Non-equilibrium thermodynamic assessment of redox-driven H+ pumps in mitochondria

Virtual mitochondrion: towards an integrated model of oxidative phosphorylation complexes and beyond

The modelling of OXPHOS (oxidative phosphorylation) in order to integrate all kinetic and thermodynamic aspects of chemiosmotic theory has a long history. We briefly review this history and show how new ways of modelling are required to integrate a local model of the individual respiratory complexes into a global model of OXPHOS and, beyond that, into a reliable overall model of central metabolism.

A turbo engine with automatic transmission? How to marry chemicomotion to the subtleties and robustness of life

Most genomes are much more complex than required for the minimum chemistry of life. Evolution has selected sophistication more than life itself. Could this also apply to bioenergetics? We first examine mechanisms through which bioenergetics could deliver sophistication. We illustrate possible benefits of the turbo-charging of catabolic pathways, of loose coupling, low-gear catabolism, automatic transmission in energy coupling, and of homeostasis. Mechanisms for such phenomena may reside at the level of individual proton pumps, or consist of rerouting of electrons over parallel pathways. The mechanisms may be confined to preexisting components, or involve the plasticity of gene expression that is so characteristic of most living organisms. These possible benefits lead us to the conjecture that also bioenergetics has evolved more for sophistication than for necessity. We next discuss a hitherto unresolved enigma, i.e. that bioenergetics does not seem to be critical for the physiological state. To decide on how critical bioenergetics is, we quantified the control exerted by catabolism on important physiological functions such as growth rate and growth yield. We also determined whether a growth inhibition mostly affected bioenergetics (catabolism) or anabolism; if ATP increases with growth rate, then growth should be considered energy (catabolism) limited. The experimental results for Escherichia coli pinpoint the enigma: its energy metabolism (catabolism) is not critical for growth rate. These results might suggest that because it has no direct control over cell function, bioenergetics is unimportant. Paradoxically however, in biology, highly important mechanisms tend to have little control on cell function, precisely because of that importance. Sophistication in terms of homeostatic mechanisms has evolved to guarantee robustness of the most important functions: The most important mechanisms are redundant in biology. Bioenergetics may be an excellent example of this paradox, in line with the above conjecture. It may be highly important and sophisticated. We then discuss work that has begun to focus on the sophistication of bioenergetics. Homeostasis of the energetics of DNA structure in E. coli is extensive. It relies both on preexisting components and on responsive gene expression. The vastly parallel electron-transfer network of Paracoccus denitrificans engages in sophisticated dynamic and hierarchical regulation. The growth yield of the organism can depend on which terminal oxidases are active. Effective proton translocation may vary due to rerouting of electrons. We conclude that much sophistication of bioenergetics will be discovered in this era of functional genomics.

Engineering a living cell to desired metabolite concentrations and fluxes: pathways with multifunctional enzymes

With molecular genetics enabling modulation of the concentrations of cellular enzymes, metabolic engineering becomes limited by the question of which modulations of the enzyme concentrations are required to bring about a desired pattern of cellular metabolism. In an earlier paper (Kholodenko et al. (1998). Biotechnol. Bioeng. 59, 239-247) we derived a method to determine the required modulations. This method, however, cannot be immediately applied to cellular pathways with enzymes catalyzing more than one step in metabolism (multifunctional enzymes). In the present paper we show to which extent the presence of multifunctional enzymes limits biotechological ambitions, which one might otherwise pursue in vain. In particular, it is impossible to change the concentration of a single intermediate and leave the rest of metabolism unperturbed if that intermediate interacts directly with a multifunctional enzyme. The analytical machinery of Metabolic Control Analysis is used to relate the desired and ensuing changes in the metabolic pattern. An explicit solution to this problem of engineering metabolism is then given in the form of a single matrix equation.

Minimal model of beta-cell mitochondrial Ca2+ handling

We develop a simplified, but useful, mathematical model to describe Ca2+ handling by mitochondria in the pancreatic beta-cell. The model includes the following six transport mechanisms in the inner mitochondrial membrane: proton pumping via respiration and proton uptake by way of the F1Fzero-ATPase (adapted from D. Pietrobon and S. Caplan. Biochemistry 24: 5764-5778, 1985), a proton leak, adenine nucleotide exchange, the Ca2+ uniporter, and Na+/Ca2+ exchange. Each mechanism is developed separately into a kinetic model for the rate of transport, with parameters taken from experiments on isolated mitochondrial preparations. These mechanisms are combined in a modular fashion first to describe state 4 (nonphosphorylating) and state 3 (phosphorylating) mitochondria with mitochondrial NADH and Ca2+ concentrations as fixed parameters and then to describe Ca2+ handling with variable mitochondrial Ca2+ concentration. Simulations are compared to experimental measurements and agree well with the threshold for Ca2+ uptake, measured mitochondrial Ca2+ levels, and the influence of Ca2+ on oxygen uptake. In the absence of Ca2+ activation of mitochondrial dehydrogenases, the simulations predict a significant reduction in the rate of production of ATP that involves a "short circuit" via Ca2+ uptake through the uniporter. This effect suggests a potential role for mitochondrial Ca2+ handling in determining the ATP-ADP ratio in the pancreatic beta-cell.

Control of mitochondrial and cellular respiration by oxygen

Control and regulation of mitochondrial and cellular respiration by oxygen is discussed with three aims: (1) A review of intracellular oxygen levels and gradients, particularly in heart, emphasizes the dominance of extracellular oxygen gradients. Intracellular oxygen pressure, pO2, is low, typically one to two orders of magnitude below incubation conditions used routinely for the study of respiratory control in isolated mitochondria. The pO2 range of respiratory control by oxygen overlaps with cellular oxygen profiles, indicating the significance of pO2 in actual metabolic regulation. (2) A methodologically detailed discussion of high-resolution respirometry is necessary for the controversial topic of respiratory control by oxygen, since the risk of methodological artefact is closely connected with far-reaching theoretical implications. Instrumental and analytical errors may mask effects of energetic state and partially explain the divergent views on the regulatory role of intracellular pO2. Oxygen pressure for half-maximum respiration, p50, in isolated mitochondria at state 4 was 0.025 kPa (0.2 Torr; 0.3 microM O2), whereas p50 in endothelial cells was 0.06-0.08 kPa (0.5 Torr). (3) A model derived from the thermodynamics of irreversible processes was developed which quantitatively accounts for near-hyperbolic flux/pO2 relations in isolated mitochondria. The apparent p50 is a function of redox potential and protonmotive force. The protonmotive force collapses after uncoupling and consequently causes a decrease in p50. Whereas it is becoming accepted that flux control is shared by several enzymes, insufficient attention is paid to the notion of complementary kinetic and thermodynamic flux control mechanisms.

The nature of mitochondrial respiration and discrimination between membrane and pump properties

A new criterion is utilized for the interpretation of flow-force relationships in rat liver mitochondria. The criterion is based on the view that the nature of the relationship between the H+/O ratio and the membrane potential can be inferred from the relationship between ohmic-uncoupler-induced extra respiration and the membrane potential. Thus a linear relationship between extra respiration and membrane potential indicates unequivocally the independence of the H+/O ratio from the membrane potential and the leak nature of the resting respiration [Brand, Chien, and Diolez (1994) Biochem. J. 297, 27-29]. On the other hand, a non-linear relationship indicates that the H+/O ratio is dependent on the membrane potential. The experimental assessment of this relationship in the presence of an additional ohmic leak, however, is rendered difficult by both the uncoupler-induced depression of membrane potential and the limited range of dependence of the H+/O ratio on the membrane potential. We have selected conditions, i.e. incubation of mitochondria at low temperatures, where the extent of non-linearity is markedly increased. It appears that the nature of the resting respiration of mitochondria in vitro is markedly dependent on the temperature: at low temperatures the percentage of resting respiration due to membrane leak decreases and that due to intrinsic uncoupling of the proton pumps increases.

Control theory of one enzyme

The analogue of metabolic control theory is developed for the control of reactions catalyzed by single enzymes. The control exerted by any of the elemental transitions of enzyme catalytic cycles on reaction rate and on concentrations (probabilities) of enzyme states is quantified in line with the principle of detailed balance. For enzyme reactions with arbitrary kinetic schemes, e.g., with several enzyme cycles, reflecting coupling and slipping of reactions, it is derived what the various sums of the control coefficients are equal to (cycle summation theorems). Total control on flux, state probability and ratios of branch fluxes are 1, 0 and 0, respectively. The general connectivity theorems are derived which indicate how control is determined by the kinetics of the elemental steps. In addition, for enzymes catalyzing single (or completely coupled) processes the control coefficients are expressed in terms of actual and standard free energy differences across the steps. The prevalent qualitative contention that the step with the smallest forward rate constant, or with the largest free energy drop is the step limiting the performance of the enzyme is shown to fail. The new theory should allow subtle analysis of the control of an enzyme catalyzed reaction.

Protons, pumps, and potentials: control of cytochrome oxidase

Cytochrome c oxidase oxidizes cytochrome c and reduces molecular oxygen to water. When the enzyme is embedded across a membrane, this process generates electrical and pH gradients, and these gradients inhibit enzyme turnover. This respiratory control process is seen both in intact mitochondria and in reconstituted proteoliposomes. Generation of pH gradients and their role in respiratory control are described. Both electron and proton movement seem to be implicated. A topochemical arrangement of redox centers, like that in the photosynthetic reaction center and the cytochrome bc1 complex, ensures charge separation as a result of electron movement. Proton translocation does not require such a topology, although it does require alternating access to the two sides of the membrane by proton-donating and accepting groups. The sites of respiratory control within the enzyme are discussed and a model presented for electron transfer and proton pumping by the oxidase in the light of current knowledge of the transmembranous location of the redox centers involved.

Role of intramitochondrial pH in the energetics and regulation of mitochondrial oxidative phosphorylation

The dependence of ATP synthesis coupled to electron transfer from 3-hydroxy-butyrate (3-OH-B) to cytochrome c on the intramitochondrial pH (pHi) was investigated. Suspensions of isolated rat liver mitochondria were incubated at constant extramitochondrial pH (pHe) with ATP, ADP, Pi, 3-OH-B, and acetoacetate (acac) (the last two were varied to maintain [3-OH-B]/[acac] constant), with or without sodium propionate to change the intramitochondrial pH. Measurements were made of the steady-state water volume of the mitochondrial matrix, transmembrane pH difference, level of cytochrome c reduction, concentration of metabolites and rate of oxygen consumption. For each experiment, conditions were used for which transmembrane pH was near maximal and minimal values and the measured extramitochondrial [ATP], [ADP], and [Pi] were used to calculate log[ATP]/[ADP][Pi]. When [3-OH-B]/[acac] and [cyt c2+]/[cyt c3+] were constant, and pHi was decreased from approx. 7.7 to 7.2, log [ATP]/[ADP][Pi] at high pHi was significantly (P less than 0.02) greater than at low pHi. The mean slope (delta log [ATP]/[ADP][Pi] divided by the change in pHi) was 1.08 +/- 0.15 (mean +/- S.E.). This agrees with the slope of 1.0 predicted if the energy available for ATP synthesis is dependent upon the pH at which 3-hydroxybutyrate dehydrogenase operates, that is, on the pH of the matrix space. The steady-state respiratory rate and reduction of cytochrome c were measured at different pHi and pHe values. Plots of respiratory rate vs.% cytochrome c reduction at different intra- and extramitochondrial pH values indicated that the respiratory rate is dependent upon pHi and not on pHe. This implies that the matrix space is the source of protons involved in the reduction of oxygen to water in coupled mitochondria.

Resting state respiration of mitochondria: reappraisal of the role of passive ion fluxes

Rat liver mitochondria respiring under resting state conditions in the presence of oligomycin were rapidly blocked with cyanide and the dissipation of the membrane potential, measured with a tetraphenylphosphonium-sensitive electrode, was followed over time. The plot of the rate of membrane potential dissipation versus the actual value of the membrane potential was nonlinear and identical to the plot of resting state respiration (titrated with small amounts of a respiratory inhibitor) versus the membrane potential. The relationship between the respiratory chain activity and the proton-motive force in mitochondria oxidizing succinate with either oxygen or ferricyanide as electron acceptors was also found to be identical. These results are interpreted as an indication that the passive permeability of the inner mitochondrial membrane toward ions is far more significant in maintaining resting state respiration than is the molecular slippage of the pumps in the respiratory chain. These results also confirm the non-ohmic characteristics of the inner mitochondrial membrane.

Slip and leak in mitochondrial oxidative phosphorylation

During oxidative phosphorylation by mammalian mitochondria part of the free energy stored in reduced substrates is dissipated and energy is released as heat. Here I review the mechanisms and the physiological significance of this phenomenon.

Proton/electron stoichiometry of mitochondrial complex I estimated from the equilibrium thermodynamic force ratio

The thermodynamic forces on electrons (delta Eh) and protons (delta p) across mitochondrial complexes I, III and IV were measured in isolated mitochondria respiring on succinate. The force ratio (delta Eh/delta p) across complex I close to equilibrium was found to be about 2. The equilibrium force ratio across complex I was measured during sulphite oxidation and was again close to 2. These results indicate that the proton/electron stoichiometry of complex I is 2, in conditions of high protonmotive force.

Estimation of the pH gradient and donnan potential in de-energized heart mitochondria

The transmembrane pH gradient maintained by nonrespiring, uncoupled heart mitochondria has been estimated using the distribution of methylamine and of 5,5-dimethyl-2,4-oxazolidinedione (DMO) and compared with the delta pH reported by the fluorescent probe 2,7-biscarboxyethyl-5(6)-carboxyfluorescein (BCECF). Under these conditions the protonmotive force approaches zero and the membrane potential (delta psi) should equal 59 delta pH (P. Mitchell and J. Moyle (1969) Eur. J. Biochem. 7, 471-484). The delta pH reported by DMO corresponds closely to that estimated by BCECF and is consistent with a Donnan potential of no greater than about -30 mV (interior negative) for nonenergized mitochondria in a sucrose medium. This potential appears to result from the presence of immobile negative charges in the matrix and is eliminated by addition of 10 to 25 mM KCl. Measurements of delta pH using the methylamine and of delta tsi using the distribution of 42K+ in the presence of valinomycin result in an apparent overestimation of these parameters due to binding of these components to negative sites on the membrane. Increasing ionic strength decreases this contribution of surface potential, but significant binding can still be detected in 100 mM KCl. These studies suggest that 42K+ (or 86Rb+) is far from an ideal probe for measuring delta tsi in respiring mitochondria and may significantly overestimate this parameter, especially in sucrose media.

The stoichiometry of charge translocation by cytochrome oxidase and the cytochrome bc1 complex of mitochondria at high membrane potential

The q+/2e stoichiometries (number of charges translocated per electron pair transferred) of cytochrome oxidase and the cytochrome bc1 complex in rat liver mitochondria were determined at a range of membrane potentials up to 180 mV. The method used was similar to the one used in the preceding paper by us in this journal to determine the q+/O stoichiometry of the mitochondrial electron transport chain from succinate to oxygen. The measured q+/2e stoichiometry of cytochrome oxidase was 3.5 positive charges per O atom reduced at low membrane potential (120 mV) and it decreased to about 1.5 at high membrane potential (180 mV). The measured q+/2e stoichiometry of the cytochrome bc1 complex was between 1 and 1.25 positive charges ejected per electron pair and did not change significantly as delta psi was varied from 85 mV to 157 mV. The sum of the q+/2e stoichiometries of cytochrome oxidase and the cytochrome bc1 complex determined separately was similar to their value determined together for electron transport from succinate to oxygen over the range of membrane potentials studied. The most probable interpretation of these results is that the stoichiometry of the cytochrome bc1 complex is invariant over a range of membrane potentials and that the q+/2e stoichiometry of cytochrome oxidase decreases from 4 at low membrane potential to 2 at high membrane potential.

On the origin of the limited control of mitochondrial respiration by the adenine nucleotide translocator

A thermodynamic control theory previously developed has been applied to mitochondrial oxidative phosphorylation with emphasis on the role of delta microH and coupling and within the paradigm of delocalized chemiosmotic coupling. The basis for the observed distribution of flux control over the participating enzymes is shown to lie in the relative magnitudes of so-called delta microH elasticity coefficients, i.e., the delta microH dependencies of the different mitochondrial processes. In particular the relatively strong delta microH dependence of mitochondrial respiration is responsible for the significant role of the adenine nucleotide translocator in the control of oxidative phosphorylation. Uncoupling decreases the control exerted by this translocator on respiration but increases that exerted on phosphorylation.

Proton pumping kinetics and origin of nitrate inhibition of tonoplast-type H+-ATPase

A tonoplast-type vesicle preparation, substantially free from other subcellular membranes, was obtained from corn roots by equilibrium sucrose density gradient centrifugation. At pH 6.5 and in the presence of chloride ions, the tonoplast-type ATPase activity as measured by Pi release, was inhibited by nitrate ions. The ATPase activity was insensitive to molybdate and vanadate, indicating a minimum nonspecific phosphatase and plasma membrane contamination. The vesicles exhibited an ATP hydrolysis-supported proton uptake which was measured by the absorption change of acridine orange. The ATP hydrolysis supported uptake and the subsequent perturbant-induced release of protons (decay) was described by a kinetic model which was previously developed to evaluate the coupling between proton pumping and the primary energy yielding process for other biomembranes. The proton pumping activity was more sensitive to nitrate ions then was ATP hydrolysis. The differential effect and the kinetic analysis of nitrate inhibition led us to suggest that (i) the coupling between Pi release and proton pumping was indirect in nature and (ii) the primary inhibitory effect of nitrate ion was originated from an interaction with a protogenic protein domain which is functionally linked to the ATPase in the tonoplast-type membrane.

Redox-linked proton translocation in cytochrome oxidase: the importance of gating electron flow. The effects of slip in a model transducer

In at least one component of the mitochondrial respiratory chain, cytochrome c oxidase, exothermic electron transfer reactions are used to drive vectorial proton transport against an electrochemical hydrogen ion gradient across the mitochondrial inner membrane. The role of the gating of electrons (the regulation of the rates of electron transfer into and out of the proton transport site) in this coupling between electron transfer and proton pumping has been explored. The approach involves the solution of the steady-state rate equations pertinent to proton pump models which include, to various degrees, the uncoupled (i.e., not linked to proton pumping) electron transfer processes which are likely to occur in any real electron transfer-driven proton pump. This analysis furnishes a quantitative framework for examining the effects of variations in proton binding site pKas and metal center reduction potentials, the relationship between energy conservation efficiency and turnover rate, the conditions for maximum power output or minimum heat production, and required efficiency of the gating of electrons. Some novel conclusions emerge from the analysis, including: An efficient electron transfer-driven proton pump need not exhibit a pH-dependent reduction potential; Very efficient gating of electrons is required for efficient electron transfer driven proton pumping, especially when a reasonable correlation of electron transfer rate and electron transfer exoergonicity is assumed; and A consideration of the importance and possible mechanisms of the gating of electrons suggests that efficient proton pumping by CuA in cytochrome oxidase could, in principle, take place with structural changes confined to the immediate vicinity of the copper ion, while proton pumping by Fea would probably require conformational coupling between the iron and more remote structures in the enzyme. The conclusions are discussed with reference to proton pumping by cytochrome c oxidase, and some possible implications for oxidative phosphorylation are noted.

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.

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.

Regulation of respiration and ATP synthesis in higher organisms: hypothesis

The present view on the regulation of respiration and ATP synthesis in higher organisms implies only Michaelis-Menten type kinetics and respiratory control as regulatory principles. Recent experimental observations, suggesting further regulatory mechanisms at respiratory chain complexes, are reviewed. A new hypothesis is presented implying regulation of respiration and ATP synthesis in higher organisms mainly via allosteric modification of respiratory chain complexes, in particular of cytochrome c oxidase. The allosteric effectors, e.g., metabolites, cofactors, ions, hormones, and the membrane potential are suggested to change the activity and the coupling degree of cytochrome c oxidase by binding to specific sites at nuclear coded subunits. Recent results on the structure and activity of cytochrome c oxidase, supporting the hypothesis, are reviewed.

A simple nonequilibrium thermodynamic description of some inhibitors of oxidative phosphorylation

We propose a macroscopic description of some inhibitors of oxidative phosphorylation based on a simple modification of the phenomenological coefficients appearing in the constitutive equations of linear irreversible thermodynamics. In this theoretical model, we consider protonophores, some ATPase inactivators and some electron-chain inhibitors, and we provide quantitative expressions for their consequences on the protonmotive force, oxidation flux and phosphorylation flux as well as on heat generation.

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.

Non-local thermodynamic effects and efficiency of oxidative phosphorylation

A non-equilibrium thermodynamic model of oxidative phosphorylation is formulated, which allows us to take into account some non-local effects. In this way, we compute the influence of the tangential resistivity of the inner mitochondrial membrane to proton current, as well as that of the distance between active sites, on the stoichiometry and efficiency of energy conversion.

The apparent non-linearity of the relationship between the rate of respiration and the protonmotive force of mitochondria can be explained by heterogeneity of mitochondrial preparations

The apparent non-linear relationship between the rate of respiration and the protonmotive force in mitochondria under resting state conditions is an observation which has led to concepts such as non-chute characteristics of the proton leak through the mitochondrial membrane, or a slippage of proton pumps. We propose that this non-linearity may be a consequence of a heterogeneity of isolated mitochondria concerning the degree of coupling, since a small proportion of totally uncoupled, or loosely coupled, organelles may considerably contribute to the total respiration but not, or only slightly, to the protonmotive force. This hypothesis is supported by a fairly good fitting of computed relationships with those determined experimentally.

The stoichiometry of H+ pumping in cytochrome oxidase and the mechanism of uncoupling

It is suggested that loose coupling in free energy transducing organelles is due partly to leaks through the phospholipid bilayer (extrinsic uncoupling) and partly to "slipping" of the proton pumps (intrinsic uncoupling). The flow ratio of the redox pumps (JH/JO) measured at level flow is not affected by extrinsic uncoupling, but it will be lower the higher the extent of intrinsic uncoupling. During operation of cytochrome oxidase with ferrocyanide or N,N,N',N'-tetraphenyl-p-phenylenediamine as substrates, the rate of resting respiration depends on substrate concentration and does not exhibit control by delta muH; the available data strongly suggest that the enzyme is intrinsically uncoupled to a high and variable (substrate concentration-dependent) extent. It is concluded that flow ratios (at level flows) provide underestimates of the cytochrome oxidase pump stoichiometry.

Homeostasis of the protonmotive force in phosphorylating mitochondria

The relationship between the respiration rate and the magnitude of the electrochemical proton potential (delta mu H+) in rat liver mitochondria was investigated. (1) Under the active-state conditions, the action of inhibitors of either phosphorylation (oligomycin) or respiration (rotenone, malonate) on the respiration and delta mu H+ was measured. Both inhibitors diminished the respiration, whereas rotenone resulted in a decrease of delta mu H+, and oligomycin produced an increase of this potential. The effect of the inhibitors was much more pronounced on the respiration rate than on delta mu H+; for example, the excess of oligomycin produced a 90% inhibition of the respiration while delta mu H+ was changed only by 9%. (2) Under the resting-state conditions, small concentrations of the uncoupler stimulated the respiration while changing delta mu H+ to a relatively small extent. The uncoupler concentrations which doubled and tripled the respiration rate produced only 5 and 9% decrease of delta mu H+, respectively. (3) The present results enabled us to propose a model describing the interrelationship between respiration and delta mu H+.

A minimal hypothesis for membrane-linked free-energy transduction. The role of independent, small coupling units

Experimental data are reviewed that are not in keeping with the scheme of 'delocalized' protonic coupling in membrane-linked free-energy transduction. It turns out that there are three main types of anomalies: (i) rates of electron transfer and of ATP synthesis do not solely depend on their own driving force and on delta mu H, (ii) the ('static head') ratio of delta Gp to delta mu H varies with delta mu H and (iii) inhibition of either some of the electron-transfer chains or some of the H+-ATPases, does not cause an overcapacity in the other, non-inhibited proton pumps. None of the earlier free-energy coupling schemes, alternative to delocalized protonic coupling, can account for these three anomalies. We propose to add a fifth postulate, namely that of the coupling unit, to the four existing postulates of 'delocalized protonic coupling' and show that, with this postulate, protonic coupling can again account for most experimental observations. We also discuss: (i) how experimental data that might seem to be at odds with the 'coupling unit' hypothesis can be accounted for and (ii) the problem of the spatial arrangement of the electrical field in the different free-energy coupling schemes.

The influence of membrane potentials on reaction rates. Control in free-energy-transducing systems

The influence of membrane potentials on the rates of reactions involving the translocation of charged species across the membrane has been studied. Depending on the location of the rate-limiting step relative to the potential gradient either the forward or the backward rate is most strongly influenced by the potential. The rate of a proton translocation process in general is thus not a unique function of the protonmotive force. It is essential to include an explicit potential dependence in the kinetic coefficients to obtain a realistic description of the dynamics.

On the effects of thiocyanate and venturicidin on respiration-driven proton translocation in Paracoccus denitrificans

A fast-responding O2 electrode has been used to confirm and extend observations of a significant kinetic discrepancy between O2 reduction and consequent proton translocation in 'O2-pulse' experiments in intact cells of P. denitrificans. The permeant, chaotropic SCN- ion abolishes this discrepancy, and greatly increases the observable----H+/O ratio, to a value approaching its accepted, true, limiting stoichiometry. The observable H+ decay rates are very slow, particularly in the absence of SCN-. The submaximal----H+/O ratios observed in the absence of SCN- are essentially independent of the size of the O2 pulse, in a manner not easily explained by a delocalised chemiosmotic energy-coupling scheme. Osmotically active protoplasts of P. denitrificans do not show a significant kinetic discrepancy between O2 reduction and H+ translocation, even in the the absence of SCN-. However, the submaximal----H+/O ratios observed in the absence of SCN- are again essentially independent of the size of the O2 pulse. As in intact cells, the observable H+ decay rates are very slow. The energy-transfer inhibitor venturicidin causes a significant increase in the----H+/O ratio observed in protoplasts of P. denitrificans in the absence of SCN-; the decay kinetics of the H+ translocation process are also somewhat modified. Nevertheless, the----H+/O ratio observed in the presence of venturicidin is also independent of the size of the O2 pulse. This observation militates further against arguments in which (a) a non-ohmic leak of protons from the bulk aqueous phase might alone be the cause of the low----H+/O ratios observed in the absence of SCN-, and (b) in which there might be a delta p-dependent change ('redox slip') in the actual----H+/O ratio. It is concluded that the observable protonmotive activity of the respiratory chain of P. denitrificans in the absence of SCN- is directly influenced by the state of the H+-ATP synthetase in the cytoplasmic membrane of this organism. We are unable to explain the data in terms of a model in which the putative protonmotive force may be acting to affect the----H+/O ratio. The possibility is considered that the delocalised bulk-to-bulk phase membrane potential set up in response to protonmotive activity is energetically insignificant.

Changes in membrane ionic conductance, but not changes in slip, can account for the non-linear dependence of the electrochemical proton gradient upon the electron-transport rate in chromatophores

Decrease in the rate of cyclic electron transport (JE) measured from the absorbance changes associated with reaction centre bacteriochlorophyll led to a less than proportionate decrease in the membrane potential (delta psi) measured by electrochromism. In principle this result can be explained either by a delta psi-dependent slip in the H+/e- coupling ratio (nE) or by a delta psi-dependent change in the membrane ionic conductance. Simultaneous measurement of the membrane ionic current (JDIS) did not reveal any significant changes in the H+/e- ratio (JDIS/JE) and showed that conductance changes (JDIS/delta psi) account quantitatively for the curved dependence of delta psi on JE. Simultaneous recordings of JDIS and the extravesicular pH from cresol-red absorbance changes, suggest that protons are the main current-carrying species across the chromatophore membrane at high values of delta psi in the presence and absence of Fo-ATPase inhibitor. At reduced delta psi the flux of other ions outweighs the hydrogen ion current.

Membrane potential and surface potential in mitochondria: uptake and binding of lipophilic cations

The uptake and binding of the lipophilic cations ethidium+, tetraphenylphosphonium+ (TPP+), triphenylmethylphosphonium+ (TPMP+), and tetraphenylarsonium+ (TPA+) in rat liver mitochondria and submitochondrial particles were investigated. The effects of membrane potential, surface potentials and cation concentration on the uptake and binding were elucidated. The accumulation of these cations by mitochondria is described by an uptake and binding to the matrix face of the inner membrane in addition to the binding to the cytosolic face of the inner membrane. The apparent partition coefficients between the external medium and the cytosolic surface of the inner membrane (K'o) and the internal matrix volume and matrix face of the inner membrane (K'i) were determined and were utilized to estimate the membrane potential delta psi from the cation accumulation factor Rc according to the relation delta psi = RT/ZF ln [(RcVo - K'o)/(Vi + K'i)] where Vo and Vi are the volume of the external medium and the mitochondrial matrix, respectively, and Rc is the ratio of the cation content of the mitochondria and the medium. The values of delta psi estimated from this equation are in remarkably good agreement with those estimated from the distribution of 86Rb in the presence of valinomycin. The results are discussed in relation to studies in which the membrane potential in mitochondria and bacterial cells was estimated from the distribution of lipophilic cations.

The relationship between the rate of respiration and the protonmotive force. The role of proton conductivity

It is shown by titrating a suspension of rat liver mitochondria with either ADP or an uncoupler that a specific rate of respiration may not have a unique associated value of the protonmotive force. Alternatively, a specific protonmotive force may not be associated with a unique rate of respiration. It seems that the rate of respiration and the protonmotive force are more sensitive to the agents used for the titrations than to each other. Such observations are not easily explained by the chemiosmotic hypothesis. It is, however, possible provided that the proton conductivities, i.e. the rates of dissipation of the protonmotive force, are considered to be different for each of the agents used to titrate the rate of respiration at the same protonmotive force, or vice versa.

Amine fluorescamine compounds inhibit oxidative phosphorylation in rat liver mitochondria

The reaction of fluorescamine with ammonia, benzylamine, o,p-dimethylbenzylamine, 2-phenylethylamine, p-aminobenzoic acid, and the mycosamine-containing macrolide antibiotic, amphotericin B, yield compounds which induce significant effects on mitochondrial activities. From their effects on energy-yielding processes which lead to transmembranous proton movements, the compounds may be divided into three classes. While all modifiers significantly inhibit proton movement induced by both ATP hydrolysis and electron transfer in mitochondria, their influence on the primary energy yielding steps are quite different. Class I modifiers, e.g., the compound made from amphotericin B, inhibit electron transfer but have no effect on the Pi release associated with ATP hydrolysis. Class II modifiers, e.g., the compound made from benzylamine, inhibit respiration but stimulate Pi release. Class III modifiers, e.g., the compound made from p-aminobenzoic acid, on the other hand, only slightly increase Pi release but have no effect on redox reactions. These and other effects of the modifiers are taken to mean that the proton movements and their associated energy-yielding processes are only linked indirectly. The effects of the modifiers on State 3 mitochondrial activities were also investigated. Although all the modifiers decrease the rates of both State 3 respiration and its coupled ATP synthesis, the efficiency of energy conversion measured by the P/O ratio remains unaltered.

Transient kinetics of thermodynamic buffering

The transient response of mitochondrial ATP production towards perturbations was studied by analyzing the trajectories leading from arbitrary initial conditions of the adenine nucleotide pool to the final steady state. These trajectories were calculated from differential equations based on linear relations between flows and thermodynamic forces of the adenylate kinase system including oxidative phosphorylation. The motion of the system along the trajectories consists of two phases: (1) a rapid phase leading from initial states to a common relaxation curve; and (2) a slow phase leading along the relaxation curve to the final steady state. The first phase corresponds to a motion close to the loci of constant adenylic energy charge. In line with this observation is the finding that the energy charge is a constant of motion of the adenylate kinase reaction. The second phase corresponds to a motion along a relaxation curve characterized by minimal Lyapunov exponents in the concentration space of the adenine nucleotides. Thus, both phases of the transient kinetics can be approximated in terms of thermodynamic functions to a high degree of precision. Incubations with isolated rat liver mitochondria were in excellent agreement with the theoretical predictions. In summary, these studies show that the adenylate kinase system not only optimizes the efficiency of oxidative phosphorylation through thermodynamic buffering but, in addition, also deeply influences the transient response of the whole system.

Temperature dependence of light-induced proton movement in reconstituted purple membrane

Bacteriorhodopsin (BR) was incorporated into phosphatidylcholine (PC) vesicles containing different amounts of other lipids. Under the conditions of nullified membrane potential, light-induced proton movement seemed to follow a kinetic scheme which assumed the existence of a proton-pumping inhibition process characterized by a rate constant, kI. The temperature dependence of both kI and the membrane proton leak rate constant (kD) obeyed a simple Arrhenius equation. The presence of cholesterol in the membrane significantly increased the activation energy (Ea) of both the inhibition and leak process. However, further addition of phosphatidic acid (PA) suppressed the increase of Ea associated with kI. The initial proton pumping rate (R0) of vesicles reconstituted with PC showed a bell-shaped temperature dependence with a maximum at approximately 20 degrees C. The addition of cholesterol abolished this dependence. These results suggest that the molecular origin of the inhibition process characterized by kI is different from that of R0 or kD. The temperature dependence of the steady-state fluorescence polarization of dansylated bacteriorhodopsin in vesicles was also investigated. The polarization of the labels in the vesicles without cholesterol showed a bell-shaped temperature dependence with a maximum at approximately 20 degrees C. However, in the presence of cholesterol, the polarization increased linearly as temperature decreased. A comparison of these results with the observed proton movement in similarly reconstituted systems with unmodified protein indicates that membranes with a low fluidity and negatively charged surfaces enhance proton pumping efficiency of bacteriorhodopsin.