Computational prediction of changes in brain metabolic fluxes during Parkinson’s disease from mRNA expression

Parkinson’s disease is a widespread neurodegenerative disorder which affects brain metabolism. Although changes in gene expression during disease are often measured, it is difficult to predict metabolic fluxes from gene expression data. Here we explore the hypothesis that changes in gene expression for enzymes tend to parallel flux changes in biochemical reaction pathways in the brain metabolic network. This hypothesis is the basis of a computational method to predict metabolic flux changes from post-mortem gene expression measurements in Parkinson’s disease (PD) brain.  We use a network model of central metabolism and optimize the correspondence between relative changes in fluxes and in gene expression. To this end we apply the Least-squares with Equalities and Inequalities algorithm integrated with Flux Balance Analysis (Lsei-FBA). We predict for PD (1) decreases in glycolytic rate and oxygen consumption and an increase in lactate production in brain cortex that correspond with measurements (2) relative flux decreases in ATP synthesis, in the malate-aspartate shuttle and midway in the TCA cycle that are substantially larger than relative changes in glucose uptake in the substantia nigra, dopaminergic neurons and most other brain regions (3) shifts in redox shuttles between cytosol and mitochondria (4) in contrast to Alzheimer’s disease: little activation of the gamma-aminobutyric acid shunt pathway in compensation for decreased alpha-ketoglutarate dehydrogenase activity (5) in the globus pallidus internus, metabolic fluxes are increased, reflecting increased functional activity.  Our method predicts metabolic changes from gene expression data that correspond in direction and order of magnitude with presently available experimental observations during Parkinson’s disease, indicating that the hypothesis may be useful for some biochemical pathways. Lsei-FBA generates predictions of flux distributions in neurons and small brain regions for which accurate metabolic flux measurements are not yet possible.

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To identify genes important to PD pathogenesis using microarrays and to investigate their potential to aid in diagnosing parkinsonism.



Microarray expression analysis of postmortem substantia nigra tissue.



Substantia nigra samples from 14 unrelated individuals were analyzed, including 6 with PD, 2 with progressive supranuclear palsy, 1 with frontotemporal dementia with parkinsonism, and 5 control subjects.



Identification of genes significantly differentially expressed (P<.05) using Affymetrix U133A microarrays.



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abstract: Prior 13C magnetic resonance spectroscopy (MRS) experiments, which simultaneously measured in vivo rates of total glutamate-glutamine cycling (Vcyc(tot)) and neuronal glucose oxidation (CMRglc(ox), N), revealed a linear relationship between these fluxes above isoelectricity, with a slope of ~1. In vitro glial culture studies examining glutamate uptake indicated that glutamate, which is cotransported with Na+, stimulated glial uptake of glucose and release of lactate. These in vivo and in vitro results were consolidated into a model: recycling of one molecule of neurotransmitter between glia and neurons was associated with oxidation of one glucose molecule in neurons; however, the glucose was taken up only by glia and all the lactate (pyruvate) generated by glial glycolysis was transferred to neurons for oxidation. The model was consistent with the 1:1 relationship between ΔCMRglc(ox), N and ΔVcyc(tot) measured by 13C MRS. However, the model could not specify the energetics of glia and γ-amino butyric acid (GABA) neurons because quantitative values for these pathways were not available. Here, we review recent 13C and 14C tracer studies that enable us to include these fluxes in a more comprehensive model. The revised model shows that glia produce at least 8% of total oxidative ATP and GABAergic neurons generate ~18% of total oxidative ATP in neurons. Neurons produce at least 88% of total oxidative ATP, and take up ~26% of the total glucose oxidized. Glial lactate (pyruvate) still makes the major contribution to neuronal oxidation, but ~30% less than predicted by the prior model. The relationship observed between ΔCMRglc(ox), N and ΔVcyc(tot) is determined by glial glycolytic ATP as before. Quantitative aspects of the model, which can be tested by experimentation, are discussed.

title: The contribution of GABA to glutamate/glutamine cycling and energy metabolism in the rat cortex in vivo.
abstract: Previous studies have shown that the glutamate/glutamine (Glu/Gln) neurotransmitter cycle and neuronal glucose oxidation are proportional (1:1), with increasing neuronal activity above isoelectricity. GABA, a product of Glu metabolism, is synthesized from astroglial Gln and contributes to total Glu/Gln neurotransmitter cycling, although the fraction contributed by GABA is unknown. In the present study, we used (13)C NMR spectroscopy together with i.v. infusions of [1,6-(13)C(2)]glucose and [2-(13)C]acetate to separately determine rates of Glu/Gln and GABA/Gln cycling and their respective tricarboxylic acid cycles in the rat cortex under conditions of halothane anesthesia and pentobarbital-induced isoelectricity. Under 1% halothane anesthesia, GABA/Gln cycle flux comprised 23% of total (Glu plus GABA) neurotransmitter cycling and 18% of total neuronal tricarboxylic acid cycle flux. In isoelectric cortex, glucose oxidation was reduced >3-fold in glutamatergic and GABAergic neurons, and neurotransmitter cycling was below detection. Hence, in both cell types, the primary energetic costs are associated with neurotransmission, which increase together as cortical activity is increased. The contribution of GABAergic neurons and inhibition to cortical energy metabolism has broad implications for the interpretation of functional imaging signals.

title: The effects of alternate optimal solutions in constraint-based genome-scale metabolic models.
abstract: Genome-scale constraint-based models of several organisms have now been constructed and are being used for model driven research. A key issue that may arise in the use of such models is the existence of alternate optimal solutions wherein the same maximal objective (e.g., growth rate) can be achieved through different flux distributions. Herein, we investigate the effects that alternate optimal solutions may have on the predicted range of flux values calculated using currently practiced linear (LP) and quadratic programming (QP) methods. An efficient LP-based strategy is described to calculate the range of flux variability that can be present in order to achieve optimal as well as suboptimal objective states. Sample results are provided for growth predictions of E. coli using glucose, acetate, and lactate as carbon substrates. These results demonstrate the extent of flux variability to be highly dependent on environmental conditions and network composition. In addition we examined the impact of alternate optima for growth under gene knockout conditions as calculated using QP-based methods. It was observed that calculations using QP-based methods can show significant variation in growth rate if the flux variability among alternate optima is high. The underlying biological significance and general source of such flux variability is further investigated through the identification of redundancies in the network (equivalent reaction sets) that lead to alternate solutions. Collectively, these results illustrate the variability inherent in metabolic flux distributions and the possible implications of this heterogeneity for constraint-based modeling approaches. These methods also provide an efficient and robust method to calculate the range of flux distributions that can be derived from quantitative fermentation data.

title: Perfusion and metabolism imaging studies in Parkinson's disease.
abstract: Positron emission tomography (PET) and single photon emission computed tomography (SPECT) are important tools in the evaluation of brain blood flow and glucose metabolism in Parkinson's disease (PD). However, conflicting results are reported in the literature depending on the type of imaging data analysis employed. The present review gives a comprehensive summary of the perfusion and metabolism literature in the field of PD research, including quantitative PET studies, normalized PET and SPECT studies, autoradiography studies in animal models of PD, and simulation studies of PD data. It is concluded that PD most likely is characterized by widespread cortical hypometabolism, probably even at early disease stages. Widespread subcortical hypermetabolism is probably not a feature of PD, although certain small basal ganglia structures, such as the external pallidum, may display true hypermetabolism in the absolute sense. This observation is also in agreement with the animal literature.

title: Proton MR spectroscopy of the brain in 14 patients with Parkinson disease.
abstract: To determine whether the proton spectra from patients with clinically diagnosed Parkinson disease differ from the spectra of age-matched healthy subjects with respect to the major cerebral metabolite resonances as well as lactate.



Fourteen patients with Parkinson disease (38 to 81 years of age) and 13 healthy control subjects (37 to 81 years of age) were studied using image-guided, single-voxel (27-cm3 volume) proton MR spectroscopy of the occipital lobe.



The peak area ratios of N-acetyl aspartate to creatine and N-acetyl aspartate to choline for Parkinson patients did not show a statistically significant difference from the corresponding ratios for control subjects. There was a very significant increase in the ratio of lactate to N-acetyl aspartate for patients with Parkinson disease, with the greatest increase (threefold) manifested by the subgroup (n = 4) with dementia. The difference in N-acetyl aspartate to choline between women (n = 7) with Parkinson disease and healthy women (n = 9) approached significance. No dependence of the peak ratios on age, duration of Parkinson disease, or medication (L-dopa) regimen was found.



Preliminary results indicating an increase in cerebral lactate in patients with Parkinson disease support the hypothesis that Parkinson disease is a systemic disorder characterized by an impairment of oxidative energy metabolism. The larger increases for Parkinson patients with dementia may be diagnostically useful in assessing clinical course and in differentiating Parkinson disease from other causes of dementia. Additional studies are needed, though, to quantitate lactate changes and identify potential contributions from lipid resonances better.

title: Dysregulation of glucose metabolism is an early event in sporadic Parkinson's disease☆
abstract: Unlike most other cell types, neurons preferentially metabolize glucose via the pentose phosphate pathway (PPP) to maintain their antioxidant status. Inhibiting the PPP in neuronal cell models causes cell death. In rodents, inhibition of this pathway causes selective dopaminergic cell death leading to motor deficits resembling parkinsonism. Using postmortem human brain tissue, we characterized glucose metabolism via the PPP in sporadic Parkinson's disease (PD), Alzheimer's disease (AD), and controls. AD brains showed increased nicotinamide adenine dinucleotide phosphate (NADPH) production in areas affected by disease. In PD however, increased NADPH production was only seen in the affected areas of late-stage cases. Quantifying PPP NADPH-producing enzymes glucose-6-phosphate dehydrogenase and 6-phosphogluconate dehydrogenase by enzyme-linked immunosorbent assay, showed a reduction in the putamen of early-stage PD and interestingly in the cerebellum of early and late-stage PD. Importantly, there was no decrease in enzyme levels in the cortex, putamen, or cerebellum of AD. Our results suggest that down-regulation of PPP enzymes and a failure to increase antioxidant reserve is an early event in the pathogenesis of sporadic PD.

title: Role of mitochondria in the etiology and pathogenesis of Parkinson's disease.
abstract: We discuss the etiology and pathogenesis of Parkinson's disease (PD). Our group and others have found a decrease in complex I of the mitochondrial electron transfer complex in the substantia nigra of patients with PD; in addition, we reported loss of the alpha-ketoglutarate dehydrogenase complex (KGDHC) in the substantia nigra. Dual loss of complex I and the KGDHC will deleteriously affect the electron transport and ATP synthesis; we believe that energy crisis is the most important mechanism of nigral cell death in PD. Oxidative stress has also been implicated as an important contributor to nigral cell death in PD, but we believe that oxidative stress is a secondary phenomenon to respiratory failure, because respiratory failure will increase oxygen free-radical formation and consume glutathione. The primary cause of mitochondrial respiratory failure has not been elucidated yet, but additive effect of environmental neurotoxins in genetically predisposed persons appears to be the most likely possibility.

title: Deficits in a tricarboxylic acid cycle enzyme in brains from patients with Parkinson’s disease
abstract: Parkinson's disease (PD) is associated with mitochondrial dysfunction, specifically a deficiency of complex I of the electron transport chain. Most, although not all, studies indicate that this deficiency is limited to brain regions with neurodegeneration. The current studies tested for deficiencies in other mitochondrial components in PD brain in a neuropathologically unaffected region where the abnormality cannot be attributed to secondary effects of neurodegeneration. The activity of a key (and arguably rate-limiting) tricarboxylic acid cycle enzyme, the alpha-ketoglutarate dehydrogenase complex (KGDHC), was measured in the cerebellum of patients with PD. Activity in 19 PD brains was 50.5% of that in 18 controls matched for age, sex, post-mortem interval, and method of preservation (P<0.0019). The protein subunits of KGDHC were present in normal amounts in PD brains, indicating a relatively discrete abnormality in the enzyme. The activities of another mitochondrial enzyme, glutamate dehydrogenase (GDH), were normal in PD brains. These results demonstrate that specific reductions in KGDHC occur even in pathologically unaffected areas in PD, where the decline is unlikely to be a non-specific result of neurodegeneration. Reductions in the activity of this enzyme, if widespread in the brain, may predispose vulnerable regions to further damage.

title: Differential neuronal activity in segments of globus pallidus in Parkinson's disease patients
abstract: Microelectrode trajectories through the globus pallidus of 6 Parkinson's disease (PD) patients yielded neurophysiological ‘landmarks' which enabled the identification of neurones located in the external segment (GPe) and internal segments, exterior (GPi,e) and interior (GPi,i) of globus pallidus and the surrounding borders (Bor). Firing rate histograms and inter-spike interval time histograms were constructed for neurones in each region. The neuronal activity in GPi,i was higher than in the other segments, and a high degree of bursting was found in GPe and GPi neurones. This profile of neuronal activity is similar to that observed in monkeys treated with MPTP, suggesting that the observed level of activity of neurones in GPi,i is excessive, and contributes to the bradykinesia and rigidity of PD patients.

title: Quantification of the GABA Shunt and the Importance of the GABA Shunt Versus the 2‐Oxoglutarate Dehydrogenase Pathway in GABAergic Neurons
abstract: We investigated the activity of the cerebral GABA shunt relative to the overall cerebral tricarboxylic acid (TCA) cycle and the importance of the GABA shunt versus 2‐oxoglutarate dehydrogenase for the conversion of 2‐oxoglutarate into succinate in GABAergic neurons. Awake mice were dosed with [1‐13C]glucose, and brain extracts were analyzed by 13C NMR spectroscopy. The percent enrichments of GABA C‐2 and glutamate C‐4 were the same: 5.0 ± 1.6 and 5.1 ± 0.2%, respectively (mean ± SD). This, together with previous data, indicates that the flux through the GABA shunt relative to the overall cerebral TCA cycle flux equals the GABA/glutamate pool size ratio, which in the mouse is 17%. It has previously been shown that under the experimental conditions used in this study, the 13C labeling of aspartate from [1‐13C]glucose specifically reflects the metabolic activity of GABAergic neurons. In the present study, the reduction in the formation of [13C]aspartate during inhibition of the GABA shunt by γ‐vinyl‐GABA indicated that not more than half the flux from 2‐oxoglutarate to succinate in GABAergic neurons goes via the GABA shunt. Therefore, because fluxes through the GABA shunt and 2‐oxoglutarate dehydrogenase in GABAergic neurons are approximately the same, the TCA cycle activity of GABAergic neurons could account for one‐third of the overall cerebral TCA cycle activity in the mouse. Treatment with γ‐vinyl‐GABA, which increased GABA levels dramatically, caused changes in the 13C labeling of glutamate and glutamine, which indicated a reduction in the transfer of glutamate from neurons to glia, implying reduced glutamatergic neurotransmission. In the most severely affected animals these alterations were associated with convulsions.

title: The operation of the gamma-aminobutyrate bypath of the tricarboxylic acid cycle in brain tissue in vitro.
abstract: 1. Cerebral-cortex slices prelabelled with gamma-amino[1-(14)C]butyrate (GABA) were incubated in a glucose-saline medium. After the initial rapid uptake there was no appreciable re-entry of (14)C into the GABA pool, either from the medium or from labelled metabolites formed in the tissue. The kinetic constants of GABA metabolism were determined by computer simulation of the experimental results by using mathematical procedures. The GABA flux was estimated to be 0.03mumol per min/g, or about 8% of the total flux through the tricarboxylic acid cycle. It was found that the assumption of compartmentation did not greatly affect the estimates of the GABA flux. 2. The time-course of incorporation of (14)C into amino acids associated with the tricarboxylic acid cycle was followed with [1-(14)C]GABA and [U-(14)C]-glucose as labelled substrates. The results were consistent with the utilization of GABA via succinate. This was confirmed by determining the position of (14)C in the carbon skeletons of aspartate and glutamate formed after the oxidation of [1-(14)C]GABA. These results also indicated that under the experimental conditions the reversal of reactions catalysed by alpha-oxoglutarate dehydrogenase and glutamate decarboxylase respectively was negligible. The conversion of [(14)C]GABA into gamma-hydroxybutyrate was probably also of minor importance, but decarboxylation of oxaloacetate did occur at a relatively slow rate. 3. When [1-(14)C]GABA was the labelled substrate there was evidence of a metabolic compartmentation of glutamate since, even before the peak of the incorporation of (14)C into glutamate had been reached, the glutamine/glutamate specific-radioactivity ratio was greater than unity. When [U-(14)C]glucose was oxidized this ratio was less than unity. The heterogeneity of the glutamate pool was indicated also by the relatively high specific radioactivity of GABA, which was comparable with that of aspartate during the whole incubation time (40min). The rates of equilibration of labelled amino acids between slice and medium gave evidence that the permeability properties of the glutamate compartments labelled as a result of oxidation of [1-(14)C]GABA were different from those labelled by the metabolism of [(14)C]glucose. The results showed therefore that in brain tissue incubated under the conditions used, the organization underlying metabolic compartmentation was preserved. The observed concentration ratios of amino acids between tissue and medium were also similar to those obtaining in vivo. These ratios decreased in the order: GABA>acidic acids>neutral amino acids>glutamine. 4. The approximate pool sizes of the amino acids in the different metabolic compartments were calculated. The glutamate content of the pool responsible for most of the labelling of glutamine during oxidation of [1-(14)C]GABA was estimated to be not more than 30% of the total tissue glutamate. The GABA content of the ;transmitter pool' was estimated to be 25-30% of the total GABA in the tissue. The structural correlates of metabolic compartmentation were considered.

title: Large-scale in silico modeling of metabolic interactions between cell types in the human brain
abstract: Metabolic interactions between multiple cell types are difficult to model using existing approaches. Here we present a workflow that integrates gene expression data, proteomics data and literature-based manual curation to model human metabolism within and between different types of cells. Transport reactions are used to account for the transfer of metabolites between models of different cell types via the interstitial fluid. We apply the method to create models of brain energy metabolism that recapitulate metabolic interactions between astrocytes and various neuron types relevant to Alzheimer's disease. Analysis of the models identifies genes and pathways that may explain observed experimental phenomena, including the differential effects of the disease on cell types and regions of the brain. Constraint-based modeling can thus contribute to the study and analysis of multicellular metabolic processes in the human tissue microenvironment and provide detailed mechanistic insight into high-throughput data analysis.

title: The Globus Pallidus, Deep Brain Stimulation, and Parkinson's Disease
abstract: Parkinson's disease (PD) is caused by the degeneration of the dopaminergic neurons in the substantia nigra. Loss of dopaminergic innervation leads to hyperactivity in the internal segment of the globus pallidus (GPi), the main output nucleus of the basal ganglia and to a profound disturbance in the function of motor circuits. Lesions of the GPi (or in its upstream modulator, the subthalamic nucleus) can greatly improve the motor symptoms of PD presumably by reducing this pathological activity. Paradoxically, high-frequency electrical stimulation of the GPi (deep brain stimulation, DBS) mimics the effects of pallidotomy and has become an accepted therapeutic technique. The mechanisms underlying the beneficial effects of pallidal DBS are not known. Various mechanisms that might account for inhibiting or disrupting the pathological pallidal outflow by high-frequency DBS have been proposed ranging from depolarization block to stimulation-evoked release of GABA, and these are discussed.

title: Effects of GPi and STN inactivation on physiological, motor, cognitive and motivational processes in animal models of Parkinson's disease.
abstract: Loss of the dopaminergic input to the striatum, characterizing Parkinson's disease, leads to the hyper-activity of two key nuclei of the basal ganglia (BG): the subthalamic nucleus (STN) and the internal segment of the globus pallidus (GPi). The anatomo-physiological organization of the BG and their output suggested that interfering with such hyper-activity could restore motor function and improve parkinsonism. Several animal models in rodents and primates, as well as clinical studies and neurosurgical treatments, have confirmed such hypothesis. This chapter will review the physiological and behavioural data obtained by inactivating the GPi or the STN by means of lesions, pharmacological approaches and deep brain stimulation. The consequences of these treatments will be examined at levels ranging from cellular to complex behavioural changes. Some of this experimental evidence suggested new and effective clinical treatments for PD, which are now routinely used worldwide. However, further studies are necessary to better understand the consequences of GPi and STN manipulation especially at the cognitive level in order to improve functional neurosurgical treatments for Parkinson's disease by minimizing risks of side-effects.

title: Reconstruction and flux analysis of coupling between metabolic pathways of astrocytes and neurons: application to cerebral hypoxia
abstract: BackgroundIt 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. 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.ResultsThe 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.ConclusionThe 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.

title: Systems-level analysis of mechanisms regulating yeast metabolic flux
abstract: Quantitation of metabolic pathway regulation Although metabolic biochemical pathways are well understood, less is known about precisely how reaction rates or fluxes through the various enzymes are controlled. Hackett et al. developed a method to quantitate such regulatory influence in yeast. They monitored concentrations of metabolites, enzymes, and potential regulators by LC-MS/MS (liquid chromatography–tandem mass spectrometry) and isotope ratio measurements for 56 reactions, over 100 metabolites, and 370 metabolic enzymes in yeast in 25 different steady-state conditions. Bayesian analysis was used to examine the probability of regulatory interactions. Regulation of flux through the pathways was predominantly controlled by changes in the concentration of small-molecule metabolites rather than changes in enzyme abundance. The analysis also revealed previously unrecognized regulation between pathways. Science, this issue p. 432 Metabolomics, proteomics, and flux analysis are used to dissect quantitatively metabolic regulation in living yeast.  Metabolism is among the most strongly conserved processes across all domains of life and is crucial for both bioengineering and disease research, yet we still have an unclear understanding of how metabolic rates (fluxes) are determined. Qualitatively, this deficiency involves missing knowledge of enzyme regulators. Quantitatively, it involves limited understanding of the relative contributions of enzyme and metabolite concentrations in controlling flux across physiological conditions. Addressing these gaps has been challenging because in vitro biochemical approaches lack the physiological context, whereas models of cellular metabolic dynamics have limited capacity for identifying or quantitating specific regulatory events because of overall model complexity.  Flux through individual metabolic reactions is directly determined by the concentrations of enzyme, substrates, products, and any allosteric regulators, as captured quantitatively by a Michaelis-Menten–style reaction equation. Analogous to how experimental variation of reaction species in vitro allows for the inference of regulators and reaction equation kinetic parameters, physiological changes in flux entail a change in reaction species that can be used to determine reaction equations on the basis of cellular data. This requires measurement across multiple biological conditions of flux, enzyme concentrations, and metabolite concentrations. We reasoned that chemostat cultures could be used to induce predictable and strong flux changes, with changes in enzymes and metabolites measurable by proteomics and metabolomics. By directly relating cellular flux to the reaction species that determine it, we can carry out regulatory inference at the level of single metabolic reactions by using cellular data. An important benefit is that the physiological significance of any identified regulator is implicit from its role in determining cellular flux.  Here we introduce systematic identification of meaningful metabolic enzyme regulation (SIMMER). We measured fluxes, and metabolite and enzyme concentrations, in each of 25 yeast chemostats. For each of 56 reactions for which the flux, enzyme, and substrates were measured, we determined whether variation in measured flux could be explained by simple Michaelis-Menten kinetics. We also evaluated alternative models of each reaction’s kinetics that included a suite of allosteric regulators drawn from across all organisms. For 46 reactions, we were able to identify a useful kinetic model, with 17 reactions not including any regulation and 29 reactions being regulated by one to two allosteric regulators. Three previously unrecognized cross-pathway regulatory interactions were validated biochemically. These included inhibition of pyruvate kinase by citrate and inhibition of pyruvate decarboxylase by phenypyruvate. These metabolites accumulated and thereby curtailed glycolytic outflow and ethanol production in nitrogen-limited yeast. For well-supported reaction forms, we were able to determine the extent to which nutrient-based changes in flux were determined by changes in the concentrations of individual reaction species. We find that substrates are the most important determinant of fluxes in general, with enzymes and allosteric regulators having a comparably important role in the case of physiologically irreversible reactions.  By connecting changes in flux to their root cause, SIMMER parallels classic in vitro approaches, but it allows simultaneous testing of numerous regulators of many reactions under physiological conditions. Its application to yeast showed that changes in flux across nutrient conditions are predominantly due to metabolite, not enzyme, levels. Thus, yeast metabolism is substantially self-regulating. Integrative analysis of fluxes and metabolite and enzyme concentrations by SIMMER. Measured flux is related, on a reaction-by-reaction basis, to enzyme and metabolite concentrations through a Michaelis-Menten equation. The extent to which variation in flux across experimental conditions can be explained by the enzyme, substrates, and products is assessed. If unregulated kinetics disagrees with the measured flux, we test a set of possible allosteric regulators to determine which, if any, regulators are supported on the basis of improvement in fit. Cellular metabolic fluxes are determined by enzyme activities and metabolite abundances. Biochemical approaches reveal the impact of specific substrates or regulators on enzyme kinetics but do not capture the extent to which metabolite and enzyme concentrations vary across physiological states and, therefore, how cellular reactions are regulated. We measured enzyme and metabolite concentrations and metabolic fluxes across 25 steady-state yeast cultures. We then assessed the extent to which flux can be explained by a Michaelis-Menten relationship between enzyme, substrate, product, and potential regulator concentrations. This revealed three previously unrecognized instances of cross-pathway regulation, which we biochemically verified. One of these involved inhibition of pyruvate kinase by citrate, which accumulated and thereby curtailed glycolytic outflow in nitrogen-limited yeast. Overall, substrate concentrations were the strongest driver of the net rates of cellular metabolic reactions, with metabolite concentrations collectively having more than double the physiological impact of enzymes.

title: Context-Specific Metabolic Networks Are Consistent with Experiments
abstract: Reconstructions of cellular metabolism are publicly available for a variety of different microorganisms and some mammalian genomes. To date, these reconstructions are “genome-scale” and strive to include all reactions implied by the genome annotation, as well as those with direct experimental evidence. Clearly, many of the reactions in a genome-scale reconstruction will not be active under particular conditions or in a particular cell type. Methods to tailor these comprehensive genome-scale reconstructions into context-specific networks will aid predictive in silico modeling for a particular situation. We present a method called Gene Inactivity Moderated by Metabolism and Expression (GIMME) to achieve this goal. The GIMME algorithm uses quantitative gene expression data and one or more presupposed metabolic objectives to produce the context-specific reconstruction that is most consistent with the available data. Furthermore, the algorithm provides a quantitative inconsistency score indicating how consistent a set of gene expression data is with a particular metabolic objective. We show that this algorithm produces results consistent with biological experiments and intuition for adaptive evolution of bacteria, rational design of metabolic engineering strains, and human skeletal muscle cells. This work represents progress towards producing constraint-based models of metabolism that are specific to the conditions where the expression profiling data is available.

title: Genome-level transcription data of Yersinia pestis analyzed with a New metabolic constraint-based approach
abstract: BackgroundConstraint-based computational approaches, such as flux balance analysis (FBA), have proven successful in modeling genome-level metabolic behavior for conditions where a set of simple cellular objectives can be clearly articulated. Recently, the necessity to expand the current range of constraint-based methods to incorporate high-throughput experimental data has been acknowledged by the proposal of several methods. However, these methods have rarely been used to address cellular metabolic responses to some relevant perturbations such as antimicrobial or temperature-induced stress. Here, we present a new method for combining gene-expression data with FBA (GX-FBA) that allows modeling of genome-level metabolic response to a broad range of environmental perturbations within a constraint-based framework. The method uses mRNA expression data to guide hierarchical regulation of cellular metabolism subject to the interconnectivity of the metabolic network.ResultsWe applied GX-FBA to a genome-scale model of metabolism in the gram negative bacterium Yersinia pestis and analyzed its metabolic response to (i) variations in temperature known to induce virulence, and (ii) antibiotic stress. Without imposition of any a priori behavioral constraints, our results show strong agreement with reported phenotypes. Our analyses also lead to novel insights into how Y. pestis uses metabolic adjustments to counter different forms of stress.ConclusionsComparisons of GX-FBA predicted metabolic states with fluxomic measurements and different reported post-stress phenotypes suggest that mass conservation constraints and network connectivity can be an effective representative of metabolic flux regulation in constraint-based models. We believe that our approach will be of aid in the in silico evaluation of cellular goals under different conditions and can be used for a variety of analyses such as identification of potential drug targets and their action.

title: Interpreting Expression Data with Metabolic Flux Models: Predicting Mycobacterium tuberculosis Mycolic Acid Production
abstract: Metabolism is central to cell physiology, and metabolic disturbances play a role in numerous disease states. Despite its importance, the ability to study metabolism at a global scale using genomic technologies is limited. In principle, complete genome sequences describe the range of metabolic reactions that are possible for an organism, but cannot quantitatively describe the behaviour of these reactions. We present a novel method for modeling metabolic states using whole cell measurements of gene expression. Our method, which we call E-Flux (as a combination of flux and expression), extends the technique of Flux Balance Analysis by modeling maximum flux constraints as a function of measured gene expression. In contrast to previous methods for metabolically interpreting gene expression data, E-Flux utilizes a model of the underlying metabolic network to directly predict changes in metabolic flux capacity. We applied E-Flux to Mycobacterium tuberculosis, the bacterium that causes tuberculosis (TB). Key components of mycobacterial cell walls are mycolic acids which are targets for several first-line TB drugs. We used E-Flux to predict the impact of 75 different drugs, drug combinations, and nutrient conditions on mycolic acid biosynthesis capacity in M. tuberculosis, using a public compendium of over 400 expression arrays. We tested our method using a model of mycolic acid biosynthesis as well as on a genome-scale model of M. tuberculosis metabolism. Our method correctly predicts seven of the eight known fatty acid inhibitors in this compendium and makes accurate predictions regarding the specificity of these compounds for fatty acid biosynthesis. Our method also predicts a number of additional potential modulators of TB mycolic acid biosynthesis. E-Flux thus provides a promising new approach for algorithmically predicting metabolic state from gene expression data.

title: RELATCH: relative optimality in metabolic networks explains robust metabolic and regulatory responses to perturbations
abstract: Predicting cellular responses to perturbations is an important task in systems biology. We report a new approach, RELATCH, which uses flux and gene expression data from a reference state to predict metabolic responses in a genetically or environmentally perturbed state. Using the concept of relative optimality, which considers relative flux changes from a reference state, we hypothesize a relative metabolic flux pattern is maintained from one state to another, and that cells adapt to perturbations using metabolic and regulatory reprogramming to preserve this relative flux pattern. This constraint-based approach will have broad utility where predictions of metabolic responses are needed.

title: The GABA and substance P input to dopaminergic neurones in the substantia nigra of the rat
abstract: In order to examine the synaptic input to dopaminergic neurones in the substantia nigra from GABAergic terminals and terminals that contain substance P, double and triple immunocytochemical studies were carried out at the light and electron microscopic levels in the rat. In a first series of experiments sections of the substantia nigra were incubated to reveal axon terminals containing either substance P or glutamate decarboxylase and then incubated to reveal dopaminergic neurones using tyrosine hydroxylase immunocytochemistry. Examination of this material in the light microscope revealed that many substance P- and glutamate decarboxylase-immunoreactive boutons were associated with the dopaminergic cells. In the electron microscope it was found that the perikarya and dendrites of the dopaminergic neurons received symmetrical synaptic input from terminals that displayed immunoreactivity for substance P or glutamate decarboxylase. A small proportion of the substance P-positive boutons formed asymmetrical synapses. In a second series of experiments sections of the substantia nigra were processed by the pre-embedding immunocytochemical technique for tyrosine hydroxylase and then the post-embedding immunogold technique for gamma-aminobutyric acid (GABA). Examination in the electron microscope revealed that the tyrosine hydroxylase-positive neurons received symmetrical synaptic input from many GABA-positive terminals. Quantitative analyses demonstrated that a minimum of 50-70% of all boutons afferent to the dopaminergic neurones display glutamate decarboxylase or GABA immunoreactivity. Triple immunocytochemical studies i.e. pre-embedding immunocytochemistry for tyrosine hydroxylase and substance P, combined with post-embedding immunogold staining for GABA, revealed that some of the substance P-immunoreactive boutons that were in contact with the dopaminergic neurones also displayed GABA immunoreactivity. In a third series of experiments the combination of anterograde transport of lectin-conjugated horseradish peroxidase or biocytin with post-embedding GABA immunocytochemistry demonstrated that at least one of the sources of GABA-containing terminals in the substantia nigra is the striatum. The results of the present study: (1) demonstrate that dopaminergic neurones in the substantia nigra receive symmetrical synaptic input from GABAergic and substance P-containing terminals, (2) show that a proportion of these terminals contain both substance P and GABA and (3) suggest that the major synaptic input to dopaminergic neurones is from GABAergic terminals and that a part of this innervation is derived from the striatum.