The metabolic control theory: Its development and its application to mitochondrial oxidative phosphorylation.

Metabolic Control Theory (MCT) and Metabolic Control Analysis (MCA) are the two sides, theoretical and experimental, of the measurement of the sensitivity of metabolic networks in the vicinity of a steady state. We will describe the birth and the development of this theory from the first analyses of linear pathways up to a global mathematical theory applicable to any metabolic network. We will describe how the theory, given the global nature of mitochondrial oxidative phosphorylation, solved the problem of what controls mitochondrial ATP synthesis and then how it led to a better understanding of the differential tissue expression of human mitochondrial pathologies and of the heteroplasmy of mitochondrial DNA, leading to the concept of the threshold effect.

One-carbon metabolism in cancer cells: a critical review based on a core model of central metabolism.

One-carbon metabolism (1C-metabolism), also called folate metabolism because the carbon group is attached to folate-derived tetrahydrofolate, is crucial in metabolism. It is at the heart of several essential syntheses, particularly those of purine and thymidylate. After a short reminder of the organization of 1C-metabolism, I list its salient features as reported in the literature. Then, using flux balance analysis, a core model of central metabolism and the flux constraints for an 'average cancer cell metabolism', I explore the fundamentals underlying 1C-metabolism and its relationships with the rest of metabolism. Some unreported properties of 1C-metabolism emerge, such as its potential roles in mitochondrial NADH exchange with cytosolic NADPH, participation in NADH recycling, and optimization of cell proliferation.

Modelling mitochondrial ROS production by the respiratory chain.

ROS (superoxide and oxygen peroxide in this paper) play a dual role as signalling molecules and strong oxidizing agents leading to oxidative stress. Their production mainly occurs in mitochondria although they may have other locations (such as NADPH oxidase in particular cell types). Mitochondrial ROS production depends in an interweaving way upon many factors such as the membrane potential, the cell type and the respiratory substrates. Moreover, it is experimentally difficult to quantitatively assess the contribution of each potential site in the respiratory chain. To overcome these difficulties, mathematical models have been developed with different degrees of complexity in order to analyse different physiological questions ranging from a simple reproduction/simulation of experimental results to a detailed model of the possible mechanisms leading to ROS production. Here, we analyse experimental results concerning ROS production including results still under discussion. We then critically review the three models of ROS production in the whole respiratory chain available in the literature and propose some direction for future modelling work.

The Fate of Glutamine in Human Metabolism. The Interplay with Glucose in Proliferating Cells.

Genome-scale models of metabolism (GEM) are used to study how metabolism varies in different physiological conditions. However, the great number of reactions involved in GEM makes it difficult to understand these variations. In order to have a more understandable tool, we developed a reduced metabolic model of central carbon and nitrogen metabolism, C2M2N with 77 reactions, 54 internal metabolites, and 3 compartments, taking into account the actual stoichiometry of the reactions, including the stoichiometric role of the cofactors and the irreversibility of some reactions. In order to model oxidative phosphorylation (OXPHOS) functioning, the proton gradient through the inner mitochondrial membrane is represented by two pseudometabolites DPH (∆pH) and DPSI (∆ψ). To illustrate the interest of such a reduced and quantitative model of metabolism in mammalian cells, we used flux balance analysis (FBA) to study all the possible fates of glutamine in metabolism. Our analysis shows that glutamine can supply carbon sources for cell energy production and can be used as carbon and nitrogen sources to synthesize essential metabolites. Finally, we studied the interplay between glucose and glutamine for the formation of cell biomass according to ammonia microenvironment. We then propose a quantitative analysis of the Warburg effect.

Modeling Protein Destiny in Developing Fruit.

Protein synthesis and degradation are essential processes that regulate cell status. Because labeling in bulky organs, such as fruits, is difficult, we developed a modeling approach to study protein turnover at the global scale in developing tomato (Solanum lycopersicum) fruit. Quantitative data were collected for transcripts and proteins during fruit development. Clustering analysis showed smaller changes in protein abundance compared to mRNA abundance. Furthermore, protein and transcript abundance were poorly correlated, and the coefficient of correlation decreased during fruit development and ripening, with transcript levels decreasing more than protein levels. A mathematical model with one ordinary differential equation was used to estimate translation (kt ) and degradation (kd ) rate constants for almost 2,400 detected transcript-protein pairs and was satisfactorily fitted for >1,000 pairs. The model predicted median values of ∼2 min for the translation of a protein, and a protein lifetime of ∼11 d. The constants were validated and inspected for biological relevance. Proteins involved in protein synthesis had higher kt and kd values, indicating that the protein machinery is particularly flexible. Our model also predicts that protein concentration is more strongly affected by the rate of translation than that of degradation.

The role of glycolysis-derived hexose phosphates in the induction of the Crabtree effect.

Evidence for the Crabtree effect was first reported by H. Crabtree in 1929 and is defined as the glucose-induced decrease of cellular respiratory flux. This effect was observed in tumor cells and was not detected in most non-tumor cells. A number of hypotheses on the mechanism underlying the Crabtree effect have been formulated. However, to this day, no consensual mechanism for this effect has been described. In a previous study on isolated mitochondria, we have proposed that fructose-1,6-bisphosphate (F1,6bP), which inhibits the respiratory chain, induces the Crabtree effect. Using whole cells from the yeast Saccharomyces cerevisiae as a model, we show here not only that F1,6bP plays a key role in the process but that glucose-6-phosphate (G6P), a hexose that has an effect opposite to that of F1,6bP on the regulation of the respiratory flux, does as well. Thus, these findings reveal that the Crabtree effect strongly depends on the ratio between these two glycolysis-derived hexose phosphates. Last, in silico modeling of the Crabtree effect illustrated the requirement of an inhibition of the respiratory flux by a coordinated variation of glucose-6-phosphate and fructose-1,6-bisphosphate to fit the respiratory rate decrease observed upon glucose addition to cells. In summary, we conclude that two glycolysis-derived hexose phosphates, G6P and F1,6bP, play a key role in the induction of the Crabtree effect.

MitoCore: a curated constraint-based model for simulating human central metabolism.

BACKGROUND: The complexity of metabolic networks can make the origin and impact of changes in central metabolism occurring during diseases difficult to understand. Computer simulations can help unravel this complexity, and progress has advanced in genome-scale metabolic models. However, many models produce unrealistic results when challenged to simulate abnormal metabolism as they include incorrect specification and localisation of reactions and transport steps, incorrect reaction parameters, and confounding of prosthetic groups and free metabolites in reactions. Other common drawbacks are due to their scale, making them difficult to parameterise and simulation results hard to interpret. Therefore, it remains important to develop smaller, manually curated models. RESULTS: We present MitoCore, a manually curated constraint-based computer model of human metabolism that incorporates the complexity of central metabolism and simulates this metabolism successfully under normal and abnormal physiological conditions, including hypoxia and mitochondrial diseases. MitoCore describes 324 metabolic reactions, 83 transport steps between mitochondrion and cytosol, and 74 metabolite inputs and outputs through the plasma membrane, to produce a model of manageable scale for easy interpretation of results. Its key innovations include a more accurate partitioning of metabolism between cytosol and mitochondrial matrix; better modelling of connecting transport steps; differentiation of prosthetic groups and free co-factors in reactions; and a new representation of the respiratory chain and the proton motive force. MitoCore's default parameters simulate normal cardiomyocyte metabolism, and to improve usability and allow comparison with other models and types of analysis, its reactions and metabolites have extensive annotation, and cross-reference identifiers from Virtual Metabolic Human database and KEGG. These innovations-including over 100 reactions absent or modified from Recon 2-are necessary to model central metabolism more accurately. CONCLUSION: We anticipate MitoCore as a research tool for scientists, from experimentalists looking to interpret their data and test hypotheses, to experienced modellers predicting the consequences of disease or using computationally intensive methods that are infeasible with larger models, as well as a teaching tool for those new to modelling and needing a small, manageable model on which to learn and experiment.

Respiration climacteric in tomato fruits elucidated by constraint-based modelling.

Tomato is a model organism to study the development of fleshy fruit including ripening initiation. Unfortunately, few studies deal with the brief phase of accelerated ripening associated with the respiration climacteric because of practical problems involved in measuring fruit respiration. Because constraint-based modelling allows predicting accurate metabolic fluxes, we investigated the respiration and energy dissipation of fruit pericarp at the breaker stage using a detailed stoichiometric model of the respiratory pathway, including alternative oxidase and uncoupling proteins. Assuming steady-state, a metabolic dataset was transformed into constraints to solve the model on a daily basis throughout tomato fruit development. We detected a peak of CO2 released and an excess of energy dissipated at 40 d post anthesis (DPA) just before the onset of ripening coinciding with the respiration climacteric. We demonstrated the unbalanced carbon allocation with the sharp slowdown of accumulation (for syntheses and storage) and the beginning of the degradation of starch and cell wall polysaccharides. Experiments with fruits harvested from plants cultivated under stress conditions confirmed the concept. We conclude that modelling with an accurate metabolic dataset is an efficient tool to bypass the difficulty of measuring fruit respiration and to elucidate the underlying mechanisms of ripening.

Modelling central metabolic fluxes by constraint-based optimization reveals metabolic reprogramming of developing Solanum lycopersicum (tomato) fruit.

Modelling of metabolic networks is a powerful tool to analyse the behaviour of developing plant organs, including fruits. Guided by our current understanding of heterotrophic metabolism of plant cells, a medium-scale stoichiometric model, including the balance of co-factors and energy, was constructed in order to describe metabolic shifts that occur through the nine sequential stages of Solanum lycopersicum (tomato) fruit development. The measured concentrations of the main biomass components and the accumulated metabolites in the pericarp, determined at each stage, were fitted in order to calculate, by derivation, the corresponding external fluxes. They were used as constraints to solve the model by minimizing the internal fluxes. The distribution of the calculated fluxes of central metabolism were then analysed and compared with known metabolic behaviours. For instance, the partition of the main metabolic pathways (glycolysis, pentose phosphate pathway, etc.) was relevant throughout fruit development. We also predicted a valid import of carbon and nitrogen by the fruit, as well as a consistent CO2 release. Interestingly, the energetic balance indicates that excess ATP is dissipated just before the onset of ripening, supporting the concept of the climacteric crisis. Finally, the apparent contradiction between calculated fluxes with low values compared with measured enzyme capacities suggest a complex reprogramming of the metabolic machinery during fruit development. With a powerful set of experimental data and an accurate definition of the metabolic system, this work provides important insight into the metabolic and physiological requirements of the developing tomato fruits.

Victor Henri: 111 years of his equation.

Victor Henri's great contribution to the understanding of enzyme kinetics and mechanism is not always given the credit that it deserves. In addition, his earlier work in experimental psychology is totally unknown to biochemists, and his later work in spectroscopy and photobiology almost equally so. Applying great rigour to his analysis he succeeded in obtaining a model of enzyme action that explained all of the observations available to him, and he showed why the considerable amount of work done in the preceding decade had not led to understanding. His view was that only physical chemistry could explain the behaviour of enzymes, and that models should be judged in accordance with their capacity not only to explain previously known facts but also to predict new observations against which they could be tested. The kinetic equation usually attributed to Michaelis and Menten was in reality due to him. His thesis of 1903 is now available in English.

Model-assisted analysis of sugar metabolism throughout tomato fruit development reveals enzyme and carrier properties in relation to vacuole expansion.

A kinetic model combining enzyme activity measurements and subcellular compartmentation was parameterized to fit the sucrose, hexose, and glucose-6-P contents of pericarp throughout tomato (Solanum lycopersicum) fruit development. The model was further validated using independent data obtained from domesticated and wild tomato species and on transgenic lines. A hierarchical clustering analysis of the calculated fluxes and enzyme capacities together revealed stage-dependent features. Cell division was characterized by a high sucrolytic activity of the vacuole, whereas sucrose cleavage during expansion was sustained by both sucrose synthase and neutral invertase, associated with minimal futile cycling. Most importantly, a tight correlation between flux rate and enzyme capacity was found for fructokinase and PPi-dependent phosphofructokinase during cell division and for sucrose synthase, UDP-glucopyrophosphorylase, and phosphoglucomutase during expansion, thus suggesting an adaptation of enzyme abundance to metabolic needs. In contrast, for most enzymes, flux rates varied irrespectively of enzyme capacities, and most enzymes functioned at <5% of their maximal catalytic capacity. One of the major findings with the model was the high accumulation of soluble sugars within the vacuole together with organic acids, thus enabling the osmotic-driven vacuole expansion that was found during cell division.

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.

Remarkable reproducibility of enzyme activity profiles in tomato fruits grown under contrasting environments provides a roadmap for studies of fruit metabolism.

To assess the influence of the environment on fruit metabolism, tomato (Solanum lycopersicum 'Moneymaker') plants were grown under contrasting conditions (optimal for commercial, water limited, or shaded production) and locations. Samples were harvested at nine stages of development, and 36 enzyme activities of central metabolism were measured as well as protein, starch, and major metabolites, such as hexoses, sucrose, organic acids, and amino acids. The most remarkable result was the high reproducibility of enzyme activities throughout development, irrespective of conditions or location. Hierarchical clustering of enzyme activities also revealed tight relationships between metabolic pathways and phases of development. Thus, cell division was characterized by high activities of fructokinase, glucokinase, pyruvate kinase, and tricarboxylic acid cycle enzymes, indicating ATP production as a priority, whereas cell expansion was characterized by enzymes involved in the lower part of glycolysis, suggesting a metabolic reprogramming to anaplerosis. As expected, enzymes involved in the accumulation of sugars, citrate, and glutamate were strongly increased during ripening. However, a group of enzymes involved in ATP production, which is probably fueled by starch degradation, was also increased. Metabolites levels seemed more sensitive than enzymes to the environment, although such differences tended to decrease at ripening. The integration of enzyme and metabolite data obtained under contrasting growth conditions using principal component analysis suggests that, with the exceptions of alanine amino transferase and glutamate and malate dehydrogenase and malate, there are no links between single enzyme activities and metabolite time courses or levels.

Commemorating the 1913 Michaelis-Menten paper Die Kinetik der Invertinwirkung: three perspectives.

Methods and equations for analysing the kinetics of enzyme-catalysed reactions were developed at the beginning of the 20th century in two centres in particular; in Paris, by Victor Henri, and, in Berlin, by Leonor Michaelis and Maud Menten. Henri made a detailed analysis of the work in this area that had preceded him, and arrived at a correct equation for the initial rate of reaction. However, his approach was open to the important objection that he took no account of the hydrogen-ion concentration (a subject largely undeveloped in his time). In addition, although he wrote down an expression for the initial rate of reaction and described the hyperbolic form of its dependence on the substrate concentration, he did not appreciate the great advantages that would come from analysis in terms of initial rates rather than time courses. Michaelis and Menten not only placed Henri's analysis on a firm experimental foundation, but also defined the experimental protocol that remains standard today. Here, we review this development, and discuss other scientific contributions of these individuals. The three parts have different authors, as indicated, and do not necessarily agree on all details, in particular about the relative importance of the contributions of Michaelis and Menten on the one hand and of Henri on the other. Rather than force the review into an unrealistic consensus, we consider it appropriate to leave the disagreements visible.

Evidence for cardiolipin binding sites on the membrane-exposed surface of the cytochrome bc1.

The respiratory chain is located in the inner membrane of mitochondria and produces the major part of the ATP used by a cell. Cardiolipin (CL), a double charged phospholipid composing ~10-20% of the mitochondrial membrane, plays an important role in the function and supramolecular organization of the respiratory chain complexes. We present an extensive set of coarse-grain molecular dynamics (CGMD) simulations aiming at the determination of the preferential interfaces of CLs on the respiratory chain complex III (cytochrome bc(1), CIII). Six CL binding sites are identified, including the CL binding sites known from earlier structural studies and buried into protein cavities. The simulations revealed the importance of two subunits of CIII (G and K in bovine heart) for the structural integrity of these internal CL binding sites. In addition, new binding sites are found on the membrane-exposed protein surface. The reproducibility of these binding sites over two species (bovine heart and yeast mitochondria) points to an important role for the function of the respiratory chain. Interestingly the membrane-exposed CL binding sites are located on the matrix side of CIII in the inner membrane and thus may provide localized sources of proton ready for uptake by CIII. Furthermore, we found that CLs bound to those membrane-exposed sites bridge the proteins during their assembly into supercomplexes by sharing the binding sites.

Mitochondrial energetic metabolism-some general principles.

In nonphotosynthetic organisms, mitochondria are the power plant of the cell, emphasizing their great potentiality for adenosine triphosphate (ATP) synthesis from the redox span between nutrients and oxygen. Also of great importance is their role in the maintenance of the cell redox balance. Even though crystallographic structures of respiratory complexes, ATP synthase, and ATP/adenosine diphosphate (ADP) carrier are now quite well known, the coupling between ATP synthesis and cell redox state remains a controversial issue. In this review, we will present some of the processes that allow a modular coupling between ATP synthesis and redox state. Furthermore, we will present some theoretical approaches of this highly integrated system.

From in silico to in spectro kinetics of respiratory complex I.

An enzyme's activity is the consequence of its structure. The stochastic approach we developed to study the functioning of the respiratory complexes is based upon their 3D structure and their physical and chemical properties. Consequently it should predict their kinetic properties. In this paper we compare the predictions of our stochastic model derived for the complex I with a number of experiments performed with a large range of complex I substrates and products. A good fit was found between the experiments and the prediction of our stochastic approach. We show that, due to the spatial separation of the two half redox reactions (NADH/NAD and Q/QH(2)), the kinetics cannot necessarily obey a simple mechanism (ordered or ping-pong for instance). A plateau in the kinetics is observed at high substrates concentrations, well evidenced in the double reciprocal plots, which is explained by the limiting rate of quinone reduction as compared with the oxidation of NADH at the other end of complex I. Moreover, we show that the set of the seven redox reactions in between the two half redox reactions (NADH/NAD and Q/QH(2)) acts as an electron buffer. An inhibition of complex I activity by quinone is observed at high concentration of this molecule, which cannot be explained by a simple stochastic model based on the known structure. We hypothesize that the distance between the catalytic site close to N2 (iron/sulfur redox center that transfers electrons to quinone) and the membrane forces the quinone/quinol to take several positions in between these sites. We represent these possible positions by an extra site necessarily occupied by the quinone/quinol molecules on their way to the redox site. With this hypothesis, we are able to fit the kinetic experiments over a large range of substrates and products concentrations. The slow rate constants derived for the transition between the two sites could be an indication of a conformational change of the enzyme during the quinone/quinol movement. This article is part of a Special Issue entitled: 17th European Bioenergetics Conference (EBEC 2012).

Chronic hypoxia-induced alterations in mitochondrial energy metabolism are not reversible in rat heart ventricles.

Chronic hypoxia alters mitochondrial energy metabolism. In the heart, oxidative capacity of both ventricles is decreased after 3 weeks of chronic hypoxia. The aim of this study was to evaluate the reversal of these metabolic changes upon normoxia recovery. Rats were exposed to a hypobaric environment for 3 weeks and then subjected to a normoxic environment for 3 weeks (normoxia-recovery group) and compared with rats maintained in a normoxic environment (control group). Mitochondrial energy metabolism was differentially examined in both left and right ventricles. Oxidative capacity (oxygen consumption and ATP synthesis) was measured in saponin-skinned fibers. Activities of mitochondrial respiratory chain complexes and antioxidant enzymes were measured on ventricle homogenates. Morphometric analysis of mitochondria was performed on electron micrographs. In normoxia-recovery rats, oxidative capacities of right ventricles were decreased in the presence of glutamate or palmitoyl carnitine as substrates. In contrast, oxidation of palmitoyl carnitine was maintained in the left ventricle. Enzyme activities of complexes III and IV were significantly decreased in both ventricles. These functional alterations were associated with a decrease in numerical density and an increase in size of mitochondria. Finally, in the normoxia-recovery group, the antioxidant enzyme activities (catalase and glutathione peroxidase) increased. In conclusion, alterations of mitochondrial energy metabolism induced by chronic hypoxia are not totally reversible. Reactive oxygen species could be involved and should be investigated under such conditions, since they may represent a therapeutic target.

[The cytochrome bc1 complex in the mitochondrial respiratory chain functions according to the Q cycle hypothesis of Mitchell: the proof using a stochastic approach?]. / Le complexe bc1 de la chaîne respiratoire mitochondriale fonctionne selon l'hypothèse du cycle Q de Mitchell: la preuve par une approche stochastique?

The bc1 complex is a central complex in the mitochondrial respiratory chain. It links the electrons transfer from ubiquinol (or coenzyme Q) to cytochrome c and proton translocation across the inner mitochondrial membrane. It is widely agreed that the "Q-cycle mechanism" proposed by Mitchell correctly describes the bc1 complex working. It is based on an unexpected separation of the two electrons coming from the coenzyme Q bound at the Q0 site of the bc1 complex. Using the stochastic approach of Gillespie and the known spatial structure of bc1 complexes with the kinetic parameters described by Moser and Dutton we demonstrated the natural emergence of the Q-cycle mechanism and the quasi absence of short-circuits in the functional dimer of bc1 complex without the necessity to invoke any additional mechanism. This approach gives a framework which is well adapted to the modelling of all oxido-reduction reactions of the respiratory chain complexes, normal or mutant.

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.