Kinetic equivalence of transmembrane pH and electrical potential differences in ATP synthesis.

ATP synthase is the key player of Mitchell's chemiosmotic theory, converting the energy of transmembrane proton flow into the high energy bond between ADP and phosphate. The proton motive force that drives this reaction consists of two components, the pH difference (ΔpH) across the membrane and transmembrane electrical potential (Δψ). The two are considered thermodynamically equivalent, but kinetic equivalence in the actual ATP synthesis is not warranted, and previous experimental results vary. Here, we show that with the thermophilic Bacillus PS3 ATP synthase that lacks an inhibitory domain of the ε subunit, ΔpH imposed by acid-base transition and Δψ produced by valinomycin-mediated K(+) diffusion potential contribute equally to the rate of ATP synthesis within the experimental range examined (ΔpH -0.3 to 2.2, Δψ -30 to 140 mV, pH around the catalytic domain 8.0). Either ΔpH or Δψ alone can drive synthesis, even when the other slightly opposes. Δψ was estimated from the Nernst equation, which appeared valid down to 1 mm K(+) inside the proteoliposomes, due to careful removal of K(+) from the lipid.

Introduction

The FoF1-ATP synthase is a ubiquitous enzyme that synthesizes ATP from ADP and inorganic phosphate (Pi) using the electrochemical potential difference of protons (or Na+ in some species) across a membrane, referred to as the proton motive force (pmf) (1–5). The Fo portion is embedded in a membrane, and its simplest subunit composition (in bacteria) is ab2c10–15 (6). The soluble F1 portion with the minimal composition of α3β3γδϵ contains three catalytic sites for ATP synthesis (or hydrolysis in the reverse reaction) at β-α interfaces (7). Rotational catalysis has been proposed (8, 9) and evidenced: in isolated F1, ATP hydrolysis drives rotation of the central γ subunit against the α3β3 ring (10), and reverse rotation forced by an external force leads to ATP synthesis (11, 12). In the whole synthase, the reverse rotation for ATP synthesis is considered to be forced by the proton-powered Fo motor, and proton-driven rotation of the ring of c subunits against the a subunit has indeed been demonstrated (13) in addition to the proton-driven rotation of γ (14) and ϵ (15) in a membrane-reconstituted synthase. The current view is that the c-ring and the γϵ subunits constitute a common rotor that rotates against ab2α3β3δ; in the tight coupling scenario, every proton that flows through the a-c interface in the direction of Fo to F1 rotates the c-ring by one c subunit in the synthesis direction, and each ATP hydrolyzed in F1 drives opposite rotation by 120°, pumping protons backward. The actual direction of rotation depends on whether Fo or F1 wins, or on the balance between the two opposing forces produced by proton flow and ATP hydrolysis. Steigmiller et al. (16) have demonstrated experimentally that the two forces can precisely be balanced in ATP synthase.

The proton motive force that drives the synthesis of ATP consists of two components: pmf = Δψ + 2.30 (kBT/e) ΔpH, where Δψ is the transmembrane electrical potential, ΔpH is the pH difference across the membrane, kB is the Boltzmann constant, T is the absolute temperature, and e is the proton charge (2.30kBT/e ∼60 mV at room temperature). The two terms are thermodynamically equivalent (17), but kinetic equivalence in an actual ATP synthase is not warranted. The two should in principle be equivalent in the core reaction, but pH and membrane potential could affect the enzyme in various ways. Kinetic equivalence of ΔpH and Δψ has been proposed for FoF1 from Wolinella succinogenes, Rhodospirillum rubrum, and spinach chloroplast (18–21) and for the Na+-driven FoF1 of Propionigenium modestum (22). With Rhodobacter capsulatus (23) and particularly with Escherichia coli FoF1 (24, 25), in contrast, ΔpH and Δψ display different kinetics. The apparent non-equivalence, however, could be ascribed to the activation of the enzyme where ΔpH and Δψ may exert different effects (23, 24). A systematic investigation is awaited for the FoF1 of thermophilic Bacillus PS3 (TFoF1), of which the F1 part has contributed much to the understanding of the mechanism of coupling between rotation and hydrolysis/synthesis of ATP (4, 5, 26).

Recently, we have developed a proteoliposome system for TFoF1 that shows a reasonable rate of synthesis at room temperature with high reproducibility (27). To facilitate activation at least partially, we removed the inhibitory domain (27, 28) of the ϵ subunit. Using this system, we inquire here whether ΔpH and Δψ are kinetically equivalent in TFoF1 and, if so, over which ranges. We show that either ΔpH or Δψ alone suffices for ATP synthesis and that the two contribute equally to the rate of synthesis for any combination of ΔpH in the range of −0.3 to 2.2 and Δψ between −30 and 140 mV (pmf up to 250 mV).

EXPERIMENTAL PROCEDURES

Preparation of TFoF1

The TFoF1 we used in this work was a mutant, termed TFoF1ϵΔc in previous studies (27, 28), that has a His10 tag at the N terminus of each β subunit and that lacks the inhibitory C-terminal domain of the ϵ subunit. TFoF1 was expressed in an FoF1-deficient E. coli strain DK8 by an expression plasmid pTR19-ASDS-ϵΔc and purified as described (27, 29) with the following modifications. At the final stage, the elution from the ion-exchange column (ResourceQ, GE Healthcare) showed four closely located protein peaks, of which the first and third gave higher rate of ATP synthesis. We thus mixed the two fractions and replaced the medium with 20 mm HEPES, 0.2 mm EDTA, and 0.15% n-decyl-β-d-maltoside (Dojindo), pH adjusted with NaOH to 7.5, in a centrifugal concentrator with a cut-off molecular mass of 50 kDa (Amicon Ultra, Millipore). The purified TFoF1 at 30 μg/μl was aliquoted into 25 μl, frozen by liquid N2, and stored at −80 °C until use. The molar concentration of TFoF1 was determined from absorbance with the molar extinction coefficient at 280 nm of 253,000 m−1 cm−1. Protein mass was calculated by taking the molecular mass of TFoF1 as 530 kDa.

Removal of K+ from Lipid

The lipid for reconstitution was crude soybean l-α-phosphatidylcholine (P5638, Type II-S, Sigma), which contained a significant amount of K+. First, we washed the lipid with acetone (30) and suspended it at 40 mg/ml in LW buffer (40 mm Tricine, 40 mm MES, 50 mm NaCl, 5 mm MgCl2, and 1 mm DTT, pH adjusted with NaOH to 8.0). The suspension was incubated for 30 min with gentle stirring to allow the lipid to swell. We then sonicated the suspension with a tip-type sonicator (UR-20P, Tomy Seiko) for 30 s. After a 4-fold dilution with LW buffer, we centrifuged the lipid at 235,000 × g for 90 min at 4 °C and resuspended it at 10 mg/ml in LW buffer. The lipid suspension was frozen with liquid N2 and thawed at 25 °C. The centrifugation, resuspension, and freezing/thawing were repeated three times. After fourth centrifugation, we suspended the lipid in R buffer (40 mm Tricine, 40 mm MES, and 5 mm MgCl2, pH adjusted with NaOH to 8.0) at 10 mg/ml. After another round of freezing/thawing and centrifugation, the final pellet was suspended in R buffer at 40 mg/ml. The purified lipid was frozen with liquid N2 and stored at −80 °C until use.

The K+ levels in the lipid suspensions in the purification above were monitored by an atomic absorption spectrophotometer (Z-2310, Hitachi). To an appropriately diluted lipid sample, we added KCl at 0, 0.01, 0.02, 0.03, and 0.04 mm. The absorbance increased linearly, giving the concentration of contaminant K+ as the intercept. The contaminant K+ was proportional to lipid (supplemental Fig. S2), as expected. At 6 mg/ml of lipid during the acidification stage of the ATP synthesis assay, contaminant K+ would be ∼0.05 mm, which is negligible. The purification resulted in ∼100-fold reduction of contaminant K+ (supplemental Fig. S2). The loss of lipid during the K+ removal procedure was negligible, as checked by the EnzyChrom phospholipid assay kit (EPLP-100, BioAssay Systems).

Reconstitution of TFoF1 into Liposomes and Acidification

TFoF1 was reconstituted into liposomes as described (27) with the following modifications. To 250 μl of the purified lipid (40 mg/ml) in R buffer, we added 250 μl of a solution containing 0.8 m sucrose, 8% (w/v) n-octyl-β-d-glucoside (Dojindo), and 100 mm in total of KCl and NaCl at a desired ratio. We then mixed 75 μg of TFoF1. To the mixture, we added 200 μl of Biobeads SM-2 (Bio-Rad), which had been pre-equilibrated with 20 mm Tricine, 20 mm MES, 2.5 mm MgCl2, and 50 mm of KCl+NaCl at the same ratio above, pH adjusted with NaOH to 8.0. The bead mixture was stirred gently for 30 min at 25 °C, and 300 μl of Biobeads were supplemented to the mixture. After another 2-h incubation, the suspension, now containing proteoliposomes, was transferred to a new tube, leaving the Biobeads behind.

For acid-base transition and formation of K+-valinomycin diffusion potential, we first acidified the proteoliposomes at a desired pH in the presence of valinomycin and the desired concentration of K+. 30 μl of the reconstituted proteoliposome suspension was mixed with 70 μl of acidic buffer (50 mm MES or HEPES or Tricine depending on pH, 14.7 mm NaH2PO4, 5 mm MgCl2, 50 mm KCl+NaCl at the desired ratio, 0.6 m sucrose, pH adjusted with NaOH to 5.0–8.9) containing 0.7 mm ADP (A2754, Sigma) and 0.3 μm fresh valinomycin (V0627, Sigma). The suspension was incubated for 10–20 h at 23–27 °C. For incubation at pH > 8.4, Pi in the acidic buffer was omitted to avoid sedimentation of MgPi. Increasing the valinomycin concentration 10- or 100-fold did not change the rate of synthesis. Mixture compositions are summarized in Table 1.

TABLE 1

Summary of mixture compositions at three stages of incubation

The compositions shown are those during incubation, after all components were mixed. The reconstitution column indicates the 2.5-h incubation with Biobeads in which proteoliposomes were formed; the acidification column indicates the 10–20-h incubation that was apparently sufficient for equilibration of pH and [K+] across the liposomal membranes; and the reaction column indicates the 60-s assay of ATP synthesis after the acidified proteoliposomes were mixed with the basic medium.

	Reconstitution	Acidification			Reaction (outside liposomes)
	pH 8.0	pH 5.6–6.8	pH 7.0–8.0	pH 8.2–8.8	pH 7.2–7.8	pH 8.0–8.2	pH 8.4–8.8
MES (mm)	20	41	6	6	4.1 or 0.6	4.1 or 0.6	4.1 or 0.6
Tricine (mm)	20	6	6	41	0.6	0.6	305 or 309
HEPES (mm)	0	0	35	0	0 or 3.5	305 or 308	0 or 3.5
MOPS (mm)	0	0	0	0	305	0	0
MgCl2 (mm)	2.5		4.25			4.78
NaH2PO4 (mm)	0		10			9.73
KCla (mm)	0.1–50		0.25–50			0.25–50
NaCla (mm)	50–0		50–0			50–0
Sucroseb (mm)	400		540			54
KOH (mm)	0		0			0–231
NaOH (mm)	30		10–50			242–7
ADPc (mm)	0		0.5			0.5
Valinomycin (nm)	0		200			20
Osmolarity (×10−3 osmol/liter)	580		730–770			750

[KCl] + [NaCl] = 50 mm, that is, [Cl−] = 50 mm in all stages (without counting MgCl2).

Osmolarity was balanced with sucrose.

ADP contained 0.05 ± 0.01% of ATP as measured with the luciferin-luciferase assay.

ATP Synthesis Assay and Data Analysis

ATP synthesis by TFoF1 was detected by luciferin-luciferase assay in a luminometer (Luminescencer AB2200, ATTO) equipped with a sample injection apparatus. We prepared a basic medium, to which the acidified proteoliposomes were to be injected, by mixing 21 μl of luciferin-luciferase medium (2× concentration, ATP bioluminescence assay kit CLSII, Roche Applied Science) supplemented with 3 mm luciferin (L9504, Sigma), 870 μl of basic buffer (350 mm HEPES or MOPS or Tricine depending on pH, 10 mm NaH2PO4, 5 mm MgCl2, 50 mm KCl+NaCl, and 272 mm KOH+NaOH both at desired ratios), and 9 μl of 50 mm ADP (Table 1). At pH during the synthesis assay (pHout) of 7.8, HEPES and MOPS gave the same rate of ATP synthesis, and HEPES and Tricine were indistinguishable at pHout of 8.0. The basic medium (900 μl) was incubated at 30 °C for 4 min in the luminometer, and then ATP synthesis reaction was initiated by the injection at time t = 0 of 100 μl of the acidified proteoliposome suspension. After 60 s, 10 μl of 10 μm ATP was added three times for calibration. The initial rate (at t = 0) of ATP synthesis was calculated from the exponential fit of the initial 0–6 s portion or 0–15 s when the rate of synthesis was low. All rate values reported in this work are the averages over three of more measurements on at least three independent reconstitutions, and the errors shown are the S.D. The pH of the acidified proteoliposome suspension and the pH of the reaction mixture were checked with a glass electrode for every condition and were reproducible. These values were taken as pHin, the pH inside the liposomes, and pHout, the pH outside liposomes. ΔpH is calculated as pHout − pHin. The transmembrane electrical potential Δψ is calculated from the Nernst equation, Δψ = (kBT/e)ln([K+]out/[K+]in) = 60.1·log([K+]out/[K+]in) in millivolts for our experiments at 30 °C, where [K+]in, the K+ concentration inside the liposomes, is assumed to be that of the acidification mixture, in which lipid concentration was 6 mg/ml, and [K+]out is taken as that of the reaction mixture. In the reaction mixture, [TFoF1] = 8.5 nm, [ADP] = 0.5 mm, [Pi] = 10 mm, and [valinomycin] = 20 nm.

RESULTS

Measurement of ATP Synthesis Activity

In this work, we used the TFoF1 lacking the inhibitory C-terminal domain of the ϵ subunit (28, 31). Hereafter, we refer to this mutant as TFoF1. TFoF1 was reconstituted into liposomes as before (27) with some modifications (see “Experimental Procedures”). The reconstitution and subsequent activity assay were highly reproducible; all of the experiments that we attempted contribute to the statistics below (every point in the graphs below shows the average over at least three assays on three or more independent reconstitutions, with the error bar showing the S.D.). In all reconstitutions, we used the same amounts of lipid (10 mg) and TFoF1 (75 μg); the weight ratio of 133:1 corresponds to two to three TFoF1 molecules per liposome for an assumed liposome diameter of 170 nm (27).

To drive ATP synthesis, we injected acidified proteoliposomes into a basic medium (acid base transition) to establish ΔpH, in the presence of valinomycin and K+ that would generate a transmembrane voltage Δψ (K+-valinomycin diffusion potential). Mixture compositions during reconstitution, acidification, and the final assay are summarized in Table 1. The concentrations of ADP and Pi, [ADP] and [Pi], were 0.5 and 10 mm, respectively, which are saturating (27). The reaction temperature was 30 °C. The amount of ATP synthesized was monitored as the luminescence of the luciferin-luciferase system (Fig. 1). We allowed the synthesis reaction to proceed for 60 s and then added 0.1 nmol ATP three times to calibrate the luminescence signal. The luminescence was proportional to ATP up to 10 nmol (per 1 ml of reaction mixture). The synthesis reaction tended to level off as the imposed pmf decayed, so we fitted the initial portion with an exponential (red lines in Fig. 1) to estimate the initial rate that we report as the synthesis activity in this work. To express the activity as the turnover rate, we took all enzymes in the reaction mixture into account: no correction for the enzyme with the wrong orientation in the membrane, and thus, the rate values are underestimated.

FIGURE 1.

Time courses of ATP synthesis at different pmf (in mV). Synthesis reaction was initiated by the injection of acidified proteoliposomes at t = 0. Vertical axes show the intensity of luciferin luminescence, which was converted to the amount of ATP in the reaction mixture by three additions of 0.1 nmol of ATP after t = 60 s. The initial rate of synthesis, v (in s−1), was calculated from the exponential fit over 0–6-s or 0–15-s portions (red curves). [K+]in = 5 mm; pHout = 8.0. A, ΔpH dependence at Δψ of 100 mV ([K+]out = 237 mm; pHin = 7.4 to 6.6). Nigericin was added at ΔpH of 2.0. B, Δψ dependence at ΔpH of 1.6 (pHin = 6.4; [K+]out = 21 to 162 mm). Nigericin at Δψ = 100 mV.

The two sets of time courses in Fig. 1, one at varying ΔpH (Fig. 1A) and the other at varying Δψ (Fig. 1B), indicate that the (initial) rate of ATP synthesis is similar under the same pmf whether the pmf is dominated by ΔpH or Δψ. The overall time courses also appear similar in Fig. 1, but Δψ tends to decay faster than ΔpH as shown below. Nigericin, an H+-K+ antiporter, collapsed the pmf and prevented synthesis.

Before we proceed to detailed analyses, several remarks are in order. We calculate ΔpH as pHout − pHin (see “Experimental Procedures”), where pHin, the pH inside the proteoliposomes, is assumed to be the same as the pH of the proteoliposome suspension after incubation for acidification. To see whether equilibration across the liposomal membranes was reached during acidification, we changed the incubation time and tested the rate of synthesis (supplemental Fig. S1). The rate rose with incubation time and leveled off at ∼6 h, so we chose the incubation time of 10–20 h in subsequent experiments.

The transmembrane electrical potential is calculated from the Nernst equation as Δψ = 60.1·log([K+]out/[K+]in) in millivolts (see “Experimental Procedures”). To avoid an osmotic imbalance, which would change [K+]in, we minimized the difference in the osmolarities of the acidification and reaction mixture with sucrose (Table 1). The Nernst equation above is valid when the transmembrane flux of K+ far exceeds fluxes of other ions (hence we added valinomycin, a K+ carrier). We checked this by changing [K+] as described below.

Another problem with regard to calculating Δψ was the K+ contamination in the lipid, which amounted to ∼5 mm at 6 mg lipid/ml (supplemental Fig. S2), the lipid concentration during acidification where we set [K+]in. Lipids of higher purity from Avanti or Lipoid company contained much less (but non-negligible) K+, but the rate of ATP synthesis was several times lower than with the crude lipid we used. We therefore washed the crude lipid in five cycles of centrifugation and freezing/thawing, reaching the contaminant K+ level of ∼0.05 mm in 6 mg/ml lipid suspension as measured by atomic absorption (supplemental Fig. S2). [K+] in other reagents was <30 μm in total.

pH Dependence of ATP Synthesis

To change ΔpH in appropriate fashions, we first inquired how the rate of ATP synthesis depends on pHout and pHin themselves. The pmf we imposed was always inside positive, and thus, those synthase molecules with the F1 portion outside the liposome were engaged in synthesis. That is, the synthesis reaction proceeded at pHout.

We applied constant ΔpH and Δψ while changing pHout and pHin simultaneously (Fig. 2). At pHout between 7.2 and 8.0, the synthesis rate was independent of pHout (and pHin). Exceptions were the leftmost points of the top and bottom curves at pHout = 7.6, where pHin was 5.6. We consistently observed a drop in the synthesis activity when pHin was decreased from 5.8 to 5.6 for an unknown reason. We did not explore the cause (possibly acid denaturation) because with MES used for buffering, we could not decrease pHin below 5.5. At pHout above 8.0, on the other hand, the activity decreased with pHout particularly at low pmf (lower curves), a possible reason being the increase of the free energy for ATP synthesis at higher pH (32). To study pmf dependence while minimizing the effect of pH itself, experiments below were carried out at pHout of 8.0, unless stated otherwise, and pHin above 5.6 (data at pHin = 5.6 are included as a reference).

FIGURE 2.

pH dependence of the initial rate of ATP synthesis, [K+]out = 180 mm and [K+]in = 0.5 mm except for diamonds where [K+]out = [K+]in = 50 mm. Δψ values shown are nominal values based on the Nernst equation.

Kinetic Equivalence of ΔpH and Δψ

The ΔpH dependence of the rate of ATP synthesis at various Δψ and at the constant pHout of 8.0 is summarized in Fig. 3A (closed circles). The drop in rate at the rightmost points (ΔpH = 2.4) is due to the low pHin of 5.6 as stated above. All points except for the rightmost ones fall on thick smooth lines that represent the consensus pmf dependence (gray line in Fig. 4A), indicating that the synthesis activity is determined by pmf, irrespective of the relative contributions of ΔpH and Δψ. Open circles in Fig. 3A show the activities at different pHout between 7.2–8.0, confirming that pHout does not affect the activity in this range (Fig. 2).

FIGURE 3.

Dependence of the initial rate of ATP synthesis, A, ΔpH dependence at different Δψ. Closed circles, pHin varied from 8.0 to 5.6 at pHout = 8.0; open circles, pHout varied from 8.0 to 7.2 at pHin = 6.6. Colors indicate [K+]in as defined in B. B, [K+] dependence at ΔpH of 1.6. Closed circles, [K+]out varied from 1 to 232–282 mm at constant [K+]in of 1, 1.5, and 50 mm (shown in different colors); open circles, [K+]in varied from 1 to 50 mm (color-coded) at [K+]out of 232–282 mm.

FIGURE 4.

Kinetic equivalence of ΔpH and Δψ for ATP synthesis. A, all rate data obtained at pHin of 5.8 to 8.0, pHout of 7.2 to 8.0, and [K+]in ≥ 1 mm. Error bars are omitted for clarity. The gray curve is an arbitrary fit with v = v0/[1 + (p0/p)], where p = pmf, p0 = 202 mV, q = 7.18, and v0 = 23.1 s−1. B, contour representation of ΔpH and Δψ dependence. Small circles show data points and synthesis rates are color-coded.

To vary Δψ in experiments in Fig. 3A, we changed [K+]in (and [K+]out) as indicated by color. If the Nernst equation holds, Δψ should depend only on the ratio, [K+]out/[K+]in. To confirm this, we measured the rate of synthesis at constant [K+]in of 1 mm, 1.5 mm or 50 mm while changing [K+]out to vary Δψ (closed circles in Fig. 3B) or kept [K+]out within 232–282 mm while varying [K+]in (open circles). The results again fall on the consensus line (thick gray curve), indicating that Δψ is determined by the ratio [K+]out/[K+]in. Below [K+]in of 1 mm, we observed apparent deviations from the consensus curve, which we ascribe to contribution of ion fluxes other than K+ (supplemental Figs. S3 and S4).

In Fig. 4, we plot all activity data, including those not shown in Fig. 3 and excluding those at [K+]in < 1 mm or at pHin = 5.6. As seen in Fig. 4A, all activity values are the function of pmf alone, irrespective of whether ΔpH or Δψ was varied or of [K+]in (1–50 mm, indicated by different colors). The combinations of ΔpH and Δψ tested are shown in Fig. 4B, ΔpH ranging between −0.3 and 2.2 and Δψ ranging between −30 and 140 mV. In Fig. 4B, the activity values are represented by colors, and the diagonal distribution attests to the kinetic equivalence of ΔpH and Δψ in ATP synthesis in the ranges shown.

ATP Synthesis by ΔpH or Δψ Alone

Of particular concern to the equivalence of ΔpH and Δψ is whether ΔpH or Δψ alone suffices for ATP synthesis and, if so, whether the two show similar rates of synthesis. The time courses in Fig. 5A show that, indeed, either alone can drive ATP synthesis. The synthesis rates were not high, but this was because we could not apply a high enough pmf: ΔpH was limited to 2.2 and the condition [K+]in ≥ 1 mm limited Δψ to below ∼140 mV. The most important observation is that either ΔpH or Δψ drove synthesis even when the other opposed (traces iii and vii in Fig. 5A).

FIGURE 5.

ATP synthesis driven by either ΔpH or Δψ alone. A, time courses of synthesis. Traces i–iv, ΔpH alone (Δψ = 0) except for trace iii; traces v–viii, Δψ alone (ΔpH = 0) except for trace vii. 500 nm nigericin was added (trace iv) to trace i, and valinomycin was eliminated (trace viii) from trace v. B, summary of the synthesis activity against pmf. Closed gray circles, ΔpH alone at [K+]out = [K+]in = 50 mm; open gray circles, negative Δψ added to ΔpH of 2.2 by decreasing [K+]out from 50 down to 12 mm; Closed magenta squares, Δψ alone at [K+]in = 1.5 mm and [K+]out from 76 to 233 mm; open magenta squares, negative ΔpH was added to Δψ of 131 mV by decreasing pHout from 8.0 down to 7.7 at fixed pHin of 8.0. pHout = 8.0 except for the open magenta squares.

The rates of synthesis are compared in Fig. 5B as functions of pmf, indicating kinetic equivalence of ΔpH alone and Δψ alone. Superposition of negative Δψ on ΔpH of 2.2 (gray open circles) or negative ΔpH on Δψ of 131 mV (magenta open squares) gave expected rates. That is, equivalence of ΔpH and Δψ holds irrespective of their signs, or the contributions of ΔpH and Δψ to pmf are additive as an algebraic sum. The data in Fig. 5 are included in Fig. 4.

In Fig. 5A, we note that the rate of synthesis slowed down faster with Δψ than with ΔpH. Whereas pH was buffered both inside and outside the liposomes, we could not buffer [K+]. Leakage of ions other than K+ breaks the K+ equilibrium across the membrane and an influx of K+ would ensue. As expected, the deceleration of synthesis (decay of Δψ) was faster for lower [K+]in (supplemental Fig. S3). Faster decay of Δψ has been documented (33, 34).

DISCUSSION

We have tested many combinations of ΔpH and Δψ, including negative values, and have observed kinetic equivalence for the ranges we were able to explore. Synthesis appeared to begin at pmf of ∼100 mV (Fig. 4). In our experiments, [ADP] and [Pi] were controlled to 0.5 mm and 10 mm, respectively, and ADP contained 0.25±0.05 μm of contaminant ATP as assessed by the luciferase assay. The Gibbs free energy of the phosphorylation of ADP at pHout of 8.0 has been measured with chloroplast FoF1 to be 37 kJ/mol (35), and the number of c subunits in our Bacillus PS3 FoF1 is 10 (36), implying an H+/ATP ratio of 3.3. These values imply that the synthesis and hydrolysis would be balanced at pmf of ∼95 mV. The starting value of ∼100 mV is consistent with this calculation. The equivalence of ΔpH and Δψ has been shown mostly at pHout of 8.0, but limited data including those in Fig. 2 and 3A suggest that the equivalence holds at least down to pHout of 7.2. In bacteria, the F1 portion is on the intracellular side and thus, contrary to our proteoliposome system, ATP synthesis occurs inside the bacterium, where the pH is ∼7.5 (37). The implication is that the kinetic equivalence may well be physiological, although the optimal temperature of our thermophilic enzyme is ∼60 °C or above, whereas the experiments described here were made at 30 °C.

The demonstration of kinetic equivalence over the wide ranges of ΔpH and Δψ depended on several key factors. First, presumably due to the removal of the inhibitory domain of the ϵ subunit, we did not encounter a serious activation problem. As noted under the Introduction, FoF1 from other sources is often partially dormant and its activation may be promoted by ΔpH and/or Δψ. Second, careful removal of contaminant K+ from the lipid allowed control of [K+]in to the precision of 0.1 mm or below. We also avoided an osmotic imbalance, which would affect [K+]in. Because [K+]out cannot be arbitrarily high, we had to work at a low [K+]in to obtain high Δψ. Our data indicate that the straightforward use of the Nernst equation is valid down to [K+]in as low as ∼1 mm (Fig. 4; also see supplemental Figs. S3 and S4). This would not be the case without the precise control of K+ concentrations. Third, we incubated the acidified proteoliposomes for >10 h to ensure equilibration of H+ (and buffer) and K+ across the membrane (supplemental Fig. S1). With a buffer such as succinate, the apparent equilibration was much faster (minutes), but a highly permeable buffer may pose a problem (38), and thus, we chose to use Good's buffers. Except for the saturation of the rate of synthesis with the incubation time (supplemental Fig. S1), we did not confirm the equilibration during acidification directly. An indirect but strong support is the overlap of all data points on the single consensus curve (Fig. 4A). Fourth, we fixed pHout, the pH at which the phosphorylation of ADP takes place, to 8.0 (down to 7.2 in some experiments), after confirming that the rate of synthesis is constant between 7.2–8.0 (Fig. 2). The phosphorylation reaction per se is pH-dependent (32, 39), which must be distinguished from the effect of ΔpH. We also removed the data at pHin of 5.6 in Fig. 4 because, at this pHin, the rate was lower irrespective of pHout.

ATP synthesis has been demonstrated at the single-molecule level (11, 12), but without the Fo portion (without the proton motive force). Proton-driven rotation of FoF1 has been demonstrated experimentally (13), but so far up to at most a few turns. Development of a better in vitro system for single-molecule observation is desired for the elucidation of the mechanisms of proton-driven rotation and the coupling between rotation and ATP synthesis. We have been trying to develop a liposome-based system, so far without success (40). The kinetic equivalence we have shown here implies that, in a single-molecule observation system, one can use voltage, pH gradient, or any combination of the two to drive rotation at an equal efficiency. The freedom will certainly help design decisive experiments.