Among the single knockout simulations, we identified 74 essential genes, whose knockout stopped growth completely. Among these, 11 genes are known have an abnormal knockout or knockdown phenotype in vivo , and 41 have human homologs associated with metabolic diseases. We also added the oxidative phosphorylation pathway, which was unavailable in the published version of ZebraGEM. The updated model performs better than the original model on a predetermined list of metabolic functions. We also determined a minimal feed composition. The oxidative phosphorylation pathways were validated by comparing with published experiments in which key components of the oxidative phosphorylation pathway were pharmacologically inhibited. To test the utility of ZebraGEM2.0 for obtaining new results, we integrated gene expression data from control and Mycobacterium marinum-infected zebrafish larvae. The resulting model predicts impeded growth and altered histidine metabolism in the infected larvae.Zebrafish is a useful modeling organism for the study of vertebrate development, immune response, and metabolism. Metabolic studies can be aided by mathematical reconstructions of the metabolic network of zebrafish. These list the substrates and products of all biochemical reactions that occur in the zebrafish. Mathematical techniques such as flux-balance analysis then make it possible to predict the possible metabolic flux distributions that optimize, for example, the turnover of food into biomass. The only available genome-scale reconstruction of zebrafish metabolism is ZebraGEM. In this study, we present ZebraGEM 2.0, an updated and validated version of ZebraGEM. ZebraGEM 2.0 is extended with gene-protein-reaction associations (GPRs) that are required to integrate genetic data with the metabolic model. To demonstrate the use of these GPRs, we performed an  Danio rerio) has become a widely used model organism for the study of vertebrate metabolism.2 Its genome has been sequenced and annotated3 and the CRIPSR-Cas technique has made it easier than ever to study the role of specific metabolic genes.4 For example, zebrafish have been used to test the toxicity of drugs on liver metabolism and the effect of liver metabolism on internal drug concentration.5 Zebrafish have also been used in studies of metabolic diseases such as diabetes, obesity, and fatty liver disease, often combining sequencing with visualization of gene expression.1The zebrafish Escherichia coli and Saccharomyces cervesiae,13–15 as well as pathogens such as Salmonella typhimurium16 and Mycobacterium tuberculosis.17 For these unicellular organisms, very accurate growth predictions have been made. Multicellular organisms, particularly vertebrates, are less well represented in the list of genome-scale metabolic models. So far, reconstructions have been made for human,18 mouse,19 Chinese hamster,20 fish,22 and recently, rat.23 Whole-organism modeling is less common for these multicellular organisms, as metabolic functions are distributed over different tissues. However, modeling specific cell types has been done, such as erythrocytes24 and cancer cell lines,25 as well as integrating different cell types into a larger model, such as a combined model, including adipocytes, myocytes, and hepatocytes.26With the increasing presence of metabolic data of healthy and diseased zebrafish, and the availability of genetic data, a genome-scale metabolic model of the zebrafish is tremendously useful. So far, genome-scale metabolic models have been proposed mainly for single-cell model organisms, such as 27 This makes inositol an essential nutrient for zebrafish.Why do we require a specific zebrafish genome-scale metabolic reconstruction when other vertebrate models exist? Despite the high metabolic similarity to human and mouse, there are subtle differences between zebrafish metabolism and the metabolism of these mammals that affect their required nutrients. For example, inositol-3-phosphate synthase is an enzyme present in humans and mice, but it is absent in zebrafish, preventing it from converting glucose-6-phosphate into inositol 3-phosphate.28 As a result, there are more paralogous genes in the zebrafish genome than in mammals. Hence, if one wants to study the effects of genes on metabolism, translating a human or mouse genome-scale metabolic reconstruction into a zebrafish specific model by orthologous genes is not sufficient. Foremost, this translation is hampered by these paralogs as it does not make the translation one-to-one, and furthermore, many paralogs have evolved different subfunctions, increasing the functional difference between the zebrafish paralogs and the human or mouse orthologs. So to model the effects of genes on zebrafish metabolism, a zebrafish-specific genome-scale model is necessary.The difference in metabolism aside, the main reason to make a specific zebrafish genome-scale metabolic model is the genomic structure. The teleost lineage underwent a whole-genome duplication event after the radiation from their common ancestor with mammals, which resulted in numerous genes still having duplicate copies compared to mammals.21 and ZebraGEM.22 MetaFishNet is a metabolic model derived from the genome of multiple fish species, including zebrafish, and focuses on individual pathways. As these pathways are not interconnected or divided into cell compartments, MetaFishNet is not suitable for whole-cell or whole-organism modeling using Flux Balance Analysis (FBA) methods, and therefore functions mainly as a reference tool, instead of a simulation tool. The fact that it combines multiple fish genomes also makes it harder to compare insights gained from this model to in vivo experimental results, as some pathways are solely based on the genome of one of those five fish species and do not occur in the other four fish species.Existing genome-scale models for zebrafish are MetaFishNet29The other model, ZebraGEM, is based on the zebrafish genome and is a whole-cell and compartmentalized reconstruction. It contains 2911 reactions, of which 2446 are gene-associated reactions based upon 1498 genes and can be used for whole-cell metabolism modeling. It was reported to fulfill a list of 160 metabolic functions, such as the production of amino acids and biosynthesis and degradation of secondary metabolites. The model also predicted that the synthesis of taurine is through a metabolic pathway dependent on cysteine sulfinic acid decarboxylase, which is in line with experimental findings.Currently, ZebraGEM cannot be used for modeling large screens of single gene knockouts or for the integration of gene expression data, as it lacks GPR. GPRs describe how gene products associated to a reaction work together, that is, whether they form a complex enzyme, are isoenzymes, or a combination of these. They provide a logical framework to decide whether a reaction can take place when one or more of its underlying genes are knocked out, and hence, they are of great importance when it comes to modeling gene knockouts.30 to ease comparison with genome-scale metabolic reconstructions of other organisms. Finally, we extended the model with essential reactions for pathways already present, or changed the reversibility of reactions already present in the model.In this article, we describe the modifications applied to ZebraGEM to fit our modeling needs and to fit standards of genome-scale metabolic reconstructions, as well as demonstrate a number of ways in which the updated model can be used. Briefly, the modifications fall into three categories. First, we added the GPRs, to facilitate gene knockout and gene expression modeling. Second, we renamed components of the model according to BiGG Models standard names,Mycobacterium marinum.We have validated the renewed model against the metabolic functions the original model was reported to fulfill. Using the updated model, we predicted a minimal feed composition and were able to make predictions of mitochondrial function with respiration simulations. Finally, we also proved the usefulness of the newly added GPRs: we performed a large single-knockout and double-knockout screening and predicted lethal knockouts, and we also integrated gene expression data with the model to predict metabolic differences between control zebrafish larvae and larvae infected with The genome-scale metabolic reconstruction (“metabolic map”) of zebrafish consists of the following: (1) a metabolic network describing the reactions that can occur in the organism and (2) the genes that are associated with those reactions . The netS  or Gurobi. In this work, we have used CPLEX IBM ILOG CPLEX.Once the linear programming problem is solved, the solution 31 (pFBA) and Flux Variability Analysis (FVA),8 which are multiobjective linear programming problems. After solving the original FBA problem, they then optimize a second objective. For pFBA, the secondary objective is to minimize the total sum of fluxes, that is, if, while also maintaining Some common variations on FBA are parsimonious FBA32 combined with the CPLEX solver.Multiple software packages for FBA exist. These function as an interface between the user and the linear programming solver. They allow for easy manipulation of bounds, easy addition and removal of reactions in the metabolic network, and modification of the GPRs, without having to keep track of the linear programming problem manually. The software used in this study is CobraPy,The second part of the metabolic map consist of the associated genes. These genes, responsible for the enzymatic reactions in the metabolic network, are represented using GPR. In its simplest form, the GPR links each enzyme with a biochemical reaction. If two enzymes catalyze the same reaction, the GPR becomes a logical expression. If they are isoenzymes, for example, they can both independently catalyze the reaction, an “OR” function is used. If the two enzymes form a complex such that both must be present to catalyze the reaction, an “AND” function is used. More complex GPRs can be described by nested logical expressions . In case33–36Using the GPRs, gene knockouts or gene expression data can be integrated into constraint-based models. A standard way of integrating gene knockouts is to set each occurrence of the knocked-out gene in a GPR to False and evaluate the GPRs. If any of these GPRs also evaluates to false, then constrain the corresponding reaction to 0 flux by setting its upper and lower bound to 0. Gene expression data can be integrated into constraint-based modeling in alternative ways.37 In this study, the linear programming problem is slightly altered from the original stoichiometric matrix-based linear programming problem. Using the GPRTransform package,38 we split up each reaction into multiple versions of the same reaction, one for every possible isoenzyme. The sum of the fluxes of all the reactions containing a certain gene in their GPR is then constrained by the expression level of that gene. Although many choices exists for how the expression level gives an upper bound, the simplest one is to take the expression level itself. So if we rephrase Although details vary, these methods either penalize fluxes over reactions with no or low expression and minimize the penalty or they set the lower and upper bound of fluxes depending on the expression level. The gene expression data integration method used in this study is Gene-centric flux (GC-flux).First optimizesuch that,gR denotes the reactions belonging to gene g, gE the expression of that gene, and G the total gene set. Basically, this algorithm distributes the gene expression among the different enzyme complexes, and hence the related reactions, of that gene, assuming that each molecule of a gene product can only take part in one complex at a time.Here if its minimum and maximum value that still allow for the objective to be optimized. To compare the flux ranges between different conditions, we compute the RFRC of reaction i as follows39:The GC-flux algorithm originally also minimized the length of the flux vector, to obtain the most parsimonious flux distribution that optimizes the objective. We did not minimize the flux vector length, but applied FVA together with computing the relative flux range change (RFRC) to compare between the different gene expression data sets. With FVA, we determine for each i in condition n, and with 40 Different elements of a metabolic map, such as metabolites, reactions, genes, and GPRs, are represented by their own class in SBML. For this, we use the fbc package, the Flux Balance Constraints extension of SBML. This package is especially designed to describe these genome-scale metabolic reconstruction elements, and has specified guidelines on how an entity should be represented in an SBML file.41 The original model was already an SBML file, but predates the fbc package's release. Therefore, we adapted the model to fit with the fbc package guidelines.To facilitate exchange of computational models, such as metabolic models, in systems biology, the Systems Biology Markup Language (SBML) has been developed.42 The metabolites and reactions were renamed using, if possible, the data standard from BiGG Models, a knowledgebase of genome-scale metabolic network reconstructions.30 Metabolites without BiGG name were renamed to their corresponding identifier in the Kyoto Encyclopedia of Genes and Genomes (KEGG) to facilitate easy lookup.43–45 Reactions without BiGG name were not renamed, as no standardized names exist for these reactions yet, making up 689 of not-renamed reactions.Aside from the file structure, there are also standards for the names of metabolites and reactions. This facilitates comparison and interfacing with metabolic maps of other organisms. We renamed the metabolites, reactions, and genes. Genes were renamed with their Entrez id.The reactions that did not need renaming can be categorized into three groups. The first group includes transport reactions of metabolites without BiGG name. These reactions can be identified by the description of the reaction. The second group consists of reactions involved in the exchange of fatty acids between metabolites. The third group contains reactions involved in oxidation and reduction of metabolites using NADH/NAD+ or NADPH/NADP+. The second and third group kept their original annotation, linking the reaction to a KEGG entry.M. marinum.In this section, we first describe the alterations in the model. These include alterations to the metabolic network, as well as the part of the model describing the relationships between genes and reactions. After that, we present the results validating our updated model. We first tested the metabolic expansion of the model by checking it for a list of metabolic functions, determining a minimal feed, and predicting mitochondrial function in respiration simulations. Next, we tested the GPRs in the model by doing knockout simulations. Finally, we apply the model to predict metabolic changes due to infection with 47 The subsystems are sorted according to the number of reactions changed in each subsystem. Changes are of three types: “reaction added,” “reaction deleted,” and “reversibility changed.”The alterations to the metabolic network encompassed the following five issues: (1) improvement of the biomass function and addition of reactions to enable synthesis of biomass precursor metabolites; (2) addition of oxidative phosphorylation; (3) correction of starch metabolism; (4) correction of the reversibility of reactions and their catalyzed or spontaneous nature; and (5) validation of the list of metabolic functions ZebraGEM was reported to be able to fulfill. 49 assume that an organism or cell channels the metabolic fluxes to optimize a metabolic function, called the objective function. This objective function is often a biomass function, describing the relative amounts of precursor metabolites required for biomass production. Realistic biomass functions improve the realism of model predictions.50 In the absence of exact data for zebrafish, we based the updated biomass function upon data from other vertebrates.FBA and related modeling approaches18) and a mouse genome-scale reconstruction (iMM141519), so far the only other vertebrates with genome-scale reconstructions, together with Chinese hamster20 and rat.23 If a metabolite was a precursor in only one of Recon 2 and iMM1415, the coefficient was taken directly from the model in which the metabolite was present. If a metabolite was not present in both models, the coefficient was the average of a third, human three-tissue model, which had a biomass function for each tissue type.26The biomass function coefficients were taken to be the average of the coefficients of biomass function of a human genome-scale reconstruction  detoxification,” to have a functional oxidative phosphorylation pathway.We have also revised glycogen metabolism, using Recon 2 as a template, as the stoichiometry in the original model led to mass imbalance. The original reactions were replaced with those from Recon 2, replacing the genes within the GPRs for zebrafish orthologs. Changes in glycogen metabolism are shown in All reactions in the model were checked for reaction reversibility. This corrected two types of unrealistic behavior. First, ZebraGEM produced essential nutrients through backward reactions . This waA final check was done to ensure that all reactions in the updated model do occur in zebrafish metabolism. Reactions without gene regulation were checked using the KEGG database, a database containing information on genes and reactions. Their KEGG entries were tested for two conditions: (1) whether the reaction could occur nonenzymatically, and if not, then (2) it was checked whether the reaction has an enzyme associated to vertebrates, thus excluding reactions that occur in bacteria only. If any of these two conditions was met, the reaction was kept; otherwise, we deleted the reaction. The subsystems with deleted reactions are also shown in 51) and KEGG for missing reactions, or for missing transport reactions that should be present in zebrafish. The missing reactions and their corresponding genes were added to the model. An overview of the subsystems with reactions added is shown in The original model was reported to fulfill 160 metabolic functions, ranging from amino acid metabolism to pyrimidine and purine metabolism. In our hands, using the downloadable SBML file of the original model in the supplements, only 92 of these functions were fulfilled . Twenty-The original model already had 2446 gene-associated reactions coded for by 4988 genes (1498 unique genes). We extended the model by putting these gene products into a GPR, and added this to the model according to the SBML guidelines. As a result, the full model can now be read and run using constraint-based modeling software, and is now suitable for gene knockout simulations and simulations with gene expression data integration.In summary, 95 reactions were removed and 140 were added to the model, and 543 reactions had changed reaction reversibility. The updated model now contains 3023 reactions with 2810 metabolites, of which 1557 were unique, and 1636 genes. Two thousand five hundred and twenty-three reactions are gene regulated and 1678 reactions are blocked, that is, are unable to carry any flux due to dead-end metabolites. A comparison between the original ZebraGEM model and the updated model is shown in 22; (2) we checked for biological validity of the minimal set of metabolites required for model growth; (3) we checked whether the model could reproduce pharmacological interference with respiration. We utilized the addition of the GPR by doing single- and double-knockout experiments, and ultimately by gene expression data integration.To check whether the changes in the model network improved the performance of the model, we tested the model predictions as follows: (1) we checked whether the model performed the metabolic functions reported in Bekaert 22). A metabolic function on this list consists of one or multiple starting metabolites and one or more end metabolites, indicating that a metabolic route between these metabolites fulfills this function. We tested these functions by setting an import reaction for the starting metabolites and an export reaction for the end metabolites. The export reaction for the end metabolites was chosen as the objective function, and a function was deemed successful if the model imported the starting metabolites and exported the end metabolites. Some of these metabolic functions could not be tested, as the starting or end metabolite was not present in the model. Metabolic functions that did not result in a success immediately were checked by hand to see whether the model has an alternative path to fulfill the demand for the end metabolite.ZebraGEM was published with a list of 160 metabolic functions it was reported to fulfill . One knockout (atp5po) resulted in a reduced biomass production rate of 0.509 of the wild-type rate. For the remaining 29 knockouts from these in vivo screens, ZebraGEM 2.0 did not predict a reduced biomass production. These genes without model phenotype are also included in To validate our single-gene knockout simulation results, we searched the literature for mutagenesis screens in zebrafish screening for visible defects .56–63 Th64 Around 232 genes present in ZebraGEM 2.0 had a knockdown phenotype in ZFIN. Of those 232 genes, 18 genes also had reduced biomass production in the single knockout simulations .ulations , 8 had nsod2 and got1 that are associated with microvascular complications of diabetes and low serum levels of aspartate aminotransferase, respectively  are shown in M. marinum.65 Briefly, zebrafish larvae were injected in the yolk with M. marinum at 2 h postfertilization.65 Gene expression in infected and control larvae was measured at 4 and 5 days postfertilization using RNA deep sequencing. This yielded a data set containing the expression of 31,388 genes.Thanks to the GPRs, ZebraGEM 2.0 can predict metabolic changes driven by changes in gene expression. We demonstrate this application of ZebraGEM 2.0 with a published dataset of infection with the fish tuberculosis bacterium p-value threshold Of these 31,388 genes, 1608 genes are present in ZebraGEM 2.0. Although this is a small fraction of the total gene set, it covers 98% of the model genes. From these 1608 genes present in ZebraGEM 2.0, we selected genes with differential expression in the infected and control groups at 4 and 5 days postinfection (dpi). Genes were considered “differentially expressed” if they had a fold change ocument} . We thusocument} , and 3.37 The GC-flux algorithm constrains the rate of the metabolic reaction in the model based on the expression levels of the genes coding for the corresponding enzymes. GC flux distributes the gene expression of a single gene over all reactions associated with that gene, such that the total sum of those reaction fluxes cannot exceed maximum flux associated with the gene expression value. We performed this analysis for control and infected larvae at 4 and 5 days dpi.We next predicted the metabolic changes caused by differential expression of these 24 expressed genes. We made use of GC-flux.8 FVA predicts the minimum and maximum possible flux ranges for each reaction, given an objective function; in this study, we used biomass production rate. To compare the flux ranges between control infected at 4 and 5 dpi, we used the RFRC.39 The RFRC is a measure that indicates how much the flux ranges differ between the control and infected simulations. When the RFRC is greater than 1 or smaller than −1, the centers of the compared flux ranges are separated by more than the averaged width of those flux ranges, with negative values indicating that the infected case has a range lower than the control case.After the model was constrained with the gene expression data, a method called FVA was applied.An important reaction with an absolute RFRC greater than 1 is the biomass function BIO_L_2 and it appears in the list for both 4 and 5 dpi. The RFRC of BIO_L_2 is negative in both cases, −18.371 for 4 dpi and −17.421 for 5 dpi, suggesting that infection reduces biomass production rate. When comparing the maximal growth rates, the growth rate of the infected simulation was 83% of the control growth rate at 4 dpi, and at 5 dpi, the infected group reached 84% of the growth rate of the control. Further examination of the list with reactions with absolute RFRC greater than one  shows the lethal . The flusi:ch1073-100f3.2, slc5a9, and tha1, all associated to monosaccharide transporters. The differential expression of slc2a11a, also associated to a monosaccharide transporter, together with limited availability of flux for the other monosaccharide transporters, puts a large restriction on the model. The low number of only four genes with differential expression  points toward a drawback of this data integration method: it only looks at the mean values of each case, but ignores whether these means are significantly different.To gain insight in which genes give rise to such restricting reactions, and hence are limiting growth in our simulations, we identified the genes that restricted biomass production by comparing the flux corresponding to each gene with the expression level of each gene . In tota> 1. These reactions are HISD, IZPN, URCN, and EX_his__L_e, and are involved in the pathway converting histidine into glutamate. The high |RFRC| of these reactions can be directly linked to the differential expression of uroc1.We observed that there was a reduction in growth rate in the infected case, and could ascribe this to a number of restricting genes. However, growth reduction might not be the only difference in metabolic activity; which metabolic pathways are contributing to biomass production can also differ between control and infected. To see if there was also a shift in which metabolic pathways contribute to biomass production, the flux ranges were normalized with the biomass flux. The RFRC was then again computed with the normalized ranges, and only for 4 dpi were there reactions with |RFRC| M. marinum infection. First of all, there is a reduction in growth in the infected cases. This can be attributed to differences in the expression of some essential genes as well as monosaccharide transporter genes. When looking at qualitative changes in metabolism, histidine metabolism is reduced at 4 dpi, due to reduced expression of uroc1. Together with the restrictive gene ftcd  reactions are blocked.19 Even if the blocked reactions are currently nonfunctional, we have decided to leave them in ZebraGEM 2.0. This prepares the model for future improvements that can unblock these reactions.Blocked reactions are reactions that cannot carry any flux due to absence of some or all pathways carrying metabolites toward or away from the reactions. Currently, 1675 out of 3018 (55.5%) of the reactions remain inactive in ZebraGEM 2.0. This number is high in comparison with similar metabolic reconstructions: in Recon 2, 2123 out of 7440 (28.5%) reactions are blocked,To unblock these reactions, we will need to add a number of missing exchange reactions. These allow the model to import metabolites and excrete waste metabolites. Due to flux balance, the whole metabolic pathway is blocked if excretion or further processing of a metabolite is impossible. One example of such a missing exchange reaction is the exchange reaction for urea; after we added it to the model, it allowed for the production and incorporation into biomass of arginine. For our current needs, further addition of exchange reactions was not needed. Besides that, improvements in the import and export reactions are complicated by three facts. First, there is the food composition, which is not predetermined for free-feeding larvae and adult fish; a solution here would be to add all possible exchange reactions and open or close them depending on fodder composition. Second, there is the unknown factor of exchange with the environment by other means than diet, such as excretion and uptake of metabolites through the skin. Third, there is exchange among cells and tissues of metabolites, such as the uptake of nutrient from the yolk in developing embryos.66–68 or using novel topology-based methods that can pinpoint missing essential reactions.69 Such automized gap-filling should be done with care, because the gaps often require reactions that have no or little literature that clearly supports those reactions.Further unblocking of reactions will be achieved by identifying unconnected parts of the network and add the missing metabolic pathways. Such gap-filling can, in part, be automated by finding the minimal set of addition to the network,20 a human platelet model,70 and a human erythrocyte model24 have parts of lipid metabolism with specified fatty acids and can serve as examples.ZebraGEM 2.0 and its predecessor have applied a number of simplifications in the description of lipid metabolism. First, a generic fatty acid is used in most lipid metabolism reactions. Also, the essential lipid linolenic acid has no reaction in the model converting it into this generic fatty acid and hence is not processed further by the model. To further improve the description of lipid metabolism in ZebraGEM 2.0, future description of lipid metabolism should include specific reactions for each type of fatty acid. This improvement would make linolenic acid essential, but because a single reaction would be part of the metabolism of a range of fatty acids, it comes at the cost of increased model size. Most likely, this will double the number of reactions, as the ∼600 reactions involved in lipid metabolism will be multiplied by the number of specified fatty acids. This will increase simulation time significantly for some of the modeling techniques, like FVA. The Chinese hamster model iCHOv1,An additional factor in lipid metabolism is that many of the associated metabolites are located in the compartment “membrane.” This compartment accounts for the plasma membrane, Golgi membrane, endoplasmic reticulum membrane, lysosome membrane, nuclear membrane, and the outer mitochondrial membrane all at once. This compartmentalization into a single compartment does not take into account the required transport processes and associated metabolic processes for such metabolites that take place within the cell. Another effect of this membrane compartment is the tunneling of NADH and NADPH over the membrane due to imbalanced reaction reversibility, as discussed in et al. determined changes in lipid composition of both the yolk and the developing embryo.71 This study provides interesting information upon which estimates for lipid exchange between embryo and yolk can be made, which can further improve metabolic modeling studies of embryonic stages.Improving lipid metabolism is also of interest when looking at the growth conditions of zebrafish. Embryos rely on the abundance of lipids present in the yolk as their source of energy, and as zebrafish are often used for experiments in their embryonal stages, insight into lipid metabolism is relevant. Fraher 50 the ratios between the required metabolites can vary as much as 30 million fold.26 The ratios of biomass precursor metabolites can have a large impact on the model predictions. Therefore, data of zebrafish cell composition, possibly for different cell types, will be of high value for increasing model prediction accuracy. So far, there has been detailed study of lipid composition only.72The current biomass function is not based upon any data on zebrafish cell composition, but on human and mouse models. Although the metabolites of which a cell consists vary little between animals, as all cells are built from amino acids, nucleic acids, and fatty acids,55–62 or ZFIN had no phenotype in ZebraGEM 2.0. They could not be ascribed to blocked reactions, no knockout effect due to the gene being redundant in the model, or the associated reaction diverting flux from the biomass optimization. The optimization for biomass production rate does likely not reflect all the required metabolic outputs of a cell. Alternative objective functions would include specific protein synthesis for antibody producing B-lymphocytes, ATP synthesis for muscle cells, or ROS production upon infection. In addition, bacterial metabolism also plays a role during infection. Therefore, results of in silico knockout experiments will deviate from the results of in vivo experiments.Genome-scale metabolic modeling focuses only on metabolism and hence has a limited scope. For example, 20 genes with a non-normal phenotype in Refs.73 Finally, these genes can cause a phenotype in vivo by other means than metabolism, that is, they could be involved in signaling and genetic regulating processes as well, and those aspects are not part of this model.A generic problem of flux balance analysis is that it does not consider kinetics and thermodynamics. Gene mutations or knockouts can change the kinetics of metabolic reactions, causing for instance accumulation of toxic compounds. Thermodynamics can also affect the rate of reactions and has been combined with constraint-based methods before.Last but not least, when using data integration methods, one has to be careful with the distribution of experimental values. As we saw now with our data-integrated simulations, most of the restricting genes were not significantly differentially expressed, which could lead to pinpointing incorrect causes of altered metabolism. The algorithm we used, as well as many others take only a single value for the expression of genes, often just the average; the original distribution underlying that average has to be considered, especially when comparing different situations. Extending data integration methods for constraint-based metabolic modeling with methods from robust optimization can offer a framework in which such distributions can be taken into account.Mycobacterium infection. Furthermore, we showed that metabolism of histidine synthesis was decreased in infected zebrafish embryos. Further improvements on the model as well as the data integration methods and analysis can lead to new applications of ZebraGEM 2.0, such as elucidating yolk and embryo metabolism or exploring the causes of metabolic diseases.Despite these limitations, the improved model combined with the zebrafish embryo data results in the prediction of lowered growth in the case of


Clay–chromophore hybrids have been employed to critically affect the kinetic landscape of the ring closure photo-oxidation reaction. en route to the complete photo-oxidation. Combining the gathered evidence, a possible mechanism for the chemical transformation has been proposed. Kinetic analysis showed that layered materials help to manipulate the rate of the electrocyclic ring closure and, in turn, accelerate the complete reaction sequence. The structural microenvironment induced by layered materials could be a unique platform to probe and stabilize a plethora of photo-oxidative reactions and intermediates.Templates with specific microenvironments have been long employed to facilitate specialized reactions. From enzymes to metal organic frameworks (MOFs), various systems have exerted their prowess to affect specific chemical reactions. Here we report, for the first time, the acceleration of a ring closure photo-oxidation reaction due to the specific structural constraints provided by layered materials. A stilbene derivative has been used as a prototype reactant and the di-hydrophenanthrene intermediate has been isolated and characterized  Enzymes and DNA are some naturally occurring examples.In this manuscript we, for the first time, observe that the kinetic pathways of organic photo-reactions can be modulated on layered inorganic templates. Photo-reactions on stilbene derivatives have been a research topic for decades, however, it is shown for the first time in this manuscript that its ring closure photo-oxidation kinetics can be biased while it is conjugated on an inorganic clay surface. To add to the novelty of the manuscript, during the photo-reaction process, we have isolated a di-hydrophenanthrene derivative as an intermediate, which has proved to be a challenging task in the past. These derivatives are generally very unstable and their complete characterization, as done in this manuscript, is very rare.AC).8Si8Mg6O16(OH)4, where R stands for covalently linked aminopropyl chains  as a soft hybrid for various photo-physical prospects have been explored.12Moreover, the optically transparent nature of TPE) and its derivatives are stilbene analogues, and have a rich history of photo-physical and photo-chemical phenomena.i.e. tetraphenylethylene tetra potassium salt (TPTS)  via the 4,4′-di-hydrophenanthrene intermediate (DHPS) (9Tetraphenylethylene (t (TPTS) . TPTS wae (DHPS) .9TPTS when conjugated with AC results in restriction of the rotation of the phenyl rings. The flattening of the 1H-NMR peaks and the emission enhancement in the clay–dye conjugate (AC-TPTS) (AC were added to a fixed concentration of aq. TPTS (10–4 M) and their dynamic light scattering (DLS) and zeta potential data were recorded   stronglyAC-TPTS) . To furtrecorded . It can AC-TPTS, we sought to understand the chemistry of an aqueous TPTS solution under light , while fraction 2 pertained to PHES, as evident from the [M – 2] ion in the MS, signifying the loss of two protons due to oxidative ring closure , i.e. the rate constant involved in the electrocyclic ring closure, can be extracted   after 30 min went to a state 1AC-f (λmax = 420 nm) and then finally after 240 min to 2AC-f (λmax = 400 nm). The AC-TPTS to 1AC-f transition was rapid and reached a maximum at around 30 min. The transformation of 1AC-f to 2AC-f was rather slow and took another 210 min to complete  and were analysed by LC-MS   analysis carried out on the intermediate showed a shift of the C–H stretch to a lower wavenumber (2962 to 2924 cm–1) as compared to the TPTS acid, which also signifies the introduction of a sp3 hybridized C–H bond   when irr changes  and S10†complete . Remarka1f was mainly the 1,2-di-hydro derivative (1ppf) instead of the 4,4′-di-hydro derivative . Owing to the intermediate’s good oxygen tolerance, it was possible for us to carry out extensive NMR characterization and elucidate its structure. Distortionless enhancement by polarization transfer (DEPT) analysis showed that 1ppf comprises –CH2 carbons, as shown by the negative peaks in 2 peaks, it became evident that the di-hydro derivative is indeed an isomerized counterpart of DHPS.Since di-hydrophenanthrene derivatives have rarely been isolated and characterized, we decided to do extensive characterization of these species.ve DHPS,   spectrum, these 1H-peaks around 2.6–2.8 ppm could be correlated with the –CH2 peaks as determined by DEPT  helped in understanding the through bond proton connections of the molecule  spectrum, thus confirming the relationship between the aromatic and the non-aromatic parts . In addition to the above discussed photoproducts, the fractions 1f and 2f also contained decarboxylated products of the di-hydrophenanthrene intermediate (1dcf) and phenanthrene, respectively, as minor products, as elucidated from the chromatogram peaks at higher retention times, which have also been characterized with various techniques  is switched off, the rates of both processes (AC-TPTS to 1AC-f and 1AC-f to 2AC-f) are significantly retarded. This points to the fact that not only is TPTS to 1ppf governed by light, 1ppf to PHES is also critically photo-controlled. Since the final oxidation cannot be done by light alone, this hints that in this case 1ppf to PHES is a rare situation of a “true” photo-oxidation, which refers to the interaction of the excited state of the molecule with oxygen to give the oxidation product.AC) acting as a base in the photo-reaction.TPTS in the presence of varying amounts of n-propyl amine (Fig. S38–S40AC, and to have any significant impact on the reaction outcome (Fig. S41 and S42Di-hydrophenanthrene derivatives are known to be highly susceptible to oxidation and most times atmospheric oxygen is capable of converting them to their oxidized counterpart. Fig. S37. This waTPTS is conjugated in galleries of amino clay (TPTS on the AC sheet is an important factor in tipping the scales of the rate constants. On clay, the ring closure, which was initially a slow step, becomes 100 times faster, hence, overtaking the oxidation step. Even though one of the demanding features of this conjugate is that it perhaps requires a strong association of the substrates to the template, hence the use of negatively charged molecules for a positively charged template, this presents a unique case in which electrocyclic ring closure is modulated on clay surfaces. This system also presents a unique study where the usually unstable, di-hydrophenanthrene derivative was isolated in the form of 1,2-di-hydrophenanthrene and structurally analysed, giving a major insight into the reaction process. The study thus opens the door to investigations of reactions involving a variety of chromophores on layered materials as well as other varieties of organic–inorganic hybrids, and not just for their rates of reactions but also for the stabilization of unusual intermediate states, which can be achieved by this strategy.22In conclusion, we have successfully shown that interlayer galleries can be used as templates to explore the increased rate of photo-oxidation reactions in stilbene-like systems. We show that there is a marked change in the rate constants of the photo-oxidation once ino clay . This chSupplementary informationClick here for additional data file.


Regrettably, the comprehensive quantification of metabolites in biological specimens does not promptly translate into knowledge on the utilization of metabolic pathways. By estimating fluxes across metabolic pathways, computational models hold the promise to bridge this gap between data and biological functionality. These models currently portray the average behavior of cell populations however, masking the inherent heterogeneity that is part and parcel of tumorigenesis as much as drug resistance. To remove this limitation, we propose single-cell Flux Balance Analysis (scFBA) as a computational framework to translate single-cell transcriptomes into single-cell fluxomes. We show that the integration of single-cell RNA-seq profiles of cells derived from lung adenocarcinoma and breast cancer patients into a multi-scale stoichiometric model of a cancer cell population: significantly 1) reduces the space of feasible single-cell fluxomes; 2) allows to identify clusters of cells with different growth rates within the population; 3) points out the possible metabolic interactions among cells via exchange of metabolites. The scFBA suite of MATLAB functions is available at  Cytotoxicity of chemotherapeutic agents and resistance to targeted treatments are the main reasons why cancer is still one of the top causes of death. As tumor cells are intrinsically resistant to therapies that target signaling pathways, targeting the metabolic hallmarks of cancer holds promise for more incisive treatments. Regrettably, the heterogeneity of cancer metabolism hinders the identification of effective treatments. To fully uncover the metabolic heterogeneity within tumors, characterization of metabolic programs (metabolic flux distributions) at the single-cell level is required. To fill the gap between current technologies for genomics and future technologies for fluxomics, both at the single-cell and the genome-wide scale, we propose to integrate cancer data from: 1) single-cell transcriptomics and 2) bulk metabolomics, into a multi-scale stoichiometric model, to deliver for the first time metabolic fluxomes at the single-cell level. To this end, we introduce a new paradigm for flux balance analysis and data integration in cancer metabolism to: 1) characterize metabolic heterogeneity, not only at the inter-, but also at the intra-tumor level 2) identify the metabolic interactions between cancer populations, whose role in resistance to metabolic treatments has been recently recognized 3) predict the collective response to drug targeting of metabolism. Cancer is a heterogeneous, multi-factorial and essentially genetic disease, in which various types of mutations alter the functioning and interactions of genes, causing cancer cells to proliferate in an uncontrolled manner. Despite the plethora of cancer-related mutations, a reduced number of recognizable phenotypic hallmarks , 2 have Metabolic rewiring, in particular, is a general feature of cancer cells, which reprogram their metabolism to feed their unrestrained proliferation, as it requires high amounts of energy and building-blocks . The desUnfortunately, a single metabolic program cannot be used to globally define an altered tumour metabolism , as cancFurthermore, in solid tumours, cancer cells are embedded within the tumour microenvironment (TME), a complex network of fibroblasts, myofibroblasts, myoepithelial cells, vascular endothelial cells, cells of the immune system and extracellular matrix. TME also includes chemical gradients of oxygen and nutrients: the complex interaction of all these elements plays a major role in tumour metabolic heterogeneity . The metKnowledge about the utilization of metabolic pathways requires quantification of metabolic fluxes . As quantification of the full complement of cell metabolites (metabolomics) alone does not provide information on internal fluxes , they caNevertheless, extracellular fluxes can be hardly measured at the single-cell level. They cannot be approximated from the spent cell culture medium, because it portrays the extracellular fluxes of the bulk. They might be measured with isotope-labeling and metabolic flux analysis techniques, but this would require single-cell metabolomics.Unfortunately, single-cell metabolomics is still at its embryonic stage, mainly because of limitations in working with minute amounts of material –23. ThisAt this purpose, we here introduce the first computational framework scFBA  to predict single-cell fluxomes and possible metabolic interactions among them, starting from (bulk) extracellular fluxes and single-cell transcriptomes. As compared to single-cell metabolomics, the field of single-cell transcriptomics has indeed progressed to a deeper resolution , 24.An established classification –29 of cuDatasets obtained from cancer biopsies or patient-derived xenografts are the ideal candidate to capture the heterogeneous composition of tumors. As currently no information on scRNA-seq and extracellular fluxes on the very same sample is publicly available, as a proof of principle, we here applied scFBA to lung adenocarcinoma (LUAD) patient derive xenograft scRNA-seq, collected by , while ta priori knowledge about the specific metabolic requirements and objectives of the intermixed populations. Unfortunately, even though metabolic growth may approximate the metabolic function of some cell populations, we cannot assume that each cell within an in vivo cancer population proliferates at the same rate, nor that it proliferates at all. A major example is given by the different proliferation rates of stem and differentiated cells [a priori knowledge, by relying on unsupervised integration of scRNA-seq data.Although some attempts to study the cooperation between different metabolic populations have been put forward –44, mosted cells . For thiWe have previously shown how Flux Balance Analysis of a population of metabolic networks (popFBA)  can in lAn identical copy of the stoichiometry of the metabolic network of the pathways involved in cancer metabolism is first considered for each single-cell in the bulk. To set constraints on the fluxes of the individual networks, represented by the single-cell compartments of the multi-scale model, we took inspiration from bulk data integration approaches that aim to improve metabolic flux predictions, without creating context-specific models from generic ones –39. At tA scheme of the scFBA approach is depicted in Here we briefly recall the popFBA approach. For a more comprehensive description, the reader is referred to .A, corresponding to a generic single-cell and defined as A, Next unbalanced reactions (exchange reactions), enabling a predefined set of metabolites (including the pseudo-metabolite representing biomass) Ncells replicates Ac of network A, each one corresponding to a single-cell c, c = 1, …, Ncells, and which can cooperate by exchanging nutrients in the tumour microenvironment.Starting from a template metabolic network map c, For each single-cell j = 1, …, Next, is a set of cooperation reactions, defined as reactions that allow to exchange metabolites among single-cells via a shared environment that represents the TME compartment. Cooperation reactions are built by transforming each exchange reaction i = 1, …, Next must also be defined.Accordingly, a new set of metabolites pertaining to the TME compartment Nblood exchange reactions Because original exchange reactions have been replaced by cooperation reactions, a new set of P is then defined by: (i) the union set of the metabolites ii) the internal reactions iii) the cooperation reactions iv) the population exchange reactions The population model SP is then built for all reactions in SP is (Ncells ⋅ M + Nblood) × (Ncells ⋅ (N + Next) + Nblood). Once the population model is obtained, the total biomass of the Ncells single-cells is maximised by means of linear programming, as in standard FBA [A stochiometric matrix dard FBA .bbiomass, with vi representing any flux i of the population model, and for each single-cell c, i-th internal flux, i-th cooperation flux and bi an exchange flux with blood. The optimization problem is postulated as follows:vi of The solution of popFBA represents the flux distribution  Toolbox .Ngenes × Ncells matrix T, where Ngenes is the number of genes and Ncells is the number of single-cells under study. Each element Tg,c, g = 1, …, Ngenes, c = 1, …, Ncells corresponds to the normalized read count of gene g in cell c such as, for instance, the TPM (Transcripts Per Kilobase Million).scFBA takes as input a template metabolic network map A, as in popFBA, plus a scRNA-seq dataset in the form of a The risk of the presence of false negatives in RNA-seq, and in particular scRNA-seq, is an established problem. Although a totally safe solution does not exist, scFBA allows to employ the information on bulk expression profile, when available, to manage the risk, by envisioning the following scenarios.Goff from the template metabolic network A, by solving the Gene-Protein-Reaction (GPR) association rules with a true-false logic , which results in removing reactions for which their expression is essential (AND operator). We refer to the obtained subnetwork of A as A*.If a gene has a zero read count in the bulk, as well as in each single-cell, we cannot totally exclude the possibility of a false-negative in the bulk, but we are confident in excluding a false-negative due to low concentrations of scRNA-seq, thus we can assume that such gene is off in all cells. We directly delete this set of genes  Toolbox  functionIf a gene has non-zero read count in the bulk, but a zero read count in each single-cell, there is a sharp inconsistency between bulk and scRNA-seq that indicates that we cannot trust scRNA-seq for this gene. In this situation, we prefer to lose information on single-cell heterogeneity and rely on the bulk value: we replace the read count for that gene in each cell with the bulk read count.ϵ.If a gene has non-zero read count in the bulk, and zero read count in some of the single-cells, we cannot be sure that the gene is actually not expressed in those cell, but we can exclude that there is a problem with the detection of that specific gene and we can hypothesize that is at least poorly expressed as compared to other cells. As a compromise between a more conservative strategy and the need to preserve information on cell heterogeneity, we retain the single-cell read count for these genes, but we do not prevent completely flux through the associated reactions, when setting boundaries of the reaction as a function of their expression. As we will illustrate in the following, we set the flux bound to a small value c = 1, …, Ncells, and each reaction We define a Reaction Activity Score (RAS), for each single-cell In order to compute the RAS we distinguish:Sj is the set of genes that encode the subunits of the enzyme catalyzing reaction j.Reactions with AND operator .Ij is the set of genes that encode isoforms of the enzyme that catalyzes reaction j.Reactions with OR operator .In case of composite reactions, we respect the standard precedence of the two operators.Ncells, according to the popFBA described above, but starting from the template metabolic network A*. As described in the subsection related to input and data pre-processing, A* is a subnetwork of the generic model A which integrates the transcriptional information that holds for all cells in the bulk.The first step of the scFBA approach is the creation of a multi-scale population model, composed of Once the population model is obtained, the scFBA approach imposes two kinds of constraints:type 1P, i.e., the upper and lower bound of the Nblood exchange reactions in set constraints on the extracellular fluxes of the overall population model type 2c, i.e. for the reactions in c = 1, …, Ncells, and for its set of cooperation reactions Cc, according to their RAS, whenever the computation of a RAS is possible, i.e., when a GPR exists for the reaction, along with the transcript values of at least one of the involved genes.constraints on internal fluxes of each single-cell j, in a given cell c, In order to project the information of the activity score of a given reaction Ff) and backward direction (Fb) of each reaction. To do so, we perform a Flux Variability Analysis [fluxVariability). We define we first estimate the possible flux that reaction Analysis , with noAnalysis  functionc = 1, …, Ncells, with respect to the total activity of reaction j, as follows:we then compute the relative reaction activity score of j = 1, …, N;c = 1, …, Ncells in the interval finally, we assign an upper bound , Linear Programming, as well as other standard constraint-based methods were applied.Once the In this work, we mainly use the following 3 LUAD datasets obtained from the NCBI Gene Expression Omnibus (GEO) data repository under accession number GSE69405.LCPT45 Composed of 34 cells acquired from a xenograft, obtained by sub-renal implantation in mice of a surgical resection of a 37-mm irregular primary lung lesion in the right middle lobea of a 60-year-old untreated male patient.H358 Composed of 50 cells from NCI-H358 bronchioalveolar carcinoma cell line.LCMBT15 Composed of 49 cells acquired from a xenograft, obtained by sub-renal implantation in mice of a surgical resection of a metachronous brain metastasis acquired from a 57-year-old female after standard chemotherapy and erlotinib treatments.We repeated all the analyses on the following independent breast cancer datasets (GEO access number: GSE75688), including scRNA-seq data of single-cell suspensions of cancer tissues obtained on the day of the surgery of untreated breast cancer patients :BC04 Composed of 59 human epidermal growth factor receptor 2 positive (HER2+) cells.BC03LN Composed of 55 lymph node metastases of human estrogen receptor positive (ER+) and human epidermal growth factor receptor 2 positive (HER2+) cells.Each of the 5 datasets includes the gene expression level of more than 20.000 genes in the form of Transcript Per Kilobase Milion (TPM). We filtered out a few cells with less than 5000 genes detected. For each dataset, we retained only the metabolic genes included in HMRcore model (418 genes). The dataset transcripts are identified by Ensembl ID, which we automatically converted into HUGO Gene Nomenclature Committee (HGNC) ID. The datasets also contain the expression profile of the bulk samples, which we used to pre-process data as described above.A, the metabolic core model HMRcore introduced in [From the computational perspective, the scFBA approach is suitable for simulation of genome-wide metabolic networks, such as , 52. Howduced in  and usedduced in , 48. As duced in , 54, we duced in  and inclhttps://github.com/BIMIB-DISCo/scFBA.The final version of the HMRcore model includes 315 reactions (of which 263 are associated with a GPR) and 418 metabolic genes. The SBML of the model is provided in Npop ⋅ 100 nmol/h) those that are the main nutrients of cancer cells according to literature, as motivated in [NH3 [The choice of the nutrients exchanged with biofluids should ideally be dictated by metabolic measurements on exo-metabolome. As we do not have this information, in the baseline experimental setting, we considered as main exogenous nutrients  biomass synthesis rate as objective function. All five population models displayed a non negligible maximal growth rate, something that cannot be taken for granted when integrating transcriptomics into FBA models , 27, 29.Ncells single-cells simulated within the population model, for each of the 5 datasets under study. We report in In order to highlight that the scFBA approach efficiently reduces the space of optimal solutions, we compared the variability of the biomass production flux of each of the 0) of the objective function value . As depicted in When no information on cells’ transcriptome is employed (as in standard popFBA settings ), the tygrRatio) of the new biomass over the previous one is computed.To show how this volume reduction in the space of alternative optima may actually affect predictions, we performed a single gene deletion analysis with and without scRNA-seq data integration . When a single gene is deleted, the reactions for which the expression of such gene is essential  are removed from the network  that are inactive in all cells of the bulk from the template metabolic network A, we include in the plots the prediction of the isolated template metabolic network A*. We refer to this third simulation setting as bulkFBA. However, bulkFBA includes information on on-off reactions only. It is not possible to modulate the flux capacity of reactions as a function of gene expression, because it not possible to compute relative expression values.grRatio = 1) in popFBA settings  may even become essential in scFBA settings  (grRatio = 0). This is the case, in lung adenocarcinoma, of the following genes: HGNC:10980, which encodes enzymes responsible for glutathione/phosphate, fumarate/phosphate or α-ketoglutarate/malate antiports; HGNC:8806, which encodes for a subunit of pyruvate dehydrogenase; HGNC:8896, which encodes for an isoform of phosphoglycerate kinase and HGNC:4141, which encodes for an isoform of glyceraldehyde 3-phosphate dehydrogenase. In breast cancer, only gene HGNC:8806 falls into this category. Conversely, some genes that display a significant effect (grRatio ≈ 0.5) in popFBA become instead redundant in scFBA. This is the case, in lung adenocarcinoma, of the genes that encode for ATP synthase , indicating that the integration of scRNA-seq data forces a  flux distribution for cancer cells which, consistently with the well-known Warburg effect, does not rely largely on ATP synthase for ATP production, thus resulting in a milder effect when the reaction is depleted. Worth of note, although these genes are not completely redundant (grRatio < 1) in breast cancer, the deletion of the respiratory chain has indeed a mild effect in both tumors, as well as in the other cancer datasets reported in Remarkably, some genes that are redundant , 1 to the one showing the highest value.As previously mentioned, single-cell fluxes are expected to be less noisy than transcript signals, which are typically analyzed by means of multi-variate statistical analysis  and, theWe evaluated which are the most different fluxes among the two major groups, by using the Z score test of statistical significance . Remarkak, by considering n = 100 bootstrap iterations (with random centroid assignments) and by selecting the clustering resulting in the maximum inter-cluster distance. We then assessed the clustering goodness, by means of traditional “elbow” and “silhouette” evaluation methods. We refer to To quantitatively compare the clustering of transcripts and fluxes, we first performed a k-means clustering with different number of clusters k = 3 for the fluxes relative to the primary tumour datasets, hence the optimal number of clusters is 3, which corresponds indeed to the k identified by the hierarchical clustering analysis for these two datasets.The elbow method in the right column of k = 3, i.e., the value identified from the elbow analysis, which also corresponds to the highest average silhouette value, when varying k in {2, ⋯, 6}.In Consistently with the more ready recognition of major clusters in the flux diagrams noted above, the drop in the sum of squared errors (SSE) is much stronger and the average silhouette value is considerably higher in the flux case than in the transcripts case (where the average coefficient is close to 0) indicating that the calculation of fluxes leads to a better clustering as compared to the evaluation of transcripts. All in all, the results of the cluster analyses indicate that fluxes can be better clustered than their transcript counterparts. Remarkably, it can also be noticed that the LUAD primary tumour xenograft  can be readily determined or approximated from measurements of the concentration of metabolites in the cell culture media at different time points for the bulk only. Another major side benefit of this approach is that it allows to identify the possible interactions among cells within a population, as pointed out in .NH3 and glutammate and uptake of lactate and palmitate. Within the dominant subpopulation, only mild differences in flux rates can be detected, whereas within the other  subpopulations heterogeneous patterns of nutrient production/consumption are observed, which result from metabolic interactions.We verified that, after data integration, some cells secret metabolites that are up-taken by other cells. The heat map in NH3 to be produced, consistently with scFBA predictions, glutamate would be produced according to iMAT only.It is also worth remarking that the predictions obtained with scFBA would not be possible with context-specific extraction methods from bulk data. In this respect, we compared the results of scFBA with two widely-used methods, GIMME  and iMATSaccharomyces cerevisiae [ad hoc experiments. As current techniques do not allow for easy determination of metabolites at the single-cell level, the heterogeneous population of alive cells should be first sorted to separate it into the sub-populations identified by scFBA. However, to sort cells based on fluorescent labeling (Fluorescence activated cell sorting), further analyses are necessary to possibly identify markers differentially expressed by the sub-populations. Less direct approaches might be taken, for example, by measuring the growth rate of wild-type cell populations and mutant populations in which the cooperation has been prevented (e.g. by blocking secretion or uptake of involved metabolites) and comparing with the model predictions. At this purpose, it should be assessed whether the metabolic interactions identified by scFBA are actually advantageous for tumor growth or are just related to the entropy of the system, i.e., to the fact that a configuration in which interactions among heterogeneous phenotypes take place is more likely than a configuration of identical and independent phenotypes. We address the issue in the following paragraphs.Metabolic interactions between cancer-associated fibroblasts and cancer cells, mediated by palmitate , 54 and revisiae . scFBA hThe optimal values for the cooperation fluxes reported in Remarkably, we observed that the ratio of the total biomass obtained in the absence of cooperation reactions over that in their presence may be lower than 1, implying that removal of cooperation limits the capability to achieve growth. In particular, we observed a ratio of: 0.90 for the LCPT45 dataset; 0.99 (H358); 0.99 (LCMBT15); 0.76 (BC04); 0.95 (BC03LN).Intriguingly, but not surprisingly, the impact of cooperation prevention is higher on those datasets corresponding to more heterogeneous populations (LCPT45 and BC04). Intuitively, cells specialized in different metabolic programs are more likely to benefit from cooperation, as compared to similar cells.For the sake of simplicity, in this study we assumed an optimal growth rate for the overall population, yet other assumptions may be readily investigated with the scFBA approach. Among others, it is common practice in constraint-based modeling to optimize for ATP production , 67. As Both in popFBA and in scFBA the cells were able to collaborate metabolically. As the integration of scRNA-seq data greatly reduced the space of feasible FBA solutions, those data encode information on how nutrient utilization should be distributed amongst the individual cells. Some cells that can no longer carry out a certain part of a pathway let their neighbors do this. However, it should still matter which nutrients are available to all cells. For a deeper characterization of given cancer populations, exo-metabolomic measurements to constrain the population boundary conditions would thus be needed. An exhaustive sensitivity analysis of scFBA results to boundary conditions is out of the scope of this work. However, it is interesting to compare the conditions in which the two major metabolites involved in cooperation  are externally supplied to the population or must be produced endogenously.de novo synthesis of palmitate-derived lipids [Notably, we observed that uptake of exogenous palmitate does not affect the biomass production rate, indicating that no growth advantage is conferred by free availability of lipids. This result is in line with experimental evidence that cancer cells rely on d lipids . Howeverd lipids , that and lipids . In lineAs opposed to palmitate, the metabolite lactate is not strictly required for growth. However, it can be observed in Also the set of metabolites allowed to be released, e.g., in the blood may affect the effect of gene deletions. For instance, if glutamate secretion is prevented, the deletion of the gene that encodes palmitate secretion becomes essential, as shown in We have here introduced scFBA to solve the problem of reconstructing the potential single-cell fluxome, starting from single-cell transcriptomes, by taking into account environmental constraints, as well as cell-cell interactions. Importantly, scFBA is able to point out the metabolic interactions that are established within a cell population.Vmax), thus neglecting the many factors that contribute to determine the expression level of a protein [Vmax. However scFBA does not predict the single-cell fluxome as a linear function of the assumed Vmax: the constraints on mass-balance and on the availability of substrates, as determined by the rates of consumption/secretion of nutrients by the entire population and by the requirement for the tumour mass to grow, are simultaneously taken into account. scFBA might also be implemented by using sc-proteomics rather than transcriptomics, should the former become available.scFBA integrates sc-transcriptomics data with (bulk) extracellular fluxes of the same cancer cell population, by means of a computational approach inspired to complex systems science . A limit protein , as wellAlthough we do not explicitly model spatial organization, the constraints on single-cell transcriptome should implicitly preserve the information on the usage/secretion of most nutrients of each cell in its original position. The method seems also to neglect communication between cells through growth factors. In reality, it mostly does not if the growth factors act by changing transcription. But if they act by phosphorylating enzymes, then this is not taken into account. In its current form scFBA can however already be implemented to investigate why metabolic drugs are often ineffective and to provide indications for more effective treatment.As a proof of principle, we have successfully applied the methodology to LUAD and breast cancer datasets. We have shown that the integration of scRNA-seq greatly reduces the space of feasible solutions that sustain metabolic growth of the overall population, which is prerequisite of tumour growth. This reduction allowed us to restrict the set of candidate drug targets, by eliminating targets that may seem obvious for the bulk, but do not work for heterogeneous populations, and, on the other hand, by revealing targets whose relevance can be appreciated only if cooperation among heterogeneous cells is accounted for. We have also illustrated that scFBA is valuable to extract features  from scRNA-seq data, in order to identify metabolic clusters of cells, which may be used to investigate other fingerprints of the cancer metabolic deregulation.Although popFBA assumes that the cells achieve optimal growth, this assumption is mitigated in scFBA, by taking into account the transcriptional constraints. Moreover, we have shown how alternative objective functions, such as ATP maximization, may be investigated. Sub-optimality may also be taken into account by using sampling methods .In this study, we have used scRNA-seq obtained with protocols based on C1 Single-Cell Auto Prep System, which have the advantage of allowing to remove dead cells before sequencing but may suffer from including low numbers of cells per sample (34—55 cells), as compared to modern emerging technologies which allow to obtain the single-cell transcriptome of thousands of cells at the cost of a bulk experiment , with anϵ rather than completely removing it. The choice of the value of ϵ is partially arbitrary. However, we verified that main results of our work are robust with respect to this choice  of the specific sequenced population may affect scFBA predictions. As opposed to intracellular fluxes, (bulk) extracellular fluxes might be readily estimated, e.g., by approximation from metabolite concentrations in spent medium (exo-metabolome), when culturing patient-derived cells.Hence, measurements of both extracellular fluxes and single-cell transcriptional information of the same heterogeneous cancer populations are needed to make scFBA predictions fully reliable. These datasets can be realistically obtained by culturing population of cancer cells and then processing the cells with scRNA-seq technologies and analyzing their spent medium with biochemical analyzers. Experiments under a controlled setting, e.g., a co-culture of metabolically characterized cancer cell lines, may first be performed to validate and tune the capability of scFBA to identify and measure the prevalence of different metabolic subpopulations of cells. The application of scFBA to analyze datasets more representative of tumor heterogeneity, obtained, for instance, by culturing cells from human biopsies, xenografts or organoids, will then pave the way to cancer personalized medicine.S1 Figϵ = 0. Right: Total biomass produced by the population of cells as a function of ϵ. The inset reports the same curve zoomed in on low ϵ values. B) Clustergram (distance metric: euclidean) of the effect of single gene deletions performed on scFBA for different values of ϵ, popFBA and bulkFBA. Growth ratio (grRatio) = 1 indicates totally redundant genes, while grRatio = 0 indicates lethal genes. C) Elbow analysis comparing cluster errors for k = 1, …, 20 (k-means clustering). Each curve refers to a different values of ϵ. D) Impact of cooperation among single cells for different values of ϵ. Curves refer to the ratio of total biomass (blue curve) and ATP (orange curve) produced by population models when cooperation reactions are blocked as compare to when they are allowed.A) Left: histogram of biomass produced by each single cell when (TIF)Click here for additional data file.S2 FigA* (bulkFBA). When grRatio = 0 , the corresponding bar is not displayed. B-C) Same information as in A for LCMBT15 and BC03LN datasets.A) Dataset H358. Variability of the fraction of the biomass synthesis flux  for each cell over the population growth rate (left panel) before (purple) and after data integration (green). Effect of gene deletion (bars in right panel) on the population growth rate before (popFBA), after data integration (scFBA), and for the template metabolic network (TIF)Click here for additional data file.S3 Figk ∈ {1, ⋯, 20} (k-means clustering) in both transcripts (blue) and fluxes (green). B-C) Same information as in A for the datasets LCMBT15 and BC03LN. D) Silhouette analysis for LCPT45 transcripts (left) and fluxes (right), when k = 3. Red dashed lines indicate the average silhouette for the entire dataset.A) H358 dataset. Clustergram (distance metric: euclidean) of the transcripts of the metabolic genes included in metabolic network (left) and of the metabolic fluxes predicted by scFBA (middle). Right panel: elbow analysis comparing cluster errors for (TIF)Click here for additional data file.S4 FigThe linear relationship between the time for an FBA (and thus a scFBA) optimization and the size of the network is well established. We estimated the computation time required to perform a complete model reconstruction, from a template metabolic network to a population model with RASs integrated, for different number of cells . We tested both our HMRcore metabolic network (panel A) and the genome-wide model Recon2.2  (panel B(TIF)Click here for additional data file.S1 Text(PDF)Click here for additional data file.S2 Text(PDF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.


EMUlator a Python-based isotope simulator which is developed on Elementary Metabolite Unit (EMU) algorithm, an efficient and powerful algorithm for isotope modeling. We propose a novel adjacency matrix method to implement EMU modeling and exemplify it stepwise. This method is intuitively straightforward and can be conveniently mastered for various customized purposes. We apply this arithmetic pipeline to understand the phosphoketolase flux in the metabolic network of an industrial microbe Clostridium acetobutylicum. The resulting design enables a high-throughput and non-invasive approach for estimating phosphoketolase flux in vivo. Our computational insights allow the systematic design and prediction of isotope-based metabolic models and yield a comprehensive understanding of their limitations and potentials.Stable isotope based metabolic flux analysis is currently the unique methodology that allows the experimental study of the integrated responses of metabolic networks. This method primarily relies on isotope labeling and modeling, which could be a challenge in both experimental and computational biology. In particular, the algorithm implementation for isotope simulation is a critical step, limiting extensive usage of this powerful approach. Here, we introduce  Furthermore, we applied this newly developed software in modeling and analyzing the flux of phosphoketolase pathway in Clostridium acetobutylicum xylose catabolism. By decomposing the network and simulating metabolite isotopomer patterns, we found a good correlation between phosphoketolase flux and the fractional labeling of acetate, which has never been characterized in an isotope tracer experiment. Coupled with GC-MS analysis of acetate, this EMUlator-enabled analysis leads to a novel and high-throughput methodology for quantitatively understanding the phosphoketolase pathway in response to environmental and genetic perturbation. As exemplified, EMUlator aims to be a universal and powerful tool for isotope tracer modeling and for gaining quantitative understanding of cell metabolism. The software and its instruction are available at Here, we develop a new computational toolbox for steady state metabolic modeling analysis, the EMUlator pipeline is designed in Python, capable of performing a complete isotope simulation and prediction of a metabolic network for 13C-MFA. Previous tools, such as Metran . All EMU reactions that are needed for this simulation can be identified iteratively via MAM. Glu12345 as a product can be found in the column of EAM (size 5)  Cit12345, we identify reaction v1, in which both OAA234 and AcCoA12 are the reactants. Since EMUs of smaller size are identified in condensation reactions, they will be used as new start points for searching. Therefore, we can follow the OAA234 , and search all other EMUs at size 3 (EMU decomposition of a metabolic network can start at the size of EMU(s) that need to be simulated. In this example, we simulate the Mass Distribution Vector   see , its pret size 3 . All pret size 3 ], can beEMUlator can also reduce the scale of EAM. In steady state isotope modeling, labeling pattern can only be modified by convolution of two or more metabolites and unimolecular reactions may be lumped without affecting simulations which helps to reduce the scale of EAM. Unimolecular reactions can be easily identified in EAM as those with solo element in a column, which means its corresponding product only has a single source. Those columns will be deleted with identical metabolites in rows all renamed by their precursors. For example, in EAM of size 1, after AKG3 column is eliminated, AKG3 in row will be renamed with Cit3 which produces AKG3 by reaction v2 (3 is still from a unimolecular reaction (v1), we eliminate the column as well and Cit3 in row will be renamed by its precursor OAA2 via v1. The deletion of the column and renaming of corresponding row continue until there is no solo-element column in EAM. Finally, multiple rows with identical metabolite name will be combined, indicating the identical reactant and product are connected by different reactions.ction v2 . Moreove2 and Fum3 are equivalent EMUs of size 1 in this example  will give rise to equivalent EMUs  is equal to the sum of the individual product of each influx vi multiplied by MDVi (∑(vi. MDVi)). Apparently, diagonal element represents the total influx of corresponding EMU. Multiplied by MDV of balanced EMU, the product is equal to the sum of all labeling pattern sources, including those unknown (Xi) and known (Yi) EMU variables. EMU balances of larger size can be established likewise until the Glu12345 are eventually simulated. EMU balances of all sizes are shown below:Where AEMU balance of size 1EMU balance of size 2EMU balance of size 3EMU balance of size 4EMUlator in a large-scale setting that reflects the complexity of realistic cell metabolism, we next performed simulation of isotope distributions in a larger network model of C. acetobutylicum. C. acetobutylicum is a solventogenic clostridium and represents a promising chassis microbe capable of utilizing lignocellulose-derived pentose sugar  for biofuels production   and flux ratio through phosphoketolase , ethanol, 3-phosphoglycerate, erythrose-4-phosphate and ribose-5-phosphate as candidate readouts for reflecting phosphoketolase activity since MDVs of these metabolites can be experimentally obtained either from direct determination or derivation from amino acid MDVs . The widest effective range of FL (slope of regression line = 0.43) indicates a good sensitivity on the flux ratio of phosphoketolase  without any loss of information, which therefore greatly facilitates 13C flux modeling of realistic and large-scaled metabolic network and dynamic systems , where n is the number of EMUs.Although equivalent to isotopomer models, EMU method is able to significantly reduce the variables needed to simulate labeling patterns of metabolites . We simulated labeling pattern of both intracellular and secretory metabolites using different xylose tracers, and identified the best tracer/readout combination reflecting phosphoketolase activity. 13C-flux measurement of the phosphoketolase pathway was enabled recently  can be a better readout due to the strong correlations with phosphoketolase flux and a wide effective range of FL. Indeed, acetate can be exclusively derived from acetyl phosphate which is directly produced from phosphoketolase. More importantly, acetate is an extracellular metabolite and its isotope pattern can be easily measured by GC-MS without derivatization. The convenience of measurement without breaking the cells provides a high-throughput and non-invasive method for prompt 13C-flux estimation, which, to our knowledge, was never developed previously. This estimation is based on the numerical relationship between fractional labeling of acetate and flux ratio through phosphoketolase which are positively correlated, even though it may not be strictly linear. It should be noticed that in the FL range 0.5-0.65, multiple flux ratio values are possible for a given value of FL. The jitter could be due to the reversibility of biochemical reactions and partial dependency of the EMU basis vectors 2SO4, 1.5 g L−1 KH2PO4, 0.13 g L−1 CaCl2·2H2O, 0.5 g L−1 L-Cysteine–HCl, 11.56 g L−1 MOPS sodium salt, 2.6 g L−1 MgCl2·6H2O, 0.001 g L−1 FeSO4·7H2O, 0.5 mL L−1 Resazurin 0.2% (w/v), supplemented with Wolfe's Vitamin solution (ATCC). D-xylose was supplied at concentration of 5 g L−1 as a carbon source. The cultures were started with the optical density at 600 nm (OD600 = 0.05-0.08) and performed in mid-log-phase. For labeling experiments, 1,2-13C-labeled xylose  was added to media at the concentration of 5 g L−1. C. acetobutylicum strains were kept by freezing log-phase cultures at −80°C with 10% glycerol.600 with a Spectronic 21D UV-Visible Spectrophotometer . To analyze extracellular metabolites, cell samples were harvested by centrifugation at 13,000 g for 10 min. After filtration with 0.2 μm filter, the supernatant was analyzed by Agilent 1200 high pressure liquid chromatography (HPLC)  and injected into a Bio-Rad Aminex HPX-87H column with a Micro Guard Cation H Cartridge. 4 m M H2SO4 was used as mobile phase at a flow rate of 0.6 mL/min. The column temperature was set to 55°C. Metabolites were detected by refractive index detector and UV/VIS detector.Cell growth was monitored by measuring the absorbance at OD−1 was held constant throughout the run with the following temperature profile: 35°C, hold for 3 min; ramped at 10 °C min−1 to 225°C, hold for 1 min; ramped at 15°C min−1 to 250°C, hold for 5 min.Labeling pattern of proteinogenic amino acids from cell mass were analyzed by Gas Chomatograph-mass spectrometry (GC-MS) as detailed in Xiong et al. . The labSimulations were repeated 1,000 times with metabolic fluxes randomly generated subjecting to mass balances determined by reactions listed in i represents components of MDV (Nanchen et al., where n is the number of carbon in a EMU, and mCW developed the software and analyzed data. WX and CW designed the experiment. CC, JL, and WM conducted the experiment. WX proposed the idea and research questions, guided all stages of the research. CW and WX prepared the manuscript with editing from PM, JL, and CC.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.