Streptomyces albus J1074 is recognized as an effective host for heterologous production of natural products. Its fast growth and efficient genetic toolbox due to a naturally minimized genome have contributed towards its advantage in expressing biosynthetic pathways for a diverse repertoire of products such as antibiotics and flavonoids. In order to develop precise model-driven engineering strategies for de novo production of natural products, a genome-scale metabolic model (GEM) was reconstructed for the microorganism based on protein homology to model species Streptomyces coelicolor while drawing annotated data from databases and literature for further curation. To demonstrate its capabilities, the Salb-GEM was used to predict overexpression targets for desirable compounds using flux scanning with enforced objective function (FSEOF). Salb-GEM was also utilized to investigate the effect of a minimized genome on metabolic gene essentialities in comparison to another Streptomyces species, S. coelicolor. Streptomyces albus J1074 is commonly utilized as a microbial host for the heterologous production of bioactive natural products and secondary metabolites [S. albus in biotechnological applications are its fast growth and an efficient genetic toolbox, which have proven it advantageous as a platform for product discovery and heterologous production [S. albus J1074 was initially isolated as a derivative of the S. albus strain G defective in the SalI restriction-modification system [The use of actinomycete microbial cell factories has been paramount to the industrialization of bioactive compounds. Possessing all the essential metabolic components and biosynthetic machinery required for their production and proper modification , actinomycetes produce among the most diverse array of compounds ,2,3. Witabolites . Two main system , which eS. albus J1074  to facilitate production of valuable compounds. The strain has been used for the heterologous expression of secondary biosynthetic gene clusters (BGC) taken from both Streptomyces and non-genus species such as the thiocoraline BGC from marine Micromonospora [S. albus has been shown to harbor 22 BGCs, but clusters mostly remain cryptic  across all stages of its growth in conventional liquid media [S. albus, paulomycins are the only identified antibacterial compounds and their production remains highly unstable [S. albus have been constructed with their native biosynthetic gene clusters removed [S. albus strain and other S. coelicolor hosts. S. albus has been used to heterologously produce natural products including various types of flavonoids [S. albus has been demonstrated to produce the flavonols myricetin, kaempferol and quercetin more efficiently than S. coelicolor [There have been numerous endeavors to engineer onospora . S. albuid media ,12. Of tunstable ,14,15,16unstable . Recentlunstable , which wavonoids , and S. elicolor .S. albus, there persists a lack of knowledge on how to best engineer the microbial host through a holistic approach. In order to glean a systems-level understanding of the metabolic potential of S. albus, a mathematical model of the organism metabolism can be developed and utilized. A genome-scale metabolic model (GEM) is a network-wide representation of the metabolism of the cell or microorganism [However, despite the numerous studies on organism ,22. GEMsS. albus as a chassis for heterologous compound production, understanding its capabilities and metabolism at the systems-wide level will yield insights by both integrating the current knowledge of the organism and informing new design strategies. To this end, the first GEM for S. albus J1074—herein denoted as Salb-GEM—was developed using Sco-GEM [S. coelicolor  as a template. In order to establish the use of this metabolic network reconstruction in metabolic engineering, this study assesses its capabilities relative to its reference model developed for S. coelicolor and demonstrates its applications in predicting gene targets for overproduction of target compounds. In order to further drive the engineering of  Sco-GEM , a high-Salb-GEM is based on the genome sequence of S. albus strain J1074. The reconstruction steps  between S. albus and S. coelicolor [Sco-GEM to form the initial draft network reconstruction of Salb-GEM. At this stage, 1645 metabolic reactions associated with 1278 genes were included into the initial model.To first reconstruct the components of metabolism conserved among actinomycetes  or more nsus GEM  of S. coelicolor , a set oSco-GEM to the draft model. Among these were exchange reactions and pseudo-reactions that contribute towards the representation of biomass within the model. Any reactions from this particular step that were disconnected from the remainder of the metabolic network were subsequently checked for and removed.Subsequently, transport and spontaneous reactions with no specified gene associations were transferred from Streptomyces involves the unique thiol mycothiol, and would therefore logically be part of the metabolic network reconstruction. However, the gene responsible for the enzymatic activity has not yet been experimentally verified and therefore remains in the model without gene association. A vast majority of these non-gene associated reactions that were added to the model were involved in lipid biosynthesis and fatty acid metabolism with multiple reactions corresponding to different levels of fatty acid chain saturation. In addition, the gap-filling identified reactions that were not captured in the first reconstruction steps, such as ATP synthase, as the stringent BLASTp parameters prevented matching of any subunits that were below the minimum length assigned. The resulting draft model was thereby able to produce all required biomass precursors.The resulting model remained unable to support growth via production of biomass. Consequently, gap-filling was implemented using the RAVEN toolbox, where a minimal number of reactions was transferred from the template model to enable the production of biomass components. From this step, an additional 18 genes and 119 reactions were incorporated into the model. A significant portion of these reactions did not have any explicit gene associations in the template model and were, therefore, not considered in the earlier semi-automated reconstruction steps. For example, mycothiol reductase is an essential reaction in thiol redox metabolism, which in S. albus were incorporated in the model, thereby differentiating it from existing Streptomyces models. While there is little detailed and extensive knowledge of S. albus specific pathways available in literature, we applied an approach where hidden Markov models (HMMs) trained on the KEGG database [S. albus proteins, and reactions associated with genes that were not already included in the draft model were thereby introduced. Through this process, 104 genes associated with 107 reactions were added to the metabolic network reconstruction. Although it is imperative for the GEM to provide a description of metabolism that is as comprehensive as possible, the majority of secondary metabolites and their associated pathways in S. albus remain relatively uncharacterized. While sequencing of the genome has revealed 22 BGCs, many of these clusters remain cryptic, typically silenced in conventional laboratory growth conditions [Following generation of the draft model, reactions and pathways specific to database  were usenditions ,7. As a S. albus produces the glycosylated antibiotics paulomycin A, B and E from activity of the paulomycin BGC. The pathway has been investigated by inactivation of genes encoding various enzymes, which are mainly involved in either transfer of glycosyl/acyl moieties or the biosynthesis of paulic acid and paulomycose. The study by Gonzalez et al. [Nonetheless, there have been experimental studies on the paulomycin BGC ,28 that z et al.  has enabSalb-GEM comprising 2231 metabolic reactions, 1872 metabolites and 1381 genes ), enabling open and reproducible curation and development, and allowing the issue of updated releases.These various reconstruction steps culminated in the genome-scale model 81 genes . The modSalb-GEM, 126 reactions, 112 metabolites and 120 genes were exclusive to S. albus  as they were drawn from KEGG and manual curation of secondary metabolite pathways , indicating an anticipated significant overlap of metabolic pathways but also species-specific functionality. Within Streptomyces species [Salb-GEM were part of the Streptomyces accessory genome. While the core genome denotes the portion of genes conserved among the 17 Streptomyces species, the accessory genome consists of genes whose presence differs considerably among Streptomyces species and confers upon them various advantageous traits to their environmental niches, generally providing functions that were not necessarily essential for viability. These 561 genes are associated to 729 reactions, with a majority of these reactions involved in secondary metabolism. With Salb-GEM containing a large fraction of accessory genes, it comprises substantially more than merely the conserved core metabolic pathways of Streptomyces but also acknowledges the diversity across species [When referencing the pan-genome established for 17  species , 561 of  species .S. albus, while cellular DNA and protein content was measured as 0.035 and 21.95 (g/gDW), respectively, from an S. albus cultivation described below. However, to date no information is available on the contribution of other components to S. albus biomass including the composition of carbohydrate, lipid and any miscellaneous components that would need to be measured in relation to the total mass of the cell (as % of cell dry weight) before inclusion in the biomass reactions. Consequently, these macromolecular components of the biomass were assumed to be identical with S. coelicolor and therefore inferred from the Sco-GEM model. In addition to the inclusion of metabolic reactions, some of the macromolecule components  of the biomass reactions were successfully tailored based on the available genome and proteome of S. albus [S. albus strain J1074 was performed, where glucose and biomass concentrations were monitored over 72 h  and non-growth associated maintenance (NGAM) can be fitted. While the exact distribution of energy costs across GAEC and NGAM could not be determined with the currently available experimental data, we were able to determine which combination of these energetic parameters result in the observed growth rate  relative to the latter at a coverage of 22.9% (with 1777 genes), indicating the genome reduction in S. albus is not differentially affecting the number of metabolic genes. With regards to pathways that have been annotated in the model, Salb-GEM has demonstrably less reactions related to carbohydrate metabolism and secondary metabolic pathways but more so in relation to lipid metabolism.However, S. albus has been remarked for its tendency to reduce the number of gene paralogues [Salb-GEM and Sco-GEM, and this revealed that Salb-GEM only has marginally more essential genes (185) than Sco-GEM (180) when set to grow on glucose minimal media, seemingly contradicting the reduced paralogues postulation. While a majority of the essential genes were associated with a common set of reactions in both organisms, certain genes were predicted to be uniquely essential for each organism, and their associated reactions were in distinct pathways  while the corresponding reaction relates to at least one paralogue in Sco-GEM. For instance, Salb-GEM possesses no paralogues for the 3-oxoacyl-(acyl carrier protein) synthase (XNR_4509), an important component responsible for the chain elongation step in fatty acid biosynthesis, but the same reaction in Sco-GEM is associated to four isozymes . This gene alone is associated with 41 distinct metabolic reactions as each reaction corresponds to various degrees of saturation on the acyl moiety. Another example of differences in absence of paralogues is observed towards the end of the shikimate pathway, where the metabolic reactions mediated by 5-enolpyruvylshikimate-3-phosphate synthase, chorismate mutase, prephenate dehydrogenase and anthranilate phosphoribosyltransferase were associated with single genes in Salb-GEM unlike in Sco-GEM. Conversely, a total of 11 essential genes in Sco-GEM  through manual curation [It is important to note that the biomass representation in curation .S. albus is used for production of endogenous and heterologous compounds, it would be imperative for Salb-GEM to be able be used to design genetic strategies to improve productivity. Therefore, we applied flux scanning with enforced objective function (FSEOF) [slope in the FSEOF analysis (As  (FSEOF) , an algoanalysis , is indiS. albus for FSEOF analysis, namely paulomycin, antimycin and candicidin, in addition to two heterologous natural products, namely the thiodepsipeptide thiocoraline [Micronospora actinomycetes and naringenin, a flavanone from which can be derived a majority of flavonoid compounds [To query a range of potential products, we selected three compounds related to the endogenous BGCs in coraline  originatompounds .When considering the various genetic targets that were predicted by FSEOF to increase productivity, subsets of various common genes were predicted for different combinations of the five endogenous and heterologous compounds. Ten genetic targets were identified as positively affecting all product compounds, of which seven targets covered the majority of the shikimate pathway , and the remaining three targets were associated with the pentose phosphate pathway. It is worth to note that the three reactions of the pentose phosphate pathway are responsible for the availability of erythrose 4-phosphate, which along with phosphoenolpyruvate from the glycolytic pathway is the direct precursor to the first metabolic reaction step of the shikimate pathway via the 3-deoxy-D-arabino-heptulosonate 7-phosphate synthetase.Considering the structure of each target compound a, which In addition, significant overlap across multiple compounds could be observed as genetic targets that function in fatty acid biosynthesis. The production of paulomycin, naringenin and candicidin which draw fatty acyl-CoA precursors  from primary metabolism, would benefit from the overexpression of fatty acid biosynthetic genes. This can likely be further extrapolated to all polyketide secondary metabolites that draw heavily from these precursors. In the case of naringenin and candicidin, which both utilize malonyl-CoA as precursor, among the overexpression targets carrying the most flux was acetyl-CoA carboxylase, a reaction that converts acetyl-CoA to malonyl-CoA by condensation ,36. IndeWhile the targets share many common reactions in the shikimate pathway and fatty acid biosynthesis, there is also a myriad of unique targets that differ starkly in regard to their associated pathways such as the previously mentioned overexpression of prephenate dehydrogenase (XNR_5061) to convert chorismate to L-tyrosine, a precursor leading to naringenin. With regards to another instance, in order to augment the availability of the L-paulomycose moiety on the basic paulomycin structure, many suggested targets originate from purine and pyrimidine metabolism. (R)-Methylmalonyl-CoA CoA-carbonylmutase (XNR_4666) and methylmalonyl-CoA epimerase (XNR_1439) are beneficial enzymes to overexpress.For other compounds such as thiocoraline that draw heavily from L-cysteine as a building block, suggested targets also encompass cysteine and sulfur metabolism such as sulfate adenyltransferase (XNR_0714 and XNR_0715) and adenylyl-sulfate kinase (XNR_0713). Other compounds that are produced from endogenous BGCs such as candicidin also reflect the role that fatty acid precursors have in limiting overall yields. For instance, in order to improve precursor flux towards candicidin biosynthesis, the S. albus. Interestingly, the overexpression of acetyl-CoA carboxylase, beneficial for both naringenin and candicidin production according Salb-GEM, has been investigated in S. albus for increased production of the flavonol myricetin, which has naringenin as a precursor. Subunits of the acetyl-CoA carboxylase complex from S. coelicolor were heterologously expressed in S. albus [Escherichia coli, coding for chorismate synthase/prephenate dehydrogenase (CHORM and PPND) and 3-deoxy-D-arabino-heptulosonate 7-phosphate synthetase (DDPA), yielded increased naringenin production [Salb-GEM indeed provides effective strategies to facilitate precursor flux from primary metabolism, an important limitation remains the limited detailed information that is available of the heterologous pathway themselves, precluding inclusion in the model.Of the various predicted overexpression targets, few have been reportedly tested to increase production formation in S. albus . As the oduction . While FS. albus J1074 was based on published genome annotation  and carried out using the RAVEN Toolbox [S. coelicolor, Sco-GEM [getModelFromHomology, which utilizes the data structure from a bi-directional homology search via BLASTp and assigns the best-fitting GPRs using the following parameters as cut-offs: a maximum E-value of 10−50, a minimum alignment length of 90 residues and a minimum identity of 40%. These values for the parameters have been selected in order to incorporate the reactions essential for various growth phenotypes and minimize the number of reactions added by the gap-filling process in later steps. Any spontaneous reactions or transport reactions with no gene-association were also imported from the Sco-GEM template model.The genome-scale metabolic network reconstruction for  Toolbox ,25. By r Sco-GEM , as a teS. albus, it was assumed that these would not deviate drastically from S. coelicolor. Therefore, the storage carbohydrate, cell wall and lipid components of the biomass reaction were taken from Sco-GEM, while the stoichiometric coefficients of ribonucleotides, nucleotides and amino acids were inferred from the S. albus genome and coding sequences. The DNA and protein content were determined from cultivations reported in this work, while also the energetic parameters GAEC and NGAM were taken from these. While the experimental data only allowed for determining the sum of GAEC and NGAM, the NGAM was set at 6.86 mmol/gDCW/h in agreement with the model prokaryotic GEM of Escherichia coli, resulting with a GAEC of 173 mmol/gDCW.Where no experimental data was available for biomass components in fillGaps to retrieve the minimum set of reactions from Sco-GEM to ensure that the model can grow in silico. After the initial gap-filling, the model was evaluated for growth solely on other carbon sources . For substrates that are known to support S. albus growth but the phenotype with which could not be replicated in silico, the minimum number of reactions were added from the template model to support utilization of the designated substrate. For latter substrates, manual gap-filling was performed by adding reactions that carried flux in Sco-GEM solely utilizing the corresponding substrates to the draft model; any new reactions that did not carry flux in the model were subsequently removed. Additional reactions were incorporated from another draft model generated from KEGG via RAVEN function getKEGGModelForOrganism, which utilizes HMMER in homology search and queries the S. albus proteome against KEGG orthology (KO)-trained hidden Markov models (HMMs). The additional reactions were checked to not be associated with any genes already included in the previous draft model.To yield a functional model, gap-filling was performed using RAVEN function Reactions added from this and later steps were subsequently curated for directionality. eQuilibrator  was usedSalb-GEM is reproducibly tracked and freely available from https://www.github.com/SysBioChalmers/Salb-GEM (accessed on 21 April 2021), and archived on Zenodo (https://doi.org/10.5281/zenodo.3693405 (accessed on 21 April 2021)). The model is versioned, and release 1.0.1 was used in the analyses presented here. The model is distributed in SBML L3V1 FBCv2 format, while an overview of the reactions in version 1.0.1 is also shown in The development and curation of , which calculates the flow, or flux, of metabolites through the metabolic network, enabling prediction of an organism’s growth rate or production rate of a desired metabolite.Within the feasible solution space at steady-state, it is possible to further identify specific points  that satisfy certain conditions specified as objective functions to be either maximized or minimized. In most cases, this objective function is based on the biomass reaction representing the organism’s main goal to grow as fast as possible. A commonly used mathematical method to analyze metabolic network reconstructions is flux balance analysis (FBA)singleGeneDeletion function on COBRA Toolbox [Gene essentiality analysis was carried out using the  Toolbox . EssentiPotential targets for metabolic engineering towards improved yield of natural products were predicted by using flux scanning with enforced objective function (FSEOF) . The metS. albus J1074 were grown in shake flasks with 100 mL of NL333 medium [8 CFU/mL. Samples were taken every 6 h for glucose concentrations as determined using glucose oxidase colorometric assay  following manufacturer’s instructions; biomass determined as dry cell weight, protein content by Bradford assay as previously described [Triplicate cultures of 3 medium  over a described  and DNA escribed .Streptomyces albus J1074, which can be used in constraint-based analysis. We demonstrated utility of the model in identifying sets of shared targets that may be tested to improve endogenous and heterologous production in S. albus. Additionally, we have used the model to glean insights into the effect of the S. albus minimal genome on its metabolism, comparing the existence of paralogues between S. albus and S. coelicolor and the resulting impact on gene essentiality. The Salb-GEM model was able to provide realistic growth predictions in comparison with experimentally measured growth and glucose consumption rates. However, the model would benefit from a more detailed description of the S. albus biomass composition, evidence of gene essentiality and general fermentation data. When such relevant experimental data will become available, the model can readily be curated and further improved. Open and reproducible model curation and distribution of an updated model are facilitated by continually hosting the model on GitHub ), where the research community can transparently reference, reproduce and contribute to the model curation and development.Here we present the first genome-scale metabolic model (GEM) for


Escherichia coli, we consolidated a coarse-grained protein allocation approach with the explicit consideration of enzymatic constraints on reaction fluxes. Besides representing physiologically relevant wild-type phenotypes and flux distributions, the resulting protein allocation model (PAM) advances the predictability of the metabolic responses to genetic perturbations. A main driver of mutant phenotypes was ascribed to inherited regulation patterns in protein distribution among metabolic enzymes. Moreover, the PAM correctly reflected metabolic responses to an augmented protein burden imposed by the heterologous expression of green fluorescent protein. In summary, we were able to model the effects of important and frequently applied metabolic engineering approaches on microbial metabolism. Therefore, we want to promote the integration of protein allocation constraints into classical constraint-based models to foster their predictive capabilities and application for strain analysis and engineering purposes.It is generally recognized that proteins constitute the key cellular component in shaping microbial phenotypes. Due to limited cellular resources and space, optimal allocation of proteins is crucial for microbes to facilitate maximum proliferation rates while allowing a flexible response to environmental changes. To account for the growth condition-dependent proteome in the constraint-based metabolic modeling of IMPORTANCE Predictive metabolic models are important, e.g., for generating biological knowledge and designing microbes with superior performance for target compound production. Yet today’s whole-cell models either show insufficient predictive capabilities or are computationally too expensive to be applied to metabolic engineering purposes. By linking the inherent genotype-phenotype relationship to a complete representation of the proteome, the PAM advances the accuracy of simulated phenotypes and intracellular flux distributions of E. coli. Being equally computationally lightweight as classical stoichiometric models and allowing for the application of established in silico tools, the PAM and related simulation approaches will foster the use of a model-driven metabolic research. Applications range from the investigation of mechanisms of microbial evolution to the determination of optimal strain design strategies in metabolic engineering, thus supporting basic scientists and engineers alike. For many decades, metabolic models have been developed to describe, unravel, and understand the drivers of microbial phenotypes. In their simplest forms, these models quantitatively connect observable phenomena such as carbon source consumption and biomass formation, leading to seminal empirical growth laws such as the Monod equation . In gene2–8–15–19–ad hoc capacity bounds on key reactions  models couple metabolism to gene expression by linking enzyme concentrations to metabolic reactions and accounting for the transcriptional and translational processes leading to enzyme expression  represents the major protein sectors and their various ratios with changing growth conditions E. coli KiML1515 model in a GECKO fashion  to arrive at model-relevant mass units relative to the cell dry weight (cdw) , is allocated to the three protein sectors, that is, the active enzymes, unused enzymes, and translational protein sectors  and other established constraint-based modeling approaches can be applied to the PAM without a significant loss in computation speed compared to purely stoichiometric models.Here, −1, which supported an observed maximal growth rate of 0.65 h−1  is accelerated to compensate for the carbon loss toward acetate.In the vicinity of the turning point from a fully respiratory to partially fermentative metabolism, the activity of the GLYXS diminishes completely. Beyond glucose uptake rates of 4.3 mmol E. coli is neither stoichiometry nor protein allocation. As we will show in the next section, maximal growth rates may be attributed to a limited, maximum molar protein synthesis rate, thus indicating transcriptional restrictions as the determining growth-limiting factor.The PAM’s stoichiometric and protein allocation constraints support feasible growth states beyond the assumed maximum glucose uptake rate . HoweverE. coli, its metabolism and regulation are adapted for an effective glucose utilization, which led us to assume that there are no unused enzymes under glucose-excess conditions. However, it is reasonable to assume that such a state of adaption does not hold for alternative carbon sources. Thus, experimentally observed substrate uptake rates may not reflect growth states with (near-)zero unused enzymes. To enable the PAM to simulate growth on alternative carbon sources without the need for cultivation data, we approximated maximum substrate uptake rates assuming a maximum total protein synthesis rate NP,max. NP,max represents a global cellular constraint for protein biosynthesis, applicable for any substrate. It manifests at the maximum substrate uptake rate and therefore at maximum growth at which the unused enzyme sector approaches zero. In the PAM, NP,max represents the sum of molar synthesis rates of proteins from the active enzymes and the translational sectors.Since glucose is the preferred carbon source of E. coli grown on several substrates  to glucose during its import, thereby producing glucose-6-phosphate and pyruvate. The omission of this alternative uptake system necessitates an elevated pyruvate kinase flux to balance PEP. In traditional 13C-based metabolic flux analysis, glucose uptake via the PTS and the ABC transporter cannot be dissected, as they do not affect the 13C isotope patterns of metabolites. It is therefore common to incorporate only one pathway in these models.By exploiting the optimality principles of microbial growth, GEMs give quantitative insights into the intracellular flux distribution and pathway usage, based purely on stoichiometric constraints. For a particular environmental condition of interest, the prediction accuracy of the stoichiometric GEM generally scales with the amount and accuracy of experimental data introduced to the model in the form of flux constraints. With a minimum need for such data, i.e., the substrate uptake rate, the PAM allows for an accurate blueprint of the intracellular metabolic processes. A comparison with fluxomics data from multiple studies shows that flux distributions of the central carbon metabolism of  to 0.97 . Here, t to 0.97 , 63  but intermediate to weak predictions, e.g., for fructose or gluconate (r > 0.65). In the case of gluconate consumption, the Entner-Doudoroff (ED) pathway was experimentally observed to be the main catabolic route, whereas the simulated carbon flux was exclusively channeled toward pyruvate through the pentose phosphate (PP) pathway. The flux split between the PP and ED pathways is highly sensitive to the ratio in the protein demands of both pathways (data not shown). Consequently, inconsistencies in the applied kcat values, particularly of backward reactions, but also the substrate-dependent differences in the biomass compositions  and compared relative growth rates with experimental data from Bienick et al. . For theg gcdw−1 . The useenotypes .Interestingly, the relation between eGFP expression strength and growth predicted by the PAM is nonlinear, which contrasts with a previous theoretical postulation . The nonE. coli.The PAM also discloses relevant effects of the protein drain on the pathway flux level. For an increasing eGFP expression strength and the accompanied protein deficiency, central carbon fluxes are progressively diverted to fermentation pathways (acetate secretion) and eventually to the ED pathway. Both routes are more protein efficient but yield fewer energy equivalents per substrate molecule than respiration or the EMP pathway , 65, 66.10.1128/mSystems.00625-20.4FIG S3−1. Download FIG S3, EPS file, 0.1 MB.Simulated ratio of ATP generated via respiration and the total ATP generation rate for a range of eGFP concentrations. The flux through the ATP synthase was used as the respiratory ATP generation rate. Growth rates relative to the growth rate at zero eGFP expression are additionally shown. The presented data are based on growth-optimal solutions of the PAM applying a total protein mass concentration of 0.31 g Copyright © 2021 Alter et al.2021Alter et al.https://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the Alongside the over- and heterologous expression of genes, rearrangement of metabolic networks and flux distributions by gene deletions is a core instrument in metabolic engineering. In recent years, many computational strain design methods have been developed to accelerate and rationalize the engineering of microbial cell factories. However, in contrast to the vast number of model-driven strain design and optimization methods , constra69–−1. The calculated phenotypes did not significantly differ from the unperturbed wild-type solutions and, hence, did not compare to experimental data   , regulatRELATCH) , which dNe between a reference, wild-type state at maximum growth and a mutant state is calculated for each enzyme within the PAM. The GMS’s maximum substrate uptake rate is determined from the flux distribution for which ΔNe meets a defined upper bound We applied the minimal response principle to the PAM for mutant phenotype predictions, and we simulated growth optimal flux distributions for a range of substrate uptake rates . For each flux distribution, the difference in the synthesis rate Δrbations , 75. The−1. r = 0.81, P = 7.76 × 10–11). By disregarding the Δrpe deletion mutant, the Pearson correlation improves to r = 0.97 with a P value of 1.5 × 10–23. For the omitted outlier, simulations show a near-wild-type behavior, whereas growth is significantly reduced in the experiment. The in vivo observed growth defect of the Δrpe GMS is peculiar since knockouts of enzymes adjacent to ribulose-phosphate 3-epimerase, such as gnd, do not show a similar phenotype. Even though the gene products of gnd and rpe catalyze consecutive reactions transforming 6-phospho-d-gluconate to d-xylulose 5-phosphate, an important intermediate in the PP pathway, deletion of gnd has a significantly smaller effect on growth, as does the deletion of rpe. Moreover, the experimentally determined phenotype of a Δrpe GMS from reference E. coli strain and thus obscures a plausible judgment of the simulated phenotype.70–r > 0.93, for all tested single deletions, except for the ΔtpiA mutant (r = 0.67). For the ΔtpiA GMS, the experimentally observed rerouting of the glycolytic flux through the methylglyoxal pathway toward pyruvate  (gnd mutant were deteriorated (r = 0.95). Here, flux was shifted from the ED pathway toward glycolysis, which contradicts experimental data. Nevertheless, the kcat value adaption only slightly lessened the PAM’s overall predictive capabilities  . The prepyruvate , 78 contecretion . This sectively) . Howeverbilities  and thus10.1128/mSystems.00625-20.7FIG S6kcat values for the two central ED pathway steps compared to experimental observations. Experimentally determined growth, glucose uptake, and acetate secretion rates were taken from Long et al. , g et al.  (green),g et al.  (red). ACopyright © 2021 Alter et al.2021Alter et al.https://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the 10.1128/mSystems.00625-20.8FIG S7kcat values for the two central ED pathway steps compared to experimental observations. Experimentally determined intracellular flux rates were taken from Long and Antoniewicz    suggest cription . We intrE. coli regulates central cellular processes to maintain a Pareto-optimum between growth rate and the ability to adapt its metabolism flexibly to changing environmental conditions. The degree of flexibility is directly linked to the amount of allocated unused enzymes, which is hard-coded in the PAM. Interestingly, the cell retains a strictly substrate uptake-orientated allocation of protein to the unused enzyme sector even when protein becomes a metabolically limiting factor, apparent from the onset of overflow metabolism. This preservation of flexibility could allow for an evolutionary advantage in the original environmental niche. However, it may be a promising target for engineering E. coli or any microbe toward a high-performance cell factory.By recognizing transcriptional limitations as hard constraints for the microbial metabolism and recalling that the presented PAM predictions represent growth optimal flux states, we deduce a cellular principle, which is supported by previous findings ; particuRecently, systems metabolic engineering was emphasized as an integral part of the development and optimization of microbial cell factories , 80–83. 80–In summary, we want to stress the importance of protein allocation constraints in GEMs for the systematic constraint-based reconstruction and analysis (COBRA) and the design of microbial metabolism without having to sacrifice computational speed or applicability of established COBRA methods . HoweverE. coli K-12 MG1655 GEM iML1515 reconstruction  is based on the truction . It inclϕT and the growth rate μ , and therefore at zero growth, the sum of unused enzymes and translational protein ϕUE,0 + ϕT,0 is 0.22 g νS = 0 the PAM explains only a fraction (84%) of the total protein mass concentration ϕP,c which is, however, assumed to be constant under any given condition. We expect this discrepancy to be caused by deviations from an otherwise constant total protein household in severely starving cells or specific protein requirements during non-growth conditions. The fraction not explained by the PAM is compensated for by nonphysiological, random activation of metabolic fluxes when calculating growth-optimal solutions near substrate uptake rates of zero. Thus, the PAM may produce feasible solutions at low metabolic activity but hardly represent physiologically relevant flux states.An evolutionary characteristic of microbes facing unforeseeable changes in environmental conditions is the synthesis of unused proteins. This protein hedging empowers the cell to quickly increase central carbon metabolism fluxes upon a sudden increase in substrate availability or to immediately catabolize a new carbon source . Enzyme  enzymes , resultiwUE is a measure of the increase in enzyme usage efficiency with increasing substrate uptake rate. It is individually assigned for each substrate under the assumption that the unused enzyme concentration is zero at the maximum substrate uptake rate. Thus, wUE is calculated fromThe slope The maximum substrate uptake rate iML1515 according to the GECKO framework  Curated enzymatic data used to build the protein allocation model  in vivo turnover numbers kapp . Thus, it appears that the ratio of kcat values between different reactions or pathways is an essential factor for the predictive capability of PAMs in general.The manual curation effort transformed the primary ers kapp , 93, reltic data . Interesated set , simulat10.1128/mSystems.00625-20.9FIG S8kcat (in vitro curated) and kapp,max (machine learning [ML] model) values. kcat values are curated data extracted from the BRENDA, SABIO-RK, and UniProt databases, whereas kapp,max values were taken from Heckmann et al.  Relative fraction (A), cumulative distribution (B), and direct comparison (C) of n et al. . The greCopyright © 2021 Alter et al.2021Alter et al.https://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the The experimental proteomic data set generated by Schmidt et al.  was usedϕP is the intracellular concentration  relation, is assigned to precisely one protein with a unique turnover number kcat,e and molar mass Me. In case a reaction e is catalyzed by an enzyme complex , the molar mass Me is the sum of molar masses of the participating gene products. If two or more enzymes can catalyze the same reaction independently from each other , the isozymes are merged into one hypothetical protein with a molar mass equal to the mean of the molar masses of the merged isozymes. Molar masses of enzymes were calculated as the sum of molar masses of the amino acids constituting the respective primary sequences reduced by the mass of one water molecule per peptide bond. The amino acid sequences were retrieved from the KEGG database  leading to NP,max by applying the experimentally observed substrate uptake rate (constraint) were extracted and are shown in To test this hypothesis, we simulated a et al.  using PA4 g mol−1. Thus, the expression strength of eGFP .All conducted simulations, model reconstructions, and data analyses were performed in MATLAB 2018a on a Windows 7 machine with 16 GB of RAM and an AMD FX-8350 eight-core (at 4.00 GHz) processor. COBRA toolbox functions  and the


Arabidopsis thaliana seed development. Through in silico perturbation of genes, targets were predicted in seed oil traits. Validation and supporting evidence were obtained for several of these predictions using published reports in the scientific literature. Furthermore, we investigated two predicted targets using omics datasets for both gene expression and metabolites from the seed embryo, and demonstrated the applicability of this network-based model. This work highlights that integration of dynamic gene expression atlases generates informative models which can be explored to dissect metabolic pathways and lead to the identification of causal genes associated with seed oil traits.Fatty acids in crop seeds are a major source for both vegetable oils and industrial applications. Genetic improvement of fatty acid composition and oil content is critical to meet the current and future demands of plant-based renewable seed oils. Addressing this challenge can be approached by network modeling to capture key contributors of seed metabolism and to identify underpinning genetic targets for engineering the traits associated with seed oil composition and content. Here, we present a dynamic model, using an Ordinary Differential Equations model and integrated time-course gene expression data, to describe metabolic networks during  Fatty acids (FAs) in crop seeds are a major source for human nutrition and potential biodiesel fuels . During in silico analysis and machine learning was recently conducted in tomato, displaying the potential of artificial intelligence in model simulation of metabolic networks  model of the metabolic networks representing the major seed development biochemical pathways in the embryo. Toward this end, we first calibrated the model using the quantitative profiles of the major seed storage compounds  from global metabolomics and gene expression profiles of Arabidopsis thaliana wild type (Col-0) and mutants (acc – SALK_017342 and epi – SALK_145945) were grown under 16 h light/8 h dark photoperiod with constant temperature of 22°C at 120 μE m–2 s–1 light intensity. The insertion positions of SALK T-DNA lines were confirmed by PCR using the following primers. acc : LP-TTCAAGCAAGTTCAGGGTGAG, RP-AGAAGTACGCCCACACATTTG; epi : LP-GTTCATCAA CCCAGGTCAATG, RP-CCTTCTCTGCACACATTTTCC.Arabidopsis embryo were isolated, including zygote, octant, globular, heart, torpedo, bent, and mature stages. The mean gene expression matrix for the microarray data was based on our previous published report presented in Embryo isolations, RNA extractions, microarray experiments, microarray normalization and bioinformatics analysis were performed as described previously . In thisacc and epi mutants, there is no significant difference between the two mutants and wildtype plants before the heart stage. The seeds of homozygous acc mutants turn white and become smaller than wildtype after the heart embryo stage, and the seeds of homozygous epi mutants turn white and become smaller than wildtype after the bent embryo stage. Thus, we used the samples of the two mutants at the heart stage for metabolite profiling. Fatty acid content was calculated based on all compounds in the fatty acid sub-pathway. The fatty acid content of the samples from the two mutants and wildtype at the heart stage were compared.The embryo samples from the same seven stages as the samples used for microarray analysis in Arabidopsis seeds revealed a poor correlation as well A round of rough tuning of the parameters to produce a numerically stable and realistic model, with concentrations and fluxes within physiological ranges from reported datasets .(2)The parameter estimation routines in the SBtoolbox are then used to optimize the parameters of the model in order to fit quantitative experimental data .(3)If step #2 cannot yield satisfactory results, we consider changing the structure of the model either by implementing metabolic reactions or feedback regulation mechanisms that were previously not included. New regulatory mechanisms are always verified against the most recent literature and databases .These steps were repeated multiple times and the final result was a robust model that can be simulated over the complete time course of development  and very good agreement was achieved with regard to available data. The following is a complete description of the ordinary differential equations (ODE) model, which includes the differential equations and kinetic equations for fluxes and parameters, with further discussion on parameter estimation and the problem of model under-determination.The model for gene expression consists of one differential equation per enzyme, in the following form:Ei is the amount of the ith enzyme in the pathways, for which the synthesis and degradation are determined by the following parameters:Where •i: the amount of mRNA that encodes for the enzyme (dimensionless);mRNA•Rb: the amount of ribosomes in the cell (dimensionless);•ksyn,i: the rate constant for enzyme synthesis (hr–1);•kdeg,i: the rate constant for enzyme degradation (hr–1), which = LN(2)/t1/2;•–1).μ: the growth rate of the cell . The enzyme concentration can be reduced by two phenomena. First, the enzyme can be degraded (deg⋅Ek) or the enzyme pool can be diluted by cell division (μ⋅E). Note that the protein degradation rate constant is inversely proportional to protein half-life (t1/2). Thus, the problem here is to determine realistic parameters so that we can solve the differential equation for each Ei. The following subsections will detail the hypotheses and development of this gene expression model.Thus, the enzyme synthesis rate (first term on the right hand side) is proportional to the amount of mRNA, E and Rb. Justification for this approach is given below. Also, the model implementation was performed so as to circumvent the use of relative concentrations for these variables. Specifically, the enzyme level (Ei) is the only variable to be connected to the rest of the metabolic network  and we will scale the enzyme levels by using a rate constant (kcat). For example, the maximal reaction rate of the ith reaction in our metabolic network is:In this framework, the parameter’s time units will be given in hours. Given that the enzyme levels are not used in absolute terms for direct comparison with experimental data, it was decided to use dimensionless  concentrations for Vmax,i) will be proportional to the enzyme level (Ei) and enzyme reaction constant (ki). As we have to determine parameters for each reaction , the absolute value for Ei is not critical because it is multiplied by ki. Thus, finding a value for ki (with a relative amount of Ei) or finding a value for both ki and Ei is the same problem in terms of curve fitting . In terms of model development, we thus ‘lump’ the absolute enzyme level in the parameter ki. What is important, though, is that if the mRNA level doubles (for example), we would like to have twice the enzyme concentration and twice the maximal reaction rate for the corresponding reaction (after a steady-state is reached). In that regard, equations S1 and S2 will achieve this.In that equation, the maximal enzyme activity (Arabidopsis embryo development2 (mRNA levels were taken from our gene expression map of lopment2 . The dat3) and BRENDA4 . To classify the enzymes in the model, we used the information available in KEGG  amounts. We will thus normalize all of our mRNA profiles with regard to the initial value  in order to scale all the initial mRNA levels to around 1:One important point to consider here is that there is no absolute and quantitative correlation between mRNA levels and protein concentrations across the genome . Proteini(t) is the normalized sum of mRNAs for enzyme ‘i’ at time ‘t’ in the metabolic network.where mRNAArabidopsis (n ≈ 200) in our gene expression database. Among the 200 genes, ≈150 were expressed at an average intensity of 2,000 or more and ≈100 were highly expressed . Since little information is available on the half-life of ribosomal proteins in Arabidopsis, we simply assumed that the amount of ribosome is proportional to the weighted sum of mRNAs for the ribosomal genes (mRNARb). Research with Chlamydomonas reinhardtii suggests such a correlation exists (t = 0) = 1.Genes that encode for ribosomal subunits are known for bidopsis  and we in exists . As for μ⋅E) can be disregarded, especially in non-dividing cells and tissues or for enzymes that have a very high turnover rate . As it is, the case of plant embryos is an interesting situation where the growth rate and enzyme degradation are on a similar timescale and we must thus consider both phenomena.In many circumstances, the dilution by growth (–1 (doubling time of ≈48 h). A similar value of 0.014 hr–1 was also reported in research on plant metabolic flux analysis (–1 in the early stages and a much lower growth rate (0.0025 hr–1) for the mature embryo. In the modeling, this is reproduced by using a logistic growth equation (Growth rate (μ) was estimated from published data , with ananalysis . The groequation .kdeg) of 0.025 h–1, which is on the same order of magnitude as the growth rate. This is much faster than turnover rates in other plant tissues, as values in the range 0.001–0.005 hr–1 are reported for leaves kdeg = 0.03 hr–1).Enzymes with a relatively fast turnover rate ((2)kdeg = 0.02 hr–1).Enzymes with an average turnover rate ((3)kdeg = 0.01 hr–1).Enzymes with a slow turnover rate  needs to be determined. Again, limited information is available in the literature, but we can use the same approach as for protein degradation, with a classification in three groups . Data from an integrative study , protein synthesis will match the turnover because of growth and degradation (ksyn = kdeg + μ). This gives us the following parameters for the three groups:Finally, the rate constant for protein synthesis (ve study  show tha(1)ksyn = 0.055 hr–1)Enzymes with a relatively fast turnover rate ((2)ksyn = 0.045 hr–1)Enzymes with an average turnover rate ((3)ksyn = 0.035 hr–1)Enzymes with a slow turnover rate (ksyn and kdeg); (b) mRNA, Rb and μ are based on reliable data; and (c) the dynamics of gene expression are described in a physiologically realistic framework.Thus, even though this modeling of enzyme level is based on some simplifying assumptions and scaling to have dimensionless enzyme levels, it does have significant advantages, namely: (a) limited number of parameters  in •Plastid metabolism and FA pathways in •Mitochondrial metabolism in •Pathways for growth, storage product accumulation and transport in •Kinetic equations for maintenance fluxes and FA oxidation in •Parameters of the model in Then, a detailed diagram of the metabolic pathways is presented in The generic form of a metabolic model is:M is the vector of metabolites, S is the stoichiometric matrix of the system , as well as by a dilution term (μ⋅S) which accounts for the increase in volume because of cellular growth (μ).…where In this model, the kinetic equations for flux regulation will have the following form:Ei is the amount of enzyme catalyzing reaction ‘i’ (modeled as described in Section “Gene Expression Model” above), ki is the reaction constant for this enzyme and f will be a function of the state of the system (M) and constant parameters (p). This function will use Michaelis–Menten, Hill and mass-action kinetics to account for the various substrates, co-factors and inhibitors involved in reaction ‘i’. A higher value for the Hill coefficient for a reaction indicates the sensitivity at low input becomes a threshold response, such that a minimal input is needed to stimulate significant change in output. Such a response seems to reflect realistic biological systems.…where The central metabolic pathways in our model include glycolysis and the pentose phosphate pathway (PPP) and these are connected to other pathways. Glycolysis is described in a simplified way, with 5 reactions . We included the non-phosphorylating glycerate dehydrogenase (NPG), which operates in parallel to glycolysis and produces NADPH that can be used for FA synthesis. However, this is not the major source of NADPH, as most of it is produced by the PPP. Ribose-5-phosphate (R5P), the intermediate product of the PPP, can link and integrate the pathways through two different mechanisms. The epimerase (EPI) reaction will direct R5P back to glycolytic intermediates, while Rubisco , can be used in many pathways. It connects to mitochondrial metabolism, but can also be transported in the plastids for FA synthesis or can be used for amino acid and ultimately, protein synthesis.The structure of the model, with the seeds operating in glycolytic mode  is in agreement with what is proposed by seed metabolic flux estimations . The mod5.It is well known that the pathways of central metabolism are regulated at the biochemical level in most organisms, including plants . We haveThe structure of the model for plastid metabolism is based on measured fluxes , with a The structure of our model for mitochondrial metabolism was again chosen to be coherent with flux measurements , with thvstas) and one for degradation (vstad). SUC accumulation is driven by the reversible enzyme, sucrose synthase (vsus), and storage proteins are accumulated by a simple reaction whose rate (vsprt) is proportional to mRNAs for storage proteins. Growth is modeled using a logistic equation, with a maximal limit on seed weight. This simplification was implemented for two reasons: it precisely describes the growth curve of Arabidopsis seeds and it allows focusing the model on storage product dynamics instead of having to describe detailed mechanisms for growth regulation in seeds (some of which are not clearly defined at the genetic level).Reports on flux estimations  show thaAs we model the dynamics of seeds metabolism up to the mature stage, where FA levels are stabilized, we have to consider FA oxidation. We thus implemented reactions for triacylglycerol (TAG) oxidation and subsequent processing of ACoA in the glyoxylate pathway (simplified to the isocitrate lyase reaction).vleak) is modeled as a simple reaction that consumes NADH, with estimates based on published modeling (vox) is modeled in a similar vein, but is based on consumption of NADPH. Finally, we use a mixed model for ATP consumption, with growth associated (α⋅μ) and non-growth associated (β) terms. It is important to highlight that these reactions operate in addition to energy and redox consumption by other pathways in the model (such as FA synthesis) and account for energy consumption by reactions not in the model.It is also important to consider reactions for maintenance. The major sources of damage and loss of efficiency in metabolism come from the mitochondrial proton leak and endogenous oxidative stress. The mitochondrial proton leak  and around 125 parameters is under-determined and the parameters cannot be uniquely identified. However, the model’s parameters were first taken from published reports  when available and the model was fine-tuned using >100 data points (with concentrations and fluxes data) covering the major pathways in the developing embryo. Thus, even though the parameters are not strictly identifiable, it is assumed that the resulting model is within physiological ranges and can produce valuable insights. In a previous metabolic modeling study on plant cells , a similin vitro cultures has also been demonstrated  modeling of metabolic networks is an established framework, with decades of development and applications. Regarding the metabolism of plant cells and tissues, the ODE approach has been applied to photosynthesis , sucrosenstrated .Arabidopsis seeds metabolism, we used the resources and information from KEGG and metabolic flux measurements of Arabidopsis seeds  synthesis and degradation, the pentose-phosphate pathway (PPP), Rubisco (RUB), synthesis of storage proteins (SPRT), and the synthesis, elongation and storage of FA’s into oil bodies (triacylglycerides or TAG). We also include the contribution of the amino acids alanine (ALA) and glutamine (GLN). The topology for the pathways is in accordance with reports on net flux estimations . We alsoTo integrate gene expression values to the model, we used gene expression profiles of seven distinct embryo developmental stages from zygote to maturity reported in Arabidopsis seed . Results obtained with this approach are shown in To obtain a realistic model, using the gene expression profiles of the embryo development as inputs, we calibrated the model parameters by multiple rounds of validation and curve fitting using the quantitative measurements of the storage products in different developmental stages of wild-type –1 for this period. This is ≈5 times higher than values reported for leaves  are consistent with fluxes measurements  each reaction and used the model to generate the simulated seed FA content at the mature stage (at 20 DAF). This allows simulating the sensitivity of seed FA contents to genetic perturbations. Complete and detailed results for single gene perturbations, with consideration for 1. 5-, 2. 5-, 5-, and 10-fold increases and decreases are presented in Finally, the sensitivity analysis results show that genes related to transport processes might be important for FA synthesis. The breakdown of external sucrose by the sucrose invertase (CWI) and the glucose transporter (GLCT) are two genes for which a KO induces the sharpest decrease in FA content. Other transport associated processes also show some potential to actually increase FA content. Overexpression of alanine aminotransferase (AAT), which incorporates amino acids from the maternal tissue, increases FA content by 8%. Transporters for PEP and PYR on the plastidial membrane  had higher FA in the heart stage of embryos   and the  embryos , which aArabidopsis seeds was investigated using a mathematical model that integrates gene expression profiles during embryo development. The dynamic model was then used to predict the effects of single gene perturbations on seed FA content. We showed that the predicted results are largely validated either from the literature or from new experiments we conducted. These observations highlight that the dynamic model also generates biological insights for understanding the genetic basis for seed FA content determination. The results suggest that our model can be used to guide metabolic engineering for oil seed crops.Integration of gene expression, enzymes and metabolites in the same conceptual model is critically important for improving our understanding of dynamics and interactions in biological systems . These iThe model can be used to integrate high-throughput data such as gene expression datasets by providing a framework for data analysis and testable predictions. We believe that our modeling framework could be used to further integrate quantitative and time-course metabolomic and proteomic datasets. Thus, the development of such modeling frameworks will be improved by the development of experimental techniques to improve data analysis and experimental design.Although high-throughput technologies have generated large omics datasets, it is still very challenging to connect and assign ‘causal’ signals from these data to phenotypic traits and diseases. Several factors make it difficult to dissect such ‘causal’ or ‘driving’ signals: the data are very complex, the biological systems are also very complex and many genes in the systems are highly interdependent/interconnected and correlated. Moreover, phenotypic traits and diseases are often controlled by multiple genes. Therefore, most of the current analysis of omic data has been focused on association but not identification of the “causal” signals. This work provides a mathematical framework for dissecting gene networks to identify the key gene “hubs” that play key roles in important plant traits associated with seed oil content, providing an insight for potential application in synthetic biology.The original contributions generated for this study are included in the article/EW, MC, DX, and RD developed the study concept. DX and MC performed the experiments and collected the data. MC, EW, DX, PG, and JZ analyzed the data. MC and EW performed the statistical analysis. MC, DX, EW, PG, JZ, LK, and RD interpreted the results and prepared the manuscript, with support from all authors.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.


Motivation: The increasing availability of metabolomic data and their analysis are improving the understanding of cellular mechanisms and how biological systems respond to different perturbations. Currently, there is a need for novel computational methods that facilitate the analysis and integration of increasing volume of available data.Results: In this paper, we present Totoro a new constraint-based approach that integrates quantitative non-targeted metabolomic data of two different metabolic states into genome-wide metabolic models and predicts reactions that were most likely active during the transient state. We applied Totoro to real data of three different growth experiments  from Escherichia coli and we were able to predict known active pathways and gather new insights on the different metabolisms related to each substrate. We used both the E. coli core and the iJO1366 models to demonstrate that our approach is applicable to both smaller and larger networks.Availability:Totoro is an open source method (available at https://gitlab.inria.fr/erable/totoro) suitable for any organism with an available metabolic model. It is implemented in C++ and depends on IBM CPLEX which is freely available for academic purposes. The increasing availability of metabolomic data and their analysis are currently enhancing our knowledge on diverse biological mechanisms and elucidating how cells and organisms respond to different perturbations . MetabolMetExplore  to integrate relative metabolomic measurements in order to make predictions about differential fluxes. They use a constraint-based approach which minimizes the distance between the two flux vectors of the two different states based on the ratio between the measured metabolite concentrations in both conditions. For both states, steady-state is assumed for the flux vectors. However, the authors identify differential fluxes between the two conditions whereas we aim at finding reactions that are likely active during the transient state. In , that is publicly available at https://gitlab.inria.fr/erable/totoro, along with the test datasets presented in this study. It is implemented in C++ and depends on IBM CPLEX which is freely available for academic purposes. We also tested our method with data from pulse experiments with different carbon sources  in Escherichia coli.We use constraint-based modeling to enumerate sets of reactions that explain the changes in concentrations for some measured metabolites, i.e., how the system moved from a state to another. We implemented our approach in a software we called Subsr, Prodr with m × n matrix where each column represents a reaction and each row a different metabolite. It contains the stoichiometric coefficients which are positive if a metabolite is produced by a reaction and negative if it is consumed.A metabolic network can be represented as a weighted directed hypergraph X, contains an interval. This interval describes by how much the internal metabolite concentration changed between two different states. Usually, small deviations for the measurements are available which can be used to calculate the minimum and the maximum possible difference between the internal metabolite concentrations. Furthermore, all reversible reactions of the network are split into forward and backward reactions.The set H and a list containing the changes for some metabolite concentrations before and after a perturbation, we want to identify sets of reactions that were involved in diverting the system from the initial state before the perturbation to the state after the perturbation X operator means that only the entries of the vector corresponding to the metabolites in X are taken into account. We use [X]t to denote the concentration for the metabolites in X at time point t. Considering two points t0 and t1 in time and φ can be interpreted as the overall number of moles that passed through the reaction j during the time interval  which corresponds to the area under the reaction rate curve in this time interval:X are represented by an interval rather than using a fixed number:uFBA (ϵ) is possible for all non-measured metabolites φj are positive and have an upper bound uj. We have that Δmin is a vector composed of ϵmin while Δmax is composed of ϵmax.The variation of the concentrations in time of the metabolites in  of uFBA  and theiφ can only be zero or have a positive value. For this, we use an additional constraint as explained in φj is zero in the solution, reaction j is proposed as inactive during the shift while if φj has a non-zero value, reaction j is proposed as active during the shift. Hence, we are only interested in the reactions that have a non-zero φ because we want to identify the part of the metabolic network that was active during the metabolic shift. These reactions are represented by the support of the vector φ.As showed above, in our formulation, the variable j, a binary variable yj is then introduced that is set to zero if and only if the corresponding φj is zero and therefore, the reaction is not part of the solution. In this way, these variables will correspond to the support vector of φ and it will be sufficient to minimize their sum:j and its reversible λ is used for both objectives:λ should lie between 0 and 1. Finding a good balance between these two objectives can be challenging but necessary to identify meaningful biological solutions  that is implemented in our software y* is a previously found solution vector:To enumerate different solutions, once a solution is found, it must be excluded for the next iteration. Two solutions are different if they do not contain the same reactions. We are using the following constraint where ϵ but it can be set to a very low or large value to imitate an infinite source or sink. Hence, specific sources or sinks can be added to the problem by specifying a large negative Δmin or a large positive Δmax for certain metabolites, but the method will remain robust to small variations, as long as the range of this parameter remains within a similar order of magnitude of the values of the measured metabolites.Source and sink reaction  of the network should be blocked to avoid that changes in the concentration are just transferred outside of the network where they cannot be taken into account by the objective function. However, no information is lost if source and sink reactions are blocked. If the substrates of a sink reaction are accumulated or the products of a source reaction are depleted in a solution, this indicates that the corresponding source/sink reaction is active. Their use is limited by the chosen λ ≈ 1) and the value of ϵ for the non-measured metabolites is higher than the one for the measured metabolites, the changes in concentration of the measured metabolites can simply be distributed to (accumulated on or taken from) the nearby non-measured metabolites  and prevents that larger sub-hypergraphs are chosen . However, this can be addressed by decreasing the value of λ in the objective function and thereby giving more weight to the portion of the function that minimizes the accumulation in non-measured metabolites ϵ > 0, λ = 0.1). This should result in solutions that are larger but that connect the measured metabolites better than when only the number of reactions is minimized. Furthermore, based on other experimental data, the user might choose smaller values of ϵ, or constrain it to the highest measured metabolite to further restrict the accumulation/depletion of the non-measured metabolites.However, if the minimization of the number of active reactions is prioritized  and ϵ (5 and 10) for each pulse experiment. Although a single solution should be enough to identify some pathways responsible for the shift, we wanted to see if we could also obtain alternative pathways. Furthermore, we wanted to investigate how the solutions evolve when they are slightly suboptimal. For each different parameter setting, 100 different solutions were therefore enumerated. The results are displayed using Escher .In general, we could observe that solutions with λ and ϵ, Totoro could propose connected sub-hypergraphs for all three pulse experiments. The predicted solutions did not use co-factors as shortcuts through the network. We therefore did not modify our method further to treat co-factors separately.By adjusting the parameters λ = 0.1 (see λ), while higher values of lambda constrained the solutions locally around the measured metabolites. For λ = 0.9, neither the TCA cycle nor the gluconeogenesis pathway were proposed to be active. Setting λ to 0.5 already improved the results: the TCA cycle was proposed as active but the complete gluconeogenesis pathway was only recovered in less than 50% of the solutions.For the pyruvate pulse, we expected that the activity of the TCA cycle would increase and that reactions for gluconeogenesis would be active see . Both obλ = 0.1. The pathway from pyruvate to G6P contains nine reactions including seven reversible ones: glucose-6-phosphate isomerase (PGI), fructose-bisphosphate aldolase (FBA_R), triose isomerase (TPI), glyceraldehyde-3-phosphate dehydrogenase (GAPD), phosphoglycerate kinase (PGK), phosphoglycerate mutase (PGM) and enolase (ENO). Especially here, it is important to state that all these reversible reactions were predicted in the correct direction going from pyruvate towards G6P. The core network results can be seen in λ and ϵ. These figures were created using Escher  or by the combination of pyruvate dehydrogenase (PDH) and citrate synthase (CS). Furthermore, the pathway from pyruvate to glucose 6-phosphate (G6P) was active in 100% of solutions for g Escher .λ = 0.1 and ϵ = 5, a total of 43 reactions with a specific direction were chosen in all solutions. Out of these 43 reactions, 24 were chosen in every solution (including reactions in the TCA cycle and the gluconeogenesis pathway). This means that certain core pathways were consistently picked also in slightly suboptimal solutions. Looking at only the ten best solutions, already 38 out of the 43 reactions were identified. The missing reactions were mostly part of the pentose phosphate pathway which also contains reactions that were part of the solution only in a few cases. Even with only ten solutions, we were able to obtain the alternative pathways feeding the TCA cycle (PPC/PDH). This indicates that it is not necessary to enumerate a large amount of solutions to get significant results and to identify alternative biological pathways.We do not fix the objective value in our optimization problem after obtaining the first solution but in every iteration, the minimization problem is solved again after excluding the newly found solution. This means that the next solution can have the same objective value but it is also possible that the objective value is worse than in the previous iteration. In this particular case, the 100th solution had an objective value that was only 5.5% worse than the objective value of the first solution see  which shTotoro for the values of λ = 0.1 and 0.9, excluding one metabolite at a time, recomputing the results, and computing the distances to the results on the complete metabolite set for reaction occurrence (in terms of absolute difference of occurrences). Overall, the results for both λ = 0.1 and 0.9 differed from less than 5% to around 20%. In general, the results were robust , but we noticed that excluding metabolites with a higher neighborhood connectivity (such as glutamate and glutamine) had a greater impact on the final results. These results show that even though the distances were small, the amount of information provided by different metabolites varied widely.To check the robustness of the method against small perturbations, we tested within the pyruvate pulse the results of Moreover, we tested 10 random sets of measured metabolites , with a λ = 0.9 and 0.5, the active reactions proposed by Totoro were disconnected and it was not possible to identify active pathways. We believe that the results coming from this pulse were less insightful since the bacteria were already grown in glucose prior to the pulse, which in turn might be a reason why the changes in metabolites were not as informative as the other pulses. This was for the most part corrected if more metabolites were added as input to Totoro when using the complete network as presented in For the glucose pulse, we expected that reactions that are part of the glycolysis pathway would be active as they convert glucose into pyruvate generating energy. Consequently, the TCA cycle should also be fed see . For λ =λ = 0.1 and ϵ = 5, only disconnected parts of the network were active . They accounted for a total of 47 reactions (with distinct directions) and 30 of these appeared in all solutions. Similarly to the pyruvate pulse, the difference in these solutions were mostly based on a few reactions that are not part of the main pathways (glycolysis/TCA cycle). One critical observation is that the D-glucose transport reaction (GLCpts) was not part of every solution although glucose should be used as important source. As previously mentioned, the bacteria were already grown in glucose prior to the glucose pulse, which is possibly a reason why glucose was already internalized prior to the initial pulse. When comparing the objective values for these 100 solutions, the absolute difference between the first solution and the 100th one was similar to the one observed for the pyruvate pulse  was produced by PEP carboxykinase (PPCK) or by PEP synthase (PPS) using pyruvate as intermediate substrate. Subsequently, PEP was, as expected, transformed to G3P. The lower right part of the TCA cycle predicted as active can be explained by the fact that the concentration of L-glutamate decreased and the concentration of citrate increased. The active reaction in this part connected these two metabolites. Furthermore, reactions of the pentose phosphate pathway were proposed as active and the biomass precursors R5P, E4P, and G3P were produced.After the succinate pulse, part of the TCA cycle should always be active. Furthermore, the gluconeogenesis pathway should be active to produce G3P and glucose-6-phosphate from succinate. Again, the results for cted see . Therefo 0.1 see . For botϵ = 5 and 10 were very similar. For example, one difference was that for ϵ = 10, the reverse D-lactate dehydrogenase (LDH) was predicted to be active in 56 solutions which led to a small accumulation of D-lactate. It does make sense biologically because in general, D-lactate is one of the main products of the fermentation but we do not have the measurements for the concentration of D-lactate for this pulse experiment to actually verify this observation. However, in total, the differences were negligible and in contrast to the glucose pulse, the parameter ϵ had a lower impact on the outcome.The results for λ = 0.1, ϵ = 5). We observed that 22 of these were always active (mostly in the gluconeogenesis pathway and part of the TCA cycle). The objective values for all 100 solutions were extremely close  appeared in all 100 solutions . This shows that the constraints describing the input deltas in the MILP have a large influence on the difficulty of the optimization problem, and thus also on the runtime.Totoro for the core metabolism were similar to the best results of the E. coli core model for all three pulse experiments. For instance, in the pyruvate pulse results, out of 12 reactions in the TCA cycle within the large network, 8 were also present in the core model. In total, 5 were chosen in 100% of the solutions in the same direction in both core and large networks. The complete network was also able to correct the only inconsistency within the TCA cycle for the core network: the direction of the reaction ICDHyr, which shows the advantage of relying on complete networks whenever available. For the glycolysis/gluconeogenesis pathways, out of 12 reactions, 9 were also included in the core model. In total, 6 reactions were chosen in 100% and 1 in more than 80% of the solutions in the same direction in both networks. Totoro predicted as active for pyruvate, glucose and succinate (in at least 1 solution) a total of 221, 284, and 189 reactions respectively. Moreover, 52% of the reactions were chosen across all iterations in the pyruvate pulse dataset, 81% in the succinate pulse dataset and 62% in the glucose pulse dataset.However, although the obtained solutions were suboptimal, the active reactions predicted by E. coli how the production cost for individual amino acids can depend on the available carbon source, and reactions close to the entry point of the carbon source might have considerably higher fluxes. A schematic representation of this is provided in Totoro predicted an activation of the pathway from pyruvate to alanine and valine, which resulted in the accumulation of these amino acids  though the method is not critically sensible to this setup, being robust to small perturbations. However, it is worth noting that a higher λ can lead to smaller solutions which might be biologically irrelevant. Here, we focused in extracting connected sub-hypergraphs that explained the changes in concentration between two different conditions. We also show that a reduction of ϵ can also be used to obtain more connected solutions. However, there might be situations where the user might be interested in only local changes around the measurements. In this context, it might be advantageous to choose higher values for λ and ϵ. We did not encounter problems specific to co-factors which is a known problem when looking for shortest paths in metabolic networks. This is probably due to the fact that we are not only minimizing the number of active reactions in the solutions but also focusing on the changes in the metabolite concentrations. By splitting reversible reactions, Totoro was able to predict distinct directions for them.E. coli were fairly similar to the results for the core network. We also showed a particular case in which the perturbation was subtle, and the results from the complete model were more insightful than the ones from the core model. It must be however noted that the predictions do depend on the measured metabolites. If for large parts of the network, no metabolite concentrations are measured, Totoro will likely not be able to find active pathways for these parts of the network.Both in the core network and in the larger network, we were able to recover biologically meaningful pathways. Additionally, although the larger network contains more reactions and we added more input deltas, the predictions for the core metabolism of Tororo increases. We enumerated 100 different solutions for the core network. However, in our case, the enumerated solutions were very similar and a large amount of reactions appeared in all 100 solutions. Therefore, already one (or few) solution(s) would have been sufficient to infer the most important reactions that were proposed to be active.Moreover, we could also see that it is not necessary to enumerate a high number of solutions which is especially important when larger networks are used and the runtime of Totoro, a method that identifies active reactions during the transient state based on the differences in the concentrations for some measured metabolites from two different conditions and we showed its prediction power on the example of different pulse experiments in E. coli. It is important to note that even though we provided several biologically trivial results, Totoro only used metabolomic data as basis for these predictions, without any other source of bias such as defined metabolic pathways. Our method was also able to handle full networks which take into account model stoichiometry, and we did not perform any type of filtering for cycles, reversible reactions or co-factors.In this paper, we presented With the current technologies, it gets more common to have different kinds of data available which creates a need for methods that combine, for instance, metabolomic, transcriptomic and proteomic data. We have recently developed a method for integration of metabolic networks and transcriptomic data  and we i