Our result shows that NOD mice display an altered metabolic profile that is partly resembling the previously observation made in children progressing to Type 1 diabetes. The level of glutamic acid was one of the most discriminative metabolites in addition to several metabolites in the TCA cycle and nucleic acid components. The in silico analysis indicated that the genes responsible for this reside within previously defined Idd regions.Altered metabolism proceeding seroconversion in children progressing to Type 1 diabetes has previously been demonstrated. We tested the hypothesis that non-obese diabetic (NOD) mice show a similarly altered metabolic profile compared to C57BL/6 mice. Blood samples from NOD and C57BL/6 female mice was collected at 0, 1, 2, 3, 4, 5, 6, 7, 9, 11, 13 and 15 weeks and the metabolite content was analyzed using GC-MS. Based on the data of 89 identified metabolites OPLS-DA analysis was employed to determine the most discriminative metabolites. In silico analysis of potential involved metabolic enzymes was performed using the dbSNP data base. Already at 0 weeks NOD mice displayed a unique metabolic signature compared to C57BL/6. A shift in the metabolism was observed for both strains the first weeks of life, a pattern that stabilized after 5 weeks of age. Multivariate analysis revealed the most discriminative metabolites, which included inosine and glutamic acid. In silico analysis of the genes in the involved metabolic pathways revealed several SNPs in either regulatory or coding regions, some in previously defined  In addition, environmental factors such as infections, diet and climate has been attributed as potential underlying contributors. Although the pathogenesis process in diabetes is so far only detectable as either the appearance of islet-specific autoantibodies and/or the mononuclear infiltration in the islets of Langerhan's, it is evident that this process is preceded by other molecular and cellular events, which in turn could be reflected by the metabolome. In line with this it has been demonstrated that children with genetic predisposition for T1D development and that progress to T1D display an altered serum metabolic profile compared to the group of non-progressors Type 1 diabetes is an autoimmune disease which in contrast to the majority of other autoimmune diseases arises already at young age The metabolic changes in relation to time of diabetes onset have also been studied in the congenic BB rat model (Idds)IDDMs. Moreover, environmental factors also play an important role where infections, diet and climate clearly has been demonstrated to play a pivotal role The NOD mouse is another vastly used model for T1D Recently it was demonstrated that female NOD mice that progress to T1D display an discrete metabolic profile compared to genetically identical individuals that do not develop T1D NOD and C57BL/6 mice were originally obtained from Bomholtgaard, Denmark and bred and maintained in the transgenic animal facility (UTCF) at Umeå University. Diabetes incidence in our colony reached 50% in females after 5 months. None of the mice in the study developed diabetes during the sampling period. Experimental procedures were performed in compliance with the relevant Swedish and Institutional laws and guidelines and approved by the Umeå research animal ethic committee (A14-09). Blood samples were taken from individual female mice at the time points 0 weeks (new born) through 6 weeks . In order to obtain sufficient blood for analysis at these early time points the animals had to be sacrificed subsequently. From the 7–15 weeks old mice individuals were consecutively sampled . None of the mice became diabetic throughout the study. After sampling the blood was kept in room temperature for one hour and stored at 4°C over night. Clots was removed, remaining sera spun in a microfuge at 13 000 rpm for five minutes, where after the sera was stored in −80°C until the GC/MS analysis.Extraction of metabolites from plasma was undertaken following the protocol of A et al. This method has been shown to produce semi-quantitative data of good linearity, making it appropriate for comparisons across specie as well as time in this study The samples were derivatized using methoxyamine and MSTFA as described by A et al. and GC-MS analyses were carried out according to the same protocol.All non-processed MS-files from the metabolic analysis were exported from the ChromaTOF software in NetCDF format to R (version 2.10.1) in which all data pre-treatment procedures, such as base-line correction chromatogram alignment, data compression and Hierarchical Multivariate Curve Resolution (H-MCR) were performed using custom scripts as described by Jonsson et al. The metabolites were identified by comparison of retention indices and mass spectra with data in commercial, as well as in-house, retention indexes and mass spectra libraries using NIST MS Search 2.0 . The data processing of the GC-MS data using the H-MCR script resulted in initial datasets. All variables were checked manually and variables originating from internal standards and analytical or processing artifacts excluded.The dataset was normalized using the 11 added internal standards; a non-centered principal component analysis (PCA) model was built on the basis of the intensity of selected ions originating from the internal standard compounds and all metabolite intensities was divided by the first component from this model In order to identify trends in the metabolite data metabolite concentration fold changes were calculated for NOD compared to B6 at each time point. This was done by dividing the average concentration in the NOD group with the average concentration in the B6 group. In cases where the fold change was below 1 it was replaced with the negative inverse value for clarity. To obtain a clear overview of the data fold changes was plotted for all time points where the difference was found statistically significant according to two-sided Student's t-tests for samples with equal variance (p = 0.05).The combination of metabolites that provided the optimal discrimination between NOD and B6 mice was found using Orthogonal Projections to Latent Structures-Discriminant Analysis (OPLS-DA) on unit variance scaled data http://www.genome.jp/kegg). The metabolic pathways were selected based on metabolomics data and are the pathways where the largest metabolic differences between NOD and B6 were observed. The extent of the pathways was defined by the availability of metabolomics data, i.e. pathways were extended as far as possible with the available data. All enzymes present in a metabolic pathway were examined. Occurrence of the enzymes in Idd regions was analyzed using the web resource from www.T1Dbase.org. SNPs in these enzymes were collected from the Mouse Phenome Database using the mouse SNP wizard (http://phenome.jax.org/db/q?rtn=snps/wiz1) listing polymorphisms between the NOD/ShiLtJ and the control C57BL/6J strains. Any SNPs present in the 5′ upstream or 3′ downstream regions were also collected by including 2000 bps on either ends in the search criteria. Non-synonymous SNPs were analyzed for their effect on change of sequence and function using SIFT at http://sift.jcvi.org/. All the analysis was carried out based on build-37 of Entrez Genome View, which is being updated as new SNPs are identified.The pathways involved in the metabolism of selected metabolites were collected from the Kyoto Encyclopedia of Genes and Genomes or KEGGs pathway database for mice  were analyzed by GC-MS. Based on the levels of 89 identified metabolites an initial overview of the data was obtained by employing Principal Component Analysis (PCA). PCA is an unsupervised statistical technique that summarizes multivariate data in a smaller number of latent variables To obtain an overview of the individual metabolites that were significantly different between the two strains we calculated fold changes for all metabolites at all time points . Blue anAt birth the NOD mice had higher levels of four out of five TCA cycle intermediates and this was reversed at week four where four of these compounds  showed a large increase in B6 but not in NOD see  and S2. As the PCA analysis and statistical tests of metabolite differences indicated major changes in the metabolic profiles the first weeks of age (i.e. weeks 3–5) we performed a more thorough analysis for these time points, also including the 0 and 15 weeks of age time points as reference time points. To identify the metabolites discriminating the two stains the most at the five time points, multivariate models with reduced number of metabolites was tested until separation of the mouse strains started deteriorating. The model that provided the optimal separation between the two stains was determined, and the including metabolites in this model is presented in The observed metabolic differences between NOD and B6 were likely due to alterations in the enzymes participating in the metabolism. Therefore, we analyzed, by using the KEGG data base, which metabolic enzymes and pathways that could be involved in metabolism of the most discriminative metabolites presented in Idd regions Click here for additional data file.Figure S1Experimental design for metabolite identification.(DOC)Click here for additional data file.Figure S2The measured values of the compounds found most significantly changed between B6 and NOD mice at time points 0, 3, 4, 5 and 15 weeks as accounted for in .(DOC)Click here for additional data file.Table S1Fold change of metabolites.(DOC)Click here for additional data file.


Penicillium chrysogenum, the main production strain for penicillin-G, has a high content of intracellular carbohydrates, especially reduced sugars such as mannitol, arabitol, erythritol, as well as trehalose and glycogen. In previous steady state 13C wash-in experiments a delay of labeling enrichments in glycolytic intermediates was observed, which suggests turnover of storage carbohydrates. The turnover of storage pools consumes ATP which is expected to reduce the product yield for energy demanding production pathways like penicillin-G.13C labeling wash-in experiment of 1 hour was performed to systematically quantify the intracellular flux distribution including eight substrate cycles. The experiments were performed using a mixed carbon source of 85% CmolGlc/CmolGlc+EtOH labeled glucose (mixture of 90% [1-13C1] and 10% [U-13C6]) and 15% ethanol [U-13C2]. It was found, that (1) also several extracellular pools are enriched with 13C labeling rapidly , (2) the intra- to extracellular metabolite concentration ratios were comparable for a large set of metabolites while for some carbohydrates  the measured ratios were much higher.In this study, a The fast enrichment of several extracellular carbohydrates and a concentration ratio higher than the ratio expected from cell lysis (2%) indicate active (e.g. ATP consuming) transport cycles over the cellular membrane. The flux estimation indicates, that substrate cycles account for about 52% of the gap in the ATP balance based on metabolic flux analysis. Substrate cycles are metabolic cycles that result in ATP-consumption without net substrate-to-product conversion. These cycles are found in a wide range of organisms, including prokaryotes , plants et al. glucose; LEU: Leucine; LNEtOH: Ethanol ; LNGlc: Glucose ; LUEtOH: Uniformly labeled [U-13C2] ethanol; LUGlc: Uniformly labeled [U-13C6] glucose; LYS: Lysine; MAL: Malate; Manol MTL: Mannitol; MET: Methionine; MYTHF: Methyltetrahydrofolate; mRNA: Pool containing messenger and other RNAs in the cell (assumed composition: CH1.23N0.416O0.715P0.104); OAA: Oxaloacetate; PEP: Phosphoenolpyruvate; PG2 2PG: 2-Phosphoglycerate; PG3 3PG: 3-Phosphoglycerate; PG6: 6-phosphogluconate; PhetaA: Phosphatidylethanolamine (and precursors); PRO: Proline; PSacch: Polysaccharide (like Glycogen); PYR: Pyruvate; R5P: Ribulose-5-Phosphate; Rbtol: Ribitol; Rib5P: Ribose 5-Phosphate; SED7P: Sedoheptulose 7-Phosphate; SER: Serine; SUCC: Succinate; THR: Threonine; TRE: Trehalose; TRE6P: Trehalose-6-Phosphate; VAL: Valine; Xylu5P: Xylulose 5-Phosphate.AAD: α-Aminoadipic acid; Ac: Acetate; AcCoA: Acetyl-CoA; AKG: α-Ketoglutarate; AKI: α-Keto-isovalerate; ALA: Alanine; ARA: Arabitol; ARG: Arginine; ASN: Asparagine; ASP: Aspartate; bIM: β-isopropylmalate; BPG: 1,3-bisphosphoglycerate; CarbP: Carbamoyl phosphate; CITR: Citrate; CO2: Carbon dioxide; CTL: Citrulline; CYS: Cysteine; DHAP: Dihydroxyacetonephosphate; E4P: Erythrose 4-Phosphate; Erytol: Erytritol; ESEA: Ergosterolester (and precursors); EtOH: Ethanol; F6P: Fructose-6-Phosphate; FBP: Fructose-1,6,-bis-Phosphate; FTHF: 5-Formyltetrahydrofolate; FUM: Fumarate; G3P: Glycerol-3-Phosphate; G6P: Glucose-6-Phosphate; GAP: Glyceraldehyde 3-Phosphate; GLC: Glucose; GLN: Glutamine; GLU: Glutamate; GLY: Glycine; GLYOX: Glyoxylate; HOMCYS: Homocysteine; HOMSER: Homoserine; ICITR: Isocitrate; ILE: Isoleucine; L1Glc: . Table S3: Metabolic flux analysis results [mmol/Cmol/h]. Table S5: 13C flux analysis results*. Tabel S7: Measured, assumed and estimated concentrations .Click here for fileTable S6. Measured mass isotopomer ratios.Click here for fileTable S4. Metabolic reaction network with atom transitions.Click here for fileTable S2. Metabolic network used for the metabolic flux analysis (unlabeled).Click here for file


Several computational methods exist to suggest rational genetic interventions that improve the productivity of industrial strains. Nonetheless, these methods are less effective to predict possible genetic responses of the strain after the intervention. This problem requires a better understanding of potential alternative metabolic and regulatory pathways able to counteract the targeted intervention.Bacillus subtilis and isolated suppressor mutant strains able to grow on glutamate as single carbon source. Our SAT approach proposed candidate alternative pathways which were decisive to pinpoint the exact mutation of the suppressor strain.Here we present SPABBATS, an algorithm based on Boolean satisfiability (SAT) that computes alternative metabolic pathways between input and output species in a reconstructed network. The pathways can be constructed iteratively in order of increasing complexity. SPABBATS allows the accumulation of intermediates in the pathways, which permits discovering pathways missed by most traditional pathway analysis methods. In addition, we provide a proof of concept experiment for the validity of the algorithm. We deleted the genes for the glutamate dehydrogenases of the Gram-positive bacterium SPABBATS is the first application of SAT techniques to metabolic problems. It is particularly useful for the characterization of metabolic suppressor mutants and can be used in a synthetic biology setting to design new pathways with specific input-output requirements. A holistic understanding of cellular metabolism is central to systems biology and metabolic engineering: In order to amplify the flux through production pathways in industrial strains we have to understand how the metabolic network responds to our interventions.Several methods can suggest rational interventions that may lead to favourable industrial phenotypes , our SAT method constructs the shortest pathway between the basal and target sets (SPABBATS) of metabolites that is stoichiometrically balanced, while allowing the concentration of the intermediate metabolites to increase, if needed. The constraints are more relaxed than the ones for e.g. flux balance analysis, thus retaining the metabolically significant pathways. Using the algorithm iteratively, we obtain a prioritized list of pathways, whose elements can be tested individually by common molecular biology techniques.A solution based on mixed-integer linear programming (MILP) has been suggested by de Figueiredo et al. , but it et al. ) for theB. subtilis that had been decryptified upon inactivation of the normal glutamate catabolic genes. By using our SAT approach, we proposed four different new pathways that could be present in the mutant to utilize glutamate as single carbon source. These predictions were experimentally tested and revealed that one of these pathways was indeed active in the mutant strain and that this novel "suppressor" pathway is required and sufficient for glutamate utilization. This proves that the results of our approach correspond to valid metabolic alternatives for living cells.To demonstrate the power of this concept, we applied the SPABBATS algorithm to a complex physiological problem, which is a result of an evolutionary experiment. We have elucidated a novel pathway of glutamate degradation present in the metabolic network of B. subtilis is unknown, it is known to account for about 40% of the internal metabolite pool of an Escherichia coli cell . B. subtilis strains used in this work are derived from the laboratory wild type strain 168. They are listed in Table E. coli DH5α [B. subtilis was grown in C minimal medium containing ammonium as basic source of nitrogen [E. coli was grown in LB medium and transformants were selected on plates containing ampicillin (100 μg/ml). LB, SP and CSE plates were prepared by the addition of 17 g Bacto agar/l (Difco) to LB, SP or CSE medium, respectively.All oli DH5α  was usednitrogen . GlutamaE. coli and plasmid DNA extraction were performed using standard procedures [B. subtilis was isolated as described [Transformation of ocedures . Restricocedures . All plaescribed .E. coli transformants were selected on LB plates containing ampicillin (100 μg/ml). B. subtilis was transformed with plasmid DNA or PCR products according to the two-step protocol described previously [eviously . TransfoansR gene in B. subtilis, we constructed plasmid pGP873. For this purpose the ansR gene was amplified with the primers KG18 and KG19 using chromosomal DNA of B. subtilis as a template. The PCR product was digested with BamHI and SalI and cloned into the overexpression vector pBQ200 [To express a plasmid-borne r pBQ200 .ansAB and ansR genes was achieved by transformation with PCR products constructed using oligonucleotides to amplify DNA fragments flanking the target genes and an intervening erythromycin and tetracyclin resistance cassettes from plasmids pDG647 and pDG1514, respectively, [ansAB and ansR, respectively.Deletion of the ctively,  as descrctively, . The PCR600 of 0.5 - 0.8 and harvested. Preparation of total RNA was carried out as described previously [ansA gene, KG38/KG39 for the ald gene and KG40/KG41 for the bcd gene, respectively. Their recommended data analysis procedure was also used. The rpsE and rpsJ genes encoding constitutively expressed ribosomal proteins were used as internal controls and were amplified with the primers rpsE-RT-fwd/rpsE-RT-rev and rpsJ-RT-fwd/rpsJ-RT-rev, respectively. The expression ratios were calculated as fold changes as described [For RNA isolation, the cells were grown to an ODeviously . cDNAs weviously . Real tiLAF, KG, and JS planned the project. LAF and RP conceived and implemented the SPABBATS algorithm. KG and ST provided the experimental validation of the method. LAF, KG, and JS wrote the manuscript and created the Table and Figures. All authors read and approved the final manuscript.Supplementary Table S1. This Table lists the sequences of the oligonucleotide primers used in the experiments.Click here for file


Rhizobium etli, a bacterium that fixes nitrogen in symbiosis with Phaseolus vulgaris. To experimentally characterize the metabolic phenotype of this microorganism, we obtained the metabolic profile of 220 metabolites at two physiological stages: under free-living conditions, and during nitrogen fixation with P. vulgaris. By integrating these data into a constraint-based model, we built a refined computational platform with the capability to survey the metabolic activity underlying nitrogen fixation in R. etli. Topological analysis of the metabolic reconstruction led us to identify modular structures with functional activities. Consistent with modular activity in metabolism, we found that most of the metabolites experimentally detected in each module simultaneously increased their relative abundances during nitrogen fixation. In this work, we explore the relationships among topology, biological function, and optimal activity in the metabolism of R. etli through an integrative analysis based on modeling and metabolome data. Our findings suggest that the metabolic activity during nitrogen fixation is supported by interacting structural modules that correlate with three functional classifications: nucleic acids, peptides, and lipids. More fundamentally, we supply evidence that such modular organization during functional nitrogen fixation is a robust property under different environmental conditions.Modular organization in biological networks has been suggested as a natural mechanism by which a cell coordinates its metabolic strategies for evolving and responding to environmental perturbations. To understand how this occurs, there is a need for developing computational schemes that contribute to integration of genomic-scale information and assist investigators in formulating biological hypotheses in a quantitative and systematic fashion. In this work, we combined metabolome data and constraint-based modeling to elucidate the relationships among structural modules, functional organization, and the optimal metabolic phenotype of  Rhizobium etli during symbiotic nitrogen fixation with Phaseolus vulgaris. As a result, we supply experimental and computational evidence supporting the concept that the optimal metabolic activity during this biological process is guided by modular structures in the metabolic network of R. etli. Even more fundamentally, we suggest that these biochemical modules interact among each other to ensure an optimal phenotype during nitrogen fixation. Finally, through the in silico analysis on the genome scale metabolic reconstruction for R.etli, we give some examples that suggest that these modular structures supporting nitrogen fixation are robust to external physiological conditions.Biological networks are an inherent concept in systems biology that is useful in elucidating how biological entities—as metabolites or proteins—work together in supporting specific phenotypes in microorganisms. Notably, topological analyses carried out over these networks have shown that modular organization is a ubiquitous property at different levels of biological organization, in such a way that modular organization may serve as an organizing principle governing the metabolic activity in microorganisms. With the aim of elucidating the relationship among functional modules, network topology, and optimal metabolic activity, here we present an integrative study that combines computational modeling and metabolome data for evaluation of the metabolic activity of the soil bacterium  With the advent of bioinformatics and high-throughput technologies, plentiful sources of information stored in databases are now available to help unveil how a variety of biological entities interact among each other and to elucidate how these interacting networks support phenotypic behaviors in microorganisms. Notably, a variety of studies accomplished with these networks have contributed to elucidation of some fundamental organizing principles by which the cell presumably regulates and coordinates its vital biological functions. Among these organizing properties, structural modularity is a systemic property that has been observed in a variety of biological networks, which range from genetic transcriptional regulation to metabolic activity On the other hand, the idea that optimization principles guide metabolic activity in microorganisms has been an interesting hypothesis that, in combination with genome-scale metabolic reconstructions, has resulted in a successful framework for a systematic, quantitative, and predictive scheme in systems biology in silico study on a metabolic reconstruction for Escherichia coli supported the idea that feedback inhibition in metabolic units, called modules, constitutes a mechanism capable of inducing an optimal growth rate In this context, an immediate and fundamental question emerges: how do these structural modules organize and coordinate among themselves to support an optimal metabolic phenotype in microorganisms?. Even though this enterprise is far from being solved, some remarkable advances have been reported in the field. For instance, a recent experimental and Rhizobium etli CFN42 during symbiotic nitrogen fixation in symbiotic association with Phaseolus vulgaris (bean plant). Here, this organism is our benchmark model, a decision that was favored based on the availability of 1) a computational description of its genome-scale metabolic reconstruction, 2) an integrative description among high-throughput technologies at nitrogen fixation stages, and 3) the valuable physiological knowledge already available that describes the metabolic activity during nitrogen fixation by this organism in symbiotic association with P. vulgarisIn this work, by using a systems biology description, we supply computational and experimental evidence that suggests that structural and functional modularities are robust properties when the cell operates under its optimal metabolic phenotype at different physiological conditions. To support our conclusions, we carried out an integrative study involving computational modeling and high-throughput sequencing technology for characterizing the metabolic activity of R.etli during nitrogen fixation, constraint-based modeling was applied on an updated version of the metabolic reconstruction for this organism (iOR450) R. etli is an integrated network of 402 reactions involving the participation of 450 genes and 377 metabolites. Unlike our previous studies, here we used metabolome technology to experimentally support our in silico interpretations of R.etli metabolism under two physiological conditions: when it fixes nitrogen in symbiosis with P. vulgaris, and under free-living conditions with succinate and ammonium as carbon and nitrogen sources, respectively  to computationally simulate this biological process. Next, with the results of our integrative analysis carried out between the constraint-based modeling and the metabolome data for R. etli, we concluded that the metabolic activity at optimal nitrogen fixation is supported by structural modules with well-defined functional activities. Furthermore, our in silico study let us show that those modular structures tend to be robust during changes in environmental conditions. Overall, our study supplies evidence that modular organization in metabolic networks is required for promoting an optimal metabolic phenotype in microorganisms.Hence, to elucidate the metabolic activity of  see the  section.R. etli metabolism, we investigated the metabolome profiles of this bacterium in two physiological situations: during nitrogen fixation with P.vulgaris and under free-living conditions  R. etli during symbiotic nitrogen fixation with P. vulgaris is clear. The role of each amino acid and which of them are essential to carry out the biological processes are some avenues to be explored in the future.A previous analysis based on transcriptome and proteome data led us to identify certain proteins required for the synthesis of different amino acids in R. etli . In our opinion, our new high-throughput data supply additional evidence that an operational TCA cycle supports bacterial nitrogen fixation.With dicarboxylic acids as the carbon source, the TCA cycle would be expected to be active. As we reported previously, an integrative analysis using high-throughput technology (on the transcriptome and proteome levels) and constraint-based modeling suggested that the TCA cycle is active during nitrogen fixation Rhizobiaceas are ineffective in symbiotic nitrogen fixation because they elicit pseudo-nodules that are devoid of an infection thread Purine and pyrimidine pathways are important during nodulation processes, given that most purine or pyrimidine auxotrophs in In a previous report, we suggested that besides gluconeogenesis, a fueling pathway based on pentoses may exist in bacteria during nitrogen fixation R.etli; however, in order to explore the relationships among network topology, functionality, and optimal metabolic phenotype, it is necessary to move toward an integrative, quantitative, and predictive description. To this end, metabolome data were used for improving and assessing the flux metabolic activity inferred from constraint-based modeling when applied on the genome-scale metabolic reconstruction of R. etli. Thus, from the set of 220 metabolites experimentally detected, we identified 119 of the 377 metabolites that participate in the metabolic reconstruction reported for R. etli OR450Undoubtedly, the above descriptions are valuable for elucidation of the metabolic landscape during bacterial nitrogen fixation in R.etli is an example of how an integrative study using computational modeling and high-throughput technology can contribute to understanding, predicting, and elucidating the metabolic activity during this biological process Constraint-based modeling is a paradigm in systems biology for exploring the metabolic phenotype in cells under specific environmental conditions and/or subject to genetic perturbations in silico analysis, we took advantage of the metabolome data to refine and improve a previous FBA carried out for this organism iOR450, we improved the FBA by suggesting a more proper OF, one capable of modeling bacterial nitrogen fixation in a more accurate and realistic fashion. Reconstruction of an OF is a crucial issue in constraint-based modeling for computationally mimicking the metabolic activity of a microorganism, in this case, bacterial nitrogen fixation. For this reason, an OF is mainly defined in terms of those metabolites whose permanent production is essential for sustaining bacterial nitrogen fixation Before proceeding with our in silico interpretations and the coherent description based on the combination with high-throughput data. In order to proceed with this improvement, our strategy was based on the argument that metabolites detected at higher concentrations at the symbiotic nitrogen fixation stage, compared with those observed under free-living conditions, may mirror their fundamental participation in sustaining a functional phenotype during the biological process. Hence, under this assumption, we identified those metabolites whose concentrations increased during nitrogen-fixing activity by applying a statistical test on the log-ratio data, as shown in p-value<0.01 ,including the one obtained with the criteria described above, is summarized in d-glycerate (3pg),2-oxoglutarate (akg), l-arginine (arg-L), l-aspartate (asp-L), citrate (cit), CMP (cmp), fumarate (fum), malate , and l-tryptophan (trp-L)). Thus, we write the OF as follows:glycogen, hist[c], lys, phb[c], val[c], ala[e], asp[e], and nh4[e], respectively. Similarly, mal, trp, arg, cit, cmp, fum, 3pg, and akg denote malate, tryptophan, arginine, citrate, CMP, fumarate, 3-phospho-d-glycerate, and 2-oxoglutarate, respectively. All these metabolites are required to support an effective symbiotic nitrogen fixation, and their spatial location in the cytoplasm is indicated by the index [c]. For the purpose of obtaining a computational profile of metabolic fluxes, we assumed that the metabolic state of the bacteroid during nitrogen fixation is one that optimizes the OF, FixZ. This problem was mathematically solved as a linear optimization algorithm subject to enzymatic and thermodynamic constraints, i.e.,i,jS represents the stoichiometric coefficient of metabolite i participating in the jth reaction. Thermodynamic and enzymatic constraints in each metabolic reaction were characterized through the parameters jα and jβ  were chosen as a unit along all the analyses. Linear optimization programming was carried out using the Tomlab optimization package from Matlab.Metabolic flux distribution supporting nitrogen fixation in R.etli, a more realistic OF for simulating bacterial nitrogen fixation was obtained by identifying those metabolites with a statistically significant change during bacteroid activity compared to levels under free-living conditions. To this end, we calculated the corresponding intensity log-ratio for each metabolite between nitrogen fixation and free-living conditions. Taking into account the three experimental replicates obtained for each physiological condition, a one-side statistical t-test was applied to determine those metabolites that significantly increased their relative quantity between the two physiological conditions , with accession numbers GPL10081 for the R.etli platform and GSE21638 for data on free-living and symbiotic forms. In addition, to enrich the set of genes required for model assessment, proteome data obtained for R.etli bacteroids were downloaded from the ProteomeCommons.org Tranche by using the following hash:BY/eCcVjwTWN1+m+2ArvJ0QVnesGx5Ekgd4wUOASACfm/ueNl7YI3iLf4xz0lnGsepV5LkpMWOQOrZtjYExlNpQkIBcAAAAAAAABjA =  = .To assess the predictive scope of the computational model, we downloaded transcriptome and proteome data so that we could integrate a set of genes whose presence and upregulation suggested an important role for sustaining nitrogen fixation in 3 plus 640 µl of milliQ water was added, and the mixture was vortexed and then centrifuged at 2,300×gat 4°C for 5 min. A 1.5-ml aliquot of the aqueous layer was filtered through a Millipore 5-kDa cutoff filter. Then, the sample was fully dried by using a centrifugal evaporator. The bacteroid metabolome extraction followed the same method, except by day 18 after inoculation with root plant, bacteroids were extracted in a self-Percoll gradient in accordance with methods previously described Bacteria were grown in minimal medium and were harvested at the exponential phase. Free-living cells were collected by centrifugation and washed once with double-distilled water, and immediately 2 ml of methanol and the internal standards were added and the mixture was treated in an ultrasonic bath for 30 s. A 1.6-ml cell suspension was transferred to centrifuge tubes,1.6 ml of CHClin silico predictions and interpretations of high-throughput data, we defined a consistency coefficient that quantified the fraction of genes predicted to be upregulated in silico and simultaneously detected or induced by proteome or transcriptome technologies (Geneη). Simultaneously, we defined a consistency coefficient that quantified the fraction of active enzymes that were predicted by constraint-based modeling and identified by high-throughput technology (Enzymeη). To proceed with this evaluation, jkeggE (jkeggG ) was denoted as the set of enzymes (genes) that conformed to the j-esime metabolic pathways in the KEGG database, with j ranging from 1 to 22. Similarly, the set of enzymes (genes) that integrated the i-esime metabolic pathway in the reconstruction and the set of enzymes that were detected by high-throughput data were denoted jRecE (jRecG )and jHTE (jHTG ), respectively. Finally, the set of enzymes obtained from constraint-based modeling were denoted jiModelE  andjiModelG . In order to evaluate and create a proper frame of comparison between in silico predictions and high-throughput data, we defined the consistency coefficient as the fraction of enzymes (genes) that were actively predicted in silico and were identified by high-throughput technology as follows:in silico with data for the proteome and transcriptome previously reported for R.etli during nitrogen fixation . Next, we calculated the association function, defined as 1/dij2, for all pairs of metabolites along the metabolic reconstruction. This parameter gives a measure of the closeness among genes, amplifying the parameter for pairs of metabolites with low path lengths and minimizing pairs of metabolites located at remote distances. With the purpose of identifying topological modules along the network, these sets of parameters were used as input to perform a hierarchical clustering Modular composition along the entire metabolic reconstruction was obtained by a clustering analysis applied on a matrix whose entries represented the inverse squares of minimal path lengths for pairs. Specifically, the clustering analysis was performed by calculating the shortest path length between every pair of genes Click here for additional data file.Dataset S2Metabolites integrating each structural module. This table contains information of the metabolites forming each one of the nine structural modules identified by the topological criteria used in the main text.(XLSX)Click here for additional data file.Dataset S3Genome-scale metabolic reconstruction for Rhizobium etli (iOR450). This file contains the entire set of biochemical reactions included in the metabolic reconstruction for R. etli. Overall, the metabolic reconstruction of R. etli is an integrated network of 402 reactions involving the participation of 450 genes and 377 metabolites.(XLSX)Click here for additional data file.


Pichia pastoris has emerged as one of the most promising yeast hosts for the production of heterologous proteins. Mixed feeds of methanol and a multicarbon source instead of methanol as sole carbon source have been shown to improve product productivities and alleviate metabolic burden derived from protein production. Nevertheless, systematic quantitative studies on the relationships between the central metabolism and recombinant protein production in P. pastoris are still rather limited, particularly when growing this yeast on mixed carbon sources, thus hampering future metabolic network engineering strategies for improved protein production.The methylotrophic yeast P. pastoris growing on a mixed feed of glucose and methanol was analyzed by Metabolic Flux Analysis (MFA) using 13C-NMR-derived constraints. For this purpose, we defined new flux ratios for methanol assimilation pathways in P. pastoris cells growing on glucose:methanol mixtures. By using this experimental approach, the metabolic burden caused by the overexpression and secretion of a Rhizopus oryzae lipase (Rol) in P. pastoris was further analyzed. This protein has been previously shown to trigger the unfolded protein response in P. pastoris. A series of 13C-tracer experiments were performed on aerobic chemostat cultivations with a control and two different Rol producing strains growing at a dilution rate of 0.09 h−1 using a glucose:methanol 80:20 (w/w) mix as carbon source.The metabolic flux distribution in the central metabolism of vs the control strain, reflected in increased glycolytic, TCA cycle and NADH regeneration fluxes, as well as higher methanol dissimilation rates.The MFA performed in this study reveals a significant redistristribution of carbon fluxes in the central carbon metabolism when comparing the two recombinant strains 13C-based MFA development to characterise the central metabolism of methylotrophic yeasts when growing on mixed methanol:multicarbon sources has been implemented, thus providing a new tool for the investigation of the relationships between central metabolism and protein production. Specifically, the study points at a limited but significant impact of the conformational stress associated to secretion of recombinant proteins on the central metabolism, occurring even at modest production levels.Overall, a further  Pichia pastoris is an attractive system for the production of recombinant proteins  glucose (isotopic enrichment 99%) and 13C-methanol (isotopic enrichment 99%) were purchased from Cortecnet . The labelled substrates were fed for a period of 1.5 residence times, after which, a volume of about 500 mL of culture broth was harvested, centrifuged at 4000 ×g for 10 min, resuspended in 20 mM Tris·HCl, pH 7.6, and centrifuged again. The recovered and washed cell pellets were freeze dried . Finally, 100 mg of the freeze dried cell pellets were suspended into 10 mL of 6 M HCl and the biomass was hydrolysed in sealed glass tubes at 110°C for 22 h. The suspensions were dried overnight in an oven at 90°C, dissolved in H2O and filtered through 0.2 μm filters (Millipore). The filtrates were vacuum-dried and dissolved in D2O for NMR experiments. The final pH of the samples was below 1 due to residual HCl.BDF lsewhere . Briefly1H-13C-HSQC nuclear magnetic resonance (NMR) spectra of the samples were acquired at 40°C on a Varian Inova spectrometer operating at a 1H-resonance frequency of 600 MHz essentially as described in [ribed in . For eacribed in . The spe13C-scalar fine structures of proteinogenic amino acid carbon signals in the 1H-13C-HSQC NMR spectra and for the calculation of relative abundances of intact carbon fragments originating from a single molecule of glucose. The nomenclature used here for the intact carbon fragments, fragmentomers, has also been described previously [f(1) represents the fraction of molecules in which the observed carbon atom and the two neighbouring carbons originate from different carbon source molecules (glucose and methanol), f(2) the fraction of molecules in which the observed carbon atom and one of the two neighbouring carbon atoms originate from the same source molecule of glucose, as methanol is a single carbon compound, and f(3) represents the fraction of molecules in which the observed carbon atom and both carbon neighbours originate from the same glucose molecule. In case that the observed carbon exhibits significantly different 13C-13C scalar coupling constants for the two neighbour carbons, two different fractions, f(2) and f(2*) are distinguished. In this case, the fraction of molecules with a conserved bond between the observed carbon atom and the neighbouring carbon with the smaller coupling is represented by f(2). Accordingly, f(2*) then denotes the fraction of molecules where the carbon bond is conserved between the observed carbon and the neighbouring carbon with the larger coupling. If the observed carbon is located at the end of a carbon chain, only the f(1) and f(2) fragmentomers can be observed. The fragmentomer information obtained from the proteinogenic amino acids can be traced back to their metabolic precursors, which are intermediates of central carbon metabolism. The carbon backbones of those eight precursors are conserved in the amino acid synthesis pathways [P. pastoris growing on glucose/methanol mixtures was described in [enolpyruvate (Pep) originating from phosphoenolpyruvate carboxykinase activity was assumed negligible on the basis that this “gluconeogenic” enzyme is not involved in methanol assimilation [P. pastoris cells growing under the experimental conditions chosen in this study. Consequently, Pep was considered to originate from three sources: the Pentose Phosphate Pathway (PPP), glycolysis and, the methanol assimilation pathway (Equation 1).The software FCAL   was usedeviously . Brieflypathways . The comribed in . Due to ribed in  was furtmilation  and its f(2) and f(2*), whereby back-tracking the amino acid synthesis pathways of Phe-Cα and Tyr-Cα to the C2 of Pep [f(2) and f(2*) fragmentomers of Phe-Cα and Tyr-Cα:Where X1 and X2 are the relative fluxes from glyceraldehyde phosphate (GAP) and dihydroxyacetone phosphate (DHAP) to Pep, respectively, both derived from the methanol assimilation pathway, X3 the relative flux from glycolysis to Pep, and X4 is the relative flux from the PPP to Pep. Glycolysis produces fully intact three carbon fragments into Pep molecules , whereas2 of Pep . Taking 2 of Pep  databaseTaking into account equations (1), (2) and (3), we have formulated the relative contributions of the different pathways to the synthesis of Pep. The relative flux from the methanol assimilation pathway to Pep (XPep_from_MetOH) is a sum of the equal contributions X1 and X2 from glyceraldehyde phosphate (GAP) and dihydroxyacetone phosphate (DHAP), respectively (Equation 4). The relative flux from PPP (X4) is named XPep_from_PPP below (Equation 5). The contribution of Glycolysis to the synthesis of Pep (X3) was solved from Equation 1.mit) originating from Pyrcyt through pyruvate carboxylase denoted by XOaamit_from_Pyrcyt, was derived from the mass balance of intact C2-C3 fragments of Oaa (Equation 4). The Oaa molecules originating from the TCA cycle are fully cleaved in C2-C3. Since the flux from Pep to Pyrcyt is known to be unidirectional under the carbon-limited cultivation conditions studied here, the Phe-Cα and Tyr-Cα fragmentomers having Pep as a precursor were used to represent the labelling status of Pyrcyt. Oaa is the precursor of Asp and Thr and the carbon backbone of Oaamit in particular is conserved also in the TCA cycle and can be observed in Glu. The Asp, Thr and Glu labelling patterns showed an equal cleavage status as their precursor Oaa. Thus, Asp-Cα and Thr-Cα fragmentomers were used here to represent Oaamit C2.The fraction of mitochondrial oxaloacetate (Oaa13C-labeling of amino acids is based on assuming both a metabolic (see above) and an isotopomeric steady state. As stated above, to establish a cost-effective protocol for a larger number of 13C labelling experiments, we fed a chemostat operating in metabolic steady state for the duration of 1.5 volume changes with the medium containing the 13C-labelled substrates before harvesting the biomass. Then, the fraction of unlabeled biomass produced prior to the start of the supply with 13C-labelled medium can be calculated following simple wash-out kinetics [As described previously ,28-30, t13C-constrained metabolic flux analysis (13C-MFA) was performed using a stoichiometric model comprising the major pathways of P. pastoris central carbon metabolism. To calculate the intracellular net fluxes, the model was constrained with extracellular flux parameters  and 3 intracellular ratios derived from the METAFoR analysis . Furthermore, it was assumed that all NADPH generated was consumed in biosynthetic reactions. Therefore, all the remaining reduction equivalents were assumed to be recycled through the respiratory chain as any other relevant possibility for recycling has already been taken into account. This allowed calculating the theoretical oxygen consumption rates. The theoretical oxygen consumption rates calculated represented 92% of the experimentally measured ones. Those results indicate that under the tested experimental conditions, the calculated variables are highly consistent with the experimental ones.p < 0.05).Data are given as mean ± SEM. Where appropriate, values were compared by a t-test, and significant differences were considered if above a 95% confidence level  allowed for the quantitative analysis of the additional energy requirements derived from cell’s adaptation to stress caused by recombinant protein secretion. Importantly, a limited but significant impact on the energy metabolism could be detected even at relatively low secretion levels when comparing the reference strain with the Rol-producing strains, suggesting that protein folding and conformational stress imposes a burden on the central metabolism. Therefore, it points at the core/energy metabolism as an important target for improvement of recombinant protein production processes in yeast, e.g. by engineering new strains with reduced maintenance requirements, more efficient mechanisms of energy generation or by designing new/improved cultivation processes. Nevertheless, metabolic differences between ROL 1-copy and 2-copy producing strains were not statistically significant, suggesting that larger differences in expression/secretion levels are needed in order to have a detectable impact on the central metabolism. Notably, methanol seems to play a key role as auxiliary substrate to compensate for the increased energy demands derived from recombinant protein secretion and favouring metabolic adaptation to the new requirements. This observation could be the underlying explanation why mixed substrate feeding strategies can boost productivities (and reduce metabolic burden) in P. pastoris.Overall, the methodology for MFA based on NMR derived The authors declare that they have no competing interests13C-labelling experiments, macroscopic data processing and metabolic flux analysis calculations. PJ and HM, together with JJ, performed the 2D-NMR and METAFoR analyses (including the formulation of new metabolic flux ratios for methanol metabolism), as well as the subsequent interpretation of results. EC constructed the ROL 2-copy strain and performed quantitative real-time PCR for gene dosage quantification. JA designed the 13C-constrained MFA approach, and participated in analysis and interpretation of MFA results, as well as in the overall conceptual and experimental design of this study. PF participated in the overall conceptual and experimental design, interpretation of results and drafted the manuscript. All authors read and approved the final manuscript.JJ performed bioreactor cultivations and Biomass macromolecular composition forP. pastoris.   Macromolecular formula for the reference and two Rol-producing P. pastoris strains growing on glucose:methanol mixture (80:20) as a carbon source in chemostat cultures at a D = 0.09 h−1, expressed as C-molecular formula. Click here for fileRelative abundances of intact carbon fragments in proteinogenic amino acids. Relative abundances of intact C2 and C3 fragments  in proteinogenic amino acids describing the conservation of carbon chain fragments in P. pastoris Rol-producing and control strains growing in glucose:methanol-limited chemostats at D = 0.09 h−1. Click here for fileMetabolic flux distributions in theP. pastoris  reference and recombinant strains during growth on glucose:methanol. Metabolic flux distributions in the P. pastoris reference strain (top), the recombinant strain with 1 copy of the ROL gene (middle) and the recombinant strain harbouring 2 copies of the ROL gene (bottom) during growth on glucose:methanol chemostat cultures at about 0.09 h−1. Activities of the malic enzyme and glyoxylate pathways were found to be negligible on the basis of the METAFoR analyses. Click here for fileStoichiometric model of the central carbon metabolism ofP. pastoris  . Reactions in the stoichiometric model of the central carbon metabolism of P. pastoris applied in the 13C-MFA determination of the metabolic fluxes under different oxygenation conditions; it also includes anabolic reactions from metabolic intermediates to biosynthesis, transport reactions across the mitochondrial membrane and uptake and excretion reactions. Note that O2, CO2, energy and redox cofactor mass balances were not included in the mass balance constraints in 13C-MFA. Click here for file


Metabolic engineering design methodology has evolved from using pathway-centric, random and empirical-based methods to using systems-wide, rational and integrated computational and experimental approaches. Persistent during these advances has been the desire to develop design strategies that address multiple simultaneous engineering goals, such as maximizing productivity, while minimizing raw material costs.Escherichia coli, Saccharomyces cerevisiae, and Shewanella oneidensis) and six industrially important byproducts . We evaluated over 435 million simulated conditions and 36 engineering metabolic traits, including product rates, costs, yields and purity.Here, we use constraint-based modeling to systematically design multiple combinations of medium compositions and gene-deletion strains for three microorganisms (The resulting metabolic phenotypes can be classified into dominant clusters (meta-phenotypes) for each organism. These meta-phenotypes illustrate global phenotypic variation and sensitivities, trade-offs associated with multiple engineering goals, and fundamental differences in organism-specific capabilities. Given the increasing number of sequenced genomes and corresponding stoichiometric models, we envisage that the proposed strategy could be extended to address a growing range of biological questions and engineering applications. Microorganisms possess metabolic capabilities that are essential to society, science, and industry. Today, most bulk and specialty chemicals are derived from crude oil. However, declining oil reserves, rising oil prices, and growing environmental concerns have prompted renewed interest in producing chemicals using microorganisms instead of fossil fuels. To tranEscherichia coli does not naturally produce succinic acid as a major fermentative product; consequently, early metabolic engineering efforts targeted metabolic pathways that were thought to be involved in succinic acid synthesis. However, these perceived improvements were often ineffective or produced undesirable side-effects (e.g. large amounts of impurities were produced or cell growth was significantly inhibited), where v is the vector of computed engineering metrics shown in Table S2. The associated multi-goal optimization problem is min f (v), bounded by the discrete set of available solutions. Each solution corresponds to a metabolic engineering design candidate . If the individual goals in f (v) do not conflict, then it is possible to find a unique optimal solution. However, if the individual goals in f (v) do conflict, then a unique solution will not exist. Instead, there will be a set of Pareto solutions. If a change (or tradeoff) in one of the solutions improves one goal without making another goal any worse, then that change is called a Pareto improvement and the initial solution is called dominated. If the subsequent solution is such that an improvement in one goal requires degradation in another goal, then that solution is called nondominated and is Pareto optimal. The set of Pareto optimal solutions is often called the Pareto frontier.Multi-goal optimization  is the process of simultaneously optimizing two or more conflicting goals (or objectives) subject to a set of constraints-65. In ogamultiobj, from the Global Optimization Toolbox. We feed into the function our set of engineering goals, f(v), and obtain as a result the set of Pareto optimal designs. The parameter values that we used are 500 maximum number of generations, population size of 100 chromosomes, 0.85 probability of crossover, 0.05 probability of mutation, distribution index of 10 for simulated crossover, distribution index of 20 for simulated mutation and a random seed of 0.6. Prior studies showed that these parameter values are generally satisfactory[To determine the Pareto optimal designs and frontiers in our study, we use a Pareto-compliant method called Nondominated Sorting Genetic Algorithm II (NSGA-II). This mesfactory,68 and wi and j represent two viable-growth engineering phenotype clusters. Edge ti,j represents the cumulative phenotype-cluster transition frequency between Nodes i and j due to either environmental perturbations or genetic perturbations. Node 0 represents the nonviable-growth phenotype. Thus, edges ti,0 and tj,0 represent the cumulative phenotype-cluster transition frequencies to the nonviable-growth phenotype due to perturbations. Edges are bidirectional, so ti,j is equivalent to tj,i. Edge thickness is proportional to the cumulative transition frequency for environmental or genetic perturbations. By performing this analysis systematically for all meta-phenotypes, we obtained a network of meta-phenotype transitions for each organism E. coli, S. cerevisiae, and S. oneidensis. Because the non-viable meta-phenotype is the sum of all possible non-viable phenotypes, it is comparatively extremely large and would effectively dwarf all viable meta-phenotype nodes. Thus, the non-viable meta-phenotype is not shown or included in the figures and results presented.Transition frequencies are computed by varying a single individual perturbation type , while maintaining fixed the remaining perturbation types. Environmental perturbations are imposed by changing the absence or presence of a nutrient in the medium (as described in the Methods “Constraint-based modeling” subsection), whereas genetic perturbations are imposed by deleting single or double genes. A resultant meta-phenotype transition network can be generated such that Nodes http://nets.bu.edu, was developed to make available the optimal metabolic engineering design results. The website provides an interface that may be used to submit customized search queries, choose engineering designs, and interact with resultant metabolic network visualizations.A public website (Additional fileFrom the website’s main page (Additional filehttp://nets.bu.edu/about. Alternatively, the tutorial can be obtained by clicking “Help” on the website’s main page. The tutorial explains the process of defining engineering optimization criteria, selecting resultant designs and visualizing metabolic pathway activity.An online tutorial for the website (Additional fileE. coli: Escherichia coli; EDD: Douderoff dehydratase; FBA: Flux balance analysis; GC-RMA: GC Robust Multi-array Average; gDW: Gram dry weight; GIMME: Gene Inactivity Moderated by Metabolism and Expression; GND: Gluconate-P dehydrogenase; LP: Linear programming; MGME: Multi-Goal Metabolic Engineering; sc/S. cerevisiae: Saccharomyces cerevisiae; so/S. oneidensis: Shewanella oneidensis; TCA: Tricarboxylic acid cycle.ec/The authors declare that they have no conflict of interest.DB conceived and designed the study. DB and AD generated the data and performed the statistical analyses. DB and DS interpreted the results and wrote the manuscript. DS supervised the project. All authors edited and approved the final version of the manuscript.Supplementary Information. Tables S1, S2, S3, S5 and Figures S1-S18.Click here for fileSupplementary Information. Table S4 (Tabulated version of FigureClick here for file


Arabidopsis thaliana was intensely studied to characterize adaptive traits to a changing environment. The availability of genetically distinct natural populations has made it an attractive system to study plant-environment interactions. The impact on metabolism caused by changing environmental conditions can be estimated by mathematical approaches and deepens the understanding of complex biological systems. In combination with experimental high-throughput technologies this provides a promising platform to develop in silico models which are not only able to reproduce but also to predict metabolic phenotypes and to allow for the interpretation of plant physiological mechanisms leading to successful adaptation to a changing environment. Here, we provide an overview of mathematical approaches to analyze plant metabolism, with experimental procedures being used to validate their output, and we discuss them in the context of establishing a comprehensive understanding of plant-environment interactions.Due to their sessile lifestyle, plants are exposed to a large set of environmental cues. In order to cope with changes in environmental conditions a multitude of complex strategies to regulate metabolism has evolved. The complexity is mainly attributed to interlaced regulatory circuits between genes, proteins and metabolites and a high degree of cellular compartmentalization. The genetic model plant  Arabidopsis thaliana, is the acclimation to low temperature leading to an improved cold tolerance. For many herbaceous plant species it was shown that they can grow at low temperature and even survive freezing [The performance and distribution of plants is significantly affected by several environmental factors, like for example temperature, drought and soil salinity. Due to their sessile lifestyle, plants have to cope with spontaneous or seasonal changes in these environmental factors in order to survive. To a certain degree, numerous plant species are able to respond to such changes by re-adjustment of their metabolism—a process that is in general termed as acclimation. It comprises a multitude of biochemical and physiological changes, ultimately leading to an increase in the capacity of the plants to cope with environmental stress. One prominent example, which was amongst others intensely studied in the model plant freezing ,2,3. It freezing ,6,7,8,9.freezing , this acfreezing . Additiofreezing ,13.Arabidopsis thaliana. This species is natural to Europe and central Asia, and the climate on a global scale was shown to be sufficient for shaping its range boundaries [The analysis of complex metabolic processes involved in acclimation of plant metabolism to environmental stress significantly benefits from the availability of genetically distinct natural populations of the model plant undaries . Arabidoundaries ,16. Due Besides such complex plant-environment interactions, latest developments in bioanalytical research comprising shotgun and next-generation genome sequencing as well as molecular analysis using OMICS technologies have driven the need for computer-assisted analysis and modeling of biological data. Systems biology has evolved in a research field focusing on the system wide understanding of biological networks, like for example the cellular metabolism in a photosynthetically active plant cell. In a systems biology approach, network elements, such as genes, proteins or metabolites, are considered as interacting components rather than isolated entities in order to deepen the comprehensive understanding of the organization of a complex biological system. A promising way to analyze such complex biological and biochemical networks is formal representation by mathematical models enabling their computer based handling and making biological data accessible to theoretical methods originating from applied mathematics and systems theory. Numerous mathematical approaches to model plant metabolic networks have been suggested and discussed, both relying on and emphasizing the importance of the iterative processes of model development, simulation and validation by experimental data ,20,21,22i.e., metabolite concentration, protein abundance or the amount of transcripts. In the context of metabolic systems, the sum of synthesizing and degrading rates of enzyme reactions defines the time-dependent change in metabolite concentrations. The representation of biological systems by sets of ODEs has successfully been applied to various processes in plant biology and also in the comprehensive analysis of plant-environment interactions, as was already outlined in [i.e., the result of model simulation [M) or inhibitory constants (Ki) are lacking. This enforces the application of parameter estimation to calculate parameter values which are either completely unknown or can be estimated within numerical bounds based on published data on a different condition or organism. Indeed, such assumptions cause uncertainties, which have to be discussed carefully when interpreting the model output. However, although there might be several uncertainties with respect to regulatory instances involved in every single reaction of metabolism, numerous studies have proven kinetic modeling to be a promising approach to comprehensively analyze complex processes in plant biology. An overview of applications is given by Schallau and Junker [Saccharum officinarum) [Arabidopsis thaliana [A main focus of mathematical modeling in biochemistry and plant science has been on the construction of kinetic models where metabolic states are simulated based on the knowledge about network topology, stoichiometry, rate equations and kinetic parameters. Typically, a system of ordinary differential equations (ODEs) is used to describe the time-dependent changes in state variables, lined in . While klined in . For examulation . Additiod Junker  exemplard Junker , leaf cad Junker , sucrosecinarum)  or the athaliana .N. Considering a metabolic reaction network, each column of N represents a reaction while rows represent metabolites. Hence, the elements of N describe the stoichiometric coefficients of metabolites in the reactions. Positive entries indicate that the metabolite is produced by the reaction, while negative values indicate consumption. Entries of zero indicate that the metabolite is not involved in this reaction. The definition of a vector v containing the rates of metabolite interconversions allows for the description of the steady state of the metabolic reaction network by a set of differential equations:In contrast to kinetic modeling, the approach of structural modeling is based on the idea of constructing models without kinetic information. This modeling approach refers only to the stoichiometry of the reactions within the system which is summarized in the stoichiometric matrix M represents a matrix containing metabolite concentrations and t is time. Solutions of this equation can be calculated applying linear algebraic rules. The advantage of this approach becomes obvious when considering the large number of reactions in a metabolic system, which can be predicted from an annotated genome sequence. The workflow from metabolic reconstruction to modeling of a metabolic network based on an annotated genome sequence was previously described in detail [Chlamydomonas reinhardtii [where n detail . Sequencnhardtii . Yet, innhardtii . Arabidopsis thaliana, both kinetic and stoichiometric modeling represent promising approaches to comprehensively study regulatory instances in plant metabolism, its re-adjustment after environmental perturbations or even the impact of changes in transcriptional control on the metabolome. On the other hand, both applications of mathematical modeling are significantly limited in their ability to reconstruct and predict the behavior of plant metabolism in vivo. Kinetic modeling typically focuses on a relatively small part of metabolism and aims at simplification to constrain the complexity and amount of kinetic information, which is needed to simulate network dynamics. In contrast, approaches of stoichiometric modeling focus on the comprehensive compilation of network interaction, ultimately aiming at the complete representation of metabolism, yet neglecting kinetic information and the estimation of non-linear network dynamics. Motivated by the limitations of each of these methods, the following sections are intended to summarize current progress in mathematical modeling of plant metabolism and to figure out its potential to analyze and predict complex plant-environment interactions. Focusing now again on the complexity of plant-environment interactions and the variability of stress responses in natural accessions of i.e., enzymatic reaction. Based on this graphical representation, the mathematical model is then derived by translating nodes and lines in metabolite concentrations and enzymatic rate laws, for example the Michaelis-Menten equation. These rate equations are characterized by kinetic parameters like enzymatic substrate affinity, i.e., the Michaelis-Menten constant KM, and the maximum enzyme activity vmax. This process is crucial for the successful modeling approach as all further steps of mathematical analysis rely on these assumptions: if the interaction between two network components is described by equations or parameters which do not agree with confirmed experimental results, validation of simulation results by experimental data is not reliable anymore and the model becomes unfeasible. Although a vast number of metabolic interactions have intensively been characterized and many underlying laws of interaction are well known, like for example the Michaelis-Menten kinetics, deriving the most realistic model structure of a metabolic network becomes difficult when assumptions about simplification have to be made. This is frequently the case for kinetic models, based on systems of ODEs, which are intended to provide an insight into the dynamics of metabolism. These dynamics are predominantly nonlinear and model systems are often characterized by a high-dimensional parameter space. Kinetic parameters, characterizing substrate affinity (KM) or inhibition (Ki), are often not directly accessible to experimental measurements. In addition to the everlasting question how results of in vitro measurements differ from in vivo data, experimental conditions, like the temperature or pH, significantly constrain their validity. Hence, besides the determination of a model structure, the process of mathematical identification of unknown kinetic parameters represents another crucial step in building a realistic ODE-based model to simulate dynamics of plant metabolism. To reduce the complexity and also the number of unknown kinetic parameters, individual enzymatic steps might be summarized in blocks of interconversions directly linking the metabolite concentrations that have been quantified. These blocks of interconversion are confined by the rate-limiting steps, i.e., the enzymatic reaction representing a regulatory bottleneck for the synthesis/degradation of a metabolite. Measurement on the kinetic parameters of the corresponding enzymes then allows for the estimation of the kinetic characteristics of this metabolic pathway. This approach was recently applied to the analysis of diurnal dynamics of the central carbohydrate metabolism in leaves of Arabidopsis thaliana [in planta metabolic network, the authors were successful in reproducing the experimentally observed data on metabolite concentrations. Furthermore, simulation results allowed for the evaluation of flux rates in the central carbohydrate metabolism revealing a significant impact of invertase activity on sink-source interaction and buffering metabolite concentrations against changes in environmental conditions [Arabidopsis thaliana, now also comprising the central steps of raffinose interconversion. Based on results of model simulation, a critical temperature for sucrose synthesis in a cold sensitive accession could be predicted at which an imbalance in photosynthetic carbon fixation is caused, ultimately resulting in oxidative stress [Arabidopsis thaliana to cope with changes in environmental conditions at low temperature. The mathematical analysis of plant metabolism first of all relies on the representation by a model, which is constructed based on information on biochemical pathways and the interaction of pathway components gained from numerous previous experimental studies. Typically, the first step of model construction consists of a graphical representation of the pathway or network of interest. In case of a kinetic model of metabolism, this may result in a map, which connects nodes by lines. Every node now represents a metabolite and every line describes a metabolite interconversion, thaliana . For modthaliana . The modnditions . The usenditions . In thisnditions  to analye stress . It was As exemplified by these approaches of mathematical modeling, realistic output of model simulations can be expected despite a significant simplification of the model structure. This was also proven by many other kinetic modeling approaches . Such sexp contains experimentally determined state variables (for example metabolite concentrations), ypred is the model prediction of state variables depending on estimated parameters p and time t, and W(t) is the weighting matrix containing information about the level of importance of single state variables and determining their influence on the cost function. This optimization problem of minimization of Z is subject to the differential/algebraic equality constraints describing the systems dynamics and additional requirements for system performance. Additionally, the estimation of model parameter p is subject to lower (plow) and upper (pup) bounds:where Z represents the cost function to be minimized, yi.e., the potential existence of multiple local solutions [i.e., the global optimum. Gradient-based local optimization methods fail to reliably determine the global optimum in multimodal problems because of nonconvexity arising from the previously mentioned nonlinearities. A graphical representation of this problem is shown in [i.e., surfaces of the cost function with multiple peaks and valleys, which do not allow for the determination of one unique optimal solution by local optimization methods. Solving such multimodal problems is the goal of global optimization [Due to nonlinearities in objective function and constraints, solving these optimization problems frequently means having to cope with multimodality, olutions ,38. Thismization , which wmization . One examization . This almization . A partimization . For evemization , the incmization .Due to its capability to develop methods for comprehensive analysis of complex data sets and provide strategies of how to solve nonlinear problems, optimization theory represents an essential component for mathematical modeling of plant metabolism and other biological systems. Beyond that, the prediction of metabolism from first principles only becomes possible by application of optimization approaches .N of the network, which provides the basis for all modeling approaches [i.e., a snapshot, of the system, which is pre-defined by the experimental design. Recently, in several studies genome-scale metabolic modeling in Arabidopsis thaliana was applied to address questions like ATP demand for growth and maintenance [Reconstruction of metabolic networks is based on information about whole genome sequences finally resulting in the stoichiometric matrix proaches . As descproaches ,44,45. Iproaches . Based oproaches . Additioproaches . Beyond ntenance , the metntenance  or to prntenance . With respect to such comprehensive metabolic network simulations, quantitative measurement of metabolism is necessary to validate the output of such simulations, which can be accomplished applying bioanalytical methods in metabolomics science . Mass spThe analysis of metabolomics results on numerous biological replicates under different environmental conditions or with genotypic variation represents a multidimensional task and results in a complex data matrix. The covariance matrix C results from multivariate statistics representing a central result of the experiments ,57,58,59ii characterize the magnitude of fluctuations of each metabolite, whereas off-diagonal entries Dij (i≠j) represent the fluctuation of metabolites caused by the interaction between enzymes i and j. The interconnection between metabolic networks and the Jacobian Matrix as well as the fluctuation matrix is described in detail elsewhere [In this equation, J represents the Jacobian matrix and D is the fluctuation/diffusion matrix. The diagonal entries Dlsewhere ,60,61. Iij, defining the relative change of two Jacobians Ja and Jb which are associated with different treatments, i.e., environmental conditions:Here, N is the stoichiometric matrix, r represents the rates for each reaction and M is the metabolite concentration. Based on equations (4) and (5), an approach of inverse calculation of a Jacobian from metabolomics covariance data was recently derived . AdditioCalculation of the differential Jacobian reveals perturbation sites between two different metabolic states hinting at a significant regulatory event, e.g., the change of enzymatic reaction rates due to environmental perturbations. In principle, using this approach it is possible to conveniently connect a large metabolomics experiment with many samples and thousands of variables directly with the predicted genome-scale metabolic network to calculate biochemical regulation in the investigated biological system (for more detail see ). The apWith regard to currently emerging discussions about world population feeding, global climate change and limited energy resources with fossil fuels, plant biology and biotechnology are central topics of life sciences in the coming decades . Latest Kinetic modeling approaches are limited by lack of kinetic information and stoichiometric modeling approaches are limited by their reference to a steady state. Yet, if a stoichiometric modeling approach delivers information about potential perturbation sites in metabolism, this will enable systematic in-depth analysis, for example by kinetic modeling, promoting a comprehensive understanding of how plant metabolism is composed functionally.


The EFMs  can be calculated given a metabolic model. cMCSs are sets of reaction deletions in such a network that will allow desired pathways to survive and disable undesired ones . Grouping the modes into desired and undesired categories had to be done manually until now.Metabolic engineering aims to design microorganisms that will generate a product of interest at high yield. Thus, a variety of Although the optimal solution for a given set of pathways will always be found with the currently available tools, manual selection may lead to a sub-optimal solution with respect to a metabolic engineering target. A small change in the selection of modes can reduce the number of necessary deletions while only slightly reducing production. Based on our recently introduced formulation of cut set calculations using binary linear programming, we suggest an algorithm that does not require manual selection of the desired pathways.E. coli using different design objectives. Furthermore we validated our method by reproducing previously obtained results without requiring manual grouping of modes.We demonstrated the principle of our algorithm with the help of a small toy network and applied it to a model of  Microorganisms are increasingly used as cell factories to produce a multitude of chemicals and promise great potential for many future applications Methods based on constraint-based reconstruction and analysis (COBRA) have been used successfully to predict complex intervention strategies in metabolic engineering. COBRA methods analyze the steady state behavior of an organism using its stoichiometric matrix as the main input. The stoichiometric matrix is a comprehensive, organism-specific collection of the stoichiometry of the biochemical reactions occurring in the organism of interest. Frameworks such as OptKnock Alternatively, elementary flux mode (EFM) analysis One important property of EFMs is that every feasible flux distribution in the network can be described as a non-negative, linear combination of EFMs. This suggests that the entire metabolic space of the system can be represented by the full set of EFMs. Consequently, an optimal production host can be designed if EFMs with unfavorable properties, e.g., low productivity, are removed, while favorable modes with high product yield are maintained. An undesirable EFM can be removed easily if one of its participating reactions is deleted. Notice that this strategy does not rely on any biologically motivated objective in contrast to OptKnock The concept of removing unwanted modes under the condition that certain modes have to “survive” the intervention is called constrained minimal cut sets (cMCSs) In this study, we address the tedious necessity of manually selecting modes that should be kept or disabled. cMCSs are dependent on allocation of the modes, and it is possible that a “better” design  could be found if only the allocation of the modes is just slightly changed . Here we present the formulation of a binary integer program (BIP) for calculating cMCSs such that manual mode selection is no longer necessary.Consider the system depicted in elds see . Based o R2, see . AlternaWe have utilized a BIP to calculate cMCSs To avoid this manual partitioning we assign each EFM We can find alternate solutions to the optimization problem equation (1) if we exclude any previous solution The BIP in equation (1) calculates cut sets that maximize Finally, the conventional BIP formulation for cMCS To illustrate our algorithm we applied it to the toy network depicted in http://www.ibm.com/software/integration/optimization/cplex-optimizer, for which free academic licenses are available. We used the specialized CPLEX’ feature populate To solve the BIP, we use the IBM ILOG CPLEX Optimizer, E. coli using the metabolic model by Trinh et al.In the previous section we described our approach to determine cMCSs without preselecting modes. Now we apply our method to optimize anaerobic ethanol production from glucose in E. coli strain. Here, efficiency, E. coli as function of the required reaction deletions using our approach , OS: Ubuntu 12.04) it took about 30 minutes to calculate all 37828 MCSs listed in E. coli model used in our calculations. All 5,010 modes are represented by circles according to ethanol yield  and specific growth rate . Modes with identical values for both were grouped. The size of the circles corresponds to the number of modes included in these groups. The solution spaces for our method are depicted as colored polygons on the right hand side of the figure, showing the increase in minimal efficiency with each step  (data not shown). In that case we used the mode’s ethanol yield as weights, whereas a selection of “essential” modes was not necessary. The definition of the design objective  suffices to recover Trinh cMCSs have recently been introduced to predict minimal intervention strategies for the rational design of cell factories The main advantage of our reformulation of the BIP in comparison to previous work et al.We select modes, calculate all MCSs, reclassify the modes naively, repeat the analysis and check if the cardinality of these new MCS is smaller than the previously calculated ones. In the worst case we would have to check every possible classification of modes, which is computationally exhaustive if we use the conventional cMCS formulation. However, our reformulation achieves the same thing but is computationally more efficient. Although we only used model-intrinsic values as weights in this study  modes, , the number of desired modes, , the number undesired modes, and n, the number of essential modes. The general procedure is the same as explained in the text.(TEX)Click here for additional data file.