On the relationship between rate of ATP synthesis and H+ electrochemical gradient in rat-liver mitochondria

The relationship between rate of ATP synthesis, JATP, and value of the proton electrochemical gradient, delta mu H, has been analyzed in intact mitochondria. Onset of phosphorylation causes a depression of delta mu H of 1.5 kJ/mol. There is a close parallelism between inhibition of JATP and restoration of delta mu H to its state-4 value during titrations with oligomycin or atractyloside. Titrations with ionophores display the following features: (a) delta mu H can be depressed by 3-4 kJ/mol by valinomycin + K+ without affecting the rate of ATP synthesis; (b) uncouplers abolish JATP completely while depressing delta mu H by 3 kJ/mol; (c) complete abolition of ATP synthesis by inhibitors of electron transport is accompanied by a depression of delta mu H of only 1 kJ/mol. The results indicate that: (a) there is a close functional relationship between redox and ATPase H+ pumps, whereby inhibition of electron transfer is accompanied by simultaneous inhibition of the ATPase H+ pumps; and (b) uncoupling of oxidative phosphorylation is not due to depression of delta mu H per se. The consistence of the present data with either a chemiosmotic model where delta mu H is the sole and obligatory intermediate for energy coupling, or models where there is a direct transfer of energy between the two pumps is discussed.     

Unique relationships between the rates of oxidation and phosphorylation and the protonmotive force in rat-liver mitochondria

The rate of ATP synthesis (JP) in isolated rat-liver mitochondria was strongly dependent on the magnitude of the protonmotive force (delta mu H+) across the mitochondrial inner membrane. Addition of different concentrations of various uncouplers or malonate to mitochondrial incubations in State 3 led to a depression of delta mu H+ and a concomitant decrease in JP. A unique relationship between JP and delta mu H+ was obtained, which was independent of the way in which delta mu H+ was varied. This unique relationship was observed when K+ (in the presence of valinomycin) was used as a probe for delta psi. Different relationships between JP and delta mu H+ were observed when K+ was used as a probe for delta psi and when K+ was measured after separation of the mitochondria by centrifugation without silicone oil. This led to a serious underestimation of delta psi, specifically when uncouplers were present, and non-unique flow-force relationships were thus obtained. Anomalous relationships between JP and delta mu H+ were also found when TPMP+ was used as a probe for delta psi. However, in uncoupler incubations the presence of TBP- strongly affected the TPMP+ accumulation ratio without any effect on the K+ accumulation or on JP and in the presence of TBP- unique relationships between JP and delta mu H+ were again obtained. This indicates that the accumulation of TPMP+ inside the mitochondria is not a straightforward function of delta psi but also depends on conditions like the presence of TBP- or uncouplers. We conclude that there is a unique relationship between the rate of phosphorylation and the protonmotive force in mitochondria and that under some conditions the behaviour of TPMP+ is anomalous.     

Free energy coupling between H+-generating and H+-consuming pumps. Ratio between output and input forces

The delta Gp/delta mu H ratio has been measured in mitochondria close to state 4 in the presence of various uncoupler or K+/valinomycin concentrations in media containing either 1 mM or 50 mM Pi. Care has been taken to control the factors affecting delta Gp and delta mu H which could lead to an artefactual increase of the delta Gp/delta mu H ratio above the highest accepted value for the H+/ATP stoichiometry (n = 4, synthesis + transport). In particular, to avoid overestimation of delta Gp due to inactivation of the ATPases at low delta mu H or to the presence of adenylate kinase, the static head state was approached from the side of net ATP synthesis and delta Gp was measured in a state close to static head but still maintaining a residual rate of aerobic phosphorylation. For each concentration of uncoupler or K+, the Pi concentration and/or the adenylate energy charge (EC) as a function of time have been measured as indicators of net ATP synthesis. Only the values of delta Gp measured during a decrease in Pi concentration and/or an increase in EC have been considered to be meaningful for calculations of delta Gp/delta mu H ratios. Both uncouplers and K+ transport cause a marked depression of delta mu H and a parallel depression of the rate of ATP synthesis. However the low rate of ATP synthesis taking place under conditions of low delta mu H eventually results, especially at high Pi concentrations, in a relatively large delta Gp. The delta Gp/delta mu H ratios obtained at the lower delta mu H values exceed 4 and approach 6. Although slightly higher delta Gp/delta mu H ratios are obtained with valinomycin-treated than with uncoupler-treated mitochondria, the pattern of the rise of the force ratio as delta mu H decreases is similar in both cases. An increase of the delta Gp/delta mu H ratio above 4, the maximal accepted H+/ATP stoichiometry is thermodynamically incompatible with the delocalized protonic coupling model.     

Delta mu Na+ drives the synthesis of ATP via an delta mu Na(+)-translocating F1F0-ATP synthase in membrane vesicles of the archaeon Methanosarcina mazei Gö1.

Methanosarcina mazei Gö1 couples the methyl transfer from methyl-tetrahydromethanopterin to 2-mercaptoethanesulfonate (coenzyme M) with the generation of an electrochemical sodium ion gradient (delta mu Na+) and the reduction of the heterodisulfide of coenzyme M and 7-mercaptoheptanoylthreoninephosphate with the generation of an electrochemical proton gradient (delta muH+). Experiments with washed inverted vesicles were performed to investigate whether both ion gradients are used directly for the synthesis of ATP. delta mu Na+ and delta mu H+ were both able to drive the synthesis of ATP in the vesicular system. ATP synthesis driven by heterodisulfide reduction (delta mu H+) or an artificial delta pH was inhibited by the protonophore SF6847 but not by the sodium ionophore ETH157, whereas ETH157 but not SF6847 inhibited ATP synthesis driven by a chemical sodium ion gradient (delta pNa) as well as the methyl transfer reaction (delta mu Na+). Inhibition of the Na+/H+ antiporter led to a stimulation of ATP synthesis driven by the methyl transfer reaction (delta mu Na+), as well as by delta pNa. These experiments indicate that delta mu Na+ and delta mu H+ drive the synthesis of ATP via an Na(+)- and an H(+)-translocating ATP synthase, respectively. Inhibitor studies were performed to elucidate the nature of the ATP synthase(s) involved. delta pH-driven ATP synthesis was specifically inhibited by bafilomycin A1, whereas delta pNa-driven ATP synthesis was exclusively inhibited by 7-chloro-4-nitro-2-oxa-1,3-diazole, azide, and venturicidin. These results are evidence for the presence of an F(1)F(0)-ATP synthase in addition to the A(1)A(0)-ATP synthase in membranes of M. Mazei Gö1 and suggest that the F(1)F(0)-type enzyme is an Na+-translocating ATP synthase, whereas the A(1)A(0)-ATP synthase uses H+ as the coupling ion.     

Uncoupling of oxidative phosphorylation. 1. Protonophoric effects account only partially for uncoupling

The mechanism of uncoupling of oxidative phosphorylation by carbonyl cyanide p-trifluoromethoxy)phenylhydrazone (FCCP), a typical weak acid protonophore, oleic acid, a fatty acid, and chloroform, a general anesthetic, has been investigated by measuring in mitochondria their effect on (i) the transmembrane proton electrochemical potential gradient (delta mu H) and the rates of electron transfer and adenosine 5'-triphosphate (ATP) hydrolysis in static head, (ii) delta mu H and the rates of electron transfer and ATP synthesis in state 3, and (iii) the membrane proton conductance. Both FCCP and oleic acid increase the membrane proton conductance, and accordingly, they cause a depression of delta mu H [generated by either the redox proton pumps or the adenosinetriphosphatase (ATPase) proton pumps]. Although their effects on ATP synthesis/hydrolysis, respiration, and delta mu H are qualitatively consistent with a pure protonophoric uncoupling mechanism and an additional inhibitory action of oleic acid on both the ATPases and the electron-transfer enzymes, a quantitative comparison between the dissipative proton influx and the rate of either electron transfer or ATP hydrolysis (multiplied by either the H+/e- or the H+/ATP stoichiometry, respectively) at the same delta mu H shows that the increase in membrane conductance induced by FCCP and oleic acid accounts for the stimulation of the rate of ATP hydrolysis but not for that of the rate of electron transfer. Chloroform (at concentrations that fully inhibit ATP synthesis) only very slightly increases the proton conductance of the mitochondrial membrane and causes only a little depression of delta mu H.(ABSTRACT TRUNCATED AT 250 WORDS)     

The phosphate potential maintained by mitochondria in State 4 is proportional to the proton-motive force

Evidence is presented for a proportional relationship between the extramitochondrial phosphate potential (delta Gexp) and the proton-motive force (delta mu H+) across the mitochondrial membrane in rat-liver mitochondria oxidising succinate in State 4, when delta mu H+ is varied by addition of uncouplers or malonate. This relationship was found when precautions were taken to minimise interference with the determination of delta Gexp and delta mu H+ by intramitochondrial nucleotides, adenylate kinase activity, the quenching method, and delta mu H+-dependent changes in matrix volume. A non-proportional delta Gexp/delta mu H+ relationship was obtained when these precautions were omitted. Our results do not support mosaic protonic coupling, but are not necessarily in conflict with other localised coupling schemes.     

Flux-dependent increase in the stoichiometry of charge translocation by mitochondrial ATPase/ATP synthase induced by almitrine

After studying the effects of almitrine, a new kind of ATPase/ATP synthase inhibitor, on two kinds of isolated mammalian mitochondrion, we have observed that: (1) Almitrine inhibits oligomycin-sensitive ATPase; it decreases the ATP/O value of oxidative phosphorylations without any change in the magnitude of delta mu H+. (2) Almitrine increases the mechanistic H+/ATP stoichiometry of ATPase as shown by measuring either (i) the extent of potassium acetate and of potassium phosphate accumulation sustained by ATP utilisation, or (ii) the electrical charge/ATP (K+/ATP) ratio at steady-state of ATPase activity. (3) Rat liver mitochondria are at least 10-times more sensitive to almitrine than beef heart mitochondria. (4) The change in H+/ATP stoichiometry induced by almitrine depends on the magnitude of the flux through ATPase. The inhibitory effect of almitrine on ATPase/ATP synthase complex, as a consequence of such an H+/ATP stoichiometry change, is discussed.     

Methanogenesis and ATP synthesis in methanogenic bacteria at low electrochemical proton potentials. An explanation for the apparent uncoupler insensitivity of ATP synthesis

The rate of methane formation from H2 and CO2, the intracellular ATP content and the electrochemical proton potential (delta mu H+) were determined in cell suspensions of Methanobacterium thermoautotrophicum, which were permeabilized for K+ with valinomycin (1.2 mumol/mg protein). In the absence of extracellular K+ the cells formed methane at a rate of 4 mumol min-1 (mg protein)-1, the intracellular ATP content was 20 nmol/mg protein and the delta mu H+ was 200 mV (inside negative). When K+ was added to the suspensions the measured delta mu H+ decreased to the value calculated from the [K+]in/[K+]out ratio. Using this method of delta mu H+ adjustment, it was found that lowering delta mu H+ from 200 mV ([K+]in/[K+]out = 1000) to 100 mV ([K+]in/[K+]out = 40) had no effect on the rate of methane formation and on the intracellular ATP content. At delta mu H+ values below 100 mV ([K+]in/[K+]out less than 40) both the rate of methanogenesis and the ATP content decreased. Methanogenesis completely ceased and the ATP content was 2 nmol/mg when delta mu H+ was adjusted to values lower 50 mV ([K+]in/[K+]out less than 7). The data show that methanogenesis from H2 and CO2 and ATP synthesis in M. thermoautotrophicum are possible at relatively low electrochemical proton potentials. Similar results were obtained with Methanosarcina barkeri. Protonophoric uncouplers like 3,5,3',4'-tetrachlorosalicylanilide (TCS) or 3,5-di-tert-butyl-4-hydroxy-benzylidenemalononitrile (SF 6847) were found not to dissipate delta mu H+ below 100 mV in M. thermoautotrophicum even when used at high concentrations (400 nmol/mg protein). This finding explains the observed uncoupler insensitivity of methanogenesis and ATP synthesis in this organism.     

ATP synthesis in Methanobacterium thermoautotrophicum coupled to CH4 formation from H2 and CO2 in the apparent absence of an electrochemical proton potential across the cytoplasmic membrane

Methanogenic bacteria are considered to couple methane formation with the synthesis of ATP by a chemiosmotic mechanism. This hypothesis was tested with Methanobacterium thermoautotrophicum. Methane formation from H2 and CO2 (2.5 - 3 mumol X min-1 X mg cells-1) by cell suspensions of this organism resulted in the formation of an electrochemical proton potential (delta mu H +) across the cytoplasmic membrane of 230 mV (inside negative) and in the synthesis of ATP up to an intracellular concentration of 5 - 7 nmol/mg. The addition of ionophores at concentrations which completely dissipated delta mu H + without inhibiting methane formation did not result in an inhibition of ATP synthesis. It thus appears that delta mu H + across the cytoplasmic membrane is not the driving force for the synthesis of ATP in M. thermoautotrophicum.     

Control processes in oxidative phosphorylation: kinetic constraints and stoichiometry

Control processes in oxidative phosphorylation have been studied in three experimental models. (1) In isolated yeast mitochondria, external ATP is a regulatory effector of cytochrome-c oxidase activity. In phosphorylating or uncoupling states, the relationships between respiratory rate and delta mu H+, and the respiratory rate and cytochrome-c oxidase reduction level are dependent on this kinetic regulation. (2) In rat liver mitochondria, the response of the respiratory rate to uncoupler addition is age-dependent: liver mitochondria isolated from young rats maintain a greater delta mu H+ than liver mitochondria isolated from adults, with the same respiratory rate obtained with the same concentration of uncoupler. This behaviour is linked to redox proton pump properties, i.e., to the degree of intrinsic uncoupling induced by uncoupler addition. (3) The effect of almitrine, a new kind of ATPase/ATPsynthase inhibitor, was studied in mammalian mitochondria. (i) Almitrine inhibits oligomycin-sensitive ATPase - it decreases the ATPase/O value without any change in delta mu H+; (ii) almitrine increased the mechanistic H+/ATP stoichiometry of ATPase/ATPsynthase; (iii) almitrine-induced changes in H+/ATPase stoichiometry depend on the flux magnitude through ATPase. These results are discussed in terms of the following interdependent parameters; flux value, force, pump efficiency and control coefficient.     

Delta mu H+ and ATP function at different steps of the catalytic cycle of preprotein translocase.

Preprotein translocation in E. coli requires ATP, the membrane electrochemical potential delta mu H+, and translocase, an enzyme with an ATPase domain (SecA) and the membrane-embedded SecY/E. Studies of translocase and proOmpA binds to the SecA domain. Second, SecA binds ATP. Third, ATP-binding energy permits translocation of approximately 20 residues of proOmpA. Fourth, ATP hydrolysis releases proOmpA. ProOmpA may then rebind to SecA and reenter this cycle, allowing progress through a series of transmembrane intermediates. In the absence of delta mu H+ or association with SecA, proOmpA passes backward through the membrane, but moves forward when either ATP and SecA or a membrane electrochemical potential is supplied. However, in the presence of delta mu H+ (fifth step), proOmpA rapidly completes translocation. delta mu H(+)-driven translocation is blocked by SecA plus nonhydrolyzable ATP analogs, indicating that delta mu H+ drives translocation when ATP and proOmpA are not bound to SecA.     

The ATPases of Propionigenium modestum and Bacillus alcalophilus. Strategies for ATP synthesis under low energy conditions.

In Propionigenium modestum, ATP synthesis is coupled via delta mu Na+ to the decarboxylation of (S)-methylmalonyl-CoA. The low energy yield of this reaction implies that approx. 4 decarboxylation cycles are necessary to synthesize 1 molecule of ATP. Theoretical considerations in accord with experimental results suggest ATP synthesis in P. modestum at delta mu Na+ = -110 mV. Other anaerobic bacteria synthesize ATP at a delta mu H+ of similar size and alkaliphilic bacteria at pH 10.3 have a delta mu H+ of only -103 mV. In these cases, the H+(Na+) to ATP stoichiometry must be at least 4.     

ATP synthase-mediated proton fluxes and phosphorylation in rat liver mitochondria: dependence on delta mu H

The dependence of the proton flux through the ATP synthases of rat liver mitochondria on a driving force composed mainly of a potassium diffusion potential was determined and compared with the relationship between rate of phosphorylation and delta mu H given by titrations with the respiratory inhibitor malonate. The two functions are in good agreement in the lower part of the delta mu H range covered. However, the maximal proton fluxes through the ATP synthases are much lower than needed to account for the rate of State 3 phosphorylation sustained by the same mitochondria oxidizing succinate. Possible reasons for this behavior are discussed.     

Modulation of the mitochondrial cyclosporin A-sensitive permeability transition pore by the proton electrochemical gradient. Evidence that the pore can be opened by membrane depolarization.

This paper reports an investigation on the relationship between the proton electrochemical gradient (delta mu H+) and the cyclosporin A-sensitive permeability transition pore (PTP) in rat liver mitochondria. Using the SH group cross-linker phenylarsine oxide as the inducer, we show that both matrix pH and the membrane potential can modulate the process of PTP induction independently of Ca2+. We find that membrane depolarization induces the PTP per se when pHi is above 7.0, while at acidic matrix pH values PTP induction is effectively prevented. Since Ca2+ uptake leads to major modifications of the delta mu H+ (i.e. matrix alkalinization and membrane depolarization), we have explored the possibility that the Ca(2+)-induced changes of the delta mu H+ may contribute to PTP induction by Ca2+. Our data in mitochondria treated with Ca2+ plus N-ethylmaleimide and Ca2+ plus phosphate show that membrane depolarization is a powerful inducer of the PTP. Taken together, our observations indicate that the PTP can be controlled directly by the delta mu H+ both in the absence and presence of Ca2+, and suggest that a collapse of the membrane potential may be the cause rather than the consequence of PTP induction under many experimental conditions. Thus, many inducers may converge on dissipation of the membrane potential component of the delta mu H+ by a variety of mechanisms.     

Thermodynamic and kinetic control of ATP synthesis in yeast mitochondria: role of delta pH

ATP synthesis rate, measured as the variation in external Pi concentration, varied as a linear function of either delta mu H+ or delta Gpin, in such a manner that the delta Gpin/delta mu H+ ratio increased while VATP increased. We also observed a linear dependence of the flux control coefficient of the Pi carrier on delta pH. All the results presented can be explained by a relatively large delta pH drop when VATP increases.     

Local protons and uncoupling of aerobic and artificial delta muH-driven ATP synthesis

Gramicidin D causes inhibition of ATP synthesis either in the absence or in the presence of depression of delta muH, in low-salt and in high-salt media, respectively, at concentrations 2 orders of magnitude higher in the former with respect to the latter case. When the number of active redox pumps is reduced by increasing the antimycin concentration, the P/O ratio of respiring, gramicidin-treated mitochondria either is slightly increased in low-salt media or is first decreased and then constant in high-salt media. Addition of gramicidin D in low-salt media to mitochondria synthesizing ATP by means of artificially imposed delta muH gradients results in (a) no effect on the K+ efflux ratio +/- ADP (equivalent to the aerobic respiratory control ratio) and (b) no effect on the ATP/K+ ratio (equivalent to the P/O ratio) except at the low gramicidin D concentrations where there is also a slight enhancement of the rate of ATP hydrolysis. During respiration-driven ATP synthesis, addition of valinomycin plus K+ causes depression of delta muH with little inhibition of ATP synthesis while addition of gramicidin D causes inhibition of ATP synthesis with little depression of delta muH. The view is discussed that the gramicidin-accessible protons which uncouple aerobic ATP synthesis in a delta muH-independent manner are of a different class from the gramicidin-inaccessible protons which uncouple diffusion potential driven ATP synthesis in a delta muH-dependent manner. The gramicidin-accessible protons are suggested to be pump associated and to reflect primary events in energy transduction.     

Phosphorylation and phosphate-ATP exchange catalyzed by the ATP synthase isolated from Wolinella succinogenes

The ATP synthase, isolated from Wolinella (formerly Vibrio) succinogenes could be fully incorporated into liposomes without significant cleavage of the enzyme or loss of activity. These proteoliposomes, but not the isolated enzyme, catalyzed phosphate-ATP exchange and the phosphorylation of ADP which was driven by an artificially imposed delta mu H across the liposomal membrane. Phosphorylation driven by light was catalyzed by proteoliposomes containing also bacteriorhodopsin. The three activities were similarly sensitive to protonophores or dicyclohexylcarbodiimide. This sensitivity was similar to that of the electron-transport-driven phosphorylation catalyzed by bacterial membrane vesicles. With a delta mu H value 280 mV to drive phosphorylation the turnover number of the enzyme was in the same order of magnitude as that measured in the electron-transport-driven phosphorylation catalyzed by the bacterial membrane. When the delta mu H was below 150 mV, the phosphorylation activity of the incorporated enzyme was two orders of magnitude slower, and was about as fast as light-driven phosphorylation or as the exchange reaction.     

Factors defining the functional coupling of bacteriorhodopsin and ATP synthase in liposomes

Optimal conditions for the co-reconstitution of bacteriorhodopsin and yeast mitochondria ATP synthase were determined. Reconstitution was achieved with a quick two-step procedure. Preparations obtained by this method displayed in optimal cases 2–3-times higher activities (up to 500 nmol ATP/min per mg protein) compared with maximal values reported in the literature, when light-driven ATP synthesis was measured under similar conditions. The final activities depended on the purification method used for the ATP synthase, and it is shown that the oligomycin-sensitive ATP hydrolysis activity was not a good measure for the ability of the ATP synthase preparations to perform ATP synthesis after co-reconstitution. Light-driven ATP synthesis activities depended also on the type of phospholipid used, soybean phospholipid giving the best results. A close relation to the bacteriorhodopsin proton pump activity was found. Using different phospholipids, different $\text{H}{}^{\mathrm{+}}\text{ATP}$ ratios were found, calculated from ATP synthesis activities and initial and steady-state light-driven proton pump activities. From this, together with the findings that the ATP synthase displayed the same ATP hydrolysis and ATP-³²P_i exchange activities with these different phospholipids used, it is concluded that the protein distribution for the two proteins among the liposomes is different relative to each other for the different phospholipids. The light-driven ATP synthesis activity did not correlate with the variation in leakiness of the membrane for protons when different phospholipids were used. An explanation is given by the finding that at high light intensities, the ATP synthesis became independent of the presence of protonophore.     

Activation of the H(+)-ATP synthase in the photosynthetic bacterium Rhodobacter capsulatus.

The regulation of the membrane-bound H(+)-ATPase from the photosynthetic bacterium Rhodobacter capsulatus was investigated. In the presence of uncouplers the rate of ATP hydrolysis was about 40 mM ATP/M bacteriochlorophyll (Bchl)/s. Without uncouplers this rate increased and if, additionally, the chromatophores were illuminated, it was almost doubled. If uncouplers were added shortly after illumination, the rate increased to 300-350 mM ATP/M Bchl/s. Obviously, energization of the membrane leads to the formation of a metastable, active state of the H(+)-ATPase. The maximal rate of ATP hydrolysis can be measured only when first all H(+)-ATPases are activated by delta mu H+ and when the delta mu H+ is abolished in order to release its back pressure on the hydrolysis rate. The half-life time of the metastable state in the absence of delta mu H+ is about 30 s. It is increased by 3 mM Pi to about 80 s and it is decreased by 1 mM ADP to about 15 s. Quantitatively, the fraction of active H(+)-ATPases shows a sigmoidal dependence on pHin (at constant pHout) and the magnitude of delta psi determines the maximal fraction of enzymes which can be activated: delta pH and delta psi are not equivalent for the activation process.     

Inhibition of energy-transducing reactions by 8-nitreno-ATP covalently bound to bovine heart submitochondrial particles: direct interaction between ATPase and redox enzymes

The photoaffinity label 8-azido-ATP has been used to study the effect of inhibition of ATP synthase on ATP-driven reverse electron transfer from succinate to NAD+ ('reversal'), succinate- and NADH-driven ATP synthesis and ATP-Pi exchange. In reversal, where ATPase functions as primary proton pump, inactivation by covalently bound nitreno-ATP results in an inhibition that is proportional to the inactivation of ATP hydrolysis, or, consequently, with the concentration of inactivated ATP synthases. Up to 60% inactivation of the reversal rate does not lead to a decrease in delta mu H+. Inhibition of ATP synthase as secondary proton pump results in case of NADH-driven ATP synthesis in a proportional inhibition, but with succinate as substrate ATP synthesis is less than proportionally inhibited, compared with inactivation of ATP hydrolysis. Inhibition of one of the primary pumps of NADH-driven ATP synthesis, the NADH:Q oxidoreductase, with rotenone also resulted in an inhibition of the rate of ATP synthesis proportional to that of the NADH oxidation. ATP-Pi exchange is much more affected than ATP hydrolysis by photoinactivation with 8-azido-ATP. Contrary to reversal and NADH-driven ATP synthesis the rate of ATP-Pi exchange does not depend linearly, but quadratically on the concentration of active ATP synthases. The observed proportional relationships between inhibition of the primary or secondary pump and the inhibition of the overall energy-transfer reactions do not support the existence of a pool intermediate in energy-transduction reactions. However, the results are consistent with a direct transfer of energy from redox enzymes to ATP synthase and vice versa.