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Keywords:

  • ATP synthase;
  • F1 ATPase;
  • F-ATPase;
  • rotation;
  • single molecule observation

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Rotating Proton Pumping F-ATPases
  5. Subunit Interactions for Catalysis and Rotation
  6. Acknowledgements
  7. References

In this article, we discuss single molecule observation of rotational catalysis by E. coli ATP synthase (F-ATPase) using small gold beads. Studies involving a low viscous drag probe showed the stochastic properties of the enzyme in alternating catalytically active and inhibited states. The importance of subunit interaction between the rotor and the stator, and thermodynamics of the catalysis are also discussed. “Single Molecule Enzymology” is a new trend for understanding enzyme mechanisms in biochemistry and physiology. © 2013 IUBMB Life, 65(3):247–254, 2013


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Rotating Proton Pumping F-ATPases
  5. Subunit Interactions for Catalysis and Rotation
  6. Acknowledgements
  7. References

Proton-translocating ATP synthase (F-ATPase) of mitochondria, chloroplasts, or bacteria synthesizes ATP (adenosine triphosphate) from ADP (adenosine diphosphate) and phosphate (Pi) coupled with a proton gradient or hydrolyzes ATP to pump protons (refs.1–5 for reviews). The basic structure of F-ATPase, the name being derived from a factor in oxidative phosphorylation, consists of membrane extrinsic catalytic sector F13β3γδε) and a transmembrane FO complex (ab2c10) formed from five and three different subunits, respectively, with a defined stoichiometry (Fig. 1a). F-ATPase couples ATP synthesis/hydrolysis and proton transport through the rotation of subunits: the γεc10 complex formed from γ and ε of F1, and a ring of multiple c subunits (c10 ring for E. coli) comprises a rotor, and the α3β3δab2 comprises a stator. The proton pumping V-ATPase (vacuolar type ATPase) found in the membranes of lumenal acidic organelles, such as lysosomes or endosomes, and the plasma membranes of specialized cells is similar to F-ATPase in subunit structure and catalytic mechanism (6).

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Figure 1. Subunit organization of F-ATPase and experimental procedures for observing rotational catalysis. The subunit organization of the F-ATPase holoenzyme (a) and the experimental system used for observing rotation of the F1 sector using actin filaments (b) or gold beads (c) are shown schematically. F-ATPase synthesizes or hydrolyzes ATP coupled with H+ transport through rotation of the γεc10 subunit complex. Gold beads of 40–60 nm diameter were used as probes.

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A key catalytic model, “Binding Change Mechanism (Table1),” proposed by Boyer (1) led to the unique mechanism of F-ATPase including rotation of the subunit complex as a part of steady state catalysis. The rotation enables cooperative interactions between three catalytic sites, each in the β subunits with different conformations. The conformational asymmetry of the three β subunits was suggested biochemically by affinity labeling, chemical crosslinking, and reconstitution from isolated subunits, as reviewed previously (1–5). The first high-resolution X-ray structure of the F1 sector from bovine heart mitochondria clearly showed that the three β subunits in F1 have different catalytic site conformations (7). A series of single molecule studies (Table 1) on thermophilic Bacillus PS3 and the Escherichia coli enzyme established that the γ subunit (8, 9) and γεc10 (10–12) assembly in F1 and F-ATPase (FOF1), respectively, rotate relative to a stator assembly. Thus, the rotation of F-ATPase is coupled with continuous proton transport through a water channel formed from subunits a and c, which include proton translocating residues Arg and Asp (or Glu), respectively (3).

Table 1. Glossary for ATP synthase (proton pumping ATPase)
Binding change mechanism: Paul Boyer proposed the basic catalytic scheme for ATP synthase, called the binding change mechanism. He predicted that the F-ATPase uses a rotational mechanism in which the three catalytic sites in each β subunit are not independent but highly cooperative as shown in Fig. 2a.
Unisite (single-site) catalysis: F1 sector of F-ATPase has three catalytic sites that hydrolyze ATP cooperatively. Unisite catalysis is assayed in the condition where the molecular ratio of ATP and F1 sector is less than 1. Thus, less than one catalytic site can bind ATP, and cooperative effects of three sites are not observed.
Multisite (steady-state) catalysis: Multisite catalysis of F1 or F-ATPase is assayed with excess ATP. In this steady-state condition, the rate of ATP hydrolysis is 104–106-fold faster than that of uni-site catalysis. Thus, the rate of ATP hydrolysis and release of ADP and phosphate from the first catalytic site is accelerated by the binding of ATP to the second and third sites.
Bulk-phase analysis: Bulk-phase analysis is a traditional biochemical assay to study enzymatic kinetics using excess substrate (ATP) and multiple enzyme molecules in solution. Thus, parameters based on bulk-phase analysis are averages obtained from multiple enzyme molecules.
Single molecule analysis: Rotational mechanism of F1 or F-ATPase has been studied using various probes to visualize single molecule. This assay enables us to study behavior of individual enzyme molecule including stochastic fluctuation, active and inhibited states, and detailed rotational mechanism.

Single molecule studies provide information that is not obtainable from bulk-phase analysis (Table 1). However, the rotation speed initially observed using an actin filament (1–3μm length and 0.5 nm thick) as a probe was at least 10-fold slower than that estimated from the steady state ATPase, assuming that three ATP molecules are hydrolyzed per 360° rotation (Fig. 1b) (5). It was not easy to explain the difference, as the activity in the bulk phase should be the average of multiple molecule rotations. As shown by titration between the rotation speed and viscous drag of the probe attached (13), the slow rate of actin was due to its high viscous drag. To analyze the rotation mechanisms of individual enzymes, the probe should exhibit low viscous drag, which minimizes experimental artifacts. We observed ATP-dependent rotation using gold beads of various sizes attached to the γ subunit (Fig. 1c). By using a low viscous drag probe (40 nm or 60 nm gold beads), we could analyze the rotation mechanism of a single molecule. Spetzler et al. (14) recently reported a new method for following the rotation of E. coli F1 using a nanorod (35 nm × 75 nm). This method allowed high time resolution and precise torque estimation. These approaches involving various probes attached to F1 or F-ATPase led a new trend, “Single Molecule Enzymology.”

In this article, we mostly discuss F-ATPase from E. coli, focusing on its stochastic properties, subunit interactions, and thermodynamics. This bacterial enzyme contributes greatly to the understanding of mammalian or plant F-ATPases, as it is similar in structure and function to those from mitochondria or chloroplasts. We refer the readers to recent review articles (1–5) because the length of this article is limited.

Rotating Proton Pumping F-ATPases

  1. Top of page
  2. Abstract
  3. Introduction
  4. Rotating Proton Pumping F-ATPases
  5. Subunit Interactions for Catalysis and Rotation
  6. Acknowledgements
  7. References

The catalytic site in each β subunit undergoes conformational changes during the continuous rotation of the γεc10 complex. The position of the γ subunit in the center of the α3β3 hexamer should define at least the major conformations of the catalytic site in the β subunit, giving βTP, βDP, and βE conformers with an ATP-bound, ADP-bound, and empty catalytic site, respectively, as revealed by the first obtained X-ray structures of bovine F1 (7).

ATP hydrolysis-dependent rotation of the thermophilic Bacillus γ subunit pauses every 120° under the two different conditions: at an ATP concentration several orders below Km and at the concentration giving Vmax (15, 16). The two pauses are obviously due to the different steps of the rotational catalysis. The 120° step was further divided into 80° and 40° substeps using a higher resolution experimental system in the presence of a low ATP concentration (16) (Fig. 2a). The pause before the 80° step became shorter with increasing ATP concentration and was practically undetectable under the Vmax conditions and thus, is defined the “ATP-waiting” or “ATP-binding” dwell. The duration of the pause before the 40° substep was independent of the ATP concentration, but significantly increased when ATPγS [adenosine 5′-O-(3-thiotriphosphate)], a slow hydrolyzing ATP analog, was the substrate (16). Thus, as the pause is attributed to the time for the catalysis, defined as “catalytic dwell,” the reciprocal of the duration giving the catalytic rate.

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Figure 2. F-ATPase rotational catalysis in the active and inhibited states. (a) Schematic model of the F-ATPase reaction in the three β-subunits during 120° revolution. The position of the γ subunit is schematically shown for each intermediate. The ATP binding dwell and catalytic dwell are shown together with the γ subunit rotation angle. The enzyme stochastically enters into the inhibited state from the catalytic dwell. Cited and modified from Sekiya et al. (18). (b) Time courses of gold beads attached to the γ subunit. The time courses of randomly selected gold beads were followed for 16 sec. Some of the catalytically inhibited states are highlighted with the bold line (red). Cited and modified from Sekiya et al. (18). (c) Examples of histograms of single revolution times (time required for 360° revolution) obtained for three single beads are shown. Cited and modified from Nakanishi-Matsui et al. (22).

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The rotation speed is clearly dependent on the viscous drag of the probe attached to the γ subunit of F1ATPase (13, 17). Although actin filament was suitable for demonstrating the rotation of F1ATPase, it is desirable to study single molecule rotational catalysis using a probe with minimal load. The rotation speed of E. coli F1 was ∼400 and ∼2 rps (rounds per sec) when gold beads (40 nm diameter) and actin filaments (0.5–3 μm) were used, respectively (13). The rotation rates of 40–60 nm diameter beads were essentially the same (about 400 rps), suggesting that the speeds observed are close to that of the γ subunit without an attached probe. Thus, we have analyzed the detailed mechanism of rotational catalysis using 60 nm beads. The 120° stepped-rotation together with the ATP waiting and catalytic dwells were confirmed with the E. coli enzyme (17, 18). The rotation of the c10 ring in FO can be also followed using gold beads, the rate being about ∼200 rps (M. Sekiya, H. Hosokawa, and M. Futai, unpublished observation). Although we do not discuss it in detail, stepped rotational catalysis of yeast V-ATPase (19) and Thermus thermophilus ATPase (20) have also been observed.

We focus mainly on E. coli F-ATPase rotational catalysis, taking advantage of its easy purification (21), and the accumulated biochemical results for the wild-type and mutant enzymes (2–5). It should be noted that this enzyme can be studied thermodynamically in the physiological temperature range (10–40 °C) of the organism. Thus, single molecule enzymology will lead to a further understanding of F-ATPases in general.

F-ATPase in the Active Rotating State

We studied stepped-rotation consisting of the catalytic dwell and 120° revolution under Vmax conditions (Fig. 2a). When we estimated the ATP-dependent rotation rates of gold beads every 10 msec, the results were apparently variable, showing a Gaussian distribution (13). Fluctuation of the rotation speed was clearly observed with smaller beads (40, 60 nm), but decreased with larger beads (200 nm), indicating that the fluctuation may be masked by large viscous drag of the probe.

As we often observed long pauses (>100 msec) during the short assay period (2 sec), we decided to extend the observation time (Fig. 2b) and recorded the times required for 360° revolution (single revolution) (18, 22). This analysis included all revolutions of a single bead. Similar to rotation rates of every 10 msec, the single revolution time also showed fluctuation (Fig. 2c). Histograms of the single revolution times were closely similar for individual beads as shown in Fig. 2c (22).

The γ subunit rotates in distinct 120° steps corresponding to the hydrolysis of one ATP, assuming that three ATP molecules are hydrolyzed per single revolution. During each 120° step, ATP binds to βE, and Pi and ADP are released from βDP, and in the catalytic dwell, βTP carries out reversible ATP hydrolysis/synthesis to/from ADP + Pi (Fig. 2a). In the ATP hydrolysis direction at 24 °C, the γ subunit rotates through a continuous cycle of a catalytic dwell (pause before 40°) of 0.20± 0.03 msec and 120° stepping of 0.57 ± 0.05 msec under the Vmax conditions. The catalytic dwells were variable, however, most (99%) of them were shorter than 2 msec. ATP binding dwell is not observed under these conditions because of the high Mg · ATP concentration.

The single revolution time, of which the reciprocal gives the rotation rate, becomes longer and its distribution becomes broader with decreasing temperature (23). These findings promoted us to study rotational catalysis of E. coli F-ATPase at varying temperatures in the physiological range. We determined the thermodynamic parameters for the rates of rotation, 120° stepping, and catalysis (the reciprocal of the duration of the catalytic dwell). The slope of an Arrhenius plot, which gives the activation energy for each reaction, indicates that the rate of 120° stepping and the catalytic rate were not steep but similar to the rotation rate. Thus, the energy pathway of single molecule catalysis is relatively flat, suggesting that highly cooperative interactions among the three catalytic sites mediated by the γ subunit rotation lower the energy barriers for ATP hydrolysis-driven rotation or rotation-driven ATP synthesis.

F-ATPase in the Inhibited State

Noji et al. (8) observed less than 2% of actin filament attached to thermophilic PS3 F1 molecules were rotating, and we observed 5% or less for E. coli. The fraction of E. coli F1 rotating increased to 10% when the observation time was increased to 2sec (M. Nakanishi-Matsui, M. Sekiya and M. Futai, unpublished data). We assumed that 10% of F1 molecules are active and hydrolyzes at a rate 10-fold faster than expected from that of steady state ATP hydrolysis (13). Using a nanorod as a probe, Frasch and coworkers (24) observed that 25% of F1 molecules were rotating dependent on ATP. Thus, the fraction of rotating molecules may depend on the time duration of the rotation assay, the viscous drag of the probe, and possibly other experimental conditions that affect observation of rotating probes.

Upon using a 60 nm bead with low drag and an extended observation time, we observed that beads paused rotation for several orders of magnitude longer than the catalytic dwell. However, the frequency of the long pauses was low, ∼3 long pauses being observed in 1000 revolutions (22). As study of the inhibited state is dependent on the observation time, only 30% of the inhibited state (from the start of the inhibited state pause to the onset of the active state) could be defined in the 2 sec data collection time (18). Thus, we extended the data collection time systematically and could define ∼90% of the inhibited state using a 16 sec observation time (Fig. 2b). The long time courses clearly show that the observed number of rotating beads decreases when the observation time becomes shorter. Similarly, ∼90% of the active periods (from the start of rotation to inhibited pause) could be defined using the 16 sec observation time. The inhibited and active states were also observed with the F-ATPase (FOF1) holoenzyme (M. Sekiya, H. Hosokawa, and M. Futai, in preparation).

We addressed the obvious question of whether the inhibited states are intrinsic properties of the F-ATPase and could be included in its kinetic path (Fig. 2a) (18). During the normal rotation cycle, the γ subunit rotation pauses in a stochastic manner, yielding a catalytically inhibited state (Fig. 2b), which averages ∼1 sec. As discussed above, ATPγS increases the catalytic dwell, whereas a low ATP concentration prolongs the ATP binding dwell. Analyzing the rotation under the two conditions, we confirmed that the enzyme in the catalytically active state (average duration, ∼0.9 sec) enters the inhibited state from the catalytic dwell (Fig. 2a) and resumes rotation after ∼1 sec at a similar speed to that before the pause. Thermodynamic analysis indicated that F1 requires approximately twofold higher activation energy for transition from the active to the inhibited or the inhibited to the active state, compared with that for continuous rotation during the active state. After analysis of rotating beads of various sizes, we concluded that the duration times of the active and inhibited states are less affected by viscous drag than the rotation rate (18).

The ε subunit, a known inhibitor of F1 ATPase, decreased the rotation rate (13) and increased the duration time of the inhibited state about threefold (18) but had essentially no effect on the duration of the active state (18). Thus, the ε subunit inhibits F1ATPase through a combined mechanism. These results indicate that individual enzyme molecules randomly alternate between the two states, which is an intrinsic property of the rotational catalysis by F-ATPase. The inhibited state may be the Mg · ADP-inhibited form of the enzyme observed previously for thermophilic Bacillus using duplex beads of 440 nm diameter (25). As free Mg2+ is inhibitory for bulk phase ATPase activity (26), we examined the effect of free Mg2+ (18). However, free Mg2+ showed essentially no significant effect on the duration of the inhibited state.

The rotation speed of the γ subunit in active state was approximately threefold faster than that estimated from the bulk phase ATPase activity (18). Could we correlate the rotation rate to the bulk phase ATPase activity assuming three ATP molecules are hydrolyzed in a single 360° rotation? To address this question, we observed the rotations of 11 beads in 16 sec, the average rotation rates being calculated by combining the rotation during the active state and the duration times of inhibited states. The average rate for multiple beads calculated was essentially the same as that from the bulk phase ATPase. These results suggest that all F1 molecules in solution alternate between the active and inhibited states similar to the single molecules shown in Fig. 2b. It should be noted that the inhibited state, an intrinsic property of F1 ATPase, branches from the catalytic dwell of the kinetic pathway of the actively rotating enzyme (Figs. 2a and 2b).

It is of interest to determine whether or not F-ATPase molecules alternate between the inhibited and active states in vivo. With alternation between the two states, some of the molecules are always resting. Thus, the population could respond to the high demand of the enzyme activity (or ATP synthesis), if an appropriate activation mechanism is present. Such a mechanism should be addressed experimentally.

Subunit Interactions for Catalysis and Rotation

  1. Top of page
  2. Abstract
  3. Introduction
  4. Rotating Proton Pumping F-ATPases
  5. Subunit Interactions for Catalysis and Rotation
  6. Acknowledgements
  7. References

Mutational Studies on F-ATPase

Catalysis, catalytic cooperativity, and subunit rotation are inseparable features of F-ATPase. We have noticed the importance of subunit/subunit interactions as early studies involving mutant enzymes (27). We found that the α or β subunit mutants apparently lack catalytic cooperativity. They had a defect in steady-state catalysis, whereas the results as to single site (unisite) kinetics (Table 1) were normal. These mutations include αSer373 [RIGHTWARDS ARROW] Phe, αArg376 [RIGHTWARDS ARROW] Cys, and αPro281 [RIGHTWARDS ARROW] Leu (28).

Of these mutant residues, αArg376 is especially interesting as it is located close to Mg and the γ phosphate moiety of ATP bound at the catalytic site of βTP conformers (7). Analyzing mutant enzymes with Lys and Cys at position 376 of the α subunit, we concluded that αArg376 does not play a catalytic role, but is important for conformational transmission among the three sites, as discussed in detail previously (5, 29). βGlu185 located near αArg376 in the catalytic site is also close to the phosphate moiety of ATP in the crystal structure (17). All substitution mutants of this residue lost the catalytic cooperativity, although they retained the ability of unisite catalysis (30). Thus, catalytic cooperativity may be transmitted initially from βGlu185 and αArg376 near the catalytic site. Although it is not located near catalytic residues, the mutant enzyme with substitution of the αSer373 residue showed a lack of catalytic cooperativity (31).

The importance of the conserved phosphate binding loop “P-loop,” the (Gly-X-X-X-X-Gly-Lys-Thr), between βGly149 and βThr156 in the β subunit was first suggested by the mutant (βAla151 [RIGHTWARDS ARROW] Val) enzyme (32). Further analysis of this region revealed catalytic residues such as βLys155, βThr156, βGlu181, and βArg182 (4, 5). These residues are located in the hinge domain (βPhe148–βGly186, P-loop/αhelixB/loop/βsheet4), which changes conformation upon nucleotide binding (7). Mutation analysis including of βSer174 [RIGHTWARDS ARROW] Phe and its suppressors indicated that the hydrophobicity of the domain is critical for rotation (33, 34).

γ and β Subunit (Rotor/Stator) Interaction

The β/γ interaction is pertinent for continuous revolution of the γεc10 complex, as the γ subunit rotates inside the α3β3 hexamer, which forms a stator with the δ, a, and b subunits. The β subunit loop domain (α helix-loop-α helix) including βDELSEED (βAsp380–βAsp386) (Fig. 3a) has attracted our attention since the first X-ray structure of F-ATPase was reported (7). This domain extends from the β subunit (βE and βTP) and is close to the γ subunit region (γLys269–γVal280). Two other loop domains are also apparently close to the γ subunit carboxyl domain (Fig. 3a).

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Figure 3. Interaction between the β and γ subunits during rotational catalysis. (a) Interaction between the β subunit and γ subunit Met23 or its carboxyl terminal domain. γMet23, the βDELSEED motif and bound-piceatannol are shown. The γM23K mutation was suppressed by βE381D in βDELSEED (boxed) and substitution of the residues indicated (closed orange circles). βTP and βDP, that is, β with bound ATP and ADP, respectively, are shown. Structure cited from Gledhill et al. (40). (b) Differences in the thermodynamic parameters between the wild type and mutant F1 or piceatannol. The transition state thermodynamic parameters of wild type and γM23K F1 are shown (left boxes). Differences in the thermodynamic parameters between the wild type and mutant F1 (γM23K or γM23K/βE381D), or F1 with piceatannol are shown (right boxes).

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The importance of the β/γ interaction became clear before the crystal structure became available, when we systematically replaced the γ subunit conserved amino acid (35, 36). One of the most important mutants is γM23K, γ subunit Met23 being replaced by Lys, which was first identified as being defective in energy coupling between catalysis and proton transport (35). The γM23R mutant, the γ subunit Met23 being replaced by Arg, is similar to γM23K. The γM23K mutation was suppressed by the second-site mutations mapped to the carboxyl terminal region of the γ subunit (37) (Fig. 3a). The positions of the first and second mutations could be discussed based on the X-ray structure. The γMet23 residue is close to the βDELSEED (βAsp380–βAsp386) domain of the βDP conformer but does not contribute to the interaction with the βE and βTP subunits. The second carboxyl terminal mutations were localized in the γ subunit domain closely interacting with the β subunit. The interaction between mutant γLys23 and βDELSEED could be confirmed, as the effect of γM23K was suppressed by the βGlu381 in βDELSEED to Asp mutation (βE381D) (38).

Steady state catalysis showed that γM23K has a significant effect on the rate-limiting transition state of ATP synthesis and hydrolysis (23). Consistent with the results, the mutation apparently affected the single molecule behavior of the enzyme (23). γM23K increased the duration of the catalytic dwell significantly, although its effect on the 120° rotation was low. The γM23K mutation caused significantly increased ΔH and TΔS of the rate of catalysis (reciprocal of catalytic dwell) by 60 kJ/mol (Fig. 3b) but had no effect on the activation energy of the 120° stepping. Consistent with the interaction between the mutant lysine at position 23, ΔH and TΔS of γM23K/βE381D became similar to those of the wild type.

The importance of the β/γ interaction was also indicated by inhibitor studies. Phytopolyphenoles, such as quercetin, piceatannol, and resveratrol, are known as F-ATPase inhibitors. One of them, piceatannol (Fig. 3a), was of interest for studying rotational catalysis (39), as the X-ray structure of bovine F1 with piceatannol was shown recently (40). Its binding pocket is formed from the carboxyl terminal residues of the γ subunit including γThr273, γGln274, γThr277, and γGlu278 and several amino acid residues from βTP, αDP, and αTP. Thus, piceatannol can be used to examine interactions between the βTP subunit and the γ carboxyl terminus. As piceatannol showed almost complete mixed type inhibition, we examined its effect on rotational catalysis. Piceatannol did not affect the 120° rotation step, but caused an increased duration of the catalytic dwell, thus lowering the catalytic rate. We then examined the temperature effect on the catalytic dwell and the time for the 120° rotation step. Piceatannol clearly showed a strong effect on the temperature dependence of the catalytic rate. As expected, piceatannol increased ΔH and TΔS about 56 kJ/mol over the control (Fig. 3b), indicating clearly that the inhibitor bound to the α–β–γ interface and affected the rate-limiting transition state that occurs possibly at the later part of the catalytic dwell right before the initiation of 120° rotation.

As piceatannol showed a similar thermodynamic effect to γM23K, we examined the effect of piceatannol on the rotation of the γM23K enzyme. Piceatannol inhibited the bulk phase ATPase activity of γM23K in the same manner as it inhibited that of the wild-type F1, giving an almost identical titration curve between the relative ATPase activity and piceatannol concentration. Piceatannol affected the catalytic rate, causing a 23 kJ/mol higher ΔH and a 18 kJ higher TΔS over the control (γM23K) (Fig. 3b). The inhibitory effects are similar but less striking than those of the wild type. These results indicate the γM23K mutation and piceatannol effects are additive. As discussed above, piceatannol causes a new β/γ interaction at the carboxyl terminus of the γ subunit and γM23K increases the interaction with βGlu381 in βDELSEED. Thus, both rotor–stator interactions perturb the formation of the rate-limiting transition state complex. Both piceatannol and γM23K had no effect on the 120° rotation state, this clearly being related to the rate-limitingstep between ATP hydrolysis (catalytic dwell) and Pi release, which was resolved by means of the presteady state kinetics of F1.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Introduction
  4. Rotating Proton Pumping F-ATPases
  5. Subunit Interactions for Catalysis and Rotation
  6. Acknowledgements
  7. References

This work was supported partly by a Grant-in-Aid from the Ministry of Education, Science and Culture of Japan, and the Japan Science and Technology Agency. We are grateful to Ms. E. Nishiyama and S. Yano for the technical assistance, and J. Wakabayashi for the expert editing.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Rotating Proton Pumping F-ATPases
  5. Subunit Interactions for Catalysis and Rotation
  6. Acknowledgements
  7. References
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