The emergence of functions in biological systems is a long-standing issue that can now be addressed at the cell level with the emergence of high throughput technologies for genome sequencing and phenotyping. The reconstruction of complete metabolic networks for various organisms is a key outcome of the analysis of these data, giving access to a global view of cell functioning. The analysis of metabolic networks may be carried out by simply considering the architecture of the reaction network or by taking into account the stoichiometry of reactions. In both approaches, this analysis is generally centered on the outcome of the network and considers all metabolic compounds to be equivalent in this respect. As in the case of genes and reactions, about which the concept of essentiality has been developed, it seems, however, that some metabolites play crucial roles in system responses, due to the cell structure or the internal wiring of the metabolic network.phenotypic essential metabolite (PEM) which influences the growth phenotype according to sustainability, producibility or optimal-efficiency criteria. We have developed and made available a tool, Conquests, which implements a method combining graph-based and flux-based analysis, two approaches that are usually considered separately. The identification of PEMs is made effective by using a logical programming approach.We propose a classification of metabolic compounds according to their capacity to influence the activation of targeted functions  in a cell. We generalize the concept of essentiality to metabolites and introduce the concept of the Conquests python package advocates for a broader use of these compounds both to facilitate network curation and to promote a precise understanding of metabolic phenotype.The exhaustive study of phenotypic essential metabolites in six genome-scale metabolic models suggests that the combination and the comparison of graph, stoichiometry and optimal flux-based criteria allows some features of the metabolic network functionality to be deciphered by focusing on a small number of compounds. By considering the best combination of both graph-based and flux-based techniques, the  These ux Modes  but remaux Modes . Complemux Modes  or severux Modes ) solutioux Modes .a priori that all reactions and metabolic compounds are equivalent, an assumption that ignores the various roles they play in systems response because of the cellular structure , producibility (stoichiometry framework) and optimal-efficiency (constraint-based modeling framework) scales. Whereas some compounds are involved in linear pathways and play very little role in system functioning , others tructure .essentiality, mainly in the stoichiometric and constraint-based modeling frameworks. In the mass-balanced formalism, an essential reaction is one where its removal  is lethal, in the sense that it prevents the system from growing according to the Flux Balance formalism  reactions consuming the metabolite in question is lethal whereas removing these reactions one by one is never lethal. This sheds lights on the dependency between parallel pathways starting in the same metabolite.To address this issue, many authors have focused on the concept of ormalism . Notice ormalism . More geormalism . A specitabolite . In otheessential reaction is one where its removal from the system leverages the optimal capability of the system to produce biomass according to the Flux Variability Formalism , or crossroads, that cannot be removed . Three categories of phenotypic essential metabolites will then be further defined based on their deliverability: (i) sustainability essential metabolites (sustainability-PEM); (ii) producibility essential metabolites (producibility-PEM); and (iii) optimal-efficiency essential metabolites . Sustainability essential metabolites are compounds that promote biomass production according to the graph-based network-expansion criteria (Conquests tool (Crossroad in metabOlic Networks from Stoichiometric and Topologic Studies). This tool combines both topological and flux-based features analysis, which are usually assumed to be three distinct approaches, graph, stoichiometry and optimal-flux based respectively.This paper studies the role of internal metabolic compounds with respect to the production of a targeted metabolite. Metabolic compounds are hence classified and compared according to their ability to influence the growth phenotype at the sustainability, producibility and optimal-efficiency modeling scales. Following such a classification, we propose to define metabolic compounds called criteria . Therefocriteria , and stacriteria . In thisi.e., most recent E. coli metabolic network) to medium standard metabolic networks . Interestingly, the three classes of phenotypic essential metabolites do not completely overlap. We provide a dynamic interpretation of metabolic network structures via differences between the sustainability, producibility and optimal-efficiency PEMs. By considering the best combination of both graph-based and flux-based techniques, Conquest advocates for a broader use of these compounds both to facilitate network curation and to promote a precise understanding of metabolic phenotypes.For the sake of application, we have studied PEMs in six genome-scale metabolic networks, ranging from the highest standard , where R and M are sets of nodes standing for reactions and metabolites, respectively  = {m ∈ M∣ ∈ E} and prds(r) = {m ∈ M∣ ∈ E}. In other words, when  ∈ E or  ∈ E for m ∈ M and r ∈ R, the metabolite m is called a reactant or product of reaction r, respectively. Quantitatively, reactions are subject to stoichiometry for balancing the relative quantities of reactants and products. This can be captured by an edge labeling giving the stoichiometric coefficient of a reaction’s reactants and products, viz. s:E → ℚ, respectively. We designate  a stoichiometric metabolic network.A reversible reactions of the system. It corresponds to the set of reactions which can be associated with another reaction of the system with reverted reactants, products and stoichiometry. Formally, it is defined as follows: We denote by r ∈ R is associated with a metabolic flux value (or activity rate) vr, a real variable confined by a upper bound ubr ∈ ℝ+.Each reaction S⊆M to model initiation seeds or nutrients, a set of metabolic compounds that are observed to be present in the system in its initial state. In addition, the graph structure includes a specific set of compounds whose production is intrinsically assumed to be activated by default. These boundary compounds or boundary seeds are defined as follows: Sb(G) = {m ∈ prds(r)|∃r ∈ R, rcts(r) = ∅}⊆M. For the sake of clarity, we assume herein all boundary compounds to be seeds: Sb(G) ⊂ S.We introduce the set targeted metabolic compounds are hence assumed to be produced by the system. These are defined to be the reactants rcts(rT) of the target reaction (see Its tion see .The concept of activated products (or reactions) can be modeled on the basis of different paradigms. According to the state-of-the-art, the most widely used formalism for producibility is Flux Balance Analysis (FBA) .r is associated with a metabolic flux value vr, a real variable confined by Eq. law of mass conservation which assumes a steady state, i.e., input and output rates of reactions consuming and producing a metabolite are balanced. In this paradigm, each reaction Definition 1R∪M, E, s) be a stoichiometric metabolic network. A reaction r0 is stoichiometrically activated if and only if the following holds: Let (ub(rS1) > 0, ub(rS2) > 0 and ub(rSH) > 0 implies that all reactions, including rT, are stoichiometrically activated. On the contrary, in the absence of S2  = 0), all reactions are stoichiometrically inactivated except r7 and r8. Indeed, applying the mass conservation law to B and S2, all flux distributions must satisfy v0 = v1 + v7, v1 = v0 + v8 with v7, v8 ≥ 0, which implies v7 = v8 = 0. In addition, the stoichiometry associated with the edge from r4 ensures that the cycle r2- r3- r4 is activated and that it produces extra quantities of C to feed the reaction rT. This stoichiometry over the reaction r4 is crucial to ensure that the cycle r2, r3, r4 is not thermodynamically infeasible , that is, the predecessors of r in the graph, are reachable from S. To deploy such a recursive definition, we say that, a metabolite m ∈ M is topologically activated from S if m ∈ S or if m ∈ prds(r) for some reaction r ∈ R, where all m′ ∈ rcts(r) are topologically activated from S. In other words, at least one predecessor of m in the graph is itself activated from S. The scope of S corresponds to the set of metabolites activated from the initial seeds of the network. Therefore, it is nothing other than the closure of the set of seeds on the hypergraph, as shown in several theoretical studies  be a stoichiometric metabolic network and let S be a set of seeds of the network such that Sb(G) ⊂ S.Let , is the closure of metabolites activated from S. It is defined as Σ = ∪iMi where M0 = S and The r0 is topologically activated from S if and only if its reactants belong to the scope of the graph, that is rcts(r0) ⊂ Σ.A reaction S1, S2, H}, implying that rT is topologically activated. Notice, however, that this property is not valid any more if we consider the seeds S1 and S2 independently. The set of reactions that are topologically activated from S1 is {r6, r9, re} and the set of metabolites that are topologically activated from S1 is {S1, A, G, F}. Indeed, the only reaction topologically activated from the seed S1 is r6. Therefore, G and A are topologically activated from S1. By recursivity, we get that r9, hence F and re are activated. On the contrary, C cannot be activated from S1 only, implying that rT is not activated. Similarly, the sets of reactions and metabolites that are topologically activated from {S2, H} are {r0, r1, r2, r3, r4, r7, r8} and {S2, B, C, D, E, H, J}. Therefore, rT is not topologically activated from {S2}. Assuming that all S1, S2 and H are seeds, all reactions and compounds are topologically activated so that rT is topologically activated from {S1, S2, H}.According to the toy example in Conquests available at https://github.com/jlaniau/conquests. For the sake of application, each metabolic network was represented using its SBML file and incorporated into Conquests as an input, along with the identifier of a targeted reaction rT. The SBML file was then parsed with lxml Python package functions in order to identify the boundary seed compounds S and the list of substrates T of the targeted reaction. Sustainability-PEMs computation was performed using Answer Set Programming (ASP) and the pyASP Python package that calls upon the clingo4 grounder and solver. Finally, the CobraPy Python package  and return an interval  of values allowed for the fluxes vr when studying an optimal targeted flux vrT.The computation of graph, stoichiometry and optimal-efficiency PEMs was performed by the Python package  package  was usedEscherichia coli str. K-12 substr. MG1655 was analyzed via three of its publicly available models: iJR904  and graph-based (reachability of biomass reactants) producibility assessments.For the sake of application, several genome-scale metabolic networks were considered. : iJR904 , iAF1260, corresponding to three different semantics for a metabolic network functionality.pruning of a metabolic network G =  with respect to a metabolic compound m ∈ M as the subgraph of G in which all reactions having m as a substrate have been removed. More precisely, we introduce prune =  such that R′ = R∖({r ∈ R∣m ∈ rcts(r)}∪{r ∈ Rev(G)∣m ∈ prds(r)}) and E′ = (M × R′∪R′ × M)∩E. In more biological settings, the network prune is a new metabolic network where there are no more reactions that consume m.We define the In order to introduce the definition of phenotypic essential metabolites, we shall point out metabolic compounds that play an important role with respect to the activation of a specific targeted reaction .Definition 3G =  be a metabolic network. Let S be a set of seeds such that Sb(G) ⊂ S. Let rT ∈ R be a targeted reaction.Let m ∈ M is called a sustainability-PEM if m⁄ ∈ S∪rcts(rT), rT is topologically activated from S with respect to the network G, and rT is not topologically activated from S with respect to the network prune.A metabolic compound m ∈ M is called a producibility-PEM if m⁄ ∈ S∪rcts(rT), rT is stoichiometrically activated from S with respect to the network G, and rT is not stoichiometrically activated from S with respect to the network prune.A metabolic compound m ∈ M is called an optimal-efficiency-PEM if m ∈ rcts(r0) where r0 ∈ R is a reaction such that A metabolic compound sustainable essential metabolite m is defined as being able to remove the system’s ability to activate a targeted reaction from the graph-based study of the metabolic network. In biological settings, as soon as all reactions consuming the compound m are removed from the network, there is no further possibility of joining the targeted reaction by recursively expanding the topology of the metabolic network. In other words, when m is a sustainability-PEM, the pruned network prune contains a component of the targeted reaction, mT ∈ rcts(rT), which no longer belongs to the scope of the seeds. Therefore, m is necessary to the production of mT and to the activation of the targeted reaction. In the example shown in E is the only sustainability-PEM, because its removal blocks activation of C, a reactant of the biomass reaction rT.According to essential metabolites introduced in E is a sustainability-PEM. In addition G is a producibility-PEM because removing the reaction r9 from the network means that any nonzero flux in r6 yields an accumulation of the compounds G.When the stoichiometry of a network is available, it becomes possible to modify the previous definition of sustainability-PEM by introducing flux constraints. The thinking behind this concept is that removing a metabolic compound may dramatically revert the stoichiometric balance of reactions and therefore prevent the target reaction flux from being activated. According to our essential reactions in the Flux Variability Analysis (FVA) framework  may not be essential  according to a producibility criteria. Indeed, in the FVA formalism, essential reactions are defined to be obligatory for the optimal production of biomass: they have a strictly positive flux in any flux distribution which optimizes the biomass production. Therefore, removing such a reaction from the network does not imply that the biomass cannot be produced. On the contrary, there may exist a non-optimal flux distribution which does not require the considered reaction and still allows the biomass to be produced. In One should notice that the definition of optimal-efficiency PEMs is slightly different from the definition of sustainability and producibility PEMs. The latter considers the case when all the reactions which consume a PEM lead to a change of phenotype (either sustainability or biomass production) whereas optimal-efficiency PEMs are restricted to the case when the considered compounds are the substrates of a single reaction whose removal leads to a change of phenotype . The motivation for such a difference is that using a similar definition for the three types of phenotypes would have introduced causalities between the PEMs: a producibility-PEM would have always been an optimal-efficiency PEM. On the contrary, as we will detail it in several case-studies, our definition of PEMs implies that there is no causality between the different concepts, increasing the relevance of comparing them.The sustainability-PEM property is purely combinatorial. The main difficulty in identifying compounds that have this property is that the set of metabolites and reactions that are activated from a set of seeds within a network has to be computed recursively. In order to improve efficiency and avoid a separate computation on each pruned network, we introduced a logic programming approach to model the full set of constraints satisfied by the set of sustainability-PEMs and allow their identification in a single run of the program, as a refinement of the network expansion and scope logical modeling introduced in In practice, the sustainability-PEM computation was performed using a logic programming approach known as Answer Set Programming (ASP) . It is ah :- b1, …, bm, notbm+1, …, notbn, where each bi and h are literals and not stands for default negation. Mainly, each literal is a predicate whose arguments can be constant atoms or variables over a finite domain. Constants start with a lowercase letter, variables start with an uppercase letter or an underscore (don’t-care variables). The rule states that the head h is proved to be true (h is in an answer set) if the body of the rule is satisfied, i.e., b1, …, bm are true and it cannot be proved that bm+1, …, bn are true.An ASP program consists of Prolog-like rules h is a fact. They are used here to represent the input network. Substrates and products of a reaction are represented by facts reactant. and product., where M and R denote metabolite and rule names. For reversible reactions, two rules are generated. We use facts seed(M). to represent seed metabolites and target(R). to represent the target reaction.If the body is empty, scope of the network is provided in listing 1. It is either a seed metabolite (line 1) or a product of a rule such that all its reactants are in the scope of the network (line 2). This second line uses a notation p:q, which is satisfied if p is true for all possible q.The recursive definition of metabolites in the      Listing 1: Computing metabolites in the scope of a network   _______________________________________________________________________________________ 1 scope (M ):− seed (M). 2 scope (M2):− product , scope (M1) : reactant .   _______________________________________________________________________________________    R that belong to the pruned network with respect to one of these metabolites M are represented by predicate pruned. They are all reactions of the network that are not using M as substrate.The definition of the pruned graph with respect to a metabolite is provided in listing 2. First, metabolites used for pruning are defined as reactants of the network scope. They are neither seeds nor reactants of a target reaction (line 1). Then reactions                           Listing 2: Computing pruned graphs   _______________________________________________________________________________________ 1 prune (M):− scope (M) ,   reactant  ,  not  seed (M) ,  not  target (R) . 2 3 pruned  :− prune (M) , reactant  , not reactant  .   ________________________________________________________________________________________    PM is computed (lines 1–3). A sustainability-PEM C is a metabolite that is necessary to produce a substrate TM of a target reaction, the latter being a metabolite that is no longer in the scope of the network when pruned with respect to C (lines 5–6). The set of sustainability-PEMs is produced with respect to any such possible substrate (line 7).Finally, according to its definition, a sustainability-PEM must be necessary to produce at least one substrate of the targeted reaction. In other words, there exists a reactant of the targeted reaction which does not belong to the scope of the set of seeds in the network pruned with respect to the sustainability-PEM. To model this property in the ASP program (listing 3), the scope of the set of seeds in a network pruned with respect to metabolite                            Listing 3: Computing the sustainability-PEMs   _______________________________________________________________________________________ 1 scope :− seed (M) . 2 scope :− product  , pruned  , 3                 scope  : reactant  . 4 5 sustainabilityPEM :− target (R) , reactant  , scope (TM) , 6                    prune (C) , not scope  7 sustainabilityPEM (C):− sustainabilityPEM  .   _________________________________________________________________________________________    E. Coli metabolic networks, less that 13%) to a large proportion  of the network metabolites. Importantly, the number of PEMs does not depend linearly on the number of network metabolites. A possible interpretation is that networks with a small percentage of PEMs depict a relatively large number of pathways besides the primary metabolism of the organism that is related to the biomass modeling. However, it is expected that PEMs are mainly related to the growth phenotype and therefore to primary metabolism. On the contrary, most recent networks for less studied organisms focus on describing the primary metabolism, because fewer have been performed on these organisms than on model ones. This could suggest that the percentage of PEMs is an indicator of both the broad range of phenotypes encountered in the organism and the level of curation in its metabolic network.As depicted in hubs, that is, nodes with a high level of connectivity  was defined as connectivity(m) = card(r ∈ R∣m ∈ rcts(r)∪prds(r)). It depicts the number of reactions which either consume or produce the metabolite m. However, we notice that this definition does not take into account the functioning role of the considered compound with respect to the metabolic network, that is, its impact on the production of targeted metabolites. As a first analysis, we ordered the compounds of each metabolic network according to both their degree of connectivity and their role in the functioning of the network classified as PEM, biomass component, seed  or generic compounds. Our analysis confirmed that, as expected, regardless the considered network, all highly connected compounds are either a PEM, a biomass component or a seed  have such a role. The only exception is the periplasmic H2O of the iJO1366 network, a component which appears to play a redundant role in the network with cytoplasmic  H2O. In the A. ferrooxidans and T. lutea networks, the 31 compounds with the highest degrees of connectivity (from 10 to 310) have such a role. We noticed however that the PEM concept encompasses a much larger set of compounds than the single family of highly connected compounds. This emphasizes that, in addition to the expected highly connected nodes, the PEM concept sheds light on metabolic compounds with a possibly impactful role in the production pathways of target compounds regardless their connectivity.Generic graph-based approaches usually point out the importance of ectivity . In our seed see . Indeed,iJO1366 network) to 99% (A. ferrooxidans network), whereas the ratio of sustainability-PEMs ranges from 46% (iJO1366 network) to 86% (T. lutea network). Similarly as before, for all networks, some PEMs are neither sustainability nor producibility-PEMs. This analysis confirms that the three classes of PEMs are complementary and must be considered together to capture the full complexity of the functioning of the network.The distribution of sustainability, producibility and optimal-efficiency-PEMs is described in iJR904, iJO1366 and iAF1260 networks highlights the fact that 20 metabolic compounds satisfy these three properties in all the three networks, including the highly connected nodes udp, h, phosphate and phosphoenolpyruvate. These four compounds can therefore be viewed as the major biomass production regulators of E. coli networks in the graph, stoichiometry and optimal flux-based formalisms. Surprisingly, the other 16 PEMs in the common skeleton of the iJR904, iJO1366 and iAF1260 networks have a low degree of connectivity in the network (from 2 to 7). These compounds are Chorismate, DTDP, ahdt, Dihydroneopterin, Dephospho-CoA, 1,2-Dihydronaphthalene-1,2-diol, 6-hydroxymethyl-dihydropterin pyrophosphate, 4-amino-4-deoxychorismate, Dihydroneopterin monophosphate, 6-hydroxymethyl dihydropterin, N-((R)-4-Phosphopantothenoyl)-L-cysteine, 6-hydroxymethyl dihydropterin, 5-O-(1-Carboxyvinyl)-3-phosphoshikimate, D-4′-Phosphopantothenate, Pantetheine 4′-phosphate. One interpretation is that these metabolites may refer to structural compounds of the network necessary to produce the biomass and may constitute a skeleton of the network structure regarding the biomass production.Overlaps between the different classes of compounds for the six metabolic networks are shown in A. ferrooxidans network, the compound g1p is a precursor to glycogen and lps_AFE, two biomass components. Their production is ensured by a pathway starting from β-f6p and β-g6p. They can be transformed into either α-g6p or in β-g1p. No other pathway can produce these targets. Therefore, β-g6p is a both a sustainability and a producibility-PEM, but it is not an optimal-efficiency PEM.This situation occurs when a compound is required to produce a biomass component from the stoichiometry and graph-based viewpoints. All the reactions consuming this component can be removed without impacting the optimal biomass growth rate. One interpretation of this is that this type of compounds is the substrate of two pathways, both equally capable of producing the targeted biomass component. An example is shown in iJO1366, A. ferrooxidans and T. lutea networks. In the Synecchocystis, iAF 1260 and iJR904 networks this situation occurs from eight to 22 times. In particular, the relatively high number of such PEMs in the Synecchocystis network suggests that its optimal functioning is not highly constrained. This could be explained by the presence of a relatively high number of export fluxes  which generate redundancies with intracellular pathways.Among the six metabolic networks studied, this situation is not frequently observed in the Synecchocystis network, the removal of the reactions for which Cytosolic O-Phospho-L-serine is a substrate causes the maximal biomass growth rate to decrease from 47.5 to 41.1 mmol/gDW/h.These PEMs are required to produce optimal biomass. Removing all reactions for which this PEM is a substrate does not prevent the biomass from being stoichiometrically and topologically activated. For instance, in the Synecchocystis network, the cytosolic putrescine is a precursor of the biomass components. In this network, two pathways produce this compound: one of them drives an import flux of extracellular putrescine and the other, an internal one, drives a pathway involving L-arginine and agmathine. CO2 is a co-product of the latter pathway. Its relationship with the production of coproduct causes the network to favor the L-arginine pathway for producing putrescine in order to optimize the biomass growth rate. Therefore, agmathine and putrescine are optimal-efficiency-PEMs. However, they are neither sustainability and producibility-PEMs because they are not required for the graph-based and the stoichiometry-based productions of putrescine.Our interpretation is that this mainly occurs when biomass components can be produced by at least two distinct pathways and when one of them is favored by the system on the basis of optimal flux-based analysis. An example is shown in iJR904, iAF1260 and iJO1366 networks, between 32% and 50% PEMs have this property. The most recent Synecchocystis and T. lutea networks includes around 10% of such PEMs. The exception is the A. ferrooxidans network with very few differences between the graph, stoichiometry and optimal flux-based formalisms.In the six networks studied in this paper, optimal-efficiency-PEMs that are neither sustainability nor producibility-PEMs are the most frequent PEMs after PEMs that are sustainability, producibility and optimal-efficiency-PEMs simultaneously. In the iJO1366 network, the cytosolic thiamine is necessary for producing the thiamine diphosphate, a biomass component. Indeed, if we prune the metabolic network by removing all the reactions whose substrate is cytosolic thiamine, the thiamine diphosphate is no longer topologically activated. On the contrary, in the pruned graph, the growth rate maximal value (the biomass reaction) is unchanged compared to the growth rate of the initial network (11.747 mmol/gDW/h). This apparent paradox is explained mainly by the dynamical assumptions underlying the stoichiometric and topological activation semantics. We assert that these different semantics impact heavily on the interpretation of a cycle functioning with respect to the dependency of metabolites on their own production , because this compound is produced by a self-induced cycle, thus the reaction flux is equal to zero for optimal flux-based analysis. This analysis suggests that the production of Peptidoglycan subunit is dependent on pyruvate, in addition to its link with a self-activated loop.An example is shown in iAF1260, iJO1366 and T. lutea networks, nine times in the Synecchocystis network and eleven times in the iJR904 network. This suggests a need for curation for networks with a medium number of sustainability-PEMs that are neither producibility nor optimal-efficiency-PEMs.To summarize, one interpretation of sustainability-PEMs that are neither producibility nor optimal-efficiency-PEMs is that it suggests the existence of a self-activated cycle in the flux-based analysis (producibility at steady state) and provides candidates for the initiation of cycles when the cell is not at steady state (sustainability during growth phases) . HoweverA. ferrooxidans network, removing the reactions which consume Alpha-D-Ribose_1-phosphate causes the optimal biomass growth rate to decrease from 3.6 to 3.4 mmol/gDW/h. Therefore it is still producible although there is no longer a pathway from the set of seeds to the biomass reaction. One interpretation of this paradox is similar to the case shown in This is a tricky situation, for when a compound has this property, it is the substrate of a reaction that is always activated when the cell produces an optimal biomass growth rate. The sustainability property means that, if this reaction is removed from the network, the targeted biomass component is no longer activated according to a graph-based criteria. Nevertheless, the biomass component still has the capability to be activated at the stoichiometric level, although with a lower growth rate. An alternative means of production of the targeted component exists, although this alternative pathway is not connected to the set of seeds from a graph-based viewpoint. For instance, in the iJO1366 network. In the cytosol compartment, Thiamin, a PEM, is the only precursor of Thiamin monophosphate, a biomass component. Its production is assured by a pathway initiated by the set of seeds that imports Thiamin from periplasm to cytosol. Also, when the reaction from Thiamin to Thiamin monophosphate is removed from the network, the network has the ability to activate a cycle to produce 4-Methyl-5-(2-phosphoethyl)-thiazole (4mpetz). Notice, however, that this cycle is not connected to the set of seeds since its components are not topologically activated. Therefore, its activation is heavily dependent on the presence of at least one of its components at the initiation of the cell dynamics.For instance, iJO1366 network (six times) and the T. lutea network (seven times). Therefore, both networks have the capacity to adapt themselves by activating internal mass-balanced cycles.Regarding the six genome-scale networks studied, this situation mainly occurs in the iAF1260 network is the cytosolic carbon dioxide. Removing this metabolite from the network, with all the reactions that use it as a substrate, does not affect the graph-based activation of any of the target metabolites. However the growth rate is reduced from 9,021 to 0 mmol/gDW/h. The biomass component cannot be produced because of the non-balanced mass equation despite the fact that it is theoretically still able to be activated topologically.Such PEMs have the ability to set the biomass flux rate to zero when all their associated substrate reactions are removed from the network even though none of the removed fluxes is required to produce the biomass in the initial network. In addition, the pruning operation does not remove the graph-based activation of the biomass component. An example in the iAF1260 network (murein5px4p (a biomass component) is a product of a reaction whose substrate is murein5p5p. Another product of this reaction is D-Alanine. When the export reactions of this co-product are removed from the network, the compound D-Alanine accumulates and can no longer satisfy the law of conservation of mass. Biomass production, in this pruned network, is impossible: flux-based analysis gives murein5px4p a production rate of zero. Nevertheless, removing reactions that export D-Alanine has no impact on the graph-based activation of the biomass components. In addition, this compound is not an optimal-efficiency PEM because there are two reactions that can export D-Alanine.As shown in  network , the comIn other words, our interpretation is that producibility PEMs that are neither sustainability nor optimal-efficiency PEMs may refer to co-products of essential reactions. They may have a very large high impact on the organism growth rate since their consumption rate is a direct controller of biomass production at steady-state.Synecchocystis network: once in the A. ferrooxidans and the T. lutea networks and two, three and four times in the iJR904, iAF1260 and iJO1366 networks, respectively. This observation may suggest that the co-products have been extensively studied in all of these networks. On the other hand, the Synecchocystis network contains 17 producibility PEMs that are neither sustainability nor optimal-efficiency PEMs. This suggests that biomass production is under the control of many co-product export fluxes which merit sensitivity analysis and reflect a need for curation.In practice, this situation is identified infrequently in all networks except the Synecchocystis, A. ferrooxidans and T. lutea networks. Indeed, removing all reactions that consume the PEM in question has no impact on the graph-based activation of the biomass component but, on the contrary, drastically reduces the biomass growth rate by removing an essential reaction. In CO2 and Ammonia have this property. The explanation is similar to the one shown in This last situation occurs very frequently in the Conquests package. The need for further study of metabolite classification has been highlighted by the lack of differentiation of them performed so far. Apart from key compounds such as seeds  or targets , no in-depth study has been done of the hundreds (or thousands) of remaining compounds, despite their crucial role in network structure. We thus advocate for the determination of PEMs that are cornerstones in the production pathways of target compounds.In this paper we have introduced a new way of analyzing, describing and differentiating metabolic models in order to gain better insight into their functionality. This method relies on the concept of phenotypic essential metabolites (PEMs), which are key metabolites of the models and can be easily computed using the Here we have defined three types of PEMs that can be distinguished on the basis of the modeling method used to compute them. Sustainability-PEMs are key components related to the graph-based structure of the graph and the initiation of production paths, whereas producibility and optimal-efficiency-PEMS are related to fluxes distribution at steady-state. The latter focuses on the optimal activation of the target reaction, thus pinpointing metabolites that enable its maximal rate. The computation of sustainability-PEMs was challenging because it relies on a difficult combinatorial problem being solved. The efficiency of the ASP solvers enabled an efficient and fast computation to be produced while allowing all PEMs computations to be contained in a single and easily distributable Python package.essential reactions which are either a reaction whose removal has a lethal effect over the system growth   are productibility-PEMs whereas the reactants of the second class of essential reactions  are optimal-efficiency-PEMs. PEMs are also related to essential metabolites introduced in The concept of PEM is related to two concepts of rmalism)  or a rearmalism) . AlthougBased on the study of individual examples, we have provided several interpretations of the different situations that may occur with respect to PEMs classification. Sustainability-PEMs provide information about the dependency of production pathways on the initial state of the system. Unlike steady-state-based flux methods, metabolites that are sustainability-PEMs only may enable components to be deciphered which initiate production that can be self-balanced at steady state. Conversely, metabolites that are producibility-PEMs only may indicate pathways that rely on a precise mass-balance equilibrium at steady state. Finally, for synthetic biology purposes, compounds that are optimal-efficiency-PEMs only may be cornerstones as they allow the maximal flux into the reaction of interest. In fact, it seems appropriate to target compounds that might have the biggest impact once altered, to ensure genetic modifications made to a system are effective.Compounds that are combinations of two types of PEM out of three also reveal interesting features of the network structure. A sustainability and producibility-PEM that is not an optimal-efficiency-PEM may indicate the beginning of alternative production pathways towards targets that are both balanced at steady state and can also be activated in the initial state of the system through a pathway that links the seeds to the PEM. If the sustainability and the optimal-efficiency properties are satisfied but the producibility property is not, a PEM may shed light on internal pathways that are initiated from the graph-based perspective but are not mandatory to activate the target reaction flux. However, those pathways are the only ones that allow the maximal flux to occur. Finally, PEMs that are producibility and optimal-efficiency-PEMs but not sustainability-PEMs may indicate compounds that are carefully balanced in all production pathways that allow the activation of target fluxes. Their consumption, non-accumulation or degradation is essential to prevent mass imbalances whereas graph-based modeling does not take this into account when assessing target activation. One perspective is to work out the terms on which these interpretations, based on phenomena observed in individual examples, can be generalized on the basis of more theoretical studies. As a second perspective, this systematic comparative approach should be applied to multi-scale networks combining regulatory and metabolic features, especially to regulatory FBA (rFBA) formalism .Conquests package in two complementary tasks. Either the information about system dynamics is biologically irrelevant and this information may be used for finalizing the curation of genome-scale metabolic networks, or the information about system dynamics is biologically relevant and allows the role of internal cycle and mass-balance equilibria with respect to the production of targeted biomass reactions to be deciphered. Interestingly, the number of PEMs belonging to one or two of the three classes we described is particularly small in genome-scale models that usually contain more than a thousand metabolites. This makes for easier model curation and analysis because those compounds can easily be examined manually.We conclude that the systematic comparison of several modeling approaches  of the same model may highlight components with different roles within the different formalisms. Our hypothesis is that these compounds often carry relevant information about system dynamics. This promotes the use of the 10.7717/peerj.3860/supp-1Supplemental Information 1x-axis, the total number of compounds with a degree of connectivity in  is given at the top of the corresponding bar. The bar is divided into four parts, the height of which is proportional to the number of such compounds classified into the four classes of functioning roles: PEM (blue), seed (i.e. extracellular nutrient) (green), target (i.e biomass component) (red), other generic compounds with no role related to PEMs (yellow). The relative percentages of each class are shown on the y-axis. This analysis suggests that the PEM concept not only encompasses highly-connected compounds in a metabolic network but also sheds light on metabolic compounds with a functional role despite their low connectivity.For each interval  shown on the Click here for additional data file.10.7717/peerj.3860/supp-2Supplemental Information 2Click here for additional data file.


We propose OptPipe - a Pipeline for Optimizing Metabolic Engineering Targets, based on a consensus approach. The method generates consensus hypotheses for metabolic engineering applications by combining several optimization solutions obtained from distinct algorithms. The solutions are ranked according to several objectives, such as biomass and target production, by using the rank product tests corrected for multiple comparisons.Corynebacterium glutamicum for maximizing malonyl-CoA, which is a valuable precursor for many phenolic compounds. In vivo experimental validation confirmed increased malonyl-CoA level in case of ΔsdhCAB deletion, as predicted in silico.OptPipe was applied in a genome-scale model of https://github.com/AndrasHartmann/OptPipe.A method was developed to combine the optimization solutions provided by common knockout prediction procedures and rank the suggested mutants according to the expected growth rate, production and a new adaptability measure. The implementation of the pipeline along with the complete documentation is freely available at The online version of this article (doi:10.1186/s12918-017-0515-0) contains supplementary material, which is available to authorized users. In the context of microbial cell factories, the optimization of genetic backgrounds has been carried out through classical mutagenesis followed by selection techniques and rational metabolic engineering strategies. The goal of metabolic engineering is to introduce a set of cooperative genetic modifications that rewire the microbial metabolism towards the production of a target compound. This is accomplished by elimination, addition or modification of metabolic reactions, resulting in a strain that shows increased target compound production, which, in an ideal case, is coupled with growth. Although promising, rational-guided metabolic engineering strategies can have unpredicted effects in distant parts of the metabolism and rely on biological intuition. For these reasons, the field has accommodated the use of genome-scale stoichiometric models to guide metabolic engineering strategies –3. A larThis work is focused on the problem of predicting relevant knockout strategies to increase target production when a genome-scale stoichiometric model is available. One of the first tools devised to meet this problem was OptKnock, which is formulated as a bi-level problem that can be translated into a single-level mixed integer problem and that delivers a list of recommended deletion strategies to increase chemical production , 10. Opta posteriori the consensus solutions obtained. From the available optimization methodologies, OptKnock was chosen, as it is one of the most used methods, as was the corresponding pessimistic prediction strategy, RobustKnock. In addition, OptGene and RobOKoD were also introduced in this procedure, as they represent very different approaches. Naturally, each method has its advantages and disadvantages: OptKnock and RobustKnock are optimization-based methods, and return an optimal solution to the defined mixed integer linear problem (MILP). Notice that there might be numerous solutions with optimal objective value, out of which only one is returned. In contrast, there are heuristic methods, like the Evolutionary Algorithms and Simulated Annealing implemented in the software tool OptFlux [Each of these methods is based on different approaches and rationales, therefore leading to distinct solutions. In fact, one key issue is the multitude of obtained results, known to be dependent on the specific algorithms and the software implementation used. In order to address this problem, a consensus-based approach is here proposed and developed. The method is based on running several optimization procedures for knockout prediction and analyzing  OptFlux  and OptG OptFlux , respectThe rationale of using multiple optimization methods is to have rankings of hypotheses that may provide confidence in particular sets of proposed genetic alterations from various aspects. Using this strategy, it is possible to combine several criteria, taking into account possible performance indexes simultaneously; for example, the maximal predicted target compound production, the minimal predicted target compound production and the distance from the wild-type flux distribution. In this sense, the user is allowed to analyze the performance of each candidate deletion mutant according to these criteria and choose which gene deletion strategies will be the best fit for the experimental problem. The consensus ranking is obtained through the application of the rank product test , 18, whiRij, with i=1,…,N and j=1,…,C be the rank of deletion i under the criteria j, i.e., one sorts all the possible strategies/mutants according to that specific metric, from the best (Rbestj=1) to the worst (Rworstj=N). The rank product (RP) is defined as RPi under the null hypothesis H0 of random ranks, which means that in each criteria the sorting is arbitrary, can be approximated with a Gamma distribution [p-value for H0 and identify which ones are statistically significant. Given the high number of hypotheses under study, a multiple testing correction must also be performed. To control the False Discovery Rate (FDR), we have used the q-value [In detail, let ribution , determiribution  and alsoribution . This al q-value .q-values, in order to obtain a ranked list of putative best strategies to be further analyzed.After this, all the possible deletions were sorted according to their Below we present the developed pipeline, which is graphically depicted in Fig. Essential reactions were determined using flux balance analysis (FBA), maximizing the biomass on each possible mutant with single reaction deletion compared to the wild type (WT) model. If by deleting a reaction the problem gets infeasible (i.e. there is no solution) or if the maximal biomass is smaller than a threshold, the reaction is considered to be essential and cannot be deleted as a metabolic engineering strategy.Blocked reactions are carrying zero flux under any condition and are artifacts from the model reconstruction. This means that when maximizing or minimizing that particular flux, the value obtained is always zero as determined using flux variability analysis (FVA).Synthetic and export reactions are explicitly noted in the network and do not have a gene-reaction association. An example of this type of reaction is the import of substrate.Prior to applying the methods, a pre-processing step is executed in order to select a set of candidate reactions that may be deleted from the network. Then the methods are only run on the candidate reactions, which may significantly reduce the search-space and enable faster computation. After careful considerations and preliminary testing, the reactions falling into the following criteria are excluded from the candidate list thereof: Three well established methods – OptKnock, OptGene and RobOKoD – are integrated into the pipeline. These methods are non-exhaustive, e.g. they return only one or a restricted set of solutions. The fourth method that is considered is based on an exhaustive enumeration (screening) of deletions, where a Flux Variability Analysis (FVA) is evaluated on all the possible gene deletions in order to calculate the maximal and minimal target compound productions given that the growth rate is optimal. Notice that enumeration of all deletions is only feasible if their maximum number considered is small. Obviously, this number depends on the model size and overall experimental constraints.The first three methods present the advantage of being already extensively tested and experimentally validated , 14, 16.−1. Also, results with zero maximal target production were not considered. This final list then undergoes a ranking step, where four measures are calculated for each mutant: 1. Maximal growth rate: Computed with FBA.2. Minimal target production: The target compound is minimized given that the growth rate is maximal; computed with FVA.3. Maximal target production: The target compound is maximized given that the growth rate is maximal; computed with FVA.4. Adaptability: This measure indicates the distance between the mutant and the wild-type flux distributions based on the FVA of all fluxes in the network.After the application of all these methods, the resulting lists are joined. The complete list of mutants is refined by filtering out those with a significant biomass loss. The threshold for growth rate was set to 0.1 h The first three measures are well established in the literature, see e.g. . The ratq-values. There were no significant changes on the final sorting list and values, and as such, we kept this strategy. There is some literature on partially ranked data and on Mallows models of permutation [p-values for lists with these characteristics. However, the development and application of such is out of the scope of this work and will be tested and analyzed in a future implementation of OptPipe.From the final list of mutants, the best candidates are retrieved, based on the four ranking criteria described above. The final list is sorted using the rank product method , 18, whimutation , 26 thatTo prevent a biased ranking stemming from parameters that have the same value for all the deletion mutants, a criterion was inserted enabling only parameters with a standard deviation above a given tolerance to be considered by the rank product method. In this case-study, no knockout strategy results in minimal target compound production higher than zero so this rate was disregarded.https://github.com/AndrasHartmann/OptPipe along with all the source code.The pipeline was implemented in MATLAB, based on the COBRA toolbox , 5 and wCorynebacterium glutamicum as described in the The OptPipe software consists of three basic directories: (I.) common_functions contains the functions that are shared between the methods; (II.) methods contains the implementation of the main methods of the pipeline based on the COBRA toolbox, which is added to the (III.) external folder together with other libraries and toolboxes that are being used by the pipeline code, such as RobOKoD , RobustKC. glutamicum, a bacterium that is routinely used in the industrial production of amino acids [C. glutamicum metabolism. This compound has interesting properties for health applications, such as being an antioxidant and chemoprotective [p-coumarate requires the expression of three heterologous genes, which code for 4-coumarate: CoA ligase (4CL), chalcone synthase (CHS) and chalcone isomerase (CHI). 4CL activates p-coumarate to its CoA-thioester p-coumaroyl-CoA. CHS then converts p-coumaroyl-CoA and three molecules of malonyl-CoA to naringenin chalcone, which is isomerized to naringenin by CHI. In C. glutamicum, the plasmid pMKEx2_chsPh_chiPh harbors the genes coding for CHS and CHI, while a 4CL-encoding gene is integrated into the genome of the tested C. glutamicum strain [In order to test and validate the proposed method and software, OptPipe was applied to the optimization of naringenin production in no acids . Naringeotective , 30, andm strain .C. glutamicum, and the maintenance of low levels of malonyl-CoA in this organism was identified as a major bottleneck during naringenin production. In order to test our method, the pipeline has been applied on the genome-scale metabolic model of C. glutamicum to find double deletion strategies that allow the strain to supply more malonyl-CoA for the production of naringenin.Malonyl-CoA is an endogenous metabolite derived from acetyl-CoA in iEZ475 for the strain ATCC 13032 of C. glutamicum was used, comprising 475 reactions and 408 metabolites of which 68 are extracellular and 340 are intracellular [iKK446 network [The model  network . The abiC. glutamicumiEZ475 and other connected resources such as the reaction and metabolite lists (including flux directions) as well as metabolic network map are available for download at http://www.13cflux.net.The SBML file for ΔackAΔmetY has the lowest q-value, with a predicted growth rate of 0.32 h −1 and a maximal naringenin production of 0.5 mmol/gDCW/h, see gene annotations in the Additional files ΔptaΔilvA and ΔptaΔmetY) were found with a q-value of 0.1197. The pta and ackA reactions are associated in the model with a phosphate acetyltransferase and an acetate kinase, respectively, responsible for the diversion of acetyl-CoA towards acetate production. Taking into account the limiting character of the malonyl-CoA flux in naringenin optimization, it is unsurprising that the knockout of this pathway is expected to increase naringenin production. The remaining 11 double mutants had the same q-values, which in some of the cases is due to their equal characteristics and in other cases might reflect a trade-off between higher growth rates and lower distances between the mutant flux distribution and the wild-type. The results obtained with OptGene and RobustKnock were excluded from this list since they did not comply with the specified growth threshold (data not shown). See detailed results and gene annotation in the Additional files After retrieving the individual rankings corresponding to the described criteria, we have obtained a list of 14 possible double deletion strategies that lead to the maximization of naringenin production (Table sdhCAB) and various reactions from the pentose phosphate pathway . These pathways can be viewed as major carbon drains, diverting glucose and acetyl-CoA towards the production of reducing equivalents and amino acid precursors.The proposed reaction deletions were categorized into main metabolic subsystems. The enrichment of the overall knockout dataset was computed to understand which sections of the bacterial metabolism were mostly identified as knockout targets when optimizing naringenin production Fig. . Out of pyc), with a role in gluconeogenesis, were also identified in the knockout set.Enzymes catalyzing anaplerotic reactions, such as pyruvate carboxylase  deletions can also have biological significance, and may constitute promising targets for testing in vivo [ΔsdhCAB and Δddh mutants, the double ΔsdhCABΔddh mutant and the reference strain. Naringenin titer and biomass were measured.It was found that the  in vivo . The envddh gene did not increase naringenin titer, and even slightly decreased naringenin levels per OD unit. On the other hand, the ΔsdhCAB mutant showed significant improvement of naringenin production, and a two-fold increase in normalized yield, while the loss in biomass was less than 10% lower than what was predicted. Interestingly, the double deletion strain ΔsdhCABΔddh behaves similar to the single deletion strain (ΔsdhCAB) with respect to all of the measured features.The validation experimental results summarized in Table ΔsdhCAB deletion, while the Δddh deletion did not increase the naringenin production any further. The difference between the predicted and the validated results as concerns naringenin and growth could be due to the incompleteness of the wild-type strain model. Indeed, this may lead to a simulation of the behaviour of the strain DelAro4 that is not fully accurate. A modification of the model and of the respective constraints might be beneficial, however this is not trivial and is thus out of the scope of the current study.In summary, the in vivo experiments confirmed the beneficial effects of the C. glutamicum, where one predicted knockout of succinate dehydrogenase (ΔsdhCAB) did result in an increased production in vivo. This however only represents an isolated case, and further experimental validation of the methodology is required in order to reach conclusion about the efficiency of the rank product method to distinguish between promising and less promising knockout strategies.Different optimization methods in metabolic engineering often lead to conflicting results that can become difficult to interpret. We propose OptPipe - a Pipeline for Optimizing Metabolic Engineering Targets, based on a consensus approach. The method is based on combining several optimization solutions obtained from distinct algorithms and ranking them according to several objectives, such as biomass and target production. In addition, an adaptability measure was introduced to account for the likelihood of a predicted flux distribution for a mutant to occur in vivo with the kinetic and regulatory constraints found within the cell. OptPipe was applied to a case-study of maximizing malonyl-CoA production using the genome-scale metabolic model of The utility of the proposed pipeline is associated with allowing the user to simultaneously obtain a list of possible strategies that are derived from methods based on different rationales. In this setting, the pessimistic and optimistic approaches of OptKnock and RobustKnock are paradigmatic. In this way, the user may browse through the proposed knockouts and evaluate their feasibility based on their performance in the rank product test. Furthermore, OptPipe is a general framework that can be applied to any organism and target product, and significantly supports metabolic engineering tasks.Project name: OptPipeProject home page:https://github.com/AndrasHartmann/OptPipeOperating system(s): Platform independentProgramming language: MATLAB (Tested on 2015a and 2016b)Other requirements:MATLAB parallel toolboxCOBRA toolbox from the openCOBRA project (release 2.0),SBML toolbox,Gurobi optimization software installed for MATLABOptFlux (recommended)License: GPL v3Any restrictions to use by non-academics: noneInstall: See detailed description on the project home pageAdditional file 1OptPipe - Supplementary Methods. Optimization algorithms and pipeline description. (PDF 189 kb)Additional file 2OptPipe - Supplementary Results. Additional Tables. (XLSX 221 kb)


K-ras transformed cell line we experimentally assessed glutamine-induced metabolic changes. We validated computational results through an extension of Flux Balance Analysis that allows prediction of metabolite variations. Taken together these findings offer new understanding of the logic of the metabolic reprogramming that underlies cancer cell growth.Cancer cells share several metabolic traits, including aerobic production of lactate from glucose (Warburg effect), extensive glutamine utilization and impaired mitochondrial electron flow. It is still unclear how these metabolic rearrangements, which may involve different molecular events in different cells, contribute to a selective advantage for cancer cell proliferation. To ascertain which metabolic pathways are used to convert glucose and glutamine to balanced energy and biomass production, we performed systematic constraint-based simulations of a model of human central metabolism. Sampling of the feasible flux space allowed us to obtain a large number of randomly mutated cells simulated at different glutamine and glucose uptake rates. We observed that, in the limited subset of proliferating cells, most displayed fermentation of glucose to lactate in the presence of oxygen. At high utilization rates of glutamine, oxidative utilization of glucose was decreased, while the production of lactate from glutamine was enhanced. This emergent phenotype was observed only when the available carbon exceeded the amount that could be fully oxidized by the available oxygen. Under the latter conditions, standard Flux Balance Analysis indicated that: this metabolic pattern is optimal to maximize biomass and ATP production; it requires the activity of a branched TCA cycle, in which glutamine-dependent reductive carboxylation cooperates to the production of lipids and proteins; it is sustained by a variety of redox-controlled metabolic reactions. In a  in vitro—utilization of glutamine by reductive carboxylation and conversion of glucose and glutamine to lactate confer advantage for biomass production. Redox homeostasis can be maintained through the use of different alternative pathways. In conclusion, this paper offers a logic interpretation to the link between metabolic rewiring and enhanced proliferation, which may offer new approaches to targeted drug discovery and utilization.Hallmarks describing common key events in initiation, maintenance and progression of cancer have been identified. One hallmark deals with rewiring of metabolic reactions required to sustain enhanced cell proliferation. The availability of molecular, mechanistic models of cancer hallmarks will mightily improve optimized personal treatment and new drug discovery. Metabolism is the only hallmark for which it is currently possible to derive large scale mathematical models, which have predictive ability. In this paper, we exploit a constraint-based model of the core metabolism required for biomass conversion of the most relevant nutrients—glucose and glutamine—to clarify the logic of control of cancer metabolism. We newly report that, when available oxygen is not sufficient to fully oxidize available glucose and glutamine carbons–a situation compatible with that observed under normal oxygen conditions in human and in cancer cells growing  Cancer is a network disease  resultinThis property requires an extensive reorganization of metabolic fluxes –9, charaIn order to integrate sets of experimental data and to formulate new testable hypotheses, complex biological systems–such as human metabolism that involves thousands of metabolites and reactions—need to be formally described by mathematical models. In this regard, constraint-based modeling and in particular Flux Balance Analysis (FBA), which is based on the definition and manipulation of stoichiometric matrices and was originally developed for the optimization of microbial strains, is rapidly gaining popularity within life sciences . FBA allFBA may be applied to genome-wide metabolic networks , 24, whiin-vivo nutrient utilization rates. Moreover, when the aim is to investigate the plethora of admissible wirings, rather than to determine optimality, their computation becomes demanding and may give origin to a combinatorial explosion of different flux patterns, which fuels mere details while masking the major regulatory connections. Manually curated core models including hundreds of metabolites, selected for the specific purpose of the analysis, help to overcome the problems above [Being highly detailed, genome-wide models require many assumptions on ms above , 30. We K-ras transformed fibroblasts, grown in high glucose together with either low or high glutamine availability.In this study, we aim to identify the regulatory principles that link the utilization of glucose and glutamine in originating the Warburg effect, and ultimately in driving cancer cell growth. We manually reconstructed a core stoichiometric model designed to evaluate the contribution of glucose and glutamine to enhanced growth, hence the name ENGRO1 (ENhanced GROwth). By exploring the space of admissible wirings of the ENGRO1 model, we newly identified and rationalized intense aerobic glycolysis and glutamine reductive carboxylation as the fittest emergent strategy that supports cancer cell growth under conditions reported to be generated by oncogenic activation: sustained glucose and glutamine uptake. This emergent phenotype is observed only when the available carbon exceeds the amount that could be fully oxidized by the available oxygen, a condition that is entirely physiological. We validated our predictions by analyzing the metabolic behavior of murine uptake flux or by specifying the maximal rate allowed for nutrient consumption reactions. We will refer to the latter case as a constraint on nutrient availability, bearing in mind that it should be interpreted as a constraint on intracellular rather than on extracellular nutrient availability, the relationship between the two being non-linear and controlled by complex signaling networks [In the context of FBA, nutritional conditions are simulated either by imposing a specific networks .in vivo is undetermined, we wanted to systematically evaluate the typical response of a human metabolic network to different boundary conditions. For the sake of feasibility, we limited our analysis to glucose and glutamine—the most abundant nutrients in plasma [Given that the actual consumption rate of each individual nutrient n plasma  as well The metabolic network ENGRO1, designed to evaluate the contribution of glucose and glutamine to biomass formation, was therefore manually reconstructed. The network includes the catabolic pathways of glucose and glutamine and the anabolic reactions necessary for the main building blocks of biomass: amino acids and fatty acids , together composing 80% of the dry cellular weight . We focuAlthough cancer cells proliferate under conditions that restrain growth of normal cells, their growth rate does not necessarily coincide with the global optimum: indeed, it has been argued that a 5% improvement in growth rate would suffice to provide a selective advance to cancer cells . We haveInstead of focusing on the optimal response to a nutrient change (standard FBA), we examined the typical properties of the ensemble of theoretical wirings whose generic properties statistically match those of cancer cells, an approach similar to the one first applied to the study of gene regulatory networks . To effein vivo and in vitro are largely variable and mostly unknown, with special regard to oxygen consumption rates, we simulated the response of 50,000 wirings to a modulation of either the glucose or glutamine uptake flux, while the maximal oxygen consumption rate  was kept constant across all the experiments.Because the precise boundary conditions of cancer cells in silico cells displayed considerable variability in flux patterns, Although the 50,000 Despite the high utilization of nutrients, ENGRO1 wirings on the average do not exhibit biomass production . Therefore, lacking a prerequisite for cell proliferation, these simulated cells would not be classified as tumorigenic . The disWe thus partitioned the total population into distinct sub-populations that respond differently to nutritional conditions. Based on the interest raised by aerobic production of lactate, a first filter was applied to investigate the mode of utilization of glutamine: the cyclic mode of TCA cycle was reduced by glutamine in 98% of cell types : the experimental concentration of these metabolites is indeed increased in low glutamine , but we failed to predict the slight increase in the level of serine. This minor inconsistency may derive from the fact that in our simulation we did not supply external serine.We did not predict ornithine and putrescine to be significantly changed because these metabolites display a large variability in our sample. Efflux of ornithine and putrescine are indeed energetically equivalent in ENGRO1 network (cofactors are not involved in the step from ornithine to putrescine). We did not predict glucose to be significantly changed, as experimentally detected.Hence, the extended computational analysis was able to capture with a good degree of accuracy how the levels of many metabolites respond to glutamine shortage, giving support to the reliability of the ENGRO1 model and of our ensemble approach. A similar pattern of response has been obtained by a biochemical interpretation of the experimental findings see .In the previous sections we used a random sampling approach coupled with parameter scan of glutamine and glucose uptake rates to highlight that in the presence of glutamine there is a trend  to increase the amount of glucose that is converted to lactate. After having validated most model predictions using a murine cancer cell line, in this and the following sections we use standard FBA to understand, from a theoretical point of view, if the preference for glutamine is related to ATP and/or biomass optimization and how this preference is affected by the boundary conditions, i.e. the relative availability of oxygen, glucose and glutamine.2GR) of at least 6  all extra glucose supplied will decrease the O2GR and will thus be fermented to lactate  value  value . Resultsy) value .Notably, although we simulated the modulation of oxygen consumption by altering the boundary on oxygen intracellular availability, comparable effects were observed when constraining the capacity of Complex I to carry flux, and thus to accept NADH electrons, to mimic mitochondrial dysfunction .Although cancer cells divert most—but not necessary all—glucose to lactate, to better understand the principles governing the utilization of glutamine carbon in cancer cells, we focused on the extreme condition identified above in which all glucose is preferentially redirected to lactate . Without loss of generality, we arbitrarily picked a critical oxygen boundary conditions. Notice that similar conclusions would be derived for different values of the ratio between glucose and glutamine consumption, by accordingly adjusting the utilization of oxygen .2GR. It can be observed that the TCA “cycle” works in a branched non-cyclic mode, in which the α-ketoglutarate (AKG) originating from glutamine  takes a reverse path to isocitrate and then fatty acid biosynthesis (for about 20%) and a clockwise path to malate (for about 80%) which is eventually converted to pyruvate and then lactate. Excess TCA intermediates not contributing to biomass (including part of the OAA derived from the synthesis of citrate that fuels fatty acid biosynthesis) are preferentially disposed via conversion to lactate. The pentose-phosphate pathway is not active, reflecting the fact that our model does not account for synthesis of nucleic acids, a small fraction of cellular biomass. The electron transport chain is nearly equally distributed between oxidation of FADH and NADH, which also generates hydrogen peroxide (H2O2). H2O2 is totally removed by the coordinated action of glutathione peroxidase and glutathione reductase, with NADPH serving as an electron donor, despite the possibility to remove H2O2 without energy costs via a demand reaction. Besides lactate, another major toxic product is excreted: the ammonia that is not used for protein synthesis is removed as such, without using the ATP-costly urea cycle.The overall flux pattern that maximizes growth, hereinafter referred to as branched TCA cycle even though TCA is not working as a cycle, is in line with literature reporting experimental findings. Conversion of most glucose to lactate in spite of oxygen availability has been observed in many cancer cell lines or tumors , 7, as wWe examined if the flux pattern in When enumerating optimal solutions, we found that 44 alternative metabolic paths, sharing the same boundary conditions, produce the same maximal growth rate. Remarkably, all of them follow the branched TCA cycle mode described above.It has been already reported that variability in the optimal solution space is captured by a small number of sub-networks constituted by reactions with variable flux . AccordiIt can be observed that the four sub-systems involve redox factors and may therefore influence one another . For insA role for redox control in CMR has been anticipated in . The preWe have shown that glutamine utilization makes aerobic glycolysis optimal for growth. Nevertheless, the results of our ensemble approach  indicateTo investigate this hypothesis, we compared the previously obtained flux distribution at critical oxygen that maximizes growth Figs  and 6A aWe wanted to verify that a cyclic TCA mode was still possible for ENGRO1 at critical oxygen, so we forced it by inhibiting lactate secretion . In thisNoteworthy, the preference for a branched TCA cycle is maintained when glutamine is the unique carbon source , even wh2 yield. The glutamine to lactate flux mode improves the ATP production over oxygen consumption ratio by 5% as compared to the glucose to CO2 mode. Glutamine to lactate coupled with glutamine driven fatty acids synthesis improves the biomass production rate by 5% with respect to glucose to CO2 and glucose driven fatty acids synthesis. The correlation between lactate secretion and the ATP cost to make biomass further supports this contention (Taken together these observations indicate that glutamine is the preferred precursor for biomass production because it optimizes the ATP/Ontention .The strength of this preference for glutamine seems to depend on the ATP/oxygen ratio (P/O) ratio for FADH and NADH, and thus on the fraction of the electrons flowing through Complex I that ends up in superoxide anion , as was In this work, we exploited a novel constraint-based approach, based on the systematic evaluation of the possible wirings of the metabolic network required for the formation of biomass from glucose and glutamine, under different nutritional conditions. The first discovery presented in this paper is the identification of boundary conditions that taken together promote the emergence of cancer metabolic rewiring.2 molecules per glucose molecule may be typical for cancer cells. Detailed calculations—based on oxygen consumption rates reported in [in vivo the oxygen to glucose ratio in the blood supply is at least 3 times less than the 6 required for complete respiration  all activities it does not depend upon.in silico flux distribution that sustains CMR. We were able to integrate and rationalize the role of the various pathways observed in independent studies on cancer metabolism, as follows:Following the agreement with a wealth of literature, as well as experimental validation, of main ENGRO1 model predictions, we analyzed the global Glutamine utilization follows a branched TCA cycle, which proceeds clockwise from glutamine/AKG to oxaloacetate and malate, or counter-clockwise from AKG to citrate, then to acetyl-CoA going to fatty acids plus oxaloacetate going to malate.Glucose is almost fully fermented to lactate even in the presence of oxygen.Glutamine is not completely respired, but it is rather converted to lactate or pyruvate.By exploiting FBA, we investigated the relationship between different flux modes and their associated growth capability. We discovered that CMR is characterized by the following novel design principles:A large number of different metabolic routes may generate a CMR, by differential use of redox potential, while fatty acid synthesis gains a significant role as an acceptor of electrons, mostly coming from the assimilation of glutamine.Glutamine utilization promotes aerobic glycolysis, making the latter advantageous for growth, because it makes it energetically more favorable. This effect is enhanced by Reactive Oxygen Species (ROS) production by Complex I, with a stricter preference for the use of glutamine as an anaplerotic precursor when ROS production increases.in silico at limiting oxygen is not simply the fermentation of spare glucose, but a competition for oxygen between glutamine and glucose. The limiting amount of oxygen is preferentially used for the oxidation of the NADH and FADH2 generated when glutamine is converted to building blocks and lactate. As all available glucose is converted to lactate, we put forward a novel interpretation to what is classically understood as the ‘Warburg effect’.Aerobic production of lactate from glucose does not utilize all chemical potential of its substrate, thus it is generally regarded as unfit. Our results indicate that this is not the case. The phenomenon we observed in vivo, if the tumor environment imposes different constraints. In particular, we showed that fermentation of glutamine to lactate  is able to sustain growth even when glutamine is the exclusive simulated carbon source, suggesting how WarburgQ cells would be able to evade therapies that target only glycolysis.As boundary conditions change, so do the flux distributions of virtual cells that allow–possibly sub-optimal—biomass accumulation under a variety of conditions, suggesting how cancer cells might be able to follow different metabolic routes In conclusion, our paper offers for the first time a “logic” to the central role of the metabolic hallmarks in cancer biology, logic that was envisioned in . As the p to produce ATP and a probability pROS = (1 − p) to produce ATP to NADH oxidation in the respiratory chain. Biomass formation is expressed in terms of ATP, non-essential amino acids and palmitate requirements. Thermodynamically infeasible loops were first identified with the algorithm presented in [Once the pathways to be included were selected, we checked that each reaction in the model was able to carry flux. We included a minimal set of exchange reactions. We avoided compartmentalization of metabolites, paying attention that this simplification would not affect the energetic requirements for biomass. We associated a probability ented in  and thenThe resulting ENGRO1 model includes 84 reactions and 67 metabolites belonging to the following pathways: glycolysis and lactic acid fermentation (10 reactions); TCA cycle (9 reactions); oxidative phosphorylation and mitochondrial ROS generation (2 reactions); glutamine reductive carboxylation (4 reactions); glutathione biosynthesis and oxidation (10 reactions); urea cycle (5 reactions); fatty acid synthesis (2 reactions); pentose phosphate pathway (5 reactions) and biosynthesis of the main non-essential amino acids (13 reactions). The complete network definition together with the biomass composition is given in the S and a set of constraints that impose the upper and lower bound of fluxes. The steady state constraint is defined by the equation dx/dt = S · v = 0, where dx/dt are time derivatives of metabolite concentrations represented by the product of the m×n matrix S times the vector of fluxes v = , where vi is the flux of reaction i, n is the number of reactions, and m is the number of metabolites. The ensemble of functional states that the system can reach given a boundary condition I determines the feasible solutions space Φ = Σ∩I. By exploiting linear programming, FBA allows for optimization of the flux through a weighted sum of fluxes. In particular, we used the COBRA Toolbox [FBA requires a stoichiometric matrix  Toolbox  and the Because FBA only returns a single solution, we exploited Flux Variability Analysis  to assesTo analyze the complete set of flux distributions that maximize growth, we identified all the extreme points that lie at the intersection of the convex polytope given by the linear constraints and the hyperplane of the optimal objective function value, which correspond to alternate optima, as in . The proAs a complement to classic FBA, Monte-Carlo approaches are emerging with the aim of exploring the entire region of feasible flux distributions . The domIn , random τ of considered reactions is randomly drawn with uniform probability in  and then filtered them according to Boolean  expressions which must return true for each ensemble member. We define a metabolic response as the modification in fluxes resulting from a specific nutritional perturbation . The perturbation is simulated by varying the flux boundaries of the corresponding reaction. As an example, a metabolic response pertains to Ensemble E if and only if the biomass production flux is greater than 0 for at least one of the simulated glutamine and/or glucose uptake rates. For a more formal description of the method, the reader is referred to .K-Ras-transformed NIH3T3-derived cells [2. Cells were plated at a density of 3000 cells/cm2 in 6-well plates in normal medium. Culture medium was replaced after 18 hours with a normal medium containing 4 mM Gln or a low Gln medium (0.5 mM glutamine). The cells were collected and counted after 54, 72 and 144 hours. Media and serum were purchased from Life Technologies Invitrogen .Mouse embryonic fibroblast ed cells –42, 72 wKit for assay of acetyl-CoA and enzyme activities were purchased from BioVision  and used according to the manufacturer’s protocols. Raw data are provided in The total ROS levels were measured using the DCFDA Cellular Ros Detection Assay Kit from Abcam  according to manufacter’s instructions. Mitochondrial ROS levels were measured using 5 μM MitoSOX Red mitochondrial superoxide indicator (Molecular Probes) in HBSS/Ca/Mg for 10 min at 37°C. Fluorescence was measured at excitation/emission wavelengths of 510/580 nm, respectively, using a Cary Eclipse Fluorescence Spectrophotometer. Raw data are provided in l of ice-cold acetonitrile was added to 40 μl of media and vortexed at 4°C for 2 minutes, and the mixture was incubated on ice for 5 minutes and centrifuged at maximum speed for 10 minutes. A 100-μl volume of the aqueous phase was collected in a new tube and evaporated under nitrogen flow at 37°C. Derivatization was performed as described [l volume of sample was injected in a 1:10 split mode at 250°C. The GC was performed as previously described [After 144 hours of growth, the metabolites were extracted and analyzed by gas chromatography-mass spectrometry (GC-MS) as previously described  and the escribed . A GC/MSescribed . The GC/The following metabolites were detected: glutamine, glutamate, aspartate, glycine, serine, alanine, trehalose, methionine, lysine, tyrosine, cysteine, ornithine, putrescine, glucose, pyruvate, lactate, citrate, succinate, fumarate, malate, acetyl-CoA. Raw data are provided in −13 to 3.5*10−13 mMol per cell per second. We measured a glucose consumption rate of 5.8*10−13 mMol/sec per cell, while Jain et al. [−13 mMol/sec per cell which would require 12.10−13 for complete respiration. Oxygen consumption is not 6 times as much as glucose, and thus–according to our terminology–an oxidative bottleneck is apparent for cancer cells growing in vitro.According to the oxygen uptake rates catalogued for a variety of cells  in , the celn et al.  reportedThe condition of limiting oxygen should also prevail in vivo. Let us approximately evaluate the molar ratio between oxygen and glucose in human blood:V of 20 ml of oxygen gas at a pressure P of 760 mmHg [T = 310K°)The concentration of oxygen in the blood  corresponds to a volume 760 mmHg  and at aP*V = n*R*T, where R is the universal gas constant 62 L*mmHg K-1*mol-1, we can obtain the moles n of oxygen per liter of blood.By using the ideal gas law n = P*V/(R*T) = (760 * 0.2)/(62*310) ~ 8 mMol/liter.n is to start form the hemoglobin concentration in blood, which we found in literature [Another procedure to compute terature  to be 15−03 mol/litre.Because the molar weight of hemoglobin is 64, the concentration of hemoglobin in blood is 2.3*10If we assume a maximal saturation for oxygen, we have 4 oxygen molecules bound to each hemoglobin.−04 *4 ~ 9 mMol/liter.Therefore, n = 2.3*10The two alternative procedures return a similar order of magnitude for the maximum concentration of oxygen in blood (in the range 8 to 9 mMol/liter). The level of glucose in blood is around 5 mol/liter . TherefoBoth glucose and oxygen are ultimately delivered to the tissue (extracellular environment) not by diffusion but by convection by the blood. Therefore, at maximum consumption of glucose from the blood, at most 2 molecules of oxygen would be available per glucose molecule. If one hypothetical cell were to consume avidly all the glucose that is supplied by the blood in a given unit of time, that cell would not have enough oxygen to completely oxidize such glucose in that unit of time.S1 Fig2GR. The level of O2GR for which a plateau is reached  increases with the QGR (purple dots). For high O2GR a plateau is not reached within the considered range. 2GR. Red dots highlight the value of the ratio when O2GR is critical. Full glutamine utilization takes place at Critical O2GR (panel C), when the PDH flux is 0 and the respiratory chain is fed exclusively by glutaminolysis leading to almost equal NADH (Complex I) and FADH (Complex II) oxidation, the ratio of NADH oxidation over FADH oxidation being around 1.2. C) Glutamine uptake (z-axis) and ammonia efflux –scaled on glutamine availability and consumption respectively–as a function of QGR and O2GR. Red points highlight the minimum level of O2GR for which full glutamine consumption is observed. The increased glutamine uptake needs to be balanced by a comparable ammonia efflux that get closer to 2 when glutamine is plentiful and oxygen is low (coloring of the mesh). D) Aconitase flux  as a function of QGR and O2GR. 2GR is critical. At Critical O2GR, pyruvate dehydrogenase is not working, TCA cycle cannot work in a cyclic mode and production of citrate by the citrate synthase is therefore not possible. The citrate required to feed biosynthesis of fatty acids (required for biomass production) must derive from reverse carboxylation of glutamine derived AKG, as indicated by a negative flux of aconitase. E-H) The optimal flux value of serine synthesis (panel F), PDH (G), aconitase (H) and LDH (I) as a function of QGR for the standard non-essential amino acid (NEAA) composition of biomass NEAAA STD  Growth rate (z-axis) and oxygen uptake  scaled on glucose uptake as a function of QGR and O(PDF)Click here for additional data file.S2 Fig2GR (panel A) and as a function of the Complex I capacity over glucose uptake ratio (CGR in panel B) for three different levels of glutamine abundance (QGR). Purple dots highlight the growth rate when O2GR or CGR is optimal (oxygen not limiting for biomass). C-D) Lactate efflux scaled on glucose uptake as a function of O2GR (panel C) and CGR (panel D) for three different levels of QGR. Red points highlight the level of O2GR or CGR for which maximum lactate secretion is observed . E-F) Aconitase flux as a function of O2GR (Panel E) and CGR (Panel F). Red dots highlight the flux when O2GR or CGR is critical.Note that because of the reaction stoichiometry, Complex I flux is proportionally higher than the corresponding oxygen consumption rate. A-B) Growth rate scaled on glucose availability as a function of O(PDF)Click here for additional data file.S3 FigThe first sub-network  includes PEP carboxykinase; pyruvate kinase, NADP and NAD dependent malic enzyme and malate dehydrogenase. Because the TCA cycle is working in a non-cyclic mode, this set of reactions allows to maintain the steady state by removing glutamine-derived TCA cycle intermediates: OAA produced by reductive carboxylation of AKG and not used for fatty acids biosynthesis and malate deriving from fumarase, which, by means of the reactions in this subnetwork, can be converted into pyruvate and then secreted as lactate. The main options to remove OAA and malate are reported in (TIFF)Click here for additional data file.S4 FigpROS that emulates the level of production of reactive oxygen species in the respiratory chain . Glucose availability: 10; glutamine availability: 40; oxygen availability: critical level 38. B) Same experiment in panel A but with a P/O ratio of 2.5 and 1.5 considered for NADH and FADH2 respectively. C) Optimal biomass and FVA centroid of lactate secretion as a function of the ATP coefficient in the biomass forming reaction.A) Maximum and minimum value for lactate secretion across optimal growth solutions according to FVA, as a function of the parameter (PDF)Click here for additional data file.S5 FigA) Standard deviation of the model fluxes (represented with different colors) as a function of the sample size. B) Zoom in on fluxes of panel A with low standard deviations. The fluxes with high standard deviations correspond to those with high variability when running FVA. C) Relative standard error of the mean of each flux as a function of the sample size.(PDF)Click here for additional data file.S1 TableThe optimal flux value obtained with FBA, the minimum and maximum value as well as the range size, obtained with FVA, are reported for each reaction.(XLSX)Click here for additional data file.S2 TableThe optimal flux value obtained with FBA, the minimum and maximum value as well as the range size, obtained with FVA, are reported for each reaction.(XLSX)Click here for additional data file.S3 Table2 consumed (column 5), ATP produced form substrate (column 6) and ATP produced by oxidation of NADH and FADH2 produced in the respiratory chain (column 7). Complex I generates ROS that may be detoxified by glutathione in a mechanism that costs one NAD(P)H per 2 molecules of superoxide anion produced. If a fraction of the electrons flowing through complex I ends up in superoxide anion, the effective P/O ratio of NADH oxidation becomes 3(1−pRos)/(1+pRos). In this computations, we assume that a mere 25% of the electrons in Complex I flow to ROS; this implies a reduction of the effective P/O for NADH from 3 to 1.8 (against a 2 P/O for FADH2). This lowers the P/O of the Gln to lactate conversion, from 3.0 to 2.2. This effect is smaller than the effect on the P/O ratio of the glucose respiration-rather-than-fermentation, i.e. from 3.0 to 2.0, explaining the preference for the flux from glutamine to lactate when so much ROS is produced by Complex I (see above). The 10% difference in P/O ratio may seem small, but as maintenance metabolism may well consume more than half the ATP produced, the difference in ATP availability for anabolism might well exceed 20%. The table considers a value of infinity (computed as 100) for the P/O ratio of the fermentation of glucose to lactate, reflecting that no oxygen is consumed in that process. When oxygen is limiting, this process comes for free and therefore glucose has a preference for this. When we compare glucose catabolism to glutamine oxidation, we correct for the phenomenon that any glucose respired comes at the cost of one glucose fermented, hence our focus on P/O ratios for glucose respiration rather than fermentation. Should lactate dehydrogenase be incapacitated, then the next best strategy is glucose respiration to CO2 at a P/O. Should glucose uptake be impossible but lactate dehydrogenase active, the table shows that the best flux pattern for the fittest cells is glutamine to lactate again. In none of these cases pyruvate production should be better than lactate production, but if lactate production is blocked, pyruvate production from glutamine should occur in optimal fittest cells because it is more profitable (P/O = 2.10) than complete respiration of glutamine (P/O = 2.07). These two numbers exceed the P/O of 1.82 for glucose to pyruvate rather than lactate, i.e. glucose carbon would not leave as pyruvate. The table also shows that the P/O ratio for glucose being converted to cytosolic acetyl-CoA, which serves as carbon substrate for the lipids in the biomass synthesized rather than being converted to lactate (-0.80), is more negative than that for Gln being converted to acetyl-CoA (-0.60). The clockwise pathway (at P/O = -1.8) and the combined clockwise and counterclockwise pathway for synthesis of 2 acetyl-CoA (at -1.0) from glutamine are even less favorable.For different possible flux routes (table rows), the P/O ratio (column 8) of as well as the moles of acetyl-CoA deriving form one mole of substrate (column 10) following the considered route is computed. In some cases, the row indicates the difference between the computations of two possible routes . Intermediate steps of the computation are also reported: moles of NADH (column 3) and FADH2 (column 4) obtained, moles of O(PDF)Click here for additional data file.S1 TextDetails on ENGRO1 model reconstruction.(PDF)Click here for additional data file.S2 TextBiochemical interpretation of experimental results.(PDF)Click here for additional data file.S1 FileExcel file of the model compliant with the RAVEN Toolbox.(XLS)Click here for additional data file.S2 FileExcel file of the model compliant with: RAVEN Toolbox and FAME.(XML)Click here for additional data file.S3 FileScalable Vector Graphics image of the model, compliant with the software FAME.(SVG)Click here for additional data file.S4 FileRaw data  used to build graphs in (XLS)Click here for additional data file.