Kinetic modeling can describe in vivo glycolysis in Entamoeba histolytica

Glycolysis in the human parasite Entamoeba histolytica is characterized by the absence of cooperative modulation and the prevalence of pyrophosphate-dependent (over ATP-dependent) enzymes. To determine the flux-control distribution of glycolysis and understand its underlying control mechanisms, a kinetic model of the pathway was constructed by using the software gepasi. The model was based on the kinetic parameters determined in the purified recombinant enzymes, and the enzyme activities, and steady-state fluxes and metabolite concentrations determined in amoebal trophozoites. The model predicted, with a high degree of accuracy, the flux and metabolite concentrations found in trophozoites, but only when the pyrophosphate concentration was held constant; at variable pyrophosphate, the model was not able to completely account for the ATP production/consumption balance, indicating the importance of the pyrophosphate homeostasis for amoebal glycolysis. Control analysis by the model revealed that hexokinase exerted the highest flux control (73%), as a result of its low cellular activity and strong AMP inhibition. 3-Phosphoglycerate mutase also exhibited significant flux control (65%) whereas the other pathway enzymes showed little or no control. The control of the ATP concentration was also mainly exerted by ATP consuming processes and 3-phosphoglycerate mutase and hexokinase (in the producing block). The model also indicated that, in order to diminish the amoebal glycolytic flux by 50%, it was required to decrease hexokinase or 3-phosphoglycerate mutase by 24% and 55%, respectively, or by 18% for both enzymes. By contrast, to attain the same reduction in flux by inhibiting the pyrophosphate-dependent enzymes pyrophosphate-phosphofructokinase and pyruvate phosphate dikinase, they should be decreased > 70%. On the basis of metabolic control analysis, steps whose inhibition would have stronger negative effects on the energy metabolism of this parasite were identified, thus becoming alternative targets for drug design.     

Metabolic flux analysis for a ppc mutant Escherichia coli based on 13C-labelling experiments together with enzyme activity assays and intracellular metabolite measurements

The physiology and central metabolism of a ppc mutant Escherichia coli were investigated based on the metabolic flux distribution obtained by (13)C-labelling experiments using gas chromatography-mass spectrometry (GC-MS) and 2-dimensional nuclear magnetic resonance (2D NMR) strategies together with enzyme activity assays and intracellular metabolite concentration measurements. Compared to the wild type, its ppc mutant excreted little acetate and produced less carbon dioxide at the expense of a slower growth rate and a lower glucose uptake rate. Consequently, an improvement of the biomass yield on glucose was observed in the ppc mutant. Enzyme activity measurements revealed that isocitrate lyase activity increased by more than 3-fold in the ppc mutant. Some TCA cycle enzymes such as citrate synthase, aconitase and malate dehydrogenase were also upregulated, but enzymes of glycolysis and the pentose phosphate pathway were downregulated. The intracellular intermediates in the glycolysis and the pentose phosphate pathway, therefore, accumulated, while acetyl coenzyme A and oxaloacetate concentrations decreased in the ppc mutant. The intracellular metabolic flux analysis uncovered that deletion of ppc resulted in the appearance of the glyoxylate shunt, with 18.9% of the carbon flux being channeled via the glyoxylate shunt. However, the flux of the pentose phosphate pathway significantly decreased in the ppc mutant.     

Increasing the flux in metabolic pathways: A metabolic control analysis perspective

The problems of engineering increased flux in metabolic pathways are analyzed in terms of the understanding provided by metabolic control analysis. Over-expression of a single enzyme is unlikely to be effective unless it is known to have a high flux control coefficient, which can be used as an approximate predictive tool. This is likely to rule out enzymes subject to feedback inhibition, because it transfers control downstream from the inhibited enzyme to the enzymes utilizing the feedback metabolite. Although abolishing feedback inhibition can restore flux control to an enzyme, it is also likely to cause large increases in the concentrations of metabolic intermediates. Simultaneous and coordinated over-expression of most of the enzymes in a pathway can, in principle, produce substantial flux increases without changes in metabolite levels, though technically it may be difficult to achieve. It is, however, closer to the method used by cells to change flux levels, where coordinated changes in the level of activity of pathway enzymes are the norm. Another option is to increase the demand for the pathway product, perhaps by increasing its rate of excretion or removal. Copyright 1998 John Wiley & Sons, Inc.     

Flux control analysis for biphenyl metabolism by Rhodococcus pyridinovorans R04

The flux control coefficients of the four enzymes involved in the upper pathway of biphenyl degradation were determined from transient metabolite concentrations. The first enzyme was indicated as the major rate-limiting step of the pathway with a control coefficient of 0.48. The flux control coefficients of the other three enzymes were 0.03, 0.23 and 0.27, respectively. This is the first experimental evidence of the control step in the pathway of biphenyl degradation using metabolic control analysis.     

Multiplicity of Steady States in Glycolysis and Shift of Metabolic State in Cultured Mammalian Cells

Cultured mammalian cells exhibit elevated glycolysis flux and high lactate production. In the industrial bioprocesses for biotherapeutic protein production, glucose is supplemented to the culture medium to sustain continued cell growth resulting in the accumulation of lactate to high levels. In such fed-batch cultures, sometimes a metabolic shift from a state of high glycolysis flux and high lactate production to a state of low glycolysis flux and low lactate production or even lactate consumption is observed. While in other cases with very similar culture conditions, the same cell line and medium, cells continue to produce lactate. A metabolic shift to lactate consumption has been correlated to the productivity of the process. Cultures that exhibited the metabolic shift to lactate consumption had higher titers than those which didn’t. However, the cues that trigger the metabolic shift to lactate consumption state (or low lactate production state) are yet to be identified. Metabolic control of cells is tightly linked to growth control through signaling pathways such as the AKT pathway. We have previously shown that the glycolysis of proliferating cells can exhibit bistability with well-segregated high flux and low flux states. Low lactate production (or lactate consumption) is possible only at a low glycolysis flux state. In this study, we use mathematical modeling to demonstrate that lactate inhibition together with AKT regulation on glycolysis enzymes can profoundly influence the bistable behavior, resulting in a complex steady-state topology. The transition from the high flux state to the low flux state can only occur in certain regions of the steady state topology, and therefore the metabolic fate of the cells depends on their metabolic trajectory encountering the region that allows such a metabolic state switch. Insights from such switch behavior present us with new means to control the metabolism of mammalian cells in fed-batch cultures.     

Modeling cancer glycolysis

Most cancer cells exhibit an accelerated glycolysis rate compared to normal cells. This metabolic change is associated with the over-expression of all the pathway enzymes and transporters (as induced by HIF-1α and other oncogenes), and with the expression of hexokinase (HK) and phosphofructokinase type 1 (PFK-1) isoenzymes with different regulatory properties. Hence, a control distribution of tumor glycolysis, modified from that observed in normal cells, can be expected. To define the control distribution and to understand the underlying control mechanisms, kinetic models of glycolysis of rodent AS-30D hepatoma and human cervix HeLa cells were constructed with experimental data obtained here for each pathway step (enzyme kinetics; steady-state pathway metabolite concentrations and fluxes). The models predicted with high accuracy the fluxes and metabolite concentrations found in living cancer cells under physiological O(2) and glucose concentrations as well as under hypoxic and hypoglycemic conditions prevailing during tumor progression. The results indicated that HK≥HPI>GLUT in AS-30D whereas glycogen degradation≥GLUT>HK in HeLa were the main flux- and ATP concentration-control steps. Modeling also revealed that, in order to diminish the glycolytic flux or the ATP concentration by 50%, it was required to decrease GLUT or HK or HPI by 76% (AS-30D), and GLUT or glycogen degradation by 87-99% (HeLa), or decreasing simultaneously the mentioned steps by 47%. Thus, these proteins are proposed to be the foremost therapeutic targets because their simultaneous inhibition will have greater antagonistic effects on tumor energy metabolism than inhibition of all other glycolytic, non-controlling, enzymes.     

Metabolic control analysis of Aspergillus niger L-arabinose catabolism

A mathematical model of the L-arabinose/D-xylose catabolic pathway of Aspergillus niger was constructed based on the kinetic properties of the enzymes. For this purpose L-arabinose reductase, L-arabitol dehydrogenase and D-xylose reductase were purified using dye-affinity chromatography, and their kinetic properties were characterized. For the other enzymes of the pathway the kinetic data were available from the literature. The metabolic model was used to analyze flux and metabolite concentration control of the L-arabinose catabolic pathway. The model demonstrated that flux control does not reside at the enzyme following the intermediate with the highest concentration, L-arabitol, but is distributed over the first three steps in the pathway, preceding and following L-arabitol. Flux control appeared to be strongly dependent on the intracellular L-arabinose concentration. At 5 mM intracellular L-arabinose, a level that resulted in realistic intermediate concentrations in the model, flux control coefficients for L-arabinose reductase, L-arabitol dehydrogenase and L-xylulose reductase were 0.68, 0.17 and 0.14, respectively. The analysis can be used as a guide to identify targets for metabolic engineering aiming at either flux or metabolite level optimization of the L-arabinose catabolic pathway of A. niger. Faster L-arabinose utilization may enhance utilization of readily available organic waste containing hemicelluloses to be converted into industrially interesting metabolites or valuable enzymes or proteins.     

Mathematical modelling of metabolic pathways affected by an enzyme deficiency. A mathematical model of glycolysis in normal and pyruvate-kinase-deficient red blood cells

A mathematical model of glycolysis in human erythrocytes is proposed to study the influence of a pyruvate kinase deficiency on the energy metabolism. The model takes into account the main regulatory properties of the non-equilibrium enzymes and the magnesium-complex formation by the adenine nucleotides and by 2,3-bisphosphoglycerate. In the normal case (no enzyme defect) the calculated flux rates and metabolite concentrations are in a good agreement with experimental data. It is shown that a severe pyruvate kinase deficiency manifested in a tenfold diminished activity of that enzyme leads to a remarkable decrease of the glycolytic flux and the ATP concentration of about 50% of the normal values. On the other hand a lowering of the pyruvate kinase activity to half of the normal value, characteristic for the heterozygotes, gives no significant alterations of the metabolite concentrations and the flux rates compared with the normal case which is in accordance with the lack of clinical symptoms for a metabolic disease of these probands. For three patients with known alterations of their pyruvate kinase mutants the calculated metabolite concentrations and the control characteristics permit estimation of the degree of disorder of the glycolytic pathway. The resulting classification corresponds well to other independent experimental and clinical findings. In particular, the calculation demonstrates that there is no simple correlation between the lowered enzyme activity and the reduced flux rate through the affected pathway.     

Matrix method for determining steps most rate-limiting to metabolic fluxes in biotechnological processes

The metabolic control theory developed by Kacser, Burns, Heinrich, and Rapoport is briefly outlined, extended, and transformed so as optimally to address some biotechnological questions. The extensions include (i) a new theorem that relates the control of metabolite concentrations by enzyme activities to flux ratios at branches in metabolic pathways; (ii) a new theorem that does the same for the control of the distribution of the flux over two branches; (iii) a method that expresses these controls into properties (the so-called elasticity coefficients) of the enzymes in the pathway; and (iv) a theorem that relates the effects of changes in metabolite concentrations on reaction rates to the effects of changes in enzyme properties on the same rates. Matrix equations relating the flux control and concentration control coefficients to the elasticity coefficients of enzymes in simple linear and branched pathways incorporating feedback are given, together with their general solutions and a numerical example. These equations allow one to develop rigorous criteria by which to decide the optimal strategy for the improvement of a microbial process. We show how this could be used in deciding which property of which enzyme should be changed in order to obtain the maximal concentration of a metabolite or the maximal metabolic flux.     

Glycolysis Is Governed by Growth Regime and Simple Enzyme Regulation in Adherent MDCK Cells

Due to its vital importance in the supply of cellular pathways with energy and precursors, glycolysis has been studied for several decades regarding its capacity and regulation. For a systems-level understanding of the Madin-Darby canine kidney (MDCK) cell metabolism, we couple a segregated cell growth model published earlier with a structured model of glycolysis, which is based on relatively simple kinetics for enzymatic reactions of glycolysis, to explain the pathway dynamics under various cultivation conditions. The structured model takes into account in vitro enzyme activities, and links glycolysis with pentose phosphate pathway and glycogenesis. Using a single parameterization, metabolite pool dynamics during cell cultivation, glucose limitation and glucose pulse experiments can be consistently reproduced by considering the cultivation history of the cells. Growth phase-dependent glucose uptake together with cell-specific volume changes generate high intracellular metabolite pools and flux rates to satisfy the cellular demand during growth. Under glucose limitation, the coordinated control of glycolytic enzymes re-adjusts the glycolytic flux to prevent the depletion of glycolytic intermediates. Finally, the model''s predictive power supports the design of more efficient bioprocesses.     

Mutated forms of phosphoglycerate mutase in yeast affect reversal of metabolic flux. Effect of reversible and irreversible function of an enzyme on pathway reversal

Phosphoglycerate mutase (GPM) functions reversibly in the glycolytic pathway. Mutations altering the reversibility of GPM have been obtained in the yeast, Saccharomyces cerevisiae. While wild-type cells grow on glycolytic (glucose) or gluconeogenic (ethanol) substrates, cells with altered GPMs fall into three categories based on their phenotypes 1) glucose- ethanol-, 2) glucose+ ethanol-, and 3) glucose- ethanol+. Cells with the first two phenotypes possessed GPMs that functioned irreversibly in the glycolytic direction. Cells that were glucose- ethanol+ possessed an enzyme that functioned reversibly. All of the altered GPMs had maximal velocities that were less than 3% of the wild-type level. The properties of the altered GPMs studied here provide a rationale for the occurrence in the glycolytic pathway of several glycolytic enzymes such as GPM, which function at high velocities in relation to the much smaller metabolic flux that they support. The altered GPMs were purified and estimates of their kinetic constants obtained. Free energy profiles were drawn for catalysis by the wild type and a mutant GPM that functioned irreversibly. The mutant enzyme was very inefficient. It was shown that an enzyme that functions irreversibly at a reaction with a Keq value close to 1 would necessarily be inefficient while it could evolve to be efficient when catalyzing a reaction that has a Keq value much greater than 1. In the glycolytic path this could be the reason for the characteristic presence of enzymes that function irreversibly at reactions with large Keq values.     

Control of gluconeogenesis in rat liver cells. Flux control coefficients of the enzymes in the gluconeogenic pathway in the absence and presence of glucagon.

We have used control analysis to quantify the distribution of control in the gluconeogenic pathway in liver cells from starved rats. Lactate and pyruvate were used as gluconeogenic substrates. The flux control coefficients of the various enzymes in the gluconeogenic pathway were calculated from the elasticity coefficients of the enzymes towards their substrates and products and the fluxes through the different branches in the pathway. The elasticity coefficients were either calculated from gamma/Keq. ratios (where gamma is the mass-action ratio and Keq. is the equilibrium constant) and enzyme-kinetic data or measured experimentally. It is concluded that the gluconeogenic enzyme pyruvate carboxylase and the glycolytic enzyme pyruvate kinase play a central role in control of gluconeogenesis. If pyruvate kinase is inactive, gluconeogenic flux from lactate is largely controlled by pyruvate carboxylase. The low elasticity coefficient of pyruvate carboxylase towards its product oxaloacetate minimizes control by steps in the gluconeogenic pathway located after pyruvate carboxylase. This situation occurs when maximal gluconeogenic flux is required, i.e. in the presence of glucagon. In the absence of the hormone, when pyruvate kinase is active, control of gluconeogenesis is distributed among many steps, including pyruvate carboxylase, pyruvate kinase, fructose-1,6-bisphosphatase and also steps outside the classic gluconeogenic pathway such as the adenine-nucleotide translocator.     

The intracellular equilibrium thermodynamic and steady-state concentrations of metabolites

A new model for the organization and flow of metabolites through a metabolic pathway is presented. The model is based on four major findings. (1) The intracellular concentrations of enzyme sites exceed the concentrations of intermediary metabolites that bind specifically to these sites. (2) The concentration of the excessive enzyme sites in the cell is sufficiently high so that nearly all the cellular intermediary metabolites are enzyme-bound. (3) Enzyme conformations are perturbed by the interactions with substrates and products; the conformations of enzyme-substrate and enzyme-product complexes are different. (4) Two enzymes, catalyzing reactions that are sequential in a metabolic pathway, transfer the common metabolite back and forth via an enzyme-enzyme complex without the intervention of the solvent environment. The model proposes that the enzyme-enzyme recognition is ligand-induced. Conversion of E₂S and E₂P results in the loss of recognition of E₂ by E₁ and the concomitant recognition of E₂ by E₃. This model substantially alters existent views of the bioenergetics and the kinetics of intracellular metabolism. The rates of direct transfer of metabolite from enzyme to enzyme are comparable to the rates of interconversion between substrate and product within an individual enzyme. Consequently, intermediary metabolites are nearly equipartitioned among their high-affinity enzyme sites within a metabolic pathway. Metabolic flux involves the direct transfer of metabolite from enzyme to enzyme via a set of low and nearly equal energy barriers.     

Channelling can decrease pool size.

It is widely considered that a possible advantage of metabolite channelling, in which a product of an enzyme is transferred to the next enzyme in a metabolic pathway without being released to the 'bulk' solution, is that channelling can decrease the steady-state concentrations of 'pool' intermediates. This then spares the limited solvent capacity of the cell, and reduces the loss of pathway flux due to leakage or instability of the free intermediate. Recently, however, based on simulations of a particular model of a 'dynamic' channel, Cornish-Bowden ["Failure of channelling to maintain low concentrations of metabolic intermediates" (1991) Eur. J. Biochem. 195, 103-108] has argued that this is not in fact the case; his simulations indicated that the channel was rather ineffective at decreasing the concentration of the pool intermediate, and in some cases actually increased it. However, although his simulations were restricted to very specific thermodynamic and kinetic parameters, he generalised his conclusions, arguing that "channelling has no effect on the free concentration of a channelled intermediate in a pathway". By showing that, for a number of kinetic cases, the concentration of the pool intermediate did decrease substantially with increased channelling, we demonstrate here that the conclusion of Cornish-Bowden is not correct. In particular, if the reaction catalysed by the enzymes forming the channel has an equilibrium constant K higher than 1, and if the enzyme removing the product of the channel reaction is kinetically competent, channelling in the model system studied by Cornish-Bowden (1991) can decrease the steady-state concentration of the pool by a factor of 1000, independently of the mechanism of the terminal reaction and under conditions of essentially constant overall flux. If the channel is a 'static' channel, the decrease in the pool can be to arbitrarily low levels. This conclusion also holds for a system in which other reactions may consume the pool intermediate. Thus, channelling can maintain metabolite concentrations at low levels.     

A Fresh View of Glycolysis and Glucokinase Regulation: History and Current Status

This minireview looks back at a century of glycolysis research with a focus on the mechanisms of flux regulation. Traditionally, glycolysis is regarded as a feeder pathway that prepares glucose for further catabolism and energy production. However, glycolysis is much more than that, in particular in those tissues that express the low affinity glucose-phosphorylating enzyme glucokinase. This enzyme equips the glycolytic pathway with a special steering function for the regulation of intermediary metabolism. In beta cells, glycolysis acts as a transducer for triggering and amplifying physiological glucose-induced insulin secretion. On the basis of these considerations, I have defined a glycolytic flux regulatory unit composed of the two fructose ester steps of this pathway with various enzymes and metabolites that regulate glycolysis.     

'Slave' metabolites and enzymes. A rapid way of delineating metabolic control.

Although control of fluxes and concentrations tends to be distributed rather than confined to a single rate-limiting enzyme, the extent of control can differ widely between enzymes in a metabolic network. In some cases, there are enzymes that lack control completely. This paper identifies one surprising origin of such lack of control: If, in a metabolic system, there is a metabolite that affects the catalytic rate of only one enzyme, the corresponding enzyme cannot control any metabolic variable other than the concentration of that metabolite. We call such enzymes 'slave enzymes', and the corresponding metabolites 'slave metabolites'. Implications of the existence of slave enzymes for the control properties of enzymes further down the metabolic pathway are discussed and examined for the glycolytic pathway of yeast. Inadvertent assumptions in metabolic models may cause the latter incorrectly to calculate absence of metabolic control. The phenomenon of slave enzymes may well be important in enhancing metabolic signal transduction.