A method for accounting for maintenance costs in flux balance analysis improves the prediction of plant cell metabolic phenotypes under stress conditions

Flux balance models of metabolism generally utilize synthesis of biomass as the main determinant of intracellular fluxes. However, the biomass constraint alone is not sufficient to predict realistic fluxes in central heterotrophic metabolism of plant cells because of the major demand on the energy budget due to transport costs and cell maintenance. This major limitation can be addressed by incorporating transport steps into the metabolic model and by implementing a procedure that uses Pareto optimality analysis to explore the trade‐off between ATP and NADPH production for maintenance. This leads to a method for predicting cell maintenance costs on the basis of the measured flux ratio between the oxidative steps of the oxidative pentose phosphate pathway and glycolysis. We show that accounting for transport and maintenance costs substantially improves the accuracy of fluxes predicted from a flux balance model of heterotrophic Arabidopsis cells in culture, irrespective of the objective function used in the analysis. Moreover, when the new method was applied to cells under control, elevated temperature and hyper‐osmotic conditions, only elevated temperature led to a substantial increase in cell maintenance costs. It is concluded that the hyper‐osmotic conditions tested did not impose a metabolic stress, in as much as the metabolic network is not forced to devote more resources to cell maintenance.     

Cardiac ATP-sensitive K+ channels. Evidence for preferential regulation by glycolysis

The ability of glycolysis, oxidative phosphorylation, the creatine kinase system, and exogenous ATP to suppress ATP-sensitive K+ channels and prevent cell shortening were compared in patch-clamped single guinea pig ventricular myocytes. In cell-attached patches on myocytes permeabilized at one end with saponin, ATP-sensitive K+ channels were activated by removing ATP from the bath, and could be closed equally well by exogenous ATP or substrates for endogenous ATP production by glycolysis (with the mitochondrial inhibitor FCCP present), mitochondrial oxidative phosphorylation, or the creatine kinase system. In the presence of an exogenous ATP-consuming system, however, glycolytic substrates (with FCCP present) were superior to substrates for either oxidative phosphorylation or the creatine kinase system at suppressing ATP-sensitive K+ channels. All three groups of substrates were equally effective at preventing cell shortening. In 6 of 38 excised inside-out membrane patches, ATP-sensitive K+ channels activated by removing ATP from the bath were suppressed by a complete set of substrates for the ATP-producing steps of glycolysis but not by individual glycolytic substrates, which is consistent with the presence of key glycolytic enzymes located near the channels in these patches. Under whole-cell voltage-clamp conditions, inclusion of 15 mM ATP in the patch electrode solution dialyzing the interior of the cell did not prevent activation of the ATP-sensitive K+ current under control conditions or during exposure to complete metabolic inhibition. In isolated arterially perfused rabbit interventricular septa, selective inhibition of glycolysis caused an immediate increase in 42K+ efflux rate, which was prevented by 100 microM glyburide, a known blocker of ATP-sensitive K+ channels. These observations suggest that key glycolytic enzymes are associated with cardiac. ATP-sensitive K+ channels and under conditions in which intracellular competition for ATP is high (e.g., in beating heart) that act as a preferential source of ATP for these channels.     

The connexion between active cation transport and metabolism in erythrocytes

1. A study has been made of the dependence on the concentrations of internal Na(+) and external K(+) of lactate and phosphate production in human erythrocytes. 2. Lactate production was stimulated by Na(+) and K(+) but only when they were internal and external respectively. The stimulation was counteracted by ouabain. The production of phosphate was affected in the same way. 3. There is a quantitative correlation between these effects and those previously found for cation movements and the membrane adenosine triphosphatase. 4. It is concluded that the rate of energy production in glycolysis is partly controlled by the magnitude of active transport; the extent of this regulation is shown to vary from 25 to 75% of a basal rate that is independent of active transport. 5. The activity of the membrane adenosine triphosphatase was also compared with rates of Na(+) and K(+) transport. The latter were varied by altering the concentrations of internal Na(+) and external K(+), and by inhibiting with ouabain. 6. A threefold variation of active transport rate was accompanied by a parallel change in the membrane adenosine-triphosphatase activity. The results show a constant stoicheiometry for the number of ions moved/mol. of ATP hydrolysed, independent of the electrochemical gradient against which the ions were moved. 7. Calculations show that the amount of ATP hydrolysed would provide enough energy for the osmotic work. The results are discussed in relation to possible mechanisms for active transport.     

Cellular volume homeostasis

All cells face constant challenges to their volume either through changes in intracellular solute content or extracellular osmolality. Cells respond to volume perturbations by activating membrane transport and/or metabolic processes that result in net solute loss or gain and return of cell volume to its normal resting state. This paper provides a brief overview of fundamental concepts of osmotic water flow across cell membranes, mechanisms of cell volume perturbation, the role of inorganic ions and organic osmolytes in cell volume regulation and the signaling mechanisms that regulate the activity of cell volume-sensitive transport and metabolic pathways.     

Electrically silent cotransport of Na+, K+ and Cl− in ehrlich cells

A cotransport system for Na⁺, K⁺ and Cl^? in Ehrlich cells is described. It is insensitive towards ouabain but specifically inhibited by furosemide and other ‘high ceiling’ diuretics at concentrations which do not affect other pathways of the ions concerned. As the furosemide-sensitive fluxes of these ions are not affected by changes in membrane potential, and as their complete inhibition by furosemide does not appreciably alter the membrane potential, they appear to be electrically silent. Application of the pulse-response methods in terms of irreversible thermodynamics reveals tight coupling between the furosemide-sensitive flows of Na⁺, K⁺ and Cl^? ($\text{q}$ close to unity for all three combinations) at a stoichiometry of 1 : 1 : 2. The site for each of the ions appears to be rather specific: K⁺ can be replaced by Rb⁺ but not by other cations tested whereas Cl^? can be poorly replaced by Br^? but not by NO₃^?, in contradistinction to the Cl^?-OH^? exchange system. The cotransport system appears to function in cell volume regulation as it tends to make the cell swell, thus counteracting the shrinking effect of the ouabain-sensitive (Na⁺, K⁺) pump.The experiments presented could not clarify whether the cotransport process is a primary or secondary active one; while incongruence between transport and conjugated driving force seems to indicate primary active transport, it is very unlikely that hydrolysis of ATP supplies energy for the transport process, since there is no stimulation of ATP turnover observable under operation of the cotransport system.     

Complex metabolic network of 1,3-propanediol transport mechanisms and its system identification via biological robustness

The bioconversion of glycerol to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae (K. pneumoniae) can be characterized by an intricate metabolic network of interactions among biochemical fluxes, metabolic compounds, key enzymes and genetic regulation. Since there are some uncertain factors in the fermentation, especially the transport mechanisms of 1,3-PD across cell membrane, the metabolic network contains multiple possible metabolic systems. Considering the genetic regulation of dha regulon and inhibition of 3-hydroxypropionaldehyde to the growth of cells, we establish a 14-dimensional nonlinear hybrid dynamical system aiming to determine the most possible metabolic system and the corresponding optimal parameter. The existence, uniqueness and continuity of solutions are discussed. Taking the robustness index of the intracellular substances together as a performance index, a system identification model is proposed, in which 1,395 continuous variables and 90 discrete variables are involved. The identification problem is decomposed into two subproblems and a parallel particle swarm optimization procedure is constructed to solve them. Numerical results show that it is most possible that 1,3-PD passes the cell membrane by active transport coupled with passive diffusion.     

Effects of dinitrophenol and oligomycin on the coupling between anaerobic metabolism and anaerobic sodium transport by the isolated turtle bladder

Dinitrophenol (1 x 10^-5 M) has been found to inhibit anaerobic sodium transport by the isolated urinary bladder of the fresh water turtle. Concurrently, anaerobic glycolysis was stimulated markedly. However, tissue ATP levels diminished only modestly, remaining at approximately 75% of values observed under anaerobic conditions without DNP. The utilization of glucose (from endogenous glycogen) corresponded closely to that predicted from the molar quantities of lactate formed. Thus the glycolytic pathway was completed in the presence of DNP and if ATP were synthesized normally during glycolysis, synthesis should have been increased. On the other hand, the decrease in Na transport should have decreased ATP utilization. Oligomycin did not block sodium transport either aerobically or anaerobically, but ATP concentrations did decrease. When anaerobic glycolysis was blocked by iodoacetate, pyruvate did not sustain sodium transport thus suggesting that no electron acceptors were available in the system. Two explanations are entertained for the anaerobic effect of DNP: (a) Stimulation by DNP of plasma membrane as well as mitochondrial ATPase activity; (b) inhibition of a high energy intermediate derived from glycolytic ATP or from glycolysis per se. The arguments relevant to each possibility are presented in the text. Although definitive resolution is not possible, we believe that the data favor the hypothesis that there was a high energy intermediate in the anaerobic system and that this intermediate, rather than ATP, served as the immediate source of energy for the sodium pump.     

Modulation of 2,3-diphosphoglycerate 31P-NMR resonance positions by red cell membrane shape.

Na+ transport in the red cells of the dog is dependent on cell volume, a 20% change in cell volume leading to a 25-fold increase in apparent Na+ flux; the effect is dependent upon metabolic energy. We have found that swelling and shrinking dog red cells causes a shift in the 31P-NMR peak of 2,3-diphosphoglycerate, which is present in dog red cells at 5.5 mM. Control experiments indicate that the 2,3-diphosphoglycerate resonance peak shifts may not be attributed to: interaction with hemoglobin, changes in cell pH, ionic strength, diamagnetic susceptibility or small changes in the Mg2+/2,3-diphosphoglycerate ratio. Experiments with chlorpromazine and pentanol which alter red cell membrane area by a mechanism different from osmotic swelling suggest that 2,3-diphosphoglycerate interacts with a binding site in the cell that is dependent upon the physical condition of the dog red cell membrane.     

The glycolytic enzyme, phosphoglycerate mutase, has critical roles in stomatal movement, vegetative growth, and pollen production in Arabidopsis thaliana

Stomatal movements require massive changes in guard cell osmotic content, and both stomatal opening and stomatal closure have been shown to be energy-requiring processes. A possible role for glycolysis in contributing to the energetic, reducing requirements, or signalling processes regulating stomatal movements has not been investigated previously. Glycolysis, oxidization of glucose to pyruvate, is a central metabolic pathway and yields a net gain of 2 ATP and 2 NADH. 2,3-biphosphoglycerate-independent phosphoglycerate mutase (iPGAM) is a key enzymatic activity in glycolysis and catalyses the reversible interconversion of 3-phosphoglycerate to 2-phosphoglycerate. To investigate functions of iPGAMs and glycolysis in stomatal function and plant growth, Arabidopsis insertional mutants in At1g09780 and At3g08590, both of which have been annotated as iPGAMs on the basis of sequence homology, were identified and characterized. While single mutants were indistinguishable from the wild type in all plant phenotypes assayed, double mutants had no detectable iPGAM activity and showed defects in blue light-, abscisic acid-, and low CO(2)-regulated stomatal movements. Vegetative plant growth was severely impaired in the double mutants and pollen was not produced. The data demonstrate that iPGAMs and glycolytic activity are critical for guard cell function and fertility in Arabidopsis.     

Liposome-loaded phenylalanine or tryptophan as sickling inhibitor: a possible therapy for sickle cell disease

Phenylalanine or tryptophan entrapped in small unilamellar liposomes was used to transport Phe or Trp across the red blood cell membrane. The incorporation of Phe or Trp into RBCs via liposomes markedly inhibited and reversed the in vitro sickling of deoxy Hb S. Furthermore, normal and SS RBCs loaded with Phe or Trp did not exhibit significant change in osmotic fragility, mechanical fragility, autohemolysis, and glycolysis when compared to untreated RBCs. In addition, the oxygen affinity measured as the P50 and concentrations of 2,3-DPG and ATP were not affected by the incorporation of Phe or Trp into AA or SS RBCs. These results demonstrate that this liposomal transport system which transferred Phe and Trp into intact RBCs did not have any adverse effect on RBC metabolism and function, and may have therapeutic implications in the treatment of sickle cell disease.     

Compartmentalized energy transfer in cardiomyocytes: use of mathematical modeling for analysis of in vivo regulation of respiration.

The mathematical model of the compartmentalized energy transfer system in cardiac myocytes presented includes mitochondrial synthesis of ATP by ATP synthase, phosphocreatine production in the coupled mitochondrial creatine kinase reaction, the myofibrillar and cytoplasmic creatine kinase reactions, ATP utilization by actomyosin ATPase during the contraction cycle, and diffusional exchange of metabolites between different compartments. The model was used to calculate the changes in metabolite profiles during the cardiac cycle, metabolite and energy fluxes in different cellular compartments at high workload (corresponding to the rate of oxygen consumption of 46 mu atoms of O.(g wet mass)-1.min-1) under varying conditions of restricted ADP diffusion across mitochondrial outer membrane and creatine kinase isoenzyme "switchoff." In the complete system, restricted diffusion of ADP across the outer mitochondrial membrane stabilizes phosphocreatine production in cardiac mitochondria and increases the role of the phosphocreatine shuttle in energy transport and respiration regulation. Selective inhibition of myoplasmic or mitochondrial creatine kinase (modeling the experiments with transgenic animals) results in "takeover" of their function by another, active creatine kinase isoenzyme. This mathematical modeling also shows that assumption of the creatine kinase equilibrium in the cell may only be a very rough approximation to the reality at increased workload. The mathematical model developed can be used as a basis for further quantitative analyses of energy fluxes in the cell and their regulation, particularly by adding modules for adenylate kinase, the glycolytic system, and other reactions of energy metabolism of the cell.     

Glycolytic oscillations in isolated rabbit ventricular myocytes

Previous studies have shown that glycolysis can oscillate periodically, driven by feedback loops in regulation of key glycolytic enzymes by free ADP and other metabolites. Here we show both theoretically and experimentally in cardiac myocytes that when the capacity of oxidative phosphorylation and the creatine kinase system to buffer the cellular ATP/ADP ratio is suppressed, glycolysis can cause large scale periodic oscillations in cellular ATP levels (0.02-0.067 Hz), monitored from glibenclamide-sensitive changes in action potential duration or intracellular free Mg2+. Action potential duration oscillations originate primarily from glycolysis, since they 1) occur in the presence of cyanide or rotenone, 2) are suppressed by iodoacetate, 3) are accompanied by at most very small mitochondrial membrane potential oscillations, and 4) exhibit an anti-phase relationship to NADH fluorescence. By uncoupling energy supply-demand balance, glycolytic oscillations may promote injury and electrophysiological heterogeneity during acute metabolic stresses, such as acute myocardial ischemia in which both oxidative phosphorylation and creatine kinase activity are inhibited.     

Energy metabolism transition in multi-cellular human tumor spheroids

It is thought that glycolysis is the predominant energy pathway in cancer, particularly in solid and poorly vascularized tumors where hypoxic regions develop. To evaluate whether glycolysis does effectively predominate for ATP supply and to identify the underlying biochemical mechanisms, the glycolytic and oxidative phosphorylation (OxPhos) fluxes, ATP/ADP ratio, phosphorylation potential, and expression and activity of relevant energy metabolism enzymes were determined in multi-cellular tumor spheroids, as a model of human solid tumors. In HeLa and Hek293 young-spheroids, the OxPhos flux and cytochrome c oxidase protein content and activity were similar to those observed in monolayer cultured cells, whereas the glycolytic flux increased two- to fourfold; the contribution of OxPhos to ATP supply was 60%. In contrast, in old-spheroids, OxPhos, ATP content, ATP/ADP ratio, and phosphorylation potential diminished 50-70%, as well as the activity (88%) and content (3 times) of cytochrome c oxidase. Glycolysis and hexokinase increased significantly (both, 4 times); consequently glycolysis was the predominant pathway for ATP supply (80%). These changes were associated with an increase (3.3 times) in the HIF-1alpha content. After chronic exposure, both oxidative and glycolytic inhibitors blocked spheroid growth, although the glycolytic inhibitors, 2-deoxyglucose and gossypol (IC(50) of 15-17 nM), were more potent than the mitochondrial inhibitors, casiopeina II-gly, laherradurin, and rhodamine 123 (IC(50) > 100 nM). These results suggest that glycolysis and OxPhos might be considered as metabolic targets to diminish cellular proliferation in poorly vascularized, hypoxic solid tumors.     

Energetics underlying the process of long-chain fatty acid transport.

The gram negative bacterium Escherichia coli has evolved a highly specific system for the transport of exogenous long-chain fatty acids (C12-C18) across the cell envelope that requires the outer membrane protein FadL and the inner membrane associated fatty acyl CoA synthetase. The transport of oleate (C18:1) across the cell envelop responds to metabolic energy. In order to define the source of metabolic energy which drives this process, oleate transport was measured in wild-type and ATP synthase-defective (Deltaatp) strains which were (i) subjected to osmotic shock and (ii) starved and energized with glucose or d-lactate in the presence of different metabolic inhibitors. Osmotic shock did not eliminate transport but rather reduced the rate to 33-55% of wild-type levels. These results suggested a periplasmic protein may participate in this process or that osmotic shock disrupts the energized state of the cell which in turn reduces the rate of oleate transport. Transport systems which are osmotically sensitive also require ATP. The process of long-chain fatty acid transport requires ATP generated either by substrate-level or oxidative phosphorylation. Following starvation, the basal rate of transport for wild-type cells was 340.4 pmol/min/mg protein compared to 172.0 pmol/min/mg protein for the Deltaatp cells. When cells are energized with glucose, the rates of transport were increased and comparable (1242.6 and 1293.8 pmol/min/mg protein, respectively). This was in contrast to cells energized with d-lactate in which only the wild-type cells were responsive. The role of ATP is likely due to the ATP requirement of fatty acyl CoA synthetase for catalytic activity. The process of oleate transport is also influenced by the energized state of the inner membrane. In the presence of carbonyl cyanide-m-chlorophenylhydrazone oleate transport is depressed to 30-50% of wild-type levels in wild-type and Deltaatp strains under starvation conditions. These results are mirrored in cells energized with glucose and d-lactate, indicating that an energized membrane is required for optimal levels of oleate transport. These data support the hypothesis that the fatty acid transport system of E. coli responds to both intracellular pools of ATP and an energized membrane for maximal proficiency.     

Extracellular Toxoplasma gondii tachyzoites do not require carbon source uptake for ATP maintenance, gliding motility and invasion in the first hour of their extracellular life

Apicomplexan parasites undergo metabolic shifts in adaptation to environmental changes. Here, we investigate the metabolic requirements which are responsible for ATP homeostasis in the extracellular stage of Toxoplasma gondii. Surprisingly, we found that freshly released tachyzoites are able to maintain a constant ATP level during the first hour of extracellular incubation without the acquisition of external carbon sources. We further demonstrated that the extent of gliding motility and that of host cell invasion is independent from the availability of external carbon sources during this one hour extracellular period. The ATP level and the invasion efficiency of extracellular parasites were severely decreased by treatment with the glycolysis inhibitor, 2-deoxy-d-glucose, but not by the F(0)F(1)-ATPase inhibitor, oligomycin. This suggests that although the uptake of glucose itself is not required during the 1h incubation period, extracellular parasites depend on the activity of the glycolytic pathway for ATP homeostasis. Furthermore, active glycolysis was evident by the secretion of lactate into the culture medium, even in the absence of external carbon sources. Together, our studies suggest that tachyzoites are independent from external carbon sources within the first hour of their extracellular life, which is the most relevant time span for finding a new host cell, but rely on the glycolytic metabolisation of internal carbon sources for ATP maintenance, gliding motility and host cell invasion.     

Experimental determination of control of glycolysis in Lactococcus lactis

The understanding of control of metabolic processes requires quantitative studies of the importance of the different enzymatic steps for the magnitude of metabolic fluxes and metabolite concentrations. An important element in such studies is the modulation of enzyme activities in small steps above and below the wild-type level. We review a genetic approach that is well suited for both Metabolic Optimization and Metabolic Control Analysis and studies on the importance of a number of glycolytic enzymes for metabolic fluxes in Lactococcus lactis. The glycolytic enzymes phosphofructokinase (PFK), glyceraldehyde-3-phosphate dehydrogenase (GAPDH), pyruvate kinase (PYK) and lactate dehydrogenase (LDH) are shown to have no significant control on the glycolytic flux in exponentially growing cells of L. lactis MG1363. Introduction of an uncoupled ATPase activity results in uncoupling of glycolysis from biomass production. With MG1363 growing in defined medium supplemented with glucose, the ATP demanding processes do not have a significant control on the glycolytic flux; it appears that glycolysis is running at maximal rate. It is likely that the flux control is distributed over many enzymes in L. lactis, but it cannot yet be excluded that one of the remaining glycolytic steps is a rate-limiting step for the glycolytic flux.     

Modelling and analysis of central metabolism operating regulatory interactions in salt stress conditions in a L-carnitine overproducing E. coli strain

Based on experimental data from E. coli cultures, we have devised a mathematical model in the GMA-power law formalism that describes the central and L-carnitine metabolism in and between two steady states, non-osmotic and hyperosmotic (0.3 M NaCl). A key feature of this model is the introduction of type of kinetic order, the osmotic stress kinetic orders (g(OSn)), derived from the power law general formalism, which represent the effect of osmotic stress in each metabolic process of the model.By considering the values of the g(OSn) linked to each metabolic process we found that osmotic stress has a positive and determinant influence on the increase in flux in energetic metabolism (glycolysis); L-carnitine biosynthesis production; the transformation/excretion of Acetyl-CoA into acetate and ethanol; the input flux of peptone into the cell; the anabolic use of pyruvate and biomass decomposition. In contrast, we found that although the osmotic stress has an inhibitory effect on the transformation flux from the glycolytic end products (pyruvate) to Acetyl-CoA, this inhibition is counteracted by other effects (the increase in pyruvate concentration) to the extent that the whole flux increases. In the same vein, the down regulation exerted by osmotic stress on fumarate uptake and its oxidation and the production and export of lactate and pyruvate are reversed by other factors up to the point that the first increased and the second remained unchanged.The model analysis shows that in osmotic conditions the energy and fermentation pathways undergo substantial rearrangement. This is illustrated by the observation that the increase in the fermentation fluxes is not connected with fluxes towards the tricaboxylic acid intermediates and the synthesis of biomass. The osmotic stress associated with these fluxes reflects these changes. All these observations support that the responses to salt stress observed in E. coli might be conserved in halophiles.Flux evolution during osmotic adaptations showed a hyperbolic (increasing or decreasing) pattern except in the case of peptone and fumarate uptake by the cell, which initially decreased. Finally, the model also throws light on the role of L-carnitine as osmoprotectant.     

From Metabolomics to Fluxomics: A Computational Procedure to Translate Metabolite Profiles into Metabolic Fluxes

We describe a believed-novel procedure for translating metabolite profiles (metabolome) into the set of metabolic fluxes (fluxome) from which they originated. Methodologically, computational modeling is integrated with an analytical platform comprising linear optimization, continuation and dynamic analyses, and metabolic control. The procedure was tested with metabolite profiles obtained from ex vivo mice Langendorff-heart preparations perfused with glucose. The metabolic profiles were analyzed using a detailed kinetic model of the glucose catabolic pathways including glycolysis, pentose phosphate (PP), glycogenolysis, and polyols to translate the glucose metabolome of the heart into the fluxome. After optimization, the ability of the model to simulate the initial metabolite profile was confirmed, and metabolic fluxes as well as the structure of control and regulation of the glucose catabolic network could be calculated. We show that the step catalyzed by phosphofructokinase together with ATP demand and glycogenolysis exert the highest control on the glycolytic flux. The negative flux control exerted by phosphofructokinase on the PP and polyol pathways revealed that the extent of glycolytic flux directly affects flux redirection through these pathways, i.e., the higher the glycolytic flux the lower the PP and polyols. This believed-novel methodological approach represents a step forward that may help in designing therapeutic strategies targeted to diagnose, prevent, and treat metabolic diseases.     

Relationship between ion distribution and membrane potential during a steady state

Equations were derived showing the relationship between the membrane potential and the quantities which influence it under steady state conditions. Essentially, the membrane potential is caused by the valence and concentration of the non-permeating ions. The permeating ions can modify the membrane potential by altering the relative concentration of the non-permeating ions with respect to the concentration of the permeating ions. For muscle, the sodium cations act as the non-permeating ions in the extracellular environment by the maintenance of some type of active metabolic process and large anions act as the non-permeating ions in the intracellular environment. Both of these non-permeating ions contribute about equally to the maintenance of the resting membrane potential. When the active metabolic process for sodium extrusion breaks down or when acids are added, the membrane potential should decrease. Water should enter the cell when the sodium metabolic process is diminished; water should leave the cell when acids are added. When acid is added, it is expected that the cations potassium and sodium will leave the cell with little or no shift of the chloride ions.