Mathematical model of carbohydrate energy metabolism. Interaction between glycolysis, the Krebs cycle and the H-transporting shuttles at varying ATPase load

A simple mathematical model for carbohydrate energy metabolism based on the stoichiometic structure of glycolysis, the Krebs cycle and oxidative phosphorylation is proposed. The only allosteric regulation involved in the model is phosphofructokinase activation by AMP. Simple as it is, the model can explain the following properties of carbohydrate metabolism: a drastic rise of the rate of glucose consumption during transition to a higher level of ATPase load; stabilization of ATP and an increase of the steady state rates of glycolysis and oxidation of cytoplasmic NADH by the H-transporting shuttles and of pyruvate in the Krebs cycle with increasing rate of the ATPase load; activation of glycolysis and a decrease of the rate of oxidative phosphorylation following an inhibition of the H-transporting shuttles. The mechanisms of the coordinated changes in the steady state rates of glycolysis, the H-transporting shuttles and the Krebs cycle at varying ATPase load in the cell are discussed.     

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.     

Mechanisms of the regulation of muscle energy metabolism on oxidation of glucose and fatty acids. A mathematical model

A mathematical model was used to study the role of various allosteric regulatory mechanisms in the oxidation of glucose and fatty acids by muscle energy metabolism. A large number of such mechanisms were shown to be involved in simultaneous oxidation of both substrates: glycolysis is regulated by the ATP/ADP ratio at the phosphofructokinase (PFK) step; the control over pyruvate dehydrogenase is exercised by the NADHm/NADm+ and CoAsAc/CoAsH ratios as well as by the level of pyruvate; the Krebs cycle is regulated by oxaloacetate and citrate concentrations in the citrate synthase reaction and by the ATP/ADP and NADHm/NADm+ ratios in the isocitrate dehydrogenase reaction. The inhibition of PFK and pyruvate dehydrogenase by excess of CoAsAcyl as well as the inhibition of PFK by citrate are additional equivalent regulatory mechanisms. When glucose alone is oxidized, the levels of citrate, CoAsAcyl, NADHm and CoAsAc decrease drastically within the whole range of physiological ATPase loads; the only regulating factors that remain efficient are the ATP/ADP ratio in glycolysis, the level of pyruvate at the pyruvate dehydrogenase step, the ATP/ADP ratio and the levels of CoAsAc, oxaloacetate and isocitrate in the Krebs cycle.     

History of the Pasteur effect and its pathobiology

Summary Long before the mechanism of fermentation was understood,Pasteur discovered an important regulatory phenomenon of carbohydrate metabolism. He observed that yeast consumes more sugar anaerobically than aerobically. This so-called Pasteur effect has been subject of many controversies and an analysis of the development of the concepts has been presented. Among the key errors made in the early evaluations was to emphasize the control of end product formation rather than of hexose utilization.The Pasteur phenomenon as understood at present is a complex coordinated control mechanism which operates at several levels. The basic phenomenon is a competition between glycolysis and oxidative phosphorylation for the available ADP and inorganic phosphate. Superimposed are allosteric controls of hexokinase (glucose-6-phosphate) and of phosphofructokinase (ATP). However, in some cells glucose-6-phosphate is not an inhibitor of hexokinase and ATP levels do not change significantly during transition from aerobic to anaerobic conditions. It is therefore clear that other secondary allosteric effectors such as inorganic phosphate play a significant role. The major conclusion is that there are multiple and different control mechanisms participating in the Pasteur effect in different cells.A loss of control in tumor cells gives rise to a high aerobic glycolysis. The history and possible significance of this in malignancy is described.     

A mathematical model of the pyruvate oxidation in liver mitochondria. 1. Regulation of the Krebs cycle by adenine and pyridine nucleotides]

A mathematical model is proposed to describe the behavior of the pyruvate metabolic reactions, Krebs cycle and oxidative phosphorylation over a wide range of changes in the pyruvate influx rate and the activities of ATPase and NADH-reoxidating dehydrogenase. The role of adenine and pyridine nucleotides in various allosteric regulations of the Krebs cycle enzymes is discussed. The accumulation of ATP and NADH has been shown to proceed in definite succession, which makes the allosteric regulation of the Krebs cycle enzymes successive too. First "works" the inhibition by ATP, then by NADH. It has been shown that the properties of the model are in qualitative agreement with the experimental data (Garber A., Hanson R. [1]) on pyruvate oxidation by mitochondria from guinea pig liver, when allosteric regulation of isocitrate dehydrogenase by adenine nucleotides is taken into account.     

Analysis of allosteric mechanisms of suppressing parasitic recirculation in the futile cycle fructose-6-P--fructose-1,6-P2

The uncontrollable substrate recirculation in the central futile cycle (FC) in the carbohydrate energy metabolism fructose-6-P (F6P) in equilibrium or formed from fructose-1,6-P2 (FBP), makes it impossible to maintain a stable level of ATP because of its wasteful expenditure in the cycle reactions which are equivalent to the ATPase reaction and also because of the diversion of FBP from glycolytic phosphorylation of ADP. It follows from the analysis of a mathematical model of the carbohydrate energy metabolism that the allosteric inhibition of fructosebisphosphatase (FBPase) by FBP and AMP leads to suppression of the recirculation in the FC and recovery of the ability of glycolysis to stabilize the level of ATP with high accuracy. The allosteric activation of phosphofrucktokinase (PFK) by AMP couples the expenditure of ATP and F6P in the FC with ATP consumption by a load.     

Metabolism in preimplantation mouse embryos

The ability of preimplantation mouse embryos to utilize glucose oxidatively is controlled, in part at least, at the level of glycolysis. Various experimental observations are reviewed that indicate the regulatory mechanism in delayed implanting blastocysts involves the classic negative allosteric feedback of high levels of ATP on phosphofructokinase while the situation in 2-cell embryos appears to be more complicated. That is, in addition to the usual negative effect of ATP and citrate on phosphofructokinase, there appears to be a modification of hexokinase that prevents phosphorylation of adequate amounts of glucose and results in low levels of fructose-6-phosphate at the 2-cell stage and consequently there is a failure to release the inhibition of phosphofructokinase even if ATP and citrate levels decrease. Although both types of embryos have limited glycolytic activity, they do have adequate capacity for citric acid cycle activity and oxidative phosphorylation, and are able to maintain a high ATP : ADP. It is argued, therefore, that the reduced levels of macromolecular synthesis characteristic of 2-cell and delayed implanting blastocysts are not due to restricted energy substrates or regulatory controls on glycolysis and a subsequent low energy state. On the contrary, it seems that the reduction in oxidative utilization of glucose in these situations is a result of diminished energy demand because of the low level of synthetic activity. The potential significance of this relationship between energy production and utilization in terms of potential regulatory mechanisms in preimplantation embryos is discussed.     

From Pasteur to Mitchell: a hundred years of bioenergetics

The discovery in 1861 by Louis Pasteur that more yeast is formed aerobically than anaerobically per gram of glucose was the first clue to the difference in efficiency of glycolysis and oxidative phosphorylation. During the first half of the 20th century the pathway of glycolysis was untraveled. Individual enzymes and cofactors were isolated and characterized. A reconstituted system of all enzymes and cofactors catalyzed steady-state glycolysis, provided an appropriate ATPase was added. The need for an ATPase, clearly demonstrated in 1945 by Otto Meyerhof, remains an important aspect of glycolysis that has been sorely neglected by textbooks. The coupling of oxidation and phosphorylation and the formation of the high-energy intermediate 1,3-diphosphoglycerate, discovered by Otto Warburg, are the key reactions of glycolysis. A high-energy intermediate formed during this process was identified as a thiolester. Early concepts of the mechanism of oxidative phosphorylation based on this model led to some frustrating and confusing years of search for high-energy intermediates. Important contributions from the laboratories of Boyer, Cohn, Chance, Green, Lardy, and Lehninger elucidated the properties of the mitochondrial process. Then Peter Mitchell proposed in 1961, 100 years after the publication by Pasteur, that the "high-energy intermediate" is an electrochemical proton gradient generated by the electron transport chain and utilized by a proton turbine (the mitochondrial ATPase complex) to generate ATP. This concept is now widely accepted. Several problems remain to be solved. How are the protons translocated during electron transport? How many protons per site? What is the mechanism of ATP generation during proton flux via the mitochondrial ATPase?     

Effect of Ca ions on the transmembrane electric potential, synthesis and hydrolysis of ATP in brain mitochondria

The transmembrane potential (delta psi) of rabbit brain mitochondria was measured with the fluorescent dye dis--C2--5. During oxidative phosphorylation a fall in delta psi in the order of 20% was observed. In the presence of inhibitors of ATP synthesis, there was a good correlation between the fall in delta psi and the ADP-stimulated increase in respiration rate. The influence of endogenous calcium on the energetic metabolism of mitochondria was studied by measuring the changes of delta psi. An amount of 12 nmol Ca2+/mg protein cause half-inhibition of the ATP synthesis rate; 50 nmol/mg completely inhibits oxidative phosphorylation. The effect of the Ca2+ load on the ATPase activity of intact mitochondria was studied. It was found that endogenous calcium inhibits in a similar degree synthesis and hydrolysis of ATP. It was shown that both Ca ATP and Mg ATP can serve as a substrate for the mitochondrial ATPase.     

Ratio between carbohydrate and lipid metabolism in muscle cell energy metabolism during ATPase loading. Mathematical model

A mathematical model is proposed to describe the interaction between glycolysis, the Krebs cycle and 3-oxidation (beta OX). The model incorporates the activations of phosphofructokinase by AMP and of isocitrate dehydrogenase by ADP as well as the inhibitions of citrate synthase by citrate, of acyl CoA synthase by excess CoAsAcyl, of pyruvate dehydrogenase (PDH) and the beta OX helix by the products CoAsAc and NADH. These regulations have been shown to provide consecutive triggering of the fatty acid and glucose oxidation systems with an increase in the ATPase load, the beta OX of fatty acids being a major source of energy at small loads. The steady state rates of glycolysis and PDH-reaction begin to increase at larger loads when the rate of beta OX is close to its maximum value. At maximum ATPase loads, the glucose oxidation accounts for more than 80% of the total energy production. Under limited fatty acid supply, the transfer to glucose oxidation gives rise to a region of the ATPase loads, where in the steady state levels of NADH and CoAsAc increase with load.     

The effect of cyclic GMP on phosphofructokinase from rat tissues.

In view of the recently proposed hypothesis of biologic regulation through opposing influences of cyclic AMP and cyclic GMP, and since cyclic AMP is a well-known allosteric activator of phosphofructokinase (ATP:D-fructose-6-phosphate 1-phosphotransferase, EC 2.7.1.11), the effect of cyclic GMP on the activity of this enzyme from several rat tissues was investigated. It was found that cyclic GMP exerted an inhibitory effect on the activity of rat heart and skeletal muscle phosphofructokinase. This effect was most pronounced under conditions in which the enzyme was partially inhibited by ATP or by citrate. Cyclic GMP also antagonized the deinhibitory action of cyclic AMP and other allosteric activators, such as glucose 1,6-bisphosphate or AMP, on the ATP or citrate-inhibited heart or muscle phosphofructokinase. In contrast to the heart and skeletal muscle phosphofructokinase, the adipose-tissue enzyme was not affected by cyclic GMP to any significant degree. The antagonistic action of cyclic GMP to the activation of heart-phosphofructokinase, may suggest a mechanism by which the activity of phosphofructokinase is synchronized with the activity of glycogen phosphorylase, as a result of acetylcholine action in heart, to achieve a decrease in total glycogenolysis and glycolysis.     

The metabolic requirements for transcellular movement and secretion of collagen.

Cultures of chick tendon fibroblasts were capable of normal ATP production and protein synthetic activity even though the normally high rate of glycolysis was markedly reduced by substitution of pyruvate for glucose. Iodoacetate and 2-deoxyglucose reduced ATP levels and protein synthesis even in the presence of pyruvate. Under these conditions, both inhibitors were shown to have effects on the energy metabolism of cells which were apparently unrelated to an inhibition of glycolysis. Selective inhibition of either glycolysis, by incubation in glucose-free medium, or of oxidative phosphorylation, by incubation with an uncoupler, was shown to have little effect on cellular ATP levels or intracellular transport and secretion of collagen. However, inhibition of both glycolysis and oxidative phosphorylation resulted in decreased cellular ATP levels and an inhibition of collagen secretion. This effect was not due to a requirement for continued protein synthesis, since inhibition of protein synthesis with cycloheximide or puromycin had little effect on collagen secretion. The ATP requirement for intracellular transport and secretion is discussed in relation to the secretory pathway for collagen.     

Energy metabolism in tumor cells

In early studies on energy metabolism of tumor cells, it was proposed that the enhanced glycolysis was induced by a decreased oxidative phosphorylation. Since then it has been indiscriminately applied to all types of tumor cells that the ATP supply is mainly or only provided by glycolysis, without an appropriate experimental evaluation. In this review, the different genetic and biochemical mechanisms by which tumor cells achieve an enhanced glycolytic flux are analyzed. Furthermore, the proposed mechanisms that arguably lead to a decreased oxidative phosphorylation in tumor cells are discussed. As the O(2) concentration in hypoxic regions of tumors seems not to be limiting for the functioning of oxidative phosphorylation, this pathway is re-evaluated regarding oxidizable substrate utilization and its contribution to ATP supply versus glycolysis. In the tumor cell lines where the oxidative metabolism prevails over the glycolytic metabolism for ATP supply, the flux control distribution of both pathways is described. The effect of glycolytic and mitochondrial drugs on tumor energy metabolism and cellular proliferation is described and discussed. Similarly, the energy metabolic changes associated with inherent and acquired resistance to radiotherapy and chemotherapy of tumor cells, and those determined by positron emission tomography, are revised. It is proposed that energy metabolism may be an alternative therapeutic target for both hypoxic (glycolytic) and oxidative tumors.     

Effect of heliomycin on the respiration and oxidative phosphorylation of the liver mitochondria of the rat

The effect of heliomycin and known uncouplers of oxidative phosphorylation on respiration and oxidative phosphorylation was studied comparatively. Heliomycin, as well as 2,4-dinitrophenol, valinomycin and gramicidin S inhibited the mitochondrial synthesis of ATP. This process was inhibited completely by heliomycin at a concentration of 1.5 x 10(-5) M. The synthesis of inorganic pyrophosphate, the other macroergic compound, was also inhibited by heliomycin, ATPase and pyrophosphatase of uncoupled mitochondria being not inhibited by the antibiotic. Like 2,4-dinitrophenol, heliomycin stimulated the synthesis of ATPase and respiration in intact mitochondria. Probably, heliomycin inhibited the synthesis of ATP and pyrophosphate by uncoupling the processes of respiration and oxidative phosphorylation. It was shown earlier that heliomycin, a specific inhibitor of bacterial RNA synthesis, also affected energy metabolism of bacterial cells by inhibiting the synthesis of ATP and active transport.     

The Pasteur effect and catabolite repression in an oxidative yeast,Kluyveromyces lactis

The presence of the Pasteur effect in Kluyveromyces lactis grown in glucose was shown by azide-stimulated glucose fermentation. Extracts from these cells contained ATP-sensitive phosphofructokinase activity. Cells grown on succinate oxidized glucose slowly at first without azide-stimulated rates of fermentation. Phosphofructokinase in these cells was ATP-insensitive. The activity of NAD+-isocitrate dehydrogenase in cell extracts did not require AMP activation. These results suggested the presence of a Pasteur effect in glucose-grown but not in succinate-grown K. lactis, mediated by (a) ATP inhibition of phosphofructokinase (b) possibly via feedback control of glucose transport, but not by AMP activation of isocitrate dehydrogenase. Azide inhibition of the Pasteur effect during growth of the cells did not lead to catabolite repression of respiratory activity. The results therefore suggest that the Pasteur effect does not inhibit the development of a Crabtree effect in oxidative yeasts.     

Regulation of rat liver phosphofructokinase by glucagon-induced phosphorylation

In perfused rat liver, the effects of various hormones on the stimulation of phosphorylation and allosteric properties of purified phosphorfructokinase were investigated. Rat livers were perfused with [³²P]phosphate followed with various hormones or cyclicAMP, and ³²P-labeled phosphofructokinase was isolated. ³²P incorporation into the enzyme and enzyme inhibition by ATP or citrate were determined. Only glucagon increased the ³²P incorporation into phosphofructokinase and this increase was approximately threefold. The cyclicAMP level was increased simultaneously approximately four- to fivefold compared to the control perfused liver. Similar results were obtained by perfusing the liver with cyclicAMP (0.1 mm). The phosphorylated phosphofructokinase showed a decrease in the K_i values for ATP (from 0.4 to 0.2 mm) and citrate (from 2 to 0.6 mm). Neither epinephrine nor insulin affected the extent of phosphorylation or the allosteric properties of the enzyme. The half-maximal concentration of glucagon required for phosphorylation of phosphofructokinase and modification of its allosteric properties was approximately 6 × 10^?11m. It is concluded that glucagon increases the inhibition of liver phosphofructokinase by ATP and citrate through phosphorylation of the enzyme involving a β-receptor-mediated cyclicAMP-dependent mechanism.     

Regulation of glycolysis in the mouse blastocyst during delayed implantation

The rate of oxidation of glucose is reduced in mouse embryos in the prolonged free living phase associated with delayed implantation and increases when the embryos are reactivated by estrogen. To determine how these changes in metabolism are regulated, several aspects of glucose metabolism were evaluated in dormant and reactivated blastocysts: 1) Embryos were exposed to 14C-pyruvate in vitro and evolved 14CO2 was measured. It was found that the rate of production of CO2 was equal in the two types of blastocysts, suggesting that aerobic pathways are fully functional during delayed implantation. 2) Production of lactate in the presence of O2 was measured and a decrease of 30% was found in delayed implanting embryos, suggesting that the overall regulatory mechanism for glucose metabolism resides in the glycolytic portion of the pathway. 3) Capacity for uptake and phosphorylation of glucose was evaluated using 3H-2-deoxyglucose and was found to be equal in the two types of embryos. 4) Total amounts of the rate-controlling enzymes for glycolysis (i.e., hexokinase and phosphofructokinase) in lysates of delayed and reactivated embryos were found to be equal, indicating that amounts of these enzymes are not limiting in delayed implantation. 5) Lactate production, measured under anaerobic conditions, was found to be equal, demonstrating that it is not the capacity for glycolysis but a difference in the degree of allosteric inhibition that is responsible for reduced glucose oxidation in delayed implantation. 6) Levels of ATP, ADP, and hexose-6-phosphates were found to be consistent with allosteric inhibition of the glycolytic pathway at phosphofructokinase during delay and a release of this inhibition with reactivation.(ABSTRACT TRUNCATED AT 250 WORDS)     

Kinetic Model of Mitochondrial Krebs Cycle: Unraveling the Mechanism of Salicylate Hepatotoxic Effects

This paper studies the effect of salicylate on the energy metabolism of mitochondria using in silico simulations. A kinetic model of the mitochondrial Krebs cycle is constructed using information on the individual enzymes. Model parameters for the rate equations are estimated using in vitro experimental data from the literature. Enzyme concentrations are determined from data on respiration in mitochondrial suspensions containing glutamate and malate. It is shown that inhibition in succinate dehydrogenase and α-ketoglutarate dehydrogenase by salicylate contributes substantially to the cumulative inhibition of the Krebs cycle by salicylates. Uncoupling of oxidative phosphorylation has little effect and coenzyme A consumption in salicylates transformation processes has an insignificant effect on the rate of substrate oxidation in the Krebs cycle. It is found that the salicylate-inhibited Krebs cycle flux can be increased by flux redirection through addition of external glutamate and malate, and depletion in external α-ketoglutarate and glycine concentrations.     

Effects of insulin and work on fructose 2,6-bisphosphate content and phosphofructokinase activity in perfused rat hearts

The effects of insulin and increased cardiac work on glycolytic rate, metabolite content, and fructose 2,6-bisphosphate (Fru-2,6-P2) content were studied in isolated perfused rat hearts. Steady-state rates of glycolysis increased 5-fold with the addition of insulin to the perfusate or by increasing cardiac pressure-volume work and correlated well in most conditions with changes in substrate concentration (Fru-6-P) and with concentration of the activator, Fru-2,6-P2. There was no correlation with changes in other well known regulators including citrate, ATP, AMP, Pi, or cytosolic phosphorylation potential. Using phosphofructokinase purified from hearts perfused under identical conditions, allosteric kinetic experiments were performed using the metabolite and effector concentrations determined from in vivo experiments. Reaction rates for phosphofructokinase calculated in vitro agreed well with the glycolytic rates measured in vivo and correlated with changes in Fru-6-P but not with other effectors. However, higher Fru-2,6-P2 levels were more effective in maintaining phosphofructokinase activity at high ATP and citrate levels. Kinetic experiments did not indicate a covalent modification of phosphofructokinase. These data indicate that control of cardiac phosphofructokinase and glycolysis may be accomplished by changes in the availability of substrate, Fru-6-P, and activator, Fru-2,6-P2, rather than by citrate, adenine nucleotides, or cytosolic phosphorylation potential as previously suggested.