Non-equilibrium thermodynamics of energy conversion in bioenergetics

Thermodynamic efficiency, reversibility, and degree of coupling in energy conservation by the mitochondrial respiratory chain

The protonmotive mitochondrial respiratory chain, comprising complexes I, III and IV, transduces free energy of the electron transfer reactions to an electrochemical proton gradient across the inner mitochondrial membrane. This gradient is used to drive synthesis of ATP and ion and metabolite transport. The efficiency of energy conversion is of interest from a physiological point of view, since the energy transduction mechanisms differ fundamentally between the three complexes. Here, we have chosen actively phosphorylating mitochondria as the focus of analysis. For all three complexes we find that the thermodynamic efficiency is about 80–90% and that the degree of coupling between the redox and proton translocation reactions is very high during active ATP synthesis. However, when net ATP synthesis stops at a high ATP/ADP^._Pi ratio, and mitochondria reach “State 4” with an elevated proton gradient, the degree of coupling drops substantially. The mechanistic cause and the physiological implications of this effect are discussed.

Wikström and Springett analyze the thermodynamic efficiency of redox reactions and proton translocation by the complexes of mitochondrial respiratory chain. They report that the thermodynamic efficiency is about 80–90% and that the degree of coupling between the redox and proton translocation reactions is very high during active ATP synthesis, but decreases when ATP synthesis stops.

Aged garlic extract and its constituent, S-allyl-L-cysteine, induce the apoptosis of neuroblastoma cancer cells due to mitochondrial membrane depolarization

Aged garlic extract (AGE) has been demonstrated to have therapeutic properties in tumors; however its mechanisms of action have not yet been fully elucidated. A previous study revealed that AGE exerts an anti-proliferative effect on a panel of both sensitive [wild-type (WT)] and multidrug-resistant (MDR) human cancer cells. Following treatment of the cells with AGE, cytofluorimetric analysis revealed the occurrence of dose-dependent mitochondrial membrane depolarization (MMD). In this study, in order to further clarify the mechanisms of action of AGE, the effects of AGE on mitochondria isolated from rat liver mitochondria (RLM) were also examined. AGE induced an effect on the components of the electrochemical gradient (Δµ_H⁺), mitochondrial membrane potential (ΔΨ_m) and mitochondrial electrochemical gradient (ΔpH_m). The mitochondrial membrane dysfunctions of RLM induced by AGE, namely the decrease in both membrane potential and chemical gradient were associated with a higher oxidation of both the endogenous glutathione and pyridine nucleotide content. To confirm the anti-proliferative effects of AGE, experiments were performed on the human neuroblastoma (NB) cancer cells, SJ-N-KP and the MYCN-amplified IMR5 cells, using its derivative S-allyl-L-cysteine (SAC), with the aim of providing evidence of the anticancer activity of this compound and its possible molecular mechanism as regards the induction of cytotoxicity. Following treatment of the cells with SAC at 20 mM, cell viability was determined by MTT assay and apoptosis was detected by flow cytometry, using Annexin V-FITC labeling. The percentages of cells undergoing apoptosis was found to be 48.0% in the SJ-N-KP and 50.1% in the IMR5 cells. By cytofluorimetric analysis, it was suggested that the target of SAC are the mitochondria. Mitochondrial activity was examined by labeling the cells with the probe, 5,5′,6,6′-tetrachloro-1,1′,3,3′-tetraethylimidacarbocyanine iodide (JC-1). Following treatment with SAC at 50 mM, both NB cell lines exhibited a marked increase in MMD. On the whole, the findings of this study indicate that both natural products, AGE and SAC, cause cytotoxicity to tumor cells via the induction of mitochondrial permeability transition (MPT).

MscCG from Corynebacterium glutamicum: functional significance of the C-terminal domain

Corynebacterium glutamicum is used in microbial biotechnology for the production of amino acids, e.g., glutamate and lysine. Excretion of glutamate into the surrounding medium under production conditions is mediated by MscCG, an MscS-type mechanosensitive channel. In difference to most other MscS-type channel proteins, MscCG carries, in addition to the N-terminal pore domain, a long C-terminal domain that amounts to about half of the size of the protein and harbors an additional transmembrane segment. Here we study the impact of the C-terminal domain on both functions of MscCG as mechanosensitive channel and as glutamate exporter. Sequential truncations of the C-terminal domain were applied, as well as deletion of particular subdomains, replacement of these segments by other amino acid sequences, and sequence randomization. Several parameters of cell physiology and bioenergetics of the obtained mutants related to both glutamate excretion and response to osmotic stress were quantified. All three subdomains of the C-terminal domain, i.e., the periplasmic loop, the fourth transmembrane segment, and the cytoplasmic loop, proved to be of core significance for MscCG function, in particular for glutamate excretion.

Modeling the respiratory chain complexes with biothermokinetic equations - the case of complex I

The mitochondrial respiratory chain plays a crucial role in energy metabolism and its dysfunction is implicated in a wide range of human diseases. In order to understand the global expression of local mutations in the rate of oxygen consumption or in the production of adenosine triphosphate (ATP) it is useful to have a mathematical model in which the changes in a given respiratory complex are properly modeled. Our aim in this paper is to provide thermodynamics respecting and structurally simple equations to represent the kinetics of each isolated complexes which can, assembled in a dynamical system, also simulate the behavior of the respiratory chain, as a whole, under a large set of different physiological and pathological conditions. On the example of the reduced nicotinamide adenine dinucleotide (NADH)-ubiquinol-oxidoreductase (complex I) we analyze the suitability of different types of rate equations. Based on our kinetic experiments we show that very simple rate laws, as those often used in many respiratory chain models, fail to describe the kinetic behavior when applied to a wide concentration range. This led us to adapt rate equations containing the essential parameters of enzyme kinetic, maximal velocities and Henri-Michaelis-Menten like-constants (KM and KI) to satisfactorily simulate these data.

[The effect of ATP-dependent K(+)-channel opener on transmembrane potassium exchange and reactive oxygen species production upon the opening of mitochondrial pore]

The effect of mitochondrial ATP-dependent K(+)-channel (K(+)ATP-channel) opener diazoxide (DZ) on transmembrane potassium exchange and reactive oxygen species (ROS) formation under the opening of mitochondrial permeability transition pore (MPTP) was studied in rat liver mitochondria. The activation of K(+)-cycling (K(+)-uptake and K(+)/H(+)-exchange) by DZ was established with peak effect at < or = 500 nM. It was shown that MPTP opening as well resulted in the activation of K(+)-cycling together with simultaneous activation of Ca(2+)-cycle in mitochondria. In the absence of depolarization Ca(2+)-cycle is supported by MPTP and Ca(2+)-uniporter. The stimulation of K(+)/H(+)-exchange by MPTP opening led to the activation of K(+)-cycle, but further activation of K(+)/H(+)-exchange resulted in MPTP inhibition. Under the same conditions the decrease in mitochondrial ROS production was observed. It was proposed that the decrease in ROS formation together with K(+)/H(+)-exchange activation could be the constituents of the complex effect of MPTP inhibition induced by K(+)ATP-channel opener.

[Estimation of ATP-dependent K(+)-channel contribution to potential-dependent potassium uptake in the rat brain mitochondria]

The effect of potassium on state 4 respiration (substrate oxidation in the absence of ADP) was investigated. It was shown that potential-dependent potassium uptake in the brain mitochondria results in mitochondrial depolarization. Taking into account depolarization effect of potassium, the contribution of the endogenous proton leak as well as K(+)-uptake to the respiration rate was calculated. It was shown that such estimation allows the share of ATP-dependent potassium channel contribution to potential-dependent potassium uptake to be determined by polarographic method.

An exploration of how the thermodynamic efficiency of bioenergetic membrane systems varies with c-subunit stoichiometry of F₁F₀ ATP synthases

Recently the F0 portion of the bovine mitochondrial F1F0-ATP synthase was shown to contain eight 'c' subunits (n = 8). This surprised many in the field, as previously, the only other mitochondrial F0 (for yeast) was shown to have ten 'c' subunits. The metabolic implications of 'c' subunit copy number explored in this paper lead to several surprising conclusions: (1) Aerobically respiring E. coli (n = 10) and animal mitochondria (n = 8) both have very high F1F0 thermodynamic efficiencies of ≈90% under typical conditions, whereas efficiency is only ≈65% for chloroplasts (n = 14). Reasons for this difference, including the importance of transmembrane potential (∆Ψ) as a rotational catalyst, as opposed to an energy source, are discussed. (2) Maximum theoretical P/O ratios in animal mitochondria (n = 8) are calculated to be 2.73 ATP/NADH and 1.64 ATP/FADH2, yielding 34.5 ATP/glucose (assuming NADH import via the malate/aspartate shuttle). The experimentally measured values of 2.44 (±0.15), 1.47 (±0.13), and 31.3 (±1.5), respectively, are only about 10% lower, suggesting very little energy depletion via transmembrane proton leakage. (3) Finally, the thermodynamic efficiency of oxidative phosphorylation is not lower than that of substrate level phosphorylation, as previously believed. The overall thermodynamic efficiencies of oxidative phosphorylation, glycolysis, and the citric acid cycle are ≈80% in all three processes.

Finite time thermodynamic coupling in a biochemical network

The paper describes some thermodynamic constrains and relations in biochemical or metabolic network and provides a basis for entropy enthalpy compensation. Conventional definition of macroscopic forces and fluxes leads to a paradox namely, non-existence of positive efficiency of a chemically driven process. This paradox is resolved by deriving an appropriate definition of macroscopic force using the local balance equations. Entropy enthalpy compensation, whose thermodynamic basis is so far unclear, also follows. The method provides an account of how reactive pathways are coupled, the strength of coupling between a pathway pair depending on the product of their respective enthalpies. The obligatory role of the presence of a common chemical intermediate in defining coupling becomes unnecessary; such intermediate-free coupling being a key feature of metabolic energy transduction. The redefined flux and force can also be exploited to explain surface to volume ratio dependence of coupled networks. Lastly, the thermodynamic rationale for the Bergman's eco-geographic rule, namely the reduced ability of larger animals to avoid stress follows from the generalized expression for coupling coefficients. Higher surface to volume ratio is shown to make the organism resistant to external perturbations.

A physical interpretation for the natural photosynthetic process

The efficiency of the process of photosynthesis is shown to depend on the molecular conversion of power. This requires establishment of a discipline that is now implicit in current thought and that offers a definition of relationship between equilibrium state and power. The quantum aspect for the microscopic process is different from the macroscopic system idealized as the heat engine and is required for the interpretation of molecular machinery. By using three postulates the ideal maximal efficiency for the molecular energy conversion is calculated from the data, which are assembled in the form of the "Z scheme" for photosynthesis. The observed and the calculated efficiencies for a green plant are substantially in agreement.

Network thermodynamics in the post-genomic era

Network models have been used to study the underlying processes and principles of biological systems for decades, providing many insights into the complexity of life. Biological systems require a constant flow of free energy to drive these processes that operate away from thermodynamic equilibrium. With the advent of high-throughput omics technologies, more and more thermodynamic knowledge about the biological components, processes and their interactions are surfacing that we can integrate using large-scale biological network models. This allows us to ask many fundamental questions about these networks, such as, how far away from equilibrium must the reactions in a network be displaced in order to allow growth, or what are the possible thermodynamic objectives of the cell.

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.

Membrane potential greatly enhances superoxide generation by the cytochrome bc1 complex reconstituted into phospholipid vesicles

The mitochondrial cytochrome bc(1) complex (ubiquinol/cytochrome c oxidoreductase) is generally thought to generate superoxide anion that participates in cell signaling and contributes to cellular damage in aging and degenerative disease. However, the isolated, detergent-solubilized bc(1) complex does not generate measurable amounts of superoxide except when inhibited by antimycin. In addition, indirect measurements of superoxide production by cells and isolated mitochondria have not clearly resolved the contribution of the bc(1) complex to the generation of superoxide by mitochondria in vivo, nor did they establish the effect, if any, of membrane potential on superoxide formation by this enzyme complex. In this study we show that the yeast cytochrome bc(1) complex does generate significant amounts of superoxide when reconstituted into phospholipid vesicles. The rate of superoxide generation by the reconstituted bc(1) complex increased exponentially with increased magnitude of the membrane potential, a finding that is compatible with the suggestion that membrane potential inhibits electron transfer from the cytochrome b(L) to b(H) hemes, thereby promoting the formation of a ubisemiquinone radical that interacts with oxygen to generate superoxide. When the membrane potential was further increased, by the addition of nigericin or by the imposition of a diffusion potential, the rate of generation of superoxide was further accelerated and approached the rate obtained with antimycin. These findings suggest that the bc(1) complex may contribute significantly to superoxide generation by mitochondria in vivo, and that the rate of superoxide generation can be controlled by modulation of the mitochondrial membrane potential.

Nonequilibrium thermodynamics and energy efficiency in weight loss diets

Carbohydrate restriction as a strategy for control of obesity is based on two effects: a behavioral effect, spontaneous reduction in caloric intake and a metabolic effect, an apparent reduction in energy efficiency, greater weight loss per calorie consumed. Variable energy efficiency is established in many contexts (hormonal imbalance, weight regain and knock-out experiments in animal models), but in the area of the effect of macronutrient composition on weight loss, controversy remains. Resistance to the idea comes from a perception that variable weight loss on isocaloric diets would somehow violate the laws of thermodynamics, that is, only caloric intake is important ("a calorie is a calorie"). Previous explanations of how the phenomenon occurs, based on equilibrium thermodynamics, emphasized the inefficiencies introduced by substrate cycling and requirements for increased gluconeogenesis. Living systems, however, are maintained far from equilibrium, and metabolism is controlled by the regulation of the rates of enzymatic reactions. The principles of nonequilibrium thermodynamics which emphasize kinetic fluxes as well as thermodynamic forces should therefore also be considered. Here we review the principles of nonequilibrium thermodynamics and provide an approach to the problem of maintenance and change in body mass by recasting the problem of TAG accumulation and breakdown in the adipocyte in the language of nonequilibrium thermodynamics. We describe adipocyte physiology in terms of cycling between an efficient storage mode and a dissipative mode. Experimentally, this is measured in the rate of fatty acid flux and fatty acid oxidation. Hormonal levels controlled by changes in dietary carbohydrate regulate the relative contributions of the efficient and dissipative parts of the cycle. While no experiment exists that measures all relevant variables, the model is supported by evidence in the literature that 1) dietary carbohydrate, via its effect on hormone levels controls fatty acid flux and oxidation, 2) the rate of lipolysis is a primary target of insulin, postprandial, and 3) chronic carbohydrate-restricted diets reduce the levels of plasma TAG in response to a single meal. In summary, we propose that, in isocaloric diets of different macronutrient composition, there is variable flux of stored TAG controlled by the kinetic effects of insulin and other hormones. Because the fatty acid-TAG cycle never comes to equilibrium, net gain or loss is possible. The greater weight loss on carbohydrate restricted diets, popularly referred to as metabolic advantage can thus be understood in terms of the principles of nonequilibrium thermodynamics and is a consequence of the dynamic nature of bioenergetics where it is important to consider kinetic as well as thermodynamic variables.

Protons @ interfaces: implications for biological energy conversion

The review focuses on the anisotropy of proton transfer at the surface of biological membranes. We consider (i) the data from "pulsed" experiments, where light-triggered enzymes capture or eject protons at the membrane surface, (ii) the electrostatic properties of water at charged interfaces, and (iii) the specific structural attributes of proton-translocating enzymes. The pulsed experiments revealed that proton exchange between the membrane surface and the bulk aqueous phase takes as much as about 1 ms, but could be accelerated by added mobile pH-buffers. Since the accelerating capacity of the latter decreased with the increase in their electric charge, it was concluded that the membrane surface is separated from the bulk aqueous phase by a barrier of electrostatic nature. The barrier could arise owing to the water polarization at the negatively charged membrane surface. The barrier height depends linearly on the charge of penetrating ions; for protons, it has been estimated as about 0.12 eV. While the proton exchange between the surface and the bulk aqueous phase is retarded by the interfacial barrier, the proton diffusion along the membrane, between neighboring enzymes, takes only microseconds. The proton spreading over the membrane is facilitated by the hydrogen-bonded networks at the surface. The membrane-buried layers of these networks can eventually serve as a storage/buffer for protons (proton sponges). As the proton equilibration between the surface and the bulk aqueous phase is slower than the lateral proton diffusion between the "sources" and "sinks", the proton activity at the membrane surface, as sensed by the energy transducing enzymes at steady state, might deviate from that measured in the adjoining water phase. This trait should increase the driving force for ATP synthesis, especially in the case of alkaliphilic bacteria.

P/O ratios of mitochondrial oxidative phosphorylation

Mitochondrial mechanistic P/O ratios are still in question. The major studies since 1937 are summarized and various systematic errors are discussed. Values of about 2.5 with NADH-linked substrates and 1.5 with succinate are consistent with most reports after apparent contradictions are explained. Variability of coupling may occur under some conditions but is generally not significant. The fractional values result from the coupling ratios of proton transport. An additional revision of P/O ratios may be required because of a report of the structure of ATP synthase (D. Stock, A.G.W. Leslie, J.E. Walker, Science 286 (1999) 1700-1705) which suggests that the H+/ATP ratio is 10/3, rather than 3, consistent with P/O ratios of 2.3 with NADH and 1.4 with succinate, values that are also possible.

Virtual mitochondria: metabolic modelling and control

Inside the eukaryotic cell, mitochondria are internal organelles of prokaryotic origin, responsible for energy supply in the cell. The control of the mitochondrial ATP production is a complex problem with different patterns according to different tissues and organs. Our aim is to continue to develop the modelling of oxidative phosphorylation in different tissues, to model other parts of mitochondrial metabolism and to include this virtual mitochondria in a virtual cell. In constructing the complete metabolic map of mitochondria, we will take advantage of the sequenced genomes of eukaryotic organism (10-15% of the yeast genome concerns mitochondria).

Energetics of protein transport across biological membranes. a study of the thylakoid DeltapH-dependent/cpTat pathway

Among the pathways for protein translocation across biological membranes, the DeltapH-dependent/Tat system is unusual in its sole reliance upon the transmembrane pH gradient to drive protein transport. The free energy cost of protein translocation via the chloro-plast DeltapH-dependent/Tat pathway was measured by conducting in vitro transport assays with isolated thylakoids while concurrently monitoring energetic parameters. These experiments revealed a substrate-specific energetic barrier to cpTat-mediated transport as well as direct utilization of protons from the gradient, consistent with a H+/protein antiporter mechanism. The magnitude of proton flux was assayed by four independent approaches and averaged 7.9 x 10(4) protons released from the gradient per transported protein. This corresponds to a DeltaG transport of 6.9 x 10(5) kJ.mol protein translocated(-1), representing the utilization of an energetic equivalent of 10(4) molecules of ATP. At this cost, we estimate that the DeltapH-dependent/cpTat pathway utilizes approximately 3% of the total energy output of the chloroplast.

Kinetics of electron transfer through the respiratory chain

We show that the rate at which electrons pass through the respiratory chain in mitochondria and respiring prokaryotic cells is described by the product of three terms, one describing electron donation, one acceptance, and a third, the thermodynamic drive. We apply the theory of nonequilibrium thermodynamics in the context of the chemiosmotic model of proton translocation and energy conservation. This approach leads to a closed-form expression that predicts steady-state electron flux as a function of chemical conditions and the proton motive force across the mitochondrial inner membrane or prokaryotic cytoplasmic membrane. The rate expression, derived considering reverse and forward electron flow, is the first to account for both thermodynamic and kinetic controls on the respiration rate. The expression can be simplified under specific conditions to give rate laws of various forms familiar in cellular physiology and microbial ecology. The expression explains the nonlinear dependence of flux on electrical potential gradient, its hyperbolic dependence on substrate concentration, and the inhibiting effects of reaction products. It provides a theoretical basis for investigating life under unusual conditions, such as microbial respiration in alkaline waters.

Thermodynamics and bioenergetics

Bioenergetics is concerned with the energy conservation and conversion processes in a living cell, particularly in the inner membrane of the mitochondrion. This review summarizes the role of thermodynamics in understanding the coupling between the chemical reactions and the transport of substances in bioenergetics. Thermodynamics has the advantages of identifying possible pathways, providing a measure of the efficiency of energy conversion, and of the coupling between various processes without requiring a detailed knowledge of the underlying mechanisms. In the last five decades, various new approaches in thermodynamics, non-equilibrium thermodynamics and network thermodynamics have been developed to understand the transport and rate processes in physical and biological systems. For systems not far from equilibrium the theory of linear non-equilibrium thermodynamics is used, while extended non-equilibrium thermodynamics is used for systems far away from equilibrium. All these approaches are based on the irreversible character of flows and forces of an open system. Here, linear non-equilibrium thermodynamics is mostly discussed as it is the most advanced. We also review attempts to incorporate the mechanisms of a process into some formulations of non-equilibrium thermodynamics. The formulation of linear non-equilibrium thermodynamics for facilitated transport and active transport, which represent the key processes of coupled phenomena of transport and chemical reactions, is also presented. The purpose of this review is to present an overview of the application of non-equilibrium thermodynamics to bioenergetics, and introduce the basic methods and equations that are used. However, the reader will have to consult the literature reference to see the details of the specific applications.

Theoretical studies on the regulation of oxidative phosphorylation in intact tissues

The theoretical studies on the regulation of oxidative phosphorylation that were performed with the aid of kinetic models of this process are overviewed. A definition of the regulation of the flux through a metabolic pathway is proposed and opposed to the control exerted by particular enzymes over this flux. Different kinetic models of oxidative phosphorylation proposed in the literature are presented, of which only the model proposed by myself and co-workers was extensively used in theoretical studies on the regulation and compensation in the oxidative phosphorylation system. These theoretical studies have led to the following conclusions: (1) in isolated mitochondria, an increase in the activity of an artificial ATP-using system stimulates mitochondria mainly via changes in [ADP], while changes in [ATP] and [P(i)] play only a minor role; (2) in non-excitable tissues (e.g. liver), hormones (acting via some cytosolic factor(s)) activate directly both ATP usage and at least some enzymes of the ATP-producing block; (3) in excitable tissues (e.g. skeletal muscle), neural signals stimulate (via some cytosolic factor(s)) in parallel all the steps of oxidative phosphorylation together with ATP usage and substrate dehydrogenation; (4) the decrease in the flux through cytochrome oxidase caused by a decrease in oxygen concentration is, at least partially, compensated by a decrease in Delta p and increase in the reduction level of cytochrome c. A theoretical prediction is formulated that there should exist and be observable a universal cytosolic factor/regulatory mechanism which directly activates (at least in excitable tissues) all complexes of oxidative phosphorylation during an increased energy demand.

How understanding the control of energy metabolism can help investigation of mitochondrial dysfunction, regulation and pharmacology

Understanding the control of mitochondrial energy metabolism is central to knowing how mitochondria function within cells. Metabolic control analysis is the best approach available for studying the control of mitochondrial energy metabolism. Here I outline how metabolic control analysis has been used to help understand mitochondrial regulation, damage and pharmacology.

Mitochondrial oxidative phosphorylation thermodynamic efficiencies reflect physiological organ roles

Mitochondria cannot maximize energy production, efficiency, and the cellular ATP phosphorylation potential all at the same time. The theoretical and observed determinations of coupling of oxidative phosphorylation in mitochondria from rat liver, heart, and brain were compared using classical and nonequilibrium thermodynamic measures. Additionally, the optimal thermodynamic efficiency and flow ratios were determined for control of the two energy-converting complexes of the respiratory chain: complex I (NADH), which reflects the integrated cellular pathway, and complex II (FADH2), the predominantly tricarboxylic acid (TCA) cycle pathway. For all three organs, the cellular respiratory pathway was more tightly coupled than the TCA pathway and resulted in a greater optimal efficiency. Liver mitochondria are the most thermodynamically efficient at ATP production using oxidative phosphorylation. Heart and brain mitochondrial systems utilize more oxygen, but can produce ATP at a faster rate than liver systems. Per the theory of economic degrees of coupling, isolated rat liver mitochondrial systems are designed for the economic production of ATP for use in cellular processes. In the brain, the mitochondrial TCA cycle pathway promotes the maximal maintenance of the cellular energy state for cellular viability, whereas in the heart the TCA cycle pathway maximizes the production of ATP. The coupling of oxidative phosphorylation not only can be expected to change with substrate availability but may also reflect an ontogenetic response of mitochondria to fit specific organ roles in the rat.

Metabolic control analysis of biochemical pathways based on a thermokinetic description of reaction rates

Metabolic control analysis is a powerful technique for the evaluation of flux control within biochemical pathways. Its foundation is the elasticity coefficients and the flux control coefficients (FCCs). On the basis of a thermokinetic description of reaction rates it is here shown that the elasticity coefficients can be calculated directly from the pool levels of metabolites at steady state. The only requirement is that one thermodynamic parameter be known, namely the reaction affinity at the intercept of the tangent in the inflection point of the curve of reaction rate against reaction affinity. This parameter can often be determined from experiments in vitro. The methodology is applicable only to the analysis of simple two-step pathways, but in many cases larger pathways can be lumped into two overall conversions. In cases where this cannot be done it is necessary to apply an extension of the thermokinetic description of reaction rates to include the influence of effectors. Here the reaction rate is written as a linear function of the logarithm of the metabolite concentrations. With this type of rate function it is shown that the approach of Delgado and Liao [Biochem. J. (1992) 282, 919-927] can be much more widely applied, although it was originally based on linearized kinetics. The methodology of determining elasticity coefficients directly from pool levels is illustrated with an analysis of the first two steps of the biosynthetic pathway of penicillin. The results compare well with previous findings based on a kinetic analysis.

Regulation of cytochrome oxidase: theoretical studies

Using the dynamic model of oxidative phosphorylation developed previously and tested for its validity under a broad range of conditions some properties of cytochrome oxidase in the whole system considered were simulated. The regulation of this enzyme by oxygen concentration, delta p and reduction level of cytochrome c were studied. Assuming at least qualitative validity of the model, the following conclusions were drawn: (1) Regulation of cytochrome oxidase is different under the same conditions, when changes in the system (oxidative phosphorylation in isolated mitochondria) are imposed by a decrease in oxygen concentration (aerobiosis-->anaerobiosis transition) or by addition of hexokinase (state 4-->state 3 transition). In the former case, cytochrome c and delta p play a very similar role in the compensation for a decrease in the respiration rate caused by lowered oxygen concentration, while in the latter case changes in delta p activate cytochrome oxidase much stronger than changes in the reduction level of cytochrome c. (2) There is no unique thermodynamic flux-force relationship for cytochrome oxidase. This relationship depends on how the thermodynamic span of the reaction catalyzed by this enzyme is changed (aerobiosis-->anaerobiosis transition vs. state 4-->state 3 transition). (3) Under some conditions (aerobiosis-->anaerobiosis transition) the flux-force relationship can be inverse, i.e. increase in a thermodynamic force occurs simultaneously with decrease in a reaction rate.

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.

The proton pumping activity of H(+)-ATPases: an improved fluorescence assay

A new method for the estimation of steady-state delta pH, and the rate of acidification, by H(+)-ATPases (and other proton transporters) in inverted membrane vesicles is described. The method is based on a combination of two widely used fluorescent delta pH probes, 9-aminoacridine and 9-amino-6-chloro-2-methoxyacridine. It is demonstrated that 9-amino-6-chloro-2-methoxyacridine fluorescence quenching, which is very sensitive to small pH gradients, is not sensitive to the magnitude of large pH gradient, while 9-aminoacridine, which does not sense small gradients, is very sensitive to large pH gradients. A proper mixture of the two probes provides a method which is equally sensitive to pH gradients from very small values up to 3.5 pH units. The probe response was evaluated by titrations of the fluorescence signal with nigericin and adjusted by changing the concentration ratio and the emission wavelength. In liposomes, submitochondrial particles and bacterial vesicles an almost linear dependence of quenching on delta pH over the entire range can be obtained with this method. It is demonstrated that the new method can be used to obtain more reliable estimates of the rate of acidification as well as the magnitude of delta pH, whereas each of these and similar probes, by themselves are not as reliable. A determination of the ratio delta Gp/delta muH over a wide range of values reveal that this ratio is not constant but decreases with delta Gp. This finding should be taken into consideration when attempting to estimate the H+/ATP ratio form the measurement of delta Gp/delta muH.

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.

Entropy balances of microbial product formation

Considering the approach of Bermudez and Wagensberg (1986) devoted to the entropy balance of growing microorganisms some equations were developed which describe particularly the entropy balance of microbial product formation. The formula allows to determine the coefficients of resistance R(mn) and of coupling L(mn) according to rates of growth, product formation, maintenance metabolism and heat evolution assuming a linear relationship between thermodynamic fluxes and forces. In order to check the usefulness of the derived model appropriate experimental data of two microbial batch processes concerning production of L-lysine and the antibiotic nourseothricine were taken into account. The results showed similar courses of entropy balances despite different pathways of product formation which were characterized by an overshoot of entropy production at the beginning of biosynthesis of the primary and secondary metabolite. This fact was interpreted as a more general phenomenon for microorganisms under inbalanced nutritional conditions.

Calpain I activates Ca2+ transport by the reconstituted erythrocyte Ca2+ pump

Calpain I purified from human erythrocyte cytosol activates both the ATP hydrolytic activity and the ATP-dependent Ca2+ transport function of the Ca2(+)-translocating ATPase solubilized and purified from the plasma membrane of human erythrocytes and reconstituted into phosphatidylcholine vesicles. Following partial proteolysis of the enzyme by calpain I, both the initial rates of calcium ion uptake and ATP hydrolysis were increased to near maximal levels similar to those obtained upon addition of calmodulin. The proteolytic activation resulted in the loss of further stimulation of the rates of Ca2+ translocation or ATP hydrolysis by calmodulin as well as an increase of the affinity of the enzyme for calcium ion. However, the mechanistic Ca2+/ATP stoichiometric ratio was not affected by the proteolytic treatment of the reconstituted Ca2(+)-translocating ATPase. The proteolytic activation of the ATP hydrolytic activity of the reconstituted enzyme could be largely prevented by calmodulin. Different patterns of proteolysis were obtained in the absence or in the presence of calmodulin during calpain treatment: the 136-kDa enzyme was transformed mainly into a 124-kDa active ATPase fragment in the absence of calmodulin, whereas a 127-kDa active ATPase fragment was formed in the presence of calmodulin. This study shows that calpain I irreversibly activates the Ca2+ translocation function of the Ca2(+)-ATPase in reconstituted proteoliposomes by producing a calmodulin-independent active enzyme fragment, while calmodulin antagonizes this activating effect by protecting the calmodulin-binding domain against proteolytic cleavage by calpain.

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.

On the nature of ion leaks in energy-transducing membranes

Diffusion is the implicit null hypothesis for ion transport across biological membranes. A proper model of ionic diffusion across the permeability barrier is needed to distinguish among leaks, channels and carriers and to determine whether changes in flux reflect changes in permeability (regulation) or merely changes in the driving force. These issues arise in all biomembranes, but they are particularly confounding in energy-transducing membranes on account of their characteristically high electrical gradients. This paper examines the nature of the barrier to ion leaks, using the classical Eyring rate theory. We introduce new practical procedures for estimating permeability coefficients from ion flux data. We also reach some general conclusions regarding ion leaks across energy-transducing membranes. (1) The dependence of ion flux on the electrical membrane potential is invariably non-linear (non-ohmic). (2) Non-ohmic behavior does not imply variable permeability. (3) Ohmic behavior is exceptional and its occurrence should alert us to the possibility of an underlying carrier or channel. (4) Leak pathways are very likely localized to protein-lipid interfaces and will exhibit quasi-specific properties such as saturation and competition. (5) The inherent non-ohmicity of leaks and the requirement for efficient energy transduction impose constraints upon the magnitude of allowable Gibbs free-energy changes in biological systems. (6) Nature adapts to these constraints by devising mechanisms for step-wise splitting of the partial reactions of energy transduction.

Differential effects of osmotic pressure on mitochondrial respiratory chain and indices of oxidative phosphorylation

Oxidative phosphorylation was critically evaluated in terms of activities which are sensitive and insensitive to variations in external osmotic pressure in mitochondria. Integrity of mitochondria was determined in terms of a variety of parameters, including the latency of the occluded enzymes, by careful titrations as a function of external osmotic pressure as well as detergent concentrations. The evidence indicated that the rate-limiting step in respiratory states 2 and 4 would be osmotically insensitive, as opposed to the osmotically sensitive respiration of states 1 and 3 and uncoupler-stimulated respiration with glutamate + malate and succinate. Cytochrome oxidase activity in mitochondria as well as in purified reconstituted systems exhibited osmotic insensitivity but marked sensitivity to ionic strength, offering an interesting model to study the osmotically insensitive respiration. Cytochrome oxidase activity led to permeation of mannitol across the mitochondrial inner membrane. Stimulation of cytochrome oxidase activity by uncouplers did not require an intact membrane.

Physical mechanism of ATP formation in biomembranes

Membrane-bound and isolated H+ ATPases of various origin are able to synthesize ATP from ADP and Pi after a jump-like pH increase. In the course of this increase the pH of solution (or suspension) must cross a value corresponding to pK of certain acid groups in the catalytic component of ATPase. In the case of isolated soluble enzymes it is possible to obtain up to 10 ATP molecules per one pH jump per one enzyme molecule. A physical mechanism of this phenomenon as well as of oxidative and photosynthetic phosphorylation is suggested.

2-Mercaptopropionylglycine improves aortic flow after reoxygenation in working rat hearts

The cardioprotective concentration range of the thiol drug 2-mercaptopropionylglycine (MPG) was investigated during reoxygenation after 30 min of hypoxia. It was found that aortic flow and frequency were increased by 1 mM MPG. Coronary flow, systolic and diastolic pressure were not significantly influenced by the drug. Mitochondria, isolated from hearts after termination of the perfusion phases, revealed increased values of RCI, when MPG had been present in the previous reoxygenation phase at 1 mM concentration. 5 mM MPG no longer showed a protective influence on the above cardiac and mitochondrial parameters. ATPase activities were decreased at 1 mM MPG by 14% and at 5 mM MPG by 40% of the controls. The latter concentration of MPG also doubled the inhibitory action of carboxyatractyloside on ATPase activity, indicating a structural change of the adenine nucleotide carrier. 1 mM MPG is considered an optimal therapeutic range in this model. The mechanism of action most probably includes an SH/-S-S-interchange reaction as well as a free radical scavenging mechanism. For many thiols, the latter is known to occur in the presence of metal ions.

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.

Changes in pyridine nucleotide levels alter oxygen consumption and extra-mitochondrial phosphates in isolated mitochondria: a 31P-NMR and NAD(P)H fluorescence study

Isolated rat-liver mitochondria were used to study the relation between mitochondrial NADH levels, oxygen consumption (QO2), and extra-mitochondrial phosphates. Alterations in NADH and QO2 were accomplished by incubating mitochondria with different substrates or varying amounts of exogenous ATPase while monitoring QO2 and NAD(P)H fluorescence. Two sets of conditions were studied: (1) in the presence of excess ADP and inorganic phosphate, an increase in NAD(P)H fluorescence was associated with a linear increase in QO2; (2) when QO2 was driven by the steady-state hydrolysis of ATP by exogenous ATPase, increases in QO2 were associated with proportional decreases in NAD(P)H fluorescence. For all substrates tested this relation was linear; however, the slope was substrate dependent. Different substrates were able to maintain different NAD(P)H levels at the same QO2. To investigate this further, effects of changing substrates at constant QO2 on NAD(P)H and extra-mitochondrial phosphates were determined. Addition of glutamate + malate to mitochondria respiring on citrate caused a 50% increase in NAD(P)H fluorescence, a 41% decrease in ADP, and a 30% decrease in inorganic phosphate. Similar changes for the substrate jump, pyruvate + malate to glutamate + malate were found. Finally, it was determined that a linear relation holds between increases in NAD(P)H fluorescence and increases in QO2 when substrates were varied at constant, physiologic levels of extra-mitochondrial ADP. These results indicate that QO2 depends on NAD(P)H levels as well as on extra-mitochondrial phosphates over a wide range of respiratory rates.

CARBON DIOXIDE AND WATER DEMAND: CRASSULACEAN ACID METABOLISM (CAM), A VERSATILE ECOLOGICAL ADAPTATION EXEMPLIFYING THE NEED FOR INTEGRATION IN ECOPHYSIOLOGICAL WORK

Plants having crassulacean acid metabolism (CAM) tend to occupy habitats where the prevailing environmental stress is scarcity of water. These are semi-arid or arid regions, salinas or epiphytic sites. CAM plants manage the dilemma of desiccation or starvation by nocturnal malic acid accumulation in the vacuoles. Malic acid serves as a form of CO₂ storage and as an osmoticum. In this way malic acid accumulation allows, firstly, separation of uptake and assimilation of atmospheric CO₂ with water-saving daytime stomatal closure and, secondly, osmotic acquisition of water. There is no very special trait which is specific for CAM. An array of biophysical and biochemical functional elements, which are also found in other plants, is integrated in CAM performance. This leads to a large diversity of behaviour which makes CAM plants highly versatile in their response to environmental variables. Besides CO₂ dark fixation, transport of malic acid across the tonoplast is one of the key elements in CAM function. This is examined in detail at the level of membrane biophysics and biochemistry. The versatility of CAM is illustrated by examples from field work, with comparisons involving different species, seasons, modes of photosynthesis (CAM vs C₃ ), kinds of stress and ways of stress imposition. Contents Summary 593 I. Studies of CAM: an example for the ecophysiological approach 594 II. Malic acid transport at the tonoplast 602 III. Regulation 605 IV. Desiccation or starvation 610 V. Comparative autecology 614 VI. Ecology: promise of integration 621 Acknowledgements 622 References 622.