Comparison of the H⁺/ATP ratios of the H⁺-ATP synthases from yeast and from chloroplast

Abstract

F₀F₁-ATP synthases use the free energy derived from a transmembrane proton transport to synthesize ATP from ADP and inorganic phosphate. The number of protons translocated per ATP (H⁺/ATP ratio) is an important parameter for the mechanism of the enzyme and for energy transduction in cells. Current models of rotational catalysis predict that the H⁺/ATP ratio is identical to the stoichiometric ratio of c-subunits to β-subunits. We measured in parallel the H⁺/ATP ratios at equilibrium of purified F₀F₁s from yeast mitochondria (c/β = 3.3) and from spinach chloroplasts (c/β = 4.7). The isolated enzymes were reconstituted into liposomes and, after energization of the proteoliposomes with acid–base transitions, the initial rates of ATP synthesis and hydrolysis were measured as a function of ΔpH. The equilibrium ΔpH was obtained by interpolation, and from its dependency on the stoichiometric ratio, [ATP]/([ADP]·[P_i]), finally the thermodynamic H⁺/ATP ratios were obtained: 2.9 ± 0.2 for the mitochondrial enzyme and 3.9 ± 0.3 for the chloroplast enzyme. The data show that the thermodynamic H⁺/ATP ratio depends on the stoichiometry of the c-subunit, although it is not identical to the c/β ratio.

Cells of all life kingdoms use H⁺-ATP synthases to produce the cellular energy carrier ATP from the energy of a transmembrane electrochemical potential difference of protons built up and maintained by proton transport mechanisms, such as the oxidative electron transport in mitochondria or the photoinduced electron transport in chloroplasts (1). The number of protons translocated for each synthesized ATP molecule (H⁺/ATP ratio) determines how large this difference of proton potential needs to be to maintain the high ATP/ADP ratio required by cell life. It is a key parameter in determining the flow of energy conversions in all living organisms. Ever since compelling experimental evidence in favor of a rotational mechanism for ATP synthases appeared (2–10), picturing them as molecular nanomachines in which two differently stepped motors (the membrane-embedded c-oligomer and the tripartite catalytic head) are connected by a central rotating shaft (γ/ε subunits), the general assumption has been that the H⁺/ATP ratio should coincide with the ratio of the number of proton-binding c-subunits to the three catalytic nucleotide-binding β-subunits. Structural data have shown that the number of c-subunit monomers varies according to species (ref. 11 and references therein), with numbers that are mostly not multiples of three. Consequences of the above assumption are (i) the H⁺/ATP ratio can vary among different species, and (ii) the H⁺/ATP ratio can be a noninteger number. The number of β-subunits is three in all F₀F₁ analyzed so far, and the number of c-subunits varies between 8 and 15, resulting in predicted H⁺/ATP ratios between 2.7 and 5.0. To our knowledge, neither of the two assumptions above has yet been experimentally challenged with the required accuracy.

In this work, we tested both assumptions by measuring in parallel the H⁺/ATP ratio of the isolated and reconstituted H⁺-ATP synthases from yeast mitochondria and from spinach chloroplasts. The c-subunit stoichiometry of the former is 10, as determined by X-ray crystallography of the whole complex (12, 13), and the stoichiometry of the latter is 14, according to X-ray crystallography (14, 15) and atomic force microscopy of the isolated c-ring (16). Hence, their respective H⁺/ATP ratios, based on the assumptions mentioned above, should be 3.3 and 4.7. We have isolated the two complexes and reconstituted them into liposomes, which, if subjected to acid–base transitions to generate a high protonmotive force, were able to synthesize ATP at physiological rates (17, 18). The technique of acid–base transitions offers the great advantages of (i) measuring the imposed transmembrane ΔpH with the accuracy of the pH electrode, thus making high-precision quantitative studies possible (18–20), and (ii) allowing the testing of ATP synthases from different species with the same method and under identical experimental conditions.

Results

According to the chemiosmotic theory (1), the synthesis of ATP catalyzed by the H⁺-ATP synthase is coupled to the translocation of n protons from the internal to the external compartment:

The factor n is the number of protons translocated per ATP, and it is called the thermodynamic H⁺/ATP ratio. The Gibbs free energy of this coupled reaction can be expressed as:

where is the transmembrane electrochemical potential difference of protons, ΔG°′_p is the Gibbs free energy of ATP synthesis, using the biochemical standard state, Q is the stoichiometric product: ([ATP]c⁰)/([ADP][P_i]) with c⁰ = 1 M, ΔpH is the transmembrane pH difference: pH_out − pH_in, Δφ is the transmembrane difference of electrical potential: φ_in − φ_out, and R, T, and F are gas constant, absolute temperature, and Faraday constant, respectively.

At the point of equilibrium (ΔG′ = 0), Eq. 2 becomes:

At constant Δφ(eq), only ΔpH(eq) and log(Q) are variables, and therefore, with a set of experimental values of log(Q) and ΔpH(eq), both the H⁺/ATP ratio n and ΔG°′_p can be determined by linear regression analysis. In the present work, a constant Δφ of 60 mV (as evaluated from the Nernst equation) was applied to all measurements, to achieve higher rates of catalysis.

To apply this method we constructed a minimal chemiosmotic system (18, 19). Liposomes from phosphatidylcholine/phosphatidic acid were prepared, and either the chloroplast or the mitochondrial enzyme was reconstituted into the liposome membrane. When these proteoliposomes were energized by acid–base transitions they catalyzed rates of ATP synthesis up to 200 s⁻¹ with CF₀F₁ (21, 22) and 100 s⁻¹ with MF₀F₁ (17) (i.e., they displayed synthesis activities in the physiological range). Because for reconstitution of the enzymes the membrane was destabilized by addition of detergent (Triton X-100), it can be assumed that during this process (2 h) a full equilibration of all ion concentrations between the internal and external phases took place, so that the composition of the internal phase was known. Correspondingly, the pH_in value was taken to be identical to the pH of the reconstitution buffer, which was measured with a glass electrode after the reconstitution. The ion concentrations of the internal and external phases are collected in Table S1. The pH_out value resulted from the mixing of the acidic reconstitution buffer containing the proteoliposomes with the basic medium. At the mixing time (t = 0), a transmembrane ΔpH is established, which decays thereafter within a few minutes owing to passive and phosphorylating proton effluxes. Because pH_in and pH_out were measured with the same calibrated glass electrode, both parameters were known with high accuracy and precision, the error in the initial ΔpH measurement being smaller than 0.02 units (18). With the glass electrode the proton activities are detected, so that no further corrections were necessary for determination of ΔpH values.

To determine the ΔpH(eq) at each Q value (i.e., the ΔpH at which the phosphate potential is exactly balanced by ΔpH and the catalytic rate is zero), the initial rates of catalysis were measured at different initial ΔpHs at a constant stoichiometric product Q, so that both synthesis and hydrolysis could be observed, and the point of zero rate could be easily interpolated. The initial rates of catalysis were measured by rapid injection of the acidified proteoliposomes into the basic mixture, containing an ATP-monitoring luciferin/luciferase system. The ATP, ADP, and P_i concentrations in the basic medium were then varied within a wide range to establish different stoichiometric products Q (Table S2). In this way the initial rates of ATP synthesis and hydrolysis were measured both at different initial ΔpHs generated by the acid–base transition and at different Qs.

Typical measurements at Q = 5.8 and pH_out = 8.38 are shown in Fig. 1 for CF₀F₁ (Upper Left) and MF₁F₀ (Upper Right). Increase of luminescence indicates ATP synthesis, and decrease indicates ATP hydrolysis. The different curves refer to different initial ΔpH values as indicated. The initial rates were calculated by nonlinear regression analysis (Materials and Methods), and they are depicted in Fig. 1 as slopes at t = 0. The initial rates switched from ATP synthesis at the highest initial ΔpH to ATP hydrolysis at the lowest initial ΔpH. In each trace the rate of ATP synthesis decreased with time after the acid–base transition. In some traces (Fig. 1, Upper Right, trace at ΔpH = 1.68) the rate switched from ATP synthesis to ATP hydrolysis. This was because the measurements were carried out in the presence of both P_i/ADP and ATP, and therefore, as soon as the ΔpH had decreased below the thermodynamic threshold value of ΔpH(eq), the catalytic reaction switched from the synthesis to the hydrolysis direction. Additionally, the increase of the rate of ATP hydrolysis, observed in most hydrolysis traces, can be attributed to the decay of the initial ΔpH, and the corresponding release of its “backpressure” exerted on proton transport-coupled ATP hydrolysis. The initial rates of catalysis were calculated from the fitted traces and plotted against the initial ΔpH in Fig. 1, Lower.

Fig. 1.

ATP synthesis and hydrolysis after generation of different ΔpHs. Upper: Basic medium with luciferin/luciferase (720 μL) was placed in the luminometer, and the baseline was registered. Black arrows show the addition of the acidic proteoliposomes (80 μL) to the basic buffer. This addition gave rise to a shift of the baseline, which was shifted for clarity to the original luminescence level. The stoichiometric product Q = [ATP]/[ADP][P_i] was 5.8 ([ATP] = 596 nM, [ADP] = 10.3 μM), the pH_out was 8.38. Red solid lines are best fittings (see Materials and Methods) of the luminescence time trace; the initial rates were calculated from the fitted trace and shown as slopes at t = 0. The calibration of the ordinate is given in ATP per F₀F₁. Upper Left: Chloroplast enzyme, [CF₀F₁] = 13 nM; Upper Right: Mitochondrial enzyme, [MF₀F₁] = 13 nM. Lower: Initial rates of ATP synthesis (positive) and hydrolysis (negative) as a function of ΔpH. Each point is the average of three measurements, and black error bars are the corresponding SDs. The equilibrium ΔpHs [ΔpH(eq), red circles] were obtained by interpolation with a sigmoidal function. Red error bars of ΔpH(eq) resulted from the interpolation with the same function of the upper or lower error limits of the rates (shaded area).

The point of equilibrium ΔpH(eq) was obtained by interpolation to zero rate using a sigmoidal function. It was ΔpH(eq) = 0.84 ± 0.02 for CF₀F₁, and ΔpH(eq) = 1.57 ± 0.04 for MF₀F₁, with a difference of 0.73 ΔpH units between both enzymes at the same stoichiometric product (Q = 5.8). The error bars of ΔpH(eq) resulted from the interpolation with the same function of the upper and lower error limits of the rates (Fig. 1, Lower, shaded areas). The fitting with other functions (exponential or polynomial) yielded within error limits the same ΔpH(eq) values.

A correct interpolation requires that the same proton transport-coupled reaction is observed both in ATP synthesis and ATP hydrolysis direction. Whereas ATP synthesis is always coupled to proton transport, ATP hydrolysis can occur either coupled to proton transport or uncoupled from it. Uncoupled ATP hydrolysis might be catalyzed by reconstituted enzymes that are partially damaged and/or by nonreconstituted enzymes. When the ΔpH was abolished by addition of 10 μM nigericin, CF₀F₁ and MF₀F₁ showed different responses: CF₀F₁ did not show any ATP hydrolysis, whereas MF₀F₁ did. This is in agreement with previous results (18, 19) and confirms that CF₀F₁ is a strongly regulated enzyme, which is inactive in the absence of a pre-energization by (23). We concluded that CF₀F₁ did not catalyze uncoupled ATP hydrolysis and that, therefore, no corrections for uncoupled ATP hydrolysis were required. For MF₀F₁ as well, the presence of a strong preactivation by has been reported (24). However, with MF₀F₁ small rates of ATP hydrolysis were detected in the presence of nigericin at Q values ≥1.87, and these rates increased with increasing Q value. The luciferin/luciferase technique detected changes of the ATP concentration in the medium, which resulted from the difference between ATP synthesis and coupled as well as uncoupled ATP hydrolysis. To calculate the rates of coupled ATP synthesis and hydrolysis from the change in ATP concentration, the rate of uncoupled ATP hydrolysis has to be determined. The two kinds of ATP hydrolysis can be distinguished by their different response to . At high , coupled ATP hydrolysis is completely inhibited, because proton pumping against a high protonmotive force is not possible, whereas uncoupled ATP hydrolysis is unaffected. The rate of ATP hydrolysis under high conditions (i.e., in the presence of a high rate of ATP synthesis) can be quantified with radioactive labeled ATP. The release of ³²P_i from [γ-³²P]ATP was measured in parallel in the absence and in the presence of a high . Under the high conditions, any rate of hydrolysis would result only from the noncoupled enzymes, and this rate must be subtracted from the rate observed in the luciferin/luciferase assay to obtain the rate of the coupled catalysis.

Fig. 2, Top, shows the [γ-³²P]ATP hydrolysis at Q = 5.8 in the presence (filled circles) and absence (+nigericin, open circles) of a high (pH_in = 6.2, ΔpH = 2.1, Δφ = 140 mV). The numbers at the slopes give the hydrolysis rates. When a higher (pH_in = 5.0, ΔpH = 3.3, Δφ= 140 mV) was used in the acid–base transition, the rates did not change, indicating that the maximal inhibition of the -dependent hydrolysis rate had already been reached at ΔpH = 2.1, Δφ = 140 mV. The rates obtained at the other Q values are reported in Fig. 2, Middle and Table S3. The rates measured at Q = 5.8 with the luciferin/luciferase assay (dotted line) and the same rates corrected for ATP hydrolysis by uncoupled enzymes (solid line) are shown in Fig. 2, Bottom. The ΔpH(eq) values before and after such correction were in this case 1.57 ± 0.04 and 1.53 ± 0.04, respectively. The corrections resulting for the ΔpH(eq)s obtained at the other Q values are reported in Table S4.

Fig. 2.

Correction of the catalytic rates for the noncoupled rate of hydrolysis. Top: The ³²P_i released was measured at Q = 5.8 ([ATP] = 596 nM, [ADP] = 10.3 μM) as a function of time, as described in Materials and Methods. The acid–base transition was carried out at pH_out = 8.38 and pH_in= 6.3 and a K⁺/valinomycin diffusion potential of 140 mV. Filled circles: the membrane was energized by the acid–base transition at time t = 0. Open circles: the acid–base transition was carried out as before, but the basic medium contained 10 μM nigericin to dissipate the generated across the membrane. The rates of ATP hydrolysis were determined by the slopes of the best-fitting straight lines. The errors in the determination of the slopes were below 4% and have been neglected. Middle: Rates of ATP hydrolysis at different stoichiometric ratios (nucleotide concentrations in Table S2) in the presence of 10 μM nigericin (open columns) or in the presence of (hatched columns). Bottom: Open circles: rate of ATP synthesis and ATP hydrolysis by MF₀F₁ as function of ΔpH. Data are from Fig. 1, Lower. The interpolating best-fitting curve (dashed line) and ΔpH(eq) are also shown. Solid circles: data obtained after correcting the rate measured with the luciferin/luciferase assay for ATP hydrolysis catalyzed by enzymes that were not coupled with proton transport. The ΔpH(eq) after correction is indicated by the solid circle.

Measurements of initial rates in the luciferin/luciferase assay at different ΔpHs were carried out at several constant Q values (Q = 0.1–16). These sets of initial rates, corrected as described above (Fig. 2, Bottom), are shown in Fig. 3 as a function of ΔpH for CF₀F₁ (Upper) and MF₀F₁ (Lower). All ΔpH(eq) values and the error limits were determined by interpolation as described in Fig. 1, and they ranged between 0.52 and 0.98 ΔpH units for CF₀F₁, and between 0.96 and 1.82 ΔpH units for MF₀F₁. As can be seen in Fig. 3, the dependencies of the rates on ΔpH were nonlinear, showing a slow rise in the ATP hydrolysis range and a steep rise in the ATP synthesis range. On the basis of the thermodynamics of irreversible processes, a linear relation between the rate and driving force (ΔpH) was expected. For CF₀F₁, this phenomenon has been analyzed (18): by correcting the observed nonlinear rate dependencies for the experimentally measured ΔpH dependency of enzyme preactivation, the expected linear relation was indeed obtained. This correction did not change, within error limits, the determined ΔpH(eq) values, because the sampling of ΔpH values was close enough to equilibrium compared with the curvature of the rate dependency. MF₀F₁ has been also shown to be preactivated by ΔpH (24), but no quantitative data are available. However, because the probed ΔpH values were similarly close to equilibrium, we concluded that no correction was needed for these data either. The dependencies of the rates on ΔpH showed different curvatures for the different Q values. Presumably, these differences can be attributed to regulatory effects of ADP and ΔpH. In particular, it can be observed that the curvature is generally less pronounced when, for a given ADP concentration, the ΔpH(eq) was increased owing to a higher ATP concentration. Regulatory phenomena, however, will not shift the point of thermodynamic equilibrium.

Fig. 3.

Rates of catalysis as a function of ΔpH (in the presence of a constant Δφ). The rates of ATP synthesis and hydrolysis catalyzed by CF₀F₁ (Upper) and MF₀F₁ (Lower) are shown (at Δφ = 60 mV) as a function of ΔpH at different stoichiometric products. For MF₀F₁ with Q ≥1.9, the initial rates were corrected for the hydrolysis rates that were not coupled with proton transport (Fig. 2). The equilibrium ΔpH for each curve was obtained by interpolation as described in Fig. 1. The different Q values were obtained by varying the ATP concentration from 50 to 750 nM and the ADP concentration from 51 to 4.6 μM at constant [P_i] = 10 mM (Table S2).

The H⁺/ATP ratio and ΔG°′_p were determined from the dependence of on the preestablished stoichiometric product Q. The quantity 2.3RTlog(Q) and the corresponding transmembrane electrochemical potential difference of protons at equilibrium, 2.3RTΔpH(eq) + FΔφ(eq), were plotted in Fig. 4 for both CF₀F₁ (circles) and MF₀F₁ (triangles) and fitted by linear regression. According to Eq. 3, the numerical values of the slopes give the thermodynamic H⁺/ATP ratios n: here, n = 3.9 ± 0.3 for CF₀F₁, and n = 2.9 ± 0.2 for MF₀F₁. In addition, the value of the y axis intercepts give the standard free energy of phosphorylation, ΔG°′_p, resulting in ΔG°′_p = 37 ± 3 kJ·mol⁻¹ for CF₀F₁ and ΔG°′_p = 36 ± 3 kJ mol⁻¹ for MF₀F₁. As expected, the same ΔG°′_p, within error limits, was obtained, because the same internal and external media were used for both enzymes.

Fig. 4.

Determination of the H⁺/ATP ratio. Plot of the stoichiometric product 2.3RTlog(Q) vs. the electrochemical potential difference of protons at equilibrium (eq) (Eq. 3) for CF₀F₁ (circles) and MF₀F₁ (triangles). The error bars indicate the error of ΔpH(eq) as described in the legend of Fig. 1. The slopes give the respective H⁺/ATP ratios with SD. The intercepts at the ordinate axis give the standard free energy of ATP synthesis.

Discussion

In this work, the H⁺/ATP ratios of the yeast mitochondrial MF₀F₁ and of the chloroplast CF₀F₁ were measured in a simple chemiosmotic system, constituted by liposomes with the membrane-integrated enzymes. According to the chemiosmotic theory, the free energy of the chemical reaction (established by the imposed stoichiometric product Q) is balanced by the imposed electrochemical potential difference of protons [] multiplied by the stoichiometry n of the transported protons (the H⁺/ATP ratio). The thermodynamics of the chemiosmotic theory does not require that the H⁺/ATP ratio is an integer number; it is just the parameter necessary to adjust the energy balance.

The parallel measurement of H⁺/ATP for both MF₀F₁ and CF₀F₁ under identical experimental conditions in this high-precision system ensured that the n values obtained for both enzymes can be directly compared, in particular the imposed values, the stoichiometric product Q, and the ΔG°′_p were identical for both enzymes. Our results were H⁺/ATP = 2.9 ± 0.2 for MF₀F₁ and H⁺/ATP = 3.9 ± 0.3 for CF₀F₁. The CF₀F₁ value is in agreement with the value 4.0 (± 0.2) reported earlier (18, 19, 25, 26). As to MF₀F₁, different numbers, mainly 2 or 3, had been reported for the mammalian enzyme over the past decades (27, 28; for review see ref. 29), but no data had been published for the yeast MF₀F₁.

In the present measurements, the statistical errors in the values of the imposed parameters were small: the concentrations of nucleotides were preestablished and controlled spectroscopically, resulting in a vanishingly small error in the determination of the stoichiometric product Q. The error in the determination of the imposed ΔpH (at constant imposed Δφ) was minimized by using the same calibrated glass electrode for all measurements, and it has been estimated to amount to 0.02 pH units (18). The determination of ΔpH(eq) required an interpolation between the ATP synthesis and the ATP hydrolysis range, and possible systematic errors in this interpolation might have arisen. A correct interpolation requires that the same reaction (proton transport-coupled catalysis) is observed in both directions. No ATP hydrolysis was detected in CF₀F₁ in the absence of , implying that the ATP hydrolysis measured in the energized CF₀F₁ proteolipomes was not due to damaged or nonreconstituted enzymes, but it resulted only from proton transport-coupled ATP hydrolysis. In MF₀F₁, ATP hydrolysis was detected also under deenergized conditions, implying that part of it could be uncoupled from the proton transport reaction. The method we have used to determine the fraction of the uncoupled reaction, and to correct for it, is based on the fact that a high will completely inhibit proton transport-coupled ATP hydrolysis, while not affecting any type of uncoupled ATP hydrolysis. This correction required the measurement of ATP hydrolysis by ³²P_i release, because this method allows the selective measurement of ATP hydrolysis in the presence of net ATP synthesis. The results of this procedure are shown in Fig. 2, and the corrected data are plotted in Fig. 4. To show the effect of this procedure on the final result, the data before and after correction were compared in Fig. S1 and Table S4. Without correction, n = 2.5 ± 0.2 and ΔG°′_p = −32 ± 3 kJ/mol were obtained.

In addition to binding to catalytic sites, ATP might also bind to noncatalytic sites, and the luciferin/luciferase method does not distinguish between the two, because only changes in the free ATP in the medium are detected. ATP hydrolysis measured by ³²P_i release detects only the ATP that was bound to catalytic sites. In MF₀F₁, the rates of ³²P_i release measured in the absence of coincided, within error limits, with those measured in the absence of with the luciferin/luciferase assay, and from this result we concluded that ATP binding to noncatalytic sites could be excluded. In CF₀F₁, there was no detectable ATP binding to noncatalytic sites, as indicated by the constant ATP level measured in the absence of in the luciferin/luciferase assay. Both results are consistent with data on ATP binding to noncatalytic sites (see, e.g., refs. 30 and 31), indicating that the rate constants for ATP binding to those sites are at least two orders of magnitude smaller than those to catalytic sites.

The numerical value of the standard Gibbs free energy of ATP synthesis (ΔG°′_p) was not required by this method of n determination, because it resulted from the extrapolation of the 2.3RTlog(Q) dependency to = 0 (Fig. 4). The same values of ΔG°′_p were expected for both, MF₀F₁ and CF₀F₁, because all experimental conditions, except for the enzyme source, were identical. The fact that both CF₀F₁ and MF₀F₁ data sets resulted independently in the same ΔG°′_p, obtained by extrapolation over a wide range, constitutes an important piece of evidence for precision and internal consistency of the data. The numerical value is in accordance with that determined earlier (18, 19, 25) (obtained from coupling ATP synthesis/hydrolysis to the proton transport reaction) and also with those obtained from coupling the ATP hydrolysis with glutamine synthesis from glutamate and ammonia (32), or with acetate kinase and phosphate acetyl transferase (33).

In this work it is shown that H⁺-ATP synthases isolated from different species can have different H⁺/ATP ratios. That the H⁺/ATP ratio differs among ATP synthases from different sources had been hypothesized (ref. 11 and references therein). As mentioned, a ratio of 4.0 (±0.2) for CF₀F₁ has been found previously (18, 19, 25, 26), and for the mammalian MF₀F₁, numbers varying from 2 to 3 have been reported (27–29). However, the key point of the present work is that the H⁺/ATP ratios for yeast MF₀F₁ and CF₀F₁ have been determined in parallel under identical experimental conditions. This excludes the possibility that the different H⁺/ATP ratios were due to different experimental conditions or methods.

High-resolution structural investigations have shown the presence of 14 c-subunits in the isolated c-ring of CF₀F₁ (14–16) and 10 c-subunits in the isolated yeast MF₀F₁ (12, 13). Our data indicate that the two H⁺/ATP ratios correlate with the number of c-subunits in the two enzymes. If the c-subunit stoichiometry is the result of an evolutionary pressure, our data give support to the hypothesis (11, 28, 34) that this stoichiometry is one of the key energetic parameters nature can modulate according to the needs of different organisms.

Recently we have used the same method to compare the H⁺/ATP ratios of the ATP synthases from Escherichia coli and from chloroplasts (19). We found that H⁺/ATP = 4.0 ± 0.2 for CF₀F₁, in accordance with the present data, and H⁺/ATP = 4.0 ± 0.3 for EF₀F₁. However, the c-subunit stoichiometry in EF₀ is not exactly known, because numbers between 12 (35) and 10 (36, 37) have been reported, and it has also been proposed to vary according to growth conditions (38). Therefore, for the E. coli enzyme, a meaningful comparison between the c/β ratio and the H⁺/ATP ratio has to await further structural data.

Based on structural features, models of rotational coupling assume that (i) a 360° rotation of the γε-subcomplex produces three ATP molecules (one at each β-subunit), (ii) this rotation is coupled with a 360° rotation of the c_n-ring, and (iii) each c-subunit translocates one proton per rotation (39, 40). The H⁺/ATP ratios predicted by these models are identical to the stoichiometric c/β ratios. With few exceptions (see, e.g., ref. 20) the number of c-subunits in the structures analyzed so far is not an integer multiple of three. Therefore, more recent models assume that the mismatch between the rotational steps in F₀ and those in F₁ is fully accommodated by the transient storage of the free energy of the protonation/deprotonation steps within the enzyme through elastic torsion mainly of the central stalk (refs. 11, 28, and 41 and references therein). The H⁺/ATP ratio predicted by these models is identical to the stoichiometric c/β ratio, implying H⁺/ATP = c/β= 14/3 = 4.7 for CF₀F₁ and H⁺/ATP = c/β= 10/3 = 3.3 for the yeast MF₀F₁. The results of the present work show that the H⁺/ATP ratios of 3.9 ± 0.3 for CF₀F₁ and 2.9 ± 0.2 for yeast MF₀F₁ correlate with but are outside error limits not identical to the predicted values of 4.7 and 3.3, respectively.

The difference between the H⁺/ATP ratio measured in this work and the c/β ratio is surprising, and at the moment we can provide no reasonable explanation. However, the data support the idea that the number of c-subunits plays a major role in determining the H⁺/ATP ratio. The finding that the thermodynamic H⁺/ATP ratio can be significantly smaller than the c/β ratio indicates that the number of the energetically significant protons should not be automatically identified with the c/β ratio of the particular ATP synthase at issue.

Materials and Methods

Enzyme Isolation and Reconstitution.

MF₀F₁ from Saccharomyces cerevisiae cells of the strain YRD15 was isolated as previously described (17). The MF₀F₁ complex was obtained in a buffer containing 20 mM Hepes/NaOH (pH 7.65), 250 mM sucrose, 1 mM EDTA, 4 mM MgCl₂, 5 mM 6-aminohexanoic acid, 1 mM DTT, 100 mM NaCl, and 1 mM dodecyl maltoside (Glycon), with a protein concentration of 5–10 μM, rapidly frozen, and stored in liquid nitrogen. CF₀F₁ was isolated from spinach chloroplasts (Spinacia oleracea) as previously described (18). The enzyme was obtained in a buffer containing 1.25 M sucrose, 30 mM NaH₂PO₄/NaOH (pH 7.2), 2 mM MgCl₂, 0.5 mM Na₂EDTA, and 4 mM dodecyl maltoside with a protein concentration of 7–10 μM, rapidly frozen in liquid nitrogen, and stored at −80 °C. The SDS/PAGE of a typical CF₀F₁ preparation is shown in Fig. S2. The nucleotides bound to the isolated complexes were determined by luciferin/luciferase ATP Kit (Roche) as described in ref. 42, resulting in 1.0 ± 0.1 ATP, 0.2 ± 0.1 ADP per MF₀F₁, and 1.1 ± 0.1 ATP, 1.0 ± 0.1 ADP per CF₀F₁. In control measurements, in which acid–base transitions were carried out in the absence of added ATP or ADP, the luciferin/luciferase signal remained constant in time, indicating that bound ATP was not released from the enzymes. Liposomes were prepared as follows: a dry lipid film was prepared by rotary evaporation of 10 mL chloroform containing 250 mg phosphatidylcholine and 12.5 mg phosphatidic acid, resuspended in 8 mL 10 mM Hepes (pH 7.6), 250 mM sucrose, 2 mM MgCl₂, and 1 mM EDTA and sonicated in 2-mL portions with a 3-mm-diameter tip for a total of 80 s (Branson Sonifier 250, step 2, 60% output), resulting in a lipid concentration of 32.8 mg/mL. MF₀F₁ or CF₀F₁ were reconstituted into the liposome membrane, similar to the method described earlier (17). To 150 μL reconstitution buffer (80 mM Mops, 80 mM Mes, 80 mM Hepes, 48 mM KCl, 40 mM NaH₂PO₄, and 70–240 mM NaOH), 150 μL liposomes, 40 μL protein solution (2 μM), 2.4 μL MgCl₂ (1 M), 52 μL Triton X-100 [10% (wt/vol)], and 206 μL H₂O were added to a final volume of 600 μL. The final enzyme concentration in this reconstitution mixture was 133 nM for both MF₀F₁ and CF₀F₁. Because of Triton X-100 treatment during reconstitution, the concentrations of all substances were equilibrated between the bulk phase and the internal proteoliposome phase; the resulting internal concentrations are collected in Table S1 and labeled as “Composition of internal phase.” The reconstitution mixture was stirred slowly at room temperature for 30 min. Addition of 200 mg Biobeads led to the removal of Triton X-100 and the insertion of either MF₀F₁ or CF₀F₁ into the liposome membrane. The pH was measured with a glass electrode after reconstitution and is referred to as pH_in. The same buffers were used for reconstitution of MF₀F₁ and CF₀F₁, so that the internal pH had exactly the same value for both enzymes.

Measurement of Catalytic Activity.

The ATP concentration was measured with a luciferin/luciferase ATP Kit (Roche) as described earlier (18, 19). All suspensions and solutions were equilibrated at room temperature (23 °C). Valinomycin was added to proteoliposomes to give a final concentration of 10 μM. A luminometer cuvette was filled with 20 μL of luciferin/luciferase kit; 700 μL of basic medium, containing 140 mM tricine, 143 mM KCl, 4 mM MgCl₂, 10.3 mM NaH₂PO₄, 98–100 mM NaOH, and different concentrations of ADP and ATP. The reaction was started by injection of 80 μL proteoliposomes into the cuvette placed in the luminometer (final volume, 800 μL). The pH value measured after this mixing was 8.38 ± 0.02, which was the pH of the external phase during the reaction (pH_out). The ion concentrations of the resulting external phase are summarized in Table S1. The final nucleotide concentrations ranged between 49 and 751 nM (ATP) and between 4.6 and 51.4 μM (ADP), and the final P_i concentration was 10 mM (Table S2). The nucleotide concentrations were determined spectroscopically as previously described (18). The final enzyme concentration in the reaction medium was 13.3 nM for both MF₀F₁ and CF₀F₁. The luminescence signal was calibrated by addition of a known amount of ATP. The luminescence data were sampled in 55-ms intervals. To determine the initial rates, the first 100–200 s of the signals were fitted with the sum of a monoexponential and a linear function (using the software package Origin), and the rates were calculated from the fitted function at t = 0.

The rates of ATP hydrolysis with superimposed high (ΔpH = 2.1, [K⁺]_in/[K⁺]_out = 0.5/150 mM) were measured in the presence and in the absence of the uncoupler nigericin by the release of ³²P_i from [γ-³²P]ATP as previously described (43). These rates were used for correction of the catalytic rates obtained with the luciferin/luciferase system. Proteoliposomes were energized by an acid–base transition and an additional K⁺/valinomycin diffusion potential in the presence of 10 mM P_i and various concentrations of ATP and ADP (Table S3) at room temperature (23 °C). Proteoliposomes (50 μL) were mixed with 50 μL of acidic medium and incubated for 3 min. Thereafter, the acid–base transition was carried out by adding 400 μL basic medium (±10 μM nigericin), which started the hydrolysis reaction, because it contained ADP and ATP at different concentrations and [γ-³²P]ATP (Hartmann Analytic) to a specific activity of 50–100 kBq/mL. Aliquots (100 μL) were withdrawn at 5, 15, and 25 s after the start of the reaction and mixed with 100 μL of 10% (wt/vol) trichloroacetic acid (TCA) for denaturation. The points at t = 0 were obtained by adding TCA (100 μL) to acidified proteoliposomes (10 μL proteoliposomes + 10 μL acidic medium), and then 80 μL of basic medium were added. The compositions of the internal and external phases were as reported in Table S1, except that the impermeant Mops, Mes, and Hepes buffers were replaced by 50 mM succinate, the internal KCl concentration was reduced to 0.5 mM, the internal pH was 6.2 (ΔpH = 2.1), and the enzyme concentration was 26 nM. The released ³²P_i was separated from [γ-³²P]ATP by organic solvent extraction of the molybdate–P_i complex, and the radioactivity was measured by liquid scintillation counting (43). The ³²P_i found at t = 0 amounted to approximately 2% of the total radioactivity and was subtracted from all data.