Application of the metabolic control theory to the study of the dynamics of substrate cycles

Substrate cycles are ubiquitous structures of the cellular metabolism (e.g. Krebs cycle, fatty acids -oxydation cycles, etc... ). Moiety-conserved cycles (e.g. adenine nucleotides and NADH/NAD, etc...) are also important.The role played by such cycles in the metabolism and its regulation is not clearly understood so far. However, it was shown that these cycles can generate multistationarity (bistability), irreversible transitions, enhancement of sensitivity, temporal oscillations and chaotic motions (Hervagault & Canu, 1987; Hervagault & Cimino, 1989; Reich & Sel'kov, 1981; Ricard & Soulié, 1982). Fig. 1: Scheme of the open binary substrate cycle under study. The substrate S is converted into P with a net rate v₂. Substrate P is converted in turn into S with a net rate v₃. Step v₂ is inhibited by excess of the substrate, S. In addition, the cycle operates under open conditions, that is zero-order input of S at rates \ga₀(v₁) and first order outputs of S and P at rates \gaS and \gaP(v₄), respectively.The metabolic control theory (see also Fell, 1990), which shows how a metabolic network reacts to small perturbations in the vicinity of a steady state, and is formulated with the so-called control coefficients, was applied to such a cycle in order to get a better knowledge on the importance of each step at the regulatory point of view.The behaviour of a binary substrate cycle (fig. 1) in which one of the enzymes may be subjected to inhibition by excess of its substrate (v₂) was studied theoretically. The flux and concentration control coefficients were calculated for various steady states of the system. The evolution of the different control coefficients is compared to the evolution of the steady states. We mainly focused our study on situations for which the steady states are stable.     

Redistribution of the flux-control coefficients in mitochondrial oxidative phosphorylations in the course of brain edema

This work describes the control exerted by dicarboxylate carrier and succinate dehydrogenase activities on the oxidative phosphorylations in rabbit brain mitochondria as an edema develops. Vasogenic edema leads to an uncompetitive inhibition of succinate dehydrogenase activity and to a large decrease of oxidative phosphorylations linked to succinate utilisation. Naftidrofuryl treatment in vivo restores both a high succinate dehydrogenase activity and a normal respiratory rate. In order to quantify the control of oxidative phosphorylations by the succinate dehydrogenase step, we applied the control analysis (Kacser, H. and Burns, J.A. (1973) in Rate Control of Biological Processes (Davies, D.D., ed.), pp. 65-104, Cambridge University Press, London; Heinrich, R. and Rapoport, T.A. (1974) Eur. J. Biochem. 42, 89-95). By using two inhibitors, one (phenylsuccinate) acting only on the dicarboxylate carrier and another (malonate) acting on both the dicarboxylate carrier and the succinate dehydrogenase, a method was developed to calculate the control coefficients of these two steps. The main result is that in mitochondria isolated from normal tissue succinate dehydrogenase exerted no control, but in the course of edema this enzymatic step became a controlling one: a transition from zero to a high control coefficient (0.5) was observed from the onset of intracellular edema for the threshold value of water/dry-weight tissue of 4.6.     

Modulation of cell calcium signals by mitochondria

It is now clearer and clearer that mitochondria play a role, and perhaps an active role, in cell calcium signalling. The fact that mitochondria can exhibit a Ca^2+>-induced Ca^2+> release (mCICR, Ichas et al. [37]) reinforces this concept and makes the mitochondria an essential element in the relay of Ca^2+> wave propagation. It must be emphasized that the modulation of cell Ca^2+> signals by mitochondria depends upon their energetic status, thus making mitochondria an essential link between energy metabolism and calcium signalling inside the cell.     

Theoretical studies on control of oxidative phosphorylation in muscle mitochondria at different energy demands and oxygen concentrations

The mathematical dynamic model of oxidative phosphorylation in muscle mitochondria developed previously was used to calculate the flux control coefficients of particular steps of this process in isolated mitochondria at different amounts of hexokinase and oxygen concentrations. The pattern of control was completely different under different conditions. For normoxic concentration, the main controlling steps in state 4, state 3.5 and state 3 were proton leak, ATP usage (hexokinase) and complex III, respectively. The pattern of control in state 4 was not changed at hypoxic oxygen concentration, while in state 3.5 and state 3 much of the control was shifted from other steps to cytochrome oxidase. The implications of the theoretical results obtained for the regulation of oxidative phosphorylation in intact muscle are discussed.     

Development and implementation of standardized respiratory chain spectrophotometric assays for clinical diagnosis

Diversity of respiratory chain spectrophotometric assays may lead to difficult comparison of results between centers. The French network of mitochondrial diseases diagnostic centers undertook comparison of the results obtained with different protocols in the French diagnostic centers. The diversity of protocols was shown to have striking consequences, which prompted the network to undertake standardization and optimization of the protocols with respect to clinical diagnosis, i.e. high velocity while maintaining linear kinetics relative to time and enzyme concentration. Assays were set up on animal tissues and verified on control human muscle and fibroblasts.Influence of homogenization buffer and narrow range of optimal concentration of phosphate, substrate and tissue were shown. Experimental data and proposed protocols have been posted on a free access website. Their subsequent use in several diagnostic centers has improved consistency for all assays.     

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).     

Modification of mitochondrial metabolism in fibroblasts from mice with a skeletal muscle mutation (muscular dysgenesis). Evidence of embryonic communication between myoblasts and fibroblasts

Muscle development during embryogenesis is a complex process involving many mechanisms. It requires a close communication among the different cellular types of the muscle, especially the fibroblasts and myoblasts. Indeed, any abnormality in one cell type might influence the differentiation of the other. Thus, any disturbance altering the metabolism of the myoblasts might lead to modifications in the fibroblasts. To study this phenomenon, we used the dysgenic mouse (mdg-"muscular dysgenesis") carrying a homozygous recessive lethal mutation expressed only in skeletal muscle cells. First, we found that fibroblasts isolated from such mutant muscle (and not from mutant skin tissue) and grown in culture exhibited an altered metabolism. Secondly, muscle fibroblasts showed a lower capacity for proliferation. We also observed that respiration and ATP synthesis of dysgenic muscle fibroblasts were deficient, while respiratory chain enzymatic activities were normal. Finally, intracellular [Ca2+] levels of dysgenic fibroblasts are 50% of those of normal fibroblasts. These results support the hypothesis that certain characteristics of fibroblasts are determined by the surrounding cellular environment during embryonic organogenesis, and that such modifications are stable when the fibroblasts are isolated in vitro. Since fibroblast differentiation was disrupted permanently, this suggests, in the case of myopathies, that the modified cells, surrounding the muscle tissue, could contribute to the muscle pathology. Synergistic activities of this type should be considered when studying the course of pathologies in different types of muscle diseases.     

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.     

The loneliness of the electrons in the bc1 complex

A stochastic approach based on Gillespie algorithm is particularly well adapted to describe the time course of the redox reactions that occur inside the respiratory chain complexes because they involve the motion of single electrons between individual unique redox centres of a given complex and not populations of electrons and redox centres as usually considered in ordinary differential equations. In this way we approach the molecular functioning of the bc(1) complex based on its known crystallographic structure and the rate constants of electron tunnelling derived from the Moser and Dutton phenomenological equation. The main features of our simulations are the dominant and robust emergence of a Q-cycle mechanism and the near absence of short-circuits in the normal functioning of the bc(1) complex. Thus, in our paper, the Mitchell Q-cycle no longer appears as an a priori hypothesis but arises out of the bc(1) complex structure and of the kinetic laws of redox reactions.     

An old paper revisited: "a mathematical model of carbohydrate energy metabolism. Interaction between glycolysis, the Krebs cycle and the H-transporting shuttles at varying ATPases load" by V.V. Dynnik, R. Heinrich and E.E. Sel'kov

We revisit an old Russian paper by V.V. Dynnik, R. Heinrich and E.E. Sel’kov (1980a, b) describing: “A mathematical model of carbohydrate energy metabolism. Interaction between glycolysis, the Krebs cycle and the H-transporting shuttles at varying ATPases load”. We analyse the model mathematically and calculate the control coefficients as a function of ATPase loads. We also evaluate the structure of the metabolic network in terms of elementary flux modes.We show how this model can respond to an ATPase load as well as to the glucose supply. We also show how this simple model can help in understanding the articulation between the major blocks of energetic metabolism, i.e. glycolysis, the Krebs cycle and the H-transporting shuttles.