The study of metabolism has attracted much attention during the last years due to its relevance in various diseases. The advance in metabolomics platforms allows us to detect an increasing number of metabolites in abnormal high/low concentration in a disease phenotype. Finding a mechanistic interpretation for these alterations is important to understand pathophysiological processes, however it is not an easy task. The availability of genome scale metabolic networks and Systems Biology techniques open new avenues to address this question.L-Cystine and Homocysteine) found in high concentration in the brain of patients with mental disorders. Our results were discussed based on literature and found a good agreement with previously reported mechanisms. In addition, we hypothesize a novel role of several enzymes for the accumulation of these metabolites, which opens new strategies to understand the metabolic processes underlying these diseases.In this article we present a novel mathematical framework to find enzymes whose malfunction explains the accumulation/depletion of a given metabolite in a disease phenotype. Our approach is based on a recently introduced pathway concept termed Carbon Flux Paths (CFPs), which extends classical topological definition by including network stoichiometry. Using CFPs, we determine the Connectivity Curve of an altered metabolite, which allows us to quantify changes in its pathway structure when a certain enzyme is removed. The influence of enzyme removal is then ranked and used to explain the accumulation/depletion of such metabolite. For illustration, we center our study in the accumulation of two metabolites (With personalized medicine on the horizon, metabolomic platforms are providing us with a vast amount of experimental data for a number of complex diseases. Our approach provides a novel apparatus to rationally investigate and understand metabolite alterations under disease phenotypes. This work contributes to the development of Systems Medicine, whose objective is to answer clinical questions based on theoretical methods and high-throughput “omics” data. Metabolism comprises the inter-conversion of small molecules (metabolites) through enzymatically catalyzed biochemical reactions. These metabolites play a key role in different cellular functions, ranging from energy production to biosynthesis of complex macro-molecules. Metabolic alterations have been reported in a number of multifactorial diseases . In partFor this purpose, it is of utmost importance to exploit the information given by the spearhead experimental technologies that directly or indirectly provide a metabolic picture of different human samples. Gene expression analysis , quantitThe field of metabolomics has experienced a remarkable advance in mass spectrometry techniques and currently can measure hundreds of metabolites simultaneously . In contAssorted methods can be found in the literature to interpret metabolomics data based on curated metabolic pathways and networks . On the In this article, we address the question as to find the key enzymes regarding the accumulation/depletion of identified metabolites ”, which summarizes the structure of pathways consuming (producing) an identified metabolite and their underlying distances in a genome-scale metabolic network. Pathway distances are used as a clue for their fluxes in line with several theoretical works that show that shorter pathways support a higher flux than longer pathways -25. UsinIn order to determine metabolic pathways and distances in CCs, we used Carbon Flux Paths (CFPs), a network-based pathway concept recently introduced by Pey et al. . The CFPL-Cysteine and Homocysteine) closely related with mental disorders.Based on CCs, we rank enzymes in the network as responsible for the accumulation (depletion) of an identified metabolite. To assess the performance of our approach, we investigated key enzymes corresponding to the accumulation of two metabolites  from such identified metabolite. In order to determine whether this identified metabolite is connected to other metabolites and their distances, we used the Carbon Flux Paths (CFPs) approach. The CFP algorithm searches for the shortest path between a pair of source and target metabolites in the context of the metabolic network, which is here represented as a metabolite-metabolite directed graph. To avoid not biologically meaningful shortcuts, we removed arcs not involving an effective carbon exchange. The use of integer linear programming allows us to impose further constraints. In particular, we incorporate reaction stoichiometry and force paths to satisfy the mass balance equation and perform in sustained steady-state. Further details can be found in Methods section.Assume a metabolite is identified in significantly high concentration and we are concerned with finding enzymes whose malfunction explains its accumulation. For this purpose, we introduce the connectivity curve (CC), which plots the number of metabolites connected after moving away Glucose (D-Glc) and three output fluxes of CO2, ribose-5-phosphate (R5P) and Pyruvate (Pyr). We assumed that Glucose-6-Phosphate (G6P) is identified in high concentration and therefore enzymes responsible for its accumulation are evaluated. Based on CFPs, we calculated the minimum number of steps (reactions) necessary to reach any metabolite from G6P, e.g. 7 steps are required to reach Pyr. Note that the CFP approach is applied once for each metabolite different to G6P. Red solid line in Figure To illustrate the concept of CCs, consider the example metabolic network in Figure E. coli evolution studies that the decrease in the number of active reaction steps and increase in growth rate occur simultaneously [We assume that distances (number of steps) provide a clue of the degradation fluxes (velocity) of the metabolite under study, namely shorter distances imply higher fluxes. A more efficient use of resources via shorter pathways overall allows reactions to carry higher fluxes, which indirectly increases the capacity to produce biomass and energy. In particular, shorter pathways reduce mass leaks, wasted energy and the amount of protein required to catalyze a process, as discussed in a number of theoretical works -25. Theraneously .i.e. we remove one-by-one each reaction from the metabolic network and re-calculate the CC for the identified metabolite. To illustrate this, green dashed line in Figure phosphoglucoisomerase (Pgi) was knocked out. We can observe now that from G6P 1 metabolite can be reached in 1 step; 2 metabolites in 2 steps; 3 metabolites in 3 steps, etc.; finally reaching 17 metabolites in 10 steps. It is clear that the knockout of Pgi causes an increase in the distances from G6P to the rest of the metabolic network. The effect of this knockout in the set of CFPs from G6P to the rest of metabolites can be found in the Additional file Based on the above, CCs can be used to evaluate changes in CFP distances in different scenarios. We particularly focus here on single reaction knockouts, We hypothesize that the distance increase observed in our CCs approach after knocking-out a particular enzyme represents a decrease in the degradation flux of our identified metabolite, which may lead to its accumulation. As noted above, the basis is that shorter paths carry higher flux -25 and tj is knocked out, we introduce the length increasing parameter (∆Lj), which essentially averages distance differences between the knockout and wild-type scenarios (see Methods section). Note that we may have the case that, when an enzyme is knocked out, a number of metabolites become disconnected from the metabolite under study. In order to determine ∆Lj, we only consider changes in the distance to metabolites that remain connected after the knockout. To illustrate this consider the blue dotted line in Figure triosephosphate isomerase (TpiA) was knocked out. We can observe that 16 metabolites are now reached from G6P, namely one less than in the wild-type scenario. In particular, dihydroxyacetone phosphate (DHAP) cannot be reached from G6P since TpiA is essential for its mass balance. Although we can still find routes linking G6P and DHAP, none of them can be mass balanced  allows us to rank enzymes as responsible for the accumulation of the metabolite under consideration. Clearly, we are interested in enzymes that when knocked out present a high ∆Lj, which can potentially explain the accumulation of the metabolite of interest. Figure ∆Lj in our example metabolic network. Pgi constitutes the most relevant enzyme for the accumulation of G6P. Indeed, blocking Pgi eliminates the classical pathways for glucose consumption, but others are still available. This can be easily observed in the analysis of Elementary Flux Modes (EFMs) conducted in the seminal work of Schuster et al. [This parameter  disconnects the biosynthesis of Pyr from D-Glc, which violates our rule above and therefore it is not considered further. Instead, when TpiA is knocked out, although DHAP is disconnected from G6P, the connectivity between D-Glc and Pyr, CO2 and R5P is still found and therefore it is a viable knockout. Rows in the table in Figure As noted above, the knockout of certain enzymes may bring about the disconnection of pairs of metabolites. Clearly, if key metabolites are disconnected, important damage in cellular functions may be caused, even leading to cellular death. As we assume that phenotypic changes in metabolite abundance are more subtle, we are not aiming here at enzyme knockouts producing radical disconnections. Instead, we search for knockouts impairing but not disrupting the normal functioning of metabolic processes. For this purpose, we only consider enzymes that when knocked out do not alter the connectivity between the inputs (medium metabolites) and outputs (excreted metabolites) of the metabolic network. Note that we could impose other criteria, i.e. knocking out a certain enzyme would only lead to significant changes in distances from a unique metabolite. To evaluate this, we introduce a parameter representing the specificity of the actual enzyme knockout for the accumulation of the metabolite under study. In particular, we assigned a p-value for each enzyme, which defines the probability of finding such enzyme in an equal/better position in the ranking of a different metabolite. Details can be found in Methods section. Figure i.e. those having a small p-value. But a high p-value might not be undesired for other questions, since complex diseases may potentially present alterations in the concentration of more than one metabolite.For the sake of simplicity, it would be preferable to relate each enzyme with a unique metabolite accumulation, L-Cysteine (LCystin) and Homocysteine (HCys), metabolites found in high concentration in some mental disorders. For this purpose, we used the human metabolic network Recon1 [i.e. available substrates. In this work a minimal medium based on glucose and amino acids was used [In this sub-section we apply the approach presented above to rank enzymes responsible for the accumulation of k Recon1 . As othewas used . We allo2, AMP, ATP and ADP, as typically done in others works [As noted above, to avoid not meaningful shortcuts when applying the CFP method, we removed arcs not involving an effective carbon exchange in each reaction. Based on Recon1, a list of pairs of metabolites exchanging carbon atoms for each reaction was built , also referred to as cysteine dioxigenase, which presents ∆Lj≈0.7. Perry et al. [The first enzyme in the ranking is y et al.  reportedformaldehyde dehydrogenase (FALDH) and S-Formylglutathione hydralase (SFGTH) both with ∆Lj=0.638. FALDH is currently split into two independent reactions: EC 4.4.1.22 Glutathione-dependent formaldehyde-activating enzyme, GFAE, and EC 1.1.1.284 S-(hydroxymethyl) glutathione dehydrogenase, ADH3 [In the second and third position appear se, ADH3 .Formaldehyde, a highly toxic metabolite previously reported in several mental disorders [Formaldehyde concentration. In light of this, some authors proposed to increase the activity of these Formaldehyde-consuming enzymes so as to decrease brain damage [Formaldehyde presence but also LCystin concentration. Note that FALDH and SFGTH have a greater p-value, which indicates that they are not as specific to the LCystin accumulation as CYSO. Hence, finding effects on other metabolites in the literature does not seem out of place.GFAE consumes isorders ,42. A knisorders . In essen damage . We suggsulfite oxidase (SULFOX) with ∆Lj=0.637. An insufficiency of this enzyme causes a disease known as sulfite oxidase deficiency, characterized by neurological disorders, mental retardation and brain degradation [Sulfite, Sulfate, H2O and H+) and cofactors (Ferricytochrome c and Ferrocytochrome c). However, this reaction is important to mass balance the obtained paths. When it is knocked out, original short paths become unavailable and the average distance increases. This remark highlights the importance of balancing the paths as previously claimed in Pey et al. [The last enzyme included in Table radation . Dublin radation , measurey et al. .A similar study was conducted for the accumulation of HCys, which has been previously linked to Alzheimer's disease (AD) ,48. FullPhosphatidylethanolamine N-methyltransferase (PEMT), with ∆Lj=0.768. This mitochondrial enzyme catalyzes the methylation of Phosphatidylethanolamine (PE) producing Phosphatidylcholine (PC). This enzyme has been previously related with AD. In Johnson and Blusztajn [S-Adenosyl-L-homocysteine (SAH) as a possible cause for the malfunction of this enzyme in liver for AD patients. Interestingly, in that work evidences are also found to relate the inhibition of PEMT and the accumulation of HCys, which is in line with our hypothesis.The first enzyme in the ranking is lusztajn , this enlusztajn . They lolusztajn , aims atS-Adenosyl-L-methionine reversible transport (SLC25A26) is found in the second position in Table ∆Lj=0.768. This enzyme transports mitochondrial SAH into cytosol and cytosolic S-Adenosyl-L-methionine (SAM) into mitochondria. It should be pointed out that this is the only mechanism producing mitochondrial SAM in the network under study [i.e. the lack of SLC25A26 inhibits PEMT since the latter cannot perform in sustained steady-state without the former. From a different perspective, note that the inhibition of SLC25A26 may lead to the accumulation of SAH in mitochondria since, to our knowledge, this enzyme is the only one consuming SAH in such compartment. Following the hypothesis presented in Selley [sport SLC5A26 is fer study . As thisn Selley , this won Selley .Phosphatidylserine decarboxylase (PISD), with ∆Lj= 0.767. This mitochondrial enzyme decarboxylases Phosphatidylserine (Pser) producing a molecule of PE and CO2. A direct effect when the activity of PISD decays is the accumulation of PSer, which has been indicated as a molecular signature of AD patients [Next enzyme appearing in Table patients . In addipatients , providephosphatidylserine flippase (PSFLIP), also with ∆Lj= 0.767. PSFLIP is an ATP-consuming transporter of Pser from the cytosol to the mitochondria. This enzyme helps to maintain the membrane lipid bilayer asymmetry. When asymmetric collapse occurs, a signaling mechanism of synaptosomal apoptosis is triggered [The last enzyme appearing in Table riggered , as it origgered . In Castriggered  it is prriggered .In conclusion, based on the literature, we found that the deficit of PEMT seems to have a direct connection with HCys accumulation in AD. Instead, the role of SLC25A26, PISD and PSFLIP is hypothetical. As SLC25A26 is essential for the activity of PEMT, its implication in HCys accumulation seems plausible, though additional experimental evidence is required. With respect to PISD and PSFLIP, we found an indirect association with HCys concentration through shared AD diagnosis. As AD is a complex disease, this link is not particularly compelling. Therefore, experimental work is required to validate the role of PISD and PSFLIP in HCys accumulation.L-Cystine (LCystin) and Homocysteine (HCys) in mental disorders. Results were then discussed based on literature and found a good agreement with previously reported mechanisms. In addition, we hypothesize a novel role of several enzymes for the accumulation of these metabolites, which opens new strategies to understand the metabolic processes underlying these diseases. This is illustrated, for example, with S-Adenosyl-L-methionine reversible transport (SLC25A26), whose relevance for the accumulation of HCys, to our knowledge, has not been previously reported.In this work, we present a novel network-based framework to find candidate enzymes whose malfunction is responsible for the accumulation of a given metabolite. Our approach was applied to investigate the accumulation of j is removed via ∆Lj, namely based on the logic that an increase of distances in its degradation (biosynthesis) pathways potentially explains its accumulation (depletion). The central hypothesis here is that shorter pathways carry higher flux than longer pathways. This assumption is supported by several theoretical works and it seems plausible, particularly according to the results obtained. However, the integration of “omics” data into our approach, especially proteomics and gene expression data, constitutes a future research direction with the aim of providing a more realistic pathway activity.Our in-silico framework is mainly founded on the study of Connectivity Curves (CCs) of the metabolite under study in different scenarios. In particular, CCs summarize the pathway structure from an identified metabolite and their underlying distances, which are used as a clue for their fluxes. For the metabolite under study, we evaluate changes in CCs when an enzyme In order to complement the ranking arising from CCs, we introduced a p-value for each enzyme, which is a quantitative parameter indicating the specificity of a particular enzyme knockout/malfunction to explain the metabolite alteration under consideration. For the sake of simplicity, we preferably focused on enzymes with higher specificity for the accumulation/depletion of the metabolite under study. However, a high p-value might not be undesired for other biological questions, since complex diseases may potentially present alterations in the concentration of more than one metabolite. This possibility will be explored in the future.In addition, in our approach we did not consider enzyme knockouts disrupting key cellular metabolic functions. Despite the fact that metabolism is typically altered in a disease scenario, we assume that essential functions can be still accomplished in the absence of an enzyme. In other words, we are not seeking lethal knockouts but possible malfunctions explaining the observed accumulations/depletions. For this purpose, we only analyzed knockouts not producing disconnections between medium metabolites (substrates) and cellular excreted metabolites. Clearly, this criterion can be revisited and modified according to the biological scenario under study, e.g. forcing the production of a particular set of metabolites required for cellular growth.In summary, our approach involves three main ingredients: CCs and their parameters, p-value and filtering criterion. These ingredients share the use of Carbon Flux Paths (CFPs) for their determination. This pathway concept was recently introduced and goes beyond path finding techniques by accounting for additional biophysical constraints. In order to apply the CFP to the human genome-scale metabolic network presented in Duarte et al. , we manuThe effect of CFPs is particularly observed when our approach predicted the association of LCystin with the enzyme Sulfite Oxidase (SULFOX). By definition, CFPs involve carbon exchange in their intermediate reaction steps. However, there is no carbon flux from LCystin to any metabolite taking part in SULFOX, since they are inorganic metabolites and cofactors. Interestingly, this reaction is important to mass balance the obtained paths from LCystin to the rest of metabolites. This case also illustrates the idea that enzymes at considerable distance from the metabolite under consideration may regulate its concentration.Given the relevance of CFPs in the performance of our approach, improving their accuracy is certainly relevant. As noted in Pey et al. , CFPs muIn addition, our approach sacrificed some accuracy by neglecting classical regulatory mechanisms with the aim to extend our analysis to genome-scale metabolic networks. Regulatory information is certainly relevant for explaining changes in metabolite levels; however, it is scarce for genome-scale networks. The issue will require further consideration when such data becomes widely available.Finally, we believe our approach will be a practical tool to study poorly understood disease phenotypes. Extending its application to other diseases  will be a major activity in the future, precisely with the emergence of metabolomics studies. This work contributes to the development of Systems Medicine, an emerging field aiming to provide answers to clinical questions based on theoretical methods and high-throughput “omics” data.In Pey et al. , we pressubject to:A CFP constitutes a steady-state  flux distribution that involves a directed path  between a given source (α) and target (β) metabolites. We first consider variables and constraints to obtain a directed path between α and β. We then illustrate constraints for steady-state flux distributions. Finally, both sets of constraints are linked.R reactions and C metabolites. Let Scr be the stoichiometric coefficient associated with metabolite c in reaction r. We used a (directed) graph representation of the network where nodes are metabolites and arcs represent carbon exchange between substrates and products of reactions.Assume we have a metabolic network that comprises uij stand for active arcs involved in the directed path between α and β, namely uij = 1 when an arc between metabolites i and j is active, uij = 0 otherwise. By means of Equations (1) and (2) we ensure that one arc leaves the source and one enters the target metabolite; and that no arc enters the source nor leaves the target. For intermediate metabolites in the path, the number of arcs entering them must be equal to the number of arcs leaving them, as imposed by Equation (3). Equation (4) ensures that a metabolite cannot be revisited in the path.Binary variables vr represents the flux through reaction r , which by definition is non-negative. We also define a set of binary variables zr closely related with flux variables, namely zr = 1 if vr > 0 and zr = 0 if vr = 0. We need Equation (6) to link vr and zr variables. M is a big scalar constant that sets an upper bound for reaction fluxes. Note that we split reversible reactions into two single irreversible steps. Therefore, we need to prevent a reaction and its reverse from appearing together in any steady-state flux distribution. This is modeled in Equation (7), where the set B={| reaction λ and reaction μ are the reverse of each other}.A steady-state flux distribution satisfies Equation (5). Note that the continuous variable r with an existing arc (carbon exchange) between metabolites i and j (dijr = 1) must carry flux. This last constraint ensures that the directed path found can perform in sustained steady-state, as claimed in Pey et al. [Equation (8) is introduced to link path constraints, Equations (1)-(4), and flux balancing constraints, Equations (5)-(7), which guarantees that if an arc is selected, at least one of the reactions y et al. .Finally, we use an objective function that minimizes the number of arcs in the directed path, i.e. the shortest path between α and β. Further details can be found in Pey et al. .∆Lj) provides the difference in the average number of steps of metabolites connected to the metabolite under study between a knockout (K) scenario of enzyme j (W) scenario ).As observed in Equation (10), j is knocked out. For this reason, we used the intersection expression in Equation (13).H0). Therefore, an adequate H0 must be defined in the first place. In our particular statistical test, H0 represents that the ranking of an enzyme is not determined by the accumulated metabolite under study. In other words, the resulting positions of the enzymes in the ranking derived from our approach are not specific of the metabolite under study.The p-value defines the probability of obtaining an at least as extreme outcome according to a predefined Null Hypothesis . We assume that all the variables Xi come from the same theoretical distribution F. In addition, we introduce F*N as the cumulative sampling distribution associated with the random sample set . In essence, F*N ascribes a probability equal to 1/N to each of the sample observations. The formal representation of F*N is presented in Equation (14). Note here that x represents a given position in the ranking of enzyme j.Based on this IA(y) is the indicator function corresponding to the set A:Note that F*N is correctly defined, the calculation of the p-values corresponding to a determined ranking is straightforward. Assuming that enzyme j appears in the k-th position in a particular ranking, the corresponding p-value is calculated as follows:Once i.e. N=1000. The position in the ranking for each enzyme in the different scenarios (1000 random metabolite accumulation) is used to build its empirical distribution (F*N). This is then used to determine the p-value associated with the enzymes top-ranked in the metabolites under study.In the case study Results section, we selected 1000 random metabolites and ranked enzymes based on the CC approach, AD: Alzheimer's disease; ADH3: S-(hydrosymethyl) glutathione dehydrogenase; CC: Connectivity curve; CFP: Carbon flux path; CYSO: Cysteine oxidase; D-Glc: Glucose; DHAP: Dihydroxyacetone phosphate; EFM: Elementary flux mode; FALDH: Formaldehyde dehydrogenase; G6P: Glucose-6-Phosphate; GFAE: Glutathione-dependent formaldehyde-activating enzyme; HCys: Homocysteine; LCystin: L-Cysteine; PC: Phosphatidylcholine; PE: Phosphatidylethanolamine; PEMT: Phosphatidylethanolamine N-methyltransferase; Pgi: Phosphoglucoisomerase; PISD: Phosphatidylserine decarboxylase; PKAN: Pantothenate kinase-associated neurodegeneration; PPP: Pentose phosphate pathway; Pser: Phosphatidylserine; PSFLIP: Phosphatidylserine flippase; Pyk: Pyruvate kinase; Pyr: Pyruvate; R5P: Ribose-5-phosphate; SAH: S-Adenosyl-L-homocysteine; SAM: S-Adenosyl-L-methionine; SFGTH: S-Formylglutathione hydralase; SLC25A26: S-Adenosyl-L-methionine reversible transport; SULFOX: Sulfite oxidase; TpiA: Triosephosphate isomerase.The authors declare that they have no competing interests.JP and FJP conceived the study; JP and LT implemented the method and performed the analyses; JPC developed the carbon exchange database; JP, LT and FJP developed the method and wrote the manuscript. All authors discussed the results and read, commented and approved the final manuscript.Toy example full details.Click here for fileManually curated carbon arcs from Recon1.Click here for fileLcystin and Hcys analysis.Click here for file


Escherichia coli and Saccharomyces cerevisiae were performed. It was found that there exist qualitative and quantitative correlations between network topology and chemical properties of metabolites. The metabolites with larger degrees of connectivity (hubs) are of relatively stronger polarity. This suggests that metabolic networks are chemically organized to a certain extent, which was further elucidated in terms of high concentrations required by metabolic hubs to drive a variety of reactions. This finding not only provides a chemical explanation to the preferential attachment principle for metabolic network expansion, but also has important implications for metabolic network design and metabolite concentration prediction.Although the metabolic networks of the three domains of life consist of different constituents and metabolic pathways, they exhibit the same scale-free organization. This phenomenon has been hypothetically explained by preferential attachment principle that the new-recruited metabolites attach preferentially to those that are already well connected. However, since metabolites are usually small molecules and metabolic processes are basically chemical reactions, we speculate that the metabolic network organization may have a chemical basis. In this paper, chemoinformatic analyses on metabolic networks of Kyoto Encyclopedia of Genes and Genomes (KEGG),  Escherichia coli and Saccharomyces cerevisiae, it was found that the metabolites with higher degrees of connectivity (hubs) are of relatively stronger polarity. The reason underlying this phenomenon is that to drive a variety of reactions, metabolic hubs have to be highly concentrated. Since the intracellular environments are hydrophilic, metabolic hubs have to be strong-polar to reach high concentrations. This finding has direct implications for metabolic network design and provides a chemical explanation to the preferential attachment principle, which has been validated by numerical simulations of metabolic network expansion. In addition, the correlations between metabolite concentration, metabolic network topology and metabolite chemical properties also suggest that we can use chemical and topological properties of metabolites to predict their intracellular concentrations. A support vector regression model has been successfully established to predict the metabolite concentrations for Escherichia coli.The metabolic networks of the three domains of life exhibit the same scale-free organization, which has been hypothetically explained in terms of preferential attachment principle. Here we reveal that the scale-free organization of metabolic networks may have a chemical basis. Through a chemoinformatic analysis on metabolic networks of Kyoto Encyclopedia of Genes and Genomes (KEGG),  One of the most intriguing findings in systems biology is that despite the varied constituents and metabolic pathways of three domains of life, their metabolic networks exhibit the same scale-free organization. That is, a small part of metabolites participate in a large number of reactions , while others are involved in a few reactions The scale-free organization of metabolic networks has been hypothetically explained in terms of evolution that the new-recruited metabolite members attach preferentially to those that are already well connected  Escherichia coli (E. coli) (Saccharomyces cerevisiae (S. cerevisiae) . As illustrated in E. coli)  and Saccevisiae) . TherefoG  =  ΔG0+ RTlnQ <0, where Q is the reaction quotient and is determined by the relative concentrations of reactants and products. Thus, for metabolites that participate in a large number of reactions as reactants . The final regression equation is: −LogC  =  6.105 + 0.431 × "ClogP" + 15.595 × "FNSA3" + 16.727 × "FPSA3" − 5.333 × "RPCG", in which ClogP, FNSA3 , FPSA3 and RPCG  are all descriptors characterizing molecular polarity. The fitted concentrations by the chemical properties correlate well with the experimental values (E. coli) are determined to a certain extent by their polarity and solubility, namely, strong-polar metabolites have relatively high concentrations. This finding is similar to the observation about protein abundance of E. coli that highly abundant proteins are on average more hydrophilic than those with low copy numbers A stepwise multiple linear regression analysis was conducted by SPSS  to select the most meaningful chemical properties from 83 descriptors to correlate with negative logarithm of l values , indicatTaken together, the above observations offer an explanation to the correlation between topology and chemistry of metabolic networks. This finding also provides new clues to understanding the molecular basis of preferential attachment principle underlying the evolution of metabolic networks.S. cerevisiae metabolomes . Second, the newly added metabolites have lower concentrations compared to the old ones, i.e., there is a declining trend for the concentrations of emerging metabolites. Third, the metabolites of higher concentrations have higher probability to be involved in the emerging reactions (edges). The present simulations start with 1 metabolite with the initial concentration (Ci) of 1,000,000 and terminate when a metabolite reaches a concentration (Cf) of ≤ 10. This concentration range spans five orders of magnitude, which coincides with the variation range of metabolite concentrations in E. coli (from ∼10−7 to ∼10−2 mol/L) d) in each step is 1,000, with a random fluctuation (f) of 1,500. As a result, the total number of generated metabolites reaches around 1,000, which is close to the real number of metabolites of organisms. The numbers of reactions (edges) added in each step are 5 or 10. As shown in This explanation was validated by numerical simulations that were based on three rules. First, the network expands continuously by adding new metabolites (vertices) with a constant rate, namely, e.g., water), one should use hydrophilic molecules as hubs, while if the environments are non-polar  i.e., a small set of strongly connected, chemically diverse substances) identified by Bishop et al.The above finding implies a chemical criterion in metabolic network design that the polarity of hubs should be compatible with the working environments to guarantee the high concentrations of these critical metabolites. If the environments are polar  method to predict intracellular metabolite concentrations A primary goal of systems biology is to quantitatively characterize cellular behaviors, which requires the information about the absolute concentrations of metabolites. As the intracellular content of metabolites is quite low E. coli metabolite concentrations by their topological and chemical properties. This model was evaluated by leave-one-out cross validation. The squared correlation coefficient is 0.5906 and the total mean squared error is 0.5316. The fitted metabolite concentrations by this model correlate well with the original experimental values (By using the support vector regression (SVR) l values . To evalE. coli metabolite concentrations that have been predicted by the NET method E. coli metabolites were also predicted and presented in E. coli metabolic network simulation. As the SVR model only depends on very basic  properties of metabolites, it is expected to be applicable in metabolite concentration prediction for other bacteria.The In summary, the present analysis indicates that the organization of metabolic networks has a chemical basis. That is, metabolic hubs prefer to select relatively strong-polar metabolites. This basis can be explained in terms of high concentrations required by metabolic hubs to drive a variety of reactions. The present finding not only provides a molecular-level explanation to the preferential attachment principle for metabolic network expansion but also has direct implications for metabolic network design and metabolite concentration prediction.http://www.genome.jp/kegg/ligand.html) (up to Sep 2009) e.g., polymers, proteins and nucleic acids) and metabolites with unspecified residues (denoted by R group) were deleted; ii) Currency metabolites, including gases, metal ions and cofactors were discarded, except that they directly participate in metabolic reactions The KEGG-based metabolic network was reconstructed by manually screening the 8100 small-molecule reactions recorded in KEGG Ligand Database  The metabolic network of S. cerevisiae was reconstructed by manually screening the 1923 small-molecule reactions recorded in YEASTNET (http://www.comp-sys-bio.org/yeastnet) The metabolic network of n is defined as the number of edges linked to n. The basic information for KEGG, E. coli and S. cerevisiae metabolites that are involved in the metabolic networks are presented in The parameters describing the network topology were calculated by Network Analyzer Plugin in Cytoscape-2.7.0 S. cerevisiae metabolome. Recently, Prachumwat and Li classified yeast proteins into five age groups, according to the occurring patterns of their orthologs in other species S. cerevisiae, in which 243 members are involved in the metabolic network of S. cerevisiae. The other 369 ( =  612−243) metabolites of S. cerevisiae metabolic network were thus regarded as late members.To elucidate the molecular basis of preferential attachment principle underlying the evolution of metabolic networks, we identified the early and late members from 83 commonly used property descriptors were calculated with Cerius2 , Sybyl , Pipeline Pilot  and Tripos Benchware DataMiner . Stepwise multiple linear regression analysis was performed by Cerius2 . The numerical simulations of metabolic network expansion were performed based on python package "networkx" (version 1.2). All of the statistical analyses were performed with SPSS .i.e., 6mem rings Molecules (number of 6 membered rings), Amide Molecules (number of amide), ALogP (the Ghose and Crippen octanol-water partition coefficient), ClogP (partition coefficient octanol/water), FNSA3 , FPSA3 , HBD Count (number of hydrogen bond donating groups in the molecule), N Count (number of Nitrogen atoms), LScore Molecules (floating point Lipinski measure) and RPCG ). Radial basis kernel function ε-SVR model. The parameters were trained by using grid search over supplied parameter ranges and the best parameters were obtained as follows: gamma  = 0.01, epsilon  = 0.22, cost  = 7.9. The SVR algorithm for metabolite concentration prediction is available on request.By a trial-and-deletion procedure, 11 properties that have largest contributions to the support vector regression (SVR) model were selected, which include degree and 10 chemical properties, Figure S1Power-law degree distribution of KEGG metabolites.(DOC)Click here for additional data file.Table S1Basic information for KEGG metabolites that are involved in the metabolic network.(XLS)Click here for additional data file.Table S2E. coli metabolites that are involved in the metabolic network.Basic information for (XLS)Click here for additional data file.Table S3S. cerevisiae metabolites that are involved in the metabolic network.Basic information for (XLS)Click here for additional data file.Table S4E. coli metabolites that have absolute concentration values and are involved in the metabolic network.Basic information for 80 (XLS)Click here for additional data file.Table S5Chemical properties for hubs of KEGG-based network and organic chemical network.(XLS)Click here for additional data file.Table S6E. coli metabolites predicted by SVR model.Absolute concentrations for (XLS)Click here for additional data file.


Escherichia coli, established mechanisms only explain a small fraction of the hundreds of genes that are regulated during electron acceptor shifts. Here we propose a qualitative model that accounts for the full breadth of regulated genes by detailing how two global transcription factors (TFs), ArcA and Fnr of E. coli, sense key metabolic redox ratios and act on a genome-wide basis to regulate anabolic, catabolic, and energy generation pathways. We first fill gaps in our knowledge of this transcriptional regulatory network by carrying out ChIP-chip and gene expression experiments to identify 463 regulatory events. We then interfaced this reconstructed regulatory network with a highly curated genome-scale metabolic model to show that ArcA and Fnr regulate >80% of total metabolic flux and 96% of differential gene expression across fermentative and nitrate respiratory conditions. Based on the data, we propose a feedforward with feedback trim regulatory scheme, given the extensive repression of catabolic genes by ArcA and extensive activation of chemiosmotic genes by Fnr. We further corroborated this regulatory scheme by showing a 0.71 r2 (p<1e-6) correlation between changes in metabolic flux and changes in regulatory activity across fermentative and nitrate respiratory conditions. Finally, we are able to relate the proposed model to a wealth of previously generated data by contextualizing the existing transcriptional regulatory network.Determining how facultative anaerobic organisms sense and direct cellular responses to electron acceptor availability has been a subject of intense study. However, even in the model organism  Escherichia coli that sense redox ratios, act on a genome-wide basis to coordinately regulate these global metabolic functions through transcriptional control of enzyme and transporter levels in changing environments. A model results from the study that shows how global transcription factors regulate global dimensions of metabolism and form a regulatory hierarchy that reflects the structural hierarchy of the metabolic network.All heterotrophic organisms must balance the deployment of consumed carbon compounds between growth and the generation of energy. These two competing objectives have been shown, both computationally and experimentally, to exist as the principal dimensions of the function of metabolic networks. Each of these dimensions can also be thought of as the familiar metabolic functions of catabolism, anabolism, and generation of energy. Here we detail how two global transcription factors (TFs), ArcA and Fnr of  Escherichia coli, the regulatory network for this fundamental metabolic function has not been fully elucidated. It has long been known that facultative anaerobes will hierarchically utilize external electron acceptors relative to the free energy change provided by each 3 in the middle, and lactate or acetate or other fermentation products are at the bottom 2Regulation of metabolism in response to shifting availability of electron acceptors is a fundamental process in all of biology and is a critical subject for the understanding of pathogenesis, cancer metabolism, and industrial biotechnology. However, even in the model organism Even though many biochemical details of redox regulation have been elucidated Here we show how the global TFs ArcA and Fnr coordinately regulate the primary metabolic dimensions of growth and energy generation. We integrated polyomic data sets and used genome-scale metabolic models to enable a mechanistic understanding of hundreds of simultaneous and individual regulatory events. This analysis subsequently provides a link between global regulatory circuits and global optimality in microbial metabolism.E. coli's transcriptional regulatory network (TRN). ChIP-chip assays for ArcA and Fnr were performed under both fermentative and nitrate respiratory conditions  Novel cases of divergent transcriptional regulation were found in this data. The integration of binding regions with gene expression data revealed 42 regions where two divergent transcriptional units (TUs) were simultaneously regulated by a single binding event. Divergent transcriptional regulation has been observed previously acs-nrfABCDE system represents a lowest common denominator coupling between acetyl-coA synthetase (acs) acetate scavenging to acetyl-coA and usage of acetyl-coA via the TCA cycle and nrfABCDE nitrite reductase. Similarly the aroP-pdhR system couples the transport of aromatic amino acids to the regulation of pyruvate that acts as their principal precursor molecule.Two examples  highlighacs and nrfABCD systems has been inferred/suggested in previous work which attempted to understand how E. coli could survive on acetate as a sole carbon source under anaerobic conditions E. coli cannot utilize acetate under fully anaerobic conditions because acetate must be scavenged into acetyl-coA via acs and then utilized by the TCA cycle. Anaerobically the TCA cycle cannot be used unless there is an electron acceptor in the ETC to enable oxidative phosphorylation. Thus, some usage of the TCA cycle via an alternative electron acceptor such as nitrite or nitrate is necessary for E. coli to utilize acetate and acetyl-coA anaerobically. This metabolic feature is physiologically crucial in the gut environment that is rich in fatty acids that cannot be used if E.coli does not utilize alternative electron acceptors like nitrite. Hence, the direct coupling of acs and nrfABCD through bidirectional transcriptional regulation is consistent with the necessity of a flux through the nrfABCD system in order for the acetyl-coA formed by acs to be utilized. The transcriptional coupling acts as bidirectional gate controlled by ArcA and the redox state of the cell to coordinate this evolutionarily crucial metabolic capability.The link between the aroP-pdhR system couples the transport of aromatic amino acids to the regulation of pyruvate that acts as their principal precursor molecule through the action of Fnr. To understand the network level connection between the aromatic amino acid transporter (aroP) and the pyruvate dehydrogenase repressor TF (pdhR) one can examine aroP and repression of pdhR is consistent with an increased need for amino acid transport when the precursors for biosynthesis (PEP) are critical to maintain cellular energy levels. This characteristic is supported by a dampening of the switch upon the transition to nitrate respiration, resulting in decreased transporter expression when less pyruvate is needed for fermentation and can thus be shuttled to amino acid biosynthesis. In general, pdhR acts as a classic repressor that “pops off” of its binding site in the presence of pyruvate and hence allows expression of pyruvate dehydrogenase and other oxidative enzymes. Anaerobically pyruvate dehydrogenase (aceEF-lpd) is repressed regardless of pdhR by ArcA and Fnr and given that there is also a higher concentration of pyruvate it would presumably not be active. Thus, while this switch is highlighted anaerobically in that full repression of pdhR is concomitant with aroP activation its physiological significance is more prevalent under nitrate or even fully aerobic conditions in which it can function to directly couple and balance the catabolic and anabolic demands around pyruvate which acts as a critical second messenger in the aerobic-anaerobic shift Similarly the E. coli metabolic model Previous work has identified biomass production and energy production as the two principal dimensions characterizing the overall function of metabolic networks ptsG. Activation of ptsG by Fnr is consistent with the fact that cells nearly double their uptake of carbon during fermentative growth compared with aerobic growth.From the data sets described above, the regulation of these three classes of genes by ArcA and Fnr can be analyzed using their metabolic functions as context. ArcA and Fnr directly regulate a total of 127 catabolic genes including 49 transporter genes, 38 recycling or secondary catabolic enzymes, 33 central metabolic genes, and 7 associated TFs ,3. In pasthA, pntAB) in E. coli. Previous work has shown that a large portion of the NADPH used for biosynthetic reactions comes from the membrane bound transhydrogenase PntAB pntAB and represses sthA in a redox-dependent fashion consistent with an increased need for NADPH under nitrate respiration relative to fermentation  for the directly regulated genes. This correlation provides quantitative evidence for the logic of the regulatory circuit in the transition from fermentation to nitrate respiration. The linear positive slope shows not only that the reactions responsible for the redox shift are regulated, but also that these reactions are quantitatively regulated to help minimize the redox ratio in concert with the quantitative model predictions. Most of the ArcA regulated reactions are de-repressed, as indicated by the lightening shade of blue under nitrate respiration  between fermentation and nitrate respiration; gDW is denotes grams dry weight. We were then able to show that 89 of the 91 reactions were regulated directly (40 reactions) or indirectly (49 reactions) by ArcA or by Fnr . We thenpiration . Most ofpiration . The bro strains . This tr strains , Text S1E. coli grown aerobically in batch under either fully respiratory galactose conditions or partially fermentative glucose conditions. Even though both conditions are aerobic, we hypothesized that a similar shift in the redox ratio as observed between fully fermentative and nitrate respiration would occur given the comparison between a partially fermentative and fully respiratory condition. We made the same plot . This plot again shows genes regulated by ArcA being de-repressed and genes regulated by Fnr being de-activated upon the shift to more oxidative conditions  This work presents a formal integration and reconstruction of over 50 years of research on Taken together, we are able to show how the two principal dimensions of metabolism are controlled in a shifting environment by global TFs through the use of polyomic data sets and genome-scale metabolic models. This study is likely to be useful as a guide for similar studies in other organisms where the same tools for experimentation and analysis are available.E. coli K-12 MG1655 and its derivatives. The E. coli strains harboring Fnr-8myc and ArcA-8myc were generated as described previously Δfnr and ΔarcA) were constructed by a λ red and FLP-mediated site-specific recombination method. Glycerol stocks of E. coli strains were inoculated into M9 minimal medium containing 0.2% (w/v) carbon source (glucose) and 0.1% (w/v) nitrogen source (NH4Cl), and cultured overnight at 37°C with constant agitation. The cultures were diluted 1∶100 into fresh minimal medium and then cultured at 37°C to an appropriate cell density with constant agitation. For the anaerobic cultures, the minimal medium were flushed with nitrogen and then continuously monitored using a polarographic-dissolved oxygen probe (Cole-Parmer Instruments) to ensure anaerobicity. For nitrate respiration 20 mmol potassium nitrate was added.All strains used in this study were To identify Fnr and ArcA binding regions in vivo, we used the ChIP-chip approach as described previously To monitor the enrichment of promoter regions, 1 µL immunoprecipitated DNA was used to carry out gene-specific qPCR. The quantitative real-time PCR of each sample was performed in triplicate using iCycler (Bio-Rad Laboratories) and SYBR green mix (Qiagen). The real-time qPCR conditions were as follows: 25 µL SYBR mix (Qiagen), 1 µL of each primer (10 pM), 1 µL of immunoprecipitated or mock-immunoprecipitated 3DNA and 22 µL of ddH2O. All real-time qPCR reactions were done in triplicates. The samples were cycled to 94°C for 15 s, 52°C for 30 s and 72°C for 30 s  on a LightCycler (Bio-Rad). The threshold cycle values were calculated automatically by the iCycler iQ optical system software (Bio-Rad Laboratories). Any primer sequences used were described previously Samples for transcriptome analysis were taken from exponentially growing cells. From the cells treated by RNAprotect Bacteria Reagent (Qiagen), total RNA samples were isolated using RNeasy columns (Qiagen) in accordance with manufacturer's instruction. Total RNA yields were measured using a spectrophotometer (A260), and quality was checked by visualization on agarose gels and by measuring the sample A260/A280 ratio (>1.8). Affymetrix GeneChip E. coli Genome 2.0 arrays were used for genome-scale transcriptional analyses. cDNA synthesis, fragmentation, end-terminus biotin labeling, and array hybridization were performed as recommended by Affymetrix standard protocol. Raw CEL files were analyzed using robust multi-array average for normalization and calculation of probe intensities. The processed probe signals derived from each microarray were averaged for both the wild type and deletion mutant strains.http://sbrg.ucsd.edu/Downloads/MetaScope). Raw gene expression CEL files were normalized using background corrected robust multi-array average implemented in the R affy package. To detect differential expression between the wild type and TF deletion strains we applied a two-tailed unpaired students t-test between the experimental triplicates for the wild type and gene deletion strains. This was followed by a false discovery rate adjustment. Before performing the FDR correction we removed all genes that exhibited an expression level below the background across all experiments. The background level was calculated as the average expression level across all intergenic probes. We then only considered genes meeting a 5% FDR -adjusted P-value cut-off to be differentially expressed. ChIP binding tracks for http://nbviewer.ipython.org/gist/steve-federowicz/7cceedba73982c0ae995. All raw and processed data have been deposited in NCBI/GEO under accession number GSE55367 (http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE55367).To identify TF-binding regions, we used the peak finding algorithm built into the NimbleScan software. Processing of ChIP-chip data was performed in three steps: normalization, IP/mock-IP ratio computation (log base 2), and enriched region identification. The log2 ratios of each spot in the microarray were calculated from the raw signals obtained from both Cy5 and Cy3 channels, and then the values were scaled by Tukey bi-weight mean. The log2 ratio of Cy5 (IP DNA) to Cy3 (mock-IP DNA) for each point was calculated from the scanned signals. Then, the bi-weight mean of this log2 ratio was subtracted from each point. Each log ratio dataset from duplicate samples was used to identify TF-binding regions using the software (width of sliding window = 300 bp). Our approach to identify the TF-binding regions was to first determine binding locations from each data set and then combine the binding locations from at least five of six datasets to define a binding region using the MetaScope software  with our TF binding regions to identify promoter architectures genome wide −1 h−1  along with the lower bound of EX_o2 set to zero. pFBA constrained models were generated by first using the convertToIrreversible function of the COBRA toolbox http://opencobra.sourceforge.net/openCOBRA), iPython notebook To perform sampling we first generated pFBA Figure S1Workflow overview of the experimental and computational analysis process. An integrated and iterative loop was used to generate the integrated regulatory and metabolic analysis.(PDF)Click here for additional data file.Figure S2http://nbviewer.ipython.org/gist/steve-federowicz/aa44c9d8add955f4ada7 for Fnr and http://nbviewer.ipython.org/gist/steve-federowicz/1c5017c6ce419234019a for ArcA.We performed a detailed comparison of the discrepancies between the ChIP data for ArcA and Fnr generated in this study vs. the ChIP data generated in the studies by Park et al. and Myers et al. This comparison is only performed for data generated under fermentative conditions as no other comparable conditions were assayed in the Park et al. and Myers et al. studies. The overall conclusion can be seen that our ArcA data is very similar but our Fnr data has significant differences. All of the code and results for this curation can be viewed at (PDF)Click here for additional data file.Figure S3Δfnr and ΔarcA strains compared to a wild type strain that were generated in our study versus that generated by the studies of Park et al. and Myers et al. This comparison is only performed for data generated under fermentative conditions as no other comparable conditions were assayed in the Park et al. and Myers et al. studies. The overall conclusion here is that most of the differences in each case were due to genes that were either not expressed or lowly expressed in our data. These differences can be primarily attributed to different measurement technologies used for gene expression measurement. We used affymetrix arrays throughout this study which generally do not have as high of a dynamic range as RNAseq or Nimblegen tiling arrays used in the studies of Park et al. and Myers et al. However, there is still a slight bias towards our ArcA data having reasonably similarity but our Fnr showing noticeable differences. All of the code and results for this curation can be viewed at http://nbviewer.ipython.org/gist/steve-federowicz/8c0e96ac208264e623b9 for Fnr and http://nbviewer.ipython.org/gist/steve-federowicz/05659c90b49abc049a42 for ArcA.We performed a detailed comparison of the expression data for (PDF)Click here for additional data file.Figure S4http://nbviewer.ipython.org/gist/steve-federowicz/1cbb68842ab0a0571ff0 for Fnr and http://nbviewer.ipython.org/gist/steve-federowicz/f2b3d25f114914147c81 for ArcA.We performed a detailed comparison of the direct regulatory targets for ArcA and Fnr between our study and the studies of Park et al. and Myers et al. Direct regulatory targets are defined as genes that contain an upstream ChIP binding region along with significant differential gene expression between the knockout TF strain and a wild type strain. These comparisons show that for ArcA, the 21 discrepancies can be almost uniformly attributed to noise in highthroughput data in which some solid information exists, but ultimately falls below stringent cutoffs. A similar picture also emerges for Fnr with almost every discrepancy containing some type of comparable data in our study. All of the code and results for this curation can be viewed at (PDF)Click here for additional data file.Figure S5http://nbviewer.ipython.org/ea455904c0d7cda4bfba.Regulation of fluxes around key metabolic intermediates is quantified via the integration of computational sampling of the iJ01366 metabolic network and experimentally generated regulation data. Twenty-four different metabolites are profiled, including 12/13 biomass precursors, 9/9 primary electron donors, and the three primary electron carriers, H+, NADH, and NADPH. Each node map diagram shows the split between the amount of regulated vs. unregulated flux that goes into the production or consumption of each metabolite. The notable pattern is repression of the consumption and often production upon a shift to nitrate respiratory conditions. This occurs primarily as a means of negative feedback on the flux through these core nodes. In fact these diagrams fail to show that under fermentative conditions these same fluxes through core nodes are even more highly repressed. This occurs because the metabolic network at optimality is already in line with the regulation, and hence does not carry flux through many of the reactions that are shown to be repressed under nitrate respiratory conditions. This result led us to make the scatter plot of (PDF)Click here for additional data file.Figure S6Δfnr or ΔarcA strains under partially fermentative glucose batch growth. It can be seen that deletion of arcA does cause de-repression of the key catabolic fluxes of the TCA cycle. This causes less flux to be directed towards the fermentative chemiosmotic pathways ultimately wasting energy.We compared C-13 MFA derived flux values (PDF)Click here for additional data file.Figure S7fre, a constitutively expressed NAD generation enzyme, and the other four, serA, tyrA, metF, and hisD all encode amino acid biosynthetic enzymes. We then took into consideration a puzzling finding of newly discovered and highly significant regulation of amino acid transporters for serine, tyrosine, methionine and histidine. We noticed that for serA and tyrA in particular, the NADH generating reactions were the subject of end product inhibition by serine and tyrosine. Thus we can hypothesize that activation of the uptake transporters for these amino acids will cause feedback inhibition of the enzymes and thus maintain the expression of critical metabolic enzymes while simultaneously modulating their redox related contributions.Transport coupled redox balancing. After sampling the metabolic model and determining all reactions that produce or consume NADH, we identified only 5 reactions that carried flux and were not regulated by ArcA of Fnr. We found that one encoded (PDF)Click here for additional data file.Figure S8ΔarcA or Δfnr strain under fully fermentative conditions. After deletion of the arcA and fnr transcription factor genes, 148 and 169 genes are differentially expressed under anaerobic conditions. We then trace the regulatory network to explain the regulation of these genes. 63 and 47 are shown to be directly regulated through binding of the TFs in the ChIP-chip data. Another 48 and 60 genes are indirectly regulated via secondary network effects . Finally the last three categories represent genes involved in the stress response, genes of unknown function, and other metabolic genes. Differentially regulated genes that are primarily stress response genes may represent variability in culture conditions or unknown regulatory interactions. Uncharacterized and metabolic genes likely represent unknown regulatory links.Causative classification of genes differentially expressed log two fold between a wild type and (PDF)Click here for additional data file.Table S1ArcA-associated regions under fermentative conditions identified by ChIP-chip analysis and its regulatory effect on the target operons determined by expression profiles. This table summarizes the results of ChIP-chip experiments to determine the genome-wide locations of DNA targets for ArcA binding in exponential phase E. coli cells growing in strictly anaerobic minimal media conditions. First and second columns indicate identified ArcA-binding peaks . The third column indicates the log2 ratio of each ArcA-binding peak.(PDF)Click here for additional data file.Table S2E. coli cells growing in strictly anaerobic minimal media with the addition of 20 mm KNO3. First and second columns indicate identified ArcA-binding peaks . The third column indicates the log2 ratio of each ArcA-binding peak.ArcA-associated regions under nitrate respiratory conditions identified by ChIP-chip analysis and its regulatory effect on the target operons determined by expression profiles. This table summarizes the results of ChIP-chip experiments to determine the genome-wide locations of DNA targets for ArcA binding in exponential phase (PDF)Click here for additional data file.Table S3Fnr-associated regions under fermentative conditions identified by ChIP-chip analysis and its regulatory effect on the target operons determined by expression profiles. This table summarizes the results of ChIP-chip experiments to determine the genome-wide locations of DNA targets for Fnr binding in exponential phase E. coli cells growing in strictly anaerobic minimal media conditions. First and second columns indicate identified Fnr-binding peaks . The third column indicates the log2 ratio of each Fnr-binding peak.(PDF)Click here for additional data file.Table S4E. coli cells growing in strictly anaerobic minimal media with the addition of 20 mm KNO3. First and second columns indicate identified Fnr-binding peaks . The third column indicates the log2 ratio of each Fnr-binding peak.Fnr-associated regions under nitrate respiratory conditions identified by ChIP-chip analysis and its regulatory effect on the target operons determined by expression profiles. This table summarizes the results of ChIP-chip experiments to determine the genome-wide locations of DNA targets for Fnr binding in exponential phase (PDF)Click here for additional data file.Table S5ArcA motifs found underneath experimentally determined ChIP binding regions. First column is the center position of the peak (averaged for peaks occuring under both fermentative and nitrate respiratory conditions).(PDF)Click here for additional data file.Table S6Fnr motifs found underneath experimentally determined ChIP binding regions. First column is the center position of the peak (averaged for peaks occuring under both fermentative and nitrate respiratory conditions).(PDF)Click here for additional data file.Table S7Mean flux values above .1 mmol/GDWH across all sampling points under anaerobic conditions. This table shows all reactions, whether or not they are directly regulated by ArcA or Fnr, their mean flux values, the percent of the total flux that this flux values corresponds too, and the list of genes associated with the reaction. For each reaction the regulation column is TRUE if at least one gene is directly regulated by ArcA or Fnr. The total percent of flux regulated can then be calculated by summing across all flux values which are regulated and dividing by the total.(PDF)Click here for additional data file.Table S8Mean flux values above .1 mmol/GDWH across all sampling points under nitrate conditons. This table shows all reactions, whether or not they are directly regulated by ArcA or Fnr, their mean flux values, the percent of the total flux that this flux values corresponds too, and the list of genes associated with the reaction. For each reaction the regulation column is TRUE if at least one gene is directly regulated by ArcA or Fnr. The total percent of flux regulated can then be calculated by summing across all flux values which are regulated and dividing by the total.(PDF)Click here for additional data file.Table S9Regulation of fluxes around key metabolites in fermentative conditions. This table shows all of the biomass precursor, electron donor, and electron carrier molecules along with the associated flux amounts in which they are produced or consumed and the amount of this flux which is activated or repressed by ArcA and Fnr.(PDF)Click here for additional data file.Table S10Regulation of fluxes around key metabolites in nitrate respiratory conditions. This table shows all of the biomass precursor, electron donor, and electron carrier molecules along with the associated flux amounts in which they are produced or consumed and the amount of this flux which is activated or repressed by ArcA and Fnr.(PDF)Click here for additional data file.Table S11This table shows the relative flux levels and differential transcriptional regulation values for reactions that differed by at least .25 mmol/GDWh mean sampled flux units between fermentative and nitrate respiratory conditions. This table contains 91 gene-associated reactions of which 89 are regulated by ArcA or Fnr. The first column is the COBRA reaction ID followed by the mean flux value in fermentative (fermen.) and nitrate respiratory (nitrate) conditions. The columns for Fermentative regulation and Nitrate regulation are the max absolute value levels of regulation  cause by(PDF)Click here for additional data file.Table S12Regulation of altered reactions based on sampling of flux solutions between fermentative and nitrate respiratory conditions. After calculating the set of reactions which differ in their flux values between fermentative and nitrate respiratory conditions we sought to understand how many of these reactions were regulated by ArcA and Fnr. Altered reactions describes the total number of reactions which differ between the conditions by the flux cutoff (e.g. 91 reactions differ between the two conditions by at least .25 mmol/GDW-h). Of these 91 reactions, 40 are directly regulated by ArcA or Fnr and another 49 are indirectly regulated.(PDF)Click here for additional data file.Table S13List of all transcription factors found in RegulonDB that map to metabolites in the iJO1366 metabolic model.(PDF)Click here for additional data file.Text S1serA and tyrA, are feedback inhibited by serine and tyrosine respectively. Thus, as shown in sstT serine transporter and the aroP tyrosine transporter with feedback inhibition of these critical biosynthetic enzymes. Under this regulatory scheme, serine and tyrosine would be produced at the expense of critical redox potential but immediately shut down if any serine or tyrosine can be scavenged exogenously.Transport coupled redox balancing as shown in (DOC)Click here for additional data file.


A recurrent bottleneck, however, is the establishment of consistent stoichiometric models for the synthesis of recombinant proteins or viruses. Although optimization algorithms for A hybrid framework is presented combining classical metabolic flux analysis with projection to latent structures to further link estimated metabolic fluxes with measured productivities. We first explore the functional metabolic decomposition of a baculovirus-producing insect cell line from experimental data, highlighting the TCA cycle and mitochondrial respiration as pathways strongly associated with viral replication. To reduce uncertainty in metabolic target identification, a Monte Carlo sampling method was used to select meaningful associations with the target, from which 66% of the estimated fluxome had to be screened out due to weak correlations and/or high estimation errors. The proposed hybrid model was then validated using a subset of preliminary experiments to pinpoint the same determinant pathways, while predicting the productivity of independent cultures.Overall, the results indicate our hybrid metabolic flux analysis framework is an advantageous tool for metabolic identification and quantification in incomplete or ill-defined metabolic networks. As experimental and computational solutions for constructing comprehensive global cellular models are in development, the contribution of hybrid metabolic flux analysis should constitute a valuable complement to current computational platforms in bridging the metabolic state with improved cell culture performance. The biotechnological industry is facing substantial pressure to achieve global process optimization. Concomitantly, the exploitation of high-throughput cellular data to support metabolic engineering has intensified in recent years ,2. At thWith the emergence of increasingly extensive genome annotations for several organisms, optimization algorithms for genome-wide fluxome estimations have become well popularized. Such estimations are based on flux balance analysis (FBA), which assumes a "metabolic objective" driving the behaviour of the cell (see for instance ). A set in silico by linear optimization/inspection may not exhibit the expected metabolic behaviour in vivo. While methods for integration of regulatory and metabolic networks have been reported [In spite of their value, and regardless of size, currently available stoichiometric models by-pass a multi-layered web of regulatory and fundamentally complex cellular events, thus constituting a simplification of cellular function . Given treported -15, stilreported , may prereported ,18. As areported ,20.These issues are herein addressed by proposing a hybrid stoichiometric/statistical framework to make sense of fluxome data either from small-scale or genome-scale metabolic models. As intended for rapid bioprocess optimization, a scenario is presented where MFA is employed to reliably estimate intracellular flux distributions in a small-scale network comprising the main pathways of carbon and nitrogen flow, substantially reducing data acquisition efforts in the early stages. Then, projection to latent structures (PLS)  is used in vivo gene therapy [In order to illustrate this approach, the metabolic behaviour of the baculovirus-insect cells system is explored. The superior versatility and safety of baculoviruses has been exploited for a wide range of applications, from recombinant protein manufacture ,23 to ge therapy . Our gro therapy ,26, from therapy . Here, tSpodoptera frugiperda cells (Sf9) comprising a well-defined central carbon and nitrogen metabolism  was combined with a set of biosynthesis reactions for recombinant baculovirus synthesis  and 77 fluxes, resulting in 26 degrees of freedom. Since a total of 30 fluxes are measured or defined, the final system is overdetermined with 4 redundant measurements. Then, the relative sensitivity of the rate of product formation in this metabolic network was compared to that of the cell growth rate (see Methods). As presented in Figure μ), having sensitivity values lower than 1 . However, they are enormously amplified when estimating the flux of baculovirus formation (vBac), often by several orders of magnitude.Supposing the composition of a recombinant product of interest is known (e.g. protein amino acids sequence or detailed virus structure), a lumped reaction system comprising all metabolic precursors in stoichiometric quantities to synthesize a unit amount of product can be formulated. If the number of measured flux constraints is high enough to yield a determined or overdetermined system, then an estimation of the rate of product synthesis can be obtained (see Methods for a description of MFA). However, this estimation will generally be inaccurate, often lying outside feasible biological boundaries, even for a consistent, overdetermined system with carbon and nitrogen balances closed within experimental error. The problem of the ill-definition of protein/virus formation in a metabolic network is mathematically expressed by the extremely large sensitivity of such estimation to the measured fluxes. As a corollary, it is only possible to accurately estimate such a rate if all measurements are precisely known, that is, devoid of experimental error. To illustrate this, a comprehensive metabolic model of μ or vBac, or of deleting the complete set of biomass or product synthesis reactions, can be assessed in terms of overall fluxome variation in relation to that estimated by the complete model , and a vector of target productivity, tV, which is not directly linked with the known part of the network  representing how strongly each flux correlates with the target. This statistical association can be used to derive hypothesis on how to perturb the metabolic network towards increased productivity .In the absence of sufficient mechanistic detail, the unknown or ill-defined part of a metabolic network can be substituted by an empirical  sub-model bridging the well-defined stoichiometry with a given cellular function, such as the synthesis of a complex recombinant product  in serum-free medium. Overall, a matrix of 13 × 47 fluxes estimated by MFA was used as predictor data for the PLS model  lower than 1  cycle and respiration reactions, and another, with lighter association strengths, comprising the uptake fluxes of phenylalanine, methionine and histidine. Remarkably, this selected group of amino acids sharing a positive correlation with productivity had on average higher ratios of catabolization (relative to their specific consumption) than the rest of the essential amino acids, which were primarily used for biomass synthesis; the interpretation of these selections can in principle be based on their contribution to oxidative metabolism as well.The reduced list of meaningful fluxes was then hierarchically clustered in the regression coefficient/confidence interval space in order to highlight groups that share a common strength of association with the target  to be used for validation. In a second validation strategy, the three experiments with the highest productivities  were left aside as a means to prevent data interpolation. In both strategies, the number of latent variables was chosen based on maximum total variance explained  and constrained by a limit of 3. As presented in Figure α values higher than 1, though other fluxes with lighter correlations were also selected. Overall, despite the somewhat limited collection of data, these results indicate the hybrid MFA framework should prove a valuable tool in designing metabolic optimization strategies for complex products, with potential applicability to a range of cellular systems.In terms of metabolic decomposition, these models corroborate our previous conclusions. Indeed, the most important pathways for viral replication previously discriminated, namely TCA cycle and respiration, showed a significant correlation with productivity for both validation strategies . Therefore, the identification of genetic targets may at times be beyond the domain of central metabolic fluxes, which themselves are upstream regulated along with the productivity phenotype. On this issue, the methodology herein presented could at least allow to hypothesize how different cell pathways/functions are commonly regulated.Besides providing a list of prospective metabolic targets to be exploited for engineering, the proposed framework adds a functional dimension to previous metabolic decomposition studies based solely on structural properties of the underlying network, namely connectivity ,37 or paAs mentioned earlier, when used to handle flux distributions estimated by FBA in genome-scale models, this approach represents an alternative hybrid framework to linear optimization techniques during metabolic target selection, which could significantly surpass existing limitations in modeling complex phenotypes. A recent paper by Melzer et al. (2009) also explores the use of multivariate statistics to correlate stoichiometrically-derived elementary modes in complex networks with stoichiometrically-defined productivity targets, as opposed to common search algorithms for strain improvement . HoweverE. coli and S. cerevisiae, in an industrial setting a larger diversity of organisms are used, particularly animal cell systems for which cellular data is much scarcer [13C flux analysis may become prohibitive for very complex networks by today's standards. Overall, our framework could potentially be more useful to steer rapid development of a broad range of organisms on the basis of a representative small-scale metabolic network. As such, it would significantly enhance the quality of information extracted from exploratory experiments compared to traditional metabolic flux analysis.Finally, from a practical point of view, several issues are worth considering before opting for a genome-scale model. In one respect, the availability of a well sequenced and annotated genome may constitute a major limitation: while accurate metabolic reconstructions are available for un-mutated, standard microorganisms such as  scarcer . Another scarcer . In partThe need to understand and manipulate cellular systems for increased biosynthesis of target products has been a consistent focus of research, now supported by the huge flows of data being obtained at different cellular levels. However, the increasingly available knowledge is still not sufficient for the construction of global metabolic models able to accurately predict cell behaviour in response to perturbations. To this end, multivariate statistical tools will keep proving useful in functionally connecting different layers of cellular information, filling the gaps in our understanding of kinetic and regulatory phenomena. At this point, we believe that combining both frameworks into a hybrid metabolic flux analysis framework constitutes a valuable and straightforward complement to purely stoichiometric models in optimizing industrially relevant complex productivity phenotypes.In MFA, material balances are derived over the metabolic nodes of a biochemical network. Under the pseudo-steady state assumption, all intracellular pools of these compounds are constant, and a homogenous system of linear equations is obtainedA the network stoichiometric matrix and V a vector of reaction fluxes. When enough constraints are available to render system (1) overdetermined , a least squares solution for the flux distribution can be derived:with m Va vector of measured fluxes , m Athe associated stoichiometric matrix, e Vthe vector of estimated intracellular reaction rates and e# Athe pseudo-inverse of the corresponding stoichiometric matrix. To provide an estimate that better approximates the real metabolic flux distribution, redundant measurements were used to balance (adjust) the measured fluxes according to their normalized variances to obtain a weighted-least squares solution [h, as defined in [h with the χ2 test function allows evaluating the consistency of experimental data with the assumed biochemistry and the pseudo-steady state assumption. For this, the number of redundant measurements was used as the degrees of freedom for statistical hypothesis testing at a 95% confidence level. These calculations were performed with FluxAnalyzer (Version 5.3) [with solution . In addifined in . Compariion 5.3) .For the two scenarios where the measurement of product formation rate or cell growth rate are individually omitted from the complete model, the Jacobian of the corresponding overdetermined system (2) was calculated asrepresenting the absolute sensitivity of each unknown flux to each metabolic constraint. In order to compute fractional sensitivities for biomass and product synthesis rates, the corresponding  elements were appropriately factored with an average value of each measured metabolite consumption/production rate and the average value of measured cell growth rate or productivity, respectively, for all metabolic conditions presented in Table eT V(with different culture conditions/steady states as rows) is performed iteratively and supervised by maximizing covariance with the target vector tTV. The result is the projection of the fluxome space into a "latent space" defined by a set of uncorrelated  latent variables (LVs):After standardizing the fluxes estimated by MFA, the decomposition of the predictor matrix T is the matrix with LVs as columns, W is a matrix of weights, T Qa matrix of "loadings", and E a residuals matrix. Similarly, the target vector can also be decomposed using the same latent space aswhere T Pthe corresponding loadings vector and F a vector of residuals. Finally, the linear model between the predictor and target variables is derived:with B = W × T Pis the column vector that maximizes the squared sample covariance between tT Vand the latent variables in T [N-Way toolbox for MATLAB" [Here, les in T . It repr MATLAB"  and is d MATLAB" .For the estimation of confidence intervals associated with each regression coefficient, 1000 fluxome states were randomly sampled considering normal error distributions associated with flux estimates that have been propagated in MFA calculations from an initial 16% error in measured exchange fluxes (including cellular growth rate). For the productivity target, a 22% error was used . PLS regB) the observed standard deviations of coefficients B and T the two-sided T-student distribution value for a 95% confidence level and number of degrees of freedom (dg) equal to 1001 (observations) minus 47 (fluxes). All calculations were implemented by the authors in MATLAB .with c) was calculated [c close to 1 indicate a good representation of the data. Additionally, for each link in the cluster tree, an inconsistency coefficient (I) was calculated, which compares the height of each link with that of neighbour links at the same level [I is, the less similar the objects are. Thus, when plotting the number of emerging tree clusters against decreasing I values, a large discontinuity, along with the appearance of clusters with unacceptable small size, suggest a natural division in the dataset. All calculations were performed using predefined functions available in MATLAB .Groups of fluxes sharing similar strengths of association with productivity were hierarchically clustered on the two-dimensional space defined by the pair correlation coefficient/confidence interval. The Euclidian norm was chosen as distance measure. To evaluate if the classification presented in the dendrogram correlates well with the distance measurements between pairs of data objects, the cophenetic correlation coefficient  was maintained in 50 mL working volume shake flasks  and kept in a humidified incubator operated at 27°C and 90 rpm. Sf900II serum- and protein-free medium  was used throughout this work. Cell density and viability were determined by cell counting using a Fuchs-Rosenthal chamber after diluting bulk samples in Trypan Blue.The host insect cell line Autographa californica nucleopolyhedrovirus Ac-vp39EGFP, coding for the baculovirus major structural capsid protein, vp39, fused N-terminally to an EGFP reporter [Sf9 cells at 1x106 cells.mL-1 with a MOI of 0.1 IP.cell-1, in 125 mL (working volume) spinner flasks , and stored as culture supernatant at 4°C, protected from light. Virus titers were determined by an end-point dilution assay in 96-well plates, screening for GFP signal under an inverted fluorescence microscope [The recombinant reporter , was kincroscope .Ac-vp39EGFP were carried out at low (1x106 cells.mL-1) or high (3-4x106 cells.mL-1) cell density, using in all cases a low multiplicity of infection (0.1 IP.cell-1). Nutritional supplements were added at the time of infection as described in [Cells were cultured in 125 mL (working volume) spinner flasks or 50 mL working volume shake flasks . Ammonia was quantified enzymatically using a UV assay . Maltose and sucrose were indirectly quantified after enzymatic hydrolysis using α-glucosidase and invertase from Sigma-Aldrich, respectively. Amino acid concentrations were profiled by high performance liquid chromatography (HPLC) using a reverse phase 3.9 × 150 mm column . A pre-column derivatization method  was used, as described in [in silico routines for data analysis and revised the manuscript.NC conceived the methodology, performed experimental cultures, analyzed the data and wrote the manuscript. VB participated in data acquisition, analysis and revised the manuscript. AT made substantial contribution to conception and revised the manuscript. MJTC and PMA contributed to the biological concept, revised the manuscript and gave final approval of the version to be published. RO was involved in the general design of the methodology, developed the Sf9 cell line metabolismMetabolic reactions of the . Includes a list of all stoichiometric reactions corresponding to exchange (measured) and intracellular (unknown) fluxes comprising the MFA model. References are provided for further information.Click here for fileViral synthesis reactions used for complete MFA model establishment. Includes information and references on the composition of insect viruses, and the set of viral synthesis reactions used to set the complete MFA model addressed in Table 1.Click here for fileValues of measured and MFA-estimated fluxes for all experiments. Includes a table containing the values of all measured and MFA-estimated fluxes for the 13 experiments presented in this work. The later were used as direct inputs for correlation with a target vector of productivities (presented in Table 2) to establish hybrid MFA.Click here for file


Integrating gene expression profiles and metabolic pathways under different experimental conditions is essential for understanding the coherence of these two layers of cellular organization. The network character of metabolic systems can be instrumental in developing concepts of agreement between expression data and pathways. A network-driven interpretation of gene expression data has the potential of suggesting novel classifiers for pathological cellular states and of contributing to a general theoretical understanding of gene regulation.Here, we analyze the coherence of gene expression patterns and a reconstruction of human metabolism, using consistency scores obtained from network and constraint-based analysis methods. We find a surprisingly strong correlation between the two measures, demonstrating that a substantial part of inconsistencies between metabolic processes and gene expression can be understood from a network perspective alone. Prompted by this finding, we investigate the topological context of the individual biochemical reactions responsible for the observed inconsistencies. On this basis, we are able to separate the differential contributions that bear physiological information about the system, from the unspecific contributions that unravel gaps in the metabolic reconstruction. We demonstrate the biological potential of our network-driven approach by analyzing transcriptome profiles of aldosterone producing adenomas that have been obtained from a cohort of Primary Aldosteronism patients. We unravel systematics in the data that could not have been resolved by conventional microarray data analysis. In particular, we discover two distinct metabolic states in the adenoma expression patterns.The methodology presented here can help understand metabolic inconsistencies from a network perspective. It thus serves as a mediator between the topology of metabolic systems and their dynamical function. Finally, we demonstrate how physiologically relevant insights into the structure and dynamics of metabolic networks can be obtained using this novel approach. Escherichia coli or[Saccharomyces cerevisiae).Genomic knowledge allows compiling an inventory of an organism’s enzymes and thus the subsequent reconstruction and simu coli or, for a sDuarte et al., publishHuman Recon 1[In the present work, we will integrate human transcriptome data from a cohort of healthy controls and aldosterone producing adenomas (APA) of adrenal glands from primary aldosteronism (PAL) patients with then Recon 1. PrimaryI) and is minimized during the GIMME optimization. Thus, the inconsistency I gives, on the one hand, an estimate of the quality of the computed flux distribution, and measures, on the other hand, the coherence of the objective and the experimental data  introduced previously[metabolic coherence (MC), which measures the amount of network coherence between gene expression profiles and metabolic pathways.We will compare the inconsistency eviously, which iI, on the one hand, measures the level of disagreement between expression data and anticipated network dynamics. The MC index, on the other hand, measures the amount of coordinated (connected) expressed reaction structure, which can only be observed after contextualization of the expression data.The comparison between these two indices is interesting, as they highlight different properties of the network dynamics. The inconsistency index I and show that valuable information can be extracted from them.Figurevobj and a minimal medium composition containing glucose and glycerol, as well as a collection of amino acids and fatty acids, was implemented using the appropriate boundaries on the their respective exchange reactions . It is important to note that these two categories (HIG and LIG) could not have been uncovered by conventional cluster analysis . The dependence of the correlation on the threshold parameter t, applied to the data in order to distinguish between expressed and not expressed metabolic genes, is checked in Figurel was found .FigureMC on the chosen growth medium is shown. The distribution of correlation coefficients is narrow (between −0.75 to −0.4 for r and −0.73 to −0.35 for ρ), regardless of which correlation measure is considered. This indicates that both inconsistency and MC and their correlation seem not be strongly dependent on the environmental conditions provided. Furthermore, the correlation values obtained for the reference medium  seem to originate in the left tail of the distributions, suggesting a rather high correspondence with the in vivo situation.In FigureWe confirmed that the observed anticorrelation between both measures is not a feature of the adenoma data, but holds true for other transcriptome data as well see Fig: Text S1Homo sapiens. Striking differences between the control group and the adenoma groups become visible in this overview, e.g., the pentose-phosphate pathway seems to be activated only in the HIG and LIG. Furthermore, the control pathway map lays out a rather consistent pattern of flux activities. Though, a few exceptions arise: pyruvate dehydrogenase (PDHm), the major entry point to the TCA cycle, and to lesser extent hexokinase (HEX1) and the pyruvate transport from cytosol to mitochondrium (PYRt2m), exhibit high contribution strengths. It is intriguing that the contribution strengths for these particular reactions is diminishingly small in the LIG case, which indicates an elevated energy metabolism for those adenomas. The HIG, on the other hand, shows a large number of reactions with elevated contribution strengths homogeneously distributed over the whole map, which indicates a significantly reduced energy metabolism.FigureThe correlation between metabolic coherence and inconsistency suggests a connection between both measures, and thus the possibility of interpreting the inconsistency values from the perspective of network topology. In order to investigate this point, we will decompose the inconsistency value into a vector of individual contributions, i.e., reactions that have been reinserted during the optimization procedure in order to achieve the targeted flux-level of the objective function. We further define the contribution strength of a reaction as the number of contributions it makes to the inconsistencies of a data set divided by the size of the respective data set.Comparing the contribution strengths of reactions in central metabolism reveals interesting changes in the physiology of LIG and HIG . This is a consequence of the rigid application of a universal threshold. Topologically, these contributions often disrupt a chain of otherwise expressed reactions (chain disruptor).1. A reaction is expressedin vivo but, e.g., wrong GPR associations, missing isozymes, wrong gene annotations, erroneous data etc., make it invisible for the analysis. Again, these artifacts are often characterized by an interrupted chain of expressed reactions (chain disruptor).2. A reaction is not expressed, but it has to be utilized by GIMME due to the following reasons: 3. The reaction is close to output layer).(a) The stated objective function does not reflect the situation present in the cell. Defining the objective functions as the output of the system, these reactions contributions should often lie close to it .(b) The chosen media composition does not reflect the invisible path).(c) Too many missing gene-protein-reaction associations (GPR), either due to non-enzymatic reaction steps or knowledge gaps, before and after the contributing reaction can lead to wrongly activated paths, as missing GPR information is not punished by GIMME .(d) Alternative TableOur network-based approach is capable of identifying similar patterns as the more sophisticated methods based on flux-balance analysis. In this way, our approach can facilitate an understanding of metabolic inconsistencies from a network perspective. It thus serves as a mediator between the topology of metabolic systems and their dynamical function. In the following we will discuss two representative sets of contributions to the inconsistency in greater detail.Δ1-pyrroline-5-carboxylate reductase (P5CRx), it is involved in a cycle that interconverts NADH into FADH2  acts as precursor as well as degradative product. In the cytosol, P5CRx seems to be expressed in most of the samples, whereas expression levels for PROD2 fall all below the GIMME threshold. It is intriguing that the gene expression profiles are almost reversed in the mitochondrion, where PROD2m  is expressed (at least in the control) and P5CRxm  is not expressed. It is known that the distinct reaction steps of the Δ1-pyrroline-5-carboxylate-proline cycle are localized over different subcellular locations[Proline dehydrogenase (PROD2) emerges as one of the major unspecific inconsistency contributors (see Tableocations: (i) the2-Oxoadipate (2oxoadp) is one of the precursors for acetyl-CoA  revealed unspecific contributions to the inconsistency, as well as a group of reactions that differentially contribute in a specific fashion. We constructed a methodological framework for the topological classification of the inconsistency contributions. Therefore, topological markers were developed for the characterization of both, specific and unspecific contributions, thus enabling a thorough understanding of the context-specific flux-activity results. It turned out, that on the one hand, the specific contributions cast light on an unforeseen diversity of alterations in the physiology of adrenal gland adenomas and, on the other hand, the unspecific contributions provide entry points for the iterative refinement of the metabolic reconstruction.We have presented a sequence of three results on the network-mediated correspondence between gene expression patterns and metabolic systems: (1) We have shown the general agreement between GIMME and a puAn extended “Methods” section is provided in the Supporting Information.All flux balance simulations were conducted using the metabolic reconstruction Recon 1, a genome-scale compartmentalized representation of human metabolism, which imin and max functions, respectively, following the protocol described in[Aldosterone producing adenomas were obtained through the COMETE network from patients who had undergone surgery for lateralized PAL at the Hôpital Européen Georges Pompidou between 2002 and 2006. Methods for screening and criteria for diagnosing PAL were in accordance with institutional guidelines and have been described recently. The cliribed in. The eleribed in). The EBribed in.t. The aldosterone objective and the parameters t=2 and l=0.8 were used throughout the study, if not stated otherwise.Context-specific flux balance analysis of human expression data was conducted using the GIMME algorithm as described in and in tI have been normalized by the objective function’s flux in order to make them comparable.The growth medium was defined as in see Tab: Text S1MC) was computed as described in[g (obtained after thresholding) are mapped onto a gene network (representing metabolism) G to obtain an effective subgraph Gsub that consists of nodes gsub=g∩V(G). Repeatedly and randomly choosing |gsub| nodes from G provides us with a distribution of N random subgraphs Grnd. Let C(G) be a function that extracts the set of connected nodes from a network. Let The metabolic coherence , control (page ii), LIG (page iii), and HIG (page iv). The thickness and color of a reaction edge corresponds to the usage frequency and the contribution strength, respectively. The pathway maps have been obtained from the BIGG database[database.Click here for filePathway map SIcarb. Central metabolism and carbohydrate pathways (see also Additional fileClick here for filePathway map SIlip. Lipid metabolism pathways (see also Additional fileClick here for filePathway map SIvit. Vitamins and cofactor pathways (see also Additional fileClick here for file