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.     

Mathematical model for carbohydrate energy metabolism. Mechanism of the Pasteur effect

The simple mathematical model based on the stoichiometric structure of carbohydrate metabolism and the only allosteric regulation presented, i. e. activation of phosphofructokinase by AMP, was used to study the mechanism of the Pasteur effect, e. g. interrelationship of glycolysis, the Krebs cycle and H-transporting shuttles at varying rates of oxidative phosphorylation and ATPase load. It was shown that the mechanism of the Pasteur effect is based on the presence of two negative feed-back mechanisms in carbohydrate metabolism, namely by the level of ATP in glycolysis and by the level of mitochondrial NADH in the Krebs cycle and H-transporting shuttles. It was also shown that the value and sign of the Pasteur effect depend on the level of ATPase load. The role of this phenomenon in stabilization of ATP in the cell is discussed. The effects of changes in the allosteric properties of phosphofructokinase and low activity of H-transporting shuttles on the Pasteur effect was studied. It was shown that the low values of the pasteur effect in tumour tissues are mainly determined by an insufficient activity of oxidative phosphorylation.     

New functions for parts of the Krebs cycle in procyclic Trypanosoma brucei, a cycle not operating as a cycle

We investigated whether substrate availability influences the type of energy metabolism in procyclic Trypanosoma brucei. We show that absence of glycolytic substrates (glucose and glycerol) does not induce a shift from a fermentative metabolism to complete oxidation of substrates. We also show that glucose (and even glycolysis) is not essential for normal functioning and proliferation of pleomorphic procyclic T. brucei cells. Furthermore, absence of glucose did not result in increased degradation of amino acids. Variations in availability of glucose and glycerol did result, however, in adaptations in metabolism in such a way that the glycosome was always in redox balance. We argue that it is likely that, in procyclic cells, phosphoglycerate kinase is located not only in the cytosol, but also inside glycosomes, as otherwise an ATP deficit would occur in this organelle. We demonstrate that procyclic T. brucei uses parts of the Krebs cycle for purposes other than complete degradation of mitochondrial substrates. We suggest that citrate synthase plus pyruvate dehydrogenase and malate dehydrogenase are used to transport acetyl-CoA units from the mitochondrion to the cytosol for the biosynthesis of fatty acids, a process we show to occur in proliferating procyclic cells. The part of the Krebs cycle consisting of alpha-ketoglutarate dehydrogenase and succinyl-CoA synthetase was used for the degradation of proline and glutamate to succinate. We also demonstrate that the subsequent enzymes of the Krebs cycle, succinate dehydrogenase and fumarase, are most likely used for conversion of succinate into malate, which can then be used in gluconeogenesis.     

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.     

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.     

Modelling of the Coupling between Brain Electrical Activity and Metabolism

In order to make an attempt at grouping the various aspects of brain functional imaging (fMRI, MRS, EEG-MEG, ...) within a coherent frame, we implemented a model consisting of a system of differential equations, that includes: (1) sodium membrane transport, (2) Na/K ATPase, (3) neuronal energy metabolism (i.e. glycolysis, buffering effect of phosphocreatine, and mitochondrial respiration), (4) blood-brain barrier exchanges and (5) brain hemodynamics, all the processes which are involved in the activation of brain areas. We assumed that the correlation between brain activation and metabolism could be due to either changes in the concentrations of ATP and ADP following activation of Na/K ATPase that result from the changes in ion concentrations, or the involvement, in different phases of metabolism, of a second messenger such as calcium. In this article, we show how this type of model enables interpretation of MRS and fMRI published data that were obtained during prolonged stimulations.     

Metabolic remodeling: a pyruvate transport affair

Metabolic remodeling is a major determinant for many cell fate decisions, and a switch from respiration to aerobic glycolysis is generally considered as a hallmark of cancer cell transformation. Pyruvate is a key metabolite at the major junction of carbohydrate metabolism between cytosolic glycolysis and the mitochondrial Krebs cycle. In this issue of The EMBO Journal, Bender et al show that yeast cells regulate pyruvate uptake into mitochondria, and thus its metabolic fate, by expressing alternative pyruvate carrier complexes with different activities.     

The puzzle of the Krebs citric acid cycle: Assembling the pieces of chemically feasible reactions,and opportunism in the design of metabolic pathways during evolution

The evolutionary origin of the Krebs citric acid cycle has been for a long time a model case in the understanding of the origin and evolution of metabolic pathways: How can the emergence of such a complex pathway be explained? A number of speculative studies have been carried out that have reached the conclusion that the Krebs cycle evolved from pathways for amino acid biosynthesis, but many important questions remain open: Why and how did the full pathway emerge from there? Are other alternative routes for the same purpose possible? Are they better or worse? Have they had any opportunity to be developed in cellular metabolism evolution? We have analyzed the Krebs cycle as a problem of chemical design to oxidize acetate yielding reduction equivalents to the respiratory chain to make ATP. Our analysis demonstrates that although there are several different chemical solutions to this problem, the design of this metabolic pathway as it occurs in living cells is the best chemical solution: It has the least possible number of steps and it also has the greatest ATP yielding. Study of the evolutionary possibilities of each one-taking the available material to build new pathways-demonstrates that the emergence of the Krebs cycle has been a typical case of opportunism in molecular evolution. Our analysis proves, therefore, that the role of opportunism in evolution has converted a problem of several possible chemical solutions into asingle-solution problem, with the actual Krebs cycle demonstrated to be the best possible chemical design. Our results also allow us to derive the rules under which metabolic pathways emerged during the origin of life.     

Kinetic simulation of malate-aspartate and citrate-pyruvate shuttles in association with Krebs cycle

In the present work, we have kinetically simulated two mitochondrial shuttles, malate–aspartate shuttle (used for transferring reducing equivalents) and citrate–pyruvate shuttle (used for transferring carbon skeletons). However, the functions of these shuttles are not limited to the points mentioned above, and they can be used in different arrangements to meet different cellular requirements. Both the shuttles are intricately associated with Krebs cycle through the metabolites involved. The study of this system of shuttles and Krebs cycle explores the response of the system in different metabolic environments. Here, we have simulated these subsets individually and then combined them to study the interactions among them and to bring out the dynamics of these pathways in focus. Four antiports and a pyruvate pump were modelled along with the metabolic reactions on both sides of the inner mitochondrial membrane. Michaelis–Menten approach was extended for deriving rate equations of every component of the system. Kinetic simulation was carried out using ordinary differential equation solver in GNU Octave. It was observed that all the components attained steady state, sooner or later, depending on the system conditions. Progress curves and phase plots were plotted to understand the steady state behaviour of the metabolites involved. A comparative analysis between experimental and simulated data show fair agreement thus validating the usefulness and applicability of the model.     

Dual Functions of α-Ketoglutarate Dehydrogenase E2 in the Krebs Cycle and Mitochondrial DNA Inheritance in Trypanosoma brucei

The dihydrolipoyl succinyltransferase (E2) of the multisubunit α-ketoglutarate dehydrogenase complex (α-KD) is an essential Krebs cycle enzyme commonly found in the matrices of mitochondria. African trypanosomes developmentally regulate mitochondrial carbohydrate metabolism and lack a functional Krebs cycle in the bloodstream of mammals. We found that despite the absence of a functional α-KD, bloodstream form (BF) trypanosomes express α-KDE2, which localized to the mitochondrial matrix and inner membrane. Furthermore, α-KDE2 fractionated with the mitochondrial genome, the kinetoplast DNA (kDNA), in a complex with the flagellum. A role for α-KDE2 in kDNA maintenance was revealed in α-KDE2 RNA interference (RNAi) knockdowns. Following RNAi induction, bloodstream trypanosomes showed pronounced growth reduction and often failed to equally distribute kDNA to daughter cells, resulting in accumulation of cells devoid of kDNA (dyskinetoplastic) or containing two kinetoplasts. Dyskinetoplastic trypanosomes lacked mitochondrial membrane potential and contained mitochondria of substantially reduced volume. These results indicate that α-KDE2 is bifunctional, both as a metabolic enzyme and as a mitochondrial inheritance factor necessary for the distribution of kDNA networks to daughter cells at cytokinesis.     

Glucose and phosphate inhibit respiration and oxidative metabolism in cultured hamster eight-cell embryos: evidence for the "crabtree effect"

The development of hamster eight-cell embryos is inhibited by glucose in culture medium containing inorganic phosphate (Pi). This is hypothetically attributed to the "Crabtree effect," in which enhanced glycolysis inhibits respiratory activity and oxidative metabolism. To examine this hypothesis, oxygen consumption of hamster eight-cell embryos was measured using a microelectrode. A two- to three-fold decrease in oxygen consumption was observed in embryos cultured with glucose and Pi. Oxidizable substrates and intermediates of the Krebs cycle supported embryo development only in the absence of glucose and Pi; Krebs cycle inhibitors (fluoroacetate and arsenite) arrested embryo development. Under anaerobic conditions, pyruvate and lactate did not support embryo development. Inhibition of both respiration and oxidative activity in cultured hamster embryos by glucose and Pi is consistent with the existence of a Crabtree effect and indicates that the metabolic properties of preimplantation embryonic cells differ markedly from those of most somatic cells and resemble some cancer cells.     

Proteomic analysis of day-night variations in protein levels in the rat pineal gland

The pineal gland secretes the hormone melatonin. This secretion exhibits a circadian rhythm with a zenith during night and a nadir during day. We have performed proteome analysis of the superficial pineal gland in rats during daytime and nighttime. The proteins were extracted and subjected to 2-DE. Of 1747 protein spots revealed by electrophoresis, densitometric analysis showed the up-regulation of 25 proteins during nighttime and of 35 proteins during daytime. Thirty-seven of the proteins were identified by MALDI-TOF MS. The proteins up-regulated during the night are involved in the Krebs cycle, energy transduction, calcium binding, and intracellular transport. During the daytime, enzymes involved in glycolysis, electron transport, and also the Krebs cycle were up-regulated as well as proteins taking part in RNA binding and RNA processing. Our data show a prominent day-night variation of the protein levels in the rat pineal gland. Some proteins are up-regulated during the night concomitant with the melatonin secretion of the gland. Other proteins are up-regulated during the day indicating a pineal metabolism not related to the melatonin synthesis.     

Pyruvate-converting activity in the spores of the microsporidian genus Paranosema (Antonospora)

Microsporidia, a large group of fungi-related protozoa with an obligate intracellular lifestyle, are characterized by a drastically reduced cell machinery and a unique metabolism. These parasites possess genes encoding glycolysis components and glycerol-phosphate shuttle, but lack typical mitochondria, Krebs cycle, respiratory chain and pyruvate-converting enzymes, except for two subunits of the E(1) enzyme of the pyruvate dehydrogenase complex. This study demonstrates that in spite of the above, destroyed spores of the microsporidian Paranosema (Antonospora) grylli and P. locustae deplete pyruvate content in the incubation medium. This activity is sensitive to heat, proportionally distributed between the soluble and the insoluble fractions and does not depend on additional ions or cofactors.     

Biochemical characterization of an E. coli cell division factor FtsE shows ATPase cycles similar to the NBDs of ABC-transporters

The peptidoglycan (PG) layer is an intricate and dynamic component of the bacterial cell wall, which requires a constant balance between its synthesis and hydrolysis. FtsEX complex present on the inner membrane is shown to transduce signals to induce PG hydrolysis. FtsE has sequence similarity with the nucleotide-binding domains (NBDs) of ABC transporters. The NBDs in most of the ABC transporters couple ATP hydrolysis to transport molecules inside or outside the cell. Also, this reaction cycle is driven by the dimerization of NBDs. Though extensive studies have been carried out on the Escherchia coli FtsEX complex, it remains elusive regarding how FtsEX complex helps in signal transduction or transportation of molecules. Also, very little is known about the biochemical properties and ATPase activities of FtsE. Because of its strong interaction with the membrane-bound protein FtsX, FtsE stays insoluble upon overexpression in E. coli, and thus, most studies on E. coli FtsE (FtsE_Ec) in the past have used refolded FtsE. Here in the present paper, for the first time, we report the soluble expression, purification, and biochemical characterization of FtsE from E. coli. The purified soluble FtsE exhibits high thermal stability, exhibits ATPase activity and has more than one ATP-binding site. We have also demonstrated a direct interaction between FtsE and the cytoplasmic loop of FtsX. Together, our findings suggest that during bacterial division, the ATPase cycle of FtsE and its interaction with the FtsX cytoplasmic loop may help to regulate the PG hydrolysis at the mid cell.     

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.     

A computational model for the identification of biochemical pathways in the krebs cycle.

We have applied an algorithmic methodology which provably decomposes any complex network into a complete family of principal subcircuits to study the minimal circuits that describe the Krebs cycle. Every operational behavior that the network is capable of exhibiting can be represented by some combination of these principal subcircuits and this computational decomposition is linearly efficient. We have developed a computational model that can be applied to biochemical reaction systems which accurately renders pathways of such reactions via directed hypergraphs (Petri nets). We have applied the model to the citric acid cycle (Krebs cycle). The Krebs cycle, which oxidizes the acetyl group of acetyl CoA to CO(2) and reduces NAD and FAD to NADH and FADH(2), is a complex interacting set of nine subreaction networks. The Krebs cycle was selected because of its familiarity to the biological community and because it exhibits enough complexity to be interesting in order to introduce this novel analytic approach. This study validates the algorithmic methodology for the identification of significant biochemical signaling subcircuits, based solely upon the mathematical model and not upon prior biological knowledge. The utility of the algebraic-combinatorial model for identifying the complete set of biochemical subcircuits as a data set is demonstrated for this important metabolic process.