A set of 131 reactions, essential for the production of primary biomass precursors is identified; deletion of any of them can inhibit the overall biomass production. Usability Index (IU) for the rest of the reactions are estimated and based on this parameter, they are classified into three categories—maximally-favourable, quasi-favourable and unfavourable for the primary biomass production. The lower value of 1 − IU of a reaction suggests that the cell cannot easily bypass it for biomass production. While some of the alternative paths are energetically equally efficient, others demand for higher photon. The variations in (i) ATP/NADPH ratio, (ii) exchange of metabolites through chloroplastic transporters and (iii) total biomass production are also presented here. Mutual metabolic dependencies of different cellular compartments are also demonstrated.More than 20% of the total caloric intake of human population comes from rice. The expression of rice genes and hence, the concentration of enzymatic proteins might vary due to several biotic and abiotic stresses. It in turn, can influence the overall metabolism and survivability of rice plant. Thus, understanding the rice cellular metabolism, its plasticity and potential readjustments under different perturbations can help rice biotechnologists to design efficient rice cultivars. Here, using the flux balance analysis (FBA) method, with the help of  Rice is a socio-economically important food grain for more than half of the world’s human population . HoweverThe metabolic modeling technique can be grouped into two categories—(i) kinetic modeling and (ii) structural modeling. Since, the kinetic modeling requires details of enzyme kinetic data, the technique is usually limited to systems having small number of reactions. On the other hand, the correct stoichiometry and the thermodynamic feasibility of the biochemical reactions are required for structural modeling. Thus, the structural modeling technique is used in genome-scale metabolic modeling and its analysis. A number of genome-scale metabolic models (GSMs) of various organisms, including bacteria , simplesAny species including rice plant is exposed to several environmental conditions, which might change the expressions of cellular proteins including enzymatic genes. The down-regulation of an enzymatic gene’s expression can result several consequences, such as (i) no change in the efficiency of the corresponding reaction, (ii) a partial blockage in enzymatic reaction’s activity, or (iii) a full blockage . The partial or full blockage of an enzymatic gene’s activity can change the metabolism of a cell. It can alter the metabolic phenotype, such as the composition and amount of the biomass precursors it synthesizes in normal condition. Whether this alteration of metabolic phenotype would be lethal or not depends on the necessity of the biomass precursors. Alternatively, the cell does not exhibit any change in metabolic phenotype and finds some alternative metabolic pathways to produce the same amount of biomass it produces in normal condition. It has been already shown that a living species has enough metabolic flexibility to adapt itself to different biotic and abiotic perturbations , 11. ThiE. coli) from an universal network of 5906 reactions and determined the essentiality of each of the reactions. The reactions required in all metabolic networks were defined as ‘superessential’ . The superessentiality index of a reaction was defined as a ‘fraction of networks in which the reaction is essential’. The value of superessentiality index helps one to understand whether a reaction can be easily bypassed by any known metabolic pathway or not. We have used this concept to derive a mathematical expression, termed as the Usability Index  the enzyme(s) associated with that particular reaction is knocked out  and (ii) severe down-regulation of the associated gene(s) so that the reaction becomes inactive. Here, we have studied the effect of reaction deletion (the full blockage of the enzymatic reaction) in a genome-scale metabolic model of rice leaf . In specin-silico reaction  deletion strategy and the cellular responses are simulated to observe the possible active metabolic states.The rice genome-scale metabolic model is used here (i) to find the essential reactions for biomass production, (ii) to classify the rest of the reactions based on their Usability Index and (iii) to observe the metabolic plasticity of rice metabolism. Further, we have analyzed how the deletion of any reaction can affect the overall cellular economy in terms of photon demand. It should be mentioned that the incident photon is the primary source of a photosynthetic organism’s ATP and NADPH productions which, in turn, are used in fixing the inorganic nutrients into biomass through a series of chemical reactions. Consequently, for the deletions of some of the reactions, the variation in ATP/NADPH ratio is also observed. How this variation is readjusted within the cellular metabolic system has also been discussed with a few examples. We also report the effects of reaction deletion on total amount of biomass production and exchange of metabolites through chloroplastic transporters. Inter-compartmental interactions within a cell play an indispensable role for any eukaryotic organism. This reaction deletion study elucidates how the metabolism of different compartments interact with each other. In summary, here, different genotypes in a rice cell is created through Oryza sativa)  and the metabolic response is simulated by FBA to test whether the modified metabolic network  is able to produce the biomass in experimentally observed fixed proportions or not. If the simulation can not find any possible solution, the reaction is termed as essential for biomass production. An essential reaction must carry a non-zero flux to produce the cellular biomass; however, it does not refer that the rest of the reactions are not at all important to produce the biomass. Rather, some of them might frequently take part in biomass production while others do not. Thus, to determine the importance of a single reaction in overall metabolism of rice leaf cell, Usability Index (Iwww.python.org).All computational implementations are done using ScrumPy metabolic modeling tool  and resuU is calculated for each of the reactions to understand how much this reaction is favourable by the metabolic system. Subsequently, the photon usage efficiency of the alternative metabolic pathways are compared with that of the WT. The analysis also includes (i) some examples to show the variation in ATP and NADPH usages, (ii) changes in the transport of C3 compound between chloroplast and cytosol through chloroplastic transporters and (iii) changes in total biomass production at a fixed value of incident photon. Then, the flux responses are analyzed to show that change in fluxes of some reactions in one compartment can influence the fluxes of reactions in other compartments.The genome-scale metabolic model of rice leaf is used here to simulate the metabolic responses under the genotypic perturbations created by the complete inhibition of individual reaction. Since primary aim of this work is to understand the metabolic flexibility, we have first identified the essential reactions; without any of them, the cell is not able to produce the primary biomass in fixed proportion. Then, I3 plant Arabidopsis thaliana, Wang et al. (2012) reported that nearly 10% of reactions are essential for biomass production [2 and its deletion shows complete inhibition of biomass production. The metabolic network in the absence of phosphoribulokinase  is not able to produce the biomass precursors in experimentally observed proportions. These are consistent with realistic behaviour of plant’s cellular biochemistry [E. coli that most of the biosynthetic pathways’ reactions are essential [A set of 131 reactions is found to be essential for biomass production . Among toduction . Here, themistry . Part ofet al. 20 reportedThe reactions other than the essential are termed as non-essential reactions for primary biomass production. Nonessentiality of a reaction does not mean that the cell does not utilize this reaction to produce the biomass. Rather, it indicates that there exist alternative possible routes within the cellular metabolism using which the cell can produce same amount of the biomass. In addition, these alternative routes might be important for a specific perturbed state caused due to environmental changes to which the cell is exposed. Under some perturbed conditions, the knockout of enzymatic reaction associated gene(s) results in complete blockage of the associated reaction. The different states of genes (knockout or knock-down) represent different cellular genotypes, and respective metabolic responses could relate to the active cellular metabolic states.U indicates how easily a reaction will be bypassed when a perturbed or mutant condition arises. The non-essential reactions are classified here into three categories—‘maximally-favourable’, ‘quasi-favourable’ and ‘unfavourable’. The 1 − IU ∼ 0 value of a reaction indicates that the probability of bypassing this reaction is less and these reactions are termed as maximally-favourable for biomass production. The reactions with 1- IU ∼ 1 are defined as quasi-favourable, i.e., they are unused most of the time; however, they might be activated for driving metabolism in rare circumstances. Unfavourable reactions are those for which 1 − IU = 1. It should be noted that all these categorization of metabolic reactions are done in fixed biomass  condition. We have identified that 101 (1 − IU ∼ 0.0006 to 0.077), 111 (1 − IU ∼ 0.923 to 0.999) and 1348 (1 − IU = 1) reactions are maximally-favourable, quasi-favourable and unfavourable for biomass production, respectively  is found to be unfavourable and this result indicates that most of the routes in the entire metabolic network are not used to produce biomass precursors considered here; but they might be active to produce other biomass components including the synthesis of secondary metabolites. On the other hand, an inference could be made by the presence of a large number of maximally-favourable and quasi-favourable reactions that the plasticity of rice metabolic network is very high.Deletion of a large number of reactions does not inhibit the production of biomass and this indicates the metabolic plasticity of the cell as well as the robustness of cellular biochemical mechanisms. Consequently, this suggests that there are alternative routes the plant can use when needed. However, it does not ensure that all the alternative routes are equally economic, i.e., the cell needs equal amount of energy to produce the biomass using these alternative pathways. This energy, indeed, comes from the photon absorbed and is utilized in biochemical machinery.U index for cytosolic malate dehydrogenase  is 0.0019. The deletion of this reaction causes no change in photon demand, but the total flux of cellular objective function in MT solution space becomes higher  than the WT. So, using this WT path, cell can maximize its overall cellular economy. Further, there is always a possibility of having different solution for a particular objective. The presence of these cannot affect our main observation; rather, it suggests higher metabolic plasticity of cellular metabolism.While a reaction is blocked and the metabolic network finds at least one alternative route , the photon fold change (FC in lux unit . Table 1f a cell . For insU = 1) do not take part in biomass production, photon demand remains unchanged due to their deletions. Interestingly, the deletions of quasi-favourable reactions (1 − IU ∼ 1) also do not show any change in photon demand. It suggests that quasi-favourable reactions can be easily bypassed and can have several alternatives to produce the biomass.As the unfavourable reactions (1 − IU ∼ 0) which show photon FC > 1 when deleted  to G3P (3-phospho-D-glycerate) producing reaction (PHOSGLYPHOS-RXN) by enzyme phosphoglycerate kinase , 21 is ithaliana . It is eα-glucose 6-phosphate) to GLC-1-P (glucose 1-phosphate) in the WT and this pathway synthesizes cellulose. The UDP-glucose pyrophosphorylase, an important enzyme for cellulose deposition, catalyzes glucose-1-phosphate and UTP to produce UDP-glucose and pyrophosphate (PPI) [Another example is illustrated in te (PPI) . When thte (PPI) , catalyzte (PPI) .It is observed that while any one of the complexes I, III, IV and V in the mitochondrial electron transport chain is deleted, the metabolic process needs significantly higher amount of photon flux to supply ATP for biomass production. It is evident from In chloroplast, glyceraldehyde 3-phosphate dehydrogenase catalyzes a step in Calvin cycle by conversion of glyceraldehyde-3-phosphate (GAP) to glycerate 1,3-bisphosphate (BPGA). This reaction is also associated with NADPH production. Thus, removal of this reaction causes an increase in photon flux to produce the biomass in fixed proportion. Similarly, the deletion of another adjacent reaction catalyzed by phosphoglycerate kinase (EC 2.7.2.3) converting PGA (3-phosphoglycerate) to BPGA in the same path causes same photon FC. The light dependent non-cyclic (LightNonCyc in our reaction list) reaction remains active all the time; however, in a few cases, slight decrement in its flux is observed which is compensated mostly by light dependent cyclic reaction. The decrease in NADPH produced by light non-cyclic reaction is tuned by other NADPH producing sources. Alternative routes for deletions of some of the maximally-favourable reactions are also presented in Rice leaf metabolism under varying light shows that photorespiration can salvage the excess energy produced at higher light intensities . ConsequPhotosynthetic organisms need NADPH as the reducing power for several carbon and nitrogen fixing metabolic processes occurring within the cell. ATP is the essential currency metabolite, needed in many metabolic processes as a supply of energy. The utilization of ATP and NADPH in a cell depends on the condition in which the cell is being exposed . The lig3 compound ), generated in the Calvin cycle within the chloroplast, can be transported to the cytosol with an exchange of cytosolic Pi through three chloroplastic transporters, namely, PGA, GAP and DHAP transporters. Thermodynamically, these exchange reactions are reversible, i.e., they can also transport cytosolic PGA, GAP and DHAP to the chloroplast with an exchange of chloroplastic Pi.The intracellular transporters of a plant cell transport metabolites from one compartment to another. There are a number of chloroplastic transporters which exchange Pi (inorganic phosphate) and specific metabolites (carbon compounds) between chloroplast and cytosol. For example, the C3 transporters are shown in We have deleted all the non-essential reactions one by one and analyzed the exchange of metabolites through these chloroplastic transporters. The results are presented in In the WT, the chloroplastic PGA transporter transports PGA from cytosol to the chloroplast. When any one of the mitochondrial MalDH , cytosolic phosphoglycerate kinase, chloroplastic G3Pdh  or PGK (phosphoglycerate kinase) reactions is blocked, the chloroplastic PGA transporter transports chloroplastic PGA to the cytosol. In WT, the G6P (glucose 6-phosphate) is produced in the chloroplast and transported to the cytosol. The transport becomes reverse when any one of the chloroplastic FBPase , G3Pdh, Ald1 (Aldolase A), R5Piso, PGI (phosphoglucose isomerase) or PGK reactions is blocked. While chloroplastic G3Pdh or PGK reaction is blocked, the GAP transporter transports GAP from cytosol to the chloroplast. The DHAP transporter exports Pi from chloroplast to cytosol when any one of the chloroplastic triosephosphate isomerase, ribose-5-phosphate isomerase, PGK or cytosolic fructose-bisphosphate aldolase catalyzed reactions is blocked.fp. This gives an estimate of how much biomass can be generated in mutant type using the amount of photon needed in WT. It is expected that MTfp would generate a lower amount of biomass using WT photon. It is clear from fp solutions for these constraints produce 58.3% and 57.7% of total biomass, respectively. It indicates that inhibition of some maximally-favourable reactions can end up with reduced biomass in lower light.The minimum amount of photon needed in WT to produce the biomass in experimentally fixed proportion is ∼ 0.32 light flux unit. However, deletions of some reactions require higher amount of incident photon for the same purpose. Here, the incident photon flux is kept fixed at ∼ 0.32 light flux unit (as obtained in WT); then a reaction is deleted and the cellular metabolism is simulated to predict the fluxes through the biomass precursors. This mutant type state, simulated in fixed photon flux is denoted as MTIt is already known that the chloroplastic and mitochondrial metabolisms are highly dependent on each other and they serve some important cellular functions including ATP production and regulation of redox state in the cell –30. HereDeletions of complexes I and V in mitochondria up-regulate malate-oxaloacetate shuttle in chloroplast and down-regulate light dependent non-cyclic reaction. In addition, the light dependent cyclic reaction becomes active. The deletions of complexes III and IV up-regulate malate-oxaloacetate shuttle, light non-cyclic reaction and GAP transport from chloroplast and down-regulate F6P (fructose 6-phosphate) to G6P conversion. Deletion of malate-dehydrogenase  in mitochondria up-regulates malate-oxaloacetate conversion, light non-cyclic reaction in chloroplast and down-regulates F6P to G6P production.While the reactions catalyzed by chloroplastic PGK (PGA → BPGA) and G3Pdh (BPGA → GAP) are blocked, the fluxes in electron transport chain (ETC) are increased along with malate to oxaloacetate shuttle in mitochondria.Elimination of cytosolic BPGA to PGA conversion reaction up-regulates some reactions of TCA cycle  is identified. The rest of the reactions are classified based on the condition that whether these reactions can be easily bypassed or they are favourable by the cellular metabolism. The photon demands of the metabolic system while using alternative paths are calculated. Some of these alternative pathways are economic in terms of photon demand, while others are not. The readjustments of metabolism to utilize the cellular ATP and NADPH through some alternative pathways are also discussed. While the biomass production remains constant, the higher photon demanding pathways might represent active metabolic states of the plant at higher light intensities. The effect of reaction deletion on (i) exchange of metabolites through chloroplastic transporters and (ii) the interactions of the metabolism of different compartments are also demonstrated.However, the present version of the rice metabolic model is partially compartmentalized. Thus, one can include other compartments and the relevant reactions in the model and extend the analysis to understand the underlying mechanism of cellular metabolism. Likewise, the system can be studied under other cellular objectives . Rice plant also produces several secondary metabolites and inclusion of those into the model might increase the number of essential reactions. However, despite the possibility of these improvements, this study should provide a platform for the rice biotechnologists to design stress-tolerant and efficient rice cultivars.S1 Dataset(XLS)Click here for additional data file.S2 Dataset(XLS)Click here for additional data file.S1 Table(PDF)Click here for additional data file.


Pseudomonas putida KT2440 (iJN746) with the aerobic pathway of PCBs degradation. We assess the effectiveness of different bioremediation scenarios in reducing PCBs concentration in species and we study indices of species centrality to measure their importance in the contaminant diffusion via feeding links. The analysis of the Adriatic sea case study suggests that our framework could represent a practical tool in the design of effective remediation strategies, providing at the same time insights into the ecological role of microbial communities within food webs.The pressure to search effective bioremediation methodologies for contaminated ecosystems has led to the large-scale identification of microbial species and metabolic degradation pathways. However, minor attention has been paid to the study of bioremediation in marine food webs and to the definition of integrated strategies for reducing bioaccumulation in species. We propose a novel computational framework for analysing the multiscale effects of bioremediation at the ecosystem level, based on coupling food web bioaccumulation models and metabolic models of degrading bacteria. The combination of techniques from synthetic biology and ecological network analysis allows the specification of arbitrary scenarios of contaminant removal and the evaluation of strategies based on natural or synthetic microbial strains. In this study, we derive a bioaccumulation model of polychlorinated biphenyls (PCBs) in the Adriatic food web, and we extend a metabolic reconstruction of  Polychlorinated biphenyls (PCBs) are a class of POPs consisting of 209 different congeners, obtained from the catalytic chlorination process of biphenyl, and characterized by high environmental persistence and resistance to natural ways of breakdown. PCBs are practically insoluble in water and, due to their lipophilic nature, they easily dissolve in fats and lipids causing bioaccumulation, i.e., the phenomenon by which the internal contaminant concentration in an organism is higher than in the external medium. Indeed, PCBs have been detected both in aquatic biota and in all the abiotic phases of marine environments . Generally, heavier chlorinated PCBs congeners tend to accumulate in oxygen-depleted zones of sediments. Moreover, they bioconcentrate in species by following biomass flows in predator-prey relationships. PCBs bioccumulation phenomena in aquatic organisms occur over time as the result of multiple contamination pathways, including processes of uptake  and elimination .Aquatic ecosystems are subject to a mixture of synthetic organic chemicals, leading to adverse effects on organisms at different levels of biological organization and at all trophic levels of the food web. Over the last decades, many removal strategies have been proposed in order to reduce the bioavailability of persistent organic pollutants (POPs) and to limit the consequent bioaccumulation phenomena on species. microbial loop , presented in Nogales et al.   are known quantities and are estimated as reported in . In order to have an effective degradation process, this aerobic step should ideally take place sequentially to the anaerobic step in the full microbial degradation pathway. As illustrated in Figure Pseudomonas putida  in Nogales et al. . Several studies report the genetic plasticity of different strains of Pseudomonas spp., showing the correspondence between gene clusters involved in biphenyl degradation pathways , by extending the metabolic reconstruction of s et al.  with thein silico analysis of the invariant characteristics of the metabolic network at a low computational cost.Starting from biochemical reactions and stoichiometric coefficients, the Flux Balance Analysis (FBA) framework is based on the assumption of a metabolic steady state  and the synthetic objective vk2 , we set fk1 = 1 and gk2 = 1. The solution of the bilevel problem (1) is a pair indicating the maximum natural objective (inner problem) allowed by the constraints Sv = 0 and V⊥k ≤ kv ≤ V⊤k, and the maximum synthetic objective allowed in the flux distribution that maximizes the natural objective. The bilevel problem can be converted to a single-level problem using the duality theory applied to the inner problem, which is replaced by additional constraints for the outer problem.where P. putida. In the following, we use the more compact notation of chemical reactions to describe our FBA encoding, omitting the translation to the matrix form given in Section 2.3.We introduce a method for integrating the PCBs bioaccumulation network with the FBA-based metabolic reconstruction of i → j in the food web with a unary irreversible reaction with substrate i (the prey) and product j (the predator). Ecological compartments are thus translated into metabolites. Specifically, we derive the following set of reactions:The basic idea is encoding each link i, j)  is upper bounded by the original corresponding flow rate ci→j. This formulation admits a space of solutions with potentially reduced (even zeroed) contaminant flows, which is required in order to reproduce the contaminant removal by the bacterial metabolism.where the rate of a reaction  but i has null contaminant concentration (iC = 0).Any admissible vector of fluxes for the reactions in Additionally, we consider the following set of exchange reactions for expressing the external inputs and outputs of the food web:FWE contains, for each external sink e of the food web, an unbounded export reaction from e. Similarly, the set of import reactions FWI has an uptake reaction for each external source, but in this case the uptake rate is set to the sum of all flows imported through i in the contaminated network (∑j ci→j). Note that it is sufficient to constrain the import reactions in order to obtain a consistent FBA encoding of the bioaccumulation model. Indeed, by mass-balance, throughflow values are conserved by the encoding and it can be shown that the food webs entailed by the reactions in FWR ∪ FWE ∪ FWI are all identical to the original network, up to redistribution of external exports.The set i, the resulting bioconcentration iC in the entailed network is computed as the ratio between the total contaminant outflows (as reaction fluxes) and the total biomass outflows:Finally, for a generic group x, which serves as the interface between the encoded bioaccumulation model and the bacterial reactions. In particular, x represents the unbounded sink for all the food web groups we aim to remediate; and the unbounded source for all the metabolites describing PCBs molecules in the P. putida metabolism . Clearly, these interface reactions could also be bounded with arbitrary or experimentally measured limiting factors to bioremediation efficiency, as done in Section 3 for evaluating different degrees of bioremediation.An effective way to accomplish this task is adding a dummy metabolite bioremediation problem, as that of maximizing the amount of remediated flow, i.e., the sum of fluxes exitingx in the integrated metabolism-food web network. Formally,We define the I denotes the set of interface reactions; R is the set of reactions in the P. putida metabolism; and FWR, FWE and FWI describe the encoded food web.where Scenario 1: Bioremediation of detritus groups. This hypothesis is based on the fact that the microbial loop, where bioremediating bacteria are assumed to naturally operate, is located at the interface between natural detritus and planktonic groups (both included in our food web). Thus, we redirect the outflows from detritus to the microbial metabolism. The same applies to the discard group, treated as a detritus in our model. The integration reactions are:Scenario 2: Bioremediation of water compartment. This case describes the effects of an in situ bioremediation process of PCBs, regarded as acting within the water compartment , decreasing PCBs concentrations in the whole surrounding environmental media. The integration reactions are:Evidently, not all integrations are ecologically and biologically plausible. In our model, we consider two bioremediation scenarios, as also shown in Figure −2 year−1) to the flux units used in FBA (mmol h−1 gDW−1). The conversion factor is k = 1/ (m · t · n), where m is the molar mass of a PCBs molecule ; t = 8760 h is the number of hours per year; and n is the amount (gDW) of actively remediating P. putida in the unit of space (1 km2). k can be applied to all the PCBs flows, or as a stoichiometric coefficient in the interface reactions. In our model, we set n = 10−3 gDW, enough to import the totality of the connected PCBs flows into the P. putida metabolism, and to avoid numerical errors in the optimization procedure due to excessively small flux values. However, marine metagenomic data can be used to have a finer estimation of parameter n.The integrated models have been obtained after converting PCBs flows   even if our framework can be applied to the study of arbitrary network indices.In order to assess the effects of bioremediation on our contaminated food web, we combine the evaluation of bioconcentrations with the study of ecological network indices. Typically, global indices  per species and, ideally, from an effective bioremediation strategy, we expect a substantial breakdown of this property. It is calculated as:We employ n is the number of groups in the network.where LIM van Oevelen et al., sna Butts, COBRA toolbox  for PCBs uptake rate up to 9.8 mmol h−1 gDW−1 . Further, the addition of the PCBs bioremediation pathways to the P. putida metabolism does not result in an increased growth rate.By applying bilevel FBA, the growth rate of 1 Figure . The max−1 gDW−1, and then remains stable even at high oxygen uptake. The P. putida is able to keep a high growth rate also with low oxygen, which reproduces the environmental conditions describing the proposed first bioremediation scenario. The linear relationship between PCBs and oxygen uptake rates is in keeping with the fact that the uptake of PCBs depends on the aerobic degradation pathway.In order to investigate the relationship between growth rate and oxygen uptake, and between PCBs uptake and oxygen uptake, we apply a single-level FBA analysis. In Figure P. putida is not able to optimally support multiple degradation pathways. We further perform a phenotypic phase plane (PhPP) analysis by coupling the biomass production objective with varying PCBs and toluene uptake rates. In this case, we seek to optimize growth on top of the configuration maximizing both degradation pathways (the sum of PCBs and toluene uptakes). The PCBs-toluene tradeoff delineates two regions in the phenotypic space: when the uptakes of PCBs and toluene are below the optimal front, maximum growth is achieved , as also seen for the PCBs case in Figure P. putida robustly gives optimal growth yields even in the strain designs targeted to the maximization of multiple degradation pathways.We also analyse the interdependence between the PCBs degradation pathways (introduced in this work) and that of toluene . We derive an optimality front between them by solving two bilevel problems. In the first, we evaluate the maximum toluene uptake when PCBs imports are favored, while in the second problem, we consider the symmetric objectives. Both problems identify the identical linear trade-off , simulating a bioremediation at the level of the microbial loop. In Scenario 2, PCBs bioremediation is assumed to act in the water compartment by reducing simultaneously all the PCBs uptakes in each functional group. The following results are obtained by solving the bioremediation problem (Section 2.4) and computing bioconcentrations and network indices on the resulting (the entailed) bioaccumulation networks.Scenario 0 [plot (a)], and of the above two scenarios when no limits to the bioremediation efficiency are imposed [plot ]. Figure In Figure In Scenario 1 [plot (b)], we clearly notice a simpler pattern of PCBs contamination among functional groups, due to a considerable reduction of feeding links active in the transport of PCBs. Specifically, the redirection of outflows from detritus and discard out of the food web causes the inactivation of several PCBs flows, and subsequent presence of groups with null PCBs concentration. Therefore, these groups (not plotted) are disconnected from the bioaccumulation network but still active in the biomass network. They include detritus (38) and discard (39); detritivores ; group 30, which only feed on planktonic groups; and groups feeding on those mentioned so far . Other variations are detectable in groups 5, 27, and 28 (detritivores and planktivores) that no longer acquire PCBs from food. Finally, we can observe that groups 12 and 27 gain in this scenario a central role in the contaminant diffusion, becoming the preferential source of most of their predators, while in Scenario 0 their contribution appears less relevant.The bioaccumulation network under Scenario 2 [plot (c)] exhibits a similar structure to Scenario 1. Detritus groups  and detritivores  are no longer connected to the rest of the food web, showing that bioremediation of the water compartment tends to disrupt the pathways of contaminant uptake at the lowest trophic levels. Another similarity is the promotion of group 12 as a central node in the acquisition of PCBs by its predators. On the other hand, group 27 has no outgoing PCBs flows, while in plot (b) the opposite situation (no inflows) is observed for the same group. In general, we notice a lower number of active links with respect to Scenario 1, especially in species at higher trophic levels.−2 year−1 and 3312 mg km−2 year−1, respectively), which mainly depends on the structure of the network. Applying the conversion factor in Section 2.4, the maximum remediated flow in Scenario 1 corresponds to a PCBs uptake rate of 3.15 mmol h−1 gDW−1 (31.5% of the maximum uptake), while in Scenario 2 to 2.45 mmol h−1 gDW−1 (24.5% of the maximum uptake).Another kind of analysis enabled by our framework is the study of the networks obtained by solving the bioremediation problem at increasing efficiencies, limiting the amount of PCBs flow allowed into the bacterial metabolism. In both scenarios, we analyse the variations in PCBs bioconcentrations Figures  and in tAs regards Scenario 1, no remarkable reductions in bioconcentrations are observed in the entire food web [see plot (a)], apart from the natural detritus and the discard groups, whose PCBs values are zeroed at 89 and 16%, respectively, of the maximum bioremediation efficiency. We register only minor drops in a number of groups at TL 4  and in group 37 (feeding on discard). This tendency is also visible in the sum of PCBs, which is practically constant.On the other hand, Scenario 2 gives a considerable decrease in the bioconcentrations of all groups [plot (b)]. This is explained by the fact that the estimated uptakes from water constitute an important fraction of imported contaminant, whose degradation also mitigates, indirectly, uptakes from food. The only exceptions are natural detritus and discard , which have null PCBs flow from water ] highlights the topological importance of natural detritus in the bioaccumulation network, which derives from the fact that every group in the food web contributes  to its contaminant uptake. Indeed, this group maintains its central role up to 89% of bioremediation efficiency. After this point, a structural disruption occurs, related to the detritus becoming disconnected from the network . This leads to cascade effects also in the centrality of groups 13, 15, 16, 19, and 32. Apart from this case, FBC exhibits quite a robust pattern, showing a number of groups  with unchanged centralities regardless of the amount of bioremediated flux. This structural robustness is evidenced also by the link density values, indicating that, globally, the number of links active in the PCBs diffusion is relatively constant.On the contrary, Scenario 2 [plot (d)] produces prominent changes in the centrality of most species. Here, natural detritus loses its dominant role in the network at 10% of maximum bioremediation. Moreover, at 34% of efficiency, we observe a sudden fall in the FBC of group 24, as also registered on its bioconcentration values [see plot (b)]. Only functional groups 2 and 25 show robust topological importance, in agreement with Scenario 1. The evolution of the link density index also evidences the high sensitivity of the network structure. Indeed, the index reaches an average of 3.1429 active links per group, 36% lower than the initial value.Pseudomonas putida. Our framework is based on a range of multi-scale analyses obtained by combining well-established methods in ecological modeling  and Systems Biology . We showed how to derive optimal remediation strategies that yield the highest decrease of bioaccumulation phenomena in species. In addition, more realistic scenarios can be reproduced that take into account environmental limiting factors influencing the potential of natural or synthetically designed microbial pathways.Recent biotechnological advances and novel discovery tools in marine metagenomics are paving the way for new integrated solutions in environmental bioengineering, turning empirical hypotheses into practical methods. In this context, we presented a computational framework for the analysis of contaminated ecosystems and for the evaluation of different hypothetical bioremediation scenarios. We considered the case of PCBs bioaccumulation in the Adriatic food web and PCBs degradation mediated by P. putida metabolic model supports well the degradation of PCBs, and that a substantial drop of PCBs concentration in Adriatic species is achieved with comprehensive bioremediation strategies , while natural bioremediation  proved to be less effective. Results also highlight how remediation patterns vary among species in function of their feeding relationships. The study of ecological network indices allowed the evaluation of emerging global ecosystem properties under different bioremediation scenarios and degradation efficiencies.Our computational experiments indicated that the extended To the best of our knowledge, this is the first computational method linking genome-scale reconstructions of bacterial metabolism with food web bioaccumulation models for designing and analysing bioremediation strategies. Approaches based on high dimensional omics data and network inference methods (Perkins et al., In this work we wanted to stress a different view on marine ecosystems, regarding them not just as ensembles of macro-species, but as complex multiscale networks linking classical food webs and microbial groups, toward a new perspective of “eco-metabolic” networks. We believe that bringing the study of microbial metabolic activity into the field of ecotoxicological modeling can highlight bottlenecks and advantages of different bioremediation approaches and shed light on the ecological role of marine microbial life. Furthermore, PCBs degrading bacteria live in communities structurally organized in biofilms (Abraham et al., The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Several methods have been developed to predict system-wide and condition-specific intracellular metabolic fluxes by integrating transcriptomic data with genome-scale metabolic models. While powerful in many settings, existing methods have several shortcomings, and it is unclear which method has the best accuracy in general because of limited validation against experimentally measured intracellular fluxes.l2 norm) and SPOT (Simplified Pearson cOrrelation with Transcriptomic data), which can be chosen and combined depending on the availability of knowledge on carbon source or objective function. This enables us to simulate a broad range of experimental conditions. We examined E. coli and S. cerevisiae as representative prokaryotic and eukaryotic microorganisms respectively. The predictive accuracy of our algorithm was validated by calculating the uncentered Pearson correlation between predicted fluxes and measured fluxes. To this end, we compiled 20 experimental conditions (11 in E. coli and 9 in S. cerevisiae), of transcriptome measurements coupled with corresponding central carbon metabolism intracellular flux measurements determined by 13C metabolic flux analysis (13C-MFA), which is the largest dataset assembled to date for the purpose of validating inference methods for predicting intracellular fluxes. In both organisms, our method achieves an average correlation coefficient ranging from 0.59 to 0.87, outperforming a representative sample of competing methods. Easy-to-use implementations of E-Flux2 and SPOT are available as part of the open-source package MOST (http://most.ccib.rutgers.edu/).We present a general optimization strategy for inferring intracellular metabolic flux distributions from transcriptomic data coupled with genome-scale metabolic reconstructions. It consists of two different template models called DC (determined carbon source model) and AC  and two different new methods called E-Flux2 (E-Flux method combined with minimization of Our method represents a significant advance over existing methods for inferring intracellular metabolic flux from transcriptomic data. It not only achieves higher accuracy, but it also combines into a single method a number of other desirable characteristics including applicability to a wide range of experimental conditions, production of a unique solution, fast running time, and the availability of a user-friendly implementation. Intracellular metabolic reactions provide a cell with biochemical building blocks, energy, and a suitable thermodynamic environment. Due to the large connectivity of metabolic networks via metabolites each of which participates in multiple metabolic reactions, determination of system-level changes in intracellular metabolic fluxes is important for understanding the fundamental mechanisms of cellular metabolic responses to environmental or genetic perturbations .13C metabolic flux analysis (13C-MFA) is available for characterizing intracellular fluxes experimentally, and is the most widely accepted approach to quantify fluxes in central carbon metabolism [13C-labeled substrates until the cells are at both metabolic steady state (i.e. when concentrations of metabolites are constant over time) and isotopic steady state (i.e. when isotopomer fractions remain stable over time). Then the level of 13C enrichment in cellular metabolites is measured by mass spectrometry (MS) or nuclear magnetic resonance (NMR). Finally, the intracellular flux distribution is reconstituted from the 13C enrichment patterns [13C-MFA can determine intracellular fluxes, extensive instrumentation and specialized expertise is required to carry out the experiment and the number of fluxes that can be accurately and uniquely determined is limited [13C-MFA is not capable of intracellular flux determination, and isotopically nonstationary MFA (INST-MFA), an even more challenging method both experimentally and computationally, is required [tabolism . In thispatterns –6. Thoug limited . Moreoverequired .An alternative widely used for system-level studies of metabolism is a computational modeling method called flux balance analysis (FBA). FBA defines the space of allowable metabolic flux distributions of a system at steady state by making use of genome-scale metabolic models . Since tAdvances in omics technologies have enabled quantitative monitoring of the abundance of biological molecules at various levels in a high-throughput manner . In the There have been previous studies to integrate transcriptomic data with genome-scale metabolic models, which are well covered in recent reviews ,11,15–20Some of them require multiple sets of input data for a single analysis ,22, whicSome methods require a user-defined threshold to define “high” or “low” expression states –26, whica priori assumption of an appropriate objective function such as biomass production rate (i.e. the growth rate) [Several methods require th rate) ,24,27,28th rate) . Althougth rate) , we needth rate) .Several methods produce non-unique solutions. That is, they produce a solution out of a space of possibilities, all of which are in theory possible. If all solutions in the space of possibilities were equally good in terms of their ability to predict fluxes, this would be acceptable, but in general, there is a range of possibilities for predictive accuracy. A single solution that is arbitrarily chosen is difficult to reproduce and is typically dependent on the software or hardware used for the analysis . Thus, iin vivo applications [Lastly, previous studies have generally focused on conditions where the carbon source of the system and its uptake rate are known. While many biotechnological and laboratory processes operate on a known single carbon source, typically glucose, we would sometimes like to study microorganisms living in conditions where the carbon source is unknown, such as for ications .Therefore, in light of various experimental and cellular conditions in practical applications, there is still a need for a method that can provide all five of the desirable features listed in E. coli and 9 in S. cerevisiae, see In this study, we compiled the most extensive dataset to date, consisting of 20 experimental conditions , a detailed description of which is given in The first step was to collect a dataset of transcriptomic and fluxomic measurements obtained from cells under the same conditions. The measured fluxes were obtained to compare them with the predicted fluxes. To this end, we obtained data published by Ishii et al. and Holm.[et al.  for E. ca et al. ,37 and C [et al.  for S. ciJO1366 and Yeast 5 for the metabolic models of E. coli and S. cerevisiae, respectively. We also tested our methods on older models of E. coli (iJR904 and iAF1260) and those of S. cerevisiae (iND750 and iMM904) to examine the applicability of our methods to the relatively incomplete models  and of  (iND750  and iMM9 [iMM904 ) to exama priori information on cellular uptake rates and ATP maintenance flux. The template model is made by setting the flux bounds either to zero or to positive or negative infinity while maintaining the stoichiometric and reversibility information of the original genome-scale model:j,v is a flux vector representing the reaction rates of the n reactions in the network, and aj and bj are the minimum and maximum reaction rates through reaction j defined in the original model. In this manner, we constructed two kinds of template models to simulate two different situations depending on whether we know which carbon source the cell uses. One template model, which we call 'DC (determined carbon source)', has a lower bound of negative infinity for the known carbon source uptake reaction. The other one, which we call 'AC ', allows all carbon sources in the model to be taken up by the cell. Among all metabolites participating in the exchange reactions, the set of possible carbon sources were selected based on their chemical formula. The list of carbon sources whose uptake rate were set as negative infinity in the AC models for both microorganisms are given in When integrating transcriptomic data with genome-scale metabolic models, a problem of scaling can occur because the units for measuring metabolic flux and the units for measuring gene expression are not related. For instance, if the carbon uptake rate is set to 1, and the transcriptome values are all in the order of 10000, then applying such values as upper bounds will not constrain the model. To avoid this issue, we construct a template model that is independent of This step, converting original genome-scale models into DC or AC template models before integrating gene expression data, resolves the scaling problem described above. The fluxes predicted by our method have an arbitrary unit. Thus, the relative magnitude of predicted fluxes across reactions is meaningful, but their absolute magnitude is not. Any known or measured reaction rate  can be used to normalize the predicted fluxes to an absolute reference.If information on the biomass composition of a certain organism is available and maximizing its growth rate is appropriate for prediction, our first method, called E-Flux2, is an effective way to study its metabolic behavior. Otherwise, our second method, called SPOT, can be used.f is a coefficient vector defining the organism’s objective function, S is the stoichiometric matrix.E-Flux is an extension of FBA that infers a metabolic flux distribution from transcriptomic data ,28. The gj, the absolute gene expression level associated with reaction j, for an upper bound, gj = The main difference between E-Flux  below anet al. and Celton et al.), we used the MAANOVA normalization method [For one-color microarrays and RNA-seq measurements, it is relatively straightforward to determine absolute gene expression . For twon method  to achien method .j,E-Flux solves the following:Gene expression data were mapped to corresponding reactions in the network based on gene-protein-reaction (GPR) associations. For example, in the case where an enzyme complex consisting of subunits encoded by multiple genes mediates a certain metabolic reaction, we put the minimum value of the expression level of the associated genes on et al. [x, also called the l2 norm, is given by:x on an n-dimensional Euclidean space Rn. Thus, as stated by Bonarius et al., the constraint of minimizing the Euclidean norm corresponds to the strategy of a cell to minimize the length of the metabolic flux vector to channel metabolites as efficiently as possible. We additionally applied this theoretical constraint after maximizing the biomass flux to find a unique metabolic flux distribution satisfying both optimal biomass flux and the flux minimizing its Euclidean norm. So, the first method that we propose, which we call "E-Flux2" (meaning E-Flux method combined with minimization of l2 norm), consists of two steps of optimization, which can be chosen when a suitable objective function is known:A problem of E-Flux is that the outcome solution is not unique, making it difficult to clearly identify predicted metabolic responses. Bonarius et al.  used minStep 1. E-Fluxl2 norm Step 2. Minimization of z* here, this method finds a unique metabolic flux distribution by minimizing the Euclidean norm of the flux vector. The square root function was ignored since removing the square root does not change the solution. Since the objective function, the Euclidean norm squared, is strictly convex, and all equality and inequality constraints are linear, which is convex, the solution of E-Flux2 is unique because the optimal solution to the problem of minimizing a strictly convex function over a convex set is unique [l1 norm (or Manhattan norm) [l1 norm, is not strictly convex.After calculating the optimal biomass flux, denoted as s unique . The outan norm) . pFBA doThough not largely different from E-Flux, E-Flux2 overcomes a major shortcoming of E-Flux, namely, that it does not yield a unique solution. Among the space of solutions that E-Flux provides, E-Flux2 provides a method to select one solution in a manner that is intuitive and yields high correlation to measured fluxes see .v, and its corresponding gene expression data, g. The assumption behind this strategy is that enzymatic transcript concentrations and metabolic fluxes can be related to each other, albeit in a complex manner, since the existence of a transcript is necessary for the presence or activity of its corresponding enzyme [If a suitable objective such as the biomass flux is unknown, we can use a second method which is to maximize correlation between a flux vector, g enzyme . To calcj into two positive irreversible reactions, the forward reaction, n − r are irreversible, while reactions n – r + 1,…,n are reversible, and that all irreversible reactions are defined in the forward reactions (i.e. their fluxes are non-negative). Then, instead of problem (6), we solve:Sirr is the submatrix consisting of the first n – r columns of S, and Srev is the submatrix consisting of columns n – r + 1 to n of S. Solving this optimization problem is computationally inefficient since the form of the objective function is nonlinear. However, this problem can be converted to an equivalent semi-definite programming problem (8):we will consider a problem with modified upper and lower bounds that are 0 or ± infinity as described in This is the second method we propose, which we call "SPOT" (Simplified Pearson cOrrelation with Transcriptomic data). SPOT can be used when biomass flux is not an appropriate optimization objective. The conversion of optimization problem (7) to SPOT (8) is based on a few steps of justification.First, the maximum Pearson product-moment correlation is not dependent on the length of the flux vector, The optimization problem described in Transcriptomic data are used to constrain fluxes in the model for E-Flux2, and they are used to define the objective function for SPOT. The process of making a choice between E-Flux2 and SPOT is described in the flow chart in l2norm) can be used. Otherwise, we can use SPOT (Simplified Pearson cOrrelation with Transcriptomic data).If we know the cell's carbon source, we use the DC (determined carbon source) template model which has a negative infinity value on the lower bound of the known carbon source uptake reaction. Otherwise, we use the AC  model which allows all carbon sources in the model to be taken up by the cell. If the biomass composition of the cell is known and the maximization of biomass flux is a suitable objective function, E-Flux2  and A-(d) in E. coli and a single flux distribution for S. cerevisiae that each achieve high correlations with the measured data in each organism (data not shown). Nevertheless, the dataset we have gathered is the largest and most comprehensive dataset that currently exists for validating methods of predicting intracellular fluxes from transcriptomic data. We expect that the high correlations obtained by E-Flux2 and SPOT will generalize beyond E. coli and S. cerevisiae growing on glucose, given how their underlying optimizations reflect our general understanding of the relationship between metabolic flux and gene expression, but we cannot conclude this without additional data. In particular, coupled trascriptomic and fluxomic data obtained in organisms under very different conditions  would help significantly in establishing the generality of our method.The reactions whose measured fluxes were used to calculate the correlation for each dataset are shown in http://most.ccib.rutgers.edu/ whose source code is open to the public [All methods in this study initially implemented in MATLAB . These were tested using MATLAB R2013b with Gurobi Optimizer 5.6 . SBMLToolbox was used to convert an SBML (Systems Biology Markup Language) model into a MATLAB data structure . Computae public .E. coli and 9 samples in S. cerevisiae. The number on the right side of the plus minus sign indicates its standard deviation.The Pearson correlation between the predicted and the measured intracellular fluxes was calculated to validate the predictive accuracy of our method. All correlation values used to draw figures and tables are summarized in E. coli and S. cerevisiae. The result implies that our method can predict the measured intracellular fluxes best when we have knowledge of both carbon source and objective function . Our algorithm is able to predict intracellular metabolic fluxes with a good correlation if the information on either biomass objective or carbon source is unknown as we can see in the category of DC+SPOT (average correlation: 0.8030), and AC+E-Flux2 (average correlation: 0.6733). In the case where there is no information on both carbon source and biomass objective, our AC+SPOT method allows us to predict intracellular metabolic fluxes with an average correlation of 0.5927. Although this value is weaker than those of the other three cases of our method, a Pearson correlation coefficient around 0.6 nevertheless represents moderate positive correlation [As summarized in relation .To see whether the good or modest correlation value between predicted and measured fluxes in each case is because of a good correlation between transcripts and measured fluxes itself, we also calculated the correlation between gene expression data and measured fluxes. When calculating the correlation with gene expression data, we used the absolute values of measured metabolic fluxes since gene expression values are always positive, while we used the signed measured fluxes when calculating the correlations with predicted fluxes. The correlation between gene expression data and the absolute values of the measured fluxes was 0.4923 (standard deviation: 0.2900), which is weaker than all of the correlations between the predicted fluxes and the measured fluxes. Although this value cannot be directly compared with correlations within the table , this relatively poor correlation between gene expression data and the measured fluxes, given as a point of comparison, suggests that the correlation is improved by incorporating the gene expression data into a genome scale model.et al. [et al. method, we used an implementation provided with the original publication.Using the same transcriptomic and fluxomic datasets, we compared the accuracy of our predictions with other competing methods. We chose to compare against E-Flux ,28 and tet al. , which aet al.  and iMATet al. ,25, and et al.  or in roet al. . For theE. coli (average correlation: 0.8887) but worse predictions in yeast (average correlation: 0.2009) than our method (DC+SPOT) whose average correlation is 0.7960 and 0.8117 in E. coli and in yeast, respectively . As can be seen in In all four scenarios with varying availability of carbon source or biomass objective information, our method outperformed existing methods in that it showed a higher average correlation with a smaller standard deviation . Particuectively . Unlike a priori information on several specific fluxes such as sugar (e.g. glucose) uptake rate and oxygen exchange rate, these fluxes were set according to the experimental conditions described in the four papers where the transcriptomic and fluxomic data sets were obtained. Simulating anaerobic growth with Yeast 5 requires the simulated medium to be supplemented with phosphadiate and sterols and modification of the biomass definition [et al. dataset  for reference . pFBA wafinition . Due to  dataset .Since standard FBA and pFBA need both carbon source and objective function information, their correlations can be compared with those of E-Flux and E-Flux2 in Importantly, the result predicted by our method is unique. The Lee et al. method also produces a unique solution using geometric FBA , which il2 norm (l2). It also showed good correlation with measured fluxes . When knowledge of uptake rates is available, the FBA+min l2 method is a good alternative to pFBA, since it is easier to implement and produces a unique metabolic flux distribution.In addition, we performed FBA along with the minimization of E. coli and S. cerevisiae, respectively. The x-axis represents a set of metabolic reactions used to calculate correlation between the measured and the predicted fluxes, and the y-axis indicates flux value. The scale and the units on the y-axis are based on those of the measured flux. The reactions are grouped functionally based on the pathways in which they are participating such as glycolysis and the tricarboxylic acid cycle. As can be seen in the figure, the predicted and the measured metabolic flux distribution look similar to each other when the correlation between them is high. We see moreover that AC+SPOT predicts negative fluxes for some reactions which are supposed to be positive, which might explain one of the reasons why the method shows relatively poor correlation compared to the other three methods . Based on this observation, possible ways to improve the correlation of AC+SPOT will be discussed in the following section.In addition to calculating correlations, we examined how the predicted and the measured metabolic flux distribution visually compare to each other. Since the predicted flux of our method has an arbitrary unit, the magnitudes of the predicted fluxes were normalized by the Euclidean norm of the measured flux vector for comparison. The results are shown in E. coli and S. cerevisiae are two of the most intensively studied model microorganisms. On the other hand, genome-scale metabolic models of many other organisms are still incomplete. Thus, it is important to examine the applicability of our methods to relatively incomplete models before applying our methods to other organisms. One of the ways to test this is by running our methods on older models of E. coli and S. cerevisiae that are relatively incomplete. Using the same transcriptomic and fluxomic datasets, we tested our methods on older models of E. coli (iJR904 and iAF1260) and of S. cerevisiae (iND750 and iMM904), and the results obtained are shown in x-axis represents the four different optimization strategies  and the y-axis identifies the average Pearson correlation coefficient between the predicted fluxes and the measured fluxes of E. coli (S. cerevisiae ( E. coli  and S. crevisiae . Each opE. coli (iAF1260 and iJO1366) showed better average correlation than the oldest model (iJR904) in most cases. We found that there is little difference in the average correlation between iAF1260 and iJO1366.In case of E. coli , the twoS. cerevisiae (iND750 and iMM904) when the carbon source is known (DC+E-Flux2 and DC+SPOT). Unlike the E. coli case, however, the newest yeast model performs worse than the older models when carbon source of a yeast cell is unknown, especially for AC+SPOT. To understand why, we explored the hypothesis that the reason for the poor performance of Yeast5 is because of the larger number of carbon sources  in both microorganisms. Thus, if we study an organism where information on both carbon source and objective function is known, applying DC+E-Flux2 is recommended.Except for E. coli and S. cerevisiae regardless of which model was used. The method seems to be the least influenced by incompleteness of the model. Thus, DC+SPOT is useful for predicting intracellular metabolic flux distribution in less well-studied organisms.Interestingly, DC+SPOT (known carbon source and unknown objective function) shows steady and constant average correlation between 0.7 and 0.8 in both From a practical perspective, short running time is a desirable characteristic. Thus, we measured the running time of our algorithm for all 80 samples (4 optimization strategies and 20 samples per strategy) using the built-in MATLAB function, profile. The execution time for our method is illustrated in Fig D in http://most.ccib.rutgers.edu/) is an open source-based software package for constraint-based modeling [As an ultimate representation of the cellular metabolic phenotype, metabolic fluxes provide important information to understand the functioning of cellular processes . Our metmodeling . It provIn this study, we developed a computational method to infer intracellular fluxes from transcriptomic data using genome-scale models, which satisfies desirable features summarized in Our method can also be easily applied to study the metabolic flux distributions of various engineered strains with little or no modification to genome-scale models since transcriptomic data themselves reflect knock-outs, knock-ins (with addition of metabolic reactions into the model that correspond to the knocked-in gene), induced-amplification or induced-repression of metabolic genes. In addition, E-Flux2 is flexible in that if there is an alternative objective to maximizing growth rate that is considered more applicable to a certain organism, then the biomass flux used in the first optimization step of E-Flux2 can be replaced with this objective function.http://most.ccib.rutgers.edu/).The multiple advantages of our method make it a useful tool for identifying fundamental mechanisms of metabolic responses and finding molecular targets for metabolic engineering. For instance, by using this tool with a set of gene expression data measured over a time course, we can determine how intracellular metabolic flux changes and where significant redirection occurs. Our method is available in a user-friendly, open source-based software package called MOST  and thr  used in(ZIP)Click here for additional data file.S2 DatasetThe transcriptomic and the fluxomic data sets that were used in this study can be found in the first four sheets of this Excel file and on the fifth sheet, respectively.(XLS)Click here for additional data file.S3 DatasetInstructions on using it with the dataset of Ishii et al. can be found in README.doc. The source code written in Java is also available (see (ZIP)Click here for additional data file.S1 FileS. cerevisiae data, Fig D. Average running time of our algorithm, Fig E. Exploration of the way to improve a poor performance of Yeast 5 in AC+SPOT) and three supplementary methods .This file contains five Supplementary figures Click here for additional data file.S2 Filehttp://most.ccib.rutgers.edu/). This document covers information on how to reproduce our results in MOST using the model files and transcriptomic data that are provided as Datasets S1 and S2.E-Flux2 and SPOT are implemented in the open source package MOST ((DOC)Click here for additional data file.S1 TableThe lower flux bounds of these reactions were relaxed to -Inf to construct AC template models for each microorganism (i.e. to simulate the condition where knowledge of carbon source is unavailable).(XLS)Click here for additional data file.S2 TableAll the Pearson correlation values between predicted fluxes of our method and measured fluxes, that are used for producing (XLS)Click here for additional data file.S3 TableiND750, iMM904, and Yeast 5) were identified to test the hypothesis that the number of carbon source uptake reactions affects the performance of the models.Total 106 exchange reactions that are common across all three yeast models ((XLS)Click here for additional data file.


We found that in ccRCC, but not in prostate adenocarcinoma, flux balance analysis could predict essential metabolic genes beyond random expectation. Five of the identified metabolic genes, AGPAT6, GALT, GCLC, GSS, and RRM2B, were predicted to be dispensable in normal cell metabolism. Hence, targeting these genes may selectively prevent ccRCC growth. Based on our analysis, we discuss the benefits and limitations of flux balance analysis for gene essentiality predictions in cancer metabolism, and its use for exposing metabolic liabilities in ccRCC, whose emergent metabolic network enforces outstanding anabolic requirements for cellular proliferation.Flux balance analysis is the only modelling approach that is capable of producing genome-wide predictions of gene essentiality that may aid to unveil metabolic liabilities in cancer. Nevertheless, a systemic validation of gene essentiality predictions by flux balance analysis is currently missing. Here, we critically evaluated the accuracy of flux balance analysis in two cancer types, clear cell renal cell carcinoma (ccRCC) and prostate adenocarcinoma, by comparison with large-scale experiments of gene essentiality  The regulation of metabolism has been recognised to be of central importance in cancer12456789101213141516Under these premises, metabolic modelling using flux balance analysis (FBA)19212223252728293031323335363738AGPAT6, GALT, GCLC, GSS, and RRM2B, which, although essential for cancer cells, are potentially nonessential in normal cells.In this study, we critically and systematically assessed the benefits and limitations of FBA for performing genome-scale predictions of gene essentiality in cancer metabolism. In particular, we were interested in the use of FBA to expose metabolic liabilities in clear cell renal cell carcinoma (ccRCC), the most common form of kidney cancerFlux balance analysis (FBA) is possibly the only modelling approach that has the potential to predict gene essentiality in cancer metabolism at the genome scale43in silico single-gene knockout, and the gene is essential if the in silico single-gene knockout ablates biomass production. A gene knockout ablates biomass production if there is no flux distribution that allows the biomass equation to carry a flux, or if the knockout results in a substantial flux reduction. However, a gene knockout consents biomass production if there is no change in the flux through the biomass equation. Single-gene knockout resulting in no change in biomass production is mostly explained due to one of the following reasons: 1) gene redundancy, i.e., more than one gene encodes for the reaction(s) associated with the knockout; 2) pathway redundancy, i.e., there is an alternative pathway with the same overall stoichiometry that can compensate for the knockout; or 3) the reaction(s) encoded by the knocked-out gene are not active (dead end) at the studied condition. Depending on this outcome, a gene is declared essential or nonessential in silico for a certain cancer. If constraint B) is implemented, an in silico single-gene knockout may ablate or consent biomass production, depending on which profile of exchange fluxes is used as a constraint. In this case, the corresponding gene is declared essential in silico for the cancer type only if biomass production is ablated using exchange flux profiles from at least 70% of its corresponding cancer cell lines.Here, we considered two typical sets of constraints: A) the topology of the cancer specific-metabolic network; and B) a profile of experimentally measured fluxes for a number of exchange metabolites  in a panel of cancer-specific cell lines . Using either of these two constraints we predicted gene essentiality using FBA by introducing a constraint that disables flux in the univocally encoded reaction(s). This constraint is commonly referred to as in vitro: in this case, a panel of cancer-specific cell lines derived from prostate adenocarcinoma (PC) or clear cell renal cell carcinoma (ccRCC), both cultured in defined serum-containing medium. The cells were transfected with a library of siRNA oligonucleotides that target approximately 230 metabolic genes. In the PC screen, induction of caspase activity was quantified after 96 h following transfection, whereas in the ccRCC screen, reduction in cell number was monitored. If at least 70% of the cancer cell lines passed a given threshold for caspase activity or cell number reduction, then the gene was declared essential in vitro for this cancer type . The accuracy of the predictions was calculated using the Matthews correlation coefficient (MCC) and the related Fisher’s exact test statistics.In principle, the proposed approach should capture all metabolic liabilities related to biomass formation induced by the network topology and to the activation of metabolic pathways induced by the exchange flux profile of a certain cancer. At the same time, it is noteworthy that the FBA problem formulated herein will not uncover other metabolic liabilities known to be associated with cancer survival, for example, maintenance of anti-oxidant poolsin vitro gene essentiality in the metabolism of ccRCC, as this is the most common form of kidney cancer4647in vitro depends on the threshold chosen for the mean cell number reduction. We selected a 30% reduction for benchmarking purposes because the quantity of essential genes appears to reach a plateau at this value; note that no siRNA caused a cell number reduction greater than 50% , namely AGPAT6 and GALT  as constraints50and ODC1 . It is lin vitro but were not captured by FBA are essential because the gene products carry out metabolic tasks that are not ascribable to the biomass production simulated here. Alternatively, it also possible that redundant pathways available in the metabolic network are not active due to the presence of regulation in vitro or in vivo that is not considered in the FBA simulations, as suggested by studies of gene deletion in yeastTaken together, these results suggest that in ccRCC metabolism, FBA is able to predict gene essentiality, although to a limited degree. Gene essentiality as exposed by FBA is in turn attributable to a rewiring of the metabolic network and exchange fluxes that contribute to biomass production. Conversely, it is conceivable that the 14 genes that were found to be essential in vitro if the corresponding siRNA caused apoptosis with a caspase activity z-score ≥ 2.5  in at least 2 of the 3 cell lines, as adopted in the original study. Using these criteria, 14 metabolic genes were found to be essential in the PC cell lines  cell lines ll lines . The topssential . We alsoential 50.p = 0.233, p = 0.635, in silico , as opposed to ccRCC (7 cell lines). However, it is also possible that the altered exchange fluxes in PC cells fuel pathways other than those required for biomass production and are therefore not captured by the FBA model used here. One of these pathways could indeed involve the synthesis of cholesterol for the production of steroid hormones, which play a major role in the development of PCContrary to the results obtained for ccRCC, the accuracy of FBA predictions in PC was considerably lower when using metabolic network topology as the sole constraint in silico even though they are not utilised in any metabolic reactions by cells in vitro . To explore the extent to which the medium composition affects the accuracy of FBA predictions, we repeated all simulations using Ham’s medium, a nutrient poor medium adopted in previous studies to predict in silico gene essentiality of cancer cells33in silico increases for both ccRCC  induced by incorrect assumptions regarding the unavailability of certain metabolites to the cells. The results of the accuracy achieved by FBA in these scenarios are reported in In FBA, the definition of metabolites available for uptake is a decisive constraint for the prediction of gene essentialityth ccRCC  and PC , we performed a sensitivity analysis on these thresholds for all tested scenarios . In the case of ccRCC, we observed a positive relationship between the accuracy of FBA predictions and the strictness of the definition of the threshold for cell death, at least up to the point where the number of essential genes in vitro is less than 10, which occurs for mean cell number reduction >40% (in silico predictions is significant in ccRCC (but not in PC) for a reasonable range of thresholds upon which a gene is declared essential in vitro.Given that the definition of gene essentiality ion >40% . This trion >40% . In partin silico predictions of gene essentiality. In particular, we tested the extent to which exchange fluxes from ccRCC cell lines can be used to infer gene essentiality attributable to the ccRCC phenotype. To this end, we selected some genes that were differentially classified as essential depending on the cell line flux profile, but still classified as essential in ccRCC according to a consensus outcome, i.e., essential in >70% of cell lines. We chose to test the predictions for GCLC, GSS, SLC7A9 , and PNP . In addition, we tested UMPS and RRM2B, which were deemed essential in silico for all ccRCC cell lines upon implementation of every exchange flux profile. Next, the corresponding genes were silenced in five of the seven cell lines whose exchange fluxes were used to constrain the FBA predictions . In accordance with the threshold for cell death adopted above, a gene was declared essential in vitro for ccRCC if more than 70% of cell lines tested  exhibited at least 30% mean cell number reduction compared to control .Because FBA proved powerful in exposing the metabolic liabilities of ccRCC, we decided to validate some of the RRM2B, GCLC, UMPS, and GSS were confirmed in vitro. However, PNP and SLC7A9 knockouts showed mixed effects across cell lines in vitro. Hence, the essentiality of these genes in ccRCC could not be inferred from this experiment. Overall, this result suggests that ccRCC cell line exchange fluxes can entail some common metabolic requirements associated with the ccRCC phenotype, which can be exploited to predict gene essentiality in ccRCC metabolism. However, the exchange flux measurements appear to be insufficient per se to achieve reliable predictions for a specific cell line. Indeed, we observe that only 17 of the 30 individual predictions were replicated in vitro if the cell-line-specific exchange fluxes were used for the prediction of essentiality for the corresponding cell line.At the level of gene essentiality in ccRCC, the consensus predictions for in silico and validated in vitro. This list includes ten metabolic genes: AGPAT6, CAD, DHCR24, FDFT1, GALT, GCLC, GSS, ODC1, RRM2B, and UMPS. First, we predicted whether these gene knockouts would be toxic for the execution of essential metabolic functions, i.e., whether the in silico gene knockouts compromise the metabolism of normal cell types. As previously describedin silico upon application of the corresponding in silico gene knockout. In all normal cell types, the simulation revealed that knockout of CAD or UMPS ablates the de novo biosynthesis of pyrimidines, while FDFT1 and DHCR24 knockouts impede the production of cholesterol in normal human cell types  using RNAi. These four genes were not part of the siRNA screening library but were predicted by FBA to be essential both in silico and in vitro. In accordance with the in silico predictions of toxicity, we observed cell death when UMPS was knocked out in HK-2 cells, while GCLC, GSS, and RRM2B knockouts caused a minor cell number reduction, above the adopted threshold for cell death . Examination of the flux space in ccRCC revealed that this reaction fuels the production of UDP-glucose, which is needed for the biosynthesis of glycogen. Knockout of in ccRCC . The essGCLC, GSS, and RRM2B, were classified as essential only when constraints on exchange fluxes were implemented. Their essentiality is likely to be due to a loss of redundancy in the ccRCC network when metabolite fluxes are constrained by measured uptake and secretion rates. To explore how the fluxes were distributed before the implementation of the exchange fluxes, we relieved each of these constraints one at the time until biomass production was restored, thereby allowing us to associate gene essentiality with a particular exchange flux. We found that RRM2B is associated with the flux of 3-ureidopropionate, a product of the uracil degradation pathway, which is secreted by all ccRCC cell lines (range: 0.016 to 0.102 fmol cell−1 h−1) . Thus, it is necessary for cells to activate a flux to degrade UDP to sustain the given 3-ureidopropionate secretion rate, and one of these steps is catalysed by RRM2B. According to the Human Protein Atlas, the two other genes associated with this step (namely RRM1 and RRM2) are not expressed in ccRCC, and thus they cannot compensate for this flux if RRM2B is knocked out, making RRM2B essential.The three additional genes, l−1 h−1) , left. TGCLC and GSS, the essentiality is associated with the secretion of glutamate, which occurs at remarkably high rates (approximately 4 to 50 fmol cell−1 h−1) in ccRCC cell lines. The analysis of the ccRCC flux space unveiled that elevated rates of extracellular glutamate accumulation derive from the catabolism of extracellular glutathione (GSH) carried out by different gamma-glutamyl transferases. Indeed, the reconstructed ccRCC metabolic network does not include alternative pathways that support the secretion of glutamate, such as the xC– system. Despite the evidence that the xC– system, an antiporter responsible for cystine uptake via a 1:1 exchange with glutamate, is expressed in the kidneySLC7A11, is reported at the protein level by the Human Protein Atlas; it was therefore not included in the reconstructed network. In the absence of alternative pathways, the only flux distribution returned by FBA that fits glutamate secretion requires the cleavage of extracellular GSH. This is in turn dependent on the secretion of de novo synthesised intracellular GSH, which is catalysed by GSS and GCLC  may be a factor that affects the reliability of this prediction, as recognised in earlier works on FBA predicted gene essentiality58In the case of and GCLC , right. in vitro. We evaluated the efficacy of this method for two cancer types, clear cell renal cell carcinoma (ccRCC) and prostate adenocarcinoma (PC), for a variety of parameters: types of FBA constraints used, complexity of the in silico medium , and the numerical threshold for cell death applied to the in vitro experiments. A summary of the accuracy for all tested scenarios is given in In the last decade, increasing evidence supports the notion that cancer cells reprogram their metabolism and are therefore susceptible to disruption of the metabolic networkin silico serum-containing medium, which allows the flexible uptake of 150 different metabolites (Matthews Correlation Coefficient = 0.235). The accuracy improved with stricter definitions of the threshold for cell death in vitro, whereas it worsened when a more restricted medium metabolite composition, as found in Ham’s medium, was applied in silico. This medium composition is not representative of the actual culture conditions used for the in vitro experiments, but had previously been used in similar studies39Our findings suggest that FBA is sufficiently accurate to expose metabolic liabilities in ccRCC. The highest accuracy was achieved by FBA using a ccRCC-specific metabolic network that was further constrained by exchange fluxes determined experimentally across a panel of seven ccRCC cell lines and using an in silico knockout cannot satisfy certain cancer type-specific metabolic requirements, here represented by the profiles of exchange fluxes in several cancer type-specific cell lines (one such requirement could be lactate secretion in a specified range of rates). The number of profiles available for a cancer type may affect the specificity of certain metabolic requirements , therefore biasing the quality of the in silico predictions when these are enforced as constraints in FBA. Third, we disregarded enzyme complexes because current human genome-scale metabolic models do not report such annotation systematically63in silico single-gene knockout and classified as redundant. Furthermore, genome-scale metabolic models such as those used for this study represent the best models to our knowledge in terms of metabolic reactions occurring in a cell, but model incompleteness is known to affect in silico predictions of essential metabolic genesin silico prediction is also affected by the accuracy of the in vitro experiments. Indeed, metabolic screens using siRNA libraries may produce false negatives due to insufficient silencing and are liable to significant off-target effects that can both positively and negatively affect the viability of transfected cells.In general, poor predictions may be ascribed to different assumptions beyond FBA. First, we considered gene essentialities in metabolism based on the ability to carry flux towards biomass formation. Although this is an undisputable requirement for cancer cell proliferation, there is evidence that survival of cancer cells also depends on other metabolic functions, most notably NADPH production and anti-oxidant synthesis45AGPAT6, GALT, GCLC, GSS, and RRM2B, which are essential to ccRCC but are potentially dispensable in normal cell types. In addition, FBA can also be used to explore the mechanisms that render a gene essential in silico.As part of this evaluation, FBA unveiled the inherent fragility of ccRCC metabolic processes that contribute to biomass growth or support certain metabolic requirements. A number of recent studies have evidenced the centrality of metabolism in ccRCC414665GALT expression. In accordance with the findings of our simulations, there is evidence that UGP2 and GALT homologs provide redundancy for this pathway in yeastGALT-deficient mice can sustain glycogen synthesis through the pathway branch catalysed by the murine homolog of UGP2GALT in ccRCC. The pivotal role of GALT in glycogen biosynthesis may in addition underscore the typical phenotype of ccRCC cells, which are characterised by high levels of glycogen accumulation. Finally, FBA using flux rates as additional constraints allowed us to identify gene essentialities associated with specific exchange fluxes in ccRCC cell lines. The essentiality of GCLC and GSS was linked to the secretion of glutamate, whereas the essentiality of RRM2B, an enzyme in deoxyribonucleotide metabolism, was linked to the secretion of 3-ureidopropionate. GCLC and GSS play a fundamental role in the intracellular detoxification of ROS by catalysing two successive steps in the biosynthesis of glutathioneGCLC and GSS in the in vitro experiments stems from their functions in the control of intracellular ROS levels.One of the mechanisms by which this essentiality arises is loss of gene redundancy. AGPAT6 is the only expressed enzyme isoform that can commit glycerol-3-phosphate into glycerolipid biosynthesis. Thus, glycerolipid synthesis is clearly a sensitive pathway in ccRCC, perhaps exacerbated by the lack of expression of enzymes within alternative routes due to a loss of heterozygosity in the corresponding gene loci, as recently suggestedde novo synthesis of GSH is also associated with glutamate secretion in the absence of other systems that can fulfil this function in ccRCC. Although this may be an artefact due to model incompleteness, we show that GCLC-GSS can sustain a flux distribution in which extracellular GSH is catabolised into cysteinylglycine and glutamate, therefore explaining the observed glutamate secretion in ccRCC cell lines. In a similar fashion, the consistent secretion of 3-ureidopropionate observed in ccRCC cell lines combined with an unmatched uptake rate of its direct precursors implies that RRM2B is active in supporting uridine-derived 3-ureidopropionate. RRM2B exerts its function in deoxyribonucleoside biosynthesis and in DNA damage repair, and in this role it appears to hinder cancer progression727374RRM2B function in ccRCC may be different given the lack of expression of RRM1 and RRM2 for supporting nucleotide biosynthesis. Indeed, this pathway was found to be compromised uniquely in ccRCC compared to four other cancer typesHere, we find that In conclusion, in this study we show the strength and limitations of FBA for the prediction of gene essentiality at a genome scale in cancer metabolism. In addition, we report five metabolic genes selectively essential in a particular cancer type, i.e., ccRCC. Importantly, FBA can be used to identify potential mechanisms by which these gene essentialities arise and thereby provide testable hypotheses. We argue that accounting for metabolic liabilities other than biomass generation and the integration of additional layers of high-throughput data may lead to an even more complete description of the essentiality landscape in cancer metabolism.GCLC, GSS, PNP, RRM2B, SLC7A9, and UMPS, 786-O, A498, CAKI-1, TK10, and UO31 cells were transfected in two independent experiments, triplicates each in a 96-well format with 37.5 nM siRNA SMARTpools (Dharmacon siGENOME) targeting the genes of interest using Dharmafect2 as transfection reagent. For the validation experiment for GCLC, GSS, RRM2B, and UMPS, HK-2 cells were transfected in two independent experiments, triplicates each in a 96-well format with 37.5 nM siRNA SMARTpools (Dharmacon siGENOME) targeting the genes of interest using Dharmafect2 as transfection reagent. In all cases, after 96 h (with a media top up after 24 h), cells were fixed in 80% ethanol over night and subsequently stained with DAPI (Sigma). Cell number was determined using an ACUMEN eX3 laser-scanning fluorescent micro plate cytometer. For the purpose of data normalization, the non-targeting RISC-free transfection was used as negative control, while ubiquitin B (UBB) and polo-like kinase 1 (PLK1) served as positive killing control.786-O, 769-P, A498, CAKI-1, RCC4, TK10, UMRC2, and UO31 clear cell renal cell carcinoma (ccRCC) cell lines were maintained (and transfected) in DMEM supplemented with 4.5 g/l D-Glucose, 0.11 g/l Sodium Pyruvate (Gibco), 4 mM Glutamine , 100 Units/ml Penicillin / 100 ug/ml Streptomycin (Gibco) and 10% Fetal Bovine Serum (Gibco). For the RNAi screen, RCC4, UMRC2, A498, 786-O and 769-P cells were transfected in triplicates in a 96-well format with 37.5 nM siRNA SMARTpools (Dharmacon siGENOME) targeting the genes of interest using Dharmafect2 as transfection reagent. For the validation experiment for UBB) and 12 negative controls (RISC-free) were transfected. In a given cell line c for a given replicate r, the cell number reduction caused by siRNA s was linearly interpolated as in equation (1):In the case of ccRCC, cell death was quantified in terms of reduction of cell number upon siRNA transfection in cells scaled to the effect of the negative and positive controls. For each replicate, 9 positive killing controls . This data is collected in z-score was retrieved from the studyin vitro in PC if the caspase activity z-score upon transfection of the corresponding siRNA for at least 2 of the 3 tested cell lines is above 2.5, as adopted in the original study.Then for each cell line, the mean cell number reduction is computed as the average across replicates. We declare a gene essential in silico single gene-knockout test as the universe and it was performed in R. The 95% highest density interval (HDI) for cell number variation relative to RISC-free control was calculated by Bayesian estimation under the following assumptions: data are sampled from a t-distribution of unknown and to be estimated normality (i.e. degrees of freedom); high uncertainty on the prior distributions; the marginal distribution is well approximated by a Markov chain Monte Carlo sampling with no thinning and chain length equal to 100’000. The estimation was performed using the BEST R-packageThe Fisher’s Exact Test was carried out using the total number of tested siRNA in the library that could be compared to the OGDH to its correct associated gene, ODC1, no other modifications to the models were operated. The lists of metabolites available for uptake or secretion in the serum-containing medium (FBS) or in Ham’s medium are given in g in the model:The ccRCC genome-scale metabolic model  was downloaded at www.metabolicatlas.org. The PC genome-scale metabolic model (iProstateCancer1675) was reconstructed using the same pipeline as for iRenalCancer1410vobj is the flux through the biomass equation, S is the stoichiometric matrix of the model  entry is the stoichiometric coefficient of the metabolite corresponding to row i in the reaction corresponding to column j), vis the vector containing the values of the fluxes through each reaction in the model, and α (resp. β) are the lower (resp. upper) bound for the exchange flux corresponding to each metabolite measured inj as DW cell−1 to accommodate the fact that exchange fluxes were measured in fmol cell−1 h−1 instead of mmol gDW−1 h−1 as normally assumed in genome-scale metabolic modelingwhere http://www.metabolicatlas.com/.The problem was formulated using native functions in the RAVEN Toolboxin silico. Besides this, a gene is deemed essential in silico when there is no solution to (2), i.e. there cannot be found a flux distribution such that the biomass equation carries flux. This is indeed valuable in light of the consideration above: among all the available metabolic states permitted by the availability of serum metabolites, no scenario allows for a flux towards all biomass precursors simultaneously.Importantly, for the purpose of the study, the optimization part is not relevant. Indeed, we are interested on whether a feasible region exists upon the constraint imposed by the gene knockout (7), i.e. whether the fact that the encoded reactions cannot carry flux implies no flux in the biomass equation. However, if also exchange fluxes were implemented to perform FBA (6), we took in account a significant reduction (min. 50%) of the optimum  to classify a gene as essential et al. studyvobj > 0. In the end, all exchange fluxes in (6) that required a supplementary flux  were instead bounded to ±1000. This procedure had been repeated for each cell line specific to a certain cancer type, and for all successive simulations, only the exchange fluxes that were feasible in all cell lines for a given cancer were retained. In ccRCC, 61 and 38 exchange fluxes were coordinately bounded for all seven ccRCC cell lines in FBS and Ham’s medium respectively . In PC, 60 and 57 exchange fluxes were coordinately bounded for all two PC cell lines in FBS and Ham’s medium respectively .It should be noticed that, when implementing cell line specific exchange fluxes, a set of numerical constraints had to be neglected and converted to ±1000. This operation is obligated by the fact that some measured fluxes are not consistent with the network topology. Thus, either the measured compounds are not used by the cellular reaction network or further experimental validation is required. It may also be that the model is not complete and it should be updated in an iterative fashion, a process normally encountered in genome-scale modelsin silico and validated as such in vitro. If no solution were found, the gene knockout is deemed toxic for a certain normal cell type. If more than 50% of the 83 normal cell types show no toxicity in any metabolic task upon knockout of a gene essential in a cancer, than the gene is regarded non toxic to normal cells. Furthermore, if knockout of a gene essential in a cancer shows no toxicity in any metabolic task in the supposed cell type of origin, than the gene is regarded selectively essential to a cancer.The test for toxicity in normal cell types was performed as previously describedin silico, different simulations were carried out according to the constraint that first resulted in an unfeasible solution:AGPAT6, and it was found by constraining the flux of the encoded reaction to zero in the generic human metabolic network from which the ccRCC metabolic network topology is derived. This constraint results in an unfeasible solution using the generic network, suggesting that at least one of the isoenzymes must be expressed to sustain biomass formation. In the second scenario, there are two alternative routes to support a flux towards the biomass equation, each encoded by a single gene, but just one is expressed in the cancer-specific metabolic network (loss of pathway redundancy). This was the case of GALT. To verify this, the reaction encoded by GALT was constrained to zero in the generic human metabolic network, and then a second round of single gene-knockouts was performed using the GALT-KO generic human metabolic network. In the end, the double GALT-UGP2 knockout results in an unfeasible solution in the generic human metabolic network, indicative that UGP2 encodes for a potential alternative pathway to GALT that is not expressed in ccRCC.In the case of genes essential using as a sole constraint to perform FBA the topology of a cancer metabolic network, there are two possible explanations. In the first scenario, a reaction essential to carry flux towards the biomass equation is encoded by a single gene in the cancer-specific metabolic network because all other isoenzymes are not expressed in the cancer (loss of gene redundancy). This was the case of GSS and GCLC, this metabolite is glutamate, while for RRM2B 3-ureidopropionate. Further interpretation of the individual mechanisms was achieved by following the fluxes around each key metabolite in the simulation, either when no knockout was applied or when the knockout was applied neglecting the constraint in the key metabolite exchange flux.In the case of genes essential when using also the exchange fluxes to perform FBA, but non essential when the sole topology was used as a constraint, an unfeasible solution is trivially attributable to the implementation of one (or more) of these additional constraints. Therefore, for each essential gene, all constraints in (6) are released (set the lower and upper bound to –1000 and +1000 respectively) one at the time, until the metabolite whose constraint on the exchange flux caused unfeasibility is spotted. For To elucidate the mechanism through which a gene is selectively essential The fraction of ccRCC samples where a protein involved in any of the mechanisms above is stained with at least a weak signal was retrieved from the Human Protein Atlas v. 11How to cite this article: Gatto, F. et al. Flux balance analysis predicts essential genes in clear cell renal cell carcinoma metabolism. Sci. Rep.5, 10738; doi: 10.1038/srep10738 (2015).