Non-equilibrium thermodynamics of oxidative phosphorylation by inverted inner membrane vesicles of rat liver mitochondria

Molecular-level understanding of biological energy coupling and transduction: Response to "Chemiosmotic misunderstandings"

In a recent paper entitled "Chemiosmotic misunderstandings", it is claimed that "enough shortcomings in Mitchell's chemiosmotic theory have not been found and that a novel paradigm that offers at least as much explanatory power as chemiosmosis is not ready." This view is refuted by a wealth of molecular-level experimental data and strong new theoretical and computational evidence. It is shown that the chemiosmotic theory was beset with a large number of major shortcomings ever since the time when it was first proposed in the 1960s. These multiple shortcomings and flaws of chemiosmosis were repeatedly pointed out in incisive critiques by biochemical authorities of the late 20th century. All the shortcomings and flaws have been shown to be rectified by a quantitative, unified molecular-level theory that leads to a deeper and far more accurate understanding of biological energy coupling and ATP synthesis. The new theory is shown to be consistent with pioneering X-ray and cryo-EM structures and validated by state-of-the-art single-molecule techniques. Several new biochemical experimental tests are proposed and constructive ways for providing a revitalizing conceptual background and theory for integration of the available experimental information are suggested.

A Simple Hydraulic Analog Model of Oxidative Phosphorylation

Mitochondrial oxidative phosphorylation is the primary source of cellular energy transduction in mammals. This energy conversion involves dozens of enzymatic reactions, energetic intermediates, and the dynamic interactions among them. With the goal of providing greater insight into the complex thermodynamics and kinetics ("thermokinetics") of mitochondrial energy transduction, a simple hydraulic analog model of oxidative phosphorylation is presented. In the hydraulic model, water tanks represent the forward and back "pressures" exerted by thermodynamic driving forces: the matrix redox potential (ΔGredox), the electrochemical potential for protons across the mitochondrial inner membrane (ΔGH), and the free energy of adenosine 5'-triphosphate (ATP) (ΔGATP). Net water flow proceeds from tanks with higher water pressure to tanks with lower pressure through "enzyme pipes" whose diameters represent the conductances (effective activities) of the proteins that catalyze the energy transfer. These enzyme pipes include the reactions of dehydrogenase enzymes, the electron transport chain (ETC), and the combined action of ATP synthase plus the ATP-adenosine 5'-diphosphate exchanger that spans the inner membrane. In addition, reactive oxygen species production is included in the model as a leak that is driven out of the ETC pipe by high pressure (high ΔGredox) and a proton leak dependent on the ΔGH for both its driving force and the conductance of the leak pathway. Model water pressures and flows are shown to simulate thermodynamic forces and metabolic fluxes that have been experimentally observed in mammalian skeletal muscle in response to acute exercise, chronic endurance training, and reduced substrate availability, as well as account for the thermokinetic behavior of mitochondria from fast- and slow-twitch skeletal muscle and the metabolic capacitance of the creatine kinase reaction.

Optimization of ATP synthase function in mitochondria and chloroplasts via the adenylate kinase equilibrium

The bulk of ATP synthesis in plants is performed by ATP synthase, the main bioenergetics engine of cells, operating both in mitochondria and in chloroplasts. The reaction mechanism of ATP synthase has been studied in detail for over half a century; however, its optimal performance depends also on the steady delivery of ATP synthase substrates and the removal of its products. For mitochondrial ATP synthase, we analyze here the provision of stable conditions for (i) the supply of ADP and Mg(2+), supported by adenylate kinase (AK) equilibrium in the intermembrane space, (ii) the supply of phosphate via membrane transporter in symport with H(+), and (iii) the conditions of outflow of ATP by adenylate transporter carrying out the exchange of free adenylates. We also show that, in chloroplasts, AK equilibrates adenylates and governs Mg(2+) contents in the stroma, optimizing ATP synthase and Calvin cycle operation, and affecting the import of inorganic phosphate in exchange with triose phosphates. It is argued that chemiosmosis is not the sole component of ATP synthase performance, which also depends on AK-mediated equilibrium of adenylates and Mg(2+), adenylate transport, and phosphate release and supply.

Revisiting the thermodynamic theory of optimal ATP stoichiometries by analysis of various ATP-producing metabolic pathways

The stoichiometry of ATP-producing metabolic pathways had been analysed theoretically by several authors by using evolutionary arguments and optimality principles. Waddell et al. (Biochem Educ 27:12-13, 1999) analysed (lactate-producing) glycolysis and used linear irreversible thermodynamics. The result was that half of the free-energy difference should be converted into free-energy of ATP and the remaining half should be used to drive the pathway. The calculated stoichiometry is in agreement with the observed yield of two moles of ATP per mole of glucose. Using the same approach, we here analyse eight other metabolic pathways. Although the deviation is not very large, the calculated values do not fit as nicely as for glycolysis as leading to lactate. For example, for O₂ respiration, the theoretical ATP yield equals 27.9. The real value varies among organisms between 26 and 38. For mixed-acid fermentation in Escherichia coli, the theoretical and experimental values are 2.24 and 2, respectively. For arginine degradation in M. pneumoniae, the calculated value is 2.43 mol of ATP, while in vivo only one mole is produced. During evolution, some pathways may not have reached their optimal ATP net production because energy yield is not their only function. Moreover, it should be acknowledged that the approach by linear irreversible thermodynamics is a rough approximation.

Metabolic systems maintain stable non-equilibrium via thermodynamic buffering

Here, we analyze how the set of nucleotides in the cell is equilibrated and how this generates simple rules that help the cell to organize itself via maintenance of a stable non-equilibrium state. A major mechanism operating to achieve this state is thermodynamic buffering via high activities of equilibrating enzymes such as adenylate kinase. Under stable non-equilibrium, the ratios of free and Mg-bound adenylates, Mg(2+) and membrane potentials are interdependent and can be computed. The adenylate status is balanced with the levels of reduced and oxidized pyridine nucleotides through regulated uncoupling of the pyridine nucleotide pool from ATP production in mitochondria, and through oxidation of substrates non-coupled to NAD(+) reduction in peroxisomes. The set of adenylates and pyridine nucleotides constitutes a generalized cell energy status and determines rates of major metabolic fluxes. As the result, fluxes of energy and information become organized spatially and temporally, providing conditions for self-maintenance of metabolism.

Proton pumping in the bc1 complex: A new gating mechanism that prevents short circuits

The Q-cycle mechanism of the bc1 complex explains how the electron transfer from ubihydroquinone (quinol, QH2) to cytochrome (cyt) c (or c2 in bacteria) is coupled to the pumping of protons across the membrane. The efficiency of proton pumping depends on the effectiveness of the bifurcated reaction at the Q(o)-site of the complex. This directs the two electrons from QH2 down two different pathways, one to the high potential chain for delivery to an electron acceptor, and the other across the membrane through a chain containing heme bL and bH to the Qi-site, to provide the vectorial charge transfer contributing to the proton gradient. In this review, we discuss problems associated with the turnover of the bc1 complex that center around rates calculated for the normal forward and reverse reactions, and for bypass (or short-circuit) reactions. Based on rate constants given by distances between redox centers in known structures, these appeared to preclude conventional electron transfer mechanisms involving an intermediate semiquinone (SQ) in the Q(o)-site reaction. However, previous research has strongly suggested that SQ is the reductant for O2 in generation of superoxide at the Q(o)-site, introducing an apparent paradox. A simple gating mechanism, in which an intermediate SQ mobile in the volume of the Q(o)-site is a necessary component, can readily account for the observed data through a coulombic interaction that prevents SQ anion from close approach to heme bL when the latter is reduced. This allows rapid and reversible QH2 oxidation, but prevents rapid bypass reactions. The mechanism is quite natural, and is well supported by experiments in which the role of a key residue, Glu-295, which facilitates proton transfer from the site through a rotational displacement, has been tested by mutation.

Simulation of state 4 → state 3 transition in isolated mitochondria

The mathematical dynamic model of oxidative phosphorylation developed previously and in the accompanying paper was modified to involve isolated mitochondria conditions; it was also used to simulate state 4 --> state 3 transition in rat liver mitochondria incubated with succinate as respiratory substrate and glucose-hexokinase as an ADP-regenerating system. Changes in the respiration rate, protonmotive force and reduction level of ubiquinone and cytochrome c as well as the internal (i) and external (e) ATP/ADP ratio between state 4 and state 3 were calculated and compared with the experimental data. Flux control coefficients with respect to oxygen consumption flux for different reactions and processes of oxidative phosphorylation were simulated for different values of the respiration rate (state 4, state 3 and intermediate states). Flux control coefficients for the oxidation, phosphorylation and proton leak subsystems with respect to the oxidation, phosphorylation and proton leak fluxes for different values of the respiration rate were also calculated. These theoretical data were compared with the experimental results obtained in the frame of metabolic control analysis and the 'top-down' approach to this analysis. A good agreement was obtained. Simulated time courses of the respiration rate, the protonmotive force (Deltap) and other parameters after addition of a small amount of ADP to mitochondria in state 4 mimicked at least semiquantitatively the experimentally measured time courses of these parameters. It was concluded, therefore, that in the present stage, the model is able to reflect different properties of the oxidative phosphorylation system in a broad range of conditions fairly well, allows deeper insight into the mechanisms responsible for control and regulation of this process, and can be used for simulation of new experiments, thus inspiring experimental verification of the theoretical predictions.

Interactions between mitochondria and cytoplasm in isolated hepatocytes

Results from a wide variety of metabolic studies have provided indirect support for conclusions derived from enzymological approaches that the enzymes of the so-called soluble cytoplasm (and the mitochondrial matrix) exist within the cell and function in the form of multienzyme complexes and that metabolite channeling takes place between the enzymes of each complex. Our studies support the possibility that the enzymes of glycolysis in liver are segregated from those of gluconeogenesis. Thus, the segregation and aggregation of Krebs cycle enzymes in the mitochondrial matrix, elucidated by Paul Srere, may be an example of a general pattern of enzyme organization pertaining to all metabolic pathways.

Two-dimensional diffusion of F1F0-ATP synthase and ADP/ATP translocator. Testing a hypothesis for ATP synthesis in the mitochondrial inner membrane

We report here the first experimentally determined lateral diffusion coefficients of the F1F0-ATP synthase and the ADP/ATP translocator in isolated inner membranes of rat liver mitochondria. Rabbit IgG developed against the F1F0-ATP synthase isolated from rat liver mitochondria was determined to be immunospecific for the synthase subunits, notably the alpha-beta doublet, gamma and delta subunits of F1 and subunits two, three and four of F0. This IgG, conjugated with lissamine-rhodamine, was used as a fluorescent probe to monitor the diffusion of the synthase in the membrane. IgG to cytochrome bc1 complex, prepared and labeled similarly, was used as a fluorescent probe for diffusion of this redox component. Eosin maleimide was determined to specifically label the ADP/ATP translocator in the isolated inner membrane and was used as a specific probe for the diffusion of the translocator. Using fluorescence recovery after photobleaching, the experimental average lateral diffusion coefficient of the F1F0-ATP synthase was determined to be 8.4 x 10(-10) cm2/s or twice that of cytochrome bc1 complex while the diffusion coefficient of the ADP/ATP translocator was 1.7 x 10(-9) cm2/s or four times that of cytochrome bc1 complex suggesting that all three components are independent two-dimensional diffusants. Using these diffusion coefficients and applying a number of basic assumptions, we calculated the theoretical two-dimensional diffusion-controlled collision frequencies and derived collision efficiencies (protons transferred per collision) between each of the three proton-transferring redox complexes and both the F1F0-ATP synthase and ADP/ATP translocator by treating the redox components as proton donors and the synthase and translocator as proton acceptors. These collision efficiencies support the physical possibility of a diffusion-based, random collision process of proton transfer and ATP synthesis in the mitochondrial inner membrane.

The polyphasic reduction of oxygen to water by purified cytochrome c oxidase

The time course of oxygen consumption by purified cytochrome oxidase has been studied in reactions where the fully reduced enzyme was rapidly mixed with molecular oxygen. Similar to intact mitochondria (Reynafarje & Davies, Am. J. Physiol. 258, 1990), the enzyme reduces oxygen to water in a kinetically and well defined polyphasic event. The initial rates of O2 consumption depended hyperbolically on O2 concentration, with a bimolecular rate constant of near 10(7) M-1 s-1. The Vmax of O2 uptake was, however, a complex function of the concentrations of both enzyme and cytochrome c. It is concluded that the reduction of oxygen to water takes place in a cyclic process in which the oxidase undergoes redox changes at rates depending on the relative concentration of the enzyme and its 3 substrates: O2, electrons and protons. No evidence was found for impairments in the intramolecular flow of electrons per se.

Alkyltin inhibition of ATPase activities in tissue homogenates and subcellular fractions from adult and neonatal rats

Inhibition of ATPase activities by triethyltin (TET), diethyltin (DET), monoethyltin (MET), and trimethyltin (TMT) was studied in homogenates of brain and liver from adult and neonatal rats. In the adult, sensitivities were as follows: mitochondrial ATPase of liver much greater than Na+, K+-ATPase of brain approximately equal to mitochondrial ATPase of brain greater than nonspecific ATPase of brain and liver. MET did not produce significant inhibition. ATPase activities in brain and liver homogenates from TET-treated adult rats did not differ from controls. Mitochondrial ATPase in brain homogenates from 5-day-old rats was two orders of magnitude more sensitive to TET than brain homogenates from adult rats (IC50 of 2.5 microM in the 5-day-old neonate vs 260 microM in the adult). By contrast, isolated mitochondria and synaptosomal fractions from adult and neonatal brains were equally sensitive to TET (IC50 = 1-3 microM). At 10 days of age, following the onset of myelination, the IC50 for TET inhibition of brain mitochondrial ATPase increased to 71 microM. Myelin added directly to isolated mitochondria also reduced TET-induced inhibition. It is concluded that in vivo brain tin concentrations in 5-day-old rats following a neurotoxic dose of TET are sufficient to inhibit brain mitochondrial ATPase, whereas in adults, tin concentrations are insufficient for inhibition. In the adult rat, TET binding to myelin appears to prevent inhibition of brain mitochondrial ATPase, and the target of toxic action may be myelin. In the neonateal rat, TET may inhibit oxidative phosphorylation in unmyelinated brain tissue, leading to neuronal cell death.

The insensitivity to uncouplers of testis mitochondrial ATPase

Albumin-free testis mitochondrial ATPase activity failed to be stimulated by either 2,4-dinitrophenol (DNP) or carbonyl cyanide rho-trifluoromethoxyphenylhydrazone (FCCP). DNP scarcely enhanced the state 4 respiration and mitochondria proved to be poorly coupled. When 1% bovine serum albumin was added to the isolation medium, DNP or FCCP stimulated ATPase nearly twofold and the dose-response curves for the uncouplers on the QO2 reached a plateau at five- to sixfold. The DNP coupling index (q) also showed a 30-40% improvement. A dose-response curve for oligomycin on the rate of [gamma-32P]ATP synthesis showed a stimulation of ATP synthase activity by 10-100 ng inhibitor/mg protein, suggesting a possible blockade of "open" F0 channels. In the albumin preparation oligomycin inhibited ATP synthesis in the range 10-100 ng/mg protein. Since testis ATPase is known to be loosely bound to the membrane, an effect of albumin, improving tightness in the interaction of the F1 and the F0 sectors of the ATPase, is suggested.

Linear relationships between mitochondrial forces and cytoplasmic flows argue for the organized energy-coupled nature of cellular metabolism

We have studied rates of formation of glucose, urea and lactate by isolated hepatocytes incubated with a variety of inhibitors of energy transduction. Linear relationships have been found between these metabolic rates and mitochondrial forces (membrane, redox and phosphorylation potentials). The findings are suggestive of extensive enzyme organization within these metabolic pathways.

An ATP/2e-stoichiometry of 1 1/2 is thermodynamically possible for site 3 of oxidative phosphorylation

Free energy changes for ATP synthesis (delta GP) and 2e(-)-transfer across Site 3 (delta GR) were determined during oxidative phosphorylation by rat liver mitochondria. At static head, -delta GR/delta GP ranged narrowly between 1.55 and 1.59 with five different respiratory substrates. Thus, an ATP/2e- of 1 1/2 at Site 3 is thermodynamically possible with regards to overall reactants and products. Using nonequilibrium thermodynamics, phenomenological stoichiometries were close to 1 1/2 for all substrates suggesting that ATP/2e- at Site 3 is, in fact, 1 1/2. An ATP/2e- of 1 1/2 can only be possible if H+/O is 4 for cytochrome oxidase.

Rhodamine 123 as a probe of transmembrane potential in isolated rat-liver mitochondria: spectral and metabolic properties

The spectral and metabolic properties of Rhodamine 123, a fluorescent cationic dye used to label mitochondria in living cells, were investigated in suspensions of isolated rat-liver mitochondria. A red shift of Rhodamine 123 absorbance and fluorescence occurred following mitochondrial energization. Fluorescence quenching of as much as 75% also occurred. The red shift and quenching varied linearly with the potassium diffusion potential, but did not respond to delta pH. These energy-linked changes were accompanied by dye uptake into the matrix space. Concentration ratios, in-to-out, approached 4000:1. A large fraction of internalized dye was bound. At concentrations higher than those needed to record these spectral changes, Rhodamine 123 inhibited ADP-stimulated (State 3) respiration of mitochondria (Ki = 12 microM) and ATPase activity of inverted inner membrane vesicles (Ki = 126 microM) and partially purified F1-ATPase (Ki = 177 microM). The smaller Ki for coupled mitochondria was accounted for by energy-dependent Rhodamine 123 uptake into the matrix. Above about 20 nmol/mg protein (10 microM), Rhodamine 123 caused rapid swelling of energized mitochondria. Effects on electron-transfer reactions and coupling were small or negligible even at the highest Rhodamine 123 concentrations employed. delta psi-dependent Rhodamine 123 uptake together with Rhodamine 123 binding account for the intense fluorescent staining of mitochondria in living cells. Inhibition of mitochondria ATPase likely accounts for the cytotoxicity of Rhodamine 123. At concentrations which do not inhibit mitochondrial function, Rhodamine 123 is a sensitive and specific probe of delta psi in isolated mitochondria.

Determination of the upper and lower limits of the mechanistic stoichiometry of incompletely coupled fluxes. Stoichiometry of incompletely coupled reactions

A rationale is formulated for the design of experiments to determine the upper and lower limits of the mechanistic stoichiometry of any two incompletely coupled fluxes J1 and J2. Incomplete coupling results when there is a branch at some point in the sequence of reactions or processes coupling the two fluxes. The upper limit of the mechanistic stoichiometry is given by the minimum value of dJ2/dJ1 obtained when the fluxes are systematically varied by changes in steps after the branch point. The lower limit is given by the maximum value of dJ2/dJ1 obtained when the fluxes are varied by changes in steps prior to the branch point. The rationale for determining these limits is developed from both a simple kinetic model and from a linear nonequilibrium thermodynamic treatment of coupled fluxes, using the mechanistic approach [Westerhoff, H. V. & van Dam, K. (1979) Curr. Top. Bioenerg. 9, 1-62]. The phenomenological stoichiometry, the flux ratio at level flow and the affinity ratio at static head of incompletely coupled fluxes are defined in terms of mechanistic conductances and their relationship to the mechanistic stoichiometry is discussed. From the rationale developed, experimental approaches to determine the mechanistic stoichiometry of mitochondrial oxidative phosphorylation are outlined. The principles employed do not require knowledge of the pathway or the rate of transmembrane leaks or slippage and may also be applied to analysis of the stoichiometry of other incompletely coupled systems, including vectorial H+/O and K+/O translocation coupled to mitochondrial electron transport.

The upper and lower limits of the mechanistic stoichiometry of mitochondrial oxidative phosphorylation. Stoichiometry of oxidative phosphorylation

Determination of the intrinsic or mechanistic P/O ratio of oxidative phosphorylation is difficult because of the unknown magnitude of leak fluxes. Applying a new approach developed to overcome this problem (see our preceding paper in this journal), the relationships between the rate of O2 uptake [( Jo)3], the net rate of phosphorylation (Jp), the P/O ratio, and the respiratory control ratio (RCR) have been determined in rat liver mitochondria when the rate of phosphorylation was systematically varied by three specific means. (a) When phosphorylation is titrated with carboxyatractyloside, linear relationships are observed between Jp and (Jo)3. These data indicate that the upper limit of the mechanistic P/O ratio is 1.80 for succinate and 2.90 for 3-hydroxybutyrate oxidation. (b) Titration with malonate or antimycin yields linear relationships between Jp and (Jo)3. These data give the lower limit of the mechanistic P/O ratio of 1.63 for succinate and 2.66 for 3-hydroxybutyrate oxidation. (c) Titration with a protonophore yields linear relationships between Jp, (Jo)3, and (Jo)4 and between P/O and 1/RCR. Extrapolation of the P/O ratio to 1/RCR = 0 yields P/O ratios of 1.75 for succinate and 2.73 for 3-hydroxybutyrate oxidation which must be equal to or greater than the mechanistic stoichiometry. When published values for the H+/O and H+/ATP ejection ratios are taken into consideration, these measurements suggest that the mechanistic P/O ratio is 1.75 for succinate oxidation and 2.75 for NADH oxidation.

The efficiencies of the component steps of oxidative phosphorylation. I. A simple steady state theory

Most earlier theoretical work on oxidative phosphorylation has emphasized the application of the formalism of nonequilibrium thermodynamics to the overall process. The resultant mathematical development and interpretation of some experimental data is complicated somewhat by the necessity of treating a system which is incompletely coupled (degree of coupling, q less than 1). Here a simple alternative approach is proposed which can be applied to many studies in the field. In this approach the overall process is broken up into sequential steps so that the product of the efficiencies of the steps is equal to the efficiency of the overall process. Steps of interest for which the degree of coupling may be quite close to unity can be "isolated" by this procedure. This approach results in a simple mathematical formalism emphasizing the power use (or energy use) at each step of the energy transduction process. The efficiencies of the steps of the process can be experimentally evaluated as is shown in the accompanying paper (B.D. Jensen, K. K. Gunter, and T. E. Gunter, 1986, Arch. Biochem. Biophys. 248, 305-323) where measurements are performed as dictated by the assumptions of the current theory. This alternative approach simplifies the analysis of changes induced in the process of oxidative phosphorylation as a result of agents added to the system or of changes in conditions. The locus (or loci) of such changes becomes rapidly apparent if the data is treated as suggested. Furthermore, the mathematical formalism lends itself both to the development of expressions and new experimental approaches which minimize the effects of a decrease in a value of q below unity and also to optimal statistical treatment of the data. As a concrete example of the use of this approach we reinvestigate the question of the equivalence of use of energy from the pH gradient and of the membrane potential in phosphorylation.

The H+/O ratio of proton translocation linked to the oxidation of succinate by mitochondria. Reply to a commentary

Costa, L.E., Reynafarje, B. and Lehninger, A.L. [(1984) J. Biol. Chem. 259, 4802-4811] have reported 'second-generation' measurements of the H+/O ratio approaching 8.0 for vectorial H+ translocation coupled to succinate oxidation by rat liver mitochondria. In a Commentary in this Journal [Krab, K., Soos, J. and Wikström, M. (1984) FEBS Lett. 178, 187-192] it was concluded that the measurements of Costa et al. significantly overestimated the true H+/O stoichiometry. It is shown here that the mathematical simulation on which Krab et al. based this claim is faulty and that data reported by Costa et al. had already excluded the criticism advanced by Krab et al. Also reported are new data, obtained under conditions in which the arguments of Krab et al. are irrelevant, which confirm that the H+/O ratio for succinate oxidation extrapolated to level flow is close to 8.

Flow-force relationships for a six-state proton pump model: intrinsic uncoupling, kinetic equivalence of input and output forces, and domain of approximate linearity

General flow-force relations have been determined, by the Hill diagram method, for a six-state proton pump model with and without intrinsic uncoupling (molecular slipping). A computer-aided analysis of the resulting sigmoidal flow-force curves has been performed by using a set of physically meaningful rate constants. It is shown that gating effects and apparent irreversibility can arise from sigmoidicity. The regions of approximate linearity in the vicinity of inflection points, which may be far from equilibrium, have been examined with a view to characterization in terms of linear phenomenological equations, with due regard to the problems of kinetic equivalence of the forces and symmetry. The determination of thermodynamic parameters such as the degree of coupling, the phenomenological stoichiometry, and the efficiency in these regions is discussed, and their meaning is analyzed in relation to the parameters characterizing the Onsager domain close to equilibrium. The application of the phenomenological equations of near-equilibrium nonequilibrium thermodynamics to such regions is at best a simplification to be treated with great caution. A knowledge of the distance from equilibrium of the flow-controlling ranges of the forces (i.e., the ranges of approximate linearity) turns out to be crucial for the interpretation of thermodynamic parameters determined by manipulating one of the forces while the other remains constant, as well as for the interpretation of measurements of force ratios at static head. The latter approaches can give good estimates of the magnitude of the mechanistic stoichiometry and of the constant force if the pumps are highly coupled and are operating not far from equilibrium. The force-flow relationships are shown to be modified by intrinsic uncoupling, reflecting the regulatory influence of the forces on the extent and nature of the slip. Thus reaction slip increases, for example, as the force against which the proton pump operates increases. The possible physiological significance of regulated intrinsic uncoupling is discussed.

Thermodynamics of reverse electron transfer across site 1: ATP/2e- is greater than one

ATP-driven, rotenone-sensitive, reverse electron transfer from succinate to acetoacetate was measured in rat liver mitochondria in the presence of cyanide. In the approach to equilibrium, the absolute ratio of the free energy change of electron transfer to that of ATP hydrolysis exceeded 1, tending towards about 1 1/4. The data support an H+/2e- stoichiometry of 5 for Site 1 as predicted by a thirteen-proton model of chemiosmotic coupling.

H+ stoichiometry of sites 1 + 2 of the respiratory chain of normal and tumor mitochondria

The mechanistic stoichiometry for vectorial H+ ejection coupled to electron transport through energy-conserving segments 1 + 2 was determined on cyanide-inhibited mitochondria from rat liver, rat heart, and Ehrlich ascites tumor cells, and on rat liver mitoplasts with ferricyanide or ferricytochrome c as electron acceptors. K+ (+ valinomycin) and Ca2+ were employed as permeant cations. Three different methods were employed. In the first, known pulses of ferricyanide were added, and the total H+ ejected was determined with a glass electrode. Such measurements gave H+/2e-values exceeding 7.0 for both normal and tumor mitochondria with beta-hydroxybutyrate and other NAD-linked substrates; uptake of Ca2+ was also measured and gave the expected q+/2e-ratios. The second type of measurement was initiated by addition of ferricytochrome c to rat liver mitoplasts, with H+ ejection monitored with the glass electrode and ferricytochrome c reduction by dual-wavelength spectrophotometry; the H+/2e-ratios generally exceeded 7.0. In the third type of measurement, mixing and dilution artifacts were eliminated by oxidizing ferrocytochrome c in situ with a small amount of ferricyanide. H+/2e-ratios for rat liver mitoplasts oxidizing beta-hydroxybutyrate consistently approached or exceeded 7.5. Over 150 measurements made under a variety of conditions gave observed H+/2e-ejection ratios significantly exceeding 7.0, which correlated closely with H+/2e-measurements on sites 1 + 2 + 3, sites 2 + 3, and site 2. Factors leading to the deficit of the observed ratios from the integral value 8 for sites 1 + 2 were discussed.

Energetics of ATP-driven reverse electron transfer from cytochrome c to fumarate and from succinate to NAD in submitochondrial particles

The maximum Gibbs free energies of reverse electron transfer from succinate to NAD+ and from cytochrome c to fumarate driven by ATP hydrolysis in submitochondrial particles from beef heart were measured as a function of the Gibbs free energy of ATP hydrolysis. The ratio of the energies delta G'redox/delta G'ATP was 1.40 from succinate to NAD+ and 0.89 from cytochrome c to succinate. The ratio, equivalent to a thermodynamic P/2e-ratio, was dependent on whether the electrochemical proton gradient was primarily a membrane potential or a pH gradient for the cytochrome c to fumarate reaction. The results are consistent with H+/ATP = 3 for F1 ATPase, H+/2e- = 4 for NADH-CoQ reductase, and H+(matrix)/2e- = 2 for succinate-cytochrome c reductase.

Efficiency of energy conversion in model biological pumps. Optimization by linear nonequilibrium thermodynamic relations

Experimental investigations showed linear relations between flows and forces in some biological energy converters operating far from equilibrium. This observation cannot be understood on the basis of conventional nonequilibrium thermodynamics. Therefore, the efficiencies of a linear and a nonlinear mode of operation of an energy converter (a hypothetical redox-driven H+ pump) were compared. This comparison revealed that at physiological values of the forces and degrees of coupling (1) the force ratio permitting optimal efficiency was much higher in the linear than in the nonlinear mode and (2) the linear mode of operation was at least 10(6)-times more efficient that the nonlinear one. These observations suggest that the experimentally observed linear relations between flows and forces, particularly in the case of oxidative phosphorylation, may be due to a feedback regulation maintaining linear thermodynamic relations far from equilibrium. This regulation may have come about as the consequence of an evolutionary drive towards higher efficiency.

Relationship between phosphorylation potential and electrochemical H+ gradient during glycolysis in Streptococcus lactis

Assays of intracellular ATP, ADP, and inorganic phosphate allowed calculation of the phosphorylation potential (delta G'ATP/F) maintained during glycolysis by Streptococcus lactis. At the same time, the electrochemical H+ gradient (delta mu-H+/F) was evaluated by distribution methods, using radioactive tetraphenylphosphonium bromide as a probe for the membrane potential and salicylic acid as a probe for the pH gradient. Detailed comparisons were made at pH 5, when the reaction mediated by the proton-translocating ATPase (BF0F1) was likely to have been poised near equilibrium; for those conditions, the ratio delta G'ATP/delta mu-H+ was used to estimate stoichiometry for BF0F1 during ATP hydrolysis. At an external pH of 5, in the presence or absence of valinomycin, this ratio was close to 3, over a range of 370 to 510 mV (8.5 to 11.7 kcal/mol) for delta G'ATP/F and a range of 128 to 167 mV for delta mu-H+/F. Other work suggested that delta G'ATP/delta mu-H+ increased from its minimum value of 3 to 4.3 as the external pH changed from pH 5 to 7.