Salmonella cause significant morbidity and mortality worldwide. Replication of Salmonella typhimurium inside its host cell is a model system for studying the pathogenesis of intracellular bacterial infections. Genome-scale modeling of bacterial metabolic networks provides a powerful tool to identify and analyze pathways required for successful intracellular replication during host-pathogen interaction.Infections with Salmonella typhimurium LT2 (iRR1083). This model accounts for 1,083 genes that encode proteins catalyzing 1,087 unique metabolic and transport reactions in the bacterium. We employed flux balance analysis and in silico gene essentiality analysis to investigate growth under a wide range of conditions that mimic in vitro and host cell environments. Gene expression profiling of S. typhimurium isolated from macrophage cell lines was used to constrain the model to predict metabolic pathways that are likely to be operational during infection.We have developed and validated a genome-scale metabolic network of Salmonella inside the host cell. This model also serves as platform for the integration of high-throughput data. Its computational power allows identification of networked metabolic pathways and generation of hypotheses about metabolism during infection, which might be used for the rational design of novel antibiotics or vaccine strains.Our analysis suggests that there is a robust minimal set of metabolic pathways that is required for successful replication of  Salmonellae are Gram-negative bacterial pathogens with a wide host range. The ability of Salmonella enterica to cause disease is closely correlated with its ability to survive inside its host cells, which include epithelial cells and macrophages [Salmonella enterica serovar Typhimurium (S. typhimurium) serves as model for the systemic disease typhoid fever. Salmonella strains that are deficient for intra-macrophage survival cannot elicit disease in the mouse model. Many genomic and proteomic datasets exist for Salmonella as a pathogen [Salmonella may hold important clues to understanding their intracellular life-style as well as to understanding host defense mechanisms [in silico models that can integrate and exploit genomic and proteomic data may provide a first step towards a quantitative analysis of the metabolism of intracellular bacteria.rophages . Infectipathogen -6. Most chanisms ,8. Genomin silico models across all the three major domains of the tree of life [Constraint-based reconstruction and analysis (COBRA) of cellular metabolism has been employed successfully to develop organism-specific genome-scale  of life -12. The  of life . The solEscherichia coli [Helicobacter pylori [Haemophilus Influenzae [Saccharomyces cerevisiae [Geobacter sulfurreducens [in silico organisms. The use of constrained based modeling has significant potential to identify new antibacterial targets [H. influenza [Mycobacterium tuberculosis [COBRA integrates and represents our current knowledge of network components and interactions and has been applied to several prokaryotic and eukaryotic organisms, including hia coli , Helicobr pylori , Haemophfluenzae , Saccharrevisiae  and Geobreducens . By syst targets . Modelinnfluenza  and for rculosis . As the rculosis -24,8, onS. typhimurium, that reconciles established genomic and high-throughput phenotyping data and that is augmented by experimental data to facilitate iterative model building efforts. Furthermore, we demonstrate how the model can be used to reconcile existing virulence data and to resolve gaps in our understanding of pathogen metabolism and host-cell nutrient environment. We also use gene expression data obtained for this study in combination with established microarray and proteomic data in the context of the model to understand pathogen metabolism in macrophage cell lines.Here we describe the reconstruction of a detailed and validated genome-scale metabolic network for Salmonella enterica serovar typhimurium LT2 (S. typhimurium LT2) accounts for 4,489 coding sequences (CDS/ORFs) including 39 pseudogenes and a 94 kb plasmid encoding 108 ORFs [in silico metabolic reconstruction of the bacterium referred to as iRR1083 contains only annotated chromosomal genes. The characteristics of the network are detailed in Figure The 4,857-kilobase (kb) chromosome of 108 ORFs . The in E. coli, we have directly measured amino acid, fatty acid and lipid profiles for Salmonella LT2 , fluoroquinolone (ciprofloxacin and fluoroquinolone), cefotaxime, and chloramphenicol [Salmonella to antibiotics, by varying efflux pump activity and/or limiting metabolic flux through the respective pathways. For example, β-lactam antibiotics result in incomplete peptidoglycan synthesis (D-Ala-D-Ala addition), which can be modeled by restricting flux through peptidoglycan synthesis. Similarly, dihydropteroate synthase inhibition by sulfonamides and dihydrofolate reductase inhibition by trimethoprim can be simulated by constraining fluxes through their corresponding reactions.In addition to accounting for these major aspects of cell metabolism and biosynthesis, the reconstruction also includes reactions required for drug efflux, proton pumps, and inhibitory effects of antibiotics on bacterial metabolism. We have included the AcrAB-TolC multi-component drug efflux pump which has been characterized in phenicol -29. An iSalmonella to counteract the host cell response to infection [Another unique aspect of our reconstruction are the reactions involved in free radical quenching that are generally used by nfection ,31. In anfection . The incin silico predicted growth rates were then compared to experimental results of aerobic batch cultivation of S. typhimurium LT2 in M9 minimal media. The calculated maximum specific growth rate (hr-1) of Salmonella for a given carbon source uptake rate was close to the experimentally determined values for S. typhimurium under similar conditions  was used to predict growth rates on six different carbon sources  using their measured substrate uptake rates. These s Figure . QuantitS. typhimurium is a mixed acid fermenter that metabolizes glucose via the Embden-Meyerhoff-Parnas pathway [Salmonella  was also tested experimentally. Growth was only observed on D-xylose and D-ribose, which is consistent with literature and model predictions [a priori to experimentation and can help understand the different pathways that are operational during growth on specific carbon and nitrogen sources.Growth of dictions . Xylose in silico predictions were then compared to (1) existing high-throughput phenotyping data from Biolog's Phenotyping MicroArray™ technology  and (2) reports from experimental literature [FBA was also used to predict which of the 163 carbon containing compounds and 98 nitrogen-containing compounds, with transport reactions (excluding antibiotics) that are included in the model, could be used for growth as sole carbon or nitrogen sources. The terature ; . Most of the inaccurately predicted carbon sources are compounds that can also serve as sole nitrogen sources experimentally (13 of 21). This suggests that regulation or enzyme kinetic limitations likely prevent these compounds from being used by S. typhimurium and E. coli are closely related microorganisms. Comparison of their physiological data and metabolic network structures suggest differences in carbon and nitrogen source utilization. For example, E. coli can utilize D-alanine, L-asparagine, L-aspartate, L-glutamine, and D-lactate as sole carbon sources experimentally, while S. typhimurium can not, even though S. typhimurium has the necessary enzymes and transporters. These phenotypic differences are likely to be caused by differences in how the organisms control metabolism through regulation and kinetics rather than by differences in metabolic network structure. The same explanation can be made for carbon sources that only S. typhimurium can use even though both organisms can catalyze the required reactions .S. typhimurium is also predicted to be able to utilize additional carbon sources due to the presence of unique transporters and/or enzymes .S. typhimurium LT2 was analyzed by simulating its growth on rich medium in the absence of the reactions catalyzed by the corresponding gene. The results were compared for consistency with a compiled list of 255 essential genes from a large-scale gene essentiality screen. Of the 255 essential genes, only 74 were included in iRR1083 and could be compared with experimental results. The total accuracy of essentiality predictions was around 40% (30 out of 74). The accuracy of predicting in vivo essential genes for growth in rich media is within the range reported for models of Pseudomonas aeroginosa (40%) [H. pylori (57%)[Bacillus subtilis (69%)[The impact of single gene deletions on growth of sa (40%) , H. pyloori (57%), and Baclis (69%). DiscrepE. coli and S. typhimurium we compared gene essentiality predictions for in silico aerobic growth in glucose minimal media using the most recent E. coli metabolic reconstruction, iAF1261 [iRR1083  essential metabolic genes and S. typhimurium having 200 (out of 1083) essential metabolic genes. The two models have 900 overlapping orthologs, meaning there are 183 genes included in iRR1083 which do not have an ortholog included in iAF1261 (142 of these do not have orthologs in E. coli and another 41 of the E. coli orthologs were not included in iAF1261).To further explore the metabolic differences between  iAF1261  and iRR1in silico growth in a glucose minimal medium under aerobic conditions. The models also agree on 136 of the 900 orthologs being essential. Comparing the predictions to experimental E. coli knock-out mutant phenotypes  can be attributed to differences in the biomass formulations that were used for the two models. The S. typhimurium model either has additional compounds  that cannot be produced in a gene's absence (contributing to 35 out of 52 discrepancies), or the E. coli model has additional compounds  that cannot be produced in a gene's absence (contributing to 37 out of 45 discrepancies).The discrepancies between essentiality predictions made by the two models can be useful in identifying model differences (biomass formulation and reaction reversibility) and metabolic network differences (isozymes and unique reactions) for the two microorganisms. In 45 of the 900 overlapping orthologs, the S. typhimurium model threonine aldolase is reversible so that threonine can be produced from glycine and acetaldehyde; however, this reaction was changed to irreversible in the updated E. coli model, iAF1261. As a result the biosynthetic genes for threonine production encoding homoserine kinase (thrB) and threonine synthase (thrC) are predicted to be essential by the E. coli model. In contrast, the S. typhimurium model predicts that in their absence threonine can be synthesized from glycine and acetaldehyde. Since both thrB and thrC are essential for E. coli growth in minimal media conditions [iAF1261 and irreversible in iRR1083. The reversible reaction provides another pathway in the E. coli model for serine production in the absence of phosphoserine phosphatase (serA) or 3-phosphoglycerate dehydrogenase (serB), and explains why these two enzymes are predicted to be essential for S. typhimurium growth and non-essential for E. coli growth. Since both serA and serB are essential experimentally in E. coli [S. typhimurium model predictions.Reaction reversibility differences are also responsible for some of the discrepancies. In the nditions  it is li E. coli , it is lS. typhimurium has genes encoding for two separate 3-isopropylmalate dehydratases (encoded by STM0110-STM0111 and STM0329-STM0330) while E. coli only has genes for one (encoded by b0071-b0072). As a result, when STM0110 or STM0111 are deleted the iRR1083 model predicts that STM0329 and STM0330 can be used instead to produce leucine, which is not possible in E. coli since it lacks the second isozyme. S. typhimurium also carries out reactions that E. coli can not. For example, an NADPH dependent sulfite reductase (unique to S. typhimurium) is predicted to be used for hydrogen sulfide production (needed for cysteine biosynthesis) when the NADH dependent sulfite reductase (present in both organisms) is absent.Gene essentiality discrepanices caused by metabolic network differences, such as additional reactions and/or isozymes, provide interesting insights. For example, E. coli has additional isozymes or metabolic reactions, that explain why genes are predicted to be non-essential in E. coli but essential in S. typhimurium. For example, there are multiple carbonic anhydrases and dihydrofolate reductases in E. coli while S. typhimurium has only one copy of each of these essential enzymes. E. coli also contains a gene encoding ribose 1,5-bisphosphokinase, for which there is no ortholog in S. typhimurium. This E. coli specific enzyme is predicted by the iAF1261 model to compensate for ribose-phosphate pyrophosphokinase in 5-phospho-alpha-D-ribose 1-diphosphate production, which is needed for histidine and nucleotide biosynthesis in the absence of ribose-phosphate pyrophosphokinase [There are also cases where hokinase . As showin silico growth of iRR1083 was compiled and compared with a set of in vivo essential and non-essential genes from the literature  of the in vivo virulent mutants and 56% (9/16) of the in vivo avirulent mutants. Most attenuated strains were also correctly predicted by the model to still be able to grow (13/15). Again a statistically significant relationship between model predictions and experimental observations was found (χ2 = 10.9 and p = 0.001). The model predicted incorrectly that mutants defective in pmrF and udg were avirulent [pmrF and udg mutant strains. This would increase the final virulence prediction accuracy to 100%. The consistencies and discrepancies between in silico and in vivo mutant phenotypes deserve further discussion and may generate potential hypotheses that can subsequently be tested.The virulent ,43. BothAceA encodes isocitrate lyase, which catalyzes the first step in the glyoxylate shunt, an anaplerotic carbon assimilatory pathway that synthesizes C4 dicarboxylates from C2 compounds like acetate or short chain fatty acids. AceA is required only for chronic Salmonella infections and not for acute infections [Some genes that are involved in major central metabolic pathways and are non-essential for intracellular survival (i.e. mutants defective in these genes are virulent) are discussed below. fections . This enfections .katE and katG) mutants [sodA and sodCII) [sodCI) are attenuated and the model incorrectly predicts that a sodCI mutant would be virulent; however, if the host-cell environment included superoxide and none of the other superoxide dismutases were expressed or active  then the bacterium would have no way of dissipating superoxide and the model would predict an avirulent phenotype.Phagocytic cells are able to generate superoxide, hydrogen peroxide and other reactive oxygen species (ROS) and pathogens possess multiple defenses to such oxidative stresses. The model also accurately predicted that catalase ( mutants  and supe sodCII) ,48 are vnagA mutant. NagA is a N-acetylglucosamine-6-phosphate deacetylase, and it's substrate acts as an inducer of the nag operon, which relieves repression by NagC. It has been proposed that nagA mutants indirectly lead to reduction in aminosugar biosynthesis, which is needed in membrane structures [E. coli model, would allow us to address the role of regulation of metabolism during Salmonella-host interaction.One of the incorrect predictions for the experimentally determined avirulent strains was for the ructures . The modaroABCD). Aro Salmonella strains have been used as oral vaccines [in silico analysis. Strains of S. typhimurium with complete non-reverting blocks in aromatic biosynthesis are avirulent [Of the experimentally determined attenuated mutants, the model predicted that mutants defective in aromatic amino acid biosynthesis are avirulent  are attenuated rather than avirulent [in vivo is then able to resolve 62.5% of the mutants that were incorrectly predicted in silico to be virulent. This approach can thus also serve as an indirect probe of the host cell intracellular environment in which the pathogen finds itself.A large portion of the experimentally determined avirulent mutants which were incorrectly predicted by the model to be virulent are associated with nucleotide biosynthesis: A Figure . These mvirulent . The expSalmonella serovar typhimurium, are missing or are pseudogenes in other Salmonella serovars  infection of macrophage cell lines, only 21% of the total genes in the genome are differentially expressed , and fatty acid degradation genes fadA, fadD/fadE are not expressed. Although these genes have been implicated for virulence in chronic Salmonella infection, they are known to be unchanged during short-term infection experiments [in vivo during the early stages of infection as suggested in literature [gltA, sdh) are over expressed.We sought to identify genes Figure  and seleeriments . Our resterature . This alcyoE and cyoA is suggestive of an aerobic environment in vivo, at least during the early stages of infection [1F0 ATP synthase subunits measured within our data set also support this. ATP synthase is primarily responsible for the oxidative phosphorylation of ADP to ATP. It also plays a role in maintaining the proton gradient to maintain intracellular pH and drive efflux pumps. The high levels of mRNA transcripts for succinate dehydrogenase and protoheme farnesyl transferase genes also suggest heme biosynthesis occurs in S. typhimurium during infection. These are in concurrence with other existing data sets [The simultaneous up regulation of succinate dehydrogenase and electron transport chain genes nfection . Increasata sets .hisC, hisD, hisG) were up regulated and those involved in aromatic amino acid synthesis pathways  were down regulated. These findings are consistent with the literature [purF) and NAD biosynthesis (nadE) were down regulated or not detected. The down regulated genes also included those involved in glycolysis and carbon metabolite repression, certain amino acid decarboxylases and some transporter genes including drug efflux genes. These results suggest that Salmonella acquires a significant amount of essential nutrients directly from the host cell, thus shutting down several biosynthetic pathways when inside the host. The genes that cannot be detected include some genes involved in glycolysis/gluconeogenesis  and anaplerotic reactions (ppc). Other genes are detectable, but do not change in expression level over the course of infection, including those in the pentose phosphate pathway (zwf), Entner Duoduroff pathway (edd) and glutathione cycle . Fatty acid biosynthesis and degradation genes are also not detected during the monitored early stages of infection.Genes belonging to the histidine biosynthesis cluster , an additional 319 reactions  could be used by Salmonella in the host cell environment . IncorpS. typhimurium extracted from macrophage cells [in silico reactome, 65% of the genes were down-regulated and formed a subset of the blocked reactions from our FVA analysis  and genetic factors (mutations or deletions) and their integrated function to orchestrate cell phenotypes (virulence or attenuation). Knowledge of the functional status of metabolic genes under defined constraints allows us to interpret the role of critical nodes in a cellular metabolic network. The function of redundant pathways under internally perturbed conditions, such as in the host cell during infection, provides important insights into metabolic network structure. Although this internal robustness has been experimentally demonstrated, building a complete catalog of genes essential for growth under a myriad of conditions for any organism is time-consuming and laborious. A computational approach that predicts gene essentiality with high accuracy is thus of great value. Model predictions of virulence for different mutants improved from 80% to 91% upon altering host-cell environment components  and this shows how the model can be used as a tool for providing insights into the role of metabolism in infection and pathogenesis. To date, constraint-based models cannot predict effects of toxic intermediates and methods are needed that allow for prediction of concentrations within constraint-based models.E. coli, there are some major differences in fatty acid and amino acid composition that require experimental measurements to determine the drain of different metabolites and the cost of their production on the function of the organism. Our study has addressed this issue by directly determining the components of Salmonella biomass, thus increasing the validity and predictive accuracy of model iRR1083.A biomass reaction (representing the conversion of biomass components into one gram dry weight of biomass) is needed to accurately predict the effects of gene deletions on growth and viability. Although predictions have been made in the past with approximations of the biomass function to that of S. typhimurium is a pathogen that is the leading cause of human gastroenteritis and is used as a mouse model for human typhoid fever. Although more than 2000 serovars exist, the LT2 strain, whose genome sequence has been used here for building model iRR1083, is one of the principal strains for cellular and molecular biology of Salmonella. Attenuated mutants have been used not only as live oral vaccines against Salmonella infection but also to express antigens from other pathogens and to deliver proteins to solid tumors. One reason for attenuation or avirulence is the deletion or functional silencing of a genetic element in the bacterium resulting in the impairment of the intracellular survival capacity of S. typhimurium. Our in silico analysis shows the ability to predict such effects with good accuracy. At this point the host cell metabolic environment has been inferred indirectly from gene-expression data. Improved accuracy in directly determining what metabolites are available in the host cell environment and incorporation of transcriptional regulatory rules into iRR1083 will allow a more precise analysis of metabolic selective pressures a pathogen encounters during infection.S. typhimurium metabolic reconstruction can be a valuable tool to interpret several 'omics' data types. Although there is not a direct correlation between gene or protein expression levels and metabolic fluxes, the genome-scale model serves as a platform to visualize these large data sets and interpret them in the context of operational, redundant or incomplete metabolic pathways. This provides a better understanding of cellular phenotypes and offers insights into how system level properties affect survival or sensitivity of pathogens to factors in the environment provided by the host cell. For example, the model prediction of fad genes not being operational during early stages of infection  and operational during sub-optimal growth can be explained by the fact that fatty acids are not utilized in the initial stages of infection by S. typhimurium [iRR1083 could suggest a switch from optimal to sub-optimal growth or a change in nutrients available for Salmonella inside host cell tissue. This switch is concomitant with a marked decrease in growth during persistence or chronic infection. Growth rates are presumably higher  during the initial stage of infection. The entire reactome of Salmonella as predicted by the model provides many hypotheses that need to be further investigated to identify the implications of metabolic pathways and functions in pathogenesis. Metabolomic data have become more readily available and easier to measure. They can be used to apply additional constraints to the model [In addition to pathogenicity and virulence analysis, the himurium . This obhe model , thus imS. typhimurium we have developed here also presents us with the opportunity to interrogate several other serovars or species that belong to the Salmonella genus. For example, panD is the only gene that is non-functional in Salmonella typhi, and is predicted to be required for virulence in specific conditions. The presence of pseudogenes in other serovars can be analyzed in the context of the genome-scale model to present us with systemic similarities and differences that may or may not play a role in the pathogenic potential of all the four species. Serovars lacking panD would require panthothenate from its host. Thus, compounds that affect pantothenate transport could potentially be used as antibiotics. Such analyses across different serovars require genome-scale models and might accelerate the identification of rational drug targets.The genome-scale model of iRR1083 model for S. typhimurium are conserved in models for E. coli MG1655, there are unique metabolic and genetic differences that affect growth phenotypes in response to different environmental or genetic perturbations. The two organisms are each capable of utilizing unique carbon sources, which are related to differences in metabolic networks (unique transporters or enzymes) or differences in regulation or kinetics that affect flow through shared reactions common to both organisms (reactions are present to catabolize carbon sources in both metabolic networks but one organism does not use them as sole carbon sources). We also found that there are differences in the number of isozymes or alternative reactions/pathways that enable one organism to be more robust against gene deletions in a glucose minimal media condition. We anticipate that comparisons of model-predicted essential genes in more environmental conditions will lead to the identification of more metabolic differences between the two organisms, as the analysis was only performed for aerobic growth in glucose minimal media. These metabolic differences might shed light onto the evolutionary differences between the two organisms and the nutrients they are or were exposed to.Although many of the reactions in the Salmonella requires for intracellular survival during infection [in silico simulation of different nutritional requirements and constraints as they may be present in different host cell types or tissues that are difficult to directly address experimentally. Our model can generate hypotheses that can be validated by using mutant strains, high-throughput data, and selective analysis of pathways. Such an endeavor has the potential to lead to an improved understanding of how intracellular pathogens utilize the existing microenvironment of the host. This in turn might lead to the identification of conserved metabolic pathways that can be targeted by novel interfering compounds.The genome-scale metabolic network reconstruction presented here supports the notion of a robust minimal set of pathways that nfection . Our modS. typhimurium (iRR1083). This model has been validated by experimental data and by legacy data. It demonstrates an accuracy of 80% for growth and virulence phenotypes. Thus the model iRR1083 provides a suitable platform for computing cellular phenotypes for Salmonella and for further integration of high-throughput data.We have presented here extensive datasets within a reconstruction of a genome-scale metabolic model for Salmonella was determined experimentally, which increased the accuracy of our model building and also showed distinctive difference to that of E. coli. Constraint-based analysis using the metabolic reconstructions iRR1083 for S. typhimurium and MG1655 for E. coli identified unique metabolic differences between these two bacteria.Biomass composition of Salmonella during infection of macrophages identified operational and non-operational metabolic pathways. Flux variabity analysis of metabolic pathways identified a minimal set of reactions required for Salmonella intracellular survival.Expression profiling of selective key metabolic enzymes in M. tuberculosis and demonstrates its suitability for analyzing bacterial metabolic networks during infection. From further validation and testing of hypotheses generated from these reconstruction efforts we expect to arrive at a conserved set of metabolic reactions that interdigitate with those of the host cell and might thus provide novel targets for therapeutic intervention.This study thus provides another high-resolution reconstruction of microbial metabolism of an intracellular pathogen next to that of S. typhimurium is outlined schematically in the Additional file The reconstruction process for Salmonella enterica serovar typhimurium LT2 (S. typhimurium LT2), which is available at TIGR. Genes to proteins to reaction associations (GPR) were confirmed by comparing homology of S. typhimurium gene sequences to E. coli gene sequences and biological information databases such as EXPASY, KEGG, and BioCyc. These GPR associations connect genetic data to reactions in the metabolic network [The initial draft reconstruction was built from the annotated genome  of Salmo network  and alloS. typhimurium LT2 data from the literature was then used to determine the amount of lipids (and their phospholipid composition), lipopolysaccharide, peptidoglycan, and glycogen. The growth associated ATP maintenance and soluble metabolite pools were assumed to be the same as reported for E. coli [S. typhimurium biomass reaction are provided in the Additional file A reaction that represents biomass production is included in the model to account for the drain of precursors and macromolecular building blocks into biomass. Biomass was represented as a linear combination of all the macromolecular components  or monomers of macromolecules (amino acids and nucleotides). Amino acid and fatty acid composition were experimentally measured using standard methods described in manual of bacteriological methods . The rel E. coli . Completv) that satisfy all the constraints in order to find optimal flux distributions. Flux through the biomass production reaction has successfully been used as an objective function for E. coli  . With FBunctions ,61, and unctions  was addiThree different environments were used to provide constraints for simulations: (i) M9 minimal medium  with an added carbon source; (ii) LB-media ; (iii) host-cell nutrient environment . While the host-cell nutrient environment was difficult to ascertain, it was based on an extensive literature review to identify a possible composition. Details of all simulated media conditions are provided in the Additional file S. typhimurium LT2  was performed by optimizing biomass production with different carbon and nitrogen sources. A maximum uptake rate of 5 mmol per gram of dry weight per hour (mmol/gDW cell/h) was used for the different carbon and nitrogen sources. Different nitrogen sources were simulated with pyruvate as a carbon source and different carbon sources were simulated with ammonium as a nitrogen source.Validation of the model against Biolog data for Genetic changes, such as gene deletions and mutations, can be simulated by adding additional constraints to individual fluxes . For exaS. enterica serovar typhimurium LT2. Aerobic batch cultivation was done in an incubator shaker at 37°C and 100 rpm. Minimal M9 medium was supplemented with 6 different carbon sources . The cell culture optical density (OD) was monitored at regular intervals using a Beckman DU spectrophotometer at 600 nm. The OD was converted into g dry weight using a previously determined biomass calibration standard curve using the same spectrophotometer (gDW = 0.7396·OD600). Samples were also withdrawn every 2 hours, filtered and the supernatants were frozen and stored at -80°C for HPLC analysis to analyze substrate utilization and product formation profiles.All growth experiments were carried out using the strain + column (Biorad). A 5 mM Sulfuric acid mobile phase at a flow rate of 0.5 ml/min at 65°C was used for separation. Both UV and RI (refractive index) detector were employed. Small molecules were quantified using a previously determined calibration curve.Organic acid and sugar analysis was done using an ion exchange Aminex 87HS. typhimurum. GeXP employs eXpress Profiling (XP-PCR), a patented technology for multiplex gene expression profiling analysis by which up to 30 genes can be easily multiplexed in the same reaction. We used a protocol that comes with GeXP Reagent kits that involved five basic steps: 1) Primer design; 2) cDNAsynthesis; 3) PCR; 4) Separation on the GenomeLab GeXP Genetic Analysis System; 5) Fragment Analysis and Expression Profiling. The data was then analyzed using the GeXP analysis proprietary software , Excel  and Matlab . Primers were designed using proprietary software provided by Beckman  was carried out as described . RNA wasSalmonella typhimurium iRR1083 and performed all the analyses. AR and SS obtained all the experimental data. AR and SD planned and designed the study, analyzed, and interpreted all the data. AR, JR, and SD wrote the manuscript. BP provided critical advice and suggestions. All authors approve the content of this manuscript.AR and JR conducted the reconstruction of Salmonella metabolic network iRR1083. Gene-Protein-Reaction associations in the final version of the reconstruction iRR1083.Click here for fileS. typhimuriumCellular composition of . Experimentally determined values for Salmonella cellular content of amino acids, carbohydrates, DNA, RNA, selected organic and inorganic compounds, and fatty acid composition of membrane and cell wall components.Click here for fileFlux Variability Analysis. In silico reactome as determined by flux variability analysis (FVA).Click here for fileComparison of qualitative phenotyping . Predictions for 163 possible carbon sources and 98 possible nitrogen sources were compared with experimental data.Click here for fileE. coli and S. typhimuriumGene essentiality comparison between . List of discrepancies in gene essentiality predictions between orthologs which are present in genome-scale models of S. typhimurium (iRR1083) and E. coli (iAF1261).Click here for filein silico for M9, LB and host cell environmentMedia compositions used . Carbohydrates, amino acids, vitamins, minerals, inorganic molecules, nucleotides, and amines used for in silico analysis.Click here for fileSalmonella serovars typhimurium, typhi, paratyphi, and enteritidis. List of genes present in serovar typhimurium and absent or non functional (pseudogenes) in serovars typhi, paratyphi and enteritidis.Click here for fileSalmonellaSelected metabolic gene expression during infection of macrophages by . Selected metabolic genes used for measuring gene expression or mRNA transcript levels in S. typhimurium extracted from macrophages post infection.Click here for fileSalmonella metabolic networkReconstruction of . Flow chart for reiterative model building for Salmonella network iRR1083.Click here for filePrimer Sequences. Primer Sequences used to measure gene expression or mRNA transcript levels of the chosen metabolic gene set described in S6 using GEXP.Click here for file


Escherichia coli. A detailed understanding of the coordination of the control of individual transporters offers possibilities to explore the potential of microorganisms e.g. in biotechnology.Global control influences the regulation of many individual subsystems by superimposed regulator proteins. A prominent example is the control of carbohydrate uptake systems by the transcription factor Crp in Crr. The model describes the relation between the growth rate and the degree of phosphorylation of EIIA crr for a number of carbohydrates by a distinctive response curve, that differentiates between PTS transported carbohydrates and non-PTS carbohydrates. With only a small number of kinetic parameters, the model is able to describe a broad range of experimental steady-state and dynamical conditions.An o.d.e. based mathematical model is presented that maps a physiological parameter – the specific growth rate – to the sensor of the signal transduction unit, here a component of the bacterial phosphotransferase system (PTS), namely EIIAThe steady-state characteristic presented shows a relationship between the growth rate and the output of the sensor system PTS. The glycolytic flux that is measured by this sensor is a good indicator to represent the nutritional status of the cell. Escherichia coli is steadily increasing. Although current research on individual uptake systems like glucose still reveals new players that maybe play a role in local control [E. coli, it was shown that the autocatalytic action of inducer allolactose is responsible for the existence of multi-stationarity [Crr. EIIACrr is a component of the phosphoenolpyruvate (PEP): carbohydrate phosphotransferase system (PTS). The PTS is not only a transport system for a number of carbohydrates but also acts as a sensory system. Sensor elements like the PTS can be seen as logic elements that process external stimuli into intracellular signals. High fluxes through the glycolysis, corresponding to high growth rates result in a low degree of phosphorylation of EIIACrr. At first view, this is surprising, since, assuming a linear reaction chain, high fluxes result in high pool concentrations, based on the  monotone dependency of the reaction rate on the substrate concentration. The PTS together with the glycolysis can now be seen as an element that allows a transformation of high fluxes into a low pool concentration. This is not only due to the existence of two complementary pools like EIIACrr and its phosphorylated form, but as we will show, depends strongly on the flux distribution at the PEP node. High fluxes through the glycolysis result in low values of the phosphorylated form of EIIACrr while low fluxes indicate a hunger situation and the global transcription factor cAMP·Crp is activated.Mathematical models of cellular systems describing metabolism, signal transduction and gene expression are becoming more and more important for the understanding of the underlying molecular processes. Since the earliest work to elucidate the molecular nature of regulatory structures by J. Monod, the knowledge of the detailed interactions between the components that are responsible for carbohydrate uptake in  control , the knoionarity . Such noionarity ,4 to eluCrr could be seen in various growth situations of the wild type strain growing on single substrates like glucose, lactose, and glycerol and for growth on mixtures of substrates, and of a PtsG deletion mutant strain missing ptsG, a gene that is central for glucose transport.Interestingly, the relationship between growth rate and degree of phosphorylation of EIIAE. coli consist of two common cytoplasmatic proteins, EI (enzymeI) and HPr (histidine containing protein), as well as of an array of carbohydrate-specific EII (enzymeII) complexes. E.g. for glucose uptake, a phosphoryl group is transferred from phosphoenolpyruvate (PEP) through EI, HPr, EIIACrr, PtsG  and finally to the substrate. Since all components of the PTS, depending on their phosphorylation status, can interact with various key regulator proteins the output of the PTS is represented by the degree of phosphorylation of the proteins involved in phosphoryl group transfer.The PTS of Crr: (i) Metabolic fluxes through the glycolysis. Extracellular glucose is taken up by PtsG and enters into the cell as glucose 6-phosphate. Other carbohydrates enter glycolysis at the same node  or at other nodes (e. g. glycerol at triose phosphate). The carbohydrates are further metabolized by glycolytic reactions. At node PEP, the flux is subdivided. One part is converted to pyruvate by pyruvate kinase while the remainder part is converted to pyruvate by the PTS. Other fluxes from or to PEP or pyruvate are marginal and hence are not considered in this study. Fluxes from e.g. acetate uptake enter gluconeogenesis via pyruvate or from TCA. (ii) Overall concentration of the PTS proteins. The expression of the pts genes  is subject to control by various regulators, with Mlc and Crp being the most important ones. Mlc is a repressor that is active if no glucose is present in the medium. A possible mechanism of the interaction between Mlc and EIICBCrr is described in [ptsG transcript is subject to post-transcriptional control by a small RNA (sRNA) regulator SgrS which is induced at different stress conditions, e.g. glucose-phosphate stress. This stress occurs when cells accumulate glucose 6-phosphate or the glucose analog a-methyl-glucoside 6-phosphate and leads to the degradation of PtsG mRNA [Crr is the overall equilibrium constant Kpts that links the PEP/pyruvate ratio to the degree of phosphorylation. Figure Crr. Furthermore, EIIACrr is considered to exist in a free form and in a form bound to a protein L involved in carbohydrate transport or metabolism . Then, the equilibrium constant Kpts can be determined as:Figure ribed in . Crp is tsG mRNA -7. (iii)K1, K2, K3, KL being the respective equilibrium constants from the single reactions shown in Figure Crr is bound to lactose permease or glycerol kinase, it acts as an inhibitor that prevents uptake and/or metabolism of the substrate, an effect that is called inducer exclusion.with Crr. The kinetic properties of the sensor which at the same time is a transport system are characterized and the output of the sensor is mapped to the rate of synthesis of genes that are under control of transcription factor cAMP·Crp. In this way, a closed loop is established that precisely adjusts the respective transport protein to maintain the incoming flux. The results are used to predict the transient behavior during glucose/glucose 6-phosphate diauxic growth and glucose/lactose diauxic growth. Finally, we also show that the approach can be generalized for other main growth substrates like acetate. In the end, a comparison with a corresponding detailed model on catabolite repression [The intention of this contribution is to develop a model with a small number of state variables and parameters to work out the basic principles for the understanding of the sensor function. Nearly all parameters could be determined from experiments  to other parts of the central metabolism is represented by rpdh. Since other fluxes from or to PEP and pyruvate are rather marginal they are not considered in the model. Proteins EI, HPr, and EIIACrr of the PTS are represented by only one component X that exists either in the unphosphorylated form X or in the phosphorylated form XP. In case of a PTS carbohydrate, XP is used for transport via rpts_up.The scheme simplifies the biological knowledge on metabolism and gene expression by lumping together reactions and components. In case A, carbohydrate uptake is represented by reactions Case B considers gluconeogenetic substrates which feed into TCA or into other central metabolites below the PEP/pyruvate branch. Here, PEP and pyruvate are produced by a number of different reactions, e.g. from the TCA or via Acetyl CoA. Among these, PEP synthase (Pps) is active converting pyruvate directly to PEP. For substrates that enter TCA, two pathways are known that connect TCA and glycolysis: PckA (PEP carboxykinase) connects oxaloacetate and PEP, MaeB/SfcA  connect malate and pyruvate. These fluxes are represented by h1 rup and h2 rup, respectively, with h1 and h2 are numbers between zero and one, representing a fraction of the uptake rate rup. In a number of subsequent gluconeogenetic reaction steps (rglu), PEP is then converted to glucose 6-phosphate.Based on the knowledge presented so far, a simplified model structure is suggested that is able to simulate the different cases proposed above.G6P, PEP, Prv and the protein that represents the PTS, XP, the following equations that describe the dynamics are obtained from the scheme:As was shown in a previous study , the metrn-pts and rpts_up are the systems inputs and are related by the yield coefficients to the specific growth rate. XP is the system output. The following conditions will hold for the defined rates in steady-state:where The kinetics for the rate laws are kept as simple as possible to describe the experimental data. The rate laws are assumed as follows:X0 is the overall concentration of the PTS protein. The focus of the analysis will be on the branch point at PEP. To elucidate the correct choice of the kinetic rate law for the pyruvate kinase reaction, function f is introduced that represents different model variants. Function f depends on PEP but may also depend on different metabolites in the network.with The steady-state concentrations can be derived from the equations above:PEP is given in implicit form since it depends on function f. In the following, growth situations on non-PTS and PTS sugars are considered separately.The steady-state equation for Equation (17) for the non-PTS case readsf has a strong influence on the steady-state characteristics: Assuming f = 1, that is, the pyruvate kinase reaction is modeled as a first order reaction, XP is constant and independent from the uptake rate. This could not be observed in the experiments (see below). Assuming a Michaelis-Menten kinetics, that is, PEP can be calculated via Equation (16):As can be seen cleary, the choice of kpyk, in this case, is the maximal reaction rate of rpyk, PEP is an increasing monotone function in dependency on the uptake rate rn-pts. Interestingly, this leads to values for XP that increase for increasing uptake rates. This result is again contradictory to the observed experimental results.Since Equation (17) for PTS substrates reads:Differences for PTS and non-PTS substrates can be seen in the numerator that is always smaller in case of growth on PTS substrates. Since the denominator is always larger than in the case of non-PTS substrates, the curve of the PTS substrates will always be below the curves for non-PTS substrates.To describe the available experimental data for growth on PTS and non-PTS substrates , values for n > 1, m ≥ 1 are analyzed. Equation (1) relates the overall PTS constant Kpts to individual reactions steps. Since measurements of proteins that influence Kpts are not available, Kpts represents a mean value for different situations considered in the experiments. For parameter identification 31 data points are considered, values n = 2, m = 1 are fixed and values for Kpts and X0 are taken from literature  -4 (parameters):The standard deviation X0 this corresponds to 13%. Figure Based on the maximal value A robustness analysis was performed as described earlier . InsteadW withbased on the sensitivity matrix j is the index of the simulated data points was calculated. Together with a constraint, considering the deflection of the parameters with W [p  while the others are kinetic parameters of the PTS reaction  and the pyruvate kinase reaction . Interestingly, in the kinetic expression f of the pyruvate kinase parameter n describing the influence of the feed-forward control (activation of the pyruvate kinase by glucose 6-phosphate) shows maximal sensitivity in both cases. In general, the amount of enzyme has a bigger influence than the kinetic parameters. This will allow the cell to adjust the degree of phosphorylation by genetic control.the maximal deviation of the trajectories can be calculated by the eigenvectors and eigenvalues of matrix W . The eigFor gluconeogentic substrates the scheme according to Figure rup is the system input. Rate rbio is the flux from pyruvate to biosynthesis and rglu is the rate of gluconeogenesis:Rate rpps the following simple approach is used:For the rate g representing the influence of pyruvate and possible effectors. Together with parameters h1, h2 and kpps the rates are adjusted in such a way that data from a flux distribution [XP can be rewritten as:with function ribution  can be dg should depend on PEP that acts as an inhibitor of PEP synthase. Otherwise, the degree of phosphorylation increases with increasing uptake rate which seems, also in this case, not to be meaningful. Indeed, literature research revealed that PEP synthase is negatively regulated by PEP [g used is:Simulation studies lead to the conclusion that function d by PEP . Functiopps mutant strain when glucose and acetate are provided in the medium. They showed that the missing Pps protein has no influence on the general physiology but shows a significant influence on the transition time from growth on glucose to growth on acetate. In this case the degree of phosphorylation is a constant value:taking into account that Pps is a dimer with two possible binding sites. A simulation study for different values of acetate uptake/growth rates are shown in Figure Liao and colleagues observed a drastic increase of the lag phase on acetate in the mutant strain during glucose/acetate diauxic growth. Our simple model predicts, that the degree of phosphorylation is a bit smaller than the values in the wild type strain. This confirms that Pps has nearly no influence on physiological parameters like the growth rate.With the model developed so far, model predictions can be performed. Two cases are considered: the PEP/pyruvate ratio and growth on different single carbon sources.The PEP/pyruvate ratio could be predicted in dependency on the growth rate. Experimental data were taken from  and compCrr dEIIA depends on the fraction of phosphorylated HPr dHPr:To confirm that the model presented here is able to describe the sensor system for a number of carbohydrates, experimental data from batch experiments with different PTS and non-PTS carbohydrates were performed and compared with the model calculations . As can K3, the equilibrium constant for the phosphoryl transfer HPr to EIIACrr is approximately 1 [dEIIA and dHPr are nearly equal. Therefore, in the model, state variable X can be used to represent HPr as well as EIIACrr.Since the value for mately 1 ,14, valuCrr on transcription efficiency is analyzed, afterwards the kinetics of the PTS transport system is investigated.In order to set up a closed loop, further modules have to be characterized. First, the influence of phosphorylated EIIACrr on the transcription efficiency were performed with the cAMP·Crp independent promoter scrKP and the cAMP·Crp dependent promoter scrYP [Crr while the cAMP·Crp dependent promoter shows a sigmoidal behavior in the range below 0.6. From the data, a sigmoidal function gT could be determined that maps the degree of phosphorylation of EIIACrr to the rate of protein synthesis:Experiments to determine the influence of the degree of phosphorylation of EIIAer scrYP . As can n = 6) indicating a high sensitivity in a narrow range of the input.Unexpectedly, the Hill coefficient is high  on the rate of synthesis gB (Equation (43)). This is done to account for possible effects on ptsG mRNA stability. The model introduced so far is complemented with equations for the substrates Glc6P, Glc, biomass B, and kinetics for the glucose 6-phosphate uptake. The additional equations are:Carbohydrate transporters are inducible, that is, the enzymes are synthesized only if the respective substrate is present in the medium. To take this into account the rate of synthesis depends on Equation (37) and a second term topic in ). Howeveμ that is calculated with the yield coefficients Yg6p and Yglc in dependence on the substrate uptake:with the specific growth rate k1 and k2 are scaling factors and gT is taken from Equation (37).Parameters Crr is a prediction based on previous results. The time course of the substrates in the medium hints to an inhibition of glucose uptake during glucose 6-phosphate uptake. After consumption of glucose 6-phosphate, the growth rate slows down which results in a small increase of the degree of phosphorylation. During subsequent growth on glucose, the degree of phosphorylation of EIIACrr is again very low. For the experiment shown in Figure In the simulation Figure , only thKI >> EG6p). As can be seen in Figure ptsG mRNA degradation.As described above, the cause for the down-regulation of PtsG is not clear. To check the intracellular levels of glycolytic metabolites, a simulation is performed that compare the experiment shown in Figure Crr on cAMP·Crp dependent promoters. The equation for the lactose in the medium, lactose transporter ELac and for the transporter kinetics read:Finally, we simulated a diauxic growth experiment with glucose and lactose already introduced in  with theAs can be seen in the simulation in Figure A very detailed model for catabolite repression was already introduced to describe a number of experiments under different conditions and with different strains . HoweverCrr, an element of the sensory system PTS, and the specific growth rate μ. Under a variety of experimental conditions with a wild type strain and a mutant strain this relationship could be verified over a broad range of the growth rates, revealing the signaling and kinetic characteristics of the sensor. For the analysis of the system, a mathematical model with a small number of state variables  described in detail for genetic systems . Here, wIn engineering science, sensor or measurement systems are designed in such a way that they don't influence the system that is measured. This is called "free of retroactivity". Considering the PTS operational mode in comparison to the non-PTS mode the difference of the curves is due to the transport activity of the PTS. Hence, the sensor PTS is not free of retroactivity; however, for small growth rates, indicating a severe stress situation, the difference between the PTS mode and the non-PTS mode is negligible.Crr are in good agreement with the predicted values. The results also confirm that the Pps enzyme has only marginal influence on growth on acetate as described by [As representative of gluconeogenetic substrates, growth on acetate was considered. The fluxes are adjusted in such a way that a flux distribution published previously, is matched. Measurements of the degree of phosphorylation of EIIAribed by . Howevern = 6 is rather high. This might be due to several reasons: although the signal transduction pathway starting from EI and ending with Crp is rather short, several components and processes are involved. First cAMP is generated by the adenylate cyclase (Cya); second cAMP interacts with Crp to activate the transcription factor. Furthermore, transcription of Cya is also under control of Crp leading to a feedback loop. Since the kinetics of the individual steps are not yet characterized, the rather high Hill-coefficient can be seen as an overall measure of the sensitivity of the system. The kinetics determined are used to simulate the two dynamical experiments and a good agreement between the simulation data and the experimental data could be observed. This shows that not only the steady-state behavior can be reproduced well but also the dynamics of the sensor/actuator system.The transcription efficiency according to Equation (37) revealed that the Hill-coefficient Escherichia coli during growth on glucose/glucose 6-phosphate and on glucose/lactose. The model has to be extended to describe the kinetics of the transporters and the kinetics of gene expression for the relevant transporters. Since experimental data that characterize the KGlc value for glucose can be found in the literature, the respective value KEIIA for the degree of phosphorylation was determined by a simulation experiment with a random bi-bi double substrate kinetics, Equation (38), and experimental data from [kmax and KEIIA are determined by a least-square fit.The simplified scheme is used to analyze the growth behavior and the dynamics of ata from . ParametptsG mRNA is under control by SgrS, a small RNA. It was shown that high levels of intracellular glucose 6-phosphate or fructose 6-phosphate lead to ptsG mRNA degradation [ptsG and global control of PtsG synthesis by Crp were taken into account and have to be adjusted very precisely.Growth on glucose/glucose 6-phosphate reveals the interesting observation that the concentration of the glucose transporter decreased during growth on glucose 6-phosphate. To match the experimental data, an inhibitory effect of the glucose 6-phosphate transporter UhpT on the glucose transporter PtsG was assumed and described with a simple kinetics. Previous studies revealed that the radation . Here, tradation . Note, tA comparison with a detailed model for catabolite repression justifies the set up of the new model. Altough validated under different experimental conditons, the detailed model fails to describe growth on PTS carbohydrates on a broad range of the growth rate.E. coli since it can be easily extended to describe other regulatory systems.The approach is based on the development of a model with a minimal number of parameters that are necessary to describe the observations. Although some of the parameters have no defined mechanistic interpretation such models will facilitate the procedure of parameter analysis and estimation. The model is capable to simulate a broad range of experimental conditions and is suited for further studies on control systems on For simulation of the algebraic system, solving the o.d.e. system, and parameter estimation MATLAB was used. Files to simulate the system with MATLAB and the experimental data can be found on a website . For theThe author(s) declares that there are no competing interests.AK performs modeling, model analysis and parameter estimation. KB performs the experiments. EDG conceived of the study, and participated in its design and coordination. All authors read and approved the manuscript.Supplementary Information. The Supplementary Information includes the description of the experimental data and the values for the kinetic parameters of the mathematical model.Click here for file


Neisseria meningitidis was constructed; a minimal medium for growth of N. meningitidis was designed using the model and tested successfully in batch and chemostat cultures.A genome-scale flux model for primary metabolism of  Neisseria meningitidis is a human pathogen that can infect diverse sites within the human host. The major diseases caused by N. meningitidis are responsible for death and disability, especially in young infants. In general, most of the recent work on N. meningitidis focuses on potential antigens and their functions, immunogenicity, and pathogenicity mechanisms. Very little work has been carried out on Neisseria primary metabolism over the past 25 years.N. meningitidis serogroup B together with biochemical and physiological information in the literature we constructed a genome-scale flux model for the primary metabolism of N. meningitidis. The validity of a simplified metabolic network derived from the genome-scale metabolic network was checked using flux-balance analysis in chemostat cultures. Several useful predictions were obtained from in silico experiments, including substrate preference. A minimal medium for growth of N. meningitidis was designed and tested succesfully in batch and chemostat cultures.Using the genomic database of N. meningitidis in a chemostat in steady state. The genome-scale model is valuable because it offers a framework to study N. meningitidis metabolism as a whole, or certain aspects of it, and it can also be used for the purpose of vaccine process development . The flux distribution of the main metabolic pathways  indicates that the major part of pyruvate (69%) is synthesized through the ED-cleavage, a finding that is in good agreement with literature.The verified metabolic model describes the primary metabolism of  Neisseria meningitidis is a human pathogen that can infect diverse sites within the human host. The major diseases caused by N. meningitidis - meningitis and meningococcal septicemia - are responsible for death and disability, especially in young infants. There are different pathogenic N. meningitidis isolates, of which serogroups B and C cause the majority of infections in industrialized countries, whereas strains of group A and C dominate in less developed countries propionic acid sodium salt  to 0.9 ml sample. The water signal was suppressed by irradiating the signal with standard NMR software. The spectra were referenced using the TMSP signal at 0 ppm. Metabolite concentrations were quantified by integration of the relevant signals.Glucose and lactate were determined with a YSI 2700 glucose/lactate analyser . Ammonium was determined with an enzymatic kit . Acetate, ethanol and other possible metabolites present in the culture supernatant were determined by The amino-acid composition of biomass protein was determined after hydrolysis  and subsequent amino-acid analysis using an HPLC method as described previously . Free amg). The aqueous layer was removed and the organic phase was washed by adding 3.0 ml washing agent (0.3 M NaOH). The samples were mixed for 5 min and centrifuged again . The organic phase was finally transferred to a gas chromatograph vial and analyzed using a 6890 Agilent gas chromatograph [N. meningitidis were made based on the identified fatty acids [The amount of total fatty acids and the fatty-acid composition were analyzed using a modified gas chromatography method . Saponifatograph . The staty acids  and confty acids . The purLPS was isolated by the hot phenol-water extraction as described before . IsolatiThe biomass RNA content was determined as described previously  and the Yx/ATP versus growth-rate data from E. coli [Biomass biosynthesis was set as a linear combination of the macromolecules protein, DNA, RNA, lipid, peptidoglycan and LPS, which were considerd to account for the overall biomass composition. The energy requirement for biomass assembly was also considered and estimated to be 13.27 mol ATP/mol biomass. This value was calculated using linear regression of available 1/ E. coli . The accThe genome-scale metabolic network was first simplified as described in the text. Next, the stoichiometric matrix was constructed from the set of reactions using a self-made computer program running in Visual Basic . Both Monte Carlo simulation and flux-balance analysis were performed in self-made computer programs running in Matlab .Methods for solving a metabolic network or set of linear equations are discussed extensively elsewhere -138. A bm × n) is the stoichiometric matrix which contains m metabolites and n reactions, including (measured) exchange reactions, and ν is the flux vector that contains the unknown fluxes x and (measured) exchange rates r. A solution to the metabolic network will exist provided that A is nonsingular. Singularities in A may arise due to reaction dependence or network observability problems. Equation (1) states a compound balance for each of the metabolites in the system. If measurements are made of substrate and product concentrations, and the conversion rates of these metabolites are calculated, such a set of measured rates should match Equation (1).where A  and δ is the vector containing the deviations between measured and balanced rates, which can be calculated using a weighed minimum last square approach according to the following equation:where rThe resulting balanced measurement rate vector can be used to calculate the unknown fluxes and production rates. As described in more detail below, Monte Carlo simulation can be used to determine the variance of a measured conversion rate.The matrix containing the mass balances over the intracellular compounds can be checked for network sensitivity problems by performing singular value decomposition (SVD). SVD is a mathematical technique that decomposes matrix A into three matrices as follows:The matrix W is an orthogonal matrix containing the eigenvalues of the matrix. The columns of U, whose corresponding elements of W are non-zero, form an orthonormal basis that spans the range of A. The columns of V, whose corresponding values of W are zero, are an othonormal basis for the nullspace of A. In other words, the columns of V contain the combination of fluxes and rates that cannot be uniquely identified. Here we use SVD to identify and isolate the combinations of fluxes and unknown exchange rates that cannot be uniquely identified  . It is wTo reduce the number of allowable solutions for the underdetermined parts of the metabolic network, limits on the range of individual flux values can be set on the basis of available biochemical and thermodynamic literature for the enzymatic reactions. These constraints have the form:where α and β are the lower and upper limits, respectively. Thermodynamic constraints regarding the reversibility or irreversibility of a reaction can be applied by setting α for the corresponding flux to zero. To further shrink the original solution space to a single solution, linear optimization can be used to find the solution that optimizes a particular objective function. Some examples of objective functions are those that maximize biomass formation or minimize the production of ATP, NADH, NADPH, or a particular metabolite ,140.An alternative objective function minimizes the sum of the squares of the fluxes, and is called the minimum-norm constraint. The minimum-norm constraint minimizes the length of the solution vector without any further restrictions using the Moore-Penrose-pseudo-inverse of A . The MooError diagnosis and balancing are important aspects of flux-balance analysis. Before error diagnosis can be done, errors in the primary measurements need to be translated to errors  in measured conversion rates. This can be done using a Monte Carlo approach ,116 as fin silico experiments were done using the simplified metabolic model. All simulations were performed in a self-made computer programs running in Matlab (version 6.5 r13). The flux through the non-growth-associated ATP-maintenance reaction was fixed to 2.8 mmol/gram dry weight/h [All weight/h . The lowin silico experiments. Additional data file The following additional data are available online with this paper. Additional data file in silico experiments.The first worksheet named 'genome-scale model' includes the complete reaction database along with involved genes, enzyme numbers and metabolites. The second worksheet named 'simplified model' contains the simplified metabolic model. The third worksheet named 'abbreviations' contains a list of abbreviations of the metabolites. The fourth worksheet named 'redundancy matrix' contains the redundancy matrices of the experimental data sets. The fifth worksheet named 'measured rates, balanced rates' contains a table in which the experimental set of measured rates and balanced rates is given. In addition, the results of the statistical acceptance test are given in this table. The sixth worksheet named 'calculated fluxes' contains the calculated flux distributions of both experimental data sets using the mimimum norm constraint. The seventh worksheet named 'in silico' contains the flux distributions of the Click here for fileA detailed description of the biomass composition and and overview of the metabolites measure in the culture supernatant and off-gas.Click here for file


Escherichia coli. Instead of using dynamic metabolite data to fit a model, the EM approach uses phenotypic data (effects of enzyme overexpression or knockouts on the steady state production rate) to screen possible models. These data are routinely generated during strain design. An ensemble of models is constructed that all reach the same steady state and are based on the same mechanistic framework at the elementary reaction level. The behavior of the models spans the kinetics allowable by thermodynamics. Then by using existing data from the literature for the overexpression of genes coding for transketolase (Tkt), transaldolase , and phosphoenolpyruvate synthase (Pps) to screen the ensemble, we arrive at a set of models that properly describes the known enzyme overexpression phenotypes. This subset of models becomes more predictive as additional data are used to refine the models. The final ensemble of models demonstrates the characteristic of the cell that Tkt is the first rate controlling step, and correctly predicts that only after Tkt is overexpressed does an increase in Pps increase the production rate of aromatics. This work demonstrates that EM is able to capture the result of enzyme overexpression on aromatic producing bacteria by successfully utilizing routinely generated enzyme tuning data to guide model learning.Ensemble Modeling (EM) is a recently developed method for metabolic modeling, particularly for utilizing the effect of enzyme tuning data on the production of a specific compound to refine the model. This approach is used here to investigate the production of aromatic products in  The manipulation of the enzymatic reactions which make up metabolic networks is at the heart of metabolic engineering. However, due to the complex and highly-interconnected nature of these networks, it is sometimes not a trivial process to understand what the effect of an enzymatic perturbation will be, or vice versa, what enzymatic perturbations are necessary to yield a desired effect. Flux distribution is often controlled by multiple enzymes in the network In typical kinetic modeling, kinetic parameters are determined in order to best fit the time-dependent metabolite concentration data obtained from experiment, using a wide variety of kinetic rate expressions. However, these types of data are rare and are not commonly generated in a typical strain improvement process. On the other hand, enzyme overexpressions or knockouts are commonly used in strain development, and the effects of enzyme expression tuning on product formation or substrate consumption are the typical readouts. To our knowledge, such data are difficult to incorporate into modeling, particularly when the results are semi-quantitative, since the fold-changes of enzyme overexpression are rarely measured.Recently, the Ensemble Modeling (EM) approach was developed for the modeling of metabolic networks In EM, initially, an ensemble of models that all reach the reference steady state in terms of flux distribution is constructed. These models span the space of kinetics allowable by thermodynamic constraints, and are based on elementary reactions, which are the most fundamental and general kinetic descriptions for enzymatic reactions Escherichia coli. Aromatic compounds are of substantial industrial importance, with many uses and high rates of production, including the aromatic amino acids and other derived compounds such as indigo, quinic acid and catechol In this work, we implement the EM approach to the production of aromatic amino acids in E. coli and many other organisms, the production of aromatic compounds begins with the condensation reaction between phosphoenolpyruvate (PEP) and erythrose-4-phosphate (E4P) to form 3-deoxy-D-arabinoheptulosonate-7-phosphate (DAHP). This reaction, catalyzed by DAHP synthase (AroG), is the committed step and the most tightly regulated reaction in the common aromatic amino acid pathway In Escherichia coli as a system to demonstrate the applicability of EM because this system is an example of both kinetic and stoichiometric limitations that takes place in metabolic systems. Stoichiometric analysis shows that the theoretical yield of DAHP production from glucose in the wildtype E. coli is 43% (mol/mol) E. coli cannot recycle pyruvate back to PEP during glycolytic growth. Thus, when PEP is converted to pyruvate during glucose transport via the phosphotransferase system (PTS), the pyruvate generated cannot be used in the aromatic synthesis, causing a decrease in yield. In order to increase the yield, either pyruvate has to be recycled back to PEP via PEP synthase (Pps) E. coli, there is no change in DAHP yield. On the other hand, overexpression of Tkt effectively increases the yield to close to 43%. Overexpression of both Pps and Tkt then increases the yield to 86%, approaching the theoretical limit We choose the production of aromatic amino acids in E.coli, utilizing existing data from the literature to screen the ensemble of models. By using data that has been reported for the overexpression of transketolase (Tkt), transaldolase  and phosphoenolpyruvate synthase (Pps), we can screen the original ensemble of models to a subset that accurately describes the kinetic phenomena that is at work in this system. The final screened ensemble of models demonstrates the property that the E4P metabolite pool is initially limiting, and only after this limitation is lifted, does the PEP pool become important. Thus, we can correctly predict that only after Tkt is overexpressed does the overexpression of Pps play a role in an increased rate of DAHP production. This work thus demonstrates that EM is able to capture properties of metabolic networks in a real biological system through the utilization of enzyme tuning data to drive model development.Here we use EM to study the production of DAHP from glucose in The metabolic network for the production of DAHP is depicted in For the production of DAHP, the external fluxes of the system  have been reported i are rescaled such that there sum is equal to one.For each glycolysis∶pentose pathway split ratio, an ensemble of 1500 models was constructed using Matlab  on an Intel  Pentium 4 processor running Microsoft  Windows XP. The total computational time to develop and perturb each ensemble to obtain the overexpression phenotypes of interest was approximately 18 hours. In addition to the steady state fluxes, the other input into the algorithm is the standard Gibbs free energies for each reaction, which are listed in In our system of interest for the production of DAHP, an important metabolic kinetic phenomenon is at work. The synthesis of DAHP draws from the pools of two metabolites, PEP and E4P, from different areas of the metabolic network. Thus, how these pools are balanced, a kinetic property, is the key to increased DAHP production. It has been demonstrated that the E4P metabolite pool is the limiting metabolite in DAHP synthesis, and that only after this limitation is lifted do perturbations in enzyme levels that increase the PEP pool size yield an increase in production. It has been reported that the overexpression of Tkt After constructing the ensemble of models for each of the split ratios, each model was perturbed by overexpressing Tkt, Tal and Pps two-fold, one at a time. After perturbation of the ensemble, the models that did not match the literature phenotypes were screened out of the ensemble. For the phenotypes where overexpression led to an increase in DAHP production , models that exhibited any increase in the DAHP production rate were kept. For the phenotype of Pps overexpression leading to no change in the DAHP rate, only models that did not exceed an increase or decrease of 10% of the maximum DAHP rate increase for that ensemble were kept. For the glucose uptake rate being unchanged with Tkt overexpression, only models that exhibited less than a 10% change in the glucose uptake rate were retained. To screen for Tkt overexpression increasing the DAHP rate more than Tal overexpression, only models where the DAHP rate when Tkt is overexpressed was greater than the DAHP rate when Tal was overexpressed were retained.The results of the screening are illustrated in While we are screening from the previously determined subset, each of the perturbations was done in parallel, not sequentially. The screening for the Tkt and Tal phenotypes could be done independently, and the models common to both screens could be retained. Further, the order in which the models are screened does not influence the final number of models that matches all phenotypes. When the phenotypes are observed relative to the same reference state , they can all be viewed independently, and the models retained after screening can be illustrated as the intersection between each phenotype, as demonstrated in From the reduced subset matching the Tkt and Tal phenotypes, screening for Pps overexpression leading to no change in DAHP production results in 8, 0, 318 and 278 models matching the phenotype for each of the split ratios. Of these models, the number that exhibited the property that the glucose uptake rate did not change when Tkt was overexpressed reduced the size of the ensembles to 7, 0, 241 and 235 models, in order of increasing glycolytic flux.The final literature observation used for screening is that of an increase in DAHP production via Tkt overexpression being greater than the increase observed from Tal overexpression. This led to a final ensemble size of 171 and 195 models for the 75∶25 and 95∶5 split ratios, respectively  was overexpressed Since PEP is used in glucose transport via the PTS to form pyruvate, most carbon is not used in aromatics biosynthesis, resulting in a low yield. This problem was identified previously For the final ensembles of 171 and 195 models for the split ratios of 75∶25 and 95∶5, respectively, the sampled parameters of these screened subsets were examined to determine what characteristics they exhibited that deviated from the original ensemble of models. The enzyme fractions of each free enzyme (enzyme not in a complex), and the net reversibilities of each overall reaction were examined to determine how their distributions for the screened models deviated from the original ensemble. For each parameter of interest, a two-sample Kolmogorov-Smirnov test For both flux states examined, it was found that three of the enzymes showed a significant deviation in their distributions relative to the original ensemble, and none of the reaction reversibilities exhibited a deviation. For both flux states, the free enzyme fractions of enzyme I (EI), pyruvate kinase (Pyk), and phosphoenolpyruvate carboxylase (Ppc) had a significantly different parameter distribution compared to the original ensemble. After determining that these three parameters were significantly distributed in the screened models, a hierarchical clustering analysis was performed examining these three free enzyme fractions in the original ensemble of models for the 95∶5 glycolysis∶pentose pathway split, as shown in To determine if the construction of 1500 models in the original ensemble was enough to adequately cover the range of possible kinetics, and thus yield screening results which were reproducible, the ensemble construction and screening process for the 95∶5 split ratio was repeated three times to see the variability in the screening results. From an initial ensemble of 1500 models for each of the three ensembles, both the final number of models retained after all screening steps, and the models retained after each individual step varied less than 10% from repeat to repeat, shown in E. coli. The difficulty in developing kinetic models for metabolic systems is well recognized, and is due to a lack of kinetic parameters. In this work, rather than attempting to construct a traditional kinetic model that matches dynamic metabolite concentration data and facing the issue of kinetic parameter identification, we focused on utilizing enzyme overexpression phenotype data, which are plentiful and relatively straightforward to acquire, to screen models. The EM approach is used to construct an ensemble of models for four different flux distributions, which are then screened using enzyme overexpression data from the literature. We show that in five screening steps, the ensembles can converge to a set of models which becomes predictive.In this work, we used the EM approach Since the entire flux map is not known, but only the external fluxes have been measured, a variety of split ratios were examined between glycolysis and the pentose phosphate pathway. The E4P metabolite pool is fed by transketolase (Tkt) “running backwards” from glycolysis, thus supporting the literature phenotypes only when the fraction of the carbon flux through glycolysis is above 60%. Interestingly, the EM approach was able to identify this property, as neither of the flux maps with less than a 60∶40 split ratio were able to retain any models that matched each of the screening phenotypes. However, many models were retained for each of the two flux distributions with greater than a 60∶40 split ratio. This indicates that a general idea of the flux distribution could be reverse engineered through the use of enzyme overexpression phenotypes and EM.any enzyme overexpression phenotype can be used as a step in screening the ensemble, making all experimental data potentially useful, whether the data shows an increase in the production rate of interest, a decrease, or no change at all. While the predictive capabilities of the EM approach are primarily qualitative, this provides a tool to drive experimentation and to learn from the results. If a prediction is proven to be incorrect, this information can also be incorporated into the screening, allowing for the formation of an alternate hypothesis.As one looks at the advantages and challenges of such an approach, it can be seen that for complicated networks with many pathways that lead to the external fluxes, there may be many degrees of freedom in determining the steady state flux, and thus the determination of the reference flux  may limit the possible systems to be studied. The iterative screening approach demonstrated here allows for the rapid collaboration and iteration between experiment and computation. As demonstrated for DAHP production, In using reported enzyme overexpression data for Tkt, Tal and Pps, it is demonstrated that the screened set of models exhibits the kinetic phenomena that is at work in the network, without the need for kinetic parameters. The final screened ensemble of models shows that Tkt is the first limiting step, and correctly predicts that only after this limitation is lifted does an increase in Pps increase the production rate of DAHP. This work thus demonstrates that EM is able to capture kinetic properties of metabolic networks by utilizing enzyme tuning data to refine and screen the ensemble.The first step in EM is to obtain the steady-state fluxes in the reference state of interest. The reference state is typically the base-line control strain before further metabolic engineering. In order to model a given steady state, the flux distribution of that state must first be determined. This flux distribution, or flux map, can be deduced via a variety of methods. Typically, the external fluxes of the system may be known, or easily measureable using GC or HPLC. In this case, the internal fluxes of the system can be estimated by a standard flux balance around each metabolite at the steady state:S is the m x n stoichiometric matrix consisting of m metabolites and n net reactions, and v is the n x 1 vector of net reaction rates. For more detailed analysis, the full flux map may be determined through the use of C13 isotopomer analysis This can be represented for the entire network in matrix form:At the molecular level, the basic elementary reactions (either bi-molecular or uni-molecular) that follow mass-action kinetics are the most fundamental kinetic events i,i, and i. To avoid quantifying the absolute concentrations of each metabolite and enzyme, we scale their concentrations by the corresponding concentration at the steady state, and Eq. (3) becomes:The general form for the elementary reactions in an enzymatic reaction of one substrate to one product can be depicted as follows:Each of the transport reactions out of the system are modeled with mass-action kinetics:For the reference state, The EM methodology is illustrated in i at the reference steady state, and j in reaction i. The reversibilities range from 0 (for an irreversible step) to 1 (for a step at equilibrium). Thus, the forward and backward rates can be calculated from the reversibility and the steady state flux determined in the first step:In the first sampling step, the reversibilities for each elementary step i,net)sign(V represents the direction of the net flux (positive if forward and negative if backwards). The reversibilities are constrained by the Gibbs free energy of the overall reaction, in represents the number of elementary steps for enzyme i. This requires that the net flux of reaction i be positive if This relationship between the reversibilities of the elementary steps, the net reaction, and the free energy bounds has been previously derived Next, the enzyme fractions are sampled. The enzyme fractions are the fractions of the total enzyme amount that exist as the free enzyme and as the various enzyme complexes at steady state, such that the sum of all the fractions are equal to one, conserving the total amount of each enzyme:At the reference steady state Once this sampling of enzyme fractions is complete, the kinetic parameters for that model can be assigned. The kinetic parameters Next the ordinary differential equations (ODEs) governing the system are solved at the reference state. The network can be described by a system of ODEs and solved numerically, where the metabolite concentrations and enzyme fractions, not the total enzyme concentrations, are the ODE variables:With enzyme fraction initial conditions set such that:Different combinations of reversibilities represent different kinetic states. Each model is a function of the reversibilities and enzyme fractions:Every model reaches the same steady state, and the reversibilities The entire ensemble can be perturbed to determine each individual model's response to the enzyme expression perturbation with which we would like to screen the ensemble. In order to perturb the concentration of an enzyme for an individual model in the ensemble, Eq. (4) is modified:n-fold  to determine its effect on production. Here we use n = 2. If the metabolic network contains any moiety conservation relationships The additional variable