A phenomenological theory considering the output characteristics of oxidative phosphorylation has been worked out by adopting the formalism of linear nonequilibrium thermodynamics. The linearity of oxidative phosphorylation in the range of the output forces of practical interest has been experimentally verified.The efficiency of oxidative phosphorylation is zero if either a load with a zero conductance (open-circuited situation) or a load with an infinite conductance (short-circuited situation) is attached to oxidative phosphorylation. In between these extreme conductances there exists a finite load conductance permitting oxidative phosphorylation to operate with optimal efficienc ,y. Th; necessary and sufficient condition for optimal efficiency was found to be L 2 3 3 / L l l = 1/ 1 -q where L1 is the phenomenological conductance of phosphorylation, LM the phenomenological conductance of the load and 4 the degree of coupling of oxidative phosphorylation driven by respiration. This condition was called conductance matching.Under the condition of conductance matching, four output functions of oxidative phosphorylation of practical interest were optimized. A maximal net rate of oxidative phosphorylation occurs at a degree of coupling qf = 0.78. A maximal output power of oxidative phosphorylation, i.e. net rate times established phosphate potential, results at q, = 0.91. The maximization of the function net rate times efficiency yielded an economic degree of coupling q; = 0.95 for maximal ATP flow. Finally, maximization of the function output power times efficiency led to a degree of coupling qr = 0.97. This last function simultaneously maximizes net rate of ATP production, developed phosphate potential and efficiency and reflects therefore the most economic solution to the output problem under the condition of conductance matching.In isolated rat livers perfused in a metabolic resting state, the condition of conductance matching is fulfilled. In addition, the degree of coupling of oxidative phosphorylation under these conditions corresponds to the economic degree of coupling 4:.

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Oxidative phosphorylation operates at optimal efficiency if and only if the condition of conductance matching L33/Lll = v m is fulfilled. In this relation LII is the phenomenological conductance of phosphorylation, L 3 3 the phenomenological conductance of the load, i.e. the irreversible ATP-utilizing processes in the cell, and q the degree of coupling of oxidative phosphorylation driven by respiration. Since during short time intervals L I I and q are constant whereas L33 fluctuates in the cell, oxidative phosphorylation would only rarely operate at optimal efficiency due to violation of conductance matching. This paper demonstrates that the reversible ATP-utilizing reaction catalyzed by adenylate kinase can effectively compensate deviations from conductance matching in the presence of a fluctuating L33 and hence allows oxidative phosphorylation to operate at optimal efficiency in the cell. Since the adenylate kinase reaction was found to buffer a thermodynamic potential, i.e. the phosphate potential, this finding was generalized to the concept of thermodynamic buffering. The thermodynamic buffering ability of the adenylate kinase reaction was demonstrated by experiments with incubated rat-liver mitochondria. Considerations of changes introduced in the entropy production by the adenylate kinase reaction allowed to establish the theoretical framework for thermodynamic buffering. The ability of thermodynamic buffering to compensate deviations from conductance matching in the presence of fluctuating loads was demonstrated by computer simulations. The possibility of other reversible ATP-utilizing reactions, like the ones catalyzed by creatine kinase and arginine kinase, to contribute to thermodynamic buffering is discussed. Finally, the comparison of the theoretically calculated steady-state cytosolic adenine nucleotide concentrations with experimental data from perfused livers demonstrated that in livers from fed rats conductance matching is fulfilled on a time average and that the degree of coupling corresponded to qy = 0.97 permitting the most economic maintenance of a maximal output power of oxidative phosphorylation. For the case of livers from starved rats this analysis suggested that the degree of coupling corresponded to 4;' = 0.95, permitting the most economic maintenance of a maximal net rate of ATP synthesis at optimal efficiency of oxidative phosphorylation.The preceding paper presented a phenomenological treatment of oxidative phosphorylation based on linear nonequilibrium thermodynamics. It was found that oxidative phosphorylation operates at the state of optimal efficiency whenever the crucial condition of conductance matching phorylation driven by oxidation of reducing equivalents in the respiratory chain. Optimization calculations including economic constraints have revealed the economic degrees of coupling qfc permitting maximal flow and 4 r permitting maximal output power of oxidative phosphorylation at low energy costs and optimal efficiency [I 3. Indirect experimental evidence indicated that in...

SUMMARY1. 45Ca efflux and resting tension were measured in isolated guinea-pig auricles under conditions known to change the intracellular free Ca ion concentration.2. In the presence of [Na]o, caffeine (2 mM) increases 45Ca efflux, but does not produce a contracture, while in the absence of [Na]0 and [Ca]o caffeine causes a contracture without increasing 45Ca efflux. Adrenaline (10-5 -10-4 M) with or without theophylline (0.5-1 0 mM) has no effect on either 45Ca efflux or resting tension.3. In the presence of caffeine the rate of net efflux of Ca depends on [Na]2. Caffeine contractures of muscles in Na-free solution relax upon the addition of [Na]o. Relaxation is correlated with the increase in net efflux of Ca. 4. Cyanide (2 mM) produces a variable increase in 45Ca efflux without a concomitant contracture in Na-containing solutions, but in Na,Ca-free solutions a large contracture occurs without significant increase in 45Ca efflux.5. A large increase in 45Ca efflux and a contracture were observed with the 'Ca-ionophore' X 537A.6. Changes in membrane potential (K-depolarization) in hypertonic solutions have no significant effect on Na-dependent 45Ca efflux, which is in agreement with an electroneutral 2: 1 Na-Ca exchange.7. Cyanide and X 537A both cause a considerable release of Ca ions from isolated guinea-pig heart mitochondria, while caffeine has no effect.

The effect of methylene blue on isolated rat liver mitochondria in the presence and absence of chloroacetaldehyde was investigated. Fatty acid oxidation was inhibited by chloroacetaldehyde and subsequently stimulated by methylene blue. Assessment of tightly coupled mitochondria revealed decreasing respiratory control ratios induced by increasing concentrations of methylene blue and methylene blue provoked mitochondrial swelling. In uncoupled mitochondria, methylene blue promoted a concentration-dependent stimulation of respiration. These findings provide evidence that methylene blue, the redox dye currently used as an antidote for encephalopathy associated with alkylating chemotherapy, uncouples oxidative phosphorylation and acts as an electron transfer mediator to stimulate mitochondrial respiration.© 1997 Federation of European Biochemical Societies.