Subsystem/pathway definition is also employed to delineate the biosynthetic routes that produce biomass building blocks. In databases, such as MetaCyc and SEED, these representations are composed of linear routes from precursors to target biomass building blocks. However, this approach cannot capture the nested, complex nature of GEMs. Here we implemented an algorithm, lumpGEM, which generates biosynthetic subnetworks composed of reactions that can synthesize a target metabolite from a set of defined core precursor metabolites. lumpGEM captures balanced subnetworks, which account for the fate of all metabolites along the synthesis routes, thus encapsulating reactions from various subsystems/pathways to balance these metabolites in the metabolic network. Moreover, lumpGEM collapses these subnetworks into elementally balanced lumped reactions that specify the cost of all precursor metabolites and cofactors. It also generates alternative subnetworks and lumped reactions for the same metabolite, accounting for the flexibility of organisms. lumpGEM is applicable to any GEM and any target metabolite defined in the network. Lumped reactions generated by lumpGEM can be also used to generate properly balanced reduced core metabolic models.In the post-genomic era, Genome-scale metabolic networks (GEMs) have emerged as invaluable tools to understand metabolic capabilities of organisms. Different parts of these metabolic networks are defined as subsystems/pathways, which are sets of  ad hoc built metabolic pathways, and biomass compositions. The development of genome scale models (GEMs) brought a standard to metabolic network modeling. However, the vast amount of detailed biochemistry in GEMs makes it necessary to develop methods to manage the complexity in them. In this study, we developed lumpGEM, a tool that can systematically identify subnetworks from metabolic networks that can perform certain tasks, such as biosynthesis of a biomass building block and any other target metabolite. By generating alternative subnetworks, lumpGEM also accounts for the redundancy in metabolic networks. We applied lumpGEM on latest E. coli GEM iJO1366 and identified subnetworks/lumped reactions for every biomass building block defined in its biomass formulation. We also compared the results from lumpGEM with existing knowledge in the literature. The lumped reactions generated by lumpGEM can be used to generate consistently reduced metabolic network models.Stoichiometric models have been used in the area of metabolic engineering and systems biology for many decades. The early examples of these models include simplified  E. coli through a small stoichiometric model is performed by Varma et al. [E. coli metabolism has been explained extensively, and all the components  that constitute 1gDW of cell were reported based on previous experiments [E. coli allowed the authors to develop a model that can describe the growth requirements and limitations of the organism without including the complex biosynthesis routes for each individual biomass building block. With such a small stoichiometric representation of the core metabolism (~50 reactions), authors were able to predict many aspects of E. coli physiology. Similar metabolic models with a reduced representation of the biosynthesis of the building blocks have been used in many other studies for E. coli and other organisms [Stoichiometric models have been extensively used since 1980s  and preda et al. ,5 in whea et al. . In thiseriments . Moreoverganisms –15.In the following years, with the development of sequencing and high-throughput technologies, the gene-protein-reaction (GPR) associations  have beeMany metabolic models for various organisms ,23–27 anE. coli contemporary GEM [K-shortest EFM, an MILP approach, and identified 10 minimal reaction sets that can produce lysine in E. coli and C.glutamicum. In lumpGEM, we follow a similar but an efficient approach compared to the previous studies and we have merged it with thermodynamics-based flux analysis (TFA) to account for bioenergetics constraints. With lumpGEM we can generate thousands of thermodynamically feasible minimal subnetworks that can produce a target metabolite from a set of selected precursor metabolites.Towards this, we developed lumpGEM, a mixed-integer linear programming algorithm that identifies all the alternative reaction subnetworks that should be used to produce a cellular metabolite or biomass building block from a defined set of metabolites. For each subnetwork, lumpGEM derives a lumped reaction that can capture the overall stoichiometry of the subnetwork, while preserving the elemental balance. The concept of identifying minimum number of reaction or enzymes to perform a certain function is not new, throughout the last two decades, different studies have been performed around this idea. Hatzimanikatis et al. developed a mixed-integer linear programming (MILP) formulation to determine the minimum number of regulatory structures to manipulate to optimize a bioprocess, along with possible alternatives . In anotrary GEM . Later, rary GEM . Elementrary GEM  and usedrary GEM . The mairary GEM  discusseE. coli iJO1366 [S. cerevisiae iMM904 [core carbon metabolism as defined in [core carbon metabolite to synthesize a biomass building block is identified and properly accounted.In this study, we focused on the biosynthesis pathways of biomass building blocks of  iJO1366 , and S. e iMM904  and withfined in . We demoE. coli and S. cerevisiae for their metabolic capabilities to produce BBBs and revealed their similarities and differences. Such studies will help us to understand the capabilities of E. coli and S. cerevisiae ‘per’ biomass building block and identify the flexibility of the organism to survive by activating different parts of the metabolism to accumulate biomass. The generality of the method makes it applicable to any GEM that has a well-defined biomass composition. In addition, lumpGEM can generate lumped reactions from any part of the metabolism for any target metabolite, either a biomass building block or a biochemical and chemical compound or sets of compounds, which makes it a versatile tool to be used for different purposes.Then, we performed a comparison between the values reported by Neidhardt and those generated by lumpGEM and found that lumpGEM recovered Neidhardt tables and extended them by including alternative biosynthetic routes/lumped reactions. We also performed a comparison between Mcore  while preserving the elemental balance. MILP formulations have been often used on biochemical networks for many purposes [RncGEM  can simulate the growth characteristics of organism since they include the necessary biosynthetic paths to biomass building blocks (BBBs), which make up 1 gDW of cell. However, when the GEM is optimized for maximum specific growth using Flux Balance Analysis, the contribution of purposes ,36,38,39E. coli IOJ1366 is very well characterized and detailed and contains 102 biomass building blocks. It is mainly composed of amino acids, lipids, nucleoside triphosphates (NTPs), deoxy-NTPs and inorganic compounds  along with cofactors such as NAD+/NADH, NADP+/NADPH, CoA/AcCoA, and FAD. Experimental estimates of the growth associated ATP maintenance and production of diphosphate are also included in the biomass composition.The biomass formulation defined in subnetworks that our method generates may include branches from linear synthesis pathways. The difference emerges from the mass conservation constraint that we force during our analysis. For instance, the smallest subnetwork that lumpGEM generated for the synthesis of histidine is composed of 21 reactions and the precursors are ribose-5-phosphate (R5P) and oxaloacetate. In the databases such as EcoCyc [core reactions and the linear pathway from ribose-5-phophate to histidine. Hence, the generated sets of reactions are not only the linear routes from precursor metabolites to biomass building blocks, but balanced subnetworks with stoichiometrically proportional branches  indicates that they are close to each other, however the overall stoichiometry that lumpGEM reports for the biosynthesis of histidine is more detailed and includes more metabolites as co-substrates and co-products . The maiecursors . Therefonon-core reactions, which are balancing the non-core metabolites in the linear route. These two sources of differences, and especially the latter, may result in an explosion in the number of subnetworks that can be generated for some of the biomass building block. For metabolites like amino acids, which are not so far from the core carbon metabolism, the number of alternative smallest subnetworks non-core metabolites that appeared along the linear synthesis route is small, since the main explosion in the number of subnetworks emerges from these reactions. As an example, all 12 alternative subnetworks for histidine include the linear 10 steps route from R5P to histidine and alternative subnetworks are generated by other non-core reactions. Moreover, there is a slight correlation between the number of alternative subnetworks and the size of the subnetworks. Most of the amino acids that have more than 2 alternative subnetworks require more than 10 steps for their biosynthesis. A big molecule, Phosphatidylglycerol  is a lipid with a non-core metabolites. However, despite the increase in the number of subnetworks, the number of unique lumped reactions remains relatively small  for the synthesis of these pool metabolites, we followed the same procedure that we did for biomass building blocks, and we built a GEM with an additional reaction with the coefficients of ATP, ADP, water, phosphate and proton from GEM biomass. Then, by forcing a flux through this reaction, and by minimizing the number of non-core reactions  and the  network  2 is capions See , we genesubnetworks that balance the diphosphate in the biomass formulation. There are 2 alternative subnetworks composed of only 1 reaction in RncGEM that can balance the diphosphate in biomass equation: Inorganic Diphosphatase (PPA) and Polyphosphate Kinase (PPKr). Both of these reactions are decomposing the diphosphate into phosphate and proton, the former with water, and the latter with ATP/ADP cofactor pair.Along with the biomass building blocks, GAM and adenylate pool metabolites, the biomass equation of iJO1366 includes diphosphate as a by-product. By following the same procedure that we have followed for adenylate pool, we generated BBB from the carbon source, specifically the yield of BBB on the carbon source. In order to calculate the yield per lumped reaction, we built a ‘mini’ core model for each of them, which is composed of Mcore—Rcore,VBBB and the lumped reactions under study. By optimizing the synthesis of the selected BBB and calculating the C-mole yield over the carbon source of interest, specifically glucose, we ranked the alternative lumped reactions for each BBB. Interestingly, different lumped reactions can produce different amounts of biomass building blocks over a wide range of yield amounts  on the product side. In the 3rd highest yield case, fumarate (C4) replaces pyruvate on the reactant side, and succinate (C4) appears on the product side as a by-product. The lowest yield producing lumped reaction has fumarate and pyruvate on the reactant side, and has AcCoA, CO2 and succinate on the product side of the equation. This signifies that the lumped reactions with lower yield are losing carbon through those core metabolites and the number of carbons in these metabolites defines the yield. However, it is not possible to generalize such a rule, since the metabolites appearing on the product side of the lumped reaction can be assimilated by the system and the capacity of the network for this re-assimilation will have a significant effect on the yield of the lumped reaction. Moreover, having a lower yield does not necessarily mean that these lumped reactions are not useful for metabolic modelling, since they can be used under sub-optimal growth conditions or under conditions when growth is not the main physiological optimality criterion or to provide flexibility under mutation. The use of these alternatives and their physiological interpretation deserves an in-depth study and lumpGEM can serve as a framework for systematic studies.dTTP is a deoxy nucleoside triphosphates and its main precursor for all the generated subnetworks is ribose-5-phosphate (R5P) from Pentose Phosphate Pathway. Consequently, the n yields  is the cBBBj. However, to produce biomass, these lumped reactions must be able carry flux under the same quasi steady state condition, in the same model with biomass as cellular objective. This requires generating a metabolic network composed of the defined core network, lumped reactions, the transport and sink reactions defined in GEM. We used the Varma model  model of Christen et al. [core reactions for S. cerevisiae network. The generated core network is composed of , the lumped reactions of E. coli and S. cerevisiae are very similar  converting carbon dioxide to bicarbonate, which is the co-substrate for the carbamoyl-phosphate synthase reaction converting glutamine to carbamoyl phosphate. The reaction that produces carbamoyl phosphate in E. coli model uses carbon dioxide instead of bicarbonate as co-substrate. Moreover, it does not use L-glutamine as co-substrate. Therefore, the last difference in the subnetworks emerges from the synthesis of glutamine by S. cerevisiae through the usage of glutamate synthase (NADH2) and glutamine synthetase enzymes.In order to define the core for n et al.  and mappposed of  2 88 rea similar . L-phenyE. coli, whereas it generated 155 subnetworks and 114 lumped reactions for S. cerevisiae for 44 biomass building blocks  are still bigger compared to E. coli (24 reactions), however this time the lumped reaction does not include any metabolite other than L-malate, glucose, water, oxygen and proton. The E. coli lumped reactions for L-malate is very similar to the succinate case. This analysis is done only for 1 Smin subnetwork for both compounds, and can be extended by generating all the minimum subnetworks, and for every common metabolite between E. coli and S. cerevisiae.We have also performed an analysis to compare E. coli iJO1366 and S. cerevisiae iMM904 and generated different subnetworks that can participate in producing biomass. We also used lumpGEM to re-define the pathway and subsystem definitions for the biosynthesis of BBBs, and identified that many different subsystems participate for the production of a single BBB. Moreover, by lumping the generated subnetworks, lumpGEM allowed us to identify the individual contribution of core metabolites and cofactors for the synthesis of each BBB. This procedure is a very promising method for many applications, such as experimental studies like MFA [in silico studies like FBA, TFA [ad-hoc selected core models consistent with genome-scale model (GEMs) in terms of biomass requirements. Metabolic Flux Analysis (MFA) analysis can benefit from such approach, since lumpGEM identifies the expenditure of core metabolites for the biosynthesis of biomass building blocks, thus accounting correctly for the metabolic costs.The complexity of cellular metabolism necessitates the development of methods to better understand and investigate the metabolic capabilities of organisms. For this purpose, small sized metabolic models are developed and widely used to study cellular physiology, and are proven to be useful platforms for many applications. With the emergence of genome scale models (GEMs), studies on metabolism entered a new era, since GEMs encapsulate all biochemistry that occurs in an organism. However, it is still crucial to be able to focus on certain parts of the metabolism with a modular manner and to understand the capabilities of these modules. Within this scope, we developed lumpGEM, a systems biology tool that captures the minimal sized subnetworks that are capable of producing target compounds from a set of defined core metabolites. In this work, we applied lumpGEM on all biomass building blocks (BBB) of like MFA  and in sFBA, TFA ,46 and aad hoc defined core with a biomass yield very close to its parent GEM model. With a systematic approach to define the core [lumpGEM can also be used to build synthesis pathways for any metabolite defined in the metabolic network. This makes it a versatile tool to study the characteristics of industrial chemical production strains , since ithe core , we can the core –51, in wThe algorithm considers a core system of metabolites and reactions and identifies them in genome scale model (GEM) of the organism. Using this GEM, it decomposes the biomass composition of the organisms into individual biomass building blocks (BBB). lumpGEM source code is available in In lumpGEM, we introduce and use the following definitions:BBBBiomass building blockcoreMMetabolites that belong to core systemcoreRReactions that belong to core system, in this specific casencGEMMMcoreMetabolites that belong to GEM that do not belong to ncGEMRRcoreReactions that belong to GEM that do not belong to jSBBBj other than McoreRcore and composed of MncGEM and RncGEMSubnetwork (set of reactions) that synthesizes subMSjMetabolites that belong to subRSjReactions that belong to rxnzRncGEM. When decision is 0, the reaction is activeBinary decision variable that controls the flux through each aDecompose the biomass composition of GEM to each of its components, such as alanine, tyrosine, biotin, etc. In most available GEMs, such decomposition is available mainly in the biomass equation.bBBB.Built a new GEM model by allowing the individual production of each cMcore and Rcore.Define dFrxn, i and backward Brxn, i components.Split all the reactions in GEM in Step a. into forward ezrxn, i for each Create binary variables fRGEM that will control the flux through these reactions as:C.Generate a constraint for each zrxn, i can operate in both directions if the existing constraints  allow it.Postulate 1: Binary control is unbiased to reaction directionality. This means that gMcore and Rcore as defined in [Apply thermodynamics constraints for fined in ,52.hBBBj:Build the following MILP formulation for each MaximizevBBB, j: The sink that is created in Step 1.a for BBBj for its biosynthesis.max: Theoretical maximum specific growth rate for the given physiology in 1/hr units.μnj, GEM: The stoichiometric coefficient for BBBj in mmol/gDW unit as defined in original GEM.Mcore is a potential precursor for the biosynthesis of BBBj.Postulate 2: Any zrxn, i results in the smallest subnetwork Sj to produce BBBj from Mcore. This subnetwork is not necessarily composed of only linear pathways as reported in databases such as KEGG [Postulate 3: Maximizing for the sum of  as KEGG , SEED [5 as KEGG  or EcoCy as KEGG  etc. andMcore to synthesize BBBj due to the degrees of freedom (DOF) that the system has.Postulate 4: The flux distribution for each generated subnetwork cannot guarantee an optimum flux distribution that will specify the individual stoichiometric contribution of each Moreover, only the defined core reactions and metabolites of the GEM built in Step f for generating subnetworks is constraint with thermodynamics, and the generated subnetworks are constrained by only mass-balance.Sj:To test the thermodynamic feasibility of these subnetworks, we have built the following MILP formulation for each aiMcore and RcoreiiSjiiivBBBGenerate a model comprised of:bApply thermodynamic constraints on this model as described in ,52.cSj [Minimize the sum of net flux in the subnetwork Sj –57.Sj generates a stoichiometrically proportional flux distribution in the subnetwork Sj. This leads to the exact stoichiometric expenditure of each Mcore to synthesize BBBj.Postulate 5: Minimizing the sum of net flux in dRsub with respect to the flux distribution obtained after minimization. This is collapsing the reactions into 1 overall reaction that is stoichiometrically equivalent to the flux distribution generated above.Lump BBBj, GEM is further constrained with the following integer cuts constraint after generating each Sj with an iterative manner [To identify alternative subnetworks for e manner .Sj,2.Postulate 6: Since S1 FileE. coli iJO1366 and S. cerevisiae iMM904.All generated subnetworks for all the biomass building blocks of (ZIP)Click here for additional data file.S2 FileE. coli and S. cerevisiae including the defined core networks and selected lumped reactions.Core models for (ZIP)Click here for additional data file.S3 FileMATLAB based code of lumpGEM that generates FBA feasible subnetworks and lumped reactions.(ZIP)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.


Arabidopsis thaliana, and liver-specific reconstructions derived from a human model with various experimental data sources. The application of these methods allows us to obtain the following results: (i) we sample the space of alternative flux distributions in the leaf- and the liver-specific case and quantify the ambiguity of the predictions. In addition, we show how the inclusion of ℓ1-regularization during data integration reduces the ambiguity in both cases. (ii) We generate sets of alternative leaf- and liver-specific models that are optimal to each one of the evaluated model reconstruction approaches. We demonstrate that alternative models of the same context contain a marked fraction of disparate reactions. Further, we show that a careful balance between model sparsity and metabolic functionality helps in reducing the discrepancies between alternative models. Finally, our findings indicate that alternative optima must be taken into account for rendering the context-specific metabolic model predictions less ambiguous.The integration of experimental data into genome-scale metabolic models can greatly improve flux predictions. This is achieved by restricting predictions to a more realistic context-specific domain, like a particular cell or tissue type. Several computational approaches to integrate data have been proposed—generally obtaining context-specific (sub)models or flux distributions. However, these approaches may lead to a multitude of equally valid but potentially different models or flux distributions, due to possible alternative optima in the underlying optimization problems. Although this issue introduces ambiguity in context-specific predictions, it has not been generally recognized, especially in the case of model reconstructions. In this study, we analyze the impact of alternative optima in four state-of-the-art context-specific data integration approaches, providing both flux distributions and/or metabolic models. To this end, we present three computational methods and apply them to two particular case studies: leaf-specific predictions from the integration of gene expression data in a metabolic model of  Arabidopsis thaliana and the human liver, we show that the analysis of alternative optima is key to adequately evaluating the specificity of the predictions in particular cellular contexts. While we provide several ways to reduce the ambiguity in the context-specific predictions, our findings indicate that the existence of alternative optimal solutions warrant caution in detailed context-specific analyses of metabolism.Recent methodological developments have facilitated the integration of high-throughput data into genome-scale models to obtain context-specific metabolic reconstructions. A unique solution to this data integration problem often may not be guaranteed, leading to a multitude of context-specific predictions equally concordant with the integrated data. Yet, little attention has been paid to the alternative optima resulting from the integration of context-specific data. Here we present computational approaches to analyze alternative optima for different context-specific data integration instances. By using these approaches on metabolic reconstructions for the leaf of  PLOS Computational Biology Methods paper.This is a i.e., if a reaction is irreversible or reversible under normal physiological conditions) and mass-balance conditions. These constraints are included in every constraint-based approach. The second type comprises constraints specific to each approach, and usually reflects the context-specific knowledge or data to be integrated. Flux distributions which satisfy the set of constraints are called feasible. A convex optimization problem is guaranteed to render a unique optimal value [Genome-scale metabolic models (GEMs) have proven instrumental in characterizing the activity of metabolic pathways in different biological scenarios. The activity of all metabolic reactions is specified by the flux distribution, which can be readily inferred from GEMs through the usage of constraint-based approaches ,2. Such al value . Howeveral value –9.i) obtaining context-specific flux distribution and (ii) determining context-specific GEMs; we refer to the respective approaches as flux- and network-centered, respectively. Alternative optima may also result from the integration of context-specific data. In both settings, the existence of alternative optima leads to ambiguity in context-specific flux distributions and/or network reconstructions, since alternative solutions may substantially differ. This is particularly important in the case of context-specific network reconstructions, where further investigations conducted on a single optimal network could lead to erroneous conclusions.Experimental systems biology studies have generated comprehensive atlases of transcript, protein, and metabolite levels from different context, such as: cell types, developmental stages, and environments, across different species from all kingdoms of life –15. AnalTo our knowledge, only three studies considered the space of alternative optimal solutions arising from flux-centered approaches: The approach termed iMAT  proposedi) the context-specific data integration approaches herein evaluated, and (ii) the methods that we propose to analyze the respective alternative optima. The second part presents the findings obtained from applying the previously described methods to two particular case studies: a leaf-specific reconstruction from the model plant Arabidopsis thaliana, and a human liver reconstruction. This second part serves as an illustration of the impact that alternative optima have in context-specific metabolic reconstructions, and may be followed independently from the first part—which is primary addressed to the specialized reader.In the present study, we propose a method to quantify the variability of alternative optimal flux values of a flux-centered approach. Additionally, we quantify the effect in the alternative optima of including an additional constraint in the flux values, minimize the total sum of absolute flux values, which has been proposed to obtain unique solutions in a flux-centered method . FurtherAOS). We then focus on Core Expansion (CorEx), also developed in this study, which we take as representative of a network-centered approach. In addition, we show how the optimization program behind CorEx can be adapted to evaluate not only its alternative optima space, but that of FastCORE [In this section, we present the mathematical formulation of the computational methods that we developed to investigate the alternative optima of three selected data integration approaches. In all three cases, we first provide an overview of the approach, which is followed by a description of the method to explore its alternative optima space. We start by a representative of a flux-centered approach—a modified version of RegrEx —and the FastCORE  and CORDFastCORE , two staGiven a GEM and (context-specific) gene or protein expression data, the Regularized metabolic model Extraction (RegrEx) method reconstructs a context-specific metabolic model, along with the corresponding flux distribution. To this end, RegrEx finds a feasible flux distribution that is closest to a given experimental data set, and is, therefore, considered a flux-centered approach.d, and a feasible flux distribution, v, i.e., the squared ℓ2 norm of the difference vector ϵ = d – v, was minimized [1 norm of v in the minimization problem, as a means to select the reactions in the GEM that are most important for a given metabolic context. However, here we used a slightly modified version of RegrEx: Instead of minimizing the sum of square errors, we minimize the sum of absolute errors, i.e., the ℓ1 norm of ϵ. Except for this substitution, the modified RegrEx version, called RegrExLAD (for Least Absolute Deviations), follows the same formulation as the original RegrEx  associated gene expression . This is accomplished by splitting reversible reactions into the forward and backward directions, each constrained to have non-negative flux value, and introducing a vector of binary variables, x, to select only one of them during the optimization. Altogether, these particularities are captured in the mixed integer linear program (MILP),The minimization problem behind RegrEx1, the flux distribution, v, is partitioned into the sets of irreversible (virr), and reversible reactions proceeding into the forward (vfor) and backward directions (vback), and the (reaction) columns of the stoichiometric matrix, Sext, are ordered to match the partition of v. In addition, the components of the error vector, ϵi = ϵ+i−ϵ–i, ϵ+i, ϵ–i≥ 0, are split into two non-negative variables, ϵ+i, ϵ–i, as a way to computationally treat the otherwise required absolute values of the components of ϵ. Thus, the ℓ1 norm ||ϵ||1 = Σi |ϵi| is replaced by ϵ+i+ ϵ–i in the objective function. . Finally, the λ parameter corresponds to the weight of the ℓ1 norm in the objective function, and is chosen during the optimization as to maximize the Pearson correlation between data and flux values [In OPx values .1 guarantees finding the minimum distance between experimental data and a feasible flux distribution that is allowed by the constraints. However, it does not guarantee that the resulting flux distribution is the only feasible one that is optimal with respect to a particular context-specific data. This variability in optimal flux distributions may be attributed to two factors. On the one hand, as mentioned above, not all reactions in a GEM are typically associated to data. In contrast to data-bounded reactions, there is a set of data-orphan reactions comprising non-enzymatically catalyzed reactions, reactions without gene-protein annotation or without associated data for a particular context. Data-orphan reactions do not contribute to the error norm in the RegrExLAD objective function, described in OP1, and their flux value can vary as long as v satisfies the imposed constraints and its ℓ1 norm is preserved. This situation is depicted in v that is closest to the data vector, d, is carried out in the projection of the flux cone, F = {v: Sv = 0, vmin ≤ v ≤ vmax}, where d resides. On the other hand, the geometry of F may preclude certain reactions to obtain an exact match with the data value, when d remains outside the projection of F. In this case, a set of flux distributions may be equidistant to d, thus generating variability also in the optimal flux value of data-bounded reactions.The convexity of OPAOS, depicted in LAD, see AOS first creates a random flux vector, vrand, which is bounded by the maximum and minimum flux values previously calculated by Flux Variability Analysis  = δ+irr(i)−δ–irr(i) = vrand(i)−virr(i), i ∈ IR, acts over the set of irreversible reactions (IR) and δfor(i) = δ+for(i)−δ–for(i) = vrand(i)−vfor(i), δback(i) = vrand(i)−vback(i), i ∈ RR, over the set of reversible reactions (RR). Note that both δirr, δfor, are defined as the difference of two non-negative components, which enables us to formulate a linear objective function that renders OP2 computationally tractable. In contrast, δback does not require this treatment since it always takes non-negative values  which facilitates the optimization process. In addition, δfor and δback are constrained to be mutually exclusive by the same binary variable, x, introduced to select only one of the directions in reversible reactions (i.e. either forward or backward). In this manner, OP2 will select the direction of reversible reactions that minimizes the overall distance to vrand. Finally, reversible reactions whose sign was originally changed in vrand are altered back to their original directions and their sampled flux values are modified accordingly.OPlues see . This isR = C∪P of reactions in the original GEM into a core set, C, that must be present in the final context-specific model, and a non-core set, P, which does not necessarily have to be in the final model. These approaches find then a subset PA⊆ P of non-core reactions that renders C consistent, i.e., all reactions in the core are able to carry a non-zero flux in at least one steady-state solution. The final context-specific subnetwork is then defined as RA = C∪PA. Some approaches, like MBA [PA, as to obtain a parsimonious final model. In contrast, CORDA [PA if desired.In this section, we analyze the alternative optimal solutions of CorEx, a method that we designed in this study to represent the network-centered approaches. In a general sense, network-centered approaches first partition the set like MBA , mCADRE like MBA  and Fastlike MBA , aim at t, CORDA  relaxes 3, which minimizes the number of reactions with non-zero flux in P while constraining all reactions in the core to carry at least a small positive flux (ϵ in constraints 2–3). This is achieved by minimizing the norm (Z in OP3) of the vector, x, of binary variables (constraints 4–7) which selects the set PA that renders the MILP feasible. Note that the selected non-core reactions are forced to carry a small positive flux  to guarantee that they are active in the final context-specific model. Finally, like in RegrEx, reversible reactions are split into the forward and backward directions, to operate only with non-negative flux values. In addition, another vector of binary variables, y in constraints 8–9 of OP3, is introduced to select the direction of reversible reactions .CorEx follows the MILP displayed in OP4. The general idea behind OP4 is to find the most dissimilar context-specific network, RA* = C∪PA*, to a previously found optimal RA, that maintains the set C consistent. Namely, it maximizes the number of differences between the reactions contained in PA and PA*. Note that OP4 inherits constraints 1–9 from OP3, and incorporates three new constraints. Constraint 10 guarantees that the cardinality of PA* equals that of the previous optimal PA in OP3. Constraint 11 introduces two additional binary variables, δ+, δ–, which measure the mismatches between the vectors x, selecting the reactions in PA*, and the optimal vector xopt, selecting the reactions in PA and previously found by OP3. Finally, constraint 12 is added to impose a δ+XOR δ− relationship to avoid the trivial optimal solution in which δ+ = δ–,To identify alternative optimal CorEx extracted networks, we developed the MILP displayed in OP4 can be used to generate alternative optimal networks to other network-centered approaches. We just need to set xopt, in constraint 11, to be the optimal x vector of the particular approach under study; in addition, we need to update Z, in constraint 10, to the corresponding number of non-core reactions added by this approach . Note that xopt can be easily constructed from the set PA, which is derived from a particular context-specific model. In addition, a similar constraint to the constraint 10 of OP4, namely ||x||1 ≥ Zlb, may be included in OP3, as a lower bound to its objective function, where Z* ≤ Zlb≤ R, and Z* is the unconstrained optimum of OP3. It is in this manner that CorEx allows relaxing the parsimony condition, as commented before, although in this study we did not constrain the CorEx optimum.However, besides CorEx, OP4 to obtain alternative optimal networks lies in its MILP formulation. This is because, with the exception of CorEx, which also relies on a single MILP, all existing network-centered approaches require iteratively solving a convex optimization problem. For instance, the linear programs behind the consistency testing step of FastCORE [4 by analyzing the alternative solutions of a single MILP. However, OP4 only generates a single, maximally different, alternative optimal network. To generate a sample of alternative networks, here we applied OP4 in an iterative way. We first used OP4 to obtain a maximally different network to a given optimal context-specific network, and then repeated this process of feeding OP4 with the successively generated alternative networks until no additional one was found. At that point, we randomly perturbed the last network by changing the state (active or inactive) of 1% of the reactions, and repeated this process until no additional network was found , medium, (MC) and negative (NC) confidence, and an additional group collecting the remaining reactions (OT) in the GEM, for which experimental evidence is not available. In this case, the group HC corresponds to the core set of reactions , and the other three groups constitute the non-core set P, although reactions in MC are preferentially added over NC and OT reactions. To account for the different reaction groups, we partitioned the vector x in OP4 into the sets of MC, NC and OT reactions, and evaluated constraint 10 for each of the three sets. In this manner, we guaranteed that an alternative optimal network contained, besides all HC reactions, the same number of MC, NC and OT reactions than the original CORDA optimum.Finally, we use the AltNet procedure to analyze the alternative optima space of CorEx, FastCORE and CORDA. In the latter case, however, OPArabidopsis thaliana, and a human, liver-specific reconstruction. In the first case, we used the AraCORE model, which includes the primary metabolism of Arabidopsis thaliana [Here, we illustrate the ambiguity found during the extraction of context-specific flux distributions and metabolic networks due to the alternative optima. To this end, we apply the methods described in the previous section to two case studies: a leaf-specific scenario, the model plant thaliana , and a lthaliana  . However, we found reactions with particularly low or high entropy values in both sets, data-bounded and data-orphan  interchanging glyceraldehyde 3-phosphate and orthophosphate between the chloroplast and cytoplasm, the P5C exporter  exporting 1-Pyrroine-5-carboxylate from mitochondria to cytoplasm and the ADP/ATP carrier , interchanging ATP and ADP also between mitochondria and cytoplasm . Therefore, it would be informative to evaluate whether integrating context-specific experimental data in a GEM could be used to fix the direction of such reactions. Interestingly, we found that a large proportion (75.81%) of the reversible reactions carrying a non-zero flux (including data-orphan) had a fixed direction, either forward or backward, in the alternative optima . This fiData, and data-orphan, HOrphan, reactions, as well as for all reactions, HTotal, the mean entropy value across all reactions,Rev.For the analyzed sequence of increasing λ-values, the table includes: The sum of entropy values for the subset of data-bounded, HLAD alternative optima space for a sequence of increasing λ-values. This was motivated to test whether the inclusion of ℓ1-regularization, besides imposing sparsity in optimal flux distributions, could also reduce the variability found in individual reaction flux values across the alternative optima space. This property could serve as a way to decrease the uncertainty, as measured by the Shannon entropy, associated to a context-specific data integration problem. To this end, we first applied RegrExLAD on AraCOREred and the same leaf data set, but using three increasing λ-values . We then applied RegrExAOS to sample the alternative optima space of each of the three RegrExLAD data integrations.We next evaluated the RegrExHOrphan = 86.82 for λ = 0, to HOrphan = 36.50 with λ = 0.5. In contrast, for the data-bounded reactions, it only decreased from a value of 73.17 with λ = 0 to 65.46 with λ = 0.5, and even led to a transient increase at λ = 0.3 , and the mean number, i.e., Hamming distance) across the alternative networks for the leaf- and the liver-specific scenarios evaluated by two methods, CorEx and FastCORE. The last column displays the p-value resulted from a one-sided ranksum test comparing the distributions of Hamming distances between any pair of the alternative networks of CorEx and FastCORE (the null hypothesis states that the distribution generated by CorEx is bigger than that of FastCORE).This table summarizes the results of the evaluation of the CorEx alternative optima space. It includes the number of added non-core reactions, CorEx, alternative networks differed on average in 29 non-core reactions, with a maximum value of 52 reactions (22% of the added non-core reactions). In LeafFastCORE, networks differed on average in 66.78 reactions, and had a maximum number of 118 discrepant reactions , with an average of 108.3. In the case of LiverFastCORE, the maximum number of discrepant reactions was as high as 398 out of the 677 (58.8%) added non-core reactions, with an average of 246.93 between alternative optimal networks  a set of non-core reactions that were always included, termed the active non-core set, (ii) a set of non-core reactions that were excluded from all alternative networks, termed the inactive non-core set, and (iii) a set of non-core reactions that were included in some of the networks, referred to as the variable non-core set. In this case, we took the size of the variable non-core set as a measurement of the uncertainty of a context-specific network extraction; 28% and a 47% of the total non-core reactions were in the variable set in the cases of LeafCorEx and LeafFastCORE. On the other hand, a 12% and a 58% were found in LiverCorEx and LiverFastCORE, respectively  are more or less frequent , in the alternative optima space. To address this issue, we assigned a score (between 0 and 1) to each metabolic pathway based on its representation in the active, variable or inactive non-core set. Specifically, the score represents the fraction of reactions of a given pathway that are assigned to a non-core subset with respect to the total size of the non-core set  provided in [CORDA was obtained from Recon1 and experimental evidence from the Human Protein Atlas [CORDA with marked differences among them. Concretely, a maximum number of 992 discrepant reactions between two alternative networks, out of the total 1527 distributed among the MC, NC and OT groups  set if it is active throughout the alternative optima sample. Finally, EXAMO uses the HFR set as a core set to MBA [The analysis of the alternative optima space can be employed to cope with the ambiguity of a context-specific network reconstruction. Notably, the authors of EXAMO (EXploration of Alternative Metabolic Optima)  proposedt to MBA , a netwoi) similar to EXAMO, obtain samples of alternative optimal flux distributions, binarize flux values and rank the reactions according to the number of times that they appear as active in the sample, ii) include the reactions that are always active (the HFR set) in a core set and the rest in a non-core set, and iii), add non-core reactions in decreasing order of frequency until consistency of the core is reached. In this manner, this ranking provides a way to select which non-core reactions are included in the final model. This idea parallels that of mCADRE [AOS that allows drawing arbitrarily large samples, as opposed to the one used in EXAMO which generates samples of restricted size. Details about this method, here called iMATAOS, can be found in A possible way to circumvent this problem in the case of iMAT could be the following: f mCADRE , althougi.e. the core set is active), non-core reactions could be again added in decreasing order of frequency to the core set until consistency is reached. Naturally, this requires the development of competent methods to sample the alternative space of network-centered approaches. In this sense, we consider our proposed AltNet procedure a first step towards this goal.In the case of the network-centered approaches here evaluated, establishing a ranking of non-core reactions could also be a way to deal with the ambiguity during network reconstructions. Non-core reactions that occur with high frequency in the alternative optima space should be preferentially included in the final network, while reactions with a low frequency should be discarded. To guarantee that the final network is consistent (i) a medium size GEM of the primary metabolism of Arabidopsis thaliana [ii) a larger GEM collecting a reconstruction of a human metabolic network [We analyzed the space of alternative optima resulting from the integration of context-specific data into GEMs. To this end, we evaluated a representative set from the flux- and network-centered approaches. We selected RegrEx  as a repthaliana  and a lethaliana , and  were implemented in MATLAB and solved using Gurobi (version 7.1) [i) reduced feasibility tolerance to 10−9 when solving OP3-4, ii) increased MIPGap parameter to 1% when solving the MILP of OP2. All generated code with the implementations is available as Supplementary Information.All optimization programs used in this study, (ion 7.1)  on a desA reduced version of the original AraCORE model  was usedArabidopsis thaliana Col-0 lines with no treatment. The corresponding CEL files were normalized using the RMA (Robust Multi-Array Average) method implemented in the affy R package [mapgene2rxn, which is available in Leaf-specific gene expression values were taken from , stored  package . In addi package , where phttp://medicalgenomics.org/rna_seq_atlas/download. In this case, we used the RPKM values corresponding to the liver . Since the RPKM values are already normalized we used them directly as input of the mapgene2rxn procedure, already described.Liver-specific gene expression values were obtained from , which ivi| < 10−6. The Flux Variability Analysis was implemented in the MATLAB function reduceGEM which also extracted the reduced model, Recon1red, in a COBRA compatible MATLAB structure. The function is available in We removed blocked reactions from the original Recon1 model to get the Recon1red model used in this study. To this end, we performed a Flux Variability Analysis (see next section) and removed reactions with a maximum absolute flux, |i.e., no reaction was forced to take a fraction of a previously calculated optimal value). This was accomplished through the following linear program,FVA.The minimum and maximum allowed values of each reaction in AraCOREred were determined through Flux Variability Analysis . Althougi.e., the flux cone) when no experimental data was been integrated. To this end, and to allow direct comparability of the results, the flux cone was sampled following a similar approach as in RegrExAOS: first, we generated a random vector of flux values, vrand, within the minimum and maximum values obtained by regular Flux Variability Analysis. The closest flux vector v to vrand within the flux cone was then obtained by minimizing the Euclidean distance between the two vectors. The following quadratic program was used to this end:To evaluate to what extent the Leaf data integration affected the entropy values of the reactions in the AraCOREred model, we also sampled the space of feasible flux distributions . The MATLAB function implementing this sampling procedure can be found in coneSampling.This procedure was iterated to obtained a sample of size Hi, was used to quantify the extent to which the flux values of a reaction, i, varied across the alternative optima space. It was calculated as follows:fi,k represents the frequency  of the k interval in the distribution, for n = 20 equally spaced flux value intervals within the flux range of i. In addition, the total entropy of an alternative optima space, HT, was defined as the sum of the entropies corresponding to the r reactions in AraCOREred, i.e.,The Shannon entropy of the sampled alternative optima distribution, v ≥ 10−6, and 0 otherwise. This process was repeated for each sampled alternative optimal flux distribution. In addition, repeated vector representations were removed from the generated set. After the binary representations were obtained, we calculated the number of mismatches between any pair, a,b, of binary vectors, with a ≠ b, i.e., the Hamming distance,In the case of CorEx, we generated the set of alternative optimal metabolic networks from the set of sampled alternative optimal flux distributions. To this end, we first generated the binary vector representations of the flux distributions. The binary vector representations were generated by assigning a value of 1 to the entries corresponding to reactions with a flux value R values whose characteristics were reported and compared.In this way, we obtained a distribution of MM, represents the fraction of the reactions in the  non-core set, P, belonging to the pathway that are assigned to the active, variable or inactive non-core . That is, in general,XM ∈ {AM, VM, IM} represents the number of reactions assigned to M that are included in the active, variable or inactive non-core, respectively.We computed a score, ranging between 0 and 1, to quantify the ambiguity found in individual metabolic pathways (subsystems in the GEM) across the space of alternative optimal networks. Concretely, the score of a pathway, CORDA model, using the same reaction identifiers in liverCORDAnew but extracting the reactions from our Recon1red version, we found that the generated model passed all metabolic 48 tasks in the test. Hence, for consistency of the results, we considered that all proper alternative optimal networks to LiverCORDA had to pass all 48 tasks as well.We performed the same metabolic test proposed in  and applS1 Figi.e., flux distributions) to the leaf-specific RegrExLAD integration problem is presented. The sequence begins with λ = 0  and ends with λ = 1, which is the value for which all fluxes are shrunk to 0. Flux distributions get sparser with increasing values for lambda. In addition, the total entropy of the alternative optima tends to decrease with increasing values for lambda. This indicates the existence of a trade-off between sparsity and entropy reduction. In this study, a mild regularization (λ = 0.1) seems sufficient to substantially reduce the total entropy value while preventing flux distributions to become too sparse .A sequence of optimal solutions ((PDF)Click here for additional data file.S1 TableLAD leaf-specific data integration. For each reaction in the list, the reaction index in the AraCOREred model, as well as reaction name, the metabolic subsystem to which it is allocated and the reaction mechanism are displayed. As commented in the main text, the entropy values may be taken as a soft measure of the importance that a reaction has in a given context. This is because small entropy values imply that a reaction is constrained to operate under a small range of flux values in the given context. To contrast the entropy values obtained after the leaf-data integration, we also provide the entropy values shown by reactions when no experimental data are integrated, that is, corresponding to a random sample of the flux cone Click here for additional data file.S2 TableLAD. The networks are generated by sampling the alternative optima space of RegrEx with RegrExAOS and considering, for each sampled flux vector, that a reaction is present in the associated network if its absolute flux value is greater than 10−6. The reaction names and the metabolic subsystems to which each reaction belongs are also included.Non-core reactions are ranked in descending order based on the frequency of the presence of these reactions among the alternative optimal networks generated by RegrEx(XLSX)Click here for additional data file.S3 TableAOS. Networks are generated by considering reactions in the sampled flux distributions with an absolute flux value is greater than 10−6. The reaction names and the metabolic subsystems to which each reaction belongs are also included.Non-core reactions are ranked in descending order based on the frequency of the presence of these reactions among the alternative optimal networks generated by iMAT(XLSX)Click here for additional data file.S4 TableNon-core reactions are ranked in descending order based on the frequency of the presence of these reactions among the alternative optimal networks generated by CorEx. The reaction names and the metabolic subsystems to which each reaction belongs are also included.(XLSX)Click here for additional data file.S5 TableNon-core reactions are ranked in descending order based on the frequency of the presence of these reactions among the alternative optimal networks generated by CorEx (through the usage of the AlterNet procedure described in the text). The reaction names and the metabolic subsystems to which each reaction belongs are also included.(XLSX)Click here for additional data file.S6 TableNon-core reactions are ranked in descending order based on the frequency of the presence of these reactions among the alternative optimal networks generated by FastCORE (through the usage of the AlterNet procedure described in the text). The reaction names and the metabolic subsystems to which each reaction belongs are also included.(XLSX)Click here for additional data file.S7 TableNon-core reactions are ranked in descending order based on the frequency of the presence of these reactions among the alternative optimal networks generated by FastCORE (through the usage of the AlterNet procedure described in the text). The reaction names and the metabolic subsystems to which each reaction belongs are also included.(XLSX)Click here for additional data file.S8 TableNon-HC reactions are ranked in descending order based on the frequency of the presence of these reactions among the alternative optimal networks generated by CORDA (through the usage of the AlterNet procedure described in the text). The reaction names and the metabolic subsystems to which each reaction belongs are also included.(XLSX)Click here for additional data file.S9 TableThe description of the score used to rank the pathways is provided in Methods.(XLSX)Click here for additional data file.S1 AppendixOLS) with the formulation used in this study (RegrExLAD) and justifies its usage. A comparison of the performance between the two versions is also provided.This appendix compares the original formulation of RegrEx (RegrEx(PDF)Click here for additional data file.S2 AppendixAOS) to sample the alternative optima space of iMAT, which is proposed in this study. We apply iMATAOS to evaluate the ambiguity of the predictions in both, the leaf and the liver scenarios.This appendix describes the alternative procedure (iMAT(PDF)Click here for additional data file.S1 FileThe GEM models as well as the (mapped to reaction) expression data used are also included.(RAR)Click here for additional data file.


Here, we show that energy-generating cycles occur in over 85% of metabolic models without extensive manual curation, such as those contained in the ModelSEED and MetaNetX databases; in contrast, such cycles are rare in the manually curated models of the BiGG database. Energy generating cycles may represent model errors, e.g., erroneous assumptions on reaction reversibilities. Alternatively, part of the cycle may be thermodynamically feasible in one environment, while the remainder is thermodynamically feasible in another environment; as standard FBA does not account for thermodynamics, combining these into an FBA model allows erroneous energy generation. The presence of energy-generating cycles typically inflates maximal biomass production rates by 25%, and may lead to biases in evolutionary simulations. We present efficient computational methods (i) to identify energy generating cycles, using FBA, and (ii) to identify minimal sets of model changes that eliminate them, using a variant of the GlobalFit algorithm.Energy metabolism is central to cellular biology. Thus, genome-scale models of heterotrophic unicellular species must account appropriately for the utilization of external nutrients to synthesize energy metabolites such as ATP. However, metabolic models designed for flux-balance analysis (FBA) may contain thermodynamically impossible energy-generating cycles: without nutrient consumption, these models are still capable of charging energy metabolites , a simplified mathematical description able to describe the simultaneous activity of hundreds of biochemical reactions. Cellular functions are often dependent on the availability of sufficient energy, and thus a correct representation of energy metabolism appears crucial to metabolic modeling. However, we found that the majority of FBA models generated directly from genome sequences, as well as a minority of carefully curated models, are capable of generating energy out of thin air. These models charge energy metabolites such as ATP without any nutrient uptake. We named the corresponding sets of reactions “erroneous energy generating cycles” (EGCs) and developed a high-throughput algorithm for their identification. We found EGCs in 238 (68%) of 350 metabolic models from three different databases. We developed a second, fully automated method for EGC removal. Simulations on the corrected models typically showed growth rates that were 25% slower than in the original models, demonstrating the importance of checking metabolic model reconstructions for EGCs. However, constraint-based analyses typically do not explicitly consider thermodynamics. As a result, the mathematical solution of constraint-based problems is often thermodynamically infeasible [H2O]) / ([ADP][Pi][H+]) is smaller than the corresponding equilibrium constant Keq = 2×10-5M-1. If we treat the concentration of H2O (55M) as constant, this cannot occur within the physiological concentration bounds assumed by Henry et al.  for reversible and  for irreversible reactions.To each GSM, we added 15 energy dissipation reactions  in the network. Because 0 ≤ ∣vi∣ ≤ 1 for all reactions other than dissipation reactions, the value of An optimal value lobalFit was used to eliminate all EGCs from the network. GlobalFit was developed to find globally minimal sets of model changes that simultaneously reconcile sets of experimental growth and non-growth observations with model predictions; a detailed description of the original GlobalFit algorithm can be found in [lobalFit for the efficient removal of EGCs as outlined below.Once a GSM was identified to contain at least one EGC, Gfound in . We modi∑d∣vd∣) = 0. To ensure that reaction removals do not abolish biomass production by eliminating EGCs, we set up a growth case with a minimal biomass production rate in a rich medium that allows uptake of all nutrients.In this modified version, the only allowed type of model change is the removal of unidirectional reactions, where reversible reactions are treated as two independent unidirectional reactions. We contrast a single growth with a single non-growth case. The non-growth case reflects the removal of all EGCs: with no nutrient uptake allowed, the maximal sum of fluxes through the energy dissipation reactions must be zero, max, the search for model corrections requires considerably more time for the yeast 7 metabolic network . The red line (“simple”) is for runs allowing all reaction removals; the blue line (“synthase”) is for runs not allowing removal of the ATP synthase reaction.Distribution of computation  times for the application of G(TIFF)Click here for additional data file.S1 TableEnergy dissipation reactions (EDRs) for each of the 15 different types of energy metabolites in the cell.(XLSX)Click here for additional data file.S2 TablelobalFit for the “simple” run  and with removal of the ATP synthase forbidden (“synthase”).For each model, this table shows whether biomass production was possible at all (hasGrowth), whether energy generating cycles are present (hasEGCs), the identified types of EGCs , and the reactions (or reaction directions) removed by G(XLSX)Click here for additional data file.S1 TextA small example network that illustrates the inability of ll-COBRA and TMFA to reliably exclude EGCs.(PDF)Click here for additional data file.


Bordetella pertussis. Despite widespread vaccination, its incidence has been rising alarmingly, and yet, the physiology of B. pertussis remains poorly understood. We combined genome-scale metabolic reconstruction, a novel optimization algorithm, and experimental data to probe the full metabolic potential of this pathogen, using B. pertussis strain Tohama I as a reference. Experimental validation showed that B. pertussis secretes a significant proportion of nitrogen as arginine and purine nucleosides, which may contribute to modulation of the host response. We also found that B. pertussis can be unexpectedly versatile, being able to metabolize many compounds while displaying minimal nutrient requirements. It can grow without cysteine, using inorganic sulfur sources, such as thiosulfate, and it can grow on organic acids, such as citrate or lactate, as sole carbon sources, providing in vivo demonstration that its tricarboxylic acid (TCA) cycle is functional. Although the metabolic reconstruction of eight additional strains indicates that the structural genes underlying this metabolic flexibility are widespread, experimental validation suggests a role of strain-specific regulatory mechanisms in shaping metabolic capabilities. Among five alternative strains tested, three strains were shown to grow on substrate combinations requiring a functional TCA cycle, but only one strain could use thiosulfate. Finally, the metabolic model was used to rationally design growth media with >2-fold improvements in pertussis toxin production. This study thus provides novel insights into B. pertussis physiology and highlights the potential, but also the limitations, of models based solely on metabolic gene content.Whooping cough is a highly contagious respiratory disease caused by IMPORTANCE The metabolic capabilities of Bordetella pertussis, the causative agent of whooping cough, were investigated from a systems-level perspective. We constructed a comprehensive genome-scale metabolic model for B. pertussis and challenged its predictions experimentally. This systems approach shed light on new potential host-microbe interactions and allowed us to rationally design novel growth media with >2-fold improvements in pertussis toxin production. Most importantly, we also uncovered the potential for metabolic flexibility of B. pertussis , although our results also highlight the importance of strain-specific regulatory determinants in shaping metabolic capabilities. Deciphering the underlying regulatory mechanisms appears to be crucial for a comprehensive understanding of B. pertussis's lifestyle and the epidemiology of whooping cough. The contribution of metabolic models in this context will require the extension of the genome-scale metabolic model to integrate this regulatory dimension. Bordetella pertussis. Despite widespread vaccination, it remains an important health burden, with an estimated 16 million cases in 2008 .Genome-scale models are inventories of the metabolic capabilities encoded in a genome. In recent years, powerful computational tools have been developed that allow the reconstruction of metabolic pathways for any organism , 15. TheB. pertussis from a systems-level perspective. In a first step, we developed a comprehensive genome-scale metabolic network for B. pertussis in an effort to reconcile physiological observations with genomic information. A detailed biomass reaction was formulated based on experimental data, and new pathways were introduced to accommodate the synthesis of biomass components. We further developed a novel algorithm that enumerates all possible minimal nutrient combinations that support the formation of this highly specific biomass. In this way, we could systematically probe the full metabolic capabilities of B. pertussis.In the present work, we used these techniques to reinvestigate the metabolism of B. pertussis can be much more versatile than previously reported and is able to grow on very minimal media, where only the carbon source must be organic, although such behaviors are strain dependent. Our model also predicted the excretion of novel nitrogen-containing products that may shed new light on potential host-pathogen interactions. Finally, we used the validated model to rationally engineer new medium formulations for the production of vaccine antigens. Improved media resulted in up to 2.4-fold increased pertussis toxin production. Our work demonstrates the innovation potential of comprehensive in silico approaches but also highlights their limitations.Through model-guided experimentation, we discovered that B. pertussis Tohama I was reconstructed based on its genome sequence  and many reactions not defined yet in the E. coli model, such as in pathways of amino acid metabolism, iron acquisition, sulfur metabolism, and biosynthesis of lipooligosaccharides and storage compounds (Data Set S3). In two pathways, a discrepancy was observed between sequence-based reconstruction and literature: (i) a fully functional TCA cycle was reconstructed  per mmolATP is in the range of previously reported values for B. pertussis . The de1 · h−1; ) but higB. pertussis in 12 chemically defined media was simulated using flux balance analysis (FBA) with model iBP1870. Two data sets were used: (i) a set of 6 shake-flask cultures in media with various ratios of glutamate, lactate, and ammonia, published by Thalen et al. . With both data sets, model predictions were in good agreement with experimentally measured yields, confirming the ability of the parameterized model iBP1870 to accurately and quantitatively predict biomass yields under various growth conditions -based approach  , 21. FVAapproach , we were 3 to 6% .The newly identified N sinks have a high N-to-C ratio . Their secretion as an alternative to ammonia is therefore an efficient way to eliminate excess nitrogen while limiting the amount of carbon wasted. Nevertheless, such biosynthetic products are energy-costly “waste” products, as confirmed by the analysis of iBP1870, which indicated that the secretion of other compounds, such as alternative amino acids, would be preferable from an energetic perspective. The observed metabolic behavior therefore suggests a role for these alternative N sinks beyond mere nitrogen excretion.B. pertussis Tohama I, we computed the combinations of minimal nutrient inputs that would support growth. As this is a combinatorial problem (the presence of one nutrient may affect the need for another), we developed enumeration of minimal active fluxes (EMAF)   and S4, s (EMAF) .B. pertussis is reported to be auxotrophic for cysteine, i.e., inorganic sulfur sources cannot support growth  and 2 organic (mercaptopyruvate and taurine) compounds. When tested experimentally, growth was confirmed with mercaptopyruvate and with thiosulfate . This pathway allows the missing reactions to be bypassed in the biosynthesis of cysteine from sulfate. This is a significant finding, as it expands the range of possible S substrates from strictly organic to inorganic and non-cysteine-containing S sources.We first applied EMAF to compute possible sulfur sources. t growth . In agreosulfate , one of osulfate  and a coB. pertussis is generally believed to require glutamate or proline exclusively for growth  could sustain in silico growth. In contrast, with a complete TCA cycle, all amino acids but histidine (for which no catabolic pathway was identified) would suffice as the sole C or N source. Experimentally, the growth of strain Tohama I was observed with four amino acids that required a functional TCA cycle for in silico growth: aspartate and asparagine sustained growth to levels only slightly below those of glutamine, while serine and alanine resulted in modest, yet significant growth (in silico predictions for 10 amino acids (tyrosine and cysteine were not tested), which can likely be explained by regulatory limitations not considered in purely stoichiometric models . Metabolic networks were reconstructed for 8 additional strains of B. pertussis, 4 strains of B. bronchiseptica, and 2 strains of B. parapertussis (28–http://f-a-m-e.org/fijo/) that facilitates the generation of genome-scale models based on genome sequence (Data Set S8). For each minimal medium composition that supported the in silico growth of B. pertussis Tohama I, the corresponding set of active reactions was retrieved from EMAF and compared to the reaction list of the reconstructed networks.Strain Tohama I is a clinical isolate that was isolated before the vaccination campaigns, and its representativeness of the estioned . We thusertussis , 28–30 bB. pertussis strains, irrespective of their geographical or temporal origin . In order to validate these predictions experimentally, we selected 5 strains of B. pertussis, including strain 18323, the strain most distantly related to Tohama I (ptxP1 (B1834 and B1920) or ptxP3 (B1831 and B1917) allele  allele . These s) allele .l-lactate) when thiosulfate was the source of S. Intriguingly, whereas Tohama I was able to grow with citrate as a sole C source and thiosulfate as a source of S , as demonstrated by their ability to grow with aspartate as a sole C or N source and an organic S source (cysteine and reduced glutathione). With this experimental setup, we could not demonstrate a functional TCA cycle in strains 18323 and B1831. Thiosulfate utilization was found to be restricted to strains Tohama I and 18323, as indicated by the absence of growth of the 4 recent isolates in a medium composed of glutamate as a sole C or N source and thiosulfate as a sole S source. Consistent with these results, only strain Tohama I was able to grow with TCA cycle-dependent C or C or N sources . However, we cannot conclude that this is a general characteristic of the species, as only Tohama I appears to combine a functional TCA cycle and the ability to use thiosulfate. The discrepancy between experimental observations and genome sequence information can possibly be explained by a differential regulation of gene expression between strains, a phenomenon recently shown to affect not only virulence genes but also metabolic genes in B. pertussis , both from a qualitative  and quantitative (energy parameters) point of view. A straightforward application of such information is the optimization of growth media. We thus tested whether improved fermentation media could be designed for vaccine production, based on this newly acquired knowledge.The new metabolic knowledge gained from our model-based approach is contained within the genome-scale model  . Significant growth was observed  . PT prodxin (PT) . This waxin (PT) . Based oially PT ), makingB. pertussis, and conditions that result in high PT production also promote high-level expression of all other virulence factors  aThe predicted medium (IMP-CDM) was tested experimentally with strain Tohama I and found to support a growth yield and rate similar to those of the initial MSS-CDM, with a 1.9-fold higher production of PT . By repeModel-driven process and medium modifications accounted for 91% of the total PT improvement of Tohama I grown in IMP2-CDM, as estimated from fermentations in which specific subsets of modifications were not implemented . The higThe third major contributor to PT improvement was the balancing of amino acid concentrations, which accounted for 21% of the PT yield increase in the improved medium . The reaBordetella pertussis. Model iBP1870 is much more detailed than the only B. pertussis model in the literature, which was limited to reactions involving amino acids and by-products considered to be main contributors to the carbon and nitrogen balance  and the siderophore alcaligin, two key virulence factors of this pathogen  whose functionality in B. pertussis was subject to debate , which demonstrates the functionality of new pathways for the de novo synthesis of cysteine. This metabolic trait was only confirmed in one additional strain (18323), whereas 4 recent clinical isolates failed to grow experimentally with thiosulfate as a sole S source, despite the presence of the genes required for thiosulfate utilization.Cysteine auxotrophy, as another major paradigm of pertussis metabolism , 16, wasB. pertussis metabolism. First, it can be versatile, as characterized by the large variety of substrate combinations that can be used for growth. Second, it can be minimal, in the sense that growth is possible in minimal, nearly mineral media (only the C source must be organic). Third, the above-mentioned characteristics seem, however, to rely on regulatory (nonmetabolic) strain-specific features, resulting in strain-to-strain variability. This likely explains discrepancies between different reports, such as the debate about the presence of a functional TCA cycle , our results indicate that the general acceptation that B. pertussis is fastidious might be too restrictive. Even if regulatory constraints or mutations make certain functions inactive in other strains, the presence of the necessary structural genes is conserved, providing potential for evolution or for expression under yet-unidentified conditions. Metabolic flexibility could participate in the survival of B. pertussis in the host, but also in external environments, although other factors, such as the known susceptibility of B. pertussis to fatty acids  by 2.4-ineering , 47, witineering . They coB. pertussis: it is much more versatile than previously reported, although this appears to depend on regulatory strain-specific determinants. This study thus highlights the potential, but also limitations, of models solely based on metabolic gene content. Deciphering and taking into account the mechanisms responsible for the regulation of metabolic capabilities therefore appear to be crucial for a comprehensive understanding of the lifestyle of B. pertussis and the epidemiology of whooping cough.The approach taken here to probe the full metabolic potential of an organism is general and can be applied to any sequenced organism for which a minimum amount of experimental data are accessible or can be generated . Here, wB. pertussis Tohama I (fermentations A and B) were performed in modified Stained-Scholte medium (MSS-CDM) (650] between 1.5 and 1.6) was used to inoculate a 20-liter fermentation vessel (Biolafitte) containing 10 liters of MSS-CDM. The fermenter was operated in batch mode at constant temperature (35°C) and head pressure . The culture was sparged with air at a constant rate of 20 liters/min. A mechanical foam breaker was used to control foaming. pH was regulated at 7.2 by automatic addition of 50% (wt/vol) acetic acid. The level of dissolved oxygen was regulated at 25% of its initial level by modulating the stirring speed. Sampling was performed at the start of fermentation and every 2 h between 18 h and the end of fermentation (abrupt decrease in oxygen demand). Supernatants and cells were separated by centrifugation  and stored at −20°C. Biomass concentration was monitored as the OD650 and dry cell weight (DCW).Two batch fermentations of MSS-CDM) . The prePT and FHA concentrations were determined by enzyme-linked immunosorbent assay (ELISA) in the culture supernatants, as previously described .DCW] for biomass) and corrected for water evaporation, acetic acid addition, and sampling. For each metabolite (including biomass), the net production/consumption was calculated at every time point by subtracting the amount initially present from the amount at the time point considered . The time courses of net production/consumption of each metabolite were then spline-fitted using the method of Klasson . The conversion of exometabolite concentrations to net fluxes is described in details in Data Set S1. Briefly, exometabolite concentrations were converted to absolute amounts  experimental measurements at different growth stages on cells issued from the two batch reference fermentations , (ii) literature data, and (iii) theoretical calculations (Data Set S2). Growth was modeled as a sink of biomass components in a proportion that matches biomass composition .B. pertussis Tohama I was reconstructed in three phases: (i) semiautomatic reconstruction based on model iAF1260 of E. coli MG1655  thMaintenance and growth-associated ATP consumption were determined using flux balance analysis (FBA) on model iBP1870, as previously described , using eFBA was used in combination with model iBP1870 to compute the maximum possible biomass production under constraints reflecting substrate availability in different media (Data Set S5). For every simulation, maintenance energy consumption was calculated based on measured growth parameters  and was introduced in the simulations as the lower bound of the R_ATPM ATP hydrolysis reaction (Data Set S5). Additional constraints were set to mimic a partially nonfunctional TCA cycle. The simulation results were compared to experimental growth yields, as derived from the literature  data of or as gem/z values  whose peak areas varied proportionally between at least two consecutive dilutions, corresponding to 13,056 possible matches in the human metabolome database  to confirm their presence in the fermentation supernatants by comparison with commercial standards: a compound was considered present in a sample provided (i) the retention time (RT) did not deviate by more than 0.5 min compared to the RT of the standard (pure compound) and (ii) at least 2 of the characteristic MS/MS transitions (as determined with the standards) were detectable. Among the 12 metabolites confirmed to be present at the end of the reference fermentations (including 11 N-containing end products), six  were quantified at different time points of the fermentations, by standard addition using LC-MS/MS (Data Set S6). Adenine was also quantified with an enzyme-based assay .For the qualitative identification of N sinks, supernatant samples from the endpoint of the two reference fermentations were mixed (1:1 ratio), diluted , and analyzed by LC-MS, as described in the details in Data Set S6. We found 108 database   was used in combination with model iBP1870 and appropriate constraint sets (Data Set S7) to screen single S, C or N (amino acids), and C sources (organic acids) that can support growth of Bordetella strains (http://f-a-m-e.org/fijo) using model iBP1870 as the template, and manually curated (Data Set S8). From the metabolic flux distribution for each minimal medium composition that did support in silico growth of B. pertussis Tohama I (Data Set S7), the set of active reactions was extracted. Growth was determined to be feasible if all required reactions for in silico growth of B. pertussis Tohama I were also present in the reconstructed network; conversely, if only one required reaction was not present, growth was assumed to be not feasible.For the 14 alternative  strains , the metl-cysteine, l-methionine, and glutathione and supplemented with sodium thiosulfate, reduced glutathione, l-cysteine–HCl, or mercaptopyruvate at different concentrations, or with water as a negative control. Growth assays were performed in 96-well plates (Greiner 655090) containing 180 μl of medium and 20 μl of inoculum. The inoculum was prepared by growing cells in MSS-CDM in a shake flask to an OD650 between 1 and 2, collecting cells by centrifugation , washing the cell pellet twice with 1 volume of 0.9% (wt/vol) NaCl, and resuspending cells in 0.9% (wt/vol) NaCl at a theoretical OD650 of 0.5. After inoculation, the 96-well plate was incubated for 7 days at 35°C and constant double orbital agitation in a Synergy H1 microplate reader (BioTek). Growth was monitored every 10 min as the OD650.Experimental validation of S sources with Tohama I was done with IMP-CDM medium  lacking 2PO4, 2.5 g/liter morpholinepropanesulfonic acid [MOPS], 0.2 g/liter KCl, 6 mg/liter niacin, 1 g/liter dimethyl-β-cyclodextrin, mineral salts ) and vitamins , to which sources of C, N, and S were added as required. Media were adjusted to pH 7.4 (25°C) by addition of 5 M NaOH or 6 M HCl; the concentrations of Na+ and Cl− were adjusted to at least 110 mM and 30 mM, respectively, with NaCl.For all other validations, the inoculum was prepared as described above (except for resuspension of the washed cells [see below]), and growth assays were performed with a basal medium containing no source of C, N, or S (0.5 g/liter KHl-Asp (30 mM) and l-Trp (40 mM) or a single organic acid  as the sole C source, together with NH4Cl (25 mM) as the sole N source. As a negative control, a medium containing ammonia but no C source was used. Growth assays were performed in 250-ml shake flasks containing 30 ml of medium and inoculated with 1 ml of a washed cell suspension  of exponentially growing B. pertussis Tohama I. After inoculation, cultures were incubated for 9 days at 35°C under constant orbital agitation (150 rpm). Growth was monitored offline as the OD650.For the validation of amino acids as sole C or N sources and organic acids as sole C sources with Tohama I, each medium contained thiosulfate 0.25 mM (S source) and either a single amino acid as the sole C or N source , reduced glutathione (233 mg/liter), and ascorbic acid (623 mg/liter). For organic acids as C sources, 1.337 g/liter NH4Cl was added as an N source, together with 21.014 g/liter citric acid monohydrate or 21.005 ml/liter of a 40% l-lactic acid solution. For amino acids as C or N sources, l-aspartate (4 g/liter) or a mixture of sodium l-glutamate monohydrate (21.79 g/liter) and l-glutamic acid (1.579 g/liter) was used. As negative controls, strains were grown in media containing the same S source as the test cultures and ammonia as an N source but no C source. As positive controls, the 6 strains were grown in IMP-CDM. Growth assays were performed in FlowerPlate 48-well microtiter plates (m2p labs), with each well containing 800 μl of culture . After inoculation, plates were covered with a Breathe-Easy membrane (Sigma) and pierced with 3 holes per well, and incubation was performed in a BioLector microbioreactor (m2p labs) at 35°C under constant agitation (800 rpm). After 9 days, the OD650 was measured offline.For validations with alternative strains , the following C, N, and S sources were added. The S source was either sodium thiosulfate (62 mg/liter) or a mixture of l-glutamate concentration of 120 mM. Additional modifications of medium composition  were as follows  were added; Mg2+ concentration increased 10-fold; iron was provided as Fe(III)-citrate instead of FeSO4; and Tris buffer was replaced with MOPS.Optimization of the basic MSS-CDM was performed using FBA, with constraints as indicated in Results (“New medium formulations for vaccine production”). FBA outputs were converted into medium formulations (IMP-CDM and IMP2-CDM) based on an  follows : niacin,650, 1.25), (iii) when the culture reached an OD650 of 3, amino acid supplements  the level of dissolved oxygen was regulated at 40%.Optimized media were tested in 20-liter scale fermentations performed under the same conditions as the reference fermentations, except for (i) medium composition , (ii) stn et al. ) were adn et al. , (iv) fon et al. , (v) the


Modeling of microbial metabolism is a topic of growing importance in biotechnology. Mathematical modeling helps provide a mechanistic understanding for the studied process, separating the main drivers from the circumstantial ones, bounding the outcomes of experiments and guiding engineering approaches. Among different modeling schemes, the quantification of intracellular metabolic fluxes (i.e. the rate of each reaction in cellular metabolism) is of particular interest for metabolic engineering because it describes how carbon and energy flow throughout the cell. In addition to flux analysis, new methods for the effective use of the ever more readily available and abundant -omics data  are urgently needed.13C Metabolic Flux Analysis. Moreover, it introduces the capability to use 13C labeling experimental data to constrain comprehensive genome-scale models through a technique called two-scale 13C Metabolic Flux Analysis (2S-13C MFA). In addition, the library includes a demonstration of a method that uses proteomics data to produce actionable insights to increase biofuel production. Finally, the use of the jQMM library is illustrated through the addition of several Jupyter notebook demonstration files that enhance reproducibility and provide the capability to be adapted to the user’s specific needs.The jQMM library presented here provides an open-source, Python-based framework for modeling internal metabolic fluxes and leveraging other -omics data for the scientific study of cellular metabolism and bioengineering purposes. Firstly, it presents a complete toolbox for simultaneously performing two different types of flux analysis that are typically disjoint: Flux Balance Analysis and jQMM will facilitate the design and metabolic engineering of organisms for biofuels and other chemicals, as well as investigations of cellular metabolism and leveraging -omics data. As an open source software project, we hope it will attract additions from the community and grow with the rapidly changing field of metabolic engineering.The online version of this article (doi:10.1186/s12859-017-1615-y) contains supplementary material, which is available to authorized users. Metabolism is the set of physical and chemical processes through which living organisms extract energy and mass from their environment in order to sustain life . Hence, 2 emissions which cause climate change, reduce society’s reliance on fossil fuels for energy and chemicals, and provide for enhanced energy security. The production of commodity chemicals from lignocellulosic biomass is critical for achieving these goals, particularly in view of expected future population growth in emergent economies coupled with a marked improvement in their living standards ).The utilities module stores small functions that are useful in a variety of modules: e.g. a function to extract the atoms numbers from an elemental composition string , while aspartate is considered unlabeled. Fluxes are fixed to predetermined values, since the goal in this case is to showcase the calculation of labeling patterns from fluxes. Jupyter Notebook B2 demonstrates how, using jQMM, EMU transitions are generated, and solved through GAMS and CONOPT without the need to decompose the network into decoupled EMU reaction networks. The computed labeling pattern is the same as obtained through 13CFLUX2 [The first demonstration Fig.  involves13CFLUX2 . These effects require significant effort to be accurately incorporated into a small-scale model, but they are properly handled by the genome-scale model, as demonstrated in the next example. Jupyter Notebook B3 shows how to calculate fluxes through 13C MFA for this case.The next demonstration of the jQMM library involves a traditional use of a et al. , in ordea et al. . Fluxes n et al. , the lar13C labeling data through the 2S-13C MFA algorithm . This sction in ). The on13C labeling data . Other ig. 6 in ) and quaig. 6 in ). Jupyteig. 6 in .13C MFA we will show how one can use this library to calculate fluxes for microbial communities as shown in Hagerty et al. [13C MFA but, at the same time, the technical details differ notably. In this and other experiments [13C or fully labeled for glucose and 1-13C or 2,3-13C for pyruvate). For each carbon source and labeling type, the labeling fraction of CO2 emmited from the soil was measured. For each carbon source, the two relative CO2 labeling profiles provided enough information to fit a small model of carbon metabolism that represented the combination of reactions for all microbial entities in the soil. The good fits supported the assumption that all members of the community display a similar metabolic flux state, and the results are used to derive the carbon utilization efficiency . Jupytee models .13C-based methods [http://cameo.bio/) are available for this purpose. Methods for FBA, FVA, Minimization of Metabolic Adjustment (MoMA [The jQMM library provides the means to perform FBA (Jupyter notebook B1) and other COBRA methods for the sake of comparison with  methods . However methods  and cament (MoMA ) and Regnt (MoMA ) are pront  were assembled together in a pathway able to produce limonene [This case represents a prototypical example of pathway engineering, in which a series of exogenous genes from a variety of organisms .We have presented here the jQMM library, an open-source modular library for modeling metabolism and the first open-source library for e METRAN , INCA [2e METRAN  and 13CFe METRAN ), it is e METRAN  and OPENe METRAN , it is w13C MFA, 2S-13C MFA, etc) and biofuels, the tools are of general aplicability to other fields  and include statistical methods as well (e.g. PCAP). jQMM presents not only methods for modeling and generating actionable items form -omics data, but also libraries for data manipulation and visualization (fluxes and labeling patterns see Figs. While the examples here are mainly focused on various types of flux analysis (FBA, jQMM will continue growing as the methods developed and used at JBEI for biofuel production expand and mature, while other authors contribute to it. At the moment jQMM is heavily dependent on the closed-source commercial platform GAMS and the CPLEX and CONOPT solvers. Our first future improvement to the jQMM library is planned to involve providing an interface to open-source and free version of solvers equivalent to GAMS. Further future improvements will likely include integration with COBRApy , cameo (Project name: jQMM libraryProject home page:https://github.com/JBEI/jqmmOperating systems: Platform independentProgramming language: Python, GAMSOther requirements: CONOPT large scale nonlinear solverAll data used in this paper can be found in the github library itself. Additional file