Torque Transmission Mechanism via DELSEED Loop of F₁-ATPase

Abstract

F₁-ATPase (F₁) is an ATP-driven rotary motor in which the three catalytic β subunits in the stator ring sequentially induce the unidirectional rotation of the rotary γ subunit. Many lines of evidence have revealed open-to-closed conformational transitions in the β subunit that swing the C-terminal domain inward. This conformational transition causes a C-terminal protruding loop with conserved sequence DELSEED to push the γ subunit. Previous work, where all residues of DELSEED were substituted with glycine to disrupt the specific interaction with γ and introduce conformational flexibility, showed that F₁ still rotated, but that the torque was halved, indicating a remarkable impact on torque transmission. In this study, we conducted a stall-and-release experiment on F₁ with a glycine-substituted DELSEED loop to investigate the impact of the glycine substitution on torque transmission upon ATP binding and ATP hydrolysis. The mutant F₁ showed a significantly reduced angle-dependent change in ATP affinity, whereas there was no change in the equilibrium for ATP hydrolysis. These findings indicate that the DELSEED loop is predominantly responsible for torque transmission upon ATP binding but not for that upon ATP hydrolysis.

Introduction

F_OF₁ ATP synthase catalyzes the terminal reaction of oxidative phosphorylation, ATP synthesis from ADP and inorganic phosphate (P_i), using the electrochemical potential of protons (or sodium in some organisms) across the mitochondrial inner membrane, the chloroplast thylakoid membrane, and the bacterial plasma membrane (1–5). F_OF₁ ATP synthase is structurally and functionally separated into two distinct parts, F₁ and F_O. F₁ is the water-soluble portion of ATP synthase responsible for catalysis. When isolated from the membrane domain, F₁ exhibits strong ATP hydrolysis activity. F₁ is an ATP-driven rotary motor in which the rotary shaft rotates against the surrounding stator upon ATP hydrolysis. F_O is also a rotary motor driven by proton flow down the electrochemical potential of the proton gradient (6,7). F_O and F₁ are connected by a shared rotary shaft and a peripheral stalk that transmit their competing rotary torques. Under physiological conditions with sufficient electrochemical potential, F_O generates greater torque than F₁ and enforces rotation of F₁ in the reverse direction to drive the reverse chemical reaction of ATP hydrolysis, ATP synthesis. When the proton electrochemical potential diminishes, F₁ reverses direction and rotates F_O to reestablish the proton electrochemical potential.

The subunit composition of bacterial F₁ is α₃β₃γδε. The minimum complex of F₁ as a rotary motor is the α₃β₃γ subcomplex (referred to here as F₁ for simplicity). Three α and three β subunits form the α₃β₃ stator ring with a central cavity that accommodates the central rotary shaft, γ. The catalytic reaction centers for ATP hydrolysis/synthesis reside at the αβ interfaces, mainly on the β subunit (8–10).

The rotary dynamics of F₁ have been well studied in single-molecule rotation assays (11–13). The basic rotational properties of F₁ from thermophilic Bacillus PS3 (TF₁), the best-characterized F₁ in terms of rotational mechanism, are summarized below. F₁ exerts a constant torque of 40 pN·nm irrespective of rotary angle, as estimated from the hydrodynamic friction of a rotation marker attached to the γ subunit (14,15). Higher torque was reported for F₁ from Escherichia coli (EF₁) (16,17), although another group reported rather lower torque for EF₁ (18). Each rotational step is 120° (14), as expected from the pseudo-threefold symmetry of F₁. Each 120° step is coupled with hydrolysis of a single molecule of ATP. The work per ATP hydrolysis is thus estimated as 80 pN·nm (torque times step size). This value corresponds to the free-energy change for hydrolysis of one ATP molecule, suggesting an extremely high energy conversion efficiency of F₁. This point was later verified in an experiment in which constant external torque was applied to a rotating F₁ (19). The 120° step can be further resolved into 80° and 40° substeps (20,21) that differ significantly in other F₁ complexes (18,22). The 80° substep is triggered by ATP binding and ADP release, which occur on different β subunits (23–25). The 40° substep is initiated after hydrolysis of bound ATP and P_i release, which are also thought to occur on different β subunits (26–28). Hereafter, the angular positions of F₁ before the 80° and 40° substeps are referred to as the binding and catalytic angles, respectively. When the rotary angle for ATP binding to a certain β subunit is defined as 0°, ATP hydrolysis, ADP release, and P_i release occur at 200°, 240°, and 320°, respectively (Fig. 1 a) (29). Thus, each β subunit catalyzes a single turnover of ATP hydrolysis for one turn of the γ subunit, but the phase of the catalytic state differs by 120° among the three β subunits. Although most of the reaction scheme has been established based on the single-molecule rotation assay, some elements are controversial in biochemical and x-ray structural studies, especially regarding the order of product release (30,31).

Figure 1.

DELSEED loop mutants. (a) Chemomechanical coupling scheme of F₁ at low ATP concentration. The circles and red arrows represent the catalytic state of the β subunits and the angular positions of the γ subunit, respectively. One catalytic site (green) is shown undergoing the binding and catalytic events. The other two catalytic sites are undergoing the same events simultaneously, but offset by 120° and 240°. (b) Crystal structure of the γ subunit (red) and the β subunit in the empty state with (green) or without (gray) the glyloop mutation. (PDB ID 2JDI or 1BMF). The structure of the glyloop mutant was determined by molecular dynamics simulations (50). (c) Time courses of rotary motion in the presence of 1 mM ATP. Gray, red, and blue represent the time courses of F₁^WT, F₁^glyloop, and F₁^{glyloop/E190D}, respectively. The traces at left are a rescaled view of those at right. The data for F₁^glyloop and F₁^WT were measured byTanigawara et al. (50). (d) Rotational velocity (V) of F₁^glyloop (red), F₁^{glyloop/E190D} (blue), and F₁^WT (gray) at various ATP concentrations. The curves represent Michaelis-Menten fits with V = V_max[ATP]/([ATP]+K_m), where V_max^glyloop = 119 s⁻¹, V_max^{glyloop/E190D} = 0.43 s⁻¹, V_max^WT = 169 s⁻¹, K_m^glyloop = 23 μM, K_m^{glyloop/E190D} = 1.0 μM, and K_m^WT = 22 μM. The corresponding rate constants for ATP binding, k_on = 3 × V_max/K_m, are k_on^glyloop = 1.5 × 10⁷ M⁻¹·s⁻¹, k_on^{glyloop/E190D} = 1.2 × 10⁶ M⁻¹·s⁻¹, and k_on^WT = 2.6 × 10⁷ M⁻¹·s⁻¹. The data for F₁^glyloop and F₁^WT were measured by Tanigawara et al. (50). To see this figure in color, go online.

In early single-molecule studies, the contribution of each catalytic step to torque generation was estimated from the substep sizes induced by each reaction (20). More quantitative estimation was provided from a recent single-molecule manipulation experiment using stall and release, where paused F₁ waiting for a certain reaction step to occur was stalled with and released from magnetic tweezers (32,33). Because F₁ does not exert torque in the absence of its catalytic reaction, the probability of the reaction can be measured as the probability that F₁ rotates after release from the magnetic tweezers. This stall-and-release experiment determined the rate and equilibrium constants of ATP binding and ATP hydrolysis as functions of the rotary angle and showed that the affinity of F₁ for ATP significantly increases upon the counterclockwise rotation in the hydrolysis direction, whereas the equilibrium constant for ATP hydrolysis is relatively independent of angle. The estimated energy released for each step suggests that F₁ generates three- to fourfold higher torque through the affinity change for ATP than in the hydrolysis step (32,34).

Crystal structures of bovine mitochondrial F₁ (MF₁) provided essential structural insights into torque generation by the catalytic β subunits and torque transmission to the γ subunit. In the original reference structure (8) or the ground-state structure (35) that represent the common structural features shared among most other crystal structures of MF₁ or F₁ from other species (9,10), the three β subunits are termed β_TP, β_DP, and β_empty according to the bound nucleotide. β_TP is bound to an analog of ATP, β,γ-imido-triphosphate (AMP-PNP), β_DP is bound to ADP and azide, and β_empty has no nucleotide bound. Both β_TP and β_DP assume a closed conformation that rotates the C-terminal helical domain inward toward the rotational axis and enclosing the bound nucleotide, whereas β_empty has an open conformation (Fig. 1 b). The open-to-closed conformational transition of β in solution was measured by NMR (36) and single-molecule imaging (37). Although no significant conformational differences were identified between β_TP and β_DP, changes in the αβ interface were observed: the αβ_DP interface is more tightly closed than the αβ_TP interface. Because tight packing of the αβ interface accompanies a positional shift of the catalytically critical arginine residue on the α subunit, referred to as the arginine finger, toward bound ATP (38–40), the αβ_DP interface is thought to be very similar to the catalytically active state. This contention is supported by several lines of experimental (41–43) and theoretical evidence (40,44). Based on these structural features, nucleotide binding and release are thought to induce the open-to-closed or closed-to-open conformational transitions of the β subunit, respectively, whereas ATP hydrolysis accompanies changes in the αβ interface. Recent theoretical studies suggest that P_i release is also coupled with the conformational transition of the αβ interface (45,46).

The α₃β₃ and γ subunits interact in the upper and lower regions. α₃β₃ forms a hydrophobic sleeve in the lower region that does not show obvious differences among the three β subunits. Therefore, the lower interface is thought to act mainly as an axle holder for the C-terminal helix of the γ subunit, although some reports suggest that this interaction is also involved in torque transmission (47). The upper contact is mainly formed by the γ subunit and the C-terminal domains of the β subunits, and this region shows distinct differences among the β subunits. The C-terminal domain of the β subunits contacts the γ subunit with a helical loop, referred to as the DELSEED loop for its conserved amino acid sequence. The DELSEED loop of TF₁ used in this study has the amino acid sequence DELSDED (amino acids 386–394). Because the DELSEED loop rotates remarkably upon the open-to-closed conformational transition, it is thought to be critical for torque transmission and has been extensively studied (48–50). Deletion or glycine substitution of DELSEED residues significantly reduced the torque production of F₁.

Thus, the critical role of the DELSEED loop in torque transmission between the β-γ subunits has been determined. However, the specific reaction steps involved in torque transmission via the DELSEED loop remain unclear. In this work, we studied the effect of glycine substitution in the DELSEED loop on torque generation in each catalytic step. We conducted stall-and-release experiments of glycine-substituted DELSEED-loop mutant F₁ (F₁^glyloop) to examine the angle dependence of ATP binding and hydrolysis. Our data indicate that although the angle dependence of the hydrolysis step was not affected by glycine substitution, the angle dependence of ATP binding (affinity change) was significantly decreased, suggesting that F₁^glyloop is deficient in torque transmission coupled with the affinity change for bound ATP.

Materials and Methods

Rotation assay

To visualize the rotation of F₁, the stator subunits (α₃β₃), which have His-tags at the N-terminus, were fixed on a glass surface modified with Ni-NTA, and a streptavidin-coated magnetic bead (ϕ = 0.2–0.4 μm; Seradyn, Indianapolis, IN) was attached on the top of a biotinylated rotor subunit (γ) to probe rotation. The flow chamber was constructed from an uncoated top coverslip and a bottomcover slip modified with Ni-NTA for immobilization of His-tagged F₁. F₁ was diluted with buffer A (50 mM MOPS-KOH and 50 mM KCl, pH 7.0) to a final concentration of 200 pM and infused into the flow chamber. After 5 min, unbound F₁ molecules were washed out with buffer A containing 10% bovine serum albumin, then streptavidin-coated beads in buffer A were infused. After 10 min, unbound beads were washed out with buffer A. Finally, buffer A containing the indicated amount of Mg-ATP and P_i was infused. The rotating beads were observed under a phase-contrast microscope (IX-70 or IX-71, Olympus, Center Valley, PA) with a 100× objective lens. The rotation assay was performed at 25°C ± 3°C.

Manipulation with magnetic tweezers

The microscope stage was equipped with magnetic tweezers (51) controlled by custom software (Celery, Library). Using progressive-scan cameras, the rotary motion of the bead was imaged at 30 frames/s for the angle-dependence experiments in Figs. 3, 4, and 5 (FC300M, Takex, Kyoto, Japan) or at 1000 frames/s for the torque and rotary potential experiments in Fig. 2 (FASTCAM 1024PCI-SE, Photoron, Tokyo, Japan). Images were stored in the HDD of a computer as AVI files and analyzed using custom software.

Figure 3.

Single-molecule manipulation of F₁. (a) Schematic of manipulation procedures. When F₁ paused at the ATP binding or hydrolysis dwell, the magnetic tweezers were turned on to stall F₁ at the target angle then off to release the motor after the set time. Released F₁ either steps forward (ON) or returns to the original pause angle (OFF). These behaviors indicate that the reaction under investigation has occurred or not, respectively. (b) Examples of stall-and-release traces for ATP binding at 200 nM ATP. During a pause, F₁^glyloop was stalled for 1 s and then released. (Left) After release, F₁^glyloop stepped to the next binding angle without moving back, indicating that ATP had already bound to F₁^glyloop before release. (Right) When stalled for 1 s, F₁^glyloop rotated back to the original binding angle, indicating that no ATP binding had occurred. To see this figure in color, go online.

Figure 4.

Angle dependence of ATP binding to F₁^glyloop. (a) Time courses of P_ON of F₁^glyloop at 200 nM ATP after stalling at θ_b = −30° (cyan), 0° (black), +30° (green), or +50° (yellow) from the original ATP-binding angle. The gray line represents the time course for free rotation. k_on^ATP and k_off^ATP were determined by fits to a single exponential function: P_ON = (k_on^ATP·[ATP]/(k_on^ATP[ATP] + k_off^ATP)) × (1 − exp(−(k_on^ATP[ATP] + k_off^ATP) × t)), according to the reversible reaction scheme F₁ + ATP ⇄ F₁ × ATP. Each data point was obtained from 20–151 trials using five molecules. The error in P_ON is given as $\sqrt{P_{\text{ON}}\left(100-P_{\text{ON}}\right)/N}$, where N is the number of trials for each stall measurement. (b) Histograms of ATP binding dwell times at 200 nM ATP in free rotation (yellow) and for F₁ after an OFF (green) or ON (red) event. Each analysis was completed for experiments with stall times long enough for P_ON to reach a plateau level. The solid lines represent curves fit to a single-order reaction scheme, y = Cexp(−kt). The first bin for F₁ after an OFF event (left gray dot) was unusually small, probably because the dwell time is sometimes too short to be recognized as a pause at 200 nM ATP. Such events would be counted as ON events, decreasing the number of short dwells observed. Therefore, the first bin in the histogram for OFF events was omitted from the fit. The rate constants were determined to be 2.9 s^–1 (yellow), 1.4 s^–1 (green), and 2.0 s^–1 (red). (c–e) Angle dependence of k_on^ATP, k_off^ATP, and K_d^ATP plotted against θ_γ. Zero degrees corresponds to the ATP binding angle in Fig. 1a. Red and gray symbols represent the values for F₁^glyloop (red), determined from Fig. 4a, and F₁^WT (gray), taken from Watanabe et al. (32). Open symbols in (c) represent the k_on of free rotation. To see this figure in color, go online.

Figure 5.

Angle dependence of ATP hydrolysis by F₁^{glyloop/E190D}. (a) Time courses for P_ON of F₁^{glyloop/E190D} at 1 mM ATP after stalling at θ_b = 0° (black), +15° (green), +45° (blue), and +75° (red) from the original catalytic angle. Time courses were fit with a function shown in Materials and Methods. The gray line represents the time course of free rotation. Each data point was obtained from 14–69 trials using 5–13 molecules. The error in P_ON is given by $\sqrt{P_{\text{ON}}\left(100-P_{\text{ON}}\right)/N}$, where N is the number of trials for each stall measurement. Cyan represents P_ON in the presence of 10 mM P_i after stalling at θ_b = +45°. (b) Zoom-up of the plotted traces in (a). (c) Histograms for the ATP hydrolysis dwell of F₁^{glyloop/E190D} in free rotation (yellow) and for F₁ after an OFF (green) or ON (red) event. Each analysis was conducted for experiments with stall times long enough for P_ON to reach a plateau. The solid lines represent curves fit to a single-order reaction scheme, y = Cexp(−kt). The rate constants were determined to be 2.9 s^–1 (yellow), 1.4 s^–1 (green), and 2.0 s^–1 (red). (d–f) Angle dependence of k_hyd^ATP, k_syn^ATP, and K_E^ATP plotted against θ_γ. Here, we defined 0° as the angle for ATP hydrolysis in Fig. 1a. Blue and gray symbols represent the values for F₁^{glyloop/E190D} (blue), determined from (a), and F₁^E190D (gray), taken from Watanabe et al. (32). To see this figure in color, go online.

Figure 2.

Torque and rotary potential. (a) The fluctuation theorem was employed for torque measurement of F₁^WT, F₁^glyloop, and F₁^{glyloop/E190D}. The plot shows ln[P(Δθ)/P(−Δθ)] versus Δθ/k_BT. The slope represents the rotary torque generated by F₁. The average torque was determined from a linear approximation of all data points (solid lines). The data for F₁^glyloop and F₁^WT are from Tanigawara et al. (50). (b) The rotary torques (N) generated by F₁^glyloop, F₁^{glyloop/E190D}, and F₁^WT are 24, 18, and 41 pN·nm, respectively. (c) Rotary potential of the F₁. Probability densities of angular positions during pauses from the five molecules, i.e., ATP binding pause for F₁^glyloop and hydrolysis pause for F₁^{glyloop/E190D}, were transformed into rotary potentials according to Boltzmann’s law: F₁^glyloop (red), and F₁^{glyloop/βE190D} (blue). The determined potentials were fit to the harmonic function ΔG = 1/2 × κ_total × θ_b², where κ_total is the torsion stiffness. Determined stiffness values were 40 and 44 pN·nm for F₁^glyloop and F₁^{glyloop/E190D}, respectively. To see this figure in color, go online.

Simulation of P_ON for F₁^{glyloop/E190D}

The kinetic scheme of stalled F₁^{glyloop/E190D} is given as

$${\beta }_{\text{E}190\text{D}}\times \text{ATP}\underset{k_{\text{syn}}^{\text{ATP}}}{\overset{k_{\text{hyd}}^{\text{ATP}}}{\rightleftarrows }}{\beta }_{\text{E}190\text{D}}\times \left(\text{ADP}+{\text{P}}_{\text{i}}\right)\stackrel{k_{\text{off}}^{\text{Pi}}}{\to }{\beta }_{\text{E}190\text{D}}\times \text{ADP},$$ (1)

where k_off^Pi is the rate constant for P_i release from β immediately after hydrolysis. Because F₁ generates torque after ATP hydrolysis, P_ON is represented as the sum of probabilities of [β_E190D × (ADP+P_i)] and [β_E190D × ADP]. Thus, P_ON is represented as a function of time, t, by

$$P_{\text{ON}}=\frac{\left[{\beta }_{\mathrm{E}190\mathrm{D}}\times \left(\mathrm{ADP}+{\mathrm{P}}_{\mathrm{i}}\right)\right]+\left[{\beta }_{\mathrm{E}190\mathrm{D}}\times \mathrm{ADP}\right]}{{\left[{\beta }_{\mathrm{E}190\mathrm{D}}\right]}_{\mathrm{total}}}=100+\frac{\epsilon }{50}\left\{\left(\eta -\epsilon \right){\mathrm{e}}^{\epsilon t}-\epsilon -\eta \right\}{\mathrm{e}}^{-\frac{1}{2}\left(\delta +\epsilon \right)t}$$ (2)

$$\delta =k_{\text{hyd}}^{\text{ATP}}+k_{\text{syn}}^{\text{ATP}}+k_{\text{off}}^{\text{Pi}}$$

$$\epsilon ={\left(k_{\text{hyd}}^{\text{ATP}}+k_{\text{syn}}^{\text{ATP}}+k_{\text{off}}^{\text{Pi}}\right)}^2-4k_{\text{hyd}}^{\text{ATP}}{k}_{\text{off}}^{\text{Pi}}$$

$$\eta =k_{\text{hyd}}^{\text{ATP}}-k_{\text{syn}}^{\text{ATP}}-k_{\text{off}}^{\text{Pi}}.$$

By fitting to the curves of P_ON, the fitting parameters k_hyd^ATP and k_syn^ATP were determined (see Fig. 5, d and e).

Angular position of γ

Fig. 2 c shows that the total stiffness of the system (κ_total) was determined to be 55, 40, and 44 pN·nm for wild-type F₁ (F₁^WT), F₁^glyloop, and F₁^{glyloop/E190D}, respectively. By modeling the system as a composition of two elastic parts, internal and external, connected in series, the total stiffness (κ_total) can be expressed as

$$1/{\kappa }_{\mathrm{total}}=1/{\kappa }_{\mathrm{internal}}+1/{\kappa }_{\mathrm{external}},$$ (3)

where κ_internal and κ_external represent the stiffness of the internal and external parts, respectively. Because glycine substitutions in the DELSEED loop do not affect the external part, κ_external is assumed to be the same as for the wild-type, 72.6 pN·nm (52). From Eq. 3, κ_internal is thus determined to be 223, 90, and 113 pN·nm for F₁^WT, F₁^glyloop, and F₁^{glyloop/E190D}, respectively. Because the internal and external parts are connected in series, the angular position of γ (θ_γ) can be calculated by

$${\theta }_{\gamma }={\kappa }_{\mathrm{external}}/\left({\kappa }_{\mathrm{internal}}+{\kappa }_{\mathrm{external}}\right)\times {\theta }_{\mathrm{b}},$$ (4)

where θ_b is the angular position of the bead. Based on Eq. 4, we determined the angular position of γ from the bead position.

Results

Rotation of DELSEED-loop mutants

In this work, we used three F₁ complexes derived from thermophilic Bacillus PS3 (TF₁), wild-type F₁ (F₁^WT), F₁^glyloop, and F₁^{glyloop/E190D}, for stall-and-release experiments. F₁^glyloop and F₁^{glyloop/E190D} contain glycine substitutions at all residues constituting the DELSEED loop of the β subunit (β384–394 in TF₁ numbering) to disrupt the specific interaction with the γ subunit and the conformational rigidity of the loop (50) (Fig. 1 b). In F₁^{glyloop/E190D}, the βE190D mutation was introduced to slow ATP hydrolysis and extend the hydrolysis waiting dwell to facilitate the stall-and-release experiment (32). Because F₁^{glyloop/E190D} was not previously characterized, we conducted a rotation assay for F₁^{glyloop/E190D} (Fig. 1 c). Magnetic beads were attached as rotation markers to the γ subunit of F₁ immobilized on a glass surface coated with Ni-NTA. Similar to F₁^E190D, F₁^{glyloop/E190D} exhibited 120° steps separated by long pauses for slowed hydrolysis at saturating ATP (21). Figs. 1 d and S1 show the Michaelis-Menten curves and the Lineweaver-Burk plots for the rotation of F₁^{glyloop/E190D} (obtained herein), F₁^WT, and F₁^glyloop (from our previous reports) (50) for comparison of kinetic parameters. The maximum rotation rate (V_max = 0.43 s⁻¹) and Michaelis constant (K_m = 1.0 μM) for F₁^{glyloop/E190D} were comparable to those of F₁^E190D (21). Thus, the rate constant for ATP binding of F₁^{glyloop/E190D} was determined to be 1.2 × 10⁶ M⁻¹·s⁻¹ (3 × V_max/K_m).

The rotary torque of F₁^{glyloop/E190D} was measured using the fluctuation theorem (15), which estimates torque as entropy generation from the time series of the centroid of a rotation probe (Fig. 2, a and b). From the time trajectories of the 120° rotation steps, the time domains of the steps were extracted. We calculated the ratio between the forward and backward movement probabilities, [P(Δθ)/P(−Δθ)], over a set period and determined the torque from the slope of this ratio versus Δθ/k_BT (Fig. 2 a). The results showed that F₁^{glyloop/E190D} generates 18 pN·nm torque (Fig. 2 b), which is less than that generated by F₁^WT (41 pN·nm) and comparable to that generated by F₁^glyloop (24 pN·nm). This indicates that glycine substitutions in the DELSEED loop dominantly affect torque generation for F₁^{glyloop/E190D}, whereas the kinetics of hydrolysis is mainly determined by the βE190D mutation.

We also examined the mutational effects on the rotary potential during the reaction waiting pauses. The probability densities of bead position (θ_b) during pauses were measured, and the rotary potentials were determined according to Boltzmann’s law (Fig. 2 c). The determined potentials fit well to a harmonic function, ΔG =1/2 × κ_total × θ_b², where κ_total is the torsion stiffness. The determined stiffness values were 55, 40, and 44 pN·nm for F₁^WT, F₁^glyloop, and F₁^{glyloop/E190D}, respectively. The lower stiffness of the mutants suggested that their rotary potentials became more gradual than that of F₁^WT.

Manipulation of single F₁ rotation

To investigate the impact of glycine substitutions in the DELSEED loop on the angle-dependent affinity change of ATP binding and equilibrium change of ATP hydrolysis, we conducted stall-and-release experiments using F₁^glyloop to measure ATP binding and F₁^{glyloop/E190D} to measure ATP hydrolysis. Experimental procedures were essentially the same as for previous stall-and-release experiments (32) (Fig. 3 a). Briefly, we turned on the magnetic tweezers to arrest F₁ at the target angle when F₁ paused for ATP binding or hydrolysis (Fig. 3 a). At the designated time, we turned off the magnetic tweezers to release F₁ from arrest. After release, F₁ showed one of two behaviors, taking a forward 120° step (on event) or resuming pause at the original pause angle (off event) (Fig. 3, a and b). The on event indicates that F₁ completed the waiting reaction and exerted a torque on the magnetic beads (Fig. 3 b, left); conversely, the off event shows that the waiting reaction has not occurred because F₁ cannot generate torque without completing the waiting reaction (Fig. 3 b, right). We conducted the stalling experiment primarily in the angle range of ±50°. The subsequent sections discuss analysis of the probability of on events against total trials, P_ON.

Angle dependence of ATP binding

Stall-and-release experiments were conducted for F₁^glyloop at 200 nM ATP, where the ATP waiting dwell is 0.34 s. Fig. 4 a shows a plot of P_ON versus stall time. P_ON increased with both the stall angle and stall time, which is similar to our previous finding for F₁^WT. Furthermore, P_ON was not always 100% saturated; it converged to a certain value, e.g., 60% for a +30° stall (Fig. 4 a, green line). These observations imply that ATP binding is reversible and that ATP release occurs during stalling. Accordingly, the plateau level indicates the equilibrium between ATP binding and release. To confirm the reversibility, we analyzed the dwell time for F₁ to spontaneously conduct a 120° step after an off event (Fig. 3 b, blue). To avoid including data from before the equilibrium, only experiments with longer stalling times in which P_ON achieved a plateau were analyzed. The dwell-time histogram exhibited single-exponential decay, allowing determination of the rate constant (Fig. 4 b). As expected, the determined rate constant corresponded to that of free rotation (Fig. 4 b). This correspondence discounted the possibility that unexpected inactivation during stalling competes with ATP binding. We also plotted a histogram of the dwell time for the second 120° step after an on event (Fig. 3 b, red). The determined rate constant was also in good agreement with that of free rotation (Fig. 4 b), confirming that manipulation did not alter the kinetic properties of F₁^glyloop.

By fitting time courses of P_ON based on the reversible reaction scheme F₁^glyloop + ATP ⇄ F₁^glyloop·ATP, the rate constants for ATP binding and release, k_on^ATP and k_off^ATP, respectively, were determined for each stall angle of magnetic beads (θ_b). The actual γ position (θ_γ) deviates from the bead position (θ_b) because the system has elastic components: the outwardly protruding domain of γ, streptavidin, and the α₃β₃ stator ring, which reduces the torsional stress by twisting itself. We corrected the data with the apparent rotary stiffness of the mutant F₁ complexes (see Materials and Methods). The corrected data for the angle dependence of ATP binding are shown in Fig. 4, c and d. k_on^ATP for F₁^glyloop increased exponentially with the stall angle by ∼2.8-fold per 20°, similar to previously reported corresponding increases for the wild-type (32). In contrast, k_off^ATP for F₁^glyloop was almost constant, which is markedly different from the ∼2.6-fold decrease per 20° for the wild-type. Therefore, the dissociation constant for ATP, K_d^ATP, decreased 2.8-fold per 20° for F₁^glyloop, which is significantly smaller than the decrease for wild-type, 6.3-fold per 20° (Fig. 4 e), suggesting that glycine substitution of the DELSEED loop impairs torque transmission during the change in affinity between F₁ and bound ATP.

Angle dependence of hydrolysis

Stall-and-release experiments to measure hydrolysis were conducted for F₁^{glyloop/E190D}, because the hydrolysis waiting dwell for F₁^glyloop is only 1 ms, which is too short for the stalling experiment. Under saturating ATP conditions, F₁^{glyloop/E190D} showed a 120° stepping rotation with hydrolysis pauses of 1.1 s (Fig. 5 c, yellow). During the 1.1 s hydrolysis waiting dwells, we stalled F₁^{glyloop/E190D} with magnetic tweezers to determine P_ON. As shown previously (26), P_ON increased in two phases (Fig. 5, a and b). After a rapid increase, P_ON gradually approached 100%. The first increase was nearly complete within 1 s, which is consistent with the time constant of ATP hydrolysis (Fig. 5 c, yellow). The subsequent increase was extremely slow for an effective catalytic reaction. We previously (26) showed that this slow increase results from the release of inorganic phosphate (P_i) by the β subunit that hydrolyzed the bound ATP (Fig. 1 a, 200° state) during stalling. This slow P_i release is suppressed by 10 mM P_i, which is also consistent with the previous study (26). We fit the time courses of P_ON using a consecutive reaction model with a reversible hydrolysis step followed by irreversible P_i release at 200°: F₁^{glyloop/E190D} × ATP ⇄ F₁^{glyloop/E190D} × ADP × P_i → F₁^{glyloop/E190D} × ADP + P_i (see Materials and Methods). The rate constants for hydrolysis and synthesis, k_hyd^ATP and k_syn^ATP, respectively, were determined from the fitted data, and the data points were corrected based on the rotary stiffness, as for the angle dependence of ATP binding. The k_hyd^ATP for F₁^{glyloop/E190D} increased exponentially with the stall angle (Fig. 5 d), whereas k_syn^ATP remained constant (Fig. 5 e). These features follow essentially the same trend observed in our previous stall-and-release experiment with F₁^E190D (32). Hence, the equilibrium constant for hydrolysis (k_hyd^ATP/k_syn^ATP = K_E^Hyd-ATP) showed angle dependence similar to F₁^E190D (Fig. 5 f). The k_off^Pi for F₁^{glyloop/E190D} at 200° was constant, ∼0.07 s⁻¹ (data not shown), and almost the same as that of F₁^E190D (0.04 s⁻¹). The similarity of these values suggests that the DELSEED loop is not involved in torque transmission during the hydrolysis step.

Discussion

Our results indicate that glycine substitution of the DELSEED loop impairs torque transmission during the power stroke of β by affecting the affinity change to bound ATP. This is consistent with the structural features of bovine mitochondrial F₁ (bMF₁) suggesting that β undergoes a conformational transition from an open to a closed conformation upon ATP binding to push the γ rotor with its C-terminal DELSEED loop (8). Thus, the crystal structures suggest that the DELSEED loop is predominantly involved in torque transmission upon ATP binding. From this perspective, it is surprising that F₁^glyloop has any capacity for angle-dependent modulation of k_on^ATP. The energy released by the affinity change, estimated from $\partial /\partial \theta \left\{k_{\text{B}}T\times \text{ln}\left[K_{\text{E}}\left(\theta \right)\right]\right\}{k}_{\text{B}}T$, was 65% of that for F₁^WT. This implies that angle-dependent affinity change is mediated not only by the DELSEED-γ interaction but also by other contact regions, such as the lower interface between the β and γ subunits. Remote communication among β subunits via the neighboring α subunits could also support the robust mechanism of the angle-dependent affinity change. The recent finding of allostery between β subunits in the isolated α₃β₃ ring supports this model (53). On the other hand, the glycine substitution did not affect the angle-dependent equilibrium change between hydrolysis and synthesis of ATP (the change is slightly enhanced compared to the wild-type), suggesting that the DELSEED loop is not responsible for torque transmission upon hydrolysis. This agrees with observations from the crystal structure indicating that hydrolysis accompanies closure of the αβ interface, which does not directly involve the DELSEED loop (41). Thus, this study shows that the principal role of the DELSEED loop is torque transmission upon the affinity change of ATP coupled with the transition between the open and closed conformations of β, and not torque transmission upon hydrolysis. For further confirmation, we conducted a rotation assay for a hybrid F₁ carrying a single copy of β^{glyloop/E190D}. Fluctuation theorem analysis showed that torque generation upon affinity change of ATP was reduced by 42% compared with the wild-type, whereas torque generation for ATP hydrolysis was unchanged (You et al., unpublished data), supporting the results of this study.

The remarkable change in angle dependence upon glycine substitution of the DELSEED loop appears only for k_off^ATP, and the change of k_on^ATP is very moderate (Fig. 4 e). One possible interpretation of the asymmetric effect is that the torque transmission upon ATP binding is composed of two processes; DELSEED loop is involved in only one of them, which presumably modulates k_off^ATP, and the lower β-γ interface compensates for the other. The stall-and-release experiment using γ-truncated mutant F₁, which eliminates the interaction via the lower β-γ interface (47), will provide detailed insights into the torque transmission mechanism upon ATP binding.

In this study, the impact of glycine substitution on torque transmission upon ATP binding and hydrolysis was studied using the stall-and-release experiment, which provides insights into the torque transmission mechanism of F₁ at a resolution of elementary reaction steps, e.g., ATP binding and hydrolysis. However, that for product release (ADP release and P_i release) remained elusive due to technical difficulties. Considering the conformational change in the β subunit depending on the presence of nucleotide (53,54), it is highly probable that the DELSEED loop is also responsible for torque transmission upon ADP release. In contrast, some theoretical studies propose that P_i release is coupled with the opening of the αβ interface (45,55), which suggests that torque transmission for this step would not be affected by the glycine substitution of the DELSEED loop. To comprehensively understand the torque transmission mechanism of F₁, we hope to evaluate the impact of glycine substitution on torque transmission upon product release using the stall-and-release experiment.

Author Contributions

R.W. and K.K. designed and performed experiments and analyzed data; H.Y. and M.T. provided technical support; H.N. designed experiments and wrote the paper with R.W.