase, which is evolutionary related to F₁-ATPase, has also been studied by single-molecule observation. Thermus thermophilus V₁-ATPase was shown to rotate without substeps (37,38). On the contrary, Enterococcus hirae V₁-ATPase rotates with 40°-substeps (39) but still supports 240°-ATP cleavage according to crystal structures. These observations so far indicate that timing of ATP cleavage for V₁-ATPase may be similar to that of Paracoccus denitrificans F₁.

Taken together, ATP cleavage by F₁- and V₁-ATPases occur at an ATP-waiting or catalytic angle. Strict separation of the ATP-waiting angle and the cleavage angle found in the present study is not a universal mechanism across rotary motors. The fundamental feature common to rotary motors may be that ATP-cleavage event does not complete within the first main 120° step and is rather carried over to the next 120°. To achieve this, there must be a sophisticated underlying mechanism for tightly keeping a nucleotide at the catalytic site for a long period over two 120° steps. Thus a premature binding of ATP to the empty site due to incorrect early product release may be prevented by this mechanism.

In the case of linear motors, the situation is different from three-step rotary motors. For example, two-headed linear processive motors, myosin V (40,41,42) and kinesin-1 (43,44,45), undergo only two steps, but not three, to complete one turnover of ATP hydrolysis at a catalytic site. These motors cleave ATP during the first step after ATP binding. For example, in the case of myosin V, ATP binding to the trailing head triggers detachment of the same head from the actin filament. Cleavage of this ATP is completed before the end of the first stepping motion, i.e., binding to the actin filament as a leading head. In the case of kinesin-1, binding of ATP to the front head triggers the first step of the rear head. Cleavage of this ATP is completed before binding of the rear head to a front position of the microtubule. In both cases, the timing of ATP cleavage corresponds to the first 120° if applied to rotary motors.

From a different viewpoint, rotary motors share a common mechanism with linear motors in which ATP cleavage occurs during the second-to-last step. ATP cleavage and product release events must be seamlessly completed within two steps to prevent improper nucleotide release. Nevertheless, retention of uncleaved ATP until at least the middle of the second step (200° or 240°) after its binding is a unique requirement of three-step rotary motors. It is directly linked to the tri-site binding-change mechanism (46) of rotary motors.

In living organisms, this motor exists as a reversible holoenzyme motor F_oF₁, and its key function in vivo is ATP synthesis. The ATP cleavage at 200° in counterclockwise rotation indicates that ATP synthesis occurs at 160° in clockwise rotation after initiation of ATP synthesis reaction (defining the angle of ATP release from the previous reaction as the starting angle 0°). If 80° cleavage model in the ATPase reaction were hypothesized, clockwise rotation of as much as 280° from starting angle 0° is required for the ATP synthesis event. It necessitates an extreme model that ADP is intact until the very final 80° without making a bond with inorganic phosphate. Indeed, the 200° cleavage that enables 160° synthesis must be an ideal angle for both directions of the reaction.

Conclusion

Here, we introduced the mutational set E190D/F414E/F420E into the β subunit. By the combination of mutations that cause slow ATP binding and cleavage rates, the new triple mutant β(E190D/F414E/F420E) enabled clear identification of both ATP-waiting and ATP-cleavage dwells on the 360° basis. Single-molecule rotation assay revealed that the ATP-cleavage dwell of this mutant appeared at 200° (Fig. 5 C, F and 6 C), which was consistent with the previous expectation. Thus, the present study finally resolved the long-standing controversy and truly established the connection between chemical reactions and rotary angles. Therefore, the previous discussions based on the 200°-cleavage scheme are also verified (15,16,17,18).

Data availability

The datasets analyzed during the current study are available from the corresponding authors on reasonable request.

Author Contributions

Y.H., M.S., T.M., and T.N. designed research; Y.H., F.A., A.T., K.S., N.T., and H.U. performed single-molecule assays; Y.H., M.S., Y.N., F.A., A.T., N.T., and H.Y. contributed to sample preparation; Y.H., M.S., F.A., A.T., K.S., H.U., H.Y., R.Y., and T.M. contributed to data analyses; T. M. and T.N. constructed the microscope; T.N. wrote the macro for the analysis; Y.H., T.M., and T.N. wrote the manuscript.

Editor: Jonathon Howard