In this way, we provide evidence that the analysis of metabolic systems on the few-node subgraph scale is meaningful for explaining dynamic patterns. This topological characterization of medium-dependent essentiality provides a better understanding of the interplay between reaction deletions and environmental conditions.Metabolism has frequently been analyzed from a network perspective. A major question is how network properties correlate with biological features like growth rates, flux patterns and enzyme essentiality. Using methods from graph theory as well as established topological categories of metabolic systems, we analyze the essentiality of metabolic reactions depending on the growth medium and identify the topological footprint of these reactions. We find that the typical topological context of a medium-dependent essential reaction is systematically different from that of a globally essential reaction. In particular, we observe systematic differences in the distribution of medium-dependent essential reactions across three-node subgraphs (the  Many et al.  used binet al. . The accE. coli and Saccharomyces cerevisiae has turned FBA into a widely accepted method for in silico studies of metabolic states [Furthermore, robustness of metabolism against gene or reaction deletions has been explored using flux-balance analysis (FBA) . Particuc states ,13. Morec states ,15.Along similar lines of research, metabolic reactions have been classified in several ways based on topological information ,16,17,18et al. [et al. [UPUC metabolites have been introduced by Samal et al. . They weet al. , they coet al. . We woul [et al. , but ratSynthetic accessibility (SA), defined by Wunderlich and Mirny , is inflX1, X2 and X3) with the environment and a two-component biomass reaction (BM). Circles represent metabolites, while boxes stand for reactions in this bipartite graph view of a metabolic system. In this Figure, R1 (highlighted in blue) is an example of an SA reaction, as it represents one of the shortest paths to BM, while R5 (highlighted in green) is consuming and producing only metabolites, which are uniquely produced (UP) and uniquely consumed (UC), and thus is an example of a UPUC reaction. R1 and R5 knockout  have an alternative path that goes along reaction R4. Thus, both reaction labels would in this case not serve as a reliable predictor of the reaction’s essentiality. Eliminating reaction R4  example illustrates why a systematic study of combinatorial subsets of these categories can be interesting for understanding the topological basis of essential reactions.In the example in n R4 see e from thA third category of reactions comes from a sampling of random environmental conditions and predicting steady-state fluxes that optimize biomass production using FBA. The set of reactions predicted to be active in all conditions has been termed metabolic core (MC) . RemarkaE. coli [i.e., the effect of a knockout under the condition of another knockout), we analyze here the above categories  in light of single-knockout mediumdependent essentiality.Although experimental data from systematic knockout studies is available for E. coli ,23, thesE. coli ,25. Whilnetwork motifs. This general concept has been introduced and developed by the Alon group [An alternative approach of exploring the relationship between network architecture and function is based on the enumeration of few-node subgraphs. It has been shown that the subgraph composition of functionally related networks tends to be similar . Also, ion group ,28, parton group ,29, but on group in silico determined knock-out data with the three reaction categories and all combinatorial three-node subgraphs.Here we explore the question if a topological understanding of reaction essentiality can be established by integrating the relative essentiality of a reaction defined on the basis of a large number of combinatorial minimal media simulations. For each medium, the essentiality of all active reactions is tested in silico. In essential), essential only in some growth media , and never essential .We start by introducing the In See non-essential, conditional lethal, and essential, we quantify the relative essentiality of a reaction by computing optimal, i.e., maximizing biomass production, steady-state flux distributions for over more than 7 × 104 combinatorial minimal media conditions. Furthermore, all subsequent single reaction knockouts of active (non-zero flux carrying) reactions are performed to identify for each medium condition the set of essential reactions (see Methods for details). An illustrative example of this concept, involving E. coli central carbon metabolism [In order to subdivide the metabolic reactions into essentiality classes, namely tabolism , is provThe relative essentiality of a particular reaction is then defined as the number of lethal outcomes due to its removal divided by the number of environmental conditions under which it has been active. An alternative definition of relative essentiality would be to normalize the number of lethal outcomes to the total number of media sampled. In this case, however, essential reactions that are rarely active would give an unrealistically low essentiality value.E. coli model, which have been active at least once during the FBA simulations; blocked reactions [non-essential). Some reactions are globally essential  and a third set is only medium-dependent essential . Excluding non-essential reactions, conditional lethal curve indicates three major groups of reactions that exhibit very similar relative essentiality scores, connected by some intermediate reactions.eactions  have thuet al. [essential. This deviation from previously reported results seems to be due to model differences . This observation provides evidence for a strong negative association between these two essentiality classes in the context of the UPUC, SA and MC categories.Next, we explore the composition of essentiality classes in combinatorial sets of reaction categories see . For allial sets a, coincieactions c. More iconditional lethal from non-essential and essential reactions is achieved by this combinatorial approach . Non-essential reactions, on the other hand, are suppressed in chains, but elevated in V-in and V-out subgraphs. Surprisingly, all the topology-motivated reaction categories  display very similar occurrence patterns across the motifs.effective network spanned by all reactions with non-zero flux optimizing biomass production. In contrast to the majority of works on network motifs, we do not take the motif composition of the total (“static”) network into account, but rather compute the subgraph associations medium by medium from each This is conceptually more plausible since the reactions comprising a subgraph in the static network may in fact be never active together and, consequently, such a subgraph may functionally never be available  given that a neighboring reaction r' is in this class: c(C) = P(r ∈ C|r' ∈ C) = P/P(r' ∈ C), r' ∈ N(r). Essential reactions exhibit the highest amount of clustering, but non-essential and conditional lethal reactions show very similar distributions . Generally, the linear optimization problem defined in FBA can be stated as follows:For a given metabolic model, flux-balance analysis (FBA)  enables c, the stoichiometric matrix S, the flux vector v and the constraint vectors minv and maxv. As we are considering reversible reactions as two independent unidirectional reactions, we set minv to zero. Problems like Equation 1 can be efficiently solved using linear programming. In order to avoid thermodynamically infeasible loops, we utilized pFBA [with an objective coefficient vector zed pFBA , effectiiAF1260 model were classified as sources for elemental carbon, nitrogen, sulfur and phosphate  All experimentally verified nutrients in the see also . Some coFor each simulation, the essentiality of all active reactions was determined by fixing the respective fluxes to zero and recomputing the maximal biomass flux for the mutants. A reaction was classified as essential if the biomass flux dropped to zero.maxv) maximal uptake and secretion rate was assigned to all available transporters in the system and then blocked reactions were confirmed by flux variability analysis [We removed all globally blocked reactions from the model to give the topological methods described in this article  the opportunity to work on the same information content as their dynamical counterpart (MC). A high  that are associated with the set of UPUC metabolites for further analysis.The UPUC reactions were determined in analogy to the algorithm published in . We detemfinder [et al., where subgraphs are grouped according to criteria , rather than the one, where three-node subgraphs are sorted according to their “identifier” . In all subgraph-related figures, this subgraph identifier is also indicated in the corresponding subgraph pictogram.Three-node motifs as well as static networks were enumerated using the software mfinder . There aUsing a variety of topological descriptors, we have been able to characterize the network properties of reactions displaying medium-dependent essentiality in a large-scale combinatorial minimal media screen employing flux-balance analysis.The two classification schemes for metabolic reactions are (1) occurrence in directed three-node subgraphs and (2) functional categories of metabolic reactions motivated by network topology and FBA. We observe that the distribution of the three classes of metabolic reactions derived from relative essentiality is non-random across the three-node subgraphs. At the same time the distribution of essentiality classes across the three functional categories  is highly diverse for the conditional lethal reactions, but far more homogeneous for the other two classes. Putting all these observations together leads to an accurate topological characterization of medium-dependent essential reactions.These two topological characterizations are quite independent. In particular, when distributing the reaction categories across the three-node subgraphs, we see almost no differences between the three reaction categories in their subgraph preference profile.conditional lethal reactions, suggesting different sub-categories of these medium-dependent essential reactions. We believe that this method of exploring combinatorial sets defined from multiple topological labels with the goal of investigating the relationship between network properties and system properties may be helpful in a broad range of contexts in systems biology.Among the diverse combinatorial sets defined from the established topological categories, several very different ones contain a large number of With the wide range of FBA models available, a natural next step of our investigation is to analyze these categories of essential reactions and their topological implementation also in other organisms. Also, other categories of metabolic reactions derived from large FBA screens can be topologically assessed, for example reactions that are active only in a very small number of environmental conditions (rarely active reactions). We expect that the topological implementation of such rarely active reactions can shed light on the robustness of metabolic systems against environmental variations.metabolic inconsistency .


First, undefined nutrients (such as yeast extract) in fermentation may contribute significantly to product synthesis, which can be quantified through an isotopic dilution method. Second, product and biomass synthesis may be dependent on the co-metabolism of multiple-carbon sources. 13C labeling experiments can track the fate of each carbon substrate in the cell metabolism and identify which substrate plays a main role in product synthesis. Third, 13C labeling can validate and quantify the contribution of the engineered pathway (versus the native pathway) to the product synthesis. Fourth, the loss of catabolic energy due to cell maintenance (energy used for functions other than production of new cell components) and low P/O ratio (Phosphate/Oxygen Ratio) significantly reduces product yields. Therefore, 13C-metabolic flux analysis is needed to assess the influence of suboptimal energy metabolism on microbial productivity, and determine how ATP/NAD(P)H are partitioned among various cellular functions. Since product yield is a major determining factor in the commercialization of a microbial cell factory, we foresee that 13C-isotopic labeling experiments, even without performing extensive flux calculations, can play a valuable role in the development and verification of microbial cell factories.This paper discusses the use of  Recent advances in metabolic engineering have enabled us to engineer microbial cell factories for the efficient synthesis of diverse products, including bulk chemicals, pharmaceutical drugs and biofuels ,2. For e13C-analysis is the recommended method to track the in vivo carbon fluxes from specific substrates to final products. Feeding microbial cultures with 13C-substrates results in unique isotopic patterns amongst the cell metabolites (13C-fingerprints) [13C-fingerprints with metabolic modeling can elucidate the intracellular metabolic fluxes . In the biotechnology field, 13C-MFA can reveal metabolic responses of microbial hosts to product synthesis and growth conditions [13C-MFA may reveal the effect of suboptimal energy metabolism on intrinsic product yields.Therefore, rprints)  to delinrprints) . Integranditions -20, idennditions , and pernditions -25. In a13C-analysis can gain insights into the carbon contribution from the nutrients to product biosynthesis.Engineered microbes have many metabolic burdens that can inhibit both biomass growth and product synthesis. Since rich media includes both primary carbon substrates  and large amounts of nutrients (such as yeast extract), it is commonly used in fermentations to provide diverse nutrients for cell growth and stabilize the production performance of microbes ,10. ThisE. coli strains engineered for isobutanol production  displayt Figure . On the s growth . This ob acetate . 13C-anae Figure . Thereby2 and organic carbon substrates. Such mixotrophic metabolisms can alleviate the dependence of algal hosts on light and CO2 limitations, and thus enable them to achieve high biomass growth rate and product titer [13C-metabolite analysis has been used to track their photomixotrophic metabolisms in different scenarios. For example, Synechocystis sp. PCC 6803  is capable of performing photomixotrophic growth. 13C-MFA has shown that CO2 contributes to 25% of Synechocystis biomass yield during its mixotrophic growth with 13C-glucose and 12CO2[13C-analysis has tracked D-lactate synthesis in an engineered Synechocystis 6803 [2 and acetate. Experiments with fully labeled acetate and 12CO2 determined that nearly all of the lactate molecules were non-labeled and that only the acetyl-CoA-derived proteinogenic amino acids  were 13C-labeled. This observation suggests that acetate entered into TCA cycle and was involved only in biomass growth, while the yield of D-lactate was completely derived from CO2  may co-metabolize multiple carbon substrates simultaneously, isotopomer feeding can reveal the contributions of each substrate to the corresponding metabolite pools, and thus predict the potential bottlenecks in biomass or product formations.Algal species are able to utilize both COct titer . 13C-metand 12CO2. On the tis 6803 . In that13C-analysis can decipher the yield of products with multiple biosynthesis routes. For example, the acetogenic bacterium Clostridium carboxidivorans uses syngas  to generate various chemicals  [2 fixation, which includes the Wood-Ljungdahl pathway, the anaplerotic pathways, and the pyruvate synthase reactions. 13C-experiments can identify the relative contribution of each CO2 fixation pathways towards product synthesis. As a demonstration, cultivation of Clostridium with labeled 13CO2 and 12CO has been shown in Figure 2 assimilation reactions to biomass and product synthesis.utyrate) . It cont13C-experiments can determine the relative fluxes through multiple pathways by measuring product labeling. Specifically, 1-butanol could be produced simultaneously from a threonine pathway and a citramalate pathway (a short-cut keto acid-mediated pathway) in E. coli[13C-pyruvate and 13C-bicarbonate were fed to 1-butanol producing cultures, labeling patterns in 1-butanol can reveal the fluxes through both the routes  ,27. To rn E. coli. If 1st E. coli consumes 7.6 mmol of ATP per gram dry weight per hour [2 and translocate protons across the membrane to establish a proton gradient to power ATP synthase. However, proton translocation through membrane is not always coupled with electron transfer from NADH to O2, which reduces the contribution of oxidative phosphorylation to the establishment of the proton motive force for ATP synthesis [Bacillus subtilis has a P/O ratio of 1.3, and a small increase in P/O ratio (from 1.3 to 1.5) could increase riboflavin yields by 20% [The theoretical product yield is generally calculated based on the stoichiometry of product synthesis from a carbon substrate. However, microbial energy metabolism also affects product yield because the synthesis of high-energy chemicals is energetically expensive, consuming large amounts of ATP/NAD(P)H. Cell maintenance  strongly competes for energy molecules and limits product synthesis. The maintenance energy involves regeneration of macromolecules, futile metabolic cycles, energy spilling reactions, proofreading, cell motility, preservation of chemical gradients, and repairing of cell damage caused by environmental stresses ,38. For per hour . Moreoveper hour . Cytochrynthesis ,42. Therynthesis . Under mynthesis ,44. For s by 20% .E. coli growth, its energy yield of substrate catabolism could be one-third of the theoretical maximum) [The amount of energy from substrate catabolism diverted to non-growth functions varies dramatically depending on different organisms and growth conditions  . To illumaximum) , a smallmaximum) . The flulb and ub are upper and lower bound for each reaction flux, v(i). Figure where the objective function is to maximize v(2) . A is the reaction stoichiometry. E. coli for fatty acid overproduction [13C-MFA showed that the theoretical ATP/NADPH generation (assuming P/O ratio = 3) from glucose catabolism was much higher than ATP/NADPH consumption for biomass growth and fatty acid synthesis. After optimization of biosynthesis pathway via 'push-pull-block' strategies, this engineered strain had a fatty acid yield of only 0.17 g fatty acid/g glucose H for both biosynthesis and cell maintenance, optimal product yield is unlikely to be achieved by overexpressing biosynthesis pathways or by redirecting metabolic fluxes to avoid carbon losses. A more promising approach would be to improve energetic prosperity or respiration efficiency, thereby allowing the cells to “burn” substrates more efficiently to satisfy the energy requirement [In a recent study of an engineered oduction , 13C-MFAe Figure B becauseositions ). Therebuirement ,53.13C analysis can characterize the hosts’ intrinsic production yields under different carbon sources, and determine the contributions of the different pathways to biosynthesis. In addition, 13C-MFA can profile microbial fluxomes and determine the amount of extra substrates that the cell consumes to compensate for ATP losses from diverse cellular processes, which is essential to understand metabolic capability of a microbial host for maximal product yields. In the end, 13C-analysis, using the labeled product as internal standards, can also be employed to correct product measurement noises in fermentation processes due to water loss, product evaporation or degradation [13C-labeling techniques to the metabolic engineering field as we foresee an extended use of 13C-experiments for the development of microbial cell factories.Product yield is one of the main considerations of microbial cell factories . Microbiradation . This reThe authors declared that they have no competing interests.AMV/YJT wrote the introduction, product yield from rich medium, multiple carbon substrates and parts of yield from alternative pathways. LH wrote the bioenergetic efficiency. LY contributed to the section of product yield from alternative pathways. WH polished the paper. All the authors approved the final manuscript.


Metabolomics provides a view of endogenous metabolic patterns not only during plant growth, development and senescence but also in response to genetic events, environment and disease. The effects of the field environment on plant hormone-specific metabolite profiles are largely unknown. Few studies have analyzed useful phenotypes generated by introducing single or multiple gene events alongside the non-engineered wild type control at field scale to determine the robustness of the genetic trait and its modulation in the metabolome as a function of specific agroecosystem environments.We evaluated the influence of genetic background  and environments  on the metabolomic profile of isogenic reverse genetic mutations and selected mulch based cropping systems in tomato fruit. Net photosynthesis and fruit yield were also determined.NMR spectroscopy was used for quantifying metabolites that are central to primary metabolism. We analyzed both the first moment (means) of metabolic response to genotypes and agroecosystems by traditional univariate/multivariate methods, and the second moment (covariances) of responses by creating networks that depicted changes in correlations of paired metabolites. This particular approach is novel and was necessary because our experimental material yielded highly variable metabolic responses that could not be easily understood using the traditional analytical approaches for first moment statistics.High endogenous spermidine and spermine content exhibited strong effects on amino acids, Krebs cycle intermediates and energy molecules (ADP + ATP) in ripening fruits of plants grown under different agroecosystem environments. The metabolic response to high polyamine genotypes was similar to the response to hairy vetch cover crop mulch; supported by the pattern of changes in correlation between metabolites. Changes in primary metabolites of genotypes mutated for the deficiency of ethylene or methyl jasmonate were unique under all growth conditions and opposite of high polyamine genotype results. The high polyamine trait was found to dominate the low ethylene and low jasmonate mutations under field conditions. For several metabolites low ethylene and low methyl jasmonate genotypes had an inverse relationship. Collectively, these results affirm that interactions between metabolite pathways and growth environments are affected by genotype, and influence the metabolite quality of a crop.This study portrays how metabolite relationships change, both in mean and in correlation, under different genotypic and environmental conditions. Although these networks are surprisingly dynamic, we also find examples of selectively conserved associations.The online version of this article (doi:10.1007/s11306-016-1037-2) contains supplementary material, which is available to authorized users. Metabolomics provides a view of endogenous metabolic patterns not only during plant growth, development and senescence but also in response to genetic events, biodiversity, environment and disease. Thus, to mention a few examples, metabolomics has contributed to mapping plant cell types  of metabolic response to genotypes and agroecosystems by traditional univariate/multivariate methods, as well as the second moment (covariances) of response by creating networks that depicting changes in correlations of paired metabolites.Previous research investigating metabolomic patterns have focused on the first  moment, i.e. changes in mean values, whereby observed metabolic mean values and differences between mean values are presented to describe the metabolomic state or change in state of the organism under study in response to an exogenous or genetic manipulation. We also investigated changes in the second  moment, covariances of metabolites; how the covariances responded to experimental treatment  in a fruit specific manner for enhanced metabolic activity and accumulate polyamines spermidine and spermine in a fruit ripening-specific manner , which have higher processing quality, longer vine life and higher lycopene content  gene under CaMV 35S promoter to constitutively suppress the production of ripening hormone ethylene , which produces half the ethylene than the control 556AZ line and has considerably longer shelf-life   homozygous for the indicated genetic event(s) were tested alongside the azygous control line (556AZ): Five genotypes  in 2006, and an additional line 2AS-2HO was added to the field trial in 2007. The codes used for each tomato line (genotypes) are summarized in Supplementary Table 1. These included three types of engineered genotypes of tomato with the modulated fruit shelf-life, fruit texture and metabolic/nutrient activity of tomato fruit. Thus, individual genetic events included tomato lines engineered with yeast SAM decarboxylase gene under ripening-specific E8 promoter  under ambient mid-day conditions of light, temperature, humidity and CO2 concentration, using a broad-leaf cuvette. Measurements were made on July 18, Aug 01, Aug 17 and Sep 07 in 2006 and on Aug 02, Aug 14, Aug 27, and Sep 12 in 2007. Leaf temperatures ranged from 26 to 30 °C across all measurement dates. Mean values of the leaf to air difference in water vapor pressure ranged from 1.2 to 1.8 kPa for the different measurement dates. Photosynthetic photon flux density exceeded 1200 µmol m−2 s−1 for all measurements, and the CO2 concentration external to the leaves was controlled at 370 µmol mol−1. Leaves selected for measurement were recently fully expanded upper canopy leaves fully exposed to light, and were found to have the highest rates of any leaves on the plants. On each date, gas exchange was measured on one leaf of each genotype in each replicate plot. The order of measurements of genotypes within mulch treatments was random, and the mulch treatments were measured such that the mean time of day was equalized. Measurements were completed in about 2 h on each date.Single leaf COIn 2006, pink and red fruit  were harvested from the five-plant subplots from each replication on two dates, the first harvest took place on Sep 12, and the final harvest on Sep 22. In 2007, the five-plant subplots were harvested from three replicates at two times. For the first harvest, all the pink and red fruits were harvested Sep 6 to 9. The same plants were harvested for a second time on Sep 25 to 28. The number and weight of fruit per plant and average fruit weight were calculated both for the early harvest and for the total of the two harvests.g for 15 min and the supernatants assayed  following the manufacturer’s instructions, in a final volume of 20 μl. The final cDNA products were diluted tenfold prior to use in real-time RT. Quantitative RT-PCR (Q-PCR) was performed with gene-specific primers (Supplementary Table 3), which were designed using Primer3 software. The Q-PCR conditions were the same as before . RNA quantification and quality were determined using a spectrophotometer and native agarose gel electrophoresis, respectively. First strand cDNA synthesis was performed using the SuperScriptUnivariate analyses were performed with analysis of variance (ANOVA) using the mixed model procedure of SAS version 9.2 . The model for analyzing fruit yield variables, photosynthesis variables, polyamines and metabolites had mulch, genotype and mulch by genotype interaction treatments as fixed effects. Year and field block nested within year were random effects for the fruit yield analyses, year and block within year and sampling date within year were random effects for the photosynthesis analyses, and year and fruit stage were random effects for the polyamine and metabolite analyses. Principal components analysis (PCA) was performed on the metabolite data set after standardization to mean zero and standard deviation one. Two ANOVA’s were performed, one for each of the first two components using mulch, genotype and mulch by genotype interaction treatments as fixed effects.Metabolites were organized into groupings of amino acids, organic acids, sugars, and energy metabolites in order to facilitate analysis of overall trends within groups. Each metabolite was standardized to mean = 0 and standard deviation = 1 to give equal weighting to each metabolite. An ANOVA was then performed on the standardized metabolic data by group with genotype or mulch treatment as a fixed effect.2 concentration) and metabolite variables. Univariate Pearson correlations between these variables were also calculated.Canonical correlation analysis (CCA) was performed to explore multivariate correlations between whole plant variables  for individual metabolite pairs, following the Fisher r-to-z transformation, and show only large changes in correlation (for P < 0.05). Pearson correlations were calculated using the R statistical software . We did not include correlation changes involving the uncharacterized “B” metabolite. We color-coded the networks, with blue representing increases in correlation  and red representing decreases in correlation . The thickness of the lines joining the metabolites was used to represent the magnitude of the change , with the thinnest line representing a change of about 0.1 in correlation and the thickest a change of about 0.7 in correlation. An important point to remember when looking at the figures is that they do not represent the correlations themselves, rather they represent changes in correlation. Thus, two metabolites that are highly correlated in both subsets of data would not be linked in the figure because their correlation did not change.To determine which changes in correlations were the important ones to depict in our networks, we established a confidence interval for the hypothesis of no change in correlation  or more generally, using approaches such as false discovery rate .We are aware that analyses repeated in different ways on the same data set leads to correlated test statistics. The ySAMDC), tomato E8 (SlE8) and tomato lipoxygenase (SlLOX) in different tomato genotypes grown in BP (black plastic mulch) and HV (hairy vetch mulch) are shown in Supplementary Fig. 1. As expected, lines 8 and 10, carrying the ySAMDC transgene, expressed ySAMDC transcripts. However, line 20 had higher expression of ySAMDC transcripts than its parent line 8. Specific effects of the BP versus HV were evident: ySAMDC transcript expression in line 20 (G20) was several-fold enhanced under BP . To ascertain if this BP effect was due to an effect on the SlE8 promoter used to drive the expression of the chimeric ySAMDC construct, the accumulation of SlE8 transcripts was also quantified under BP and HV. The pattern of SlE8 transcript accumulation in BP-grown lines 8 and 10 was similar to the pattern of ySAMDC transcripts . In fact, BP-grown line 12 had higher expression of SlE8 transcripts than when grown under HV , and in contrast these transcripts in control azygous line 5 accumulated maximally under HV. SlLOX transcripts were suppressed in both line 12 and its sibling, genotype 20, as expected while mulch systems had little differential effect. HV mulch had a more enhancing effect on SlLOX expression in line 5 (G5) and line 8 (G8). In general, the relative accumulation levels of SlE8 transcripts were considerably lower than ySAMDC and SlLOX transcripts.We first ascertained the stability of the introduced genes in tomato plants in the field and/or their biochemical phenotype. In addition to the engineered lines mentioned above, we developed and tested additional tomato lines with double genetic events by making backcrosses between one high polyamine line (line 10) and ethylene-suppressed line 2 , as well as another high polyamine line (line 8) and meJAS-deficient line 12  with an azygous line as a control (description in Supplementary Table 1). Q-PCR data of three genes—yeast SAM decarboxylase . There were no significant effects for any of these variables among genotypes 5, 8, 12, and 20.Constitutive suppression of ethylene was found to result in higher net photosynthesis and stomatal conductance in line 2 than in the azygous control (Supplementary Table 5). This was true also for its sibling line 4 (crossed with high polyamine line 10), which behaved like parent 2 for all variables. In contrast, line 10 with fruit-specific high polyamine content had the lowest net photosynthesis, stomatal conductance and fruit yield. This phenotypic trait was, as expected, absent from line 4, likely because of the differential regulation of the genetic events introduced, suggesting that this fruit-specific event was not transferred to vegetative parts of the tomato plant. In all genotypes, the differences in net photosynthesis were found unrelated to internal COTomato fruit yield was higher in plants grown in hairy vetch or black polyethylene mulch than in rye mulch or bare soil Fig. , in lineP values >0.05, results not shown). Although this analysis did not adequately resolve genotype and mulch system treatments, we further explored the data set, looking at the variables independently using univariate ANOVA, and then with metabolite networks.Principal components analysis (PCA) was performed on the metabolite data set after standardization to zero mean and unit standard deviation. PCA decomposed the metabolome data set to two principal components with 36 % of the explainable variation described by the first component and 20 % of the explainable variation described by the second component. Other components each described less than 10 % of this variation. The first principal components axis was most positively correlated with the metabolites histidine (HIS), asparagine (ASN), phenylalanine (PHE), and threonine (THR) (eigenvectors > +0.25) and most negatively correlated with glucose (bGLC) and fructose (FRU) (eigenvectors < −0.08) . In contrast genotype 2 had higher levels of inositol and adenosine than either genotypes 8 and 10. Genotype 10 had higher levels of choline and mNAM than all other genotypes. Sibling 20 was more similar to its parent genotype 8 for valine, citrate, succinate, and adenosine, but more similar to genotype 12 for asparagine. Sibling 4 was more like its parent genotype 10 for valine, inositol, and adenosine, but more like its parent genotype 2 for choline and mNAM.Significant univariate effects due to agroecosystem environment, created by different mulches, on amino acids, organic acids, sugars, and energy fruit metabolites are summarized in Supplementary Table 7. The hairy vetch (HV) mulching system led to higher levels of selected amino acids , and organic acids  and mNAM, and lower levels of the sugars (glucose and fructose). Like HV, rye mulch (Rye) also increased glutamate and threonine but its effect on aspartate was greater than HV, the black polyethylene (BP) mulching system, and bare soil (BS) . In contrast to HV and Rye systems, both glucose and fructose, and NUC2, were higher under BP and BS environments.P < 0.05) among standardized amino acid and organic acid means for both mulch and genotype, but not for means of standardized sugar or energy metabolites (Supplementary Tables 6 and 7). Plants grown in the HV mulch system had higher overall amino acid and organic acid levels, whereas plants grown in the BP mulch system had the lowest levels . Univariate correlations between plant and fruit metabolite variables were generally low . Thus, there was little linkage between plant performance and fruit metabolism in these genotypes and mulching systems.changes in correlations between metabolite pairs among subsets of data. A listing of the correlation between all pairs of metabolites for each data subset is presented in Supplementary Table 8. The data were partitioned into subsets of interest for this study, namely, (a) genotypes whose fruit have low  versus high polyamine content (Spd and Spm) , (b) normal  versus deficient (lines 12 and 20) meJAS content, and (c) mulch system in which the plants were grown (two categories: bare and black polyethylene versus hairy vetch and rye cover mulches).When we used PCA and WCNA . The least stable metabolite pairs are colored darkest red  in the heat map while the most stable are yellow . The most stable was the pair, TRP-SUCR, with the smallest standard deviation of 0.109, and the least stable was AMP-Nucl2, with the highest standard deviation of 0.518. Metabolites that had the most stable associations with other metabolites were citrate and formate  and sucrose . Correlational relationships amongst these metabolite pairs with low standard deviations were least disturbed by perturbations caused by differences in genotype or mulching system and represent the most stable linkages between metabolites in this experiment. In contrast, metabolite pairs with large standard deviations illustrate pairs whose linkage changed most in contrasting treatments; analyzed in more detail below.Figure Cytoscape (v. 3.1.1)  generated via transgenic intervention, and by the agroecosystem environment. Our data on metabolic changes reinforce the need to account for agroecosystem effects on ‘novel’ and other engineered genotypes for variables like fruit yield, metabolite/nutrient content and longevity. Studies like ours contribute information necessary for agricultural sustainability by identifying genotypes that have robust agronomic and other desirable traits under different agroecosystems  versus under different agroecosystems in the field. Such a comparison proved quite revealing, when data generated in the present study were compared to those using GH-grown tomatoes  trait was dominant in the background of methyl jasmonate deficiency in maintaining higher levels of several amino acids  under field conditions. Similarly, the high polyamine trait was found to be dominant for Krebs cycle intermediates—citrate, succinate and fumarate—and energy-related metabolites (ATP + ADP) under field conditions but not under greenhouse conditions. Collectively, these results affirm that specific interactions which exist between a particular metabolite pathway and growth environment are affected by the genotype being tested, and will therefore influence the metabolite quality of a crop.Arabidopsis mutants and transgenic crops have shown involvement of polyamines in plant resistance to drought, salinity and heat  the precursors of polyamine biosynthesis are themselves amino acids—arginine (ARG) and ornithine (ORN)—whose decarboxylation reactions form putrescine (Put), which is subsequently converted step-wise to spermidine (Spd), spermine (Spm) and thermo-spermine (T-Spm); (2) studies with Many of these metabolites were affected by genotype in our analyses. Univariate analyses showed alanine and succinate levels were increased in high polyamine genotypes, suggesting an accelerated movement of carbon through polyamines into Krebs cycle along with generation of ATP + ADP, which were also increased in high polyamine genotypes. Network analysis also showed alanine and succinate as hubs of metabolic changes as genotype changes from low to high polyamine accumulation Fig. a. AlthouFinally, our data analysis highlights the distinctive fluidity of metabolite networks associated with agroecosystem environment. Not only were metabolic profiles different in the field (this experiment) versus greenhouse (previous experiments) environments, but modification of the field agroecosystem had a profound effect on metabolites. The traditional culture of tomatoes in black polyethylene mulch increases soil temperature, and accelerates vegetative growth and the advent of reproductive development leading to higher relative growth rates of fruit Below is the link to the electronic supplementary material.


Metabolic network models describing the biochemical reaction network and material fluxes inside microorganisms open interesting routes for the model-based optimization of bioprocesses. Dynamic metabolic flux analysis (dMFA) has lately been studied as an extension of regular metabolic flux analysis (MFA), rendering a dynamic view of the fluxes, also in non-stationary conditions. Recent dMFA implementations suffer from some drawbacks, though. More specifically, the fluxes are not estimated as specific fluxes, which are more biologically relevant. Also, the flux profiles are not smooth, and additional constraints like, e.g., irreversibility constraints on the fluxes, cannot be taken into account. Finally, in all previous methods, a basis for the null space of the stoichiometric matrix, i.e., which set of free fluxes is used, needs to be chosen. This choice is not trivial, and has a large influence on the resulting estimates.i) a small-scale network with 7 fluxes, to illustrate the operation of the algorithm, and (ii) a medium-scale network with 68 fluxes, to show the algorithm’s capabilities for a realistic network. The results show an accurate correspondence to the reference fluxes used to simulate the measurements, both in a theoretically ideal setting with no experimental noise, and in a realistic noise setting.In this work, a new methodology based on a B-spline parameterization of the fluxes is presented. Because of the high degree of non-linearity due to this parameterization, an incremental knot insertion strategy has been devised, resulting in a sequence of non-linear dynamic optimization problems. These are solved using state-of-the-art dynamic optimization methods and tools, i.e., orthogonal collocation, an interior-point optimizer and automatic differentiation. Also, a procedure to choose an optimal basis for the null space of the stoichiometric matrix is described, discarding the need to make a choice beforehand. The proposed methodology is validated on two simulated case studies:  contains supplementary material, which is available to authorized users. Based on measurements of exchange fluxes between the environment and the cell, and possibly thermodynamic, physiological, statistical , cint the (mint×1) vector of intracellular concentrations [mmol/gDW], Sint the mint rows of the stoichiometric matrix which correspond to the intracellular metabolites, v the (n×1) vector of specific fluxes [mmol/gDW/h] and μ the scalar specific growth rate of the organism [1/h] which equals the flux of the pseudo-reaction to biomass. The first term on the right hand side is the reaction term, the second term is a dilution term which arises due to the growth of the biomass. To get a fully defined model, expressions for all intracellular fluxes are needed.with multi-scale model describing both intracellular and extracellular concentration variables: The intracellular model (Equation ) can be cext the (mext×1) vector of extracellular concentrations [mmol/L], cbio the scalar biomass concentration [gDW/L], Sext the mext rows of the stoichiometric matrix which correspond to the extracellular metabolites and cext and cbio are defined per liter of medium, while cint is defined per gram of biomass dry weight. As the fluxes are specific, i.e., defined per gram of biomass dry weight, which is more descriptive from a kinetics point of view, the fluxes are multiplied with the biomass concentration in Equations  system of linear equations: Because the number of fluxes, and hence the number of expressions which need to be identified and estimated from experimental data, grows quite large for even a medium-scale metabolic reaction network, a simplification is typically made in the form of a Equation  is discad in the system equals the number of unknowns minus the number of independent equations, i.e., d=n−rank(Sint). All solutions to this system can be written as a linear combination of a set of independent fluxes, called the free fluxes: In the majority of metabolic reaction networks, the number of intracellular metabolites is smaller than the number of reactions, making this an underdetermined system of linear equations. The number of degrees of freedom K a suitable basis for the null space of Sint of dimensions (n×d) and u the (d×1) vector of free fluxes. By substituting this into the extracellular model, the following simplified model arises: with Note that to fully define this simplified model, only expressions for the free fluxes need to be identified, resulting in a substantial reduction in experimental and numerical cost.mext+1×1) state vector x: The resulting model can be written in a more concise way by putting together all concentration variables in the (with: Se of size (mext+1×n), and mext+1) row vector which selects the last element of x, the biomass concentration, i.e., with dynamic metabolic flux analysis (dMFA) problem now consists of identifying the free flux profiles over time, based on measurements of the states, i.e., the extracellular metabolite concentrations, or the fluxes themselves. This problem can be written as a dynamic input estimation problem using a least-squares objective function: The subject to: ntime the total number of time points at which measurements were taken and nout the number of outputs of the system. This system includes algebraic states z(t), which represent the irreversible fluxes. By constraining these states to be positive, the irreversible fluxes are also kept positive. Furthermore, y(t) is the (nout×1) vector of outputs of the system, which can be any non-linear function f of the states and free fluxes, and yj(ti) is the model output j at time ti. The objective function is a weighted sum of least squares, with mij and σij respectively the average and the standard deviation for the measurement of output j at time point ti, and x0 is the vector of initial values for the states, which is typically also an optimization variable.with i) The first approach , which is controlled between 0 and 1 following the input profile in Figure xin the (10×1) vector of feed concentrations [mmol/L] of the different metabolites. As only glucose is in the feed, with a concentration of 20, this vector is the following: with The reference fluxes for the six free fluxes were the following: The starting values for the concentrations in the simulation were chosen to be In total, 31 measurements at equidistant points between 0 and 10 hours were generated for 8 concentrations  and 2 fluxes (oxygen and carbon dioxide). In typical settings, oxygen and carbon dioxide concentrations are not measured directly, but their uptake and production fluxes, respectively, are measured through off-gas analysis on the bioreactor. The resulting set of 310 measurements is not shown separately, but can be found in Figures All reactions, all stoichiometric matrices, the irreversibility matrix, the null space basis matrix, and the simulated measurements and measurement variances for this case study are given in the Additional files K matrix, again the same one as used to simulate the measurements, and an optimized K matrix. The estimated fluxes for the fixed K are shown in Figure K matrix are shown in Figure AIC criterion, this is the best possible fit while at the same time keeping the uncertainty as low as possible. Also, the difference between the estimates with a fixed and an optimal K matrix is again very small. This again confirms the fact that the algorithm can be successfully used in the optimal K mode, i.e., without making an a priori choice on the free fluxes, as the results are very similar in the two cases. This is an important advantage of this method as in practice the set of free fluxes is not known.The estimation of the fluxes in the medium-scale network was carried out with both a fixed ntime·d, and thus scales linearly with both the number of measurement time points and the number of free fluxes. The average time per optimization problem is harder to assess, as this is dependent on the total number of variables, as indicated in Table The time needed to solve the dMFA problem using this methodology is the product of on the one hand the total number of optimization problems to solve, and on the other hand the average time per optimization problem. If only one knot addition is allowed for every measurement time point which is added, and when making abstraction of the possibility that in the first iteration(s) no knot can be inserted, the total number of optimization problems equals K matrices are shown in Table K, in Figure d mutually independent optimization problems have to be solved. These can be easily assigned to different cores on a multi-core CPU. Finally, the automatic differentiation of the objective and constraint functions of the different subproblems can also be further exploited, as at this point, these are basically repeated when going from one iteration to the next. The only part which is added, though, is the part for the interval between the last and the newly added time point, while everything before this point stays the same. This initialization of the different subproblems offers opportunities for further reductions in CPU times in future research. Nevertheless, the algorithm can already at present perfectly run in real-time on standard equipment as bioprocesses typically involve multiple days.To give a general idea about the computational complexity of the algorithm, the total CPU times of the estimations for the small-scale and medium-scale network for both fixed and optimal In this contribution, a novel systematic methodology for dynamic metabolic flux analysis, based on B-spline parameterizations, has been presented. Because of the high degree of non-linearity in the estimation of the knot locations, an incremental knot insertion algorithm is proposed. By using this algorithm, at least an excellent local minimum is found. Furthermore, the algorithm is fully contained, as the user does not have to make any choices regarding the null space basis of the intracellular stoichiometric matrix. This methodology tackles the disadvantages of previous methods for dMFA by making sure that the estimates are smooth, that specific fluxes are estimated and that extra constraints can be taken into account. The algorithm is validated on a small-scale simulated case study in both a low noise and a realistic noise setting. In both cases, an accurate dynamic estimation of the fluxes is obtained. The algorithm was also tested on a more realistic network with 68 fluxes and 6 free fluxes. Although CPU times are longer, mainly due to a larger number of measurements, the algorithm was also able to successfully estimate the fluxes in this larger case study. The algorithm can still be run in real-time as biological processes are typically slow. To keep CPU times under control, the total number of measurements should be reduced if possible, as the CPU time per iteration tends to grow exponentially over the iterations. This can be done, e.g., by only considering time horizons which are of specific interest to the researcher. Possible further improvements of the algorithm, mainly in the regions of parallellization and subproblem initialization, are indicated.


Microbial communities play important roles in health, industrial applications and earth's ecosystems. With current molecular techniques we can characterize these systems in unprecedented detail. However, such methods provide little mechanistic insight into how the genetic properties and the dynamic couplings between individual microorganisms give rise to their dynamic activities. Neither do they give insight into what we call “the community state”, that is the fluxes and concentrations of nutrients within the community. This knowledge is a prerequisite for rational control and intervention in microbial communities. Therefore, the inference of the community structure from experimental data is a major current challenge. We will argue that this inference problem requires mathematical models that can integrate heterogeneous experimental data with existing knowledge. We propose that two types of models are needed. Firstly, mathematical models that integrate existing genomic, physiological, and physicochemical information with metagenomics data so as to maximize information content and predictive power. This can be achieved with the use of constraint-based genome-scale stoichiometric modeling of community metabolism which is ideally suited for this purpose. Next, we propose a simpler coarse-grained model, which is tailored to solve the inference problem from the experimental data. This model unambiguously relate to the more detailed genome-scale stoichiometric models which act as heterogeneous data integrators. The simpler inference models are, in our opinion, key to understanding microbial ecosystems, yet until now, have received remarkably little attention. This has led to the situation where the modeling of microbial communities, using only genome-scale models is currently more a computational, theoretical exercise than a method useful to the experimentalist. Microbial communities are ubiquitous in nature and play key roles in the ecosystems of our planet. Humans depend on their activities as they play essential roles in element cycling and agriculture, e.g., through interactions between plants on the one hand and mycorrhiza and nitrogen fixing bacteria on the other hand  metabolic potentials and their (relative) abundances. Yet, the information gained from such meta-omics studies  is still relatively limited, as they only provide an indirect view into the metabolic activities of such microorganisms and virtually none about their relationship with the environment and each other. These properties must, in turn, be inferred from the data  . We cannot exclude that social traits may play an important role in specific cases. Phages, for instance, can shape and alter whole ecosystems Fuhrman, , yet thiWe will argue that limited quantitative experimental data, when combined with coarse-grained metabolic models, will be able to help researchers infer the community structure, i.e., the topology of species interactions (see Glossary for our definition of these often loosely defined terms). What do we mean by coarse-grained models? Basically, reduced complexity of the model. There are several ways to coarse-grain models, but in general it involves either ignoring parts of the system that are deemed less relevant, or lumping of many details of a subsystem into a higher-order description of that subsystem. A whole metabolic pathway can be lumped into one enzymatic reaction; the growth of a cell can be described by one Monod-type equation; a group of organisms can be summarized as one ecotype with an archetypical metabolic profile (“acetate consumer”). Such coarse-grained models can be gradually increased in detail over time. Parallel to these coarse-grained models, genome-scale metabolic models can be used as data repositories where new data and constraints are imposed on the models. These two approaches should in the end converge into the same description of the community. We will provide an example to illustrate how the combination of these approaches could aid in improving mechanistic understanding of microbial communities.In metabolic networks, metabolites are produced and consumed by enzymes that together form a complete set of chemical processes in the cell. Since enzymes are proteins encoded on the genome, and our biochemical knowledge of metabolic reactions has a long and rich history, it is possible to reconstruct a draft metabolic network largely from genomics data alone. Tools exist that automate this process and generate a complete metabolic network  in particular, any data that is available is combined with computational optimization techniques to predict a  flux distribution through the metabolic network. Both methods have their merits and draw-backs, which we will discuss briefly.One of the methods used to extract more information from data is the use of MFA. MFA is a powerful tool in biotechnology and systems biology as it aims to estimate intracellular fluxes in living cells. It generally applies to systems operating at a metabolic steady-state, but is not limited to steady-state conditions. MFA tries to infer intracellular fluxes from measured extracellular fluxes using a coarse-grained metabolic model where steady-state mass balances constrain the model. In the early days of MFA, there was no standard description of how the metabolism of a cell could be defined in the stoichiometric model and therefore such descriptions could vary between models. Some defined coarse-grained metabolic blocks in which multi-reaction pathways are reduced to a single reaction, such as catabolism, respiration, product formation, anabolism, and maintenance , using stoichiometric metabolic models. These models are based on biochemical data or genomic information and cover mostly the central metabolism. These approaches enable the estimation of a large fraction of the intracellular fluxes operative in central metabolism, in steady-state or dynamic states .Genome-scale metabolic models contain the coupled metabolic reactions encoded by the genome of an organism . The At any given moment in time, this community state is characterized by: (i) the abundances of all microorganisms in the community; (ii) the intracellular and extracellular concentrations of their metabolites, mRNAs, enzymes, and other cellular constituents; and (iii) the process rates (fluxes), i.e., the growth rates of all microorganisms, and the rates of all the intracellular and extracellular biotic metabolic reactions and abiotic processes. Thus, the community state describes the quantitative values of all the concentrations and process rates occurring in the community. For single species cultures, such a data set could be acquired but already constitutes a major task. There are huge experimental complications for microbial communities, and this makes the inference of the community structure also challenging. In theory, if we were to have a kinetic representation of all the processes, the characterization of the community state would suffice to determine the rates of change of all the concentrations in the community. Clearly, we do not know most of the kinetic parameters that would be required. This inference problem is still an enormous challenge in modeling monocultures  are very suitable for data integration, as their mathematical description directly maps onto genomic, metabolomic, proteomic, and flux data of the metabolism of individual microorganisms in the community. The mapping can be done on a visualized metabolic map corresponding to the microbial ecosystem according to methods described in Maarleveld et al. .CSSMs allow for calculation of the community state and structure with numerical algorithms.Experimental data can be used as constraints in the associated modeling formalism, to improve predictions when more data has become available  the supra-organism approach  description, at a lower level of granularity, is always possible. Ultimately, there is the genome of the individual consortium species that allows for a reconstruction of the metabolic potential, which is a solid ground on which to build more detailed reconstructions. When the genome of the consortium species is not present, data from metagenomics is suitable for more detailed metabolic reconstructions. However, the level of detail of the metabolic reconstructions will be largely dependent on the sequencing depth of the metagenome.We will make use of an elegant study performed on a nitrate respiring community  or nitrogen gas (denitrification) . The model of the carbon fermenting organism will be the simplest, that is: uptake reactions of glucose and amino-acids and secretion reactions of acetate, formate and hydrogen, because testing the given hypothesis only requires the secretion of fermentation products that can act as substrate for the other functional groups. The ammonifiers model should contain the metabolic pathway of nitrate to ammonium conversion, transport reactions, carbon metabolism and other energy generating pathways. The denitrifiers require the same level of detail in their model as the ammonifiers. Now, these simple coarse-grained models allow to first investigate whether the experimentally observed differences might be explained without requiring the inclusion of the affinities for nitrite. If not, a kinetic description of the nitrite reductase in both functional groups can be included. Subsequently, it is possible to determine how big the difference in nitrite affinity should be to explain the experimental results.Kraft et al.  also obsFinally, Kraft et al.  observedThe aforementioned examples show how the question determines the level of detail of the “Inference models.” These coarse-grained models of the players in the ecosystem should be based on knowledge of the (genome-derived) metabolic networks of the species. Therefore, parallel to this “Inference model,” genome-scale stoichiometric metabolic models are maintained to act as data repositories (shown in Simulation in Figure Finally, a synergistic approach emerges where the interplay between the simple coarse-grained models and the genome-scale metabolic models are determined by the type of question being asked about the community. An important aspect is that the output of models with different levels of description should be consistent with each other and agree with available data. This process of iterative model making should inform the experimentalists about knowledge gaps and suggests new experiments.As demonstrated by Kraft et al. culturing communities under well-controlled conditions, for instance in chemostats, enables quantification of community-level fluxes, biomass abundances and gene expression levels of specific populations, and allows for applying well-tractable perturbations. This type of experimental approach will be very helpful to develop and optimize methods for species-specific flux descriptions on basis of CSSMs, to understand the community function and eventually control the microbial ecosystem.In this paper, we described current methods to model the metabolism of single species and how we think such system approaches could be used at the microbial community level. These methods go from genomic information to understanding and directing microbial community metabolism. We argued that metagenomics data are great, but they need to be augmented with flux measurements and model-based inference methods to identify the community structure and state. We arrive at a proposed approach where models are combined with quantitative data. Such models can vary in their level of coarse-graining depending on the research questions, data and experimental options at hand. Genome-scale stoichiometric models will be the knowledge base with which to integrate genomic, physiological and physicochemical data, and can be developed parallel to coarse-grained models to understand the community structure, state and function. We feel that what is missing -but is within reach- is a description of the functioning of a microbial community in terms of the fluxes through its members. We therefore advocate that flux analysis specialists from the fields of biotechnology, microbial physiology, and systems biology team up with microbial ecologists, as they increasingly do.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.


HEPNet is an electronic representation of metabolic reactions occurring within human cellular organization focusing on inflow and outflow of the energy currency ATP, GTP and other energy associated moieties. The backbone of HEPNet consists of primary bio-molecules such as carbohydrates, proteins and fats which ultimately constitute the chief source for the synthesis and obliteration of energy currencies in a cell. A series of biochemical pathways and reactions constituting the catabolism and anabolism of various metabolites are portrayed through cellular compartmentalization. The depicted pathways function synchronously toward an overarching goal of producing ATP and other energy associated moieties to bring into play a variety of cellular functions. HEPNet is manually curated with raw data from experiments and is also connected to KEGG and Reactome databases. This model has been validated by simulating it with physiological states like fasting, starvation, exercise and disease conditions like glycaemia, uremia and dihydrolipoamide dehydrogenase deficiency (DLDD). The results clearly indicate that ATP is the master regulator under different metabolic conditions and physiological states. The results also highlight that energy currencies play a minor role. However, the moiety creatine phosphate has a unique character, since it is a ready-made source of phosphoryl groups for the rapid synthesis of ATP from ADP. HEPNet provides a framework for further expanding the network diverse age groups of both the sexes, followed by the understanding of energetics in more complex metabolic pathways that are related to human disorders. This was followed by a large number of studies where metabolic models were reconstructed and used as a device to assess and understand different physiological conditions [A comprehensive knowledge of metabolism is fundamental to study and analyze the phenotypic and physiological attributes of all biological system . Normal nditions . Severalnditions . An illuBased on the central hypothesis of energy pool reactions, a comprehensive model of human energy metabolic pool was constructed at the cellular level using CellDesigner suite. On the basis of the information available in the public domain it was postulated to find a consensus of fundamental reactions taking place to maintain and modulate the production of ATP. The metabolic model was built by a bottom-up approach. A complete list of the reactions were assembled together and their mathematical expressions, developed [Table A in in silico and in vitro model layout, a redundant series of model building and hypothesis-driven simulation processes were employed. This was achieved using the Systems Biology Markup Language (SBML) to semantically represent the biochemical reactions in biological models [The model was semantically annotated as per the MIRIAM guidelines . To undel models . The usein vivo concentrations of metabolites in humans through which seven different conditions selected were tested for evaluation of the model. The first parameter that was tested was the glycaemic condition where concentration values were used for hypoglycaemic and hyperglycaemic conditions and variations were observed. The parameter to be tested was the starvation / fasting conditions and the variation in the energy curves were seen. The regulation of energy by the Creatine phosphate stands well demonstrated. Creatine phosphate is known for its energy buffer capability. In the muscle and the brain, Creatine phosphate acts as a rapid reservoir for ATPs and thus a reversible reaction catalyzed by phosphocreatine kinase even restores the excited state to a repository of ADPs. Moreover, the effects on the metabolic regulation during the period of exercise were analyzed. Additionally to check the workability of HEPNet, we studied two disease conditions, which are due to metabolic perturbations namely uremia and Dihydrolipoamide dehydrogenase deficiency(DLDD). The basis of uptake of different parameters was to study the effect on the central energy pool under various physiological and disease conditions. Also the physiological states of obesity, starvation and fasting have been implemented. The complete set of reactions can be found in Table H in Metabolic constraints affecting various conditions were studied. An extensive exploration was performed for the available All living cells require constant energy to sustain life processes. There is a constant bartering between demand and supply of energy under normal circumstances. Any system maintains the state of homeostasis i.e. total amount of energy remains constant. HEPNet  depicts The network consists of a total of 173 metabolic reactions including 4 compartments namely mitochondria, inner mitochondrial membrane, intra-mitochondrial space, outer mitochondrial membrane and 158 metabolites ranging from substrates to enzymes. The network model constructed using various components of CellDesigner 4.2  is annotA combination of tools is required to model a biological system mathematically . The proTime course simulation using COPASI was carried out for validating the different metabolic states and physiological conditions like glycaemic, uremic and DLDD, physical and feeding states and is included in Table B in Integrating w.r.t. xGlucose factor-Glucose factor is that parameter in the equation which is based on the Glucose concentration pertaining to hyper/hypo glycaemic condition. That is if we consider the rate of glucose:*Vdefault, a Km value of 0.048 is responsible. Under steady state condition, the elementary flux modes result can be found in Table A in Glucose factor is calculated by using the specific concentration of glucose where the other components of the equation remains constant and do not require to be changed.We see that it is being consumed as being denoted by the negative sign. Also, irrespective of the default flux value, Hypoglycaemic:Hyperglycaemic:Glucose factor in both the two states of glycaemia, it is well understandable that till a precision of 10–3 there is no change. But from 10–5 there are significant changes. This may sound that at such small levels of precision the equation does not change remarkably. But in actual physiological state, a minute change even in picomolar concentration may lead to severe glycaemic condition as we have can see through Comparing the Starvation was evaluated on the basis of the simplified ODEThe solution to the equation above obtained is“Starvation factor” is derived from the glucose metabolite and plays a key role. Apart from ODE in general, 6 reactions play a major role in starvation but it is the glucose whose limiting nature makes the study important. This distinguishes its role from that of the glycaemic study as we see the difference in both the factors.Considering the above equation which is logarithmic and also has an arbitrary constant C1, it is well clear that, a negative factor of -2.1586 plays the role in starvation. This constant value termed as Exercise was evaluated on the basis of the simplified ODEThe solution to the equation above obtained is“Exercise factor” is derived from the acetyl CoA metabolite and plays a key role. Apart from the ODE, in general, 16 reactions play a major role in starvation but it is the acetyl CoA whose limiting nature makes the study important.Considering the above equation which is logarithmic and also has an arbitrary constant C1, it is well clear that, a negative factor of -1.9976 plays the role in exercise. This constant value termed as Obesity was evaluated on the basis of the simplified ODEThe solution to the equation above obtained isConsidering the above equation which is logarithmic and also has an arbitrary constant C1, it is well clear that, a product of -2 plays the role in the obesity.“Obesity factor” is derived from the fact that triglycerides are stored in liver. Triglycerides are generated due to the presence of both glycerol-3-phosphate and fatty acids. The accumulation of triglycerides hence is responsible for obese condition. Only Re82 defines the behavior of the reaction and is responsible for obesity.This constant value termed as + was plotted simultaneously as shown in + and blue line denotes concentration change of NADH with respect to time in seconds. A change in concentrations of C22 trans-enoyl-CoA and C22 L3Hydroxy acyl-CoA as shown in A plot of dynamic simulation of the constructed model was performed showing comparative time course simulation in CellDesigner and COPASI. A plot showing concentration rates as a function of time was plotted using COPASI. From the graph as shown in + in agreement with the concentration increase of NADH depicts that, the concentration of NAD+ decreases with time (as shown in plot of NADH with time). Concentrations versus time plot of NADH and NAD+ were obtained in a single graph to study their correlation. Green line denotes NAD+ and blue line denotes concentration change of NADH with respect to time. The second step of beta-oxidation was studied, after the conversion of C22 acetyl-CoA to C22 trans-enoyl-CoA. A plot of change in concentrations of C22 trans-enoyl-CoA (blue) and C22 L3 hydroxy acyl-CoA (green) over period of time was generated. As a result of dynamic simulation it could be seen that, concentration of substrate decreases initially very fast but later equilibrium is attained and it is also notable that the product concentration increases with time. Scatter plots were generated as well, to gain insights into beta-oxidation of C22 acyl CoA, the reactions were in accordance with classical pathway. A scatter plot of C22 hydroxy acyl-CoA (x-axis) versus C22 trans-enoyl-CoA (y-axis) shows that these two have negative correlation. This is logically validated by the fact that with metabolic cycle progression concentration of C22 Trans-enoyl-CoA decreases whereas that of hydoxy-acyl-CoA increases [Comparative time course simulation plots [Table I in ncreases . Relatedncreases . The resncreases .DLD deficiency is an autosomal recessive metabolic disorder characterized biochemically by a combined deficiency of the branched-chain alpha-keto acid dehydrogenase complex, pyruvate dehydrogenase complex and alpha-ketoglutarate dehydrogenase complex .Change of succinyl CoA concentration with time. A simulation plot was generated depicting the change of succynl CoA (SCoA) in TCA cycle with respect to time as shown in (i) Simulated concentration of alpha-ketoglutarate as a function of time. A plot of simulated concentration of alpha-ketoglutarate (AKG) as a function of time shows an initial increase, as it acts as a substrate in the rate limiting step as shown in (ii) +, AKG and NADH.Correlation between NAD The plots of concentration as shown in + (purple), AKG (blue) and NADH (yellow). This integrated plot shows that rate of change of NADH with NAD+ and AKG. It clearly shows that rate of NADH formation depends upon AKG.(iii) Next, a plot as shown in To understand the effect of reduced AKGDHC on mitochondrial energy metabolism by TCA cycle, a comprehensive SBML model was generated. This model is advancement over the available models of TCA and can be used for studying the effect of AKGDH on the TCA cycle and its substrates. In agreement with the experimental findings, the model simulations confirm a decline in reaction fluxes and NADH level. The finding suggests that it is the rate limiting step of the TCA As has been indicated earlier. Since ATP production is also affected by NADH production rate it can be safely assumed that decrease in NADH also causes change in the rate of ATP production.Decrease in AKGDH also correlates with loss of glutamatergic neurons as seen in Alzheimer’s and Parkinson’s disease. The simulation suggests a deviations from normal course may lead to the discovery of steps responsible for the disease. Moreover, change in pyruvate concentration on changing the concentration of AKGDH also underpins the importance of the enzymes involved in DLDD. Simulations clearly indicate that AKGDH deficiency may cause increase in pyruvate concentration.In HEPNet we have made the steady state assumption. The modeled system has entered a steady state, where the concentration of metabolite no longer change, i.e. in each metabolite node the producing and consuming fluxes cancel each other out. The steady-state assumption reduces the system to a set of linear equations, which is then solved to find a flux distribution  that satIt is inferable that the flux decreases exponentially in the first 0.02 seconds from Several metabolic pathways suffer a setback due to lack of glucose leading to an imbalance in homeostasis although the rate is comparatively low in hypoglycemia.A remarkable inference to the creatine phosphate can be demonstrated from the flux generated. It is known that, creatine phosphate acts like an ATP reservoir and during the body’s need it gives ATP. Similarly, it also breaks to give creatine and return back ADP where the backward reaction is catalyzed by creatine phosphokinase. Upon observing the flux generated , we obseIn terms of an electronic outlook of the representation of HEPNet, manual curation is an added advantage. It can be subjected to plethora of automated simulation to study the effect of ATP generation/loss in a wide range of metabolic diseases and physiological states. For example, the amount of glucose consumed during exercise or starvation could be calculated. All the reactions are compartmentalized and hence the model will be useful in metabolic and metabolomic diagnostics. Its usage is vast and not limited to glycaemia or uremia but even open up dimensions to work upon metabolic biomarkers for the diagnosis of cancer. We envision developing the HEPNet version 2.0 where we intend to use it in case of acid lipase disease (error in fat digestion), Farber’s disease (storage of fats in joints) where a deterministic approach would be necessary. Hyperoxalourea or disease of the urea cycle can even be identified by the faulty flux behavior since HEPNet works on the basis of the energy pool. Another disease named the von Gierke’s disease affecting storage of Type I glycogen could be diagnosed and counter measures can be taken where HEPNet serves as a model for such case, ATP playing a major role.S1 DatasetTable A_HEPNet complete set of Reactions. Table B_HEPNet compartments. Table C_Condition based reactions. Table D_Classification and complete annotation of all specied used in HEPNet. Table E_concentration references and values of HEPNet. Table F_abbreviations used in HEPNet. Table G_HEPNet species km value chart. Table H_HEPNet complete set of Reactions. Table I_0.1 sec conc variation of subtrates. Table J_HEPNet categorised species.(ZIP)Click here for additional data file.S2 DatasetTable A_elementary mode of HEPNet. Equations A_Differential equations of HEPNet. Simulation A_ HEPNet at steady state. Table B_Time course simulation data. Model_HEPNet model in SBML format.(ZIP)Click here for additional data file.


Stoichiometric models provide a structural framework for analyzing steady-state cellular behavior. Models are developed either through augmentations of existing models or more recently through automatic reconstruction tools. There is currently no standardized practice or method for validating the properties of a model before placing it in the public domain. Considerable effort is often required to understand a model’s inconsistencies before its reuse within new research efforts.3, Model and Constraint Consistency Checker, a computational tool that can be used for two purposes: (a) identifying potential connectivity and topological issues for a given stoichiometric matrix, S, and (b) flagging issues that arise during constraint-based optimization. The MC3 tool includes three distinct checking components. The first examines the results of computing the basis for the null space for Sv = 0; the second uses connectivity analysis; and the third utilizes Flux Variability Analysis. MC3 takes as input a stoichiometric matrix and flux constraints, and generates a report summarizing issues.We present a review of common issues in stoichiometric models typically uncovered during pathway analysis and constraint-based optimization, and we detail succinct and efficient ways to find them. We present MC3 to published models for several systems including Escherichia coli, an adipocyte cell, a Chinese Hamster Ovary cell, and Leishmania major. Several issues with no prior documentation are identified. MC3 provides a standalone MATLAB-based comprehensive tool for model validation, a task currently performed either ad hoc or implemented in part within other computational tools.We report the results of applying MC Stoichiometric models play a fundamental role in the analysis and optimization of biochemical networks in Systems Biology and Metabolic Engineering, especially in the absence of detailed kinetic models. A stoichiometric model specifies the relative quantities of reactants and products for each reaction within a network. There are two fundamental and commonly used computational techniques that utilize stoichiometric models to elucidate steady-state function. The first technique is Elementary Flux Mode (EFM) analysis ,2, used E. coli organism that lead to improved predictive capabilities and elucidation of phenotypic behavior  for reversible reactions, and [0 1000] for irreversible ones. If the file type is ‘SBML’, then the remaining parameters are arrays containing the exchange reactions, external metabolites, and user-defined bounds. The exchange reactions are expressed as a single column. Each entry contains a reaction ID. The external metabolites are also expressed as a single column. Each entry contains a metabolite ID. The bonds are specified as they were for the xls’ case. All three parameters are optional.The main module of MCr ‘SBML’  dependinAn example of running mc_checkmodel with all checks for the SBML formatted model (Ec_iAF1260_flux1)  is provi = mc_checkmodel ;S matrix, and reaction and metabolite names. The example model, Ec_iAF1260_flux1, results in the report shown below.When the command finishes executing, the return elements  are arrays that contain indices of either metabolites or reactions that pertain to that check, or will be empty if that check did not return any results. The indices can be correlated with the SBML file by examining the struct that holds the Statistics:2382 reactions852 reversible reactions299 exchange reactions1668 metabolitesConnectivity Checks:87 Singly connected metabolites (SCM)118 dead-end metabolites (DEM)Basis-based checks:970 coupled reactions (CR)45 reversibly coupled reactions (RCR)FVA-based checks:184 zero-flux reactions (ZFR)420 unsatisfied reversibility (UR)The report has four sections. The first reports various statistics associated with the network and ensures that the whole network was read in. The second section reports the results of connectivity analysis. The third section reports the results from the analysis that used the basis vectors. In the last section, we report the results of FVA-based analysis.3 with other available tools, namely, the COBRA toolbox [3, CellNetAnalyzer and MetaNetX. Both MC3 and MetaNetX can find coupled reactions. All other discussed issues can only be identified using MC3. The comparison is summarized in Table We have compared the functionality of MC toolbox , CellNet toolbox  and Meta toolbox ,35. Whil3. The checked models included those of E.coli (3 different sizes) [L. major [3 checks for all conditions specified in section ‘Common Model issues’. A summary of the results is shown in Table We checked the consistency of some available models using MCt sizes) ,25,32, at sizes) , Chineset sizes) , and L. L. major . For eveE. coli central metabolic network [3 reports two dead-end metabolite (BIOMASS and ATP_main) and three related zero-flux reactions. In the supplementary section of the paper [3 as dead-end metabolites. Reactions directly connected to these metabolites are identified as zero-flux reactions.The  network , compose network  plus BIOhe paper , it is nE. coli model iJR904 [iJR904 are purposefully included for later amendments when more annotation data is available. MC3 identifies 67 dead-end metabolites and 150 zero-flux reactions in this network. The difference in the number of dead-end metabolites compared to the reported results is due to metabolites cardiolipin, lipopolysaccharide, and peptidoglycan. Each participates as a reactant in the biomass reaction.l iJR904  containsE. coli model iAF1260 [iJ904R. The model documentation  of the model. Validation of biological models will become more prominent in this field with its maturity, and with the increase use of automated reconstruction tools.It is important to realize that our tool (and others) can only validate a 3, a tool available for others to validate their model. The results of applying MC3 to several models have found some inconsistencies between the models and their respective published articles. It would be important for the community to have a standard method of documenting and reporting issues with each published models. The MC3 MATLAB files are available by contacting the authors or through GitHub at https://github.com/sohahassoun/mc3.While model and consistency constraint issues have been identified in various contexts, this article offers a review and detailed methodology for checking common issues. All checks are packaged within MCEFM: Elementary flux mode; CBM: Constraint-based modeling; FBA: Flux balance analysis; FVA: Flux-variability analysis; MC3: Model & constraint consistency checker; GLPK: GNU linear programming kit; SCM: Singly connected metabolite; DEM: Dead-end metabolite; ZFR: Zero flux reactions; UR: Unsatisfied reversibility; CR: Coupled reactions; RCR: Reversibly coupled reactions; CHO: Chinese hamster ovary.The authors declare that they have no competing interests.SH conceived the idea. MY, EU, and RS wrote and documented the code. MY and EU ran the test cases. Everyone contributed to the writing of the manuscript. SH and MY revised the document. All authors read and approved the final manuscript.


Genome-scale models require an objective function representing what an organism strives for. A method has been developed to infer this fundamental biological function from data.www.dx.doi.org/10.1186/s13059-016-0968-2Please see related Research article:  Reconstruction of the metabolic network in an organism of interest. Reconstruction consists of building the specific metabolic reactome and linking it to its encoding genes.Recasting of this biochemical, genetic and genomic information into a mathematical network. This model formulation process defines the constraints under which the network must operate.Formulation and application of an objective function to search through the network for the “best” solution to optimize the objective function. Application of an objective function is often necessary as metabolic networks inherently have multiple degrees of freedom and can possess non-unique solutions.Genome-scale models of metabolism appeared soon after the first genome sequences became available . MetabolTheodosius Dobzhansky famously wrote, “Nothing in biology makes sense except in the light of evolution” . The objIt is a grand challenge to determine what actual objective functions are. Two approaches have been used to elucidate appropriate objective functions. The first one is hypothesis based. For instance, the hypothesis that cells optimize their growth rate in nutritionally complete medium has been fairly revealing in studies of optimal metabolism in microorganisms , 4. In fThe second approach is to infer the objective function from observed cellular functions in their natural state. The initial constraint-based study of mammalian metabolism used experimental data to conclude that its observed state was most likely determined by minimizing formation of reactive oxygen species (ROS) . This inIn a study appearing in this issue, Danel Segré and colleagues further study the inference approach though the development of a method they call inverse flux-balance analysis (invFBA). Their goal is to address “…whether it is possible to use the flux balance framework to associate possible metabolic objective functions to a given measured set of genome-scale fluxes. In other words, we seek to understand whether it is possible to say that a given organism was optimized to favor some reactions at the expense of others” .Escherichia coli growing on different carbon sources. They show that if these flux states are fed to invFBA, it infers the growth rate objective functions accurately. However, the solution to an inverse problem is not unique and alternative objective functions can generate the same flux map. Using an “objective variability analysis” to search the range of alternative objective functions, the authors show that maximizing the substrate uptake rate represents an equivalent objective, based on the fixed metabolic flux state given to invFBA.The authors first perform a computationally based test of their method. They generate optimal growth solutions for a genome-scale model of Unlike computational solutions, actual data come with experimental error. The authors next examine the robustness of invFBA in the face of experimental error. They find that, as the magnitude of the noise increases, the performance of invFBA deteriorates, as expected, with a major downshift when the noise level is between 1 and 10 % relative to the flux norm.Shewanella oneidensis over a time-series, and E. coli strains evolved for over 50,000 generations. For the first case, they find that invFBA was able to capture trends in secretion and update of exchanged metabolite fluxes for pyruvate, glycolate, and acetate in S. oneidensis. Furthermore, it was determined that biomass production was the likely objective function during the experiment at the different time steps. For the second case, examining evolved cell lines, invFBA was used to understand the tradeoff between two specific “biologically interesting fluxes” from the evolved cell lines—growth versus respiration flux. The algorithm was able to link high-acetate-producing cell lines to a low respiratory objective, and vice versa, providing a link between correlated pathways for the observed phenotypes.The authors apply invFBA to two experimental situations: data generated in their lab for The majority of published studies use the growth rate  equation as an appropriate objective function. However, there are many situations of interest where the primary function of the cell being analyzed is not growth. Such situations include the homeostatic functions of human cells in tissues, the metabolic function of the mitochondria or chloroplasts, or microbial cells in a biofilm community. The invFBA approach might be able to analyze such circumstances and provide novel insights into their cellular physiology.13C-labeled experiments that are used to measure experimental fluxes generate relatively few flux values, and, in fact, often reduced-stoichiometric models are used to compute some of these fluxes. Thus, further development of inverse methods might follow that make optimal use of the available fragmented experimental data. Together, such efforts move us closer to the goal of being able to determine objective functions based on experimentation and yield a realistic understanding of perhaps the most fundamental of all biological  functions.The invFBA method represents progress towards the important goal of inferring objective functions from experimental data, although, as the authors state, significant challenges remain. Perhaps the major hurdle is to generate data sets large enough to fully implement invFBA. The