Reconstruction and flux analysis of coupling between metabolic pathways of astrocytes and neurons: application to cerebral hypoxia

Background

It is a daunting task to identify all the metabolic pathways of brain energy metabolism and develop a dynamic simulation environment that will cover a time scale ranging from seconds to hours. To simplify this task and make it more practicable, we undertook stoichiometric modeling of brain energy metabolism with the major aim of including the main interacting pathways in and between astrocytes and neurons.

Model

The constructed model includes central metabolism (glycolysis, pentose phosphate pathway, TCA cycle), lipid metabolism, reactive oxygen species (ROS) detoxification, amino acid metabolism (synthesis and catabolism), the well-known glutamate-glutamine cycle, other coupling reactions between astrocytes and neurons, and neurotransmitter metabolism. This is, to our knowledge, the most comprehensive attempt at stoichiometric modeling of brain metabolism to date in terms of its coverage of a wide range of metabolic pathways. We then attempted to model the basal physiological behaviour and hypoxic behaviour of the brain cells where astrocytes and neurons are tightly coupled.

Results

The reconstructed stoichiometric reaction model included 217 reactions (184 internal, 33 exchange) and 216 metabolites (183 internal, 33 external) distributed in and between astrocytes and neurons. Flux balance analysis (FBA) techniques were applied to the reconstructed model to elucidate the underlying cellular principles of neuron-astrocyte coupling. Simulation of resting conditions under the constraints of maximization of glutamate/glutamine/GABA cycle fluxes between the two cell types with subsequent minimization of Euclidean norm of fluxes resulted in a flux distribution in accordance with literature-based findings. As a further validation of our model, the effect of oxygen deprivation (hypoxia) on fluxes was simulated using an FBA-derivative approach, known as minimization of metabolic adjustment (MOMA). The results show the power of the constructed model to simulate disease behaviour on the flux level, and its potential to analyze cellular metabolic behaviour in silico.

Conclusion

The predictive power of the constructed model for the key flux distributions, especially central carbon metabolism and glutamate-glutamine cycle fluxes, and its application to hypoxia is promising. The resultant acceptable predictions strengthen the power of such stoichiometric models in the analysis of mammalian cell metabolism.     

The principle of flux minimization and its application to estimate stationary fluxes in metabolic networks.

Cellular functions are ultimately linked to metabolic fluxes brought about by thousands of chemical reactions and transport processes. The synthesis of the underlying enzymes and membrane transporters causes the cell a certain 'effort' of energy and external resources. Considering that those cells should have had a selection advantage during natural evolution that enabled them to fulfil vital functions (such as growth, defence against toxic compounds, repair of DNA alterations, etc.) with minimal effort, one may postulate the principle of flux minimization, as follows: given the available external substrates and given a set of functionally important 'target' fluxes required to accomplish a specific pattern of cellular functions, the stationary metabolic fluxes have to become a minimum. To convert this principle into a mathematical method enabling the prediction of stationary metabolic fluxes, the total flux in the network is measured by a weighted linear combination of all individual fluxes whereby the thermodynamic equilibrium constants are used as weighting factors, i.e. the more the thermodynamic equilibrium lies on the right-hand side of the reaction, the larger the weighting factor for the backward reaction. A linear programming technique is applied to minimize the total flux at fixed values of the target fluxes and under the constraint of flux balance (= steady-state conditions) with respect to all metabolites. The theoretical concept is applied to two metabolic schemes: the energy and redox metabolism of erythrocytes, and the central metabolism of Methylobacterium extorquens AM1. The flux rates predicted by the flux-minimization method exhibit significant correlations with flux rates obtained by either kinetic modelling or direct experimental determination. Larger deviations occur for segments of the network composed of redundant branches where the flux-minimization method always attributes the total flux to the thermodynamically most favourable branch. Nevertheless, compared with existing methods of structural modelling, the principle of flux minimization appears to be a promising theoretical approach to assess stationary flux rates in metabolic systems in cases where a detailed kinetic model is not yet available.     

Modulation of extracellular proton fluxes from retinal horizontal cells of the catfish by depolarization and glutamate

Self-referencing H(+)-selective microelectrodes were used to measure extracellular proton fluxes from cone-driven horizontal cells isolated from the retina of the catfish (Ictalurus punctatus). The neurotransmitter glutamate induced an alkalinization of the area adjacent to the external face of the cell membrane. The effect of glutamate occurred regardless of whether the external solution was buffered with 1 mM HEPES, 3 mM phosphate, or 24 mM bicarbonate. The AMPA/kainate receptor agonist kainate and the NMDA receptor agonist N-methyl-D-aspartate both mimicked the effect of glutamate. The effect of kainate on proton flux was inhibited by the AMPA/kainate receptor blocker CNQX, and the effect of NMDA was abolished by the NMDA receptor antagonist DAP-5. Metabotropic glutamate receptor agonists produced no alteration in proton fluxes from horizontal cells. Depolarization of cells either by increasing extracellular potassium or directly by voltage clamp also produced an alkalinization adjacent to the cell membrane. The effects of depolarization on proton flux were blocked by 10 microM nifedipine, an inhibitor of L-type calcium channels. The plasmalemma Ca(2+/)H(+) ATPase (PMCA) blocker 5(6)-carboxyeosin also significantly reduced proton flux modulation by glutamate. Our results are consistent with the hypothesis that glutamate-induced extracellular alkalinizations arise from activation of the PMCA pump following increased intracellular calcium entry into cells. This process might help to relieve suppression of photoreceptor neurotransmitter release that results from exocytosed protons from photoreceptor synaptic terminals. Our findings argue strongly against the hypothesis that protons released by horizontal cells act as the inhibitory feedback neurotransmitter that creates the surround portion of the receptive fields of retinal neurons.     

Response of the central metabolism in Corynebacterium glutamicum to the use of an NADH-dependent glutamate dehydrogenase

The extensive use of 13C enrichments in precursor metabolites for flux quantification does not rely on NADPH stoichiometries and can therefore be used to quantify reducing power fluxes. As an application of this concept, the NADPH fluxes were quantified in an L-lysine producer of Corynebacterium glutamicum grown into metabolic and isotopic steady state with [1-13C]glucose. In this case, where the organism's NADPH-dependent glutamate dehydrogenase consumes reducing power, the NADPH flux generated is 210% (molar flux relative to glucose uptake rate) with its major part (72% of the total) generated via the pentose phosphate pathway activity. An isogenic strain in which the glutamate dehydrogenase of C. glutamicum was replaced by the NADH-dependent glutamate dehydrogenase of Peptostreptococcus asaccharolyticus was made and the metabolite fluxes were again estimated. The major response to this local perturbation is a drastically reduced NADPH generation of only 139%. Most of the NADPH (62% of the total) is now generated via the tricarboxylic acid cycle activity. This shows the extraordinary flexibility of the central metabolism and provides a picture of the global regulatory properties of the central metabolism. Furthermore, a detailed analysis of the fluxes and exchange fluxes within the anaplerotic reactions is given. It is hypothesized that these reactions might also serve to balance the total reducing power budget as well as the energy budget within the cell.     

Effect of amino acid supplementation on titer and glycosylation distribution in hybridoma cell cultures—Systems biology‐based interpretation using genome‐scale metabolic flux balance model and multivariate data analysis

Genome‐scale flux balance analysis (FBA) is a powerful systems biology tool to characterize intracellular reaction fluxes during cell cultures. FBA estimates intracellular reaction rates by optimizing an objective function, subject to the constraints of a metabolic model and media uptake/excretion rates. A dynamic extension to FBA, dynamic flux balance analysis (DFBA), can calculate intracellular reaction fluxes as they change during cell cultures. In a previous study by Read et al. (2013), a series of informed amino acid supplementation experiments were performed on twelve parallel murine hybridoma cell cultures, and this data was leveraged for further analysis (Read et al., Biotechnol Prog. 2013;29:745–753). In order to understand the effects of media changes on the model murine hybridoma cell line, a systems biology approach is applied in the current study. Dynamic flux balance analysis was performed using a genome‐scale mouse metabolic model, and multivariate data analysis was used for interpretation. The calculated reaction fluxes were examined using partial least squares and partial least squares discriminant analysis. The results indicate media supplementation increases product yield because it raises nutrient levels extending the growth phase, and the increased cell density allows for greater culture performance. At the same time, the directed supplementation does not change the overall metabolism of the cells. This supports the conclusion that product quality, as measured by glycoform assays, remains unchanged because the metabolism remains in a similar state. Additionally, the DFBA shows that metabolic state varies more at the beginning of the culture but less by the middle of the growth phase, possibly due to stress on the cells during inoculation. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:1163–1173, 2016     

Classification and sensitivity analysis of a proposed primary metabolic reaction network for Streptomyces lividans

Constructing a metabolic flux analysis model is in principle fairly straightforward. However, there are a number of mathematical pitfalls. First, dependent reactions are a recurring problem and, second, the choice of reactions to measure may not be straight-forward. A method for systematic identification of dependent reactions and a thorough reactions classification procedure is presented. A well-defined stoichiometric presentation can provide significant insight into metabolic control mechanisms. Two methods for analyzing the impact of perturbations in the measured fluxes on the remaining metabolism and the impact of changes in biomass composition on the calculated metabolic reactions is developed. A metabolic reaction network proposed for Streptomyces lividans is used as an example to demonstrate the outlined analysis. It is concluded that oxygen utilization has the highest influence on the pathway fluxes and that realistic perturbations in the biomass composition do not significantly alter the flux patterns.     

Metabolism of [2-13C]succinate in renal cells determined by 13C NMR

[2-13C]Succinate has been used to examine the metabolic carbon flux from the Krebs cycle in rat renal proximal convoluted tubular (PCT) cells under physiological and pathophysiological conditions. Therefore, we developed a mathematical model that enabled us to determine the metabolic fluxes of the Krebs cycle. A mathematical model for the calculation of flux from [2-13C]succinate was used to determine fluxes in rat PCT cells during chronic acidosis in the presence and absence of 0.1 mM angiotensin II. The relative carbon efflux via glutamate dehydrogenase in rat renal PCT cells increases during chronic acidosis from 0.27 to 0.39, whereas this carbon flux is not affected by the presence of peptide hormone angiotensin II in the incubation medium. The fraction of intermediate 13C-labelled oxaloacetate transformed into the phosphoenolpyruvate and aspartate pools increases significantly from 0.41 to 0.57 in the case of chronic acidosis. The carbon efflux is not affected by angiotensin II. The 13C-NMR data also show that the carbon efflux through phosphoenolpyruvate carboxykinase increases from 0.35 to 0.56 in rat renal PCT cells derived from chronic acidotic animals, as well as in the presence of angiotensin II. The present results indicate that angiotensin II affects only the flux through phosphoenolcarboxykinase, whereas chronic acidosis increases the flux through phosphoenolpyruvate carboxykinase as well as the gluconeogenic flux.     

A kinetic model of Escherichia coli core metabolism satisfying multiple sets of mutant flux data

In contrast to stoichiometric-based models, the development of large-scale kinetic models of metabolism has been hindered by the challenge of identifying kinetic parameter values and kinetic rate laws applicable to a wide range of environmental and/or genetic perturbations. The recently introduced ensemble modeling (EM) procedure provides a promising remedy to address these challenges by decomposing metabolic reactions into elementary reaction steps and incorporating all phenotypic observations, upon perturbation, in its model parameterization scheme. Here, we present a kinetic model of Escherichia coli core metabolism that satisfies the fluxomic data for wild-type and seven mutant strains by making use of the EM concepts. This model encompasses 138 reactions, 93 metabolites and 60 substrate-level regulatory interactions accounting for glycolysis/gluconeogenesis, pentose phosphate pathway, TCA cycle, major pyruvate metabolism, anaplerotic reactions and a number of reactions in other parts of the metabolism. Parameterization is performed using a formal optimization approach that minimizes the discrepancies between model predictions and flux measurements. The predicted fluxes by the model are within the uncertainty range of experimental flux data for 78% of the reactions (with measured fluxes) for both the wild-type and seven mutant strains. The remaining flux predictions are mostly within three standard deviations of reported ranges. Converting the EM-based parameters into a Michaelis–Menten equivalent formalism revealed that 35% of K_m and 77% of k_cat parameters are within uncertainty range of the literature-reported values. The predicted metabolite concentrations by the model are also within uncertainty ranges of metabolomic data for 68% of the metabolites. A leave-one-out cross-validation test to evaluate the flux prediction performance of the model showed that metabolic fluxes for the mutants located in the proximity of mutations used for training the model can be predicted more accurately. The constructed model and the parameterization procedure presented in this study pave the way for the construction of larger-scale kinetic models with more narrowly distributed parameter values as new metabolomic/fluxomic data sets are becoming available for E. coli and other organisms.     

Dynamic activation model for a glutamatergic neurovascular unit

This article considers a dynamic spatially lumped model for brain energy metabolism and proposes to use the results of a Markov chain Monte Carlo (MCMC) based flux balance analysis to estimate the kinetic model parameters. By treating steady state reaction fluxes and transport rates as random variables we are able to propagate the uncertainty in the steady state configurations to the predictions of the dynamic model, whose responses are no longer individual but ensembles of time courses. The kinetic model consists of five compartments and is governed by kinetic mass balance equations with Michaelis-Menten type expressions for reaction rates and transports between the compartments. The neuronal activation is implemented in terms of the effect of neuronal activity on parameters controlling the blood flow and neurotransmitter transport, and a feedback mechanism coupling the glutamate concentration in the synaptic cleft and the ATP hydrolysis, thus accounting for the energetic cost of the membrane potential restoration in the postsynaptic neurons. The changes in capillary volume follow the balloon model developed for BOLD MRI. The model follows the time course of the saturation levels of the blood hemoglobin, which link metabolism and BOLD FMRI signal. Analysis of the model predictions suggest that stoichiometry alone is not enough to determine glucose partitioning between neuron and astrocyte. Lactate exchange between neuron and astrocyte is supported by the model predictions, but the uncertainty on the direction and rate is rather elevated. By and large, the model suggests that astrocyte produces and effluxes lactate, while neuron may switch from using to producing lactate. The level of ATP hydrolysis in astrocyte is substantially higher than strictly required for neurotransmitter cycling, in agreement with the literature.     

Bayesian flux balance analysis applied to a skeletal muscle metabolic model

In this article, the steady state condition for the multi-compartment models for cellular metabolism is considered. The problem is to estimate the reaction and transport fluxes, as well as the concentrations in venous blood when the stoichiometry and bound constraints for the fluxes and the concentrations are given. The problem has been addressed previously by a number of authors, and optimization-based approaches as well as extreme pathway analysis have been proposed. These approaches are briefly discussed here. The main emphasis of this work is a Bayesian statistical approach to the flux balance analysis (FBA). We show how the bound constraints and optimality conditions such as maximizing the oxidative phosphorylation flux can be incorporated into the model in the Bayesian framework by proper construction of the prior densities. We propose an effective Markov chain Monte Carlo (MCMC) scheme to explore the posterior densities, and compare the results with those obtained via the previously studied linear programming (LP) approach. The proposed methodology, which is applied here to a two-compartment model for skeletal muscle metabolism, can be extended to more complex models.     

Response of the central metabolism of Corynebacterium glutamicum to different flux burdens

To evaluate the importance of reactions within the central metabolism under different flux burdens the fluxes within the pentose phosphate pathway (PPP), as well as the other reactions of the central metabolism, were intensively analyzed and quantitated. For this purpose, Corynebacterium glutamicum was grown with [1-(13)C]glucose to metabolic and isotopic steady state and the fractional enrichments in precursor metabolites (e.g., pentose 5-phosphate) were quantified. Matrix calculus was used to express these data together with metabolite mass data. The detailed analysis of the dependence of (13)C enrichments on exchange fluxes enabled the transketolase-catalyzed exchange rate (2 pentose 5-phosphate <--> sedoheptulose 7-phosphate + glyceraldehyde 3-phosphate) to be quantified as 74.3% (molar metabolite flux) at a net flux of 10.3% and the exchange rate (pentose 5-phosphate + erythrose 4-phosphate <--> fructose 6-phosphate + glyceraldehyde 3-phosphate) to be quantified as 5.6% at a net flux of 8.1%. The flux entering the tricarboxylic acid cycle was 93.3%. The same comprehensive flux analysis as performed for the nonexcreting condition was done with the identical strain that had been forced to excrete L-glutamate. Because we had already quantified the fluxes for L-lysine excretion with an isogenic strain, three directly comparable flux situations are thus available. Consequently, this comparison permits a direct cause-and-effect relationship to be specified. In response to the different flux burdens of the cell, the PPP flux decreased from a maximum of 67% to 26%, with the glycolytic flux increasing accordingly. The carbon flux through isocitrate dehydrogenase increased from 20% to 36%. The bidirectional carbon flux between pyruvate and oxaloacetate decreased from 36% to 9%. Since the cause of the three different flux states was the allelic exchange in the final L-lysine assembling pathway or the glutamate export activity, respectively, the flexible response is the effect. This shows conclusively the enormous flexibility within the central metabolism of C. glutamicum to supply precursors upon their withdrawal for the synthesis of amino acids. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 168-180, 1997.     

Metabolic flux analysis for serine alkaline protease fermentation by Bacillus licheniformis in a defined medium: effects of the oxygen transfer rate.

The metabolic fluxes through the central carbon pathways in the bioprocess for serine alkaline protease (SAP) production by Bacillus licheniformis were calculated by the metabolic flux-based stoichiometric model based on the proposed metabolic network that contains 102 metabolites and 133 reaction fluxes using the time profiles of citrate, dry cell, organic acids, amino acids, and SAP as the constraints. The model was solved by minimizing the SAP accumulation rate in the cell. The effects of the oxygen-transfer rate (OTR) on the metabolic fluxes were investigated in a defined medium where citrate was used as the sole carbon source. The central pathways were active for the growth and the SAP synthesis in all the periods of the bioprocess at low (LOT), medium (MOT), and high (HOT) oxygen-transfer conditions. The flux partitioning in the TCA cycle at alpha-ketoglutarate towards glutamate group and at oxalacetate (OA) toward aspartic acid group amino acids were dependent on the OTR. The flux of the anaplerotic reaction that connects the TCA cycle either from malate or OA to the gluconeogenesis pathway via the main branch point pyruvate (Pyr) was also influenced by the OTR. With the decrease in the OTR, the intracellular flux values after glycerate 3-phosphate (PG3) in the gluconeogenesis pathway and the specific growth rate decreased. The total ATP-generation rate increased with the increase in OTR. The pathway towards the aspartic acid family amino acids which is important for sporulation that precedes the SAP synthesis were all active throughout the bioprocess. Metabolic flux analysis results at LOT, MOT, and HOT conditions encourage the design of an oxygen-transfer strategy in the bioreactor; moreover, asparagine synthetase or aspartate kinase could be the potential metabolic engineering sites due to the low value of the flux from the branch point aspartate toward asparagine.     

Turnover rates of amino acid neurotransmitters in regions of rat cerebellum

The turnover rates of aspartate, gamma-aminobutyric acid (GABA), glutamate, glutamine, alanine, serine, and glycine were measured in five regions of rat cerebellum. Turnover rates of the putative neurotransmitters (aspartate, glutamate, and GABA) were 2-20-fold higher than those of alanine and serine, and generally consistent with the proposed neurotransmitter functions for these amino acids. However, glutamate turnover was high and similar in magnitude in the deep nuclei and granule layer, suggesting possible release, not only from parallel fibers, but from mossy fibers as well. The differential distribution of turnover rates for GABA supports its neuronal release by Purkinje, stellate, basket, and Golgi cells, whereas aspartate may be released by both climbing and mossy fibers. The distribution of glycine turnover rates is consistent with release from Golgi cells, whereas alanine may be released from granule cell parallel fibers. Turnover rates measured in two other motor areas, the striatum and motor cortex, indicated that utilization of these amino acid neurotransmitters is differentially distributed in brain motor regions. The data indicate that turnover rate measurements may be useful in identifying neurotransmitter function where content measurements alone are insufficient.     

Bonded Cumomer Analysis of Human Melanoma Metabolism Monitored by 13C NMR Spectroscopy of Perfused Tumor Cells

A network model for the determination of tumor metabolic fluxes from ¹³C NMR kinetic isotopomer data has been developed and validated with perfused human DB-1 melanoma cells carrying the BRAF V600E mutation, which promotes oxidative metabolism. The model generated in the bonded cumomer formalism describes key pathways of tumor intermediary metabolism and yields dynamic curves for positional isotopic enrichment and spin-spin multiplets. Cells attached to microcarrier beads were perfused with 26 mm [1,6-¹³C₂]glucose under normoxic conditions at 37 °C and monitored by ¹³C NMR spectroscopy. Excellent agreement between model-predicted and experimentally measured values of the rates of oxygen and glucose consumption, lactate production, and glutamate pool size validated the model. ATP production by glycolytic and oxidative metabolism were compared under hyperglycemic normoxic conditions; 51% of the energy came from oxidative phosphorylation and 49% came from glycolysis. Even though the rate of glutamine uptake was ∼50% of the tricarboxylic acid cycle flux, the rate of ATP production from glutamine was essentially zero (no glutaminolysis). De novo fatty acid production was ∼6% of the tricarboxylic acid cycle flux. The oxidative pentose phosphate pathway flux was 3.6% of glycolysis, and three non-oxidative pentose phosphate pathway exchange fluxes were calculated. Mass spectrometry was then used to compare fluxes through various pathways under hyperglycemic (26 mm) and euglycemic (5 mm) conditions. Under euglycemic conditions glutamine uptake doubled, but ATP production from glutamine did not significantly change. A new parameter measuring the Warburg effect (the ratio of lactate production flux to pyruvate influx through the mitochondrial pyruvate carrier) was calculated to be 21, close to upper limit of oxidative metabolism.     

Quantification of central metabolic fluxes in the facultative methylotroph methylobacterium extorquens AM1 using 13C-label tracing and mass spectrometry

The metabolic fluxes of central carbon metabolism were measured in chemostat-grown cultures of Methylobacterium extorquens AM1 with methanol as the sole organic carbon and energy source and growth-limiting substrate. Label tracing experiments were carried out using 70% (13)C-methanol in the feed, and the steady-state mass isotopomer distributions of amino acids derived from total cell protein were measured by gas chromatography coupled to mass spectrometry. Fluxes were calculated from the isotopomer distribution data using an isotopomer balance model and evolutionary error minimization algorithm. The combination of labeled methanol with unlabeled CO(2), which enters central metabolism in two different reactions, provided the discriminatory power necessary to allow quantification of the unknown fluxes within a reasonably small confidence interval. In wild-type M. extorquens AM1, no measurable flux was detected through pyruvate dehydrogenase or malic enzyme, and very little flux through alpha-ketoglutarate dehydrogenase (1.4% of total carbon). In contrast, the alpha-ketoglutarate dehydrogenase flux was 25.5% of total carbon in the regulatory mutant strain phaR, while the pyruvate dehydrogenase and malic enzyme fluxes remained insignificant. The success of this technique with growth on C(1) compounds suggests that it can be applied to help characterize the effects of other regulatory mutations, and serve as a diagnostic tool in the metabolic engineering of methylotrophic bacteria.     

The anaplerotic substrate alanine stimulates acetate incorporation into glutamate and glutamine in rabbit kidney tubules. A (13)C NMR study

Although acetate, the main circulating volatile fatty acid in humans and animals, is metabolized at high rates by the renal tissue, little is known about the precise fate of its carbons and about the regulation of its renal metabolism. Therefore, we studied the metabolism of variously labeled [(13)C]acetate and [(14)C]acetate molecules and its regulation by alanine, which is also readily metabolized by the kidney, in isolated rabbit renal proximal tubules. With acetate as the sole substrate, 72% of the C-1 and 49% of the C-2 of acetate were released as CO(2); with acetate plus alanine, the corresponding values were decreased to 49 and 25%. The only other important products formed from the acetate carbons were glutamine, and to a smaller extent, glutamate. By combining (13)C NMR and radioactive and enzymatic measurements with a novel model of acetate metabolism, fluxes through the enzymes involved were calculated. Thanks to its anaplerotic effect, alanine caused a stimulation of acetate removal and a large increase in fluxes through pyruvate carboxylase, citrate synthase, and the enzymes involved in glutamate and glutamine synthesis but not in flux through alpha-ketoglutarate dehydrogenase. We conclude that the anaplerotic substrate alanine not only accelerates the disposal of acetate but also prevents the wasting of the latter compound as CO(2).     

Identification of Enzymes and Quantification of Metabolic Fluxes in the Wild Type and in a Recombinant Aspergillus oryzae Strain

Two α-amylase-producing strains of Aspergillus oryzae, a wild-type strain and a recombinant containing additional copies of the α-amylase gene, were characterized with respect to enzyme activities, localization of enzymes to the mitochondria or cytosol, macromolecular composition, and metabolic fluxes through the central metabolism during glucose-limited chemostat cultivations. Citrate synthase and isocitrate dehydrogenase (NAD) activities were found only in the mitochondria, glucose-6-phosphate dehydrogenase and glutamate dehydrogenase (NADP) activities were found only in the cytosol, and isocitrate dehydrogenase (NADP), glutamate oxaloacetate transaminase, malate dehydrogenase, and glutamate dehydrogenase (NAD) activities were found in both the mitochondria and the cytosol. The measured biomass components and ash could account for 95% (wt/wt) of the biomass. The protein and RNA contents increased linearly with increasing specific growth rate, but the carbohydrate and chitin contents decreased. A metabolic model consisting of 69 fluxes and 59 intracellular metabolites was used to calculate the metabolic fluxes through the central metabolism at several specific growth rates, with ammonia or nitrate as the nitrogen source. The flux through the pentose phosphate pathway increased with increasing specific growth rate. The fluxes through the pentose phosphate pathway were 15 to 26% higher for the recombinant strain than for the wild-type strain.     

A new framework for the estimation of control parameters in metabolic pathways using lin-log kinetics.

The control properties of biochemical pathways can be described by control coefficients and elasticities, as defined in the framework of metabolic control analysis. The determination of these parameters using the traditional metabolic control analysis relationships is, however, limited by experimental difficulties (e.g. realizing and measuring small changes in biological systems) and lack of appropriate mathematical procedures (e.g. when the more practical large changes are made). In this paper, the recently developed lin-log approach is proposed to avoid the above-mentioned problems and is applied to estimate control parameters from measurements obtained in steady state experiments. The lin-log approach employs approximative linear-logarithmic kinetics parameterized by elasticities and provides analytical solutions for fluxes and metabolite concentrations when large changes are made. Published flux and metabolite concentration data are used, obtained from a reconstructed section of glycolysis converting 3-phosphoglycerate to pyruvate [Giersch, C. (1995) Eur. J. Biochem. 227, 194-201]. With the lin-log approach, all data from different experiments can be combined to give realistic elasticity and flux control coefficient estimates by linear regression. Despite the large changes, a good agreement of fluxes and metabolite concentrations is obtained between the measured and calculated values according to the lin-log model. Furthermore, it is shown that the lin-log approach allows a rigorous statistical evaluation to identify the optimal reference state and the optimal model structure assumption. In conclusion, the lin-log approach addresses practical problems encountered in the traditional metabolic control analysis-based methods by introducing suitable nonlinear kinetics, thus providing a novel framework with improved procedures for the estimation of elasticities and control parameters from large perturbation experiments.     

Application of hybrid cybernetic model in simulating myeloma cell culture co-consuming glucose and glutamine with mixed consumption patterns

A dynamic model called hybrid cybernetic model (HCM) based on structured metabolic network is established for simulating mammalian cell metabolism featured with partially substitutable and partially complementary consumption patterns of two substrates, glucose and glutamine. Benefiting from the application of elementary mode analysis (EMA), the complicated metabolic network is decomposed into elementary modes (EMs) facilitating the employment of the hybrid cybernetic framework to investigate the external and internal flux distribution and the regulation mechanism among them. According to different substrate combination, two groups of EMs are obtained, i.e., EMs associated with glucose uptake and simultaneous uptake of glucose and glutamine. Uptake fluxes through various EMs are coupled together via cybernetic variables to maximize substrate uptake. External fluxes and internal fluxes could be calculated and estimated respectively, by the combination of the stoichiometrics of metabolic networks and fluxes through regulated EMs. The model performance is well validated via three sets of experimental data. Through parameter identification of limited number of experimental data, other external metabolites are precisely predicted. The obtained kinetic parameters of three experimental cultures have similar values, which indicates the robustness of the model. Furthermore, the prediction performance of the model is successfully validated based on identified parameters.     

Optimal selection of metabolic fluxes for in vivo measurement. I. Development of mathematical methods.

The measurement of uptake and secretion rates is often not sufficient to allow the calculation of all internal metabolic fluxes. Measurements of internal fluxes are needed and these additional measurements are used in conjunction with mass-balance equations to calculate the complete metabolic flux map. A method is presented that identifies the fluxes that should be selected for experimental measurement, and the fluxes that can be computed using the mass-balance equations. The criterion for selecting internal metabolic fluxes for measurement is that the values of the computed fluxes should have low sensitivity to experimental error in the measured fluxes. A condition number indicating the upper bound on this sensitivity, is calculated based on stoichiometry alone. The actual sensitivity is dependent on both the flux measurements and the error in flux measurements, as well as the stoichiometry. If approximate physiologic ranges of fluxes are known a realistic sensitivity can be computed. The exact sensitivity cannot be calculated since the experimental error is usually unknown. The most probable value of the actual sensitivity for a given selection of measured fluxes is estimated by selecting a large number of representative error vectors and calculating the actual sensitivity for each of these. A frequency distribution of actual sensitivities is thus obtained giving a representative range of actual sensitivities for a particular experimental situation.