Introduction

Two types of rotary ATPases are present in various cellular membranes: V-ATPases and F-ATPases (Forgac 2007; Yokoyama and Imamura 2005; Yoshida et al. 2001). They couple both ATP synthesis and hydrolysis to proton translocation across the membrane by rotation of the rotary shaft in the catalytic hexamer ring (Fig. 1a). Overall, these ATPases possess a similar structure composed of a water-soluble domain (V1 and F1) and a membrane-embedded domain (Vo and F0). Both domains can act as rotary motor proteins (Yoshida et al. 2001; Imamura et al. 2003).

The rotational catalysis of F1 has been investigated in detail (Okuno et al. 2011). The minimal functional unit of F1, which acts as the ATP-driven motor, is \(\alpha _3\beta _3\gamma\) (Fig. 1a, left). The rotary shaft \(\gamma\)-subunit comprises a coiled-coil domain, and rotates in the central cavity of the \(\alpha _3\beta _3\) ring by hydrolyzing ATP (Noji et al. 1997). Three \(\beta\)-subunits undergo ATP hydrolysis, and the conformation of the \(\beta\)-subunits changes as the elementary chemical steps involved in ATP hydrolysis proceed. The push-pull motion of the C-terminal domains of the \(\beta\)-subunit produces torque for the rotation of the \(\gamma\)-subunit (Wang et al. 1998). The torque generation efficiency of F1, achieved by this push-pull motion, is nearly 100 %, far higher than other ATP-driven motors (Yasuda et al. 1998). The interaction between the globular domain of the \(\gamma\)-subunit and the C-terminal domain of the \(\beta\)-subunit plays a key role in reinforcing torque generation, and thus, in achieving this high efficiency (Usukura et al. 2012; Tanigawara et al. 2012). This interaction allows F1 to generate torque and to rotate in the correct direction even when the coiled-coil domain of the shaft is truncated, leaving only the globular domain (Furuike et al. 2008).

However, compared to F1, the rotary mechanisms of V1, including the mechanism of torque generation, have not yet been fully elucidated, and V\(_1\) has recently received increasing attention (Yokoyama and Imamura 2005; Kishikawa et al. 2013; Arai et al. 2013; Kishikawa et al. 2014; Nagamatsu et al. 2013). In V1 (Fig. 1a, right), the rotary shaft (DF subcomplex), which contains a coiled-coil domain and a globular domain, as found in the \(\gamma\)-subunit of F1, is thought to be a structural analog of the \(\gamma\)-subunit. The globular domain of the rotary shaft of V\(_1\) is comprised of the F-subunit (Fig. 1b, blue) and the loop region of the D-subunit (Fig. 1b, red). In the present paper, we performed single-molecule experiments on V\(_1\) to investigate how the absence of the globular domain of the rotary shaft in V1 affects torque generation. First, we investigated a mutant in which the F-subunit had been deleted, A3B3D, which was reported to be the minimal rotary unit of V\(_1\), as the ATP-driven motor (Imamura et al. 2004). Our single-molecule experiments showed that with a low ATP concentration, A3B3D rotated stepwise every 120° accompanied by a single ATP hydrolysis, and exhibited frequent 120° backward steps, which were seldom observed in the rotation of V\(_1\). These backward steps were hypothesized to be caused by the absence of the F-subunit. To quantitate the effect of the absence of the F-subunit, we measured the torque of A3B3D by applying the fluctuation theorem (see Sect. 2.3), which is based on non-equilibrium statistical mechanics, and has recently been used to measure the torque of rotary motors (Usukura et al. 2012; Tanigawara et al. 2012; Hayashi et al. 2010, 2012; Hayashi and Hayashi 2012; Kim et al. 2011). We observed that A3B3D produced half the torque produced by V\(_1\). This result indicates that the interaction between the hexamer ring and the globular domain of the shaft is important to generate full torque. Further, we created a mutant, A3B3D\(_\mathrm{\Delta loop}\), in which the loop region of the D-subunit (Fig. 1b, red) was deleted in addition to the F-subunit. The torque generated by A3B3D\(_\mathrm{\Delta loop}\) did not differ from that generated by A3B3D within the error margin of our experiments. Although the loop region of the D-subunit is also part of the globular domain of the rotary shaft, the region seems not to play an important role in torque generation, unlike the F-subunit. Finally, we constructed an expression vector for A3B3DFf, containing a fusion of the genes coding for the D-subunit and the F-subunit, to mimic the \(\gamma\)-subunit of F1. We observed that A3B3DFf generated as much torque as the wild-type V1. This result is consistent with a previous report on the evolutionary relationship between the F-subunit of V1 and the globular domain of the \(\gamma\)-subunit (Kishikawa et al. 2013).

Fig. 1
figure 1

a The schematics of F0F1 (left) and VoV1 (right). b The structures of the rotary shafts of F1 (top, PDB:1H8E) and V1 (bottom, PDB:3W3A). The \(\alpha\), \(\beta\), \(\varepsilon\) and the globular domain of the \(\gamma\)-subunit are represented in red, red, green, and yellow, respectively in the case of F1. The A, B, D, F, and D-loop, and the C-terminal domain of the F-subunit are represented in green, green, gray, blue, red, and aqua, respectively in the case of V1. The globular domain of the rotary shaft consists of the F-subunit and the D-loop

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Material and methods

Preparation of proteins

All mutant V1 were constructed using a T. thermophilus His-tagged V1 (A3B3DF) expression plasmid (A\(_\mathrm{(His-8 /C28S/S232A/T235S/C255A/C508A)3}\) B\(_\mathrm{(C264S)3}\)D\(_\mathrm{(E48C/Q55C)}\)F), as described in the Supplementary Material (Fig. S1). V1 and the V1 mutants were expressed in Escherichia coli cells. The E. coli cells were suspended in 100 mM sodium phosphate (pH 8.0), 200 mM NaCl, and 20 mM Imidazole, and disrupted by sonication, followed by heat treatment at 65 °C for 30 min. Following the removal of denatured E. coli proteins by centrifugation at 19,000×g for 60 min, the supernatant was subjected to Ni2+-affinity chromatography (Qiagen) followed by ion exchange on a RESOURCE Q column (GE Healthcare). Purified samples were stored at 4 °C until use. The purified His-tagged enzymes were biotinylated at the two cysteines of the D-subunit with a five-fold molar excess of 6-{\(N\)′-[2-(\(N\)-maleimide)ethyl]-\(N\)-piperazinylamide}hexyl-D-biotinamide (Dojindo, Kumamoto, Japan) in 20 mM MOPS-KOH (pH 7.0) containing 100 mM KCl. After a 60-min incubation at 25 °C, the proteins were separated from the unbound reagent on a Superdex HR200 column equilibrated with 20 mM MOPS-NaOH (pH 7.0), containing 150 mM NaCl. The bound ADP in each enzyme was partially removed by successive EDTA-heat treatments.

Preparation of beads and rotation assay

The streptavidin-coated magnetic beads (100–300 nm) and the Ni2+-NTA coated cover glass depicted in Fig. 2a were prepared as follows (Okuno et al. 2011). Because asymmetric-shaped beads are suitable for clear observation of the rotation of the motors, the magnetic beads were sonicated to produce asymmetric-shaped beads. Bead size had a broad distribution (100–300 nm).

Each flow cell (5–10 μl) was composed of two coverslips: a Ni2+-NTA coated coverslip on the bottom (24 × 36 mm2) and an untreated coverslip on the top (24 × 24 mm2) separated by two spacers of 50-μm thickness (Fig. 2a). The biotinylated V1 (or the V1 mutants) (1–5 nM) in buffer A (50 mM Tris-Cl, pH 8.0, 100 mM KCl, and 2 mM MgCl2) was applied to the flow cell and incubated for a few minutes at room temperature. Unbound enzymes were removed by washing with 20 μl of buffer A. Then, 20 μl of buffer A with 2 mg/ml BSA was infused into the flow cell and incubated for 30 s to prevent nonspecific binding. The BSA solution in the flow cell was removed by washing with 20 μl of buffer A. Then, buffer A containing the streptavidin-coated magnetic beads (107 particles/ml) was infused into the flow cell and incubated for a few minutes. Unbound beads were removed by washing with 20 μl of buffer A. Following the infusion of 80 μl of buffer A containing Mg-ATP at the indicated concentration (2 mM MgCl2, 2.5 mM phosphoenol pyruvate, and 0.5 mg/ml pyruvate kinase), the rotation of a magnetic bead attached to a motor was recorded using a high-speed camera (Eclips, IN) at 1,000 frames per second (fps) using a phase-constant microscope (IX70, Olympus) with an −100 objective lens (N.A., 1.30, Olympus). Images were captured as a 32-bit AVI file. The centroid of the bead images was calculated.

Fig. 2
figure 2

a Schematic of the experimental setup (see Sect. 2.2 for details). b Rotary angle \(\theta (t)\) plotted as a function of time for V1 (red), A\(_3\)B\(_3\)D (blue), and A\(_3\)B\(_3\)DF\(_\mathrm{f}\) (green). The recording rate was 1,000 fps. c Ten trajectories of \(\theta (t)\) during a 120° step were superposed to investigate angular velocities. The thick lines (black) show the averages over 10 trajectories. The slopes of the graphs correspond to the angular velocities

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Torque measurement method based on the fluctuation theorem

In our single-molecule experiments, the rotary torque was measured using the fluctuation theorem. The fluctuation theorem, which presents the statistical properties of entropy production in a small, non-equilibrium system, was first proposed in 1993 (Evans et al. 1993) [See Ref. (Ciliberto et al. 2010) for a review of the fluctuation theorem]. Recently, the fluctuation theorem has been suggested as a new method to measure the torque of rotary motor proteins (Usukura et al. 2012; Tanigawara et al. 2012; Hayashi et al. 2010, 2012; Hayashi and Hayashi 2012; Kim et al. 2011). In the present paper, we applied the theorem to measure the rotary torque of V\(_1\) and its mutants.

In previous studies (Yasuda et al. 1998; Noji et al. 2001; Yasuda et al. 2001; Pänke et al. 2001), the rotary torque of a rotary motor, \(N\), was estimated using the equation \(N=\Gamma \omega\) where \(\Gamma\) and \(\omega\) are the friction coefficient and mean angular velocity of a probe (e.g., a bead) attached to the rotary motor. Using fluid mechanics calculations, the functional forms of \(\Gamma\) were derived under the assumption that the rotation of the probe occurs in bulk. This results in inaccuracy when estimating \(\Gamma\) for single-molecule experiments using rotary motors. Because a rotary motor is attached to a glass slide and rotates the probe near the glass surface, the interaction between the probe and the glass causes the value of the friction coefficient estimated using fluid mechanics to differ from the actual value. In addition, in single-molecule experiments, probe sizes are sometimes distributed and their exact shapes are unknown (see Sect. 2.3 for the preparation of beads). To overcome this difficulty in estimating the friction coefficient of a probe, we use the fluctuation theorem, which aids in estimating \(N\) without using the value of \(\Gamma\).

For a continuous rotation during a 120° forward step (as highlighted in black in Fig. 3a, b), assuming that the effect of inertia is small in the case of a probe attached to a rotary motor (see the experimental setup depicted in Fig. 2a), the time evolution of \(\theta (t)\) is described by an over-damped Langevin equation

$$\begin{aligned} \Gamma \frac{d\theta }{dt}=N+\xi (t),\quad\left\langle \xi (t)\xi (t')\right\rangle =2\Gamma k_\mathrm{B}T \delta (t-t'), \end{aligned}$$
(1)

where \(\xi\) is a random force that represents the effect of thermal noise, \(k_\mathrm{B}\) is the Boltzmann constant, and \(T\) is the room temperature. We also assumed that \(N\) is constant, as has been suggested in previous studies (Yasuda et al. 1998; Noji et al. 2001; Yasuda et al. 2001; Pänke et al. 2001). On the basis of the above model, the fluctuation theorem for torque measurement is expressed as

$$\begin{aligned} \ln [P(\Delta \theta )/P(-\Delta \theta )]=N\Delta \theta /k_\mathrm{B}T, \end{aligned}$$
(2)

where \(\Delta \theta =\theta (t+\Delta t)-\theta (t)\) and \(P(\Delta \theta )\) are the probability distribution of \(\Delta \theta\) (See Ref. (Hayashi et al. 2012) for the derivation of Eq. 2).

Results

Fig. 3
figure 3

The rotary angles \(\theta (t)\) were plotted as a function of time for V1 (a, top) and A3B3D (b, top) (the recording rate was 1,000 fps). From the probability distribution \(P(\Delta \theta )\) , where \(\Delta \theta =\theta (t+\Delta t)-\theta (t)\) (a, b, bottom, left), the torque was calculated using the fluctuation theorem Eq. 2 that states \(N=k_\mathrm{B}T\ln [P(\Delta \theta )/P(-\Delta \theta )]/\Delta \theta\) (a, b, bottom, right) (See Supplementary Material for the detailed calculation). Each case is represented by a color: \(\Delta t=2\) ms (red), \(\Delta t=4\) ms (blue), \(\Delta t=6\) ms (green), \(\Delta t=8\) ms (yellow), and \(\Delta t=10\) ms (aqua). c Torque plotted as a function of \(\Delta t\) for V1 (red), A3B3D (blue), and A3B3DF\(_f\) (green). The error bars represent the standard deviations

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Backward step and angular velocity

From the centroid of the bead attached to V1, the rotary angle, \(\theta\), of the bead was calculated as a function of time. At a low ATP concentration (10 μM), V1 rotated stepwise, pausing every 120° (Fig. 2b, red). Next, to elucidate the role of the globular domain of the rotary shaft, which is comprised of the F-subunit (Fig. 1b, blue) and the loop region of the D-subunit (Fig. 1b, red), the F-subunit deletion mutant, A3B3D, was investigated first. For A3B3D, we observed rotation (Fig. 2b, blue), but it often exhibited frequent 120° backward steps (Fig. 2b, inset), which were seldom observed in the rotation of the wild type V1. The frequency of 120° backward steps for V1 and A3B3D is summarized in Table 1. In Fig. 2c, the angular velocities of V1 and A3B3D are shown; we observed that the angular velocity of A3B3D was significantly lower than that of V\(_1\).

Table 1 The ratio of 120° backward steps to 120° forward steps
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Fig. 4
figure 4

Torque values obtained using Eq. 2 for V1 (top, left), A3B3D (middle, left), A3B3DF\(_\mathrm{f}\) (bottom, left), A3B3DF\(_\mathrm{\Delta Cterm}\) (top, right), and A3B3D\(_\mathrm{\Delta loop}\) (middle, right). Each case is represented by a different color: \(\Delta t=2\) ms (red), \(\Delta t=4\) ms (blue), \(\Delta t=6\) ms (green), \(\Delta t=8\) ms (yellow), and \(\Delta t=10\) ms (aqua). See the Supplementary Material for the torque values of all molecules (Table S1)

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Rotary torque

To measure the rotary torque of V1 and its mutants using the fluctuation theorem (Sect. 2.3), the probability distributions \(P(\Delta \theta )\) were calculated for \(\Delta t=2.0\)–10 ms, where \(\Delta \theta = \theta (t+\Delta t)-\theta (t)\) (Fig. 3a, b, bottom, left. See the Supplementary Material for the calculation). Using these values, \(P(\Delta \theta )\), \(\ln [P(\Delta \theta )\) \(/P(-\Delta \theta )]\) was plotted as a function of \(\Delta \theta /k_\mathrm{B}T\) (Fig. 3a, b, bottom, right). The slopes of the graphs in Fig. 3a, b (bottom, right) correspond to the rotary torque values, \(N\), according to Eq. 2. In Fig. 3c, it can be seen that \(N\) does not depend on \(\Delta t\) for 2 ms \(\le \Delta t\) within the error margins of our experiments. We regarded \(N\) in the case of \(\Delta t=10\) ms as the torque value of the motors (see Table S1 in the Supplementary Material for the torque values of all molecules). The torque value of the wild-type V1 was 29 \(\pm\) 4.4 (mean \(\pm\) standard deviation) pNnm, which is consistent with previous studies (Hayashi et al. 2010; Imamura et al. 2005). For the F-subunit deletion mutant A3B3D, the torque value was estimated to be 18 \(\pm\) 5.8 pNnm; this value was significantly lower than that of V1. This indicates that the torque generation of V1 was weakened by the absence of the F-subunit.

To elucidate which part of the F-subunit is most important for reinforcing torque generation, we further investigated the mutant (A3B3DF\(_\mathrm{\Delta Cterm}\)) in which the C-terminal helix of the F subunit (Fig. 1b, aqua) was deleted. Note that a previous single-molecule study (Imamura et al. 2004) and a recent structure study (Arai et al. 2013) noted the importance of the interaction between the C-terminal helix of the F-subunit and the A3B3 ring for torque generation. For A3B3DF\(_\mathrm{\Delta Cterm}\), we obtained a low torque value (14 \(\pm\) 2.8 pNnm), which is similar to that of the F-subunit deletion mutant A3B3D. The similarity of these values suggests that the lack of the interaction between the C-terminal helix of the F-subunit and the A3B3 ring most strongly influences torque generation.

Further, when the loop region of the D-subunit (Fig. 1b, red), which is also part of the globular domain of the rotary shaft, was deleted (A3B3D\(_\mathrm{\Delta loop}\)) in addition to the F-subunit (i.e., the globular domain of the rotary shaft was fully removed in A3B3D\(_\mathrm{\Delta loop}\)), we found that the torque value of A3B3D\(_\mathrm{\Delta loop}\) was 16 \(\pm\) 3.7 pNnm. The fact that the torque value of A3B3D\(_\mathrm{\Delta loop}\) did not differ from that of A3B3D indicates that the absence of the loop region did not strongly affect torque generation, whereas the absence of the F-subunit did. The role of the loop region of the D-subunit may be to combine the D-subunit with the F-subunit. The rotary torque measurements for V1 and the V1 mutants are summarized in Fig. 4.

Fused rotary shaft

The rotary shaft, \(\gamma\)-subunit of F1, contains both helical and globular domains. In contrast, in V1, these two domains are comprised of two separate subunits, the D-subunit and the F-subunit. Noting that our recent report suggested an evolutionary relationship between the F-subunit of V1 and the globular domain of \(\gamma\)-subunit of F1 (Kishikawa et al. 2013), we constructed an expression vector for A3B3DF\(_\mathrm{f}\) containing a fusion of the genes coding for the subunits D and F to mimic \(\gamma\)-subunit of F1, which is a more advanced shaft. In this V1 mutant, the F-subunit appeared artificially in the middle of the D-subunit (DF\(_\mathrm{f}\) complex). Using a bulk assay, we observed that the ATPase activity of A3B3DF\(_\mathrm{f}\) was almost identical to that of the wild-type V1 (Kishikawa et al. 2013). We also measured the torque of A3B3DF\(_\mathrm{f}\), which was not measured in the previous study (Kishikawa et al. 2013). We found that A3B3DF\(_\mathrm{f}\) exhibited high torque (30 \(\pm\) 6.0 pNnm), as was observed in V1 (Fig. 4, bottom). In addition, we seldom observed 120° backward steps in A3B3DF\(_\mathrm{f}\) (Table 1). These results, combined with the previously reported results (Kishikawa et al. 2013), indicate that the DF\(_\mathrm{f}\) subunits function as a complete rotary shaft with respect to ATP-hydrolysis-driven torque generation.

Conclusion

In this study, we quantitatively investigated the importance of the globular domain of a rotary shaft from the viewpoint of ATP-hydrolysis-driven torque generation. Although a study of the crystal structure of V1 (Arai et al. 2013) reported the possibility that the globular domain of the rotary shaft interacts with the A3B3 ring, the prediction was not quantitative. Our torque measurements made it clear that the effect of deleting the globular domain of the rotary shaft decreased torque by half. This degree of change is similar to that observed in F1, in which the absence of the interaction between the rotary shaft and the ring also weakened torque generation (Usukura et al. 2012; Tanigawara et al. 2012).

In wild-type V1, the globular domain of the rotary shaft is comprised of the F-subunit (Fig. 1b, blue) and the loop region of the D-subunit (Fig. 1b, red). First, we investigated an F-subunit deletion mutant, A3B3D. A3B3D often exhibited 120° backward steps (Fig. 2b; Table 1) and exerted half the torque of the wild-type V1 (Fig. 3). The torque values observed for A3B3DF\(_\mathrm{\Delta Cterm},\) in which the C-terminal helix of the F-subunit was deleted, were similar to the value observed for A3B3D (Fig. 4). Based on these results, the F-subunit, particularly its C-terminal domain, plays an important role in the exertion of full torque. However, the loop region of the D-subunit, which is also part of the globular domain of the rotary shaft (Fig. 1b, red), is not significant for torque generation; the torque generated by A3B3D\(_\mathrm{\Delta loop}\), in which the loop region was also deleted from A3B3D, was identical to that generated by A3B3D (Fig. 4, middle, right).

In A3B3DF\(_\mathrm{f}\), in which the F-subunit was genetically fused with the D-subunit to mimic the \(\gamma\)-subunit of F1, the rotary shaft DF\(_\mathrm{f}\) was found to retain full function as a rotary shaft, in terms of torque generation (Fig. 4, bottom, left; Table 1). However, the V\(_\mathrm{o}\) and A3B3DF\(_\mathrm{f}\) complex is known to be unable to synthesize ATP (data not shown), which indicates that in this complex, the torque is not fully transmitted from V\(_\mathrm{o}\) to A3B3DF\(_\mathrm{f}\). Because the main part of the globular domain of the F-subunit appeared artificially in the middle of the D-subunit in the rotary shaft DF\(_\mathrm{f}\), the function of this globular domain may differ from the original, particularly with respect to torque transmission. This indicates that the original globular domain of the rotary shaft is important to reinforce torque transmission, as well as torque generation. The role of the globular domain should be quantitatively investigated in future, from the viewpoint of torque transmission between V\(_\mathrm{o}\) and V1.

In the present study, we computed the rotary torque of V1 using the fluctuation theorem. This method for torque measurement, based on non-equilibrium statistical mechanics, has been actively applied to single-molecule experiments on rotary motors (Usukura et al. 2012; Tanigawara et al. 2012; Hayashi et al. 2010, 2012; Hayashi and Hayashi 2012; Kim et al. 2011). The theorem enabled us to measure the rotary torque of V1 without determining the value of the friction coefficient of the rotary probe (Sect. 2.3). Although our rotary probes (sonicated beads) were useful to visualize the rotary motion of the motors, because they were irregularly shaped, their friction coefficients could not be theoretically calculated using fluid mechanics (Hayashi et al. 2010). Because it is difficult to precisely measure friction coefficients in both in-vitro (Harada et al. 2001) and in-vivo (Hayashi et al. 2013) single-molecule experiments, it is important to broaden the applicability of the theorem to a wide range of biological motors to measure their force and torque. We hope that application of new relations of non-equilibrium statistical mechanics on non-equilibrium fluctuation (Hayashi et al. 2013; Mizuno et al. 2007; Toyabe et al. 2010; Liphardt et al. 2002; Collin et al. 2005; Alemany et al. 2012) will facilitate a better understanding of the mechanisms of biological motors, and that the present study contributes to this effort.