Lactobacillus casei strains are widely used in industry and the utility of this organism in these industrial applications is strain dependent. Hence, tools capable of predicting strain specific phenotypes would have utility in the selection of strains for specific industrial processes. Genome-scale metabolic models can be utilized to better understand genotype-phenotype relationships and to compare different organisms. To assist in the selection and development of strains with enhanced industrial utility, genome-scale models for L. casei ATCC 334, a well characterized strain, and strain 12A, a corn silage isolate, were constructed. Draft models were generated from RAST genome annotations using the Model SEED database and refined by evaluating ATP generating cycles, mass-and-charge-balances of reactions, and growth phenotypes. After the validation process was finished, we compared the metabolic networks of these two strains to identify metabolic, genetic and ortholog differences that may lead to different phenotypic behaviors. We conclude that the metabolic capabilities of the two networks are highly similar. The L. casei ATCC 334 model accounts for 1,040 reactions, 959 metabolites and 548 genes, while the L. casei 12A model accounts for 1,076 reactions, 979 metabolites and 640 genes. The developed L. casei ATCC 334 and 12A metabolic models will enable better understanding of the physiology of these organisms and be valuable tools in the development and selection of strains with enhanced utility in a variety of industrial applications. Lactobacillus casei are Gram positive, non-sporulating, nutritionally fastidious and strictly fermentative bacteria that produce lactic acid as their principal metabolic end product L. casei strains are used in the manufacture of fermented foods, as probiotics, and has significant potential for the production of biofuels and co-products with a broad range of applications such as food ingredients L. casei in all of these applications is strain dependent, due to significant variation in gene content that is present in this species. Comparative genome analysis of seventeen L. casei strains has revealed this species has an average of 2,800 orthologous genes (±151), of which 1,715 are shared by all the strains, and 4,220 non-conserved orthologous genes with an average of 119 unique genes found in each strain Genome-scale metabolic models can serve as tools for evaluating the metabolic potential of strains based on genomic data. These models are becoming a common tool for linking genomic data to the biochemical reaction networks that govern cellular processes in silico models are available for four species of lactic acid bacteria (LAB): Lactococcus lactisLactobacillus plantarumStreptococcus thermophilusLactobacillus reuteriin silico minimal medium and to improve diacetyl production Lactococcus lactis MG1363 was developed; this model couples the carbon and nitrogen metabolism of the strain with catabolic pathways that lead to flavor formation in cheese L. plantarum was successfully used to evaluate nutrient requirements of the WCFS1 strain S. thermophilusS. thermophilus and other LAB. The most recent LAB genome-scale metabolic models have been developed for three strains of Lactobacillus reuteri, the model strain JCM1112, and two human-derived strains, 6475 and 55730; these models were utilized to identify probiotic features of these strains L. casei strains would enhance current understanding of how strain specific characteristics influence the utility of these species in various industrial applications.To date, L. casei: L. casei ATCC 334, a cheese isolate, and 12A a corn silage isolate. A draft genome sequence for 12A was available (GenBank accession number AFYJ00000000) and this genome was closed for the purposes of this study. These models were then utilized to conduct a detailed comparison of these two strains.In this study, genome-scale metabolic models were constructed for two fully sequenced strains of L. casei 12A was prepared using the DNA Isolation Bacterial CTAB protocol as requested by the Department of Energy (DOE) Joint Genome Institute (JGI). This protocol can be found at http://my.jgi.doe.gov/general/protocols.html. Genomic DNA quality was confirmed by agarose gel electrophoresis and was submitted to the Department of Energy Joint Genome Institute for genome sequencing, where Ilumina HiSeq 2000 technology was used. JGI delivered a draft genome containing 397 DNA Scaffolds. This draft genome was assembled in collaboration with DuPont Inc., utilizing a previously available 12A draft genome as a scaffold L. casei ATCC 334 as a scaffold Genomic DNA of L. casei ATCC 334 (GenBank accession number NC_008526 and NC_008502) http://www.ncbi.nlm.nih.gov) and at the RAST Server (Rapid Annotations using Subsystems Technology) (http://rast.nmpdr.org/). The genome sequence for L. casei 12A was imported into the RAST server (http://rast.nmpdr.org/) for gene calling and annotation with subsequent manual inspection and curation. This information was used in the metabolic reconstruction and validation processes, as described below.The complete genome sequence and annotation of L. casei metabolic networks. Genome-scale metabolic draft models for both L. casei strains were generated in 2011 using the RAST server L. casei metabolic models. FBA simulations were performed by maximizing biomass, with an in-silico growth medium containing nutrients in the chemically defined medium (CDM) L. casei 12A simulations. We first maximized growth using just the essential amino acids (without a carbohydrate present). We then introduced each carbohydrate to the in silico media. An increase in maximum growth rate in the presence of a particular carbohydrate indicated the ability of the model to utilize the carbohydrate as a carbon source.Flux balance analysis (FBA) identifies a steady-state metabolic flux distribution that maximizes a stated objective, such as cellular growth rate or product formation Working cultures were prepared from frozen stocks by two sequential transfers in de Man, Rogosa and Sharpe (MRS) medium and CDM broth prepared as described by Christensen and Steele 1- µ2, subject to common gene deletions).We used CONGA to identify functional differences between the two metabolic networks L. casei 12A genome consists of a circular chromosome of 2,907,945 bp. The general features of the 12A genome are presented in L. casei ATCC 334, the 12A genome is 12,681 bp larger. The number of pseudogenes in 12A is 152, a relatively high number compared to the 82 in L. casei ATCC 334, which could indicate that L. casei 12A has undergone more extensive gene decay. Comparative genome analysis between the strains indicates that they share 2,222 orthologous genes; L. casei 12A has 507 unique genes compared to L. casei ATCC334, whereas L. casei ATCC334 has 423 unique genes compared to L. casei 12A. The complete genome sequence of 12A was deposited at GenBank with the accession number CP006690.The closed L. casei ATCC 334 and 12A each contain an extracellular and cytoplasm compartment, and exchange and transport reactions allow metabolites to be imported into or secreted from these compartments. The model for L. casei ATCC 334 (iLca334_548) consists of 548 genes, 905 metabolic reactions and 959 metabolites. The model for L. casei 12A (iLca12A_640) consists of 640 genes, 932 metabolic reactions and 979 metabolites. The properties of the models are summarized in The genome-scale metabolic models of L. casei strains showed the strains have similar amino acids requirements, where the branched-chain amino acids , the aromatic amino acids , and arginine are essential for both strains. However, glutamate is essential for L. casei 12A growth, while in ATCC 334 the absence of glutamate only caused a growth defect.Single amino acid omission experiments in both in vivo results; the draft model incorrectly predicted tryptophan to be non-essential  while cysteine and methionine were incorrectly predicted to be essential . The draft 12A model predictions agreed with the in vivo data for 16 of the 20 simulations. The inconsistencies for tryptophan, methionine and cysteine observed with the ATCC 334 model were also observed with the 12A model. In addition, the 12A model predicted that glutamate was non-essential, while the in vivo data indicated it was essential. SMILEY L. casei ATCC 334 model to fix the model's requirement for methionine. While correcting the methionine requirement in the L. casei 12A model involved adding methionine synthase (E.C. 2.1.1.13) and O-succinylhomoserine sulfhydrylase (E.C. 4.2.99.9). To correct the discrepancy between the model predictions and the in vivo data requirements for tryptophan, some reactions that were initially gap filled by Model SEED  annotated as glucosamine-fructose-6-phosphate aminotransferase (E.C. 2.6.1.16), which converts glutamine into glutamate. After making these corrections the L. casei ATCC 334 model was able to correctly predict the amino acid requirements and the L. casei 12A model was able to correctly predict 19 out of the 20 amino acid requirements  relationships differ in the models; orthology differences, in which genes encoding enzymes with identical functions were not assigned as orthologs; and metabolic differences, where one organism has additional reactions that grant it unique capabilities CONGA identifies gene deletion sets, sets of one or more genes whose deletion are predicted to be lethal by only one of two models. Gene deletion sets are classified based on the reason for differences in growth predictions: iLca334_548  and five gene deletion sets that were lethal only in iLca12A_640. For the second condition , two gene deletion sets were lethal only to iLca334_548; and four gene deletion sets were lethal only to iLca12A_640. These deletion sets were a subset of those found in the first condition . CONGA results are summarized in The CONGA results were insensitive to carbon source . Therefore, the results are summarized based on amino acid availability. For the first condition , CONGA found five gene deletion sets that were lethal only in iLca334_548. This highlights the presence of more isozymes in iLca12A_640, suggesting it is more robust to gene deletions than iLca334_548.Four of the ten unique gene deletions sets identified by CONGA were attributed to genetic differences, which arise due to differences in the number of isozymes between the two models for essential reactions. Three of these four gene deletion sets were lethal in 2-THF) dehydrogenase (E.C. 1.5.1.5) is lethal only in the iLca334_548 model. This means that the iLca12A_640 model has a unique mechanism (shown in 2-THF is a precursor to 10-formyltetrahydrofolate (10-CHO-THF) a cofactor involved in purine biosynthesis, an essential activity for cellular growth. The deletion of 5,10-CH2-THF dehydrogenase prevents the biosynthesis of THF in L. casei ATCC 334. Our model for L. casei 12A predicts that this deletion can be rescued by the actions of 5,10-CH2-THF:3-methyl-2-oxobutanoate (E.C. 2.1.2.11) and formate: THF ligase (E.C. 6.3.4.3), in which 5,10-CH2-THF is converted directly to THF, producing 2-dehydropantoate as a by-product. The reactions pantoate 2-oxidoreductase (E.C. 1.1.1.169) and pantothenate amidohydrolase (E.C. 3.5.1.22) convert 2-dehydropantoate to pantothenate, which can be secreted by a transporter unique to the iLca12A_640 model, or some pantothenate can also be used for CoA biosynthesis, important for biomass formation.Using CONGA we also identified one metabolic difference, in which deletion of the enzyme 5, 10-methylenetetrahydrofolate . On the other hand, our strains have considerably more requirements than Lc. lactis and S. thermophilus  biosynthesis pathways in L. casei strains. In the biosynthesis pathway of tryptophan, the enzyme anthranilate synthase (E.C. 4.1.3.27) was not found in the genome annotation of L. casei ATCC 334 strain; presumably this reaction was added to the draft metabolic models as a mean to complete the pathway. Experimental data indicating tryptophan must be supplied support the idea that this pathway is incomplete. In L. casei 12A the reaction catalyzed by tryptophan synthase (E.C. 4.2.1.20) was found to confer the model, the ability to synthesize tryptophan, therefore it was removed base on experimental data. Since tryptophan was required for growth by both strains, a reaction was deleted from both metabolic models. The requirement for phenylalanine and tyrosine for growth was expected, as an enzyme needed for their biosynthesis, prephenate dehydratase, was not found in the genome annotation of either strain.Aromatic amino acids  had incomplete biosynthesis pathways in the two L. casei strains are reported to require arginine for growth L. casei ATCC 334 and no growth for L. casei 12A. This has been well documented in other LAB, due to an incomplete citric acid cycle and limited supply of α-ketoglutarate iLca12A_640, glutamate is predicted to be an essential amino acid, however, this deletion would also make glutamine a predicted essential amino acid, but glutamine is not required experimentally, therefore the reaction was not removed. Experimental studies suggest that the interconversion of glutamine to glutamate results in low yields of glutamate The omission of glutamate in the medium caused a severe defect in growth for L. casei models highlights the presence of additional enzymes that gives the L. casei 12A model the ability to utilize D-rafinnose, panose and pullulan. For instance, the 12A model possesses an ABC transporter predicted to function for raffinose uptake. This model also includes a pullulanase and a neopullulanase, important in pullulan and panose degradation into maltotriose and maltose and glucose, respectively. As discussed by Broadbent et al. (2012), the ability of strains to utilize different carbohydrates predicts the adaptation of the strains to diverse ecological niches; D-rafinnose, panose and pullulan are components commonly found in plant material, the environment from which L. casei 12A was isolated. On the other hand, as observed in growth experiments and confirmed by the metabolic models, L. casei ATCC 334, can utilize fewer of the carbohydrates tested (see Comparison of the two sted see . This comyo-inositol (MI), a component of phytic acid, which can serve as a phosphate storage molecule in plant seeds et al. (2007) reported the identification of a gene cluster which enables L. casei BL23 to utilize myo-inositol under aerobic conditions. The catabolic pathway of MI is absent in L. casei ATCC 334, and experimental studies and prediction by the metabolic models confirmed no growth on MI. Surprisingly, the genome-scale metabolic model for L. casei 12A predicted growth using MI as a carbon source, implying the catabolic pathway for MI is complete in this strain. Further analysis in the genome annotation of L. casei 12A reveals the presence of all the enzymes  needed for converting MI to glyceraldehyde-3P. The environment from which the 12A strain was isolated could have played a role in the retention of the pathway. The reason why L. casei 12A was unable to utilize MI is speculated to be due to regulatory effects that genome-scale metabolic models do not capture.One of the most abundant stereoisomers of inositol is iLca12A_640 for pantothenate was found to confer the model with the ability to overcome the deletion of 5,10-CH2-THF dehydrogenase. This transporter prevents the accumulation of pantothenate inside the cell, therefore allowing the reactions, catalyzed by the enzymes E.C. 2.1.2.11 and 6.3.4.3 to be active, yielding to the synthesis of 10-CHO-THF.A unique transporter (pantothenate sodium symporter) in iLca12A_640 (added by Model SEED) lacks a gene association, however further analysis of L. casei 12A genome annotation reveals the presence of a pantothenate energy-coupling factor (ECF) transporter (GI 410523916). An ortholog of this gene was found in L. casei ATCC 334, which is annotated as a predicted membrane protein which may be the reason it was missed during the automated reconstruction of the model. This provides an example of how CONGA can be used to aide in further model development.The pantothenate transporter in CONGA simulations performed under the glucose and galactose conditions, both six carbon carbohydrates, identified the same differences between the models. Simulations with ribose where also conducted (data not shown), but no new gene deletions sets were found. Even though we were able to identify genetic, orthology and metabolic differences between the models, it appears that pathways in catabolism of these three sugars and central metabolism are shared by the strains.L. casei strains provide a comprehensive overview of the metabolism of the strains. These models are valuable tools for the development of strains with enhanced utility in a variety of industrial applications (e.g. food ingredients), as well as in the design of new metabolic engineering approaches in the production of commodity chemicals such as biofuels.The genome-scale metabolic models of two Table S1Comparison of essential amino acids (listed as E) determined from experiments among lactic acid bacteria, for which metabolic models have been built.(DOCX)Click here for additional data file.Table S2Compounds allowed to be taken up during flux balance analysis in both L. casei models. Flux represents uptake rate, units are mmol/gDW/h.(DOCX)Click here for additional data file.Table S3Type of gene deletion sets, with glucose or galactose with essential amino acids condition, found in iLca12A_640 and iLca334_548.(DOCX)Click here for additional data file.Table S4Type of gene deletion sets, with glucose or galactose and all amino acids, found in iLca12A_640 and iLca334_548.(DOCX)Click here for additional data file.Table S5Complete list of reactions and compounds present in GapfillMatrix.(XLSX)Click here for additional data file.Table S6Complete list of reactions and compounds present in iLca12A_640.(XLSX)Click here for additional data file.Table S7Complete list of reactions and compounds present in iLca334_548.(XLSX)Click here for additional data file.Table S8Enzymes and transporters added to L. casei ATCC 334 and 12A models to fix false negative predictions. Addition of an enzyme/transporter is indicated with filled circles; open circles indicate no addition of enzyme/transporter.(DOCX)Click here for additional data file.Table S9GapfillMatrix in SBML format.(XML)Click here for additional data file.Table S10iLca12A_640 in SBML format.(XML)Click here for additional data file.Table S11iLca334_548 in SBML format.(XML)Click here for additional data file.


A set of 131 reactions, essential for the production of primary biomass precursors is identified; deletion of any of them can inhibit the overall biomass production. Usability Index (IU) for the rest of the reactions are estimated and based on this parameter, they are classified into three categories—maximally-favourable, quasi-favourable and unfavourable for the primary biomass production. The lower value of 1 − IU of a reaction suggests that the cell cannot easily bypass it for biomass production. While some of the alternative paths are energetically equally efficient, others demand for higher photon. The variations in (i) ATP/NADPH ratio, (ii) exchange of metabolites through chloroplastic transporters and (iii) total biomass production are also presented here. Mutual metabolic dependencies of different cellular compartments are also demonstrated.More than 20% of the total caloric intake of human population comes from rice. The expression of rice genes and hence, the concentration of enzymatic proteins might vary due to several biotic and abiotic stresses. It in turn, can influence the overall metabolism and survivability of rice plant. Thus, understanding the rice cellular metabolism, its plasticity and potential readjustments under different perturbations can help rice biotechnologists to design efficient rice cultivars. Here, using the flux balance analysis (FBA) method, with the help of  Rice is a socio-economically important food grain for more than half of the world’s human population . HoweverThe metabolic modeling technique can be grouped into two categories—(i) kinetic modeling and (ii) structural modeling. Since, the kinetic modeling requires details of enzyme kinetic data, the technique is usually limited to systems having small number of reactions. On the other hand, the correct stoichiometry and the thermodynamic feasibility of the biochemical reactions are required for structural modeling. Thus, the structural modeling technique is used in genome-scale metabolic modeling and its analysis. A number of genome-scale metabolic models (GSMs) of various organisms, including bacteria , simplesAny species including rice plant is exposed to several environmental conditions, which might change the expressions of cellular proteins including enzymatic genes. The down-regulation of an enzymatic gene’s expression can result several consequences, such as (i) no change in the efficiency of the corresponding reaction, (ii) a partial blockage in enzymatic reaction’s activity, or (iii) a full blockage . The partial or full blockage of an enzymatic gene’s activity can change the metabolism of a cell. It can alter the metabolic phenotype, such as the composition and amount of the biomass precursors it synthesizes in normal condition. Whether this alteration of metabolic phenotype would be lethal or not depends on the necessity of the biomass precursors. Alternatively, the cell does not exhibit any change in metabolic phenotype and finds some alternative metabolic pathways to produce the same amount of biomass it produces in normal condition. It has been already shown that a living species has enough metabolic flexibility to adapt itself to different biotic and abiotic perturbations , 11. ThiE. coli) from an universal network of 5906 reactions and determined the essentiality of each of the reactions. The reactions required in all metabolic networks were defined as ‘superessential’ . The superessentiality index of a reaction was defined as a ‘fraction of networks in which the reaction is essential’. The value of superessentiality index helps one to understand whether a reaction can be easily bypassed by any known metabolic pathway or not. We have used this concept to derive a mathematical expression, termed as the Usability Index  the enzyme(s) associated with that particular reaction is knocked out  and (ii) severe down-regulation of the associated gene(s) so that the reaction becomes inactive. Here, we have studied the effect of reaction deletion (the full blockage of the enzymatic reaction) in a genome-scale metabolic model of rice leaf . In specin-silico reaction  deletion strategy and the cellular responses are simulated to observe the possible active metabolic states.The rice genome-scale metabolic model is used here (i) to find the essential reactions for biomass production, (ii) to classify the rest of the reactions based on their Usability Index and (iii) to observe the metabolic plasticity of rice metabolism. Further, we have analyzed how the deletion of any reaction can affect the overall cellular economy in terms of photon demand. It should be mentioned that the incident photon is the primary source of a photosynthetic organism’s ATP and NADPH productions which, in turn, are used in fixing the inorganic nutrients into biomass through a series of chemical reactions. Consequently, for the deletions of some of the reactions, the variation in ATP/NADPH ratio is also observed. How this variation is readjusted within the cellular metabolic system has also been discussed with a few examples. We also report the effects of reaction deletion on total amount of biomass production and exchange of metabolites through chloroplastic transporters. Inter-compartmental interactions within a cell play an indispensable role for any eukaryotic organism. This reaction deletion study elucidates how the metabolism of different compartments interact with each other. In summary, here, different genotypes in a rice cell is created through Oryza sativa)  and the metabolic response is simulated by FBA to test whether the modified metabolic network  is able to produce the biomass in experimentally observed fixed proportions or not. If the simulation can not find any possible solution, the reaction is termed as essential for biomass production. An essential reaction must carry a non-zero flux to produce the cellular biomass; however, it does not refer that the rest of the reactions are not at all important to produce the biomass. Rather, some of them might frequently take part in biomass production while others do not. Thus, to determine the importance of a single reaction in overall metabolism of rice leaf cell, Usability Index (Iwww.python.org).All computational implementations are done using ScrumPy metabolic modeling tool  and resuU is calculated for each of the reactions to understand how much this reaction is favourable by the metabolic system. Subsequently, the photon usage efficiency of the alternative metabolic pathways are compared with that of the WT. The analysis also includes (i) some examples to show the variation in ATP and NADPH usages, (ii) changes in the transport of C3 compound between chloroplast and cytosol through chloroplastic transporters and (iii) changes in total biomass production at a fixed value of incident photon. Then, the flux responses are analyzed to show that change in fluxes of some reactions in one compartment can influence the fluxes of reactions in other compartments.The genome-scale metabolic model of rice leaf is used here to simulate the metabolic responses under the genotypic perturbations created by the complete inhibition of individual reaction. Since primary aim of this work is to understand the metabolic flexibility, we have first identified the essential reactions; without any of them, the cell is not able to produce the primary biomass in fixed proportion. Then, I3 plant Arabidopsis thaliana, Wang et al. (2012) reported that nearly 10% of reactions are essential for biomass production [2 and its deletion shows complete inhibition of biomass production. The metabolic network in the absence of phosphoribulokinase  is not able to produce the biomass precursors in experimentally observed proportions. These are consistent with realistic behaviour of plant’s cellular biochemistry [E. coli that most of the biosynthetic pathways’ reactions are essential [A set of 131 reactions is found to be essential for biomass production . Among toduction . Here, themistry . Part ofet al. 20 reportedThe reactions other than the essential are termed as non-essential reactions for primary biomass production. Nonessentiality of a reaction does not mean that the cell does not utilize this reaction to produce the biomass. Rather, it indicates that there exist alternative possible routes within the cellular metabolism using which the cell can produce same amount of the biomass. In addition, these alternative routes might be important for a specific perturbed state caused due to environmental changes to which the cell is exposed. Under some perturbed conditions, the knockout of enzymatic reaction associated gene(s) results in complete blockage of the associated reaction. The different states of genes (knockout or knock-down) represent different cellular genotypes, and respective metabolic responses could relate to the active cellular metabolic states.U indicates how easily a reaction will be bypassed when a perturbed or mutant condition arises. The non-essential reactions are classified here into three categories—‘maximally-favourable’, ‘quasi-favourable’ and ‘unfavourable’. The 1 − IU ∼ 0 value of a reaction indicates that the probability of bypassing this reaction is less and these reactions are termed as maximally-favourable for biomass production. The reactions with 1- IU ∼ 1 are defined as quasi-favourable, i.e., they are unused most of the time; however, they might be activated for driving metabolism in rare circumstances. Unfavourable reactions are those for which 1 − IU = 1. It should be noted that all these categorization of metabolic reactions are done in fixed biomass  condition. We have identified that 101 (1 − IU ∼ 0.0006 to 0.077), 111 (1 − IU ∼ 0.923 to 0.999) and 1348 (1 − IU = 1) reactions are maximally-favourable, quasi-favourable and unfavourable for biomass production, respectively  is found to be unfavourable and this result indicates that most of the routes in the entire metabolic network are not used to produce biomass precursors considered here; but they might be active to produce other biomass components including the synthesis of secondary metabolites. On the other hand, an inference could be made by the presence of a large number of maximally-favourable and quasi-favourable reactions that the plasticity of rice metabolic network is very high.Deletion of a large number of reactions does not inhibit the production of biomass and this indicates the metabolic plasticity of the cell as well as the robustness of cellular biochemical mechanisms. Consequently, this suggests that there are alternative routes the plant can use when needed. However, it does not ensure that all the alternative routes are equally economic, i.e., the cell needs equal amount of energy to produce the biomass using these alternative pathways. This energy, indeed, comes from the photon absorbed and is utilized in biochemical machinery.U index for cytosolic malate dehydrogenase  is 0.0019. The deletion of this reaction causes no change in photon demand, but the total flux of cellular objective function in MT solution space becomes higher  than the WT. So, using this WT path, cell can maximize its overall cellular economy. Further, there is always a possibility of having different solution for a particular objective. The presence of these cannot affect our main observation; rather, it suggests higher metabolic plasticity of cellular metabolism.While a reaction is blocked and the metabolic network finds at least one alternative route , the photon fold change (FC in lux unit . Table 1f a cell . For insU = 1) do not take part in biomass production, photon demand remains unchanged due to their deletions. Interestingly, the deletions of quasi-favourable reactions (1 − IU ∼ 1) also do not show any change in photon demand. It suggests that quasi-favourable reactions can be easily bypassed and can have several alternatives to produce the biomass.As the unfavourable reactions (1 − IU ∼ 0) which show photon FC > 1 when deleted  to G3P (3-phospho-D-glycerate) producing reaction (PHOSGLYPHOS-RXN) by enzyme phosphoglycerate kinase , 21 is ithaliana . It is eα-glucose 6-phosphate) to GLC-1-P (glucose 1-phosphate) in the WT and this pathway synthesizes cellulose. The UDP-glucose pyrophosphorylase, an important enzyme for cellulose deposition, catalyzes glucose-1-phosphate and UTP to produce UDP-glucose and pyrophosphate (PPI) [Another example is illustrated in te (PPI) . When thte (PPI) , catalyzte (PPI) .It is observed that while any one of the complexes I, III, IV and V in the mitochondrial electron transport chain is deleted, the metabolic process needs significantly higher amount of photon flux to supply ATP for biomass production. It is evident from In chloroplast, glyceraldehyde 3-phosphate dehydrogenase catalyzes a step in Calvin cycle by conversion of glyceraldehyde-3-phosphate (GAP) to glycerate 1,3-bisphosphate (BPGA). This reaction is also associated with NADPH production. Thus, removal of this reaction causes an increase in photon flux to produce the biomass in fixed proportion. Similarly, the deletion of another adjacent reaction catalyzed by phosphoglycerate kinase (EC 2.7.2.3) converting PGA (3-phosphoglycerate) to BPGA in the same path causes same photon FC. The light dependent non-cyclic (LightNonCyc in our reaction list) reaction remains active all the time; however, in a few cases, slight decrement in its flux is observed which is compensated mostly by light dependent cyclic reaction. The decrease in NADPH produced by light non-cyclic reaction is tuned by other NADPH producing sources. Alternative routes for deletions of some of the maximally-favourable reactions are also presented in Rice leaf metabolism under varying light shows that photorespiration can salvage the excess energy produced at higher light intensities . ConsequPhotosynthetic organisms need NADPH as the reducing power for several carbon and nitrogen fixing metabolic processes occurring within the cell. ATP is the essential currency metabolite, needed in many metabolic processes as a supply of energy. The utilization of ATP and NADPH in a cell depends on the condition in which the cell is being exposed . The lig3 compound ), generated in the Calvin cycle within the chloroplast, can be transported to the cytosol with an exchange of cytosolic Pi through three chloroplastic transporters, namely, PGA, GAP and DHAP transporters. Thermodynamically, these exchange reactions are reversible, i.e., they can also transport cytosolic PGA, GAP and DHAP to the chloroplast with an exchange of chloroplastic Pi.The intracellular transporters of a plant cell transport metabolites from one compartment to another. There are a number of chloroplastic transporters which exchange Pi (inorganic phosphate) and specific metabolites (carbon compounds) between chloroplast and cytosol. For example, the C3 transporters are shown in We have deleted all the non-essential reactions one by one and analyzed the exchange of metabolites through these chloroplastic transporters. The results are presented in In the WT, the chloroplastic PGA transporter transports PGA from cytosol to the chloroplast. When any one of the mitochondrial MalDH , cytosolic phosphoglycerate kinase, chloroplastic G3Pdh  or PGK (phosphoglycerate kinase) reactions is blocked, the chloroplastic PGA transporter transports chloroplastic PGA to the cytosol. In WT, the G6P (glucose 6-phosphate) is produced in the chloroplast and transported to the cytosol. The transport becomes reverse when any one of the chloroplastic FBPase , G3Pdh, Ald1 (Aldolase A), R5Piso, PGI (phosphoglucose isomerase) or PGK reactions is blocked. While chloroplastic G3Pdh or PGK reaction is blocked, the GAP transporter transports GAP from cytosol to the chloroplast. The DHAP transporter exports Pi from chloroplast to cytosol when any one of the chloroplastic triosephosphate isomerase, ribose-5-phosphate isomerase, PGK or cytosolic fructose-bisphosphate aldolase catalyzed reactions is blocked.fp. This gives an estimate of how much biomass can be generated in mutant type using the amount of photon needed in WT. It is expected that MTfp would generate a lower amount of biomass using WT photon. It is clear from fp solutions for these constraints produce 58.3% and 57.7% of total biomass, respectively. It indicates that inhibition of some maximally-favourable reactions can end up with reduced biomass in lower light.The minimum amount of photon needed in WT to produce the biomass in experimentally fixed proportion is ∼ 0.32 light flux unit. However, deletions of some reactions require higher amount of incident photon for the same purpose. Here, the incident photon flux is kept fixed at ∼ 0.32 light flux unit (as obtained in WT); then a reaction is deleted and the cellular metabolism is simulated to predict the fluxes through the biomass precursors. This mutant type state, simulated in fixed photon flux is denoted as MTIt is already known that the chloroplastic and mitochondrial metabolisms are highly dependent on each other and they serve some important cellular functions including ATP production and regulation of redox state in the cell –30. HereDeletions of complexes I and V in mitochondria up-regulate malate-oxaloacetate shuttle in chloroplast and down-regulate light dependent non-cyclic reaction. In addition, the light dependent cyclic reaction becomes active. The deletions of complexes III and IV up-regulate malate-oxaloacetate shuttle, light non-cyclic reaction and GAP transport from chloroplast and down-regulate F6P (fructose 6-phosphate) to G6P conversion. Deletion of malate-dehydrogenase  in mitochondria up-regulates malate-oxaloacetate conversion, light non-cyclic reaction in chloroplast and down-regulates F6P to G6P production.While the reactions catalyzed by chloroplastic PGK (PGA → BPGA) and G3Pdh (BPGA → GAP) are blocked, the fluxes in electron transport chain (ETC) are increased along with malate to oxaloacetate shuttle in mitochondria.Elimination of cytosolic BPGA to PGA conversion reaction up-regulates some reactions of TCA cycle  is identified. The rest of the reactions are classified based on the condition that whether these reactions can be easily bypassed or they are favourable by the cellular metabolism. The photon demands of the metabolic system while using alternative paths are calculated. Some of these alternative pathways are economic in terms of photon demand, while others are not. The readjustments of metabolism to utilize the cellular ATP and NADPH through some alternative pathways are also discussed. While the biomass production remains constant, the higher photon demanding pathways might represent active metabolic states of the plant at higher light intensities. The effect of reaction deletion on (i) exchange of metabolites through chloroplastic transporters and (ii) the interactions of the metabolism of different compartments are also demonstrated.However, the present version of the rice metabolic model is partially compartmentalized. Thus, one can include other compartments and the relevant reactions in the model and extend the analysis to understand the underlying mechanism of cellular metabolism. Likewise, the system can be studied under other cellular objectives . Rice plant also produces several secondary metabolites and inclusion of those into the model might increase the number of essential reactions. However, despite the possibility of these improvements, this study should provide a platform for the rice biotechnologists to design stress-tolerant and efficient rice cultivars.S1 Dataset(XLS)Click here for additional data file.S2 Dataset(XLS)Click here for additional data file.S1 Table(PDF)Click here for additional data file.


Pseudomonas putida KT2440 (iJN746) with the aerobic pathway of PCBs degradation. We assess the effectiveness of different bioremediation scenarios in reducing PCBs concentration in species and we study indices of species centrality to measure their importance in the contaminant diffusion via feeding links. The analysis of the Adriatic sea case study suggests that our framework could represent a practical tool in the design of effective remediation strategies, providing at the same time insights into the ecological role of microbial communities within food webs.The pressure to search effective bioremediation methodologies for contaminated ecosystems has led to the large-scale identification of microbial species and metabolic degradation pathways. However, minor attention has been paid to the study of bioremediation in marine food webs and to the definition of integrated strategies for reducing bioaccumulation in species. We propose a novel computational framework for analysing the multiscale effects of bioremediation at the ecosystem level, based on coupling food web bioaccumulation models and metabolic models of degrading bacteria. The combination of techniques from synthetic biology and ecological network analysis allows the specification of arbitrary scenarios of contaminant removal and the evaluation of strategies based on natural or synthetic microbial strains. In this study, we derive a bioaccumulation model of polychlorinated biphenyls (PCBs) in the Adriatic food web, and we extend a metabolic reconstruction of  Polychlorinated biphenyls (PCBs) are a class of POPs consisting of 209 different congeners, obtained from the catalytic chlorination process of biphenyl, and characterized by high environmental persistence and resistance to natural ways of breakdown. PCBs are practically insoluble in water and, due to their lipophilic nature, they easily dissolve in fats and lipids causing bioaccumulation, i.e., the phenomenon by which the internal contaminant concentration in an organism is higher than in the external medium. Indeed, PCBs have been detected both in aquatic biota and in all the abiotic phases of marine environments . Generally, heavier chlorinated PCBs congeners tend to accumulate in oxygen-depleted zones of sediments. Moreover, they bioconcentrate in species by following biomass flows in predator-prey relationships. PCBs bioccumulation phenomena in aquatic organisms occur over time as the result of multiple contamination pathways, including processes of uptake  and elimination .Aquatic ecosystems are subject to a mixture of synthetic organic chemicals, leading to adverse effects on organisms at different levels of biological organization and at all trophic levels of the food web. Over the last decades, many removal strategies have been proposed in order to reduce the bioavailability of persistent organic pollutants (POPs) and to limit the consequent bioaccumulation phenomena on species. microbial loop , presented in Nogales et al.   are known quantities and are estimated as reported in . In order to have an effective degradation process, this aerobic step should ideally take place sequentially to the anaerobic step in the full microbial degradation pathway. As illustrated in Figure Pseudomonas putida  in Nogales et al. . Several studies report the genetic plasticity of different strains of Pseudomonas spp., showing the correspondence between gene clusters involved in biphenyl degradation pathways , by extending the metabolic reconstruction of s et al.  with thein silico analysis of the invariant characteristics of the metabolic network at a low computational cost.Starting from biochemical reactions and stoichiometric coefficients, the Flux Balance Analysis (FBA) framework is based on the assumption of a metabolic steady state  and the synthetic objective vk2 , we set fk1 = 1 and gk2 = 1. The solution of the bilevel problem (1) is a pair indicating the maximum natural objective (inner problem) allowed by the constraints Sv = 0 and V⊥k ≤ kv ≤ V⊤k, and the maximum synthetic objective allowed in the flux distribution that maximizes the natural objective. The bilevel problem can be converted to a single-level problem using the duality theory applied to the inner problem, which is replaced by additional constraints for the outer problem.where P. putida. In the following, we use the more compact notation of chemical reactions to describe our FBA encoding, omitting the translation to the matrix form given in Section 2.3.We introduce a method for integrating the PCBs bioaccumulation network with the FBA-based metabolic reconstruction of i → j in the food web with a unary irreversible reaction with substrate i (the prey) and product j (the predator). Ecological compartments are thus translated into metabolites. Specifically, we derive the following set of reactions:The basic idea is encoding each link i, j)  is upper bounded by the original corresponding flow rate ci→j. This formulation admits a space of solutions with potentially reduced (even zeroed) contaminant flows, which is required in order to reproduce the contaminant removal by the bacterial metabolism.where the rate of a reaction  but i has null contaminant concentration (iC = 0).Any admissible vector of fluxes for the reactions in Additionally, we consider the following set of exchange reactions for expressing the external inputs and outputs of the food web:FWE contains, for each external sink e of the food web, an unbounded export reaction from e. Similarly, the set of import reactions FWI has an uptake reaction for each external source, but in this case the uptake rate is set to the sum of all flows imported through i in the contaminated network (∑j ci→j). Note that it is sufficient to constrain the import reactions in order to obtain a consistent FBA encoding of the bioaccumulation model. Indeed, by mass-balance, throughflow values are conserved by the encoding and it can be shown that the food webs entailed by the reactions in FWR ∪ FWE ∪ FWI are all identical to the original network, up to redistribution of external exports.The set i, the resulting bioconcentration iC in the entailed network is computed as the ratio between the total contaminant outflows (as reaction fluxes) and the total biomass outflows:Finally, for a generic group x, which serves as the interface between the encoded bioaccumulation model and the bacterial reactions. In particular, x represents the unbounded sink for all the food web groups we aim to remediate; and the unbounded source for all the metabolites describing PCBs molecules in the P. putida metabolism . Clearly, these interface reactions could also be bounded with arbitrary or experimentally measured limiting factors to bioremediation efficiency, as done in Section 3 for evaluating different degrees of bioremediation.An effective way to accomplish this task is adding a dummy metabolite bioremediation problem, as that of maximizing the amount of remediated flow, i.e., the sum of fluxes exitingx in the integrated metabolism-food web network. Formally,We define the I denotes the set of interface reactions; R is the set of reactions in the P. putida metabolism; and FWR, FWE and FWI describe the encoded food web.where Scenario 1: Bioremediation of detritus groups. This hypothesis is based on the fact that the microbial loop, where bioremediating bacteria are assumed to naturally operate, is located at the interface between natural detritus and planktonic groups (both included in our food web). Thus, we redirect the outflows from detritus to the microbial metabolism. The same applies to the discard group, treated as a detritus in our model. The integration reactions are:Scenario 2: Bioremediation of water compartment. This case describes the effects of an in situ bioremediation process of PCBs, regarded as acting within the water compartment , decreasing PCBs concentrations in the whole surrounding environmental media. The integration reactions are:Evidently, not all integrations are ecologically and biologically plausible. In our model, we consider two bioremediation scenarios, as also shown in Figure −2 year−1) to the flux units used in FBA (mmol h−1 gDW−1). The conversion factor is k = 1/ (m · t · n), where m is the molar mass of a PCBs molecule ; t = 8760 h is the number of hours per year; and n is the amount (gDW) of actively remediating P. putida in the unit of space (1 km2). k can be applied to all the PCBs flows, or as a stoichiometric coefficient in the interface reactions. In our model, we set n = 10−3 gDW, enough to import the totality of the connected PCBs flows into the P. putida metabolism, and to avoid numerical errors in the optimization procedure due to excessively small flux values. However, marine metagenomic data can be used to have a finer estimation of parameter n.The integrated models have been obtained after converting PCBs flows   even if our framework can be applied to the study of arbitrary network indices.In order to assess the effects of bioremediation on our contaminated food web, we combine the evaluation of bioconcentrations with the study of ecological network indices. Typically, global indices  per species and, ideally, from an effective bioremediation strategy, we expect a substantial breakdown of this property. It is calculated as:We employ n is the number of groups in the network.where LIM van Oevelen et al., sna Butts, COBRA toolbox  for PCBs uptake rate up to 9.8 mmol h−1 gDW−1 . Further, the addition of the PCBs bioremediation pathways to the P. putida metabolism does not result in an increased growth rate.By applying bilevel FBA, the growth rate of 1 Figure . The max−1 gDW−1, and then remains stable even at high oxygen uptake. The P. putida is able to keep a high growth rate also with low oxygen, which reproduces the environmental conditions describing the proposed first bioremediation scenario. The linear relationship between PCBs and oxygen uptake rates is in keeping with the fact that the uptake of PCBs depends on the aerobic degradation pathway.In order to investigate the relationship between growth rate and oxygen uptake, and between PCBs uptake and oxygen uptake, we apply a single-level FBA analysis. In Figure P. putida is not able to optimally support multiple degradation pathways. We further perform a phenotypic phase plane (PhPP) analysis by coupling the biomass production objective with varying PCBs and toluene uptake rates. In this case, we seek to optimize growth on top of the configuration maximizing both degradation pathways (the sum of PCBs and toluene uptakes). The PCBs-toluene tradeoff delineates two regions in the phenotypic space: when the uptakes of PCBs and toluene are below the optimal front, maximum growth is achieved , as also seen for the PCBs case in Figure P. putida robustly gives optimal growth yields even in the strain designs targeted to the maximization of multiple degradation pathways.We also analyse the interdependence between the PCBs degradation pathways (introduced in this work) and that of toluene . We derive an optimality front between them by solving two bilevel problems. In the first, we evaluate the maximum toluene uptake when PCBs imports are favored, while in the second problem, we consider the symmetric objectives. Both problems identify the identical linear trade-off , simulating a bioremediation at the level of the microbial loop. In Scenario 2, PCBs bioremediation is assumed to act in the water compartment by reducing simultaneously all the PCBs uptakes in each functional group. The following results are obtained by solving the bioremediation problem (Section 2.4) and computing bioconcentrations and network indices on the resulting (the entailed) bioaccumulation networks.Scenario 0 [plot (a)], and of the above two scenarios when no limits to the bioremediation efficiency are imposed [plot ]. Figure In Figure In Scenario 1 [plot (b)], we clearly notice a simpler pattern of PCBs contamination among functional groups, due to a considerable reduction of feeding links active in the transport of PCBs. Specifically, the redirection of outflows from detritus and discard out of the food web causes the inactivation of several PCBs flows, and subsequent presence of groups with null PCBs concentration. Therefore, these groups (not plotted) are disconnected from the bioaccumulation network but still active in the biomass network. They include detritus (38) and discard (39); detritivores ; group 30, which only feed on planktonic groups; and groups feeding on those mentioned so far . Other variations are detectable in groups 5, 27, and 28 (detritivores and planktivores) that no longer acquire PCBs from food. Finally, we can observe that groups 12 and 27 gain in this scenario a central role in the contaminant diffusion, becoming the preferential source of most of their predators, while in Scenario 0 their contribution appears less relevant.The bioaccumulation network under Scenario 2 [plot (c)] exhibits a similar structure to Scenario 1. Detritus groups  and detritivores  are no longer connected to the rest of the food web, showing that bioremediation of the water compartment tends to disrupt the pathways of contaminant uptake at the lowest trophic levels. Another similarity is the promotion of group 12 as a central node in the acquisition of PCBs by its predators. On the other hand, group 27 has no outgoing PCBs flows, while in plot (b) the opposite situation (no inflows) is observed for the same group. In general, we notice a lower number of active links with respect to Scenario 1, especially in species at higher trophic levels.−2 year−1 and 3312 mg km−2 year−1, respectively), which mainly depends on the structure of the network. Applying the conversion factor in Section 2.4, the maximum remediated flow in Scenario 1 corresponds to a PCBs uptake rate of 3.15 mmol h−1 gDW−1 (31.5% of the maximum uptake), while in Scenario 2 to 2.45 mmol h−1 gDW−1 (24.5% of the maximum uptake).Another kind of analysis enabled by our framework is the study of the networks obtained by solving the bioremediation problem at increasing efficiencies, limiting the amount of PCBs flow allowed into the bacterial metabolism. In both scenarios, we analyse the variations in PCBs bioconcentrations Figures  and in tAs regards Scenario 1, no remarkable reductions in bioconcentrations are observed in the entire food web [see plot (a)], apart from the natural detritus and the discard groups, whose PCBs values are zeroed at 89 and 16%, respectively, of the maximum bioremediation efficiency. We register only minor drops in a number of groups at TL 4  and in group 37 (feeding on discard). This tendency is also visible in the sum of PCBs, which is practically constant.On the other hand, Scenario 2 gives a considerable decrease in the bioconcentrations of all groups [plot (b)]. This is explained by the fact that the estimated uptakes from water constitute an important fraction of imported contaminant, whose degradation also mitigates, indirectly, uptakes from food. The only exceptions are natural detritus and discard , which have null PCBs flow from water ] highlights the topological importance of natural detritus in the bioaccumulation network, which derives from the fact that every group in the food web contributes  to its contaminant uptake. Indeed, this group maintains its central role up to 89% of bioremediation efficiency. After this point, a structural disruption occurs, related to the detritus becoming disconnected from the network . This leads to cascade effects also in the centrality of groups 13, 15, 16, 19, and 32. Apart from this case, FBC exhibits quite a robust pattern, showing a number of groups  with unchanged centralities regardless of the amount of bioremediated flux. This structural robustness is evidenced also by the link density values, indicating that, globally, the number of links active in the PCBs diffusion is relatively constant.On the contrary, Scenario 2 [plot (d)] produces prominent changes in the centrality of most species. Here, natural detritus loses its dominant role in the network at 10% of maximum bioremediation. Moreover, at 34% of efficiency, we observe a sudden fall in the FBC of group 24, as also registered on its bioconcentration values [see plot (b)]. Only functional groups 2 and 25 show robust topological importance, in agreement with Scenario 1. The evolution of the link density index also evidences the high sensitivity of the network structure. Indeed, the index reaches an average of 3.1429 active links per group, 36% lower than the initial value.Pseudomonas putida. Our framework is based on a range of multi-scale analyses obtained by combining well-established methods in ecological modeling  and Systems Biology . We showed how to derive optimal remediation strategies that yield the highest decrease of bioaccumulation phenomena in species. In addition, more realistic scenarios can be reproduced that take into account environmental limiting factors influencing the potential of natural or synthetically designed microbial pathways.Recent biotechnological advances and novel discovery tools in marine metagenomics are paving the way for new integrated solutions in environmental bioengineering, turning empirical hypotheses into practical methods. In this context, we presented a computational framework for the analysis of contaminated ecosystems and for the evaluation of different hypothetical bioremediation scenarios. We considered the case of PCBs bioaccumulation in the Adriatic food web and PCBs degradation mediated by P. putida metabolic model supports well the degradation of PCBs, and that a substantial drop of PCBs concentration in Adriatic species is achieved with comprehensive bioremediation strategies , while natural bioremediation  proved to be less effective. Results also highlight how remediation patterns vary among species in function of their feeding relationships. The study of ecological network indices allowed the evaluation of emerging global ecosystem properties under different bioremediation scenarios and degradation efficiencies.Our computational experiments indicated that the extended To the best of our knowledge, this is the first computational method linking genome-scale reconstructions of bacterial metabolism with food web bioaccumulation models for designing and analysing bioremediation strategies. Approaches based on high dimensional omics data and network inference methods (Perkins et al., In this work we wanted to stress a different view on marine ecosystems, regarding them not just as ensembles of macro-species, but as complex multiscale networks linking classical food webs and microbial groups, toward a new perspective of “eco-metabolic” networks. We believe that bringing the study of microbial metabolic activity into the field of ecotoxicological modeling can highlight bottlenecks and advantages of different bioremediation approaches and shed light on the ecological role of marine microbial life. Furthermore, PCBs degrading bacteria live in communities structurally organized in biofilms (Abraham et al., The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Several methods have been developed to predict system-wide and condition-specific intracellular metabolic fluxes by integrating transcriptomic data with genome-scale metabolic models. While powerful in many settings, existing methods have several shortcomings, and it is unclear which method has the best accuracy in general because of limited validation against experimentally measured intracellular fluxes.l2 norm) and SPOT (Simplified Pearson cOrrelation with Transcriptomic data), which can be chosen and combined depending on the availability of knowledge on carbon source or objective function. This enables us to simulate a broad range of experimental conditions. We examined E. coli and S. cerevisiae as representative prokaryotic and eukaryotic microorganisms respectively. The predictive accuracy of our algorithm was validated by calculating the uncentered Pearson correlation between predicted fluxes and measured fluxes. To this end, we compiled 20 experimental conditions (11 in E. coli and 9 in S. cerevisiae), of transcriptome measurements coupled with corresponding central carbon metabolism intracellular flux measurements determined by 13C metabolic flux analysis (13C-MFA), which is the largest dataset assembled to date for the purpose of validating inference methods for predicting intracellular fluxes. In both organisms, our method achieves an average correlation coefficient ranging from 0.59 to 0.87, outperforming a representative sample of competing methods. Easy-to-use implementations of E-Flux2 and SPOT are available as part of the open-source package MOST (http://most.ccib.rutgers.edu/).We present a general optimization strategy for inferring intracellular metabolic flux distributions from transcriptomic data coupled with genome-scale metabolic reconstructions. It consists of two different template models called DC (determined carbon source model) and AC  and two different new methods called E-Flux2 (E-Flux method combined with minimization of Our method represents a significant advance over existing methods for inferring intracellular metabolic flux from transcriptomic data. It not only achieves higher accuracy, but it also combines into a single method a number of other desirable characteristics including applicability to a wide range of experimental conditions, production of a unique solution, fast running time, and the availability of a user-friendly implementation. Intracellular metabolic reactions provide a cell with biochemical building blocks, energy, and a suitable thermodynamic environment. Due to the large connectivity of metabolic networks via metabolites each of which participates in multiple metabolic reactions, determination of system-level changes in intracellular metabolic fluxes is important for understanding the fundamental mechanisms of cellular metabolic responses to environmental or genetic perturbations .13C metabolic flux analysis (13C-MFA) is available for characterizing intracellular fluxes experimentally, and is the most widely accepted approach to quantify fluxes in central carbon metabolism [13C-labeled substrates until the cells are at both metabolic steady state (i.e. when concentrations of metabolites are constant over time) and isotopic steady state (i.e. when isotopomer fractions remain stable over time). Then the level of 13C enrichment in cellular metabolites is measured by mass spectrometry (MS) or nuclear magnetic resonance (NMR). Finally, the intracellular flux distribution is reconstituted from the 13C enrichment patterns [13C-MFA can determine intracellular fluxes, extensive instrumentation and specialized expertise is required to carry out the experiment and the number of fluxes that can be accurately and uniquely determined is limited [13C-MFA is not capable of intracellular flux determination, and isotopically nonstationary MFA (INST-MFA), an even more challenging method both experimentally and computationally, is required [tabolism . In thispatterns –6. Thoug limited . Moreoverequired .An alternative widely used for system-level studies of metabolism is a computational modeling method called flux balance analysis (FBA). FBA defines the space of allowable metabolic flux distributions of a system at steady state by making use of genome-scale metabolic models . Since tAdvances in omics technologies have enabled quantitative monitoring of the abundance of biological molecules at various levels in a high-throughput manner . In the There have been previous studies to integrate transcriptomic data with genome-scale metabolic models, which are well covered in recent reviews ,11,15–20Some of them require multiple sets of input data for a single analysis ,22, whicSome methods require a user-defined threshold to define “high” or “low” expression states –26, whica priori assumption of an appropriate objective function such as biomass production rate (i.e. the growth rate) [Several methods require th rate) ,24,27,28th rate) . Althougth rate) , we needth rate) .Several methods produce non-unique solutions. That is, they produce a solution out of a space of possibilities, all of which are in theory possible. If all solutions in the space of possibilities were equally good in terms of their ability to predict fluxes, this would be acceptable, but in general, there is a range of possibilities for predictive accuracy. A single solution that is arbitrarily chosen is difficult to reproduce and is typically dependent on the software or hardware used for the analysis . Thus, iin vivo applications [Lastly, previous studies have generally focused on conditions where the carbon source of the system and its uptake rate are known. While many biotechnological and laboratory processes operate on a known single carbon source, typically glucose, we would sometimes like to study microorganisms living in conditions where the carbon source is unknown, such as for ications .Therefore, in light of various experimental and cellular conditions in practical applications, there is still a need for a method that can provide all five of the desirable features listed in E. coli and 9 in S. cerevisiae, see In this study, we compiled the most extensive dataset to date, consisting of 20 experimental conditions , a detailed description of which is given in The first step was to collect a dataset of transcriptomic and fluxomic measurements obtained from cells under the same conditions. The measured fluxes were obtained to compare them with the predicted fluxes. To this end, we obtained data published by Ishii et al. and Holm.[et al.  for E. ca et al. ,37 and C [et al.  for S. ciJO1366 and Yeast 5 for the metabolic models of E. coli and S. cerevisiae, respectively. We also tested our methods on older models of E. coli (iJR904 and iAF1260) and those of S. cerevisiae (iND750 and iMM904) to examine the applicability of our methods to the relatively incomplete models  and of  (iND750  and iMM9 [iMM904 ) to exama priori information on cellular uptake rates and ATP maintenance flux. The template model is made by setting the flux bounds either to zero or to positive or negative infinity while maintaining the stoichiometric and reversibility information of the original genome-scale model:j,v is a flux vector representing the reaction rates of the n reactions in the network, and aj and bj are the minimum and maximum reaction rates through reaction j defined in the original model. In this manner, we constructed two kinds of template models to simulate two different situations depending on whether we know which carbon source the cell uses. One template model, which we call 'DC (determined carbon source)', has a lower bound of negative infinity for the known carbon source uptake reaction. The other one, which we call 'AC ', allows all carbon sources in the model to be taken up by the cell. Among all metabolites participating in the exchange reactions, the set of possible carbon sources were selected based on their chemical formula. The list of carbon sources whose uptake rate were set as negative infinity in the AC models for both microorganisms are given in When integrating transcriptomic data with genome-scale metabolic models, a problem of scaling can occur because the units for measuring metabolic flux and the units for measuring gene expression are not related. For instance, if the carbon uptake rate is set to 1, and the transcriptome values are all in the order of 10000, then applying such values as upper bounds will not constrain the model. To avoid this issue, we construct a template model that is independent of This step, converting original genome-scale models into DC or AC template models before integrating gene expression data, resolves the scaling problem described above. The fluxes predicted by our method have an arbitrary unit. Thus, the relative magnitude of predicted fluxes across reactions is meaningful, but their absolute magnitude is not. Any known or measured reaction rate  can be used to normalize the predicted fluxes to an absolute reference.If information on the biomass composition of a certain organism is available and maximizing its growth rate is appropriate for prediction, our first method, called E-Flux2, is an effective way to study its metabolic behavior. Otherwise, our second method, called SPOT, can be used.f is a coefficient vector defining the organism’s objective function, S is the stoichiometric matrix.E-Flux is an extension of FBA that infers a metabolic flux distribution from transcriptomic data ,28. The gj, the absolute gene expression level associated with reaction j, for an upper bound, gj = The main difference between E-Flux  below anet al. and Celton et al.), we used the MAANOVA normalization method [For one-color microarrays and RNA-seq measurements, it is relatively straightforward to determine absolute gene expression . For twon method  to achien method .j,E-Flux solves the following:Gene expression data were mapped to corresponding reactions in the network based on gene-protein-reaction (GPR) associations. For example, in the case where an enzyme complex consisting of subunits encoded by multiple genes mediates a certain metabolic reaction, we put the minimum value of the expression level of the associated genes on et al. [x, also called the l2 norm, is given by:x on an n-dimensional Euclidean space Rn. Thus, as stated by Bonarius et al., the constraint of minimizing the Euclidean norm corresponds to the strategy of a cell to minimize the length of the metabolic flux vector to channel metabolites as efficiently as possible. We additionally applied this theoretical constraint after maximizing the biomass flux to find a unique metabolic flux distribution satisfying both optimal biomass flux and the flux minimizing its Euclidean norm. So, the first method that we propose, which we call "E-Flux2" (meaning E-Flux method combined with minimization of l2 norm), consists of two steps of optimization, which can be chosen when a suitable objective function is known:A problem of E-Flux is that the outcome solution is not unique, making it difficult to clearly identify predicted metabolic responses. Bonarius et al.  used minStep 1. E-Fluxl2 norm Step 2. Minimization of z* here, this method finds a unique metabolic flux distribution by minimizing the Euclidean norm of the flux vector. The square root function was ignored since removing the square root does not change the solution. Since the objective function, the Euclidean norm squared, is strictly convex, and all equality and inequality constraints are linear, which is convex, the solution of E-Flux2 is unique because the optimal solution to the problem of minimizing a strictly convex function over a convex set is unique [l1 norm (or Manhattan norm) [l1 norm, is not strictly convex.After calculating the optimal biomass flux, denoted as s unique . The outan norm) . pFBA doThough not largely different from E-Flux, E-Flux2 overcomes a major shortcoming of E-Flux, namely, that it does not yield a unique solution. Among the space of solutions that E-Flux provides, E-Flux2 provides a method to select one solution in a manner that is intuitive and yields high correlation to measured fluxes see .v, and its corresponding gene expression data, g. The assumption behind this strategy is that enzymatic transcript concentrations and metabolic fluxes can be related to each other, albeit in a complex manner, since the existence of a transcript is necessary for the presence or activity of its corresponding enzyme [If a suitable objective such as the biomass flux is unknown, we can use a second method which is to maximize correlation between a flux vector, g enzyme . To calcj into two positive irreversible reactions, the forward reaction, n − r are irreversible, while reactions n – r + 1,…,n are reversible, and that all irreversible reactions are defined in the forward reactions (i.e. their fluxes are non-negative). Then, instead of problem (6), we solve:Sirr is the submatrix consisting of the first n – r columns of S, and Srev is the submatrix consisting of columns n – r + 1 to n of S. Solving this optimization problem is computationally inefficient since the form of the objective function is nonlinear. However, this problem can be converted to an equivalent semi-definite programming problem (8):we will consider a problem with modified upper and lower bounds that are 0 or ± infinity as described in This is the second method we propose, which we call "SPOT" (Simplified Pearson cOrrelation with Transcriptomic data). SPOT can be used when biomass flux is not an appropriate optimization objective. The conversion of optimization problem (7) to SPOT (8) is based on a few steps of justification.First, the maximum Pearson product-moment correlation is not dependent on the length of the flux vector, The optimization problem described in Transcriptomic data are used to constrain fluxes in the model for E-Flux2, and they are used to define the objective function for SPOT. The process of making a choice between E-Flux2 and SPOT is described in the flow chart in l2norm) can be used. Otherwise, we can use SPOT (Simplified Pearson cOrrelation with Transcriptomic data).If we know the cell's carbon source, we use the DC (determined carbon source) template model which has a negative infinity value on the lower bound of the known carbon source uptake reaction. Otherwise, we use the AC  model which allows all carbon sources in the model to be taken up by the cell. If the biomass composition of the cell is known and the maximization of biomass flux is a suitable objective function, E-Flux2  and A-(d) in E. coli and a single flux distribution for S. cerevisiae that each achieve high correlations with the measured data in each organism (data not shown). Nevertheless, the dataset we have gathered is the largest and most comprehensive dataset that currently exists for validating methods of predicting intracellular fluxes from transcriptomic data. We expect that the high correlations obtained by E-Flux2 and SPOT will generalize beyond E. coli and S. cerevisiae growing on glucose, given how their underlying optimizations reflect our general understanding of the relationship between metabolic flux and gene expression, but we cannot conclude this without additional data. In particular, coupled trascriptomic and fluxomic data obtained in organisms under very different conditions  would help significantly in establishing the generality of our method.The reactions whose measured fluxes were used to calculate the correlation for each dataset are shown in http://most.ccib.rutgers.edu/ whose source code is open to the public [All methods in this study initially implemented in MATLAB . These were tested using MATLAB R2013b with Gurobi Optimizer 5.6 . SBMLToolbox was used to convert an SBML (Systems Biology Markup Language) model into a MATLAB data structure . Computae public .E. coli and 9 samples in S. cerevisiae. The number on the right side of the plus minus sign indicates its standard deviation.The Pearson correlation between the predicted and the measured intracellular fluxes was calculated to validate the predictive accuracy of our method. All correlation values used to draw figures and tables are summarized in E. coli and S. cerevisiae. The result implies that our method can predict the measured intracellular fluxes best when we have knowledge of both carbon source and objective function . Our algorithm is able to predict intracellular metabolic fluxes with a good correlation if the information on either biomass objective or carbon source is unknown as we can see in the category of DC+SPOT (average correlation: 0.8030), and AC+E-Flux2 (average correlation: 0.6733). In the case where there is no information on both carbon source and biomass objective, our AC+SPOT method allows us to predict intracellular metabolic fluxes with an average correlation of 0.5927. Although this value is weaker than those of the other three cases of our method, a Pearson correlation coefficient around 0.6 nevertheless represents moderate positive correlation [As summarized in relation .To see whether the good or modest correlation value between predicted and measured fluxes in each case is because of a good correlation between transcripts and measured fluxes itself, we also calculated the correlation between gene expression data and measured fluxes. When calculating the correlation with gene expression data, we used the absolute values of measured metabolic fluxes since gene expression values are always positive, while we used the signed measured fluxes when calculating the correlations with predicted fluxes. The correlation between gene expression data and the absolute values of the measured fluxes was 0.4923 (standard deviation: 0.2900), which is weaker than all of the correlations between the predicted fluxes and the measured fluxes. Although this value cannot be directly compared with correlations within the table , this relatively poor correlation between gene expression data and the measured fluxes, given as a point of comparison, suggests that the correlation is improved by incorporating the gene expression data into a genome scale model.et al. [et al. method, we used an implementation provided with the original publication.Using the same transcriptomic and fluxomic datasets, we compared the accuracy of our predictions with other competing methods. We chose to compare against E-Flux ,28 and tet al. , which aet al.  and iMATet al. ,25, and et al.  or in roet al. . For theE. coli (average correlation: 0.8887) but worse predictions in yeast (average correlation: 0.2009) than our method (DC+SPOT) whose average correlation is 0.7960 and 0.8117 in E. coli and in yeast, respectively . As can be seen in In all four scenarios with varying availability of carbon source or biomass objective information, our method outperformed existing methods in that it showed a higher average correlation with a smaller standard deviation . Particuectively . Unlike a priori information on several specific fluxes such as sugar (e.g. glucose) uptake rate and oxygen exchange rate, these fluxes were set according to the experimental conditions described in the four papers where the transcriptomic and fluxomic data sets were obtained. Simulating anaerobic growth with Yeast 5 requires the simulated medium to be supplemented with phosphadiate and sterols and modification of the biomass definition [et al. dataset  for reference . pFBA wafinition . Due to  dataset .Since standard FBA and pFBA need both carbon source and objective function information, their correlations can be compared with those of E-Flux and E-Flux2 in Importantly, the result predicted by our method is unique. The Lee et al. method also produces a unique solution using geometric FBA , which il2 norm (l2). It also showed good correlation with measured fluxes . When knowledge of uptake rates is available, the FBA+min l2 method is a good alternative to pFBA, since it is easier to implement and produces a unique metabolic flux distribution.In addition, we performed FBA along with the minimization of E. coli and S. cerevisiae, respectively. The x-axis represents a set of metabolic reactions used to calculate correlation between the measured and the predicted fluxes, and the y-axis indicates flux value. The scale and the units on the y-axis are based on those of the measured flux. The reactions are grouped functionally based on the pathways in which they are participating such as glycolysis and the tricarboxylic acid cycle. As can be seen in the figure, the predicted and the measured metabolic flux distribution look similar to each other when the correlation between them is high. We see moreover that AC+SPOT predicts negative fluxes for some reactions which are supposed to be positive, which might explain one of the reasons why the method shows relatively poor correlation compared to the other three methods . Based on this observation, possible ways to improve the correlation of AC+SPOT will be discussed in the following section.In addition to calculating correlations, we examined how the predicted and the measured metabolic flux distribution visually compare to each other. Since the predicted flux of our method has an arbitrary unit, the magnitudes of the predicted fluxes were normalized by the Euclidean norm of the measured flux vector for comparison. The results are shown in E. coli and S. cerevisiae are two of the most intensively studied model microorganisms. On the other hand, genome-scale metabolic models of many other organisms are still incomplete. Thus, it is important to examine the applicability of our methods to relatively incomplete models before applying our methods to other organisms. One of the ways to test this is by running our methods on older models of E. coli and S. cerevisiae that are relatively incomplete. Using the same transcriptomic and fluxomic datasets, we tested our methods on older models of E. coli (iJR904 and iAF1260) and of S. cerevisiae (iND750 and iMM904), and the results obtained are shown in x-axis represents the four different optimization strategies  and the y-axis identifies the average Pearson correlation coefficient between the predicted fluxes and the measured fluxes of E. coli (S. cerevisiae ( E. coli  and S. crevisiae . Each opE. coli (iAF1260 and iJO1366) showed better average correlation than the oldest model (iJR904) in most cases. We found that there is little difference in the average correlation between iAF1260 and iJO1366.In case of E. coli , the twoS. cerevisiae (iND750 and iMM904) when the carbon source is known (DC+E-Flux2 and DC+SPOT). Unlike the E. coli case, however, the newest yeast model performs worse than the older models when carbon source of a yeast cell is unknown, especially for AC+SPOT. To understand why, we explored the hypothesis that the reason for the poor performance of Yeast5 is because of the larger number of carbon sources  in both microorganisms. Thus, if we study an organism where information on both carbon source and objective function is known, applying DC+E-Flux2 is recommended.Except for E. coli and S. cerevisiae regardless of which model was used. The method seems to be the least influenced by incompleteness of the model. Thus, DC+SPOT is useful for predicting intracellular metabolic flux distribution in less well-studied organisms.Interestingly, DC+SPOT (known carbon source and unknown objective function) shows steady and constant average correlation between 0.7 and 0.8 in both From a practical perspective, short running time is a desirable characteristic. Thus, we measured the running time of our algorithm for all 80 samples (4 optimization strategies and 20 samples per strategy) using the built-in MATLAB function, profile. The execution time for our method is illustrated in Fig D in http://most.ccib.rutgers.edu/) is an open source-based software package for constraint-based modeling [As an ultimate representation of the cellular metabolic phenotype, metabolic fluxes provide important information to understand the functioning of cellular processes . Our metmodeling . It provIn this study, we developed a computational method to infer intracellular fluxes from transcriptomic data using genome-scale models, which satisfies desirable features summarized in Our method can also be easily applied to study the metabolic flux distributions of various engineered strains with little or no modification to genome-scale models since transcriptomic data themselves reflect knock-outs, knock-ins (with addition of metabolic reactions into the model that correspond to the knocked-in gene), induced-amplification or induced-repression of metabolic genes. In addition, E-Flux2 is flexible in that if there is an alternative objective to maximizing growth rate that is considered more applicable to a certain organism, then the biomass flux used in the first optimization step of E-Flux2 can be replaced with this objective function.http://most.ccib.rutgers.edu/).The multiple advantages of our method make it a useful tool for identifying fundamental mechanisms of metabolic responses and finding molecular targets for metabolic engineering. For instance, by using this tool with a set of gene expression data measured over a time course, we can determine how intracellular metabolic flux changes and where significant redirection occurs. Our method is available in a user-friendly, open source-based software package called MOST  and thr  used in(ZIP)Click here for additional data file.S2 DatasetThe transcriptomic and the fluxomic data sets that were used in this study can be found in the first four sheets of this Excel file and on the fifth sheet, respectively.(XLS)Click here for additional data file.S3 DatasetInstructions on using it with the dataset of Ishii et al. can be found in README.doc. The source code written in Java is also available (see (ZIP)Click here for additional data file.S1 FileS. cerevisiae data, Fig D. Average running time of our algorithm, Fig E. Exploration of the way to improve a poor performance of Yeast 5 in AC+SPOT) and three supplementary methods .This file contains five Supplementary figures Click here for additional data file.S2 Filehttp://most.ccib.rutgers.edu/). This document covers information on how to reproduce our results in MOST using the model files and transcriptomic data that are provided as Datasets S1 and S2.E-Flux2 and SPOT are implemented in the open source package MOST ((DOC)Click here for additional data file.S1 TableThe lower flux bounds of these reactions were relaxed to -Inf to construct AC template models for each microorganism (i.e. to simulate the condition where knowledge of carbon source is unavailable).(XLS)Click here for additional data file.S2 TableAll the Pearson correlation values between predicted fluxes of our method and measured fluxes, that are used for producing (XLS)Click here for additional data file.S3 TableiND750, iMM904, and Yeast 5) were identified to test the hypothesis that the number of carbon source uptake reactions affects the performance of the models.Total 106 exchange reactions that are common across all three yeast models ((XLS)Click here for additional data file.