Characterization of the temperature-sensitive reaction of F1-ATPase by using single-molecule manipulation

F1-ATPase (F1) is a rotary motor protein that couples ATP hydrolysis to mechanical rotation with high efficiency. In our recent study, we observed a highly temperature-sensitive (TS) step in the reaction catalyzed by a thermophilic F1 that was characterized by a rate constant remarkably sensitive to temperature and had a Q10 factor of 6–19. Since reactions with high Q10 values are considered to involve large conformational changes, we speculated that the TS reaction plays a key role in the rotation of F1. To clarify the role of the TS reaction, in this study, we conducted a stall and release experiment using magnetic tweezers, and assessed the torque generated during the TS reaction. The results indicate that the TS reaction generates the same amount of rotational torque as does ATP binding, but more than that generated during ATP hydrolysis. Thus, we confirmed that the TS reaction contributes significantly to the rotation of F1.

F 1 -ATPase (F 1 ) is a rotary motor protein that couples ATP hydrolysis to mechanical rotation with high efficiency. In our recent study, we observed a highly temperature-sensitive (TS) step in the reaction catalyzed by a thermophilic F 1 that was characterized by a rate constant remarkably sensitive to temperature and had a Q 10 factor of 6-19. Since reactions with high Q 10 values are considered to involve large conformational changes, we speculated that the TS reaction plays a key role in the rotation of F 1 . To clarify the role of the TS reaction, in this study, we conducted a stall and release experiment using magnetic tweezers, and assessed the torque generated during the TS reaction. The results indicate that the TS reaction generates the same amount of rotational torque as does ATP binding, but more than that generated during ATP hydrolysis. Thus, we confirmed that the TS reaction contributes significantly to the rotation of F 1 .
with an aspartic acid 26,27 . Glu-190 of the b-subunit of TF 1 has been identified as a critical residue in ATP hydrolysis 5,[28][29][30] , and is termed the ''general base'' since this residue seems to induce an in-line attack of the water molecule on the c phosphate and initiate the hydrolysis reaction by activating the water molecule. Another single molecule study revealed that this new reaction intermediate occurs at the angle where the b subunit waits for ATP binding (0u in Fig. 1) 26 . Although this reaction has not been further characterized, the rate constant was found to be remarkably sensitive to temperature. The rate constant increased by a factor of 6-19 for every 10uC rise in temperature 25,26 (Q 10 5 6-19), which was unusually high compared to conventional Q 10 values of around 2. In general, reactions with high Q 10 values involve large conformational changes. Therefore, this reaction may play a key role in rotation and torque generation. Hereafter, this reaction has been referred to as the temperature-sensitive reaction (TS reaction).
To evaluate the torque generated during each step of the reaction, we recently developed a novel method to measure the equilibrium constant of the F 1 reaction at various rotational angles 31 . Through this method, we arrested F 1 in the transient conformation using magnetic tweezers and observed the behavior of F 1 immediately after release from arrest. From the analysis of the behavior of F 1 , we could simultaneously determine the rate constant for each forward and reverse step of the reaction at various rotational angles. Thus, we could measure the equilibrium constant of each step of the reaction. Because the equilibrium constant is a measure of the difference in the free energy of the pre-and post-reaction states, DG(h) 5 2k B T?lnK E (h), the torque generated during the reaction can be estimated from the derivative of the free energy, dDG(h)/dh.
In the present study, we perform a stalling experiment to elucidate how F 1 modulates the rate and equilibrium constants of the TS reaction as a function of the rotational angle and attempt to assess its contribution in torque generation. The results will contribute to understanding the chemomechanical energy coupling of F 1 at the resolution of the elementary reaction step.

Results
Temperature dependence of the rotation of the TF 1 (bE190D) mutant. We observed the rotation of the mutant TF 1 , namely, a 3 b(E190D) 3 c, in the presence of 1 mM ATP at 18, 23, and 28uC (Fig. 2a). Between 18 and 28uC, the mutant F 1 rotated with 80u and 40u substeps (Fig. 2b); the rate limiting steps of the 80u and 40u substeps were identified to be the TS reaction and ATP hydrolysis, respectively, in our previous study 26 . The dwell time prior to the 80u substep (TS dwell) showed a strong dependence on temperature (Fig. 2c). By fitting the histograms with exponential functions, the time constants of the TS reaction at 18, 23, and 28uC were determined to be 330, 96, and 43 ms, respectively (Fig. 2c). In contrast, the dwell time before the 40u substep (hydrolysis dwell) was not dependent on temperature and was determined to be 208 ms for 18uC, 235 ms for 23uC, and 270 ms for 28uC (Fig. 2d). These results were consistent with the results of our previous study on the TS reaction 26 .
Manipulation of single F 1 rotation. For manipulating the rotation of the c subunit of F 1 , a magnetic bead (w < 200 nm) was attached to it and the a 3 b 3 ring was immobilized on the glass surface. For the stalling experiments, the rotation of F 1 was observed under conditions under which the TS dwell was lengthened enough to   enable recording at approximately 1,000 fps using a mutant F 1 , a 3 b(E190D) 3 c. As mentioned above, we can distinguish between the angular positions for the TS reaction and the hydrolysis by analyzing the TS and hydrolysis dwell times (Figs. 2c, 2d). When F 1 paused for the TS reaction, we turned on the magnetic tweezers to arrest F 1 at the target angle (Fig. 3a). After the set period had elapsed, we turned off the magnetic tweezers and released F 1 from the arrest. Following release, F 1 showed one of two behaviors: rotating directly forward to the next catalytic angle (red in Fig. 3b), i.e., skipping the pause at the original ATP-binding angle, or returning to the original ATP-binding angle (blue in Fig. 3b) without exception. Forward rotation of F 1 implied that it had completed the TS reaction and exerted a torque on the magnetic beads; backward rotation of F 1 meant that it had not completed the TS reaction because it did not catalyze the reaction and hence could not generate a torque. These behaviors of F 1 are hereafter referred to as ''ON'' (forward rotation) and ''OFF'' (backward rotation), respectively. Using the abovementioned methodology, we conducted the stalling experiments in the angle range of 650u, where the standard deviation of the arrested angle was 5.8u. The following sections discuss the analysis of the probability (P ON ) of ON events against the total trials. Angular dependence of the kinetic parameters of the TS reaction. Using the mutant F 1 , experiments were conducted at 18uC, where the TS dwell time was 330 ms (Fig. 2c). Fig. 4a shows P ON plotted against the stall time. P ON increased with both the stall angle and the stall time ( Fig. 4a), which is similar to our previous observation of ATP binding to wild-type F 1 31 . In addition, P ON did not always saturate to 100% but converged to a certain value, e.g., 60% for 110u stall (green line in Fig. 4a). These observations imply that the TS reaction is reversible, and that reverse reaction also occurs during stalling. Therefore, the plateau level indicates the equilibrium level between the pre-and post-TS reaction states. To confirm the reversibility, we analyzed the behaviors immediately after the OFF events; i.e., dwell times to spontaneously conduct 80u steps (dwell times at 0u in Fig. 1) immediately after the OFF events (blue points in Fig. 3b). Here, 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 obtained from all the stall angles showed a single exponential decay, providing a rate constant of 1.1 s 21 (bottom panel in Fig. 4b), which corresponded to that obtained for freely rotating F 1 s, which were not manipulated with magnetic tweezers (Fig. 2c). This correspondence excluded the possibility of any unexpected inactivation occurring during the stalling that might compete with the TS reaction. We also plotted a histogram of the dwell times to conduct 40u steps (dwell times at 80u in Fig. 1) after the ON events (red points in Fig. 3b). This histogram (top panel in Fig. 4b) was also in good agreement with that obtained for freely rotating F 1 s (Fig. 2d), confirming that the manipulation did not alter the kinetic properties of F 1 .
By fitting the time courses of P ON based on a reversible reaction scheme, F 1 / ? F 1 *, the rate constants of the TS reaction and its reverse reaction, k TS on (18uC) and k TS off (18uC), were determined for each stall angle (Figs. 5a and 5b). k TS on (18uC) increased exponentially with the stall angle by approximately 6.2 fold per 20u, which was double that reported previously for ATP binding 31 . k TS on (18uC) at 60u was evidently slower than that determined for freely rotating F 1 s. This phenomenon, which is similar to the ATP-binding step, is attributed to thermal agitated rotary fluctuation that occasionally pushes c forward, accelerating the TS reaction. In contrast, k TS off (18uC) was almost constant at approximately 0.3 s 21 . Therefore, the equilibrium constant of the TS reaction [k TS on (18uC)/k TS off (18uC) 5 K E TS (18uC)] increased 2.2 times from 210u to 1 10u (blue points in Fig. 5c), which is a steeper angle dependence than that observed for ATP hydrolysis in the previous study 31 .
To confirm the strong angle dependence of the TS reaction under a different condition, the stalling experiments were also conducted at 23 and 28uC, where the time constants of the TS reaction were 96 and 43 ms, respectively (Fig. 2c). The time courses of P ON showed the same tendency as that observed at 18uC (Figs. 4c, 4e). The reversibility of the TS reaction at 23 and 28uC was also confirmed from the analysis of the dwell time after arrest (Figs. 4d and 4f). The rate and equilibrium constants were determined as mentioned above (Figs. 5a, 5b, and 5c). The equilibrium constants determined for the TS reaction at 23 and 28uC showed essentially the same angle dependence as that at 18uC (red and green points in Fig. 5c). Thus, the strong angle dependence of the TS reaction is inherent in F 1 , regardless of the temperature.
Rotational energy potential. We examined the rotational energy potential during TS dwell, i.e., the waiting state for the TS reaction. The probability distribution of c-orientation during the TS dwell of mutant F 1 , a 3 b(E190D) 3 c, was measured (orange points in Fig. 6a). The probability distributions obtained were then transformed into the rotational energy potential according to the Boltzmann's Law, DG 5 2k B T?ln(P/P o ) (orange points in Fig. 6b). The potential determined was fitted to the harmonic function, DG 5 1/2?k?h 2 , where k is the torsion stiffness. The determined value of stiffness The gray solid and dashed lines represent the ATP-binding and catalytic angles, respectively. When F 1 paused due to TS dwell at the ATP-binding angle, the magnetic tweezers were switched on to stall F 1 at the target angle and then turned off to release the motor after the set period had elapsed. A released F 1 showed forward (ON) or backward (OFF) rotation with respect to the original ATP binding angle. The behavior of F 1 indicated whether the TS reaction was completed (in case of ON) or not (in case of OFF). (b). Examples of stalling experiments for the TS reaction at 18uC. During a pause, F 1 was stalled at 26.6u from the original pausing angle for 1.0 s and then released. After being released, F 1 rotated to the next catalytic angle without any backward rotation, indicating that the TS reaction had been completed by F 1 upon release (red). When F 1 was stalled at 29.1u for 1.0 s, it rotated back to its original pausing angle, implying that the TS reaction had not been completed (blue). was 75 pN?nm, which was similar to the values for ATP binding of wild-type F 1 and hydrolysis of mutant F 1 , a 3 b(E190D) 3 c, determined in the previous study 31 (red and blue points in Fig. 6b). This result suggested that the magnitude of rotational energy potential in the pre-reaction state did not depend on individual reaction steps.

Discussion
The equilibrium constant of the TS reaction determined in this study, as well as those of the other reaction steps, that is, ATP binding, hydrolysis, and P i release, determined in our previous studies 15,31 , are shown in Fig. 7. Data points are plotted in the angular diagram of the reaction scheme for one b subunit (Fig. 1), where the pause angles for ATP binding, TS reaction, hydrolysis, and P i release were assigned as 0u, 0u, 200u and 320u, respectively. The magnitude of rotational torque (N) is determined by the slope of the rotational energy potential in the post-reaction state, dU post (h)/dh 31,32 . It is very difficult to measure the rotational potential directly in the postreaction state, U post (h). Therefore, in our previous studies, we had estimated the torque generated during each reaction step from the angular dependence of the reverse reaction rate, DG 1 (h) 5 2k B T?[lnk 21 (h)] 31,32 , which is a measure of the energy difference between the transition state and the post-reaction state, DG 1 (h) 5 U post (h) 2 U TS (h). When we assume that the energy level at the transition state, U TS (h), is a constant, and does not depend on the rotational angle, the derivative of the energy difference responds to the slope of the potential in the post-reaction state (equivalent to the torque), dDG 1 (h)/dh 5 dU post (h)/dh. Therefore, we previously estimated the torque generation from the reverse reaction rate based on this assumption with respect to the energy level for the transition state 31,32 , which has not been verified experimentally so far. In this study, we used the angle dependence of the equilibrium constant, K E (h), which is a more robust approach to estimate the torque generation. The free energy difference between the pre-and post-reaction states can be determined from the angle dependence of the equilibrium constant; DG 2 (h) 5 U post (h) -U pre (h) 5 k B T?[ln(K E (h))]. Because U pre (h) was not affected by the elastic component located on the transmission line to the beads 9 , and was almost the same for each reaction step (Fig. 6), the derivative of the free energy difference may be regarded as a measure of the slope of the rotational potential in the post-reaction state (equivalent to the torque), dDG 2 (h)/dh < dU post (h)/dh. Therefore, the slopes of the equilibrium constants in a semi-log plot (Fig. 7) reflect the magnitude of torque generated upon each reaction step. The estimation shows that , according to the reversible reaction scheme, F 1 / ? F 1 *. Each data point was obtained from 13-63 trials using 4 molecules. The error in P ON is represented as ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi , where N is the number of trials for each stall measurement. (b, d, f). Histograms of dwell times immediately after the stalling at 18, 23, and 28uC. Top panels represent the dwell time to conduct another 40u step (hydrolysis dwell) after the ON event (red points in Fig. 3b). Bottom panels represent the dwell time to conduct spontaneously an 80u step after an OFF event (blue points in Fig. 3b). Curves were obtained by fitting the data to a single-order reaction scheme.  , and K E TS Blue circle, green square, and red triangle symbols represent the values for 18, 23, and 28uC, as determined from Figs. 4a, 4c, and 4e, respectively. In (a), the black symbols represent k TS on obtained from the freely rotating F 1 s (Fig 2c). In (c), the gray symbols represent the average of K E TS for 18, 23, and 28uC. the TS reaction has a slope similar to those of ATP binding and P i release and a steeper slope than that of ATP hydrolysis. This suggests that the contribution of the TS reaction to torque generation is similar to those of ATP binding and P i release and is much higher than that of ATP hydrolysis, i.e., the TS reaction contributes significantly to the torque generation of F 1 . Considering the extremely high temperature dependence of the TS reaction, this reaction may involve a large-scale conformational rearrangement of the catalytic b-subunit when the c is oriented to the angle for ATP binding. Recent single-molecule studies have revealed that the C-terminal region of the b subunit shows a large-scale conformational change at around 0u 5,33 , which contributes to generating half of the rotational torque, that is, approximately 20 pN?nm rad 2134, 35 . Our experimental results suggest that the TS reaction contributes greatly to torque generation at around 0u. Therefore, it is probable that the TS reaction is somehow related to the large-conformational change in the C-terminal region of the b subunit at 0u; however, there has been no direct verification so far. To identify the TS reaction, we hope to visualize simultaneously the conformational change in the b subunit and the rotational motion at the temperature, where F 1 shows a distinctive pause due to the TS reaction. Improper ATP hydrolysis due to an alternative catalytic pathway 27 may be another possible reason for the occurrence of the TS reaction. According to this mechanism, P i release in the b-subunit at the 320u state (cyan circle at 320u in Fig. 1) may drive the rotation of the 40u substep from 320u to 360u (50u) without hydrolyzing ATP in another b-subunit at the 200u state (left green circle at 320u in Fig. 1). This may cause the dwell at 0u for waiting the ATP hydrolysis to occur in the aforementioned b-subunit at the 240u state (left green circle at 0u in Fig. 1). In our experimental data, the angle dependence of the rate constants of the TS reaction and its reverse reaction (Fig. 5) was similar to those of ATP hydrolysis and synthesis 31 . The forward reaction rate was accelerated towards the anticlockwise direction, while the reverse reaction rate was almost constant and did not depend on the rotary angle, although the slopes of angle dependence are different from each other. Therefore, our result suggests that the TS reaction might occur due to improper ATP hydrolysis at the 240u state (left green circle at 0u in Fig. 1). Simultaneous monitoring of the catalytic events, i.e., ATP binding, hydrolysis, and products release, with the rotational motion will provide insights into this mechanism.
Using single-molecule manipulations, we measured the rate and equilibrium constants of F 1 in the transient conformational states, which could not be obtained in the conventional single molecule assay. Moreover, from the equilibrium constants determined by single-molecule manipulations, we evaluated the force generated during the elementary reaction steps. Thus, single-molecule manipulation is a powerful tool for understanding the chemomechanical energy coupling mechanism and holds promise for understanding the functioning of other molecular machines.

Methods
Rotation assay. The mutant form of F 1 from thermophilic Bacillus PS3 (TF 1 ), a 3 b(E190D) 3 c, was prepared as described previously 36 . To visualize the rotation of F 1 , the stator region (a 3 b 3 subunits) was fixed to a glass surface, and magnetic beads (w approximately 0.3 mm; Seradyn, USA) were attached to the rotor (c subunit), as the probe for monitoring rotation and for further manipulation. The rotation assay was carried out in a 50 mM MOPS-KOH (pH 7.0) buffer containing 50 mM KCl, 5 mM MgCl 2 , and 1 mM ATP. Rotating beads were observed under a phase-contrast microscope (IX-70 or IX-71; Olympus, Japan) with a 1003 objective lens. The temperature in the room was controlled with a room air conditioner and monitored with a thermometer located on the sample stage of the microscope. The precision of the temperature control was 61uC.
Manipulation with magnetic tweezers. The stage of the microscope was equipped with magnetic tweezers that could be controlled with the custom-made software Rotational energy potentials determined from probability distribution according to the Boltzman's law, DG 5 2k B T?ln(P/P o ). The potentials determined were fitted to the harmonic function DG 5 1/2?k?h 2 , where k is the torsion stiffness. Stiffness values determined were 80, 75, and 64 pN?nm for the ATP binding of wild-type F 1 , the TS reaction, and the hydrolysis of mutant F 1 , respectively. Modulation of equilibrium constants upon rotation. All data points are plotted along the reaction scheme for one b subunit (Fig. 1), where the angles for ATP binding, TS reaction, hydrolysis, and P i release are assigned as 0u, 0u, 200u, and 320u, respectively. Red, blue, and green symbols represent the dissociation constant of ATP (K d