Kinetic Mechanism of F_o·F₁ Mitochondrial ATPase: Mg²⁺ Requirement for Mg·ATP Hydrolysis

A. V. Syroeshkin, M. A. Galkin, A. V. Sedlov, and A. D. Vinogradov^*

Department of Biochemistry, School of Biology, Lomonosov Moscow State University, Moscow, 119899 Russia; fax: (7-095) 939-3955; E-mail: adv@biochem.bio.msu.su

^* To whom correspondence should be addressed.

Received February 4, 1999; Revision received March 9, 1999

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The initial rates of ATP hydrolysis catalyzed by F_o·F₁ (bovine heart submitochondrial particles) preincubated in the presence of P_i for complete activation of the oligomycin-sensitive ATPase were measured as a function of ATP, Mg²⁺, and Mg·ATP concentrations. The results suggest the mechanism in which Mg·ATP complex is the true substrate of the ATPase and the second Mg²⁺ bound at a specific pH-dependent site is needed for the catalysis. Simple hyperbolic Michaelis--Menten dependences of the reaction rate on the substrate (Mg·ATP) and activating Mg²⁺ were found. In contrast to the generally accepted view, no inhibition of ATPase by free Mg²⁺ was found. Inhibition of the reaction by free ATP is due to a decrease of free Mg²⁺ needed for the catalysis. In the presence of both Ca²⁺ and Mg²⁺ the kinetics of ATP hydrolysis suggest that the Ca·ATP complex is neither hydrolyzed nor competes with Mg·ATP, and free Ca²⁺ does not affect the hydrolysis of Mg·ATP complex. A crucial role of free Mg²⁺ in the time-dependent inhibition of ATPase by azide is shown. The dependence of apparent K_m for Mg·ATP on saturation of the Mg²⁺-specific site suggests the formal ping-pong mechanism in which bound Mg²⁺ participates in the overall reaction after dissociation of one product (most likely P_i) thus promoting either release of ADP (catalytic turnover) or slow isomerization of the enzyme--product complex (formation of the dead-end ADP(Mg²⁺)-inhibited enzyme). The rate of Mg·ATP hydrolysis only slightly depends on pH at saturating Mg²⁺. In the presence of limited amounts of free Mg²⁺ the pH dependence of the initial rate corresponds to the titration of a single group with pK_a = 7.5. The simple competition between H⁺ and activating Mg²⁺ was observed. The specific role of Mg²⁺ as a coupling cation for energy transduction in F_o·F₁-ATPase is discussed.

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KEY WORDS: F_o·F₁-ATP synthase, F₁-ATPase, mitochondria, ATP hydrolysis, oxidative phosphorylation

Abbreviations: MF₁, CF₁, TF₁) solubilized F₁s from mitochondria, chloroplasts, and thermophylic bacteria, respectively; CCCP) carbonyl cyanide m-chlorophenylhydrazone; AMP-PNP) 5´-adenylylimidodiphosphate; SMP) submitochondrial particles.

Oxidative phosphorylation and photophosphorylation are catalyzed by F_o·F₁-ATP synthases which are oligomeric proteins embedded in the coupling membranes of mitochondria, chloroplasts, and bacteria. The F₁ component (a peripheral part of ATP synthase) has molecular mass of about 380 kD and is composed of five different polypeptide chains in the stoichiometry alpha₃·beta₃·gamma·delta·epsilon [1-3]. F₁ units from various sources, being energetically uncoupled, rapidly hydrolyze ATP in the presence of bivalent cations, and their catalytic properties have been extensively examined for more than 35 years since the enzyme was first isolated [4]. The 2.8 Å resolution structure for bovine mitochondrial F₁, which is the largest asymmetric protein structure ever solved, recently become available [5].

The membrane-embedded hydrophobic F_o part contains at least three types of subunits (a, b, and c in stoichiometry a·b₂·c_9-12 in E. coli [6]) and has more complex structure for bovine heart F_o [7]. The F_o complex contains a proton pathway conducting protons coupled by an unknown mechanism with ATP synthesis at the F₁ active site(s) at the expense of an electrochemical H⁺ gradient (Deltaµ_H+) across the coupling membrane. Several hypotheses on the mechanism for Deltaµ_H+-consuming ATP synthesis or Deltaµ_H+-producing ATP hydrolysis catalyzed by F_o·F₁-ATP synthase have been proposed and reviewed [8-13]. None of them is conclusively proved, and the molecular mechanism of coupling between proton flow through F_o and ATP synthesis on F₁ seems to be the most challenging problem in bioenergetics.

Three out of six nucleotides which can be cooperatively bound to one F₁ molecule are rather rapidly exchangeable with medium ATP or ADP [14, 15], thus suggesting that three sites on F₁ are potentially capable of participation in the catalytic steady-state turnovers during ATP hydrolysis or synthesis. The presence of three exchangeable nucleotide-binding sites in addition to one or two P_i-binding site(s) [16] and several Me²⁺-specific sites [17-21] per F₁ molecule gives rise to numerous possible enzyme--substrate (product) complexes which may exist during the steady-state catalysis in either direction. In contrast to several reports in the literature on the substrate--velocity curves for the complex [22-26], we found simple Michaelis--Menten dependence of the reaction rate on ATP concentration in the presence of Mg²⁺ [27] under the conditions where the true initial azide-insensitive steady-state rates of ATP hydrolysis were measured. Our results suggest that either a single nucleotide-binding site is involved in the catalysis or an extremely strong cooperativity such as a nucleotide binding exchange mechanism [28, 29] exists during the steady-state enzyme turnovers. It should be emphasized that the true initial rates of ATP hydrolysis (when no ADP is present in the assay system) are azide-insensitive, whereas the apparent initial rates (when the enzyme contains tightly bound ADP) are significantly decreased in the presence of azide [27].

The essential requirement of bivalent cations for ATP hydrolysis catalyzed by mitochondrial preparations of different degree of resolution was recognized many years ago [30-34]. However, an adequate answer to the simple question of the actual ATP- and Mg²⁺-containing species participating as the substrate and activator during ATP hydrolysis has not been found. Numerous studies on this problem have appeared in the literature. It is generally believed that Mg·ATP is the substrate of F₁-type ATPase, whereas free ATP and free Mg²⁺ are inhibitors.

The standard kinetic analysis of enzymatic reactions involving metal--nucleotide complexes must be applied to F₁-type ATPase with great precautions for several reasons. When ATP hydrolysis is followed by continuous monitoring methods, the release of product is biphasic or triphasic depending on the "history" of the preparation. It shows a "burst" or "lag" on the minute time scale, and the time dependence for active --> inactive or inactive --> active transitions is a complex function of the nucleotides and Mg²⁺ concentrations [27, 35, 36]. Thus the possibility of reaching erroneous conclusions from measurements of apparent "initial" rates can hardly be overestimated. Another difficulty in the kinetic analysis of F₁-type ATPase is the possible presence of a small inhibitory peptide [37] which seems to be an intrinsic part of the mitochondrial F_o·F₁-ATP synthase. The inhibitory effect of this protein is also time- and ATP-dependent in addition to the strong pH and ionic strength dependences [37, 38]. It appears that the presence of uncontrolled contaminations of the protein inhibitor might be a source of serious errors in the measurements of the actual rates of ATP hydrolysis, especially in early studies including our own [30-33]. The third difficulty is concerned with the strong requirement of Mg²⁺ for pyruvate kinase [39] which is routinely used for removal of inhibitory ADP in the coupled enzyme assay [40]. Thus variations of free Mg²⁺ in the continuous coupled assay mixtures are limited.

Our search of the literature reveals no report on the kinetic properties of F_o·F₁ (which may or may not be identical to those of energetically uncoupled F₁) conclusively answering the question of whether ATP or Mg·ATP or Mg·ATP and Mg²⁺ serve as the substrate(s) of ATPase. In this paper we present initial rate analysis which shows that the Mg·ATP complex is the substrate for the F_o·F₁-ATPase and the second Mg²⁺ bound in pH-dependent fashion is required for the catalysis. The data are suggestive of an ordered reaction mechanism where free Mg²⁺ participates in the reaction as an uncompetitive (with Mg·ATP complex) activator.

MATERIALS AND METHODS

Submitochondrial particles (SMP). SMP freed of the ATPase inhibitor were protein were prepared from bovine heart mitochondria as described [41] and stored as a suspension (small samples) in 0.25 M sucrose (30-40 mg/ml) in liquid nitrogen. Before the experiments a sample was thawed and diluted to a protein content of 5-10 mg/ml in a mixture containing (final concentrations) 0.25 M sucrose, 0.1 M KCl, 50 µM EDTA, 10 mM Hepes/KOH, and 5 mM potassium phosphate, pH 7.4. The suspension was incubated at 20°C for 1 h and further stored at room temperature (~20°C) during the experiments. The particles treated as described showed no lag in their initial azide-insensitive ATPase activity [42, 43] which was more than 95% inhibited by oligomycin (0.5 nmole/mg protein).

ATPase assay. ATPase activity was measured at 25°C in the standard reaction mixture containing (final concentrations) 0.25 M sucrose, 0.1 M KCl, 10 mM Hepes/KOH buffer, pH 7.4, 3 µM rotenone, 4 µM CCCP, and various concentrations of ATP and MgCl₂. The pH of the reaction mixture was adjusted after ATP and MgCl₂ were added. The pH was 8.0 when La·ATP was used as the substrate.

When the calculated free Mg²⁺ concentration was higher than 10^-4 M, the activity was followed as a decrease in the absorption of NADH (160 µM) at 340 nm; 1.5 mM phosphoenolpyruvate (tricyclohexylammonium salt), pyruvate kinase (12 units/ml), and lactate dehydrogenase (10 units/ml) were added to the standard mixture, and the reaction was initiated by the addition of SMP (15-25 µg/ml).

When the free Mg²⁺ concentration was lower than 10^-4 M, ATP hydrolysis was followed by "stoichiometric" H⁺ release [44] as a decrease in the absorption of Phenol Red (DeltaA_{557-620 nm}). Phenol Red (30 µM) was added to the standard reaction mixture and the reaction was initiated by the addition of SMP (30-40 µg/ml). The stoichiometry of ADP formed/H⁺ released which is dependent on pH and Mg²⁺ concentration [44] was determined as follows. After the reaction followed at 557-620 nm proceeded for 1-2 min, the ATP hydrolysis was stopped by addition of oligomycin (12 nmoles/ml) and the instrument sensitivity was calibrated by the additions of titrated HCl solution. The amount of ADP formed was then determined in the same sample by measuring of the absorption decrease at 340 nm after the addition of 160 µM NADH, 5 mM MgCl₂, 1.5 mM phosphoenolpyruvate, pyruvate kinase (12 units/ml), and lactate dehydrogenase (12 units/ml). It was shown in separate experiments that the pH indicator responded linearly to HCl concentration added and no absorption change of Phenol Red was observed at 340 nm when a pH shift of 0.05 unit was induced by HCl addition. All the activity measurements were performed using a Hitachi-557 spectrophotometer.

It should be noted that all the data and conclusions reported in this paper are valid only for the initial, constant (<30 sec) azide-insensitive rates [42].

Preparation of La·ATP. Equal volumes of 5 mM solutions of LaCl₃ and ATP (pH 3.0) were mixed, and the supernatant after centrifugation (to separate a precipitate formed) was used. The concentration of La·ATP was determined by the absorption at 259 nm. No turbidity was observed when the complex thus prepared was added to the assay mixture.

Estimation of ATP, Mg²⁺, and Mg·ATP concentrations. The concentrations of the variable substrate (or activator or inhibitor) were calculated by solving for the positive roots of the polynomial equations derived from the multiple equilibria:

where Cit stands for citrate, and the conservation equations for the total (analytical) concentrations of added Mg²⁺ ([Mg]_t), ATP^4- ([ATP]_t), EDTA^4- ([EDTA]_t), ADP^3- ([ADP]_t), and citrate ([Cit]_t) were used. The dissociation constants K_Mg·ATP (1·10^-4 M), K_Mg·EDTA (1.6·10^-6 M), K_Mg·ADP (1·10^-3 M), K_Mg·Cit (2.5·10^-4 M), and K_Ca·ATP (2.5·10^-4 M) corrected for pH 7.4 [45, 46] were used for the calculations. All calculations were performed using the GIM version 2 computer program (copyrighted by A. Drachev). It should be noted that slight variations in the absolute values for the dissociation constants found in the literature do not change our conclusions, although proportional variations in the values of K_m(i) for substrate (or activator or inhibitor) are expected.

Reagents. ATP (sodium salt), lactate dehydrogenase, Hepes, EDTA, NADP⁺, CCCP, oligomycin, and glucose 6-phosphate dehydrogenase were obtained from Sigma Chemical Co. (USA). Phosphoenolpyruvate (tricyclohexylammonium salt), pyruvate kinase, and NADH were from Reanal (Hungary). Hexokinase and rotenone were from Ferak (Germany), Chelex-100 was from Bio-Rad (USA). Other chemicals were of the purest grade commercially available.

The stock solutions of ATP and standard reaction mixture (when no EDTA or citrate were added) were treated with Chelex-100 ion-exchange resin (potassium form) to remove contaminating bivalent cations. The concentration of ATP in stock solutions was determined enzymatically (NADP⁺, glucose, glucose-6-phosphate dehydrogenase). The concentration of Mg²⁺ in stock solutions was determined by titration with the standard EDTA in the presence of Eriochrome Black T in NH₄OH/NH₄Cl buffer (pH 10). The enzymes used for the analyses and assays were extensively dialyzed before use. The protein content was determined by the biuret method [47].

RESULTS

Mg·ATP as the substrate for F_o·F₁-ATPase. No measurable ATP hydrolysis was observed in the absence of added Mg²⁺. At fixed added ATP concentrations the ATPase activity (initial rates) increased as the concentration of added Mg²⁺ increased, and no inhibition of the reaction was seen up to the ratio [Mg]_t/[ATP]_t of ~ 30 (Fig. 1a). The dependence of the initial rate on the added ATP concentration at constant [Mg²⁺]_t is shown in Fig. 1b. When the data were plotted as a function of calculated Mg·ATP complex, a single straight line was obtained (Fig. 1c), suggesting simple Michaelis--Menten kinetics of the reaction where Mg·ATP complex is the true substrate (K_m^Mg·ATP = 0.15 mM; V_max = 6.7 µmoles/min per mg protein). These results show that free ATP^4- (in the presence of Mg²⁺) is neither a substrate or inhibitor of ATP hydrolysis. In agreement with our previous finding [27], we were unable to demonstrate any deviation from a simple hyperbolic dependence of the initial rate on the substrate concentration. No hydrolysis of ATP was observed in the presence of Ca²⁺. At limited concentration of Mg·ATP (~K_m^Mg·ATP), Ca²⁺ inhibited the reaction as it would be quantitatively expected if the inhibition were due to redistribution between catalytically inert Ca·ATP and active Mg·ATP complexes (table).

Fig. 1. Dependence of the initial rate of ATP hydrolysis on Mg²⁺ and ATP concentrations. a) Variations of [Mg²⁺]_t at constant concentrations of added ATP (indicated by the figures on the curves). The ATPase activity was assayed with ATP-regenerating system when [Mg²⁺]_t > [ATP]_t and by H⁺ release when [Mg²⁺]_t < [ATP]_t. b) Varying [ATP]_t at 5 (1) and 10 mM [Mg²⁺]_t (2). c) The double reciprocal plot of the combined data presented in (a, Delta) and (b, {} and {}) recalculated assuming that Mg·ATP is the substrate for hydrolysis.

Apparent inhibition of F_o·F₁-ATPase by Ca²⁺

^*ATPase activity was measured as H⁺-release (see "Materials and Methods" section). 100% correspond to the activity calculated using the parameters: V_max = 6.7 µmoles/min per mg protein and K_m^Mg·ATP = 0.15 mM. The concentrations of Mg·ATP were calculated by solving the cubic equation derived from the equilibria between ATP, Mg²⁺, and Ca²⁺ at pH 7.4. The expected rates were calculated assuming a simple Michaelis--Menten dependence of the velocity on [Mg·ATP] and inability of Ca·ATP binding and hydrolysis at the catalytic site. [ATP]_t and [Mg²⁺]_t were 0.2 and 1 mM, respectively.

Binding of free Mg²⁺ is needed for hydrolysis of Mg·ATP. When added ATP was a variable parameter with a limited concentration of Mg²⁺, the ATPase activity reached a maximum at the ratio [ATP]_t/[Mg²⁺]_t of approximately 1 and decreased upon further increase of free ATP (Fig. 2). The ascending parts of the curves are consistent with the results presented in the previous section suggesting that Mg·ATP is the substrate for the hydrolysis. At least two reasons for the descending parts of the curves may be considered. The possibility that free ATP^4- is an inhibitor of the reaction seemed to be unlikely in light of the results presented in Fig. 1c. An inhibition of the reaction at [ATP]_t/[Mg²⁺]_t >> 1 would be also expected if the presence of free Mg²⁺ is needed for the hydrolysis of Mg·ATP. To test the latter explanation the buffer system containing Mg²⁺, ATP, and other anions capable of Mg²⁺ binding was used to create a system in which concentration of the substrate (Mg·ATP) would be maintained at a constant level upon variation of free Mg²⁺. For instance, if the reaction mixture contained 1.65 mM EDTA and 1 mM Mg²⁺ (total concentrations) the variation in [ATP]_t from 0.2 to 1 mM results in variation of [Mg·ATP] from 4.7 to 23 µM, whereas the concentration of free Mg²⁺ remains almost constant (~2.4 µM). This complex buffer system allow varying the substrate concentration at a particular constant free [Mg²⁺].

Fig. 2. Dependence of the initial rate of ATP hydrolysis on [ATP]_t at fixed added Mg²⁺ concentrations. Concentrations of added Mg²⁺ are indicated on the curves. Symbols (o, Delta), the experimental points; continuous lines, the theoretical values calculated according Eq. (1) with the parameters: V_max = 6.1 µmoles/min per mg protein; K_s^Mg·ATP = 0.1 mM; and K_s^Mg = 0.025 mM.

Figure 3 presents an example of the dependences of the reaction rate on the substrate concentrations ([Mg·ATP]) at different constant [Mg²⁺]. When apparent maximal rates extrapolated to infinite [Mg·ATP] were plotted as a function of free Mg²⁺ concentrations, a simple hyperbolae was obtained with the parameters: K_m^Mg = 0.02 mM and V_max = 6.3 µmoles/min per mg protein (Fig. 3a). It appears that a single activating Mg²⁺-specific site is operating during the steady-state catalysis. The kinetic behavior of the reaction (Fig. 3b) suggests the formal ping-pong mechanism, where the substrate (Mg·ATP) transformation at the enzyme active site (hydrolysis of Mg·ATP and/or release of one product (ADP or P_i)) precedes the involvement of free Mg²⁺, which is needed to complete the catalytic cycle. The kinetic equation for such a mechanism (see scheme shown in Fig. 8 in the "Discussion" section) appears as:

and it is expected that an inhibition of the reaction would occur at high concentrations of added ATP at any given Mg²⁺ concentration. Figure 2 shows that the experimentally determined initial rates fit the theoretical prediction when the approximated values of K_s^Mg·ATP and K_s^Mg were used. Taken together, the results presented in this and previous section strongly suggest that Mg·ATP is a true substrate for F_o·F₁-ATPase and free Mg²⁺ is needed as an obligatory activator for the steady-state ATP hydrolysis.

Fig. 3. Kinetic parameters of Mg·ATP hydrolysis at different Mg²⁺ concentrations. a) The reaction rates (v) extrapolated to infinite Mg·ATP were measured as a function of free Mg²⁺ (double reciprocal plot). Concentrations of constant free Mg²⁺ were maintained utilizing Mg²⁺/citrate/ATP buffer (o) or Mg²⁺/EDTA/ATP buffer (o) (see "Materials and Methods" section). b) Secondary plot (V_max versus K_m^Mg·ATP) of data obtained as in (a).

It should be noted that an alternative interpretation of the data shown in Fig. 2 is possible assuming that Mg·ATP is the substrate and free ATP is an inhibitor. An ambiguity in interpretation is due to the fact that the concentrations of ATP and Mg²⁺ at equilibrium are certain to obey the mass action low. It was desirable to find a more direct experimental approach to show the requirement of free Mg²⁺ for the ATPase reaction. The kinetically inert complexes of metals with ATP [48, 49] seemed to be a useful tool to discriminate between the two possible interpretations. This approach was used previously by Pedersen's group for the soluble rat liver F₁ [48]. As depicted in Fig. 4, the La·ATP complex is not hydrolyzed unless Mg²⁺ is added. In the presence of free Mg²⁺ the rate of ATP hydrolysis is about 15% of that observed for the Mg·ATP maximal rate.

Fig. 4. Hydrolysis of La·ATP by F_o·F₁-ATPase. The reaction was followed as H⁺ release measured with Phenol Red (see "Materials and Methods" section). La·ATP (0.2 mM), MgCl₂ (0.2 mM), SMP (0.4 mg/ml), and oligomycin (12 nmoles/ml) were added where indicated by the arrows. The rate of La·ATP hydrolysis initiated by the addition of Mg²⁺ was 0.7 µmole/min per mg protein.

Since the affinity of the binding site for a cation is expected to be pH dependent, it was of interest to determine how the pH dependence of the enzyme activity (if it exists) is related to the Mg²⁺ requirement. Figure 5 demonstrates that the initial rate of ATP hydrolysis was only slightly changed within the pH interval from 6.8 to 8.0 when free Mg²⁺ was in excess (~10 K_m^Mg) and becomes strongly pH dependent when free Mg²⁺ was limiting. An apparent pK_a of 7.4 for a group or groups involved in Mg²⁺ binding was estimated from the titration curve, and simple competition was observed between activating free Mg²⁺ and H⁺ (Fig. 6).

Fig. 5. pH dependence of ATPase activity. 1) Mg²⁺ concentration was 0.5 mM; ATP-regenerating system was used for ATPase assay; 2) Mg²⁺ concentration was 5 µM; ATPase activity was assayed as H⁺ release. H⁺ released/ADP formed ratio was varied from 0.68 at pH 7.0 to 0.96 at pH 8.2 and the rates were corrected as described in "Materials and Methods" section.

Fig. 6. Competitive inhibition of ATPase by H⁺. [Mg·ATP] was 0.1 mM; calculated reciprocal free concentrations of Mg²⁺ are plotted on the abscissa.

Mg²⁺(ADP)-specific time-dependent inhibition and requirement of free Mg²⁺ for ATP hydrolysis. It has been shown that ADP-loaded F_o·F₁-ATPase is sensitive to Mg²⁺-induced slow isomerization of the ADP--enzyme complex, producing inactive ATPase which is stabilized by azide [42, 50]. Since the binding of free Mg²⁺ at the enzyme specific site was shown to be required for the steady-state ATP hydrolysis (see previous section), it was of interest to get deeper insight into the relations between the role of Mg²⁺ in the catalysis and in the deactivation process. The parameters of ATP hydrolysis activation by Mg²⁺ (Fig. 3a) and those determined as the first-order rate constant for the azide-induced deactivation [42] (Fig. 7) were quantitatively estimated. Both dependences were found to fit a simple hyperbolic function with the dissociation constant for Mg²⁺ of about 4·10^-5 M. These results are in accord with the proposal on a single free Mg²⁺ binding site.

Fig. 7. Mg²⁺ dependence of inhibition of ATPase by azide. a) The standard reaction mixture contained 200 µM sodium azide and increased amount of pyruvate kinase (300 units/ml) to avoid rate limitation at low free [Mg²⁺]. The concentration of Mg·ATP was 1 mM. The reaction was initiated by the addition of SMP and followed continuously. The first-order rate constant of azide-induced inhibition was calculated [42] and plotted as a function of free [Mg²⁺]. Concentrations of free Mg²⁺ were varied by the excess of ATP added. b) Double reciprocal plot of the data shown in (a).

DISCUSSION

Many years ago we reported that depending on the "history" of the preparation the mitochondrial F₁- or F_o·F₁-ATPase shows either lag-phase or burst in the activity assayed in the presence of an ATP-regenerating system [27]. The interplay of Mg²⁺-dependent deactivation of the enzyme--ADP intermediate [27, 50] and ATP-dependent reactivation of the inhibited enzyme [27] (both reactions are slow compared with the enzyme turnover) could lead to erroneous interpretation of the velocity versus substrate curves. Moreover, the meaning of the "initial rate", which is a standard parameter used for steady-state kinetic analysis, becomes ambiguous when applied to a system where the amount of catalytically competent enzyme is changed within the time scale comparable with the resolution limit of the assay. These considerations prompted us to reinvestigate a long standing problem: what are the true species which interact with F_o·F₁-ATPase during steady-state ATP hydrolysis? Our data confirm and reinforce the generally accepted belief (for exceptions, see [51, 52]) that Mg·ATP complex is the specie taken up from solution as the substrate for the reaction. However, our results reject another generally accepted view, that free Mg²⁺ is an inhibitor of the reaction [34]. The most likely reason for the latter is that no precautions for complete activation of ATPase (removal of tightly bound ADP [27]) were taken in the previously published works. When the concentration of free Mg²⁺ in the assay system is high, a fraction of the enzyme preparation becomes rapidly deactivated, and the apparent "initial rate" is underestimated.

Our data show that free Mg²⁺ (in addition to Mg·ATP) is needed for the catalysis. This is in accord with the conclusion reached by other authors for F₁ from rat liver [48] and from Halobacterium saccharovorum [53]. In addition to providing new information about the participation of free Mg²⁺ in Mg·ATP hydrolysis by F_o·F₁-ATPase, the results presented here are relevant to the sequence of the catalytic steps. The extended kinetic scheme of the reaction is shown in Fig. 8. As shown in this study, the activating effect of free Mg²⁺ is described by the formal ping-pong mechanism. Mechanistically this would mean that activating Mg²⁺ participates in the overall reaction after one of the products (ADP or P_i) is released. Several findings suggest that P_i leaves the ATPase active site before ADP. First, it is well documented that P_i is not required for ADP binding. Moreover, P_i reverses ADP-induced (in the presence of Mg²⁺) deactivation of the ATPase [43] or Mg²⁺-induced deactivation of the ADP-preloaded ATPase [50]. Second, both the steady-state rate of ATP hydrolysis (routes (1)-(5)) and the deactivation rate (routes (1)-(6)) are changed proportionally when either Mg·ATP [27] or free Mg²⁺ (this paper) are variable parameters, independently of the presence of P_i. The absence of any inhibitory effect of P_i on F_o·F₁-ATPase [43] suggests that P_i leaves the enzyme during uncoupled ATP hydrolysis from a very low-affinity site. The low affinity for leaving P_i compared to the high affinity for ADP [35] can provide a thermodynamic basis for the kinetic sequence of the release of the products during ATP hydrolysis. It worth noting that the apparent K_m value for P_i during oxidative phosphorylation under conditions similar to those used in this work for ATPase assay is about 1 mM (our unpublished observation). The absence of the inhibitory effect of P_i on the ATPase is hard to reconcile with simple reversibility of the reaction steps during hydrolysis and synthesis of ATP.

Fig. 8. Reaction scheme for hydrolysis of ATP catalyzed by the mitochondrial F_o·F₁-ATPase. E, T, D, P_i, M, and M_a stand for the enzyme, ATP, ADP, inorganic phosphate, Mg²⁺ originated from Mg·ATP, and free activating Mg²⁺, respectively. The scheme does not attempt to portray the interactions between the enzyme subunits during the reaction. The hydrolytic steps (2)-(5) may certainly depend on the cooperative interactions within multisubunit enzyme (binding change mechanism [12]) possibly including rotation of the gamma-subunit [54]. The scheme is rather intended to describe the fate of the substrate during catalytic turnover. It should be noted that steps (4) and (5) are shown as binding and release of Mg²⁺ for the sake of clarity; no difference in the kinetic behavior of the system (Eq. (1)) would be seen if the activating Mg²⁺ (M_a) remains permanently bound to the enzyme during the catalysis, participating in the reaction cycle after P_i release. For simplicity, a combination of equilibrium (steps (1)-(2) and (4)) and steady-state (steps (3) and (5)) approximations were applied to derive Eq. (1) describing the reaction scheme.

Strong data for the presence of a Mg²⁺-specific site on mitochondrial F_o·F₁-ATPase [50] and CF₁ [55] which is responsible for Mg²⁺-induced deactivation of ATPase have been reported. A two-step mechanism for Mg²⁺-induced deactivation of ADP-loaded enzyme was proposed, which includes rapid, pH and nucleotide-dependent binding of Mg²⁺ (K_s value of 1·10^-4 M at pH 7.4) and subsequent isomerization of the complex resulting in the inactive enzyme [50]. The apparent affinities for free Mg²⁺ determined from quantitation of: (1) Mg²⁺-induced deactivation of ADP-preloaded F_o·F₁ [50], (2) Mg²⁺ requirement of Mg·ATP hydrolysis (this paper), and (3) Mg²⁺ dependence of azide-induced inhibition (this paper) at pH 7.4 are 1·10^-4, 2·10^-5, and 4·10^-5 M, respectively. The latter two values are similar, and it is not unexpected that the value determined for (1) is considerably higher: a strong dependence of the apparent affinity for deactivating Mg²⁺ on occupation of nucleotide-binding sites has been documented [21]. The actual occupancy of three rapidly exchangeable nucleotide-binding sites during steady-state ATP hydrolysis is not known. Thus, we believe that the same Mg²⁺-specific site is responsible for all three processes, and the reaction sequences (3)-(4)-(5) and (3)-(4)-(6) (Fig. 8) describe the final steps of ATP hydrolysis and deactivation, respectively. The simple competitive inhibition of Mg·ATP hydrolysis by free ADP (our results which are not included in this paper) is expected if the reaction sequence proceeds as depicted in the reaction scheme whereby free ADP leaves the ATPase catalytic site via a Mg²⁺-dependent mechanism. The tight binding of ADP and some nucleotide derivatives to TF₁ and MF₁ in the absence of Mg²⁺ and major rearrangements of the nucleotide-binding sites after subsequent addition of Mg²⁺ have been documented [56, 57]. On the other hand, Mg·ADP serves as the substrate for photo- [58] or oxidative phosphorylation (our unpublished results). The difference in the reactive species leaving the catalytic site during steady-state ATP hydrolysis and entering the catalytic site during steady-state ATP synthesis is in accord with our hypothesis of different catalytic mechanisms for operation of F_o·F₁ in the hydrolytic and synthetic directions [59, 60].

Since the structure at 2.8 Å resolution of bovine heart mitochondrial F₁-ATPase became available [5], an obvious question arises: where is the single Mg²⁺-specific site located? Structures of the nucleotide-binding sites of asymmetric F₁ containing Mg²⁺--nucleotide complexes with a slight difference in the ligands to Mg²⁺ in the alpha- and beta-subunits were identified [5]. Surprisingly, no Mg²⁺ other than that originating from the Mg²⁺--nucleotide complexes was visualized despite the presence of 250 µM AMP-PNP, 5 µM ADP, 6 mM Mg²⁺, and 3 mM sodium azide and the absence of P_i in the crystallization medium [61], i.e., conditions which must produce the deactivated Mg²⁺-containing enzyme. Several possibilities for an explanation of the absence of visualized Mg²⁺ can be offered. Major rearrangement of F₁ subunits and the substrate/activator binding sites induced by interaction of F₁ and F_o is one possible reason [62]. Another possibility is that the Mg²⁺-specific site is located on a disordered "invisible" part of the gamma-subunit. Such speculation may be supported by the findings that ATP hydrolysis catalyzed by the reconstituted 3alpha·3beta TF₁ is not sensitive to azide [63, 64], which is known to inhibit ATPase by a Mg²⁺-dependent mechanism ([21, 42, 50] and this paper). If this hypothesis is correct, the structural arrangements of the events shown in the reaction scheme (Fig. 8) are that free ADP formed at the catalytic site after (P_i·Mg) release is removed to the solution via the interaction between the Mg²⁺-liganded arm of the gamma-subunit and beta-subunit. A key role of Mg²⁺ in the energy transducing enzymes has long been suggested [65, 66]. The large pH dependence of the Mg²⁺-specific site evidenced from the Mg²⁺-dependent steady-state hydrolysis of Mg·ATP (Figs. 5 and 6) is in line with this proposal. The prediction of the hypothesis on the key role of Mg²⁺ in coupling between transmembrane proton or sodium [67] flows and binding/release of nucleotides at the catalytic site(s) is that the binding of Mg²⁺ to the F₁ part of F_o·F₁-ATPase/synthase must be Deltaµ_H+-dependent. Experiments aimed to clarify this possibility are currently underway in our laboratory.

We thank Drs. E. Maklashina, V. Grivennikova, and E. Gavrikova for their help in the preparation of SMP.

This work was supported by the Russian Foundation for Basic Research (grants 96-04-48185 and 99-04-48082) and by the Program for Advanced Schools in Science (grant 96-15-97822).

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