Plasmodium falciparum is an auxotroph for purines, which are required for nucleic acid synthesis during the intra-erythrocytic developmental cycle (IDC) of the parasite. The capabilities of the parasite and extent to which it can use compensatory mechanisms to adapt to purine deprivation were studied by examining changes in its metabolism under sub-optimal concentrations of hypoxanthine, the primary precursor utilized by the parasite for purine-based nucleic acid synthesis.The malarial parasite P. falciparum to hypoxanthine deprivation.The concentration of hypoxanthine that caused a moderate growth defect over the course of one IDC was determined. At this concentration of hypoxanthine (0.5 μM), transcriptomic and metabolomic data were collected during one IDC at multiple time points. These data were integrated with a metabolic network model of the parasite embedded in a red blood cell (RBC) to interpret the metabolic adaptation of P. falciparum parasites were observed after the 24-h midpoint of the IDC. Parasites grown under these conditions experienced a slowdown in the progression of the IDC. After 72 h of deprivation, the parasite growth could not be recovered despite supplementation with 90 µM hypoxanthine. Simulations of P. falciparum metabolism suggested that alterations in ubiquinone, isoprenoid, shikimate, and mitochondrial metabolism occurred before the appearance of these vacuole-like structures. Alterations were found in metabolic reactions associated with fatty acid synthesis, the pentose phosphate pathway, methionine metabolism, and coenzyme A synthesis in the latter half of the IDC. Furthermore, gene set enrichment analysis revealed that P. falciparum activated genes associated with rosette formation, Maurer’s cleft and protein export under two different nutrient-deprivation conditions (hypoxanthine and isoleucine).At a hypoxanthine concentration of 0.5 μM, vacuole-like structures in the cytosol of many P. falciparum invokes specific purine-recycling pathways to compensate for hypoxanthine deprivation and maintains a hypoxanthine pool for purine-based nucleic acid synthesis. However, this compensatory mechanism is not sufficient to maintain long-term viability of the parasite. Although P. falciparum can complete a full IDC in low hypoxanthine conditions, subsequent cycles are disrupted.The metabolic network analysis presented here suggests that The online version of this article (10.1186/s12936-019-2720-3) contains supplementary material, which is available to authorized users. Plasmodium falciparum, the most lethal malaria parasite, is responsible for 99% of malaria-related deaths in sub-Saharan Africa [In 2016, there were 216 million cases of malaria and 445,000 malaria-related deaths worldwide [n Africa , which gP. falciparum parasites [In contrast to most human cells, arasites  and RBCsarasites  lack thearasites , but thaarasites . Therefoarasites –8. Figurarasites , 5. Prevarasites .Fig. 1ScP. falciparum was first cultured under a range of hypoxanthine concentrations to identify appropriate nutrient-deprived conditions. At a concentration of 0.5 μM, transcriptomic and metabolomic data were first collected and then integrated with metabolic network models of uninfected and parasite-infected RBCs to predict the metabolism of P. falciparum under hypoxanthine-deprivation conditions. Model simulations of uninfected and parasite-infected RBCs were validated by comparing them with relevant experimental data. Lastly, the metabolic adaptations of the parasite under hypoxanthine-deprivation conditions were investigated and gene set enrichment analysis (GSEA) was performed to identify biological processes that were altered significantly beyond metabolic adaptations. The GSEA results were used to identify pathways and processes invoked by the parasite in response to hypoxanthine deprivation. These pathways and processes were then contrasted with those invoked in response to a different nutrient-deprivation condition [To determine how hypoxanthine deprivation affects parasite metabolism, ondition , to idenPlasmodium falciparum Nf54attB parasites  were cultivated in RBCs at 2% haematocrit (HCT) under a mixed gas atmosphere  at 37 °C. The parasite cultures were maintained in Roswell Park Memorial Institute (RPMI)-1640 medium  supplemented with 25 mM HEPES, 90 µM hypoxanthine, 0.3% sodium bicarbonate, 25 µg/mL gentamicin, 0.5 µM R-lipoic acid, and 0.5% AlbuMAX II . This medium is referred to as the hypoxanthine-rich medium.g, 5 min) to pellet the RBCs within 0–2 h after they were infected. The pellet was washed once in medium lacking hypoxanthine and then seeded into a medium containing a hypoxanthine concentration of 0, 0.5, 2, 5, or 90 µM. Parasite morphology and parasitaemia were monitored by Giemsa staining of blood smears at 24 and 40 h. To assess re-infection of RBCs, a tenth of each culture was transferred into fresh hypoxanthine-rich medium with 2% HCT at 40 h. Blood smears were prepared at 72 h for these diluted cultures to assess re-infection of RBCs.To determine the hypoxanthine-deprivation conditions, experiments were first carried out in 24-well culture plates to identify the concentration range in which parasite viability was affected. RBCs containing late-stage parasites were collected by Magnetic Activated Cell Sorting (MACS). Parasite-infected RBCs were purified and diluted in fresh hypoxanthine-rich medium to approximately 0.8% parasitaemia with 2% HCT. The culture was centrifuged  and 0.5 (hypoxanthine-deprived) for over a period of 120 h, and blood smears were prepared at 24, 40, and 48 h. A tenth of the hypoxanthine-deprived culture was transferred to hypoxanthine-rich medium at 40, 48, 60, 72, and 96 h, while the hypoxanthine-rich culture was transferred at 40 h to serve as a control. Twenty-4 h after transfer, the cultures were assessed for parasitaemia using a blood smear test. All growth experiments were carried out in triplicate wells for each condition and the procedure was repeated at least twice.P. falciparum metabolic network model, which consists of 1025 metabolic reactions and 923 metabolites [P. falciparum Nf54attB strain maintained in RPMI-1640 medium during the IDC, as determined by (1) ultrahigh-performance liquid chromatography (UPLC) tandem mass spectrometry (MS/MS) [The present study used the latest version of a abolites . This moabolites  of 273 mr, the level of expression of an enzymatic reaction, which is a function of the gene(s) transcribing the enzyme(s) catalyzing a given reaction . For a OR’ gate .Fig. 2ScFigure A previously described computational framework was used for simulating hypoxanthine deprivation . BrieflyP. falciparum during the IDC, the following equations were solved:R denotes the set of all metabolic reactions of P. falciparum, M represents the set of metabolic reactions influenced by the metabolomic data, S represents a matrix containing the stoichiometry coefficients of all reactions, vg represents the metabolic reaction governing the growth of the parasite, ith metabolic reaction. ith value of N denotes the set of reactions transporting nutrients across the parasite plasma membrane and N. The other variables are as defined above.To obtain the metabolic flux distribution of entclass1pt{minimavref, which were modulated using the time-dependent transcriptomic and metabolomic data to obtain the temporal profile of P. falciparum metabolism. The time-dependent transcriptomic and metabolomic data were incorporated by solving the following:G denotes the set of all intracellular reactions of P. falciparum, jth reaction at time t, t for the ith reaction, and the bar above m denotes normalization of metabolite abundance by its median over the IDC. jth and ith values, respectively, of The optimization problems shown in Eqs.  and 2)  2) yieldThe method to solve the optimization problems in Eqs. –4) was  was 4) wμ) and standard deviation (σ) of the absolute values were calculated based on the absolute fold-change values of all genes. The average score of a given gene set  in response to parasite infection under hypoxanthine-rich and -deprived conditions. A complete list of the RBC metabolic pathways perturbed under these two conditions is provided in Additional file Parasite-infected RBC metabolism did not significantly change in response to hypoxanthine deprivation. In fact, the metabolic pathways of a parasite-infected RBC were perturbed to a similar degree regardless of the culture medium. Table In the culture conditions used here, malaria parasites had access to only hypoxanthine as their sole purine source, which was kept at a pre-determined low concentration of 0.5 µM. Figure P. falciparum to synthesize DNA, RNA, and protein. The extent to which the proposed model could capture the time-dependent changes in DNA, RNA, and protein synthesis over the course of the IDC in the hypoxanthine-deprived condition was examined , intracellular signalling, Maurer’s cleft, rosette formation, protein export, and mitosis.Thus far, the analysis has only focused on identifying alterations in the metabolism of the parasite. This section presents the results of GSEA, which includes analyses of all biological processes of the parasite. Figure P. falciparum, along with their enrichment level at each time point and deprivation condition, is provided in Additional files To ascertain whether enrichment of these gene sets constitutes a general response or a response specific to hypoxanthine deprivation, GSEA was also performed on published data obtained under isoleucine deprivation at the 30-h mark, when parasites enter a hibernatory state . Figure P. falciparum is capable of effectively responding to short-term nutrient stress.Parasites deprived of hypoxanthine displayed morphological and developmental aberrations during the first IDC and could not be rescued after two IDCs in the deprived medium. The formation of vacuole-like structures was evident in many parasites at 24 h into the IDC. Such vacuole formation, which has previously been observed in parasites exposed to heat stress, is attributed to autophagic programmed cell death . The hypBased on model simulations, it can be inferred that the hypoxanthine-deprived parasite invokes mechanisms to maintain a sufficient pool of purine bases, which thereby supports its growth under limited availability of hypoxanthine. Model-predicted reaction fluxes that support this hypothesis are presented below Fig. . First, S-adenosylhomocysteine (SAH). The cycle is futile because SAH requires S-adenosylmethionine (SAM), which cannot be synthesized without ATP. Therefore, although the parasite can synthesize hypoxanthine through this pathway, it must also redistribute (enhance or suppress) reactions associated with ATP to maintain the synthesis of purine-based nucleic acids. The deprived parasites suppressed metabolic fluxes through ATP-consuming reactions, such as those of phosphoenolpyruvate carboxykinase (PPCK), adenylate kinase and carbamoyl-phosphate synthase, while also increasing metabolic fluxes through certain ATP-consuming reactions, such as those of glutathione synthase and guanylate kinase  and is essential for ubiquinone synthesis. Therefore, an increase in flux through SAM should also increase flux through reactions associated with ubiquinone synthesis and create a demand for the precursors necessary for ubiquinone synthesis, such as chorismate. One of the top pathways significantly altered under hypoxanthine deprivation in the simulations was that of shikimate biosynthesis , and, consequently, influence other reactions that require PEP. PEP is also an important precursor in the methylerythritol phosphate pathway (MEP) pathway of isoprenoid synthesis, and as with shikimate synthesis, the flux through the MEP pathway significantly increased under hypoxanthine deprived conditions Table . InteresFigure Plasmodium falciparum lacks the machinery to synthesize purine bases de novo and relies on purine salvage to meet its need [P. falciparum utilizes pathways to recycle available purine and maintain DNA replication. However, enhanced flux through the pathways that recycle purines causes an imbalance in redox and mitochondrial metabolism, which is detrimental to the parasite. These findings suggest the following conclusions:P. falciparum survival during the blood stage;Maintenance of redox reactions and mitochondrial function within their normal range is essential for Plasmodium falciparum redistributes metabolic reactions to maintain synthesis of purine-based nucleic acids under limited concentrations of hypoxanthine;P. falciparum by making them unviable for replication after 72 h of deprivation, despite supplementation with a hypoxanthine-rich medium.The compensatory mechanisms, induced under hypoxanthine-deprivation conditions, cause irreparable damage to its need . The preAdditional file 1. Supplementary computational details Text S1–S2 and additional Figures S1–S3.Additional file 2. Significantly altered erythrocyte reactions in response to parasite infection and hypoxanthine concentration.Additional file 3. List of metabolites detected under hypoxanthine-rich and -deprived conditions.Additional file 4. Significantly altered metabolic genes and reactions of Plasmodium falciparum in response to hypoxanthine deprivation.Additional file 5. Gene set enrichment analysis of transcriptomic data from hypoxanthine-deprived Plasmodium falciparum.Additional file 6. Gene set enrichment analysis of transcriptomic data from isoleucine-deprived Plasmodium falciparum.


Protocell multilevel selection models have been proposed to study the evolutionary dynamics of vesicles encapsulating a set of replicating, competing and mutating sequences. The frequency of the different sequence types determines protocell survival through a fitness function. One of the defining features of these models is the genetic load generated when the protocell divides and its sequences are assorted between the offspring vesicles. However, these stochastic assortment effects disappear when the redundancy of each sequence type is sufficiently high. The fitness dependence of the vesicle with its sequence content is usually defined without considering a realistic account on how the lower level dynamics would specify the protocell fitness. Here, we present a protocell model with a fitness function determined by the output flux of a simple metabolic network with the aim of understanding how the evolution of both kinetic and topological features of metabolism would have been constrained by the particularities of the protocell evolutionary dynamics. In our model, the sequences inside the vesicle are both the carriers of information and Michaelis-Menten catalysts exhibiting saturation. We found that the saturation of the catalysts controlling the metabolic fluxes, achievable by modifying the kinetic or stoichiometric parameters, provides a mechanism to ameliorate the assortment load by increasing the redundancy of the catalytic sequences required to achieve the maximum flux. Regarding the network architecture, we conclude that combinations of parallel network motifs and bimolecular catalysts are a robust way to increase the complexity of the metabolism enclosed by the protocell. The protocell hypothesis conjectures the existence of a vesicle containing catalytic and replicating sequences as the primordial cellular organization during the early stages of the evolution of life. Mathematical models of protocells traditionally consider RNA sequences being encapsulated and having both an informational and a catalytic role in the same molecule. Because of this dual function, the protocell sequences are evolutionarily constrained. Mathematical models have been extensively used to study the evolutionary dynamics of protocells with a focus on the processes, like mutation or stochastic sequence assortment upon division, that affect the protocell information capacity in terms of the coexistence of different sequence types. Here we introduce a simple model of metabolic networks whose output determines the survival of the protocell with the aim of studying the effect of modifying the kinetic and architectural properties of the network on sequence coexistence. We find that stochastic assortment and mutation limit the architectures able to be encapsulated by the protocell with a given fraction of the population harbouring all possible sequence types. Trying to address this issue led to the consideration of distributing the information encoded by the sequences in a mutualistic community of replicators known as the hypercycle model  and [S] denote the concentrations of enzyme and substrate respectively and kcat is the turnover number  of the enzyme and Km its Michaelis constant. We will also study bimolecular reactions with mechanisms of the following form:a1 and a2 can be determined from either the forward and the backward rates of the underlying reactions or from thermodynamic potentials. Special values of these constants correspond to the cases of random order, definite order, non-interacting. We will model the depletion reactions as exponential decay or diffusionδi is the decay rate or diffusion constant for S.We will model the metabolic activity of our protocell as a well-stirred reactor in which ribozymes, environmental inputs, and metabolites interact. More specifically, the metabolic dynamics will be modelled as Michaelis-Menten enzyme dynamics where each flux is given by the expressionwithin the protocell may vary due to the permeability of the membrane). We assume that the intermediates that leak out to the environment are degraded and do not accumulate. We assume that the characteristic timescale of the metabolic reactions is sufficiently faster than the timescale of sequence replication that we may ignore initial transients, approximate the metabolic reactions by their (dynamic) equilibrium solution, and describe the metabolic outputs by their averaging their rates of production over a metabolic timescale.We assume that even though the protocell development will be accompanied by an increase in the vesicle volume, this will be negligible and will not dilute significantly the concentrations of the catalysts and intermediates of the reaction network. Therefore we can identify the catalysts’ concentrations with the catalyst number in our model of metabolism. We will augment this hypothesis with three further assumptions. We assume that the supply of this input in the environment is high enough that we can disregard depletion and treat its concentration as constant (v − kcat[E]) = 0, which has the solutions v = j and v = kcat[E]. The choice of solution depends upon the value of j and is determined by the conditions that the concentration is positive; thus, when j < kcat[E], we should choose the solution v = j and, when j ≥ kcat[E], we should choose v = kcat[E]. As a result, the zeroth order term in the expansion of the the velocity is a piecewise linear function of the incoming flux,v = min. The higher order terms can be regarded as corrections which account for deviations from piecewise linearity. Most notably, they replace the sharp peak at the maximum with a smooth peak whose maximum value is lower.The first class of motifs consist of a unimolecular reaction in which an enzyme E reacts with molecule of substrate S1 and a molecule of substrate S2 to produce one or more products Pi. This is described by the reactionsS1] and [S2] and collecting powers of δ leads to the equationδ → 0, this reduces to (v − j1)(v − j2)(v − kcat[E]) = 0. As previously, the choice of root is determined by the values of j1 and j2 through the condition that the concentrations [S1] and [S2] not be negative. This leads to a piecewise linear form of the leading term in the expansion of the solution,v = min.The second class of motifs consist of a bimolecular reaction in which an enzyme A, two enzymes α and β, an intermediate metabolite W and an output metabolite M and reactionsα, referred in the text as the keystone, is given by the Michaelis-Menten formula. However, since we assume that the input A is plentiful in the environment, we expect this reaction to be happening well within the saturation regime, hence will approximate its velocity by the limiting velocity:β (referred in the text as the recycler) takes part are an instance of the first type of motif, so we havej is the flux of W. Since the stochiometry of the first reaction produces one molecule of W for every molecule of input, we have j = vα, henceM will include the output of both reactions:As a simple illustration of how to use these motifs, consider a network consisting of an environmental input Using exactly the same techniques and assumptions as in the foregoing simple example, we calculated the flux-fitness functions for several more complicated networks involving three and four enzymes. The results of these calculations were then inserted into the evolutionary population model described below to study the effects of network architecture.x and the scaled flux ϕ:α to β remains constant during development. Since ϕ only depends upon α and β through their ratio, ϕ will also remain constant. As per the “slow-fast” minority control hypothesis of Kaneko and Yomo [M and W will approach an equilibrium values after an initial transient. Combining the equations, we conclude thatOur aim is to enrich the evolutionary population genetic models with relevant biochemical features rather than go on the direction of a full-blown simulation of a cellular system. However, in order to introduce these features realistically, we will derive them from a simplified “whole protocell” model in which the metabolic reactions described above are augmented with reactions that describe the replication of the sequences:and Yomo , we shalg, that, in principle will be of cardinality ω, that will not contribute to the metabolic activity.The general protocell model for our study will be built following a similar approach to the package model , 32. We N independent samplings with replacement from the initial contents of the vesicle to represent the replication of sequences. Let ji denote the number of number of sequences of type i present at the beginning of the cycle. The probability of sampling a sequence of type i equals ji/N. The probability that a replication will produce a sequence of non-error type i equalsω equalski offspring of the sequence type i is given asmi sequences of type i and an offspring with ki − mi sequences of type i equals toWe will model the protocell development process as 2F(ji) which is the frequency in the population of protocells which began their development process with ji copies of the i-th sequence. Let W(ji) denote the survivability of a typical protocell which begins its development process with ji copies of the i-th sequence. Such a population may be modelled either as a branching process to describe a growing population or as a Moran process to describe a population which has reached its carrying capacity. In the limit of large population size, the dynamics of either of these models become deterministic and the equilibrium frequencies of both models are determined by the same eigenvalue equationK(mi|ji) are non-negative, this equation may be solved numerically by using Perron-Frobenius iteration for small ploidy values (up to 100) and few sequence types (up to three). For higher ploidy values, both the Perron-Frobenius iteration or the Moran Process become cumbersome, so an agent based simulation which also approaches the same limit for large population size was used instead. As in [https://github.com/jopejor/protocell_metabolism.Our population is comprised of a number of non-interacting protocells each of which undergoes a lifecycle as described above. To describe this population, we introduce the summary statistic d. As in , the aged. As in  and the S1 FigThe figure shows the dependence of the average mean metabolic flux of the stationary population with the ploidy and the replication accuracy for the case in (PDF)Click here for additional data file.S2 FigThe figure shows the dependence of the average mean metabolic flux of the stationary population with the ploidy for the case in (PDF)Click here for additional data file.S3 FigThe curves show the dependence of the average defective type frequency in the stationary population with the ploidy and the replication accuracy for the case in (PDF)Click here for additional data file.S1 TextChemical reactions, network diagrams and fluxes for each of the networks studied in this work.(PDF)Click here for additional data file.


Bifidobacterium longum subsp. longum JCM 1217, and to the same modeling conditions — anaerobic growth under four nutrients producing 53 biomass metabolites.Reaction gap filling is a computational technique for proposing the addition of reactions to genome-scale metabolic models to permit those models to run correctly. Gap filling completes what are otherwise incomplete models that lack fully connected metabolic networks. The models are incomplete because they are derived from annotated genomes in which not all enzymes have been identified. Here we compare the results of applying an automated likelihood-based gap filler within the Pathway Tools software with the results of manually gap filling the same metabolic model. Both gap-filling exercises were applied to the same genome-derived qualitative metabolic reconstruction for The solution computed by the gap-filling program GenDev contained 12 reactions, but closer examination showed that solution was not minimal; two of the twelve reactions can be removed to yield a set of ten reactions that enable model growth. The manually curated solution contained 13 reactions, eight of which were shared with the 12-reaction computed solution. Thus, GenDev achieved recall of 61.5% and precision of 66.6%. These results suggest that although computational gap fillers are populating metabolic models with significant numbers of correct reactions, automatically gap-filled metabolic models also contain significant numbers of incorrect reactions.B. longum.Our conclusion is that manual curation of gap-filler results is needed to obtain high-accuracy models. Many of the differences between the manual and automatic solutions resulted from using expert biological knowledge to direct the choice of reactions within the curated solution, such as reactions specific to the anaerobic lifestyle of The online version of this article (10.1186/s12918-018-0593-7) contains supplementary material, which is available to authorized users. Constructing metabolic models requires the creation of connected network paths from the nutrient compounds that fuel an organisms growth to the end products of the biosynthetic machinery of the organism that comprise the biomass of the organism (the biomass metabolites). However, because the reactions within most metabolic models are derived from the enzyme annotations assigned to genes within a sequenced genome, and because methods for genome annotation are incomplete and fail to assign functions to many genes (and in some cases assign incorrect functions), genome-derived metabolic networks usually contain multiple gaps (missing reactions).Because filling these gaps manually can take months of effort, computational gap-filling methods have been developed –5. They However, there have been few past studies of the accuracy of gap-filling methods. Two studies , 6 evaluBifidobacterium longum subsp. longum JCM 1217 with an automatically gap-filled metabolic model for the same strain. In both cases, we began with the same genome sequence; we annotated that sequence (gene finding and gene-function prediction) using KBase; and we ran the GenBank entry produced by the KBase annotator through Pathway Tools ” — since they do not match exactly we count this result as a false-positive prediction.four reactions in MetaCyc that, if added to the model, enables production of L-asparagine. The correct reaction to add is RXN-12460, because of the presence in B. longum of the two other enzymes in the MetaCyc pathway L-asparagine biosynthesis III (tRNA-dependent) (PWY490-4). These four reactions have equal cost, thus the gap filler is randomly selecting among them.ASNSYNA-RXN: This reaction is one of Let us consider the four reactions predicted by GenDev but not by manual gap filling: B. longum annotation and no hits to Pfam PF00334 in the genome, but there is an adenylate kinase at blongannot.CDS.3717, ndk knockout [GDPKIN-RXN: In the manually curated model, a GDP kinase activity, GDPKIN-RXN, forms GTP from GDP. In the GenDev model, pyruvate kinase RXN-14117 is instead used to transfer phosphate from phosphoenolpyruvate to GDP. There is no clear dedicated NDP kinase in the knockout , 13. Pyrknockout . Both meGLUCOKIN-RXN: This reaction was originally included as a model-building convenience and used to convert glucose (GLC) supplied in the cytosol to glucose 6-phosphate for entry into the glycolysis reactions. We then identified a polyphosphate-based glucokinase activity (EC 2.7.1.63) in the KBase annotation at gene blongannot.CDS.3457. MetaCyc contains a polyphosphate glucokinase reaction (2.7.1.63-RXN) but GenDev cannot include polymerization/depolymerization reactions such as2.7.1.63-RXN during gap filling, so GLUCOKIN-RXN remains as a way of marshaling polyphosphate reserves. Glucose can enter the cell through the glucose/galactose transporter at blongannot.CDS.3321 (PF07690.14 Major Facilitator Superfamily bitscore 52.89) and the phosphotransferase system (PTS) elements present at blongannot.CDS.2260 and blongannot.CDS.2261. The automated GenDev solution uses the PTS-based transport reactions for glucose and does not show glucokinase activity.RXN-17018 is very similar to RXN-1381 inferred by GenDev.RXN-12460: See preceding discussion of ASNSYNA-RXN.B. longum PGDB to represent cytoplasmic ferredoxin-NADP+ reductase activity (EC 1.18.1.2) carried out by the blongannot.CDS.2132 product, since the existing MetaCyc reaction is a membrane reaction. PSORTdb [RXN-17897: We added this reaction to MetaCyc and the  PSORTdb  classifiThe following five reactions were predicted to be present by manual gap filling but not by GenDev: B. longum. The methods started with the same initial reaction network: a qualitative metabolic reconstruction computed by the PathoLogic component of Pathway Tools that underwent some subsequent curation — mostly the addition of reactions based on manual review of enzyme names that were not recognized by PathoLogic.We describe a comparison of automated and manual metabolic-model gap-filling methods applied to a gapped PGDB for Three important restrictions on automatic gap-filling methods should be mentioned. Gap-filling methods drawing from a reaction database  can only operate within the space of knowledge contained in that database. If the reaction database does not contain a needed reaction, as for RXN-17897 in our work, then an automatic gap filler could not include that reaction in its solution set. Similarly, if appropriate compound instances are not present in the relevant PGDB, then the automatic gap filler could not include instantiated reactions containing those compounds in its solution set. These restrictions, along with the need to verify genome-annotation quality, suggest continued importance for human curation of reaction databases and supervision of automatic model-building processes.B. longum example, its 12-reaction solution contained two extra, unneeded reactions. Based on more detailed studies of this topic [We found that GenDev did not return solutions that were minimum cost; in our is topic , we beliThis result suggests cause for concern that larger solutions containing more reactions ; but in fact, their fluxes fr were all equal or above Bl, violating the constraints. In such a case, despite what the variables sr say, the candidate reactions are suggested to be added, because in general, such reactions are likely needed to obtain growth. Such cases can be detected and are reported by MetaFlux, which did not occur in this work. On the other hand, the constraints maintaining the steady state can have cumulative numerical imprecision that is much harder to detect, and where a reaction is erroneously made active to satisfy them and the constraint that the biomass flux must be greater than 10−3. Such cases are not detected by MetaFlux.where the Boolean variable minimal-cost solution, where cost reflects not simply the number of reactions added, but also factors such as changes to the direction of existing reactions, and whether the organism in which a reaction is inserted is within the expected taxonomic range of the reaction.Our results also call into question the basic assumption that gap fillers should seek solutions containing a minimal number of reactions. Our manually curated solution contains 13 reactions compared to the minimum solution of 10 reactions — a 30% increase over the minimum solution. This result supports our design of GenDev as computing a Further analysis revealed that although we had thought this manual solution to be minimal, it was not. If we remove CDPKIN-RXN from the model, the model still grows. This solution is minimal, but the model grows 45% more slowly without this reaction. The model secretes CMP because it can no longer recycle CMP produced from RXN0-302  and nrdDG (RNR class III) gene clusters. Based on B. longum’s anaerobic lifestyle the strictly anaerobic class III RNR is likely to play a prominent role and was chosen for the manual solution.The manually gap-filled solution uses class III ribonucleotide reductase reactions  to form We added the new reaction RXN-17897 to ensure availability of reduced ferredoxin for the isoprenoid pathway.We added reaction RXN-12460 — marked as a hypothetical reaction in MetaCyc — because of the presence of other enzymes in its pathway. Note that had we used the default pathway prediction behavior in PathoLogic, this reaction and pathway would have been imported by PathoLogic. However, we used a stringent setting in which a pathway had to have enzymes for all of its reactions present for the pathway to be inferred. Since no enzyme is known for hypothetical reactionRXN-12460, the pathway was not inferred. In the future we will modify PathoLogic to not require the presence of enzymes for hypothetical reactions.Observed differences between the manual solution and the automatic gap-filled solution arose from our ability to evaluate preferences among different potential reactions to add based on expert biological knowledge. For example: In some cases, multiple MetaCyc reaction objects describe the same chemical transformation. This is most commonly the case with chemical transformations that are described by both an object denoting a specific reaction and an object denoting a generic reaction that can be instantiated to that specific reaction. For example, one reaction may specifically describe hydrolysis of ATP to ADP and phosphate, while another reaction hydrolyzes NTPs to NDPs and phosphate. This situation can lead to semantically redundant alternative solutions that complicate the user’s task of reviewing and understanding the alternative solutions that may be generated across multiple executions of the gap filler.Lack of an appropriate cytosolic-only electron transfer from NADPH to ferredoxin in MetaCyc caused us to create the new reaction RXN-17897 to satisfy a requirement for reduced ferredoxin in the isoprenoid pathway. The existing MetaCyc activity involved membrane transport as part of the reaction. Manual reaction network curation plays an important role in repairing problems of this kind, since automatic gap-filling methods cannot yet suggest new reaction activities to address network problems.We urge other groups to perform similar analyses to that presented herein for other genomes and for other gap-filling software. Comparison of different gap-filling programs will be problematic unless all programs use the same reference reaction database . However, modifying various programs to use the same reference database may be quite time consuming.B. longum. B. longum was obtained from GenBank record NC_015067.1.The nucleic acid sequence of B. longum sequence was submitted to the KBase microbial genome annotation pipeline for gene finding and protein-function prediction. 2172 genes were identified (2043 protein-coding genes). The resulting annotation was exported from KBase to a GenBank-format file. We did not use the original annotation present in GenBank record NC_015067.1 because the KBase annotation contained significantly more enzyme functions; which annotation is more accurate, we do not know.The B. longum PGDB, BlongCyc. A very strict pathway score cutoff of 1.0 was supplied to PathoLogic to predict into BlongCyc (from MetaCyc) only the pathways that have gene annotations associated with all pathway reactions, to minimize the effects of pathway inference on biomass goal reachability. PathoLogic inference of a metabolic pathway causes all reactions within the pathway to be imported from the MetaCyc database into the new PGDB, including reactions lacking gene assignments — using the 1.0 cutoff means that no reactions lacking gene assignments were imported from MetaCyc during pathway inference. The resulting PGDB was subjected to the following manual refinement steps. That is, some manual refinement occurred before gap filling began.That GenBank-format file  there existed a human-recognizable name match and a match of the first three sections of the EC number between the assignment and MetaCyc, or (b) the best HMMER3 TIGRFAM hit to the sequence of the probable enzyme had a bitscore of higher than 100 and a GO molecular functional annotation corresponding to a MetaCyc reaction.BlongCyc reactions were curated to explicitly specify reversibility to avoid inconsistencies arising from automatic reaction direction inference. Twenty-eight reactions  in which the reaction occurs in one or more pathways. We found that this inference process added a significant degree of unpredictability to reaction directions. We therefore explicitly specified reaction directions in both B. longum biosynthetic metabolism made it especially important to carefully curate routes to NADPH in this work.Consequently, we specified reaction directionality for all reactions involved in the model and propagated these specifications to MetaCyc to improve the quality of subsequent models constructed in PathoLogic. In deciding on reaction directionality and reversibility, we follow the general advice given by Thiele and Palsson : ATP forB. longum was identified through literature research. This research yielded a simple nutrient set ; 53 core biomass metabolites , SAdoMet, UDPNacGlc, and undecaprenyl diphosphate) and 8 fermentative waste products . These metabolites defined the inputs and outputs of the B. longum metabolic model.A minimal set of nutrients, biomass metabolites, and waste products for GenDev — also known as General Development Mode). Technique C is described in detail in [B. longum PGDB from MetaCyc [B. longum PGDB is less than the cost of inserting a new reaction from MetaCyc where B. longum is within the taxonomic range of that reaction, which in turn is less than the cost of inserting a new reaction from MetaCyc where B. longum is outside the taxonomic range of that reaction.We used the MetaFlux module of Pathway Tools (a pre-release version of version 22.0) to perform automated gap filling of the BlongCyc PGDB produced from step (5) above. We used the Technique C variant of the full MetaFlux gap filler , 21 Manual inference from text or EC number in the genome annotationHidden Markov Model (HMM) searches against the genome sequence using TIGRFAMS It took about three weeks to manually gap-fill the reaction network to produce a metabolic model capable of execution by MetaFlux. We employed three main techniques during manual gap-filling to infer the presence of reactions in the metabolic model: The model should successfully reach a basic biomass synthesis objective representing simple metabolic activity at the level of amino acids, nucleotides, lipids, and so onIt should do so while carrying out a recognizable fermentative anaerobic metabolism and maintaining a membrane potentialIt should maintain biochemically sensible reaction direction in regard to redox and phosphorylation processes, avoiding NADP+ reduction by NADH and ATP formation without coupling to an energy-yielding reactionOur manual model gap-filling process was based on the fundamental principle that the genome must encode a complete capacity for self-reproduction within a basic nutritional context and that: B. longum genome.Briefly, the metabolic model was constructed by starting from glucose and working forward through the pathways and reactions to reach the goal metabolites, using the reactions catalyzed by identified genes as a guide. We performed curation of the PGDB to repair model gaps by adding compounds required for reaction instantiation that had been skipped in the automatic metabolite-import process, and in some cases, we curated reactions in both the PGDB and MetaCyc to explicitly specify reaction directionality. In a handful of cases, the reactions deemed necessary for metabolic function could not be associated with genes in the B. longum [We determined the fermentative and transport behavior of the model based on the reported systematic microbiology of . longum . TransmeThe one-carbon folate pathway required transfer of several folate compound instances for proper instantiation, because folate compound instances must all be in the same polyglutamation state to pass through the instantiation process correctly. We have previously observed that PathoLogic can fail to import all folate instances required for the folate pathway instantiation, and we encourage MetaFlux model builders working with instantiated reactions to check carefully that all needed compound instances are present for each instantiated reaction.E. coli [A large number of manually created model reactions were transport reactions involved with fermentation. Indeed, the single cytosolic metabolic reaction we created, RXN-17897, was created to fix a compartmentalization issue in fermentative electron transfer. The protons carried across the membrane by weak acids play a vital role in creating the transmembrane proton gradient, and proton balancing of transport reactions is essential to producing the correct stoichiometric ratios of fermentative products. We have taken a simple approach of co-transporting enough protons to neutralize the charges on weak acids (one proton for monocarboxylates and two protons for dicarboxylates) except for formate, which we allow to pass through the membrane alone based on FocA channel activity in E. coli . ReactioIn this empirical investigation of gap filling of metabolic networks, we compared a manually curated gap-filling solution with a solution obtained by the GenDev software. The solution computed by GenDev contained 12 reactions, but closer examination showed that solution was not minimal; a ten-reaction subset would enable model growth. The failure to produce a minimal solution was due to numerical imprecision. The manually curated solution contained 13 reactions. The two solutions contained eight reactions in common. Based on these results, GenDev achieved recall of 61.5% (the fraction of reactions predicted from the correct solution) and precision of 66.6% (the fraction of predicted reactions that were correct).If the results from this study generalize to other applications of automatic gap fillers, they suggest that although computational gap fillers are populating metabolic models with significant numbers of correct reactions, automatically gap-filled metabolic models also contain significant numbers of incorrect reactions. Our conclusion is that manual curation of gap-filler results is needed to obtain high-accuracy models. Although that statement has been made in other publications, it has not been supported by empirical evidence.We also observed that the manually curated solution contains 30% more reactions (13 reactions) than the minimal automatically gap-filled solution (10 reactions) computed by GenDev, calling into question the minimality objective of gap fillers.B. longum, and reactions that yielded flux rates for specific reactions within the model that were closer to flux rates measured experimentally. Future work could attempt to capture such expert knowledge within a gap filler, which would require specifying information about the organism’s environment and physiology to the gap filler, and modifying the gap-filler objective function to use this information.Some of the differences between the manual and automatic solutions resulted from using expert biological knowledge to direct the choice of reactions within the curated solution, such as reactions specific to the anaerobic lifestyle of Additional file 1B. longum PGDB suitable for loading into Pathway Tools version 22.0 for browsing and exploration. This archived directory tree will expand to a set of files readable by Pathway Tools version 22.0. (ZIP 2472 kb)Curated Additional file 2B. longum metabolic model suitable for execution by Pathway Tools version 22.0. This file defines the nutrients, secretions, and biomass metabolites for execution of the model in conjunction with the B. longum PGDB. (TXT 69 kb)FBA definition file for curated Additional file 3B. longum metabolic model with Pathway Tools version 22.0. (TXT 67 kb)Results of executing the curated


Setaria viridis with extensive gene-reaction associations can accelerate target identification for desired metabolic manipulations and thereafter in vivo validation. Moreover, metabolic reconstructions have also been shown to be a significant tool to investigate fundamental metabolic traits.C4 photosynthesis is a key domain of plant research with outcomes ranging from crop quality improvement, biofuel production and efficient use of water and nutrients. A metabolic network model of C4 “lab organism” Setaria viridis was constructed, which was tested to be able to produce all major biomass components in phototrophic and heterotrophic conditions. Our model predicted an important role of the utilization of NHA mass and charge balance genome-scale metabolic model of Setaria viridis, a model C4 plant, provides the possibility of system-level investigation to identify metabolic characteristics based on stoichiometric constraints. This study demonstrated the use of metabolic modeling in identifying genes associated with the synthesis of particular biomass components, and elucidating new role of previously known metabolic processes.A mass and charge balance model of The online version of this article (10.1186/s12859-019-2941-z) contains supplementary material, which is available to authorized users. Pennisetum glaucum (Pearl millet or ‘Bajra’) and Eleusine coracana (finger millet or ‘Ragi’) have been used in Indian subcontinent , mostly in rural regions as the low cost staple food crops [Zea mays), sugarcane (Saccharum officinarum) and Sorghum of tribe Andropogoneae and bioenergy crop switchgrass (Panicum virgatum) also use C4 photosynthesis [2 into a C4 compound in the mesophyll (M) cells before transporting the C4 compound to the bundle sheath (BS) cells where it is decarboxylated to generate a high CO2 concentration which minimizes oxygenase activity of rubisco [S. viridis uses the NADP-ME  subtype of C4 pathway which is also used by many important C4 crop plants like maize, sorghum, and sugarcane and bioenergy feedstock Miscanthus x giganteus [S. viridis or green millet is a close weedy relative of domesticated Setaria italica (foxtail millet) [S. italica has been used as the model to study bioenergy grasses thus, as a domesticated crop, it is an advantageous biofuel feedstock [S. viridis has some advantages over S. italica regarding its application in biological research like having small diploid genome, short height (30 cm at maturity), shorter harvest time (6-8 weeks) and distinct advantages for forward and reverse genetics and high throughput phenotyping [S. viridis has the potential to obtain similar reputation among researchers as a lab organism for the study of C4 photosynthesis as Arabidopsis thaliana has for C3 plants.Plants belonging to the millet species have been cultivated in many developing countries as the important source of calories. od crops , 2. Besiynthesis , where p rubisco , 4. C4 p rubisco , 6. Thus rubisco , modific rubisco , 9 and t rubisco . Importaiganteus . S. virieedstock . S. viriS. viridis as a tool for C4 systems biological research. GSMs were built in an attempt to explore complex multi-cell interactions of C4 photosynthesis. C4GEM, the first set of genome-scale models of C4 plant metabolism, was utilized to explore the metabolic interactions between two different cell types observing classical C4 photosynthesis and its complex interaction in M and BS cells [S. italica was developed and applied to analyze plant developmental stages and their different levels of regulation [In this study, we constructed a mass and charge balanced genome-scale metabolic model (GSM) of BS cells . RecentlBS cells . A GSM ogulation .S. viridis to study the balancing of protons (H +) and charges in C4 plants. H + gradient across the thylakoid membrane has elemental role in ATP synthesis [+ flow mechanism also serves to prevent photodamage by regulating light capture by the photosynthetic antenna and can also regulate ATP/NADPH output ratio [+ gradients maintained by H +-pumps contributing to plant chemiosmotic circuits [+ gradients, charge balancing has been shown to be important in plants, e.g. anion uptake stimulates cation uptake and translocation, which is used to balance organic anions on nitrate  available from Plant Metabolic Network  as illu version .0 availaReactions in the draft reaction dataset were compartmentalized (placing reactions in different sub-cellular organelles where they are known to occur) into five sub-cellular compartments based on the information from Arabidopsis  and C4 G2+ and photon as well as water, H +, CO2 and O2 exchanges with the environment. Generic ATP consuming and NADPH oxidase steps were also included with suffix ‘_tx’ which can be used to provide maintenance requirements [Ten different external transport reactions (‘_tx’) were included in the model that can supply input nutrients including NOirements . BiomassS. viridis, referred to as Sv3376   using CoS. viridis metabolic model was used to obtain the metabolic reactions and genes involved in M, BS and S cells for the production of cellulose, hemicellulosic polysaccharide XLFG xyloglucan and monolignols in stem, which are the materials used as feedstock for biofuel [Here, we obtained the flux distributions under the modelling constraints shown in Fig.  biofuel , 36. The biofuel  and in c biofuel .H), guaiacyl (G) and syringyl (S) units of the lignin polymer was fixed by simultaneous production of three hydroxy-cinnamyl alcohols namely, coumaryl alcohol (Coumol), coniferyl alcohol (Conol) and sinapyl alcohol (Sinap), respectively. Ratio of these monomers were fixed according to the composition of lignin found in C4 monocotyledon plants [2 to enter through M, form C4 intermediate  that can diffuse to BS and decarboxylate to provide CO2 for the Calvin-Benson (C-B) cycle. In addition to the above constraints, ribulose-1,5-bisphosphate carboxylase (RBC):oxygenase (RBO) ratio in M was set to 3:1 [Our model showed that sucrose from BS to S was capable of being the sole source of energy and C building block in stem for the synthesis of cellulose, hemi-cellulose and lignin. Synthesis of p-hydroxyphenyl  with or without external H + exchanges, where the latter imposes the internal proton balance (P B) condition.To investigate the effect of H S. viridis contains 2473 reactions including external transport and inter-compartmental metabolite exchanges and 2429 metabolites. A total of 3376 unique genes are associated with the reactions and 1597 reactions have at least one gene association. All reactions in the model are balanced in atomic mass and charges, making it a robust system to predict metabolic fluxes with respect to proton balancing. A summary of the number of internal reactions and exchanges (transporters), metabolites and genes in different sections/modules of Sv3376 is given in Table The genome-scale metabolic model of We have tested the model for energy conservation to make sure that 1) no biomass can be produced without any form of energy input; 2) no ATP and NADPH generation without energy input; and 3) no transhydrogenation transferring electrons from NADH to NADPH without energy consumption. In brief, the tests were performed by constraining the model to perform one of the metabolic processes stated above while blocking all energy inputs, e.g. the generic ATPase reaction was constrained in the direction of ATP consumption with all inputs and outputs blocked to test for the presence or absence of ATP generating cycles. After several iterations of simulation and manual curation based on , we were2+, H2O and H + uptake, model was able to produce all biomass components. For testing purposes, simultaneous synthesis of one mol of each biomass component were simulated under these conditions.Sv3376 is able to produce all biomass components under phototrophic and heterotrophic conditions . The multi-tissue model was used to simulate the production of these biopolymers in the stem using the constraints given in Fig. S. italica [Table  italica . Similar italica , 43.FigB constraint was relaxed, i.e. with allowed exchanges of H + from M and BS to outer environment (data not shown). Moreover, the scenario of relaxed P B constraint required more photon through BS than M unlike the high photon demand in M compared to BS for the simulations under P B  influenced the model predictions on the metabolite shuttles between M and BS cells, demonstrating a previously unnoticed role of the 3-PGA/DHAP shuttle in balancing the utilization and production of protons, and possibly oxygen flux, between M and BS cells.The flux distribution in M and BS under the constraints of producing lignocellulosic biomass Fig.  utilized B Table . InteresS. italica was developed using a C4 plant specific metabolic model framework, C4GEM, [S. italica model was used to study different metabolic characteristics in young and mature stem/leaf phytomers by integrating multi-omics data. The S. italica reconstruction was mainly used to develop annotation and multi-omics protocols for systems analysis which is also applicable to our S. viridis metabolic model to observe many C4 metabolic traits using ‘ideal lab organism’, similar to how A. thaliana has been used to study C3 plants [B constraint, lignocellulose gene mapping and biomass production. Prior to this study, a mass and charge balanced maize (Zea mays) genome-scale metabolic model [S. viridis genome-scale metabolic reconstruction is available that merits potential for direct comparison.Recently, a genome-scale metabolic model of , C4GEM,  as an in, C4GEM, . The S. 3 plants  was on iic model  was deriic model  and otheic model . HoweverS. viridis accompanying with modern computational and experimental techniques has the potential to improve C4 engineering that is directly related to improving crop and biofuel production [S. viridis can be a useful tool for identifying target genes for achieving several desired metabolic actions as demonstrated by our model’s ability to predict genes involved in the biosynthesis of individual biomass components .The mass and charge balanced Sv3376 favors the use of both NH process . This besupplied . The usef fruits  and presB constraint where PSII activity was lower in BS than in M  could impose a stoichiometric constraint in reducing PSII activity in BS. It would be interesting to test if the same applies to other C4 subtypes.In NADP-ME subtype of C4 species,  observed2 assimilation. Thus, in the condition of balancing in internal H + production and consumption, we observed a division of labor where M was mainly utilized for energy generation and BS was used for CO2 (re)fixation with reduced activity of some enzymes for better utilization of enzymatic machinery. For instance, flux distribution in BS plastid shows a significant reduction in the flux from H + consuming reactions , whereas plastidial ATP synthase activity was also reduced generating reduced amount of ATP and H + in BS. Thus, to satisfy the energy demand, photon influx in M was higher than BS, which may coincide with the evolution of Kranz anatomy in C4 leaves.Lower PSII activity can limit the production of reduction equivalents in BS and necessitates the shuttling of 3-PGA/DHAP to supply NADPH for COOur model highlighted the requirement of 3-PGA/triosephosphate shuttle between M and BS under proton balance condition. This 3-carbon sugar phosphate shuttle is known to have a role in the net transfer of reducing power between M and BS and might be able to control energetic load on mesophyll chloroplast . Metabol+ transport mechanism in the model. In this scenario, H + exchanges directly from Ext to M and BS were blocked  and two new transporters were temporally added from stem to bundle sheath and from bundle sheath to mesophyll (S ⇔BS⇔M). With these modifications, the model preferred to use H + transport in the direction from M to BS in place of the 3-PGA/DHAP shuttle  was also inactive and similar photon was utilized as original model . Reactions, metabolites, chemical formulae, pathways, EC numbers and gene association of reactions. (XLS 1727 kb)Genome-scale metabolic model of Additional file 2S. viridis comprising leaf and stem tissues. Multi-tissue version of Sv3376 to simulate C4 photosynthesis. (XLS 3944 kb)Multi-tissue metabolic model of Additional file 3Biomass production using Sv3376 under phototrophic and heterotrophic condition. One mol of each biomass production in phototrophic and heterotrophic condition under allowed and blocked proton. (XLS 131 kb)Additional file 4Setaria viridis leaf biomass. (XLSX 14 kb)Leaf biomass composition. Biomass proportions used to simulate the production of one gram of Additional file 5B and both nitrate and ammonium, ii) with P B constrained and ammonium as sole N source and iii) with P B constrained and nitrate as sole N source. Biomass production using Sv3376 for different N sources. Flux distributions for the production of one gram leaf biomass i) with P Additional file 6Genes expressed in stem. Different set of genes expressed in stem for the production of cellulose, hemi-cellulose and lignin. These sets represent the genes which are common and/or unique to different biomass production. Phytozome  database identifiers are included for these genes. (XLS 135 kb)Additional file 7Reactions activated in stem. Different set of reactions in stem for the production of cellulose, hemi-cellulose and lignin. These sets represent the reactions associated with the genes  which are common and/or unique to different biomass production. (XLS 43 kb)Additional file 8Flux distributions for the production of cellulose, hemi-cellulose and lignin. Flux solutions obtained using the multi-tissue model for the production of cellulose, hemi-cellulose and lignin in stem. (XLSX 24 kb)Additional file 9Flux distributions under modified proton transport mechanism between M, BS and S. Flux solutions obtained when proton transport mechanism temporarily modified in the multi-tissue model. Two flux solutions provided: proton and 3-PGA/DHAP shuttle allowed between M and BS and when both exchanges were blocked. (XLS 68 kb)


Caenorhabditis elegans have been published, each having unique features. We have established the WormJam Community to merge and reconcile these (and other unpublished models) into a single consensus metabolic reconstruction. In a series of workshops and annotation seminars this model was refined with manual correction of incorrect assignments, metabolite structure and identifier curation as well as addition of new pathways. The WormJam consensus metabolic reconstruction represents a rich data source not only for in silico network-based approaches like flux balance analysis, but also for metabolomics, as it includes a database of metabolites present in C. elegans, which can be used for annotation. Here we present the process of model merging, correction and curation and give a detailed overview of the model. In the future it is intended to expand the model toward different tissues and put special emphasizes on lipid metabolism and secondary metabolism including ascaroside metabolism in accordance to their central role in C. elegans physiology.Metabolism is one of the attributes of life and supplies energy and building blocks to organisms. Therefore, understanding metabolism is crucial for the understanding of complex biological phenomena. Despite having been in the focus of research for centuries, our picture of metabolism is still incomplete. Metabolomics, the systematic analysis of all small molecules in a biological system, aims to close this gap. In order to facilitate such investigations a blueprint of the metabolic network is required. Recently, several metabolic network reconstructions for the model organism  Caenorhabditis elegans is emerging as a key resource for the study of metabolism in multicellular organisms, as while it shares much of its central metabolic pathways with humans, it is easy to culture in laboratory conditions, can be grown in large populations of isogenic individuals in order to study purely environmental differences, and has a short life span enabling rapid longitudinal data acquisition even across multiple generations , but this is continuously evolving, and the estimated size of the full metabolome under ordinary conditions may be even > 10,000 distinct molecules based on recent metabolomics work uncovering new metabolites  and its derivatives permit the use of whole-genome reconstructions together with experimental molecular phenotypes and biological objective functions in order to obtain optimal fluxes landscapes at steady-states . We chose to work with the WormBase gene identifiers (WBGeneXXXXXXXX) for the sake of their simplicity in parsing and formatting, and accompanying ease of access to the online WormBase database  and parsed through the reactions in the second model . RC is the total number of reactions including duplicates in both the models. We performed the following steps on each reaction  from the first model:For reactions, we employed a script that does the following steps to identify whether the reactions being compared are the same. All used scripts are available from stoichiometry of 1+1 to RC reactions)  coming from the second model.If the gene-reaction association is the same, remove the reaction (r2) coming from the second modelIf the gene-reaction association is different, append the gene rules in the first model using an OR rule and add the relevant gene associations to the gene-reaction association matrix of the first model, then remove the reaction  again.Ensure that in-model meta information is consistent. The in-model reaction meta information is copied from the source model of the reaction; for e.g., if RXNA  in the second model and is identified as a duplicate of RXNB  in the first model, all in-model meta information will be set to the reaction values from the second model.Check the stoichiometry after removing protons to identify if the reactions are the same but have different charge/element balance .In certain cases, only charged or neutral structures were available in the databases, so the corresponding missing structure was then also drawn in MarvinSketch 18.1.0. All structures missing in ChEBI were submitted via the batch submission tool to assign new ChEBI identifiers  in Microsoft Excel 2016. To define cut-offs for structural similarity to identify potential reaction pairs, Tanimoto similarities were calculated from known reaction pairs from the WormJam consensus model.http://cts.fiehnlab.ucdavis.edu/) from the Fiehn lab was used to retrieve secondary identifiers from different databases  by the InChIKey if missing. All spectra from MassBank of North America  were downloaded and sorted according to type: LC-MS, GC-MS, CE-MS, in silico and others. InChIKey and SPLASH IDs for each spectrum together with the compound name were isolated for comparison against predicted metabolites .The first public release of the reconstruction, as described in the current paper can be accessed from BioModels  and KEGG to map common gene names (nomenclature used in the models) to WormBase gene identifiers. We chose to work with the WormBase gene identifiers (WBGeneXXXXXXXX) for the sake of their simplicity in parsing/formatting, and ease of access to the online WormBase database  and 1537 genes (GC) and 3878 reactions (RC).The above processing resulted in versions of ElegCyc and iCEL1273 with annotations in the same format including their in-model meta information . Identification of metabolites (M) and genes (G) were followed by performing a merge such that MCycCEL) and 1537 genes (GCycCEL) and 3267 reactions (R'CycCEL), with unique lists of gene, metabolites, and reactions with their respective in-model meta information  on its own , maoc-1 (WBGene00017123), dhs-28 (WBGene00000991), and daf-22 (WBGene00013284), these long chain ascarosides are broken down in the form of CoA thioesters to shorter versions  and very long chain (VLC) fatty acids, which are either ω- or ω-1-hydroxylated and attached to ascarylose. In several rounds of peroxisomal β-oxidation, involving the genes All metabolic reconstructions developed so far did not contain this biosynthetic pathway, as no corresponding human pathway exists. We have added this pathway by manually curating data from different publications. In a similar fashion, structures of ascaroside-CoA thioesters where drawn and their charged version (−4) was used to construct the peroxisomal β-oxidation pathway. Additionally, hydrolysis reactions to free the individual ascarosides have been added together with export reactions for the extracellular export.acox-1, maoc-1, dhs-28, and daf-22 in the biosynthesis has been established, which work together for the peroxisomal beta-oxidation of long and very long chain fatty acid versions of ascarosides. Experiments using axenic media have shown that C. elegans is still able to produce ascarosides without the presence of bacteria. Therefore, ascarylose biosynthetic genes must be present in C. elegans. The exact biosynthetic pathway is not known yet, there are some hints that ascaroside biosynthesis is distinct from the dTDP-rhamnose biosynthesis  representing the major microspecies at a given pH (mostly 7.3 in the cytosol) are required for stoichiometrically correct model representation. This approach is also chemically accurate, since acetate is not acetic acid, they are two different molecules and therefore cannot have the same identifier. However, metabolomics scientists who would like to map their results to metabolic pathways in the model are accustomed to working with neutral formulas and molecules, and directly using charged formulas from the metabolic model to calculate m/z ratios of different adducts leads to incorrect results. In the WormJam consensus model we are using ChEBI as primary source for the structures of charged and uncharged molecules for structural identification. ChEBI represents a rich data source with established chemical ontology relationships to link charged and uncharged variants of different molecules. Therefore, it is essential to also supply the correct neutral form of a molecule that can be used in metabolomics for annotation of signals.We have added chemical structures encoded as InChIs for each metabolite, where possible. Several metabolites represent generic structures, e.g., “Ceramide” containing an R group for different acyl chain lengths. In such cases we report only the formula containing the R group.Curation of metabolites from C. elegans metabolomics studies).In several cases either the neutral or charged version of the molecules were missing in ChEBI. These have been drawn manually in MarvinSketch 18.1.0 and structures were submitted via the batch submission tool to ChEBI. In total we have submitted >500 new metabolite structures either from the model or the curation of metabolites from literature  and Glycine (CHEBI:15428) were the most frequently detected metabolites, with each being detected 30 times. However, multiple detection and identification have to be handled with great care, since confidence scores or experiments for identification were not always given. It might also happen that wrong annotations spread across several papers once it has been assumed to be positively identified.Different analytical techniques (and combinations thereof) were used for analysis of the worm metabolome. Most studies used NMR (14 publications) or NMR in combination with GC- or LC-MS , followed by LC-MS (9 publications) and GC-MS (5 publications) alone. Furthermore, for lipid analysis, shotgun lipidomics was employed several times. Several metabolites were detected with different techniques, which might increases the confidence of the different identifications. Thirty seven percent of the metabolite structures were detected at least twice, <5% ten times and more. Glutamic acid , but allows a fairer comparison of the predicted and detected metabolites by ignoring stereochemistry. Three hundred eighty-two metabolite entities overlapped between the model and the detected metabolites , however this might also act as arginine kinase. This enzyme was expressed at a higher rate, together with muscle related proteins, in daf-2 worms  are not present in the model. Currently, only two publications have detected a C30:0 fatty acid . Spectra were sorted into LC-MS, GC-MS, CE-MS, in silico and others (no method available in metadata). Metabolites from the WormJam model were used for the search.Correct identification of metabolites from non-targeted metabolomics plays an important role for biological interpretation and relies on the availability of reference standards and reference spectral libraries. Therefore, we checked the availability of tandem MS spectra in MassBank of North America . However, for future metabolite annotation and identification in Although many metabolites have been detected, so far only a few papers report absolute concentrations of known substances. One particular example is presented by Gao A. W. et al. . ResultsC. elegans metabolic model to date, the task is by no means completed. The accuracy of the metabolic reconstructions is not uniform across biochemistry. For example, the metabolism of carbohydrates and peptides is well-described, but the coverage of nucleic acids and lipids can be improved. The number of different compartments is limited, and in particular some organelles featuring very specific biochemistry, such as lysosomes and peroxisomes, are not explicitly represented. Moreover, C. elegans is a multi-cellular organism interacting with a complex environment, and its cellular metabolism cannot be understood in isolation.While the current WormJam reconstruction is a good consensus between existing efforts, and the most accurate C. elegans involves maintenance on three possible Escherichia coli strains OP50, HB101, and HT115. Dietary  and nutritional changes have been known to alter health, lifespan . Thus, integration of diet is of particular relevance with respect to the utilization of C. elegans on E. coli OP50 as a model system for microbiome host-interactions in the context of the influence of the microbiome on the efficacy of pharmaceutic therapies . Here identifications might be not correct. Different levels of identification have been proposed by the Metabolomics Standard Initiative (MSI), which should be used to report confidence .We have shown that there is discrepancy between the model metabolites and metabolites detected by different metabolomics approaches. Specific metabolites from the WormJam model have not been detected so far. Although several are simply not stable enough or have a high turnover rate will be probably never be detected, others might be not accessible with current approaches to low concentrations. On the other side, many detected and reported metabolites could not be found in the model. This is of major interest, since either the identifications are wrong or the model is incomplete. Several examples shown in this paper highlight that we might actually miss several aspects in the metabolism and biology of MWi curated the sphingolipid metabolism, metabolite structures, and metabolites detected in the literature. MWi and FS created an initial draft for the ascaroside biosynthesis pathway. MWa and MvW curated the fatty acid metabolic pathways. AG, MvW, and RH helped with metabolite curation from literature. JPNH created WormCon with the advice of H-JS, PE, and CK, and wrote the relevant manuscript sections on WormCon. H-JS assisted in the development of WormCon, curation of metabolic pathways. PE assisted in the development of WormCon, curation of metabolic pathways and editing the manuscript. CJ, SS, and NL performed the merging of ElegCyc and iCEL1273. JPNH, H-JS, PE, and CK performed the merging of CeCon and ElegCyc. JH, NR, AM, OC, MWi, and NLN performed model validation and have supervised and overseen the manual curation process. All authors wrote and edited the manuscript.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.


Constraint-based modeling has been applied to analyze metabolism of numerous organisms via flux balance analysis and genome-scale metabolic models, including mammalian cells such as the Chinese hamster ovary (CHO) cells—the principal cell factory platform for therapeutic protein production. Unfortunately, the application of genome-scale model methodologies using the conventional biomass objective function is challenged by the presence of overly-restrictive constraints, including essential amino acid exchange fluxes that can lead to improper predictions of growth rates and intracellular flux distributions. In this study, these constraints are found to be reliably predicted by an “essential nutrient minimization” approach. After modifying these constraints with the predicted minimal uptake values, a series of unconventional objective functions are applied to minimize each individual non-essential nutrient uptake rate, revealing useful insights about metabolic exchange rates and flows across different cell lines and culture conditions. This unconventional uptake-rate objective functions (UOFs) approach is able to distinguish metabolic differences between three distinct CHO cell lines  not directly observed using the conventional biomass growth maximization solutions. Further, a comparison of model predictions with experimental data from literature correctly correlates with the specific CHO-DG44-derived cell line used experimentally, and the corresponding dual prices provide fruitful information concerning coupling relationships between nutrients. The UOFs approach is likely to be particularly suited for mammalian cells and other complex organisms which contain multiple distinct essential nutrient inputs, and may offer enhanced applicability for characterizing cell metabolism and physiology as well as media optimization and biomanufacturing control. Efficient application of genome-scale metabolic models for mammalian cells can be challenging due to the large number of restrictions posed on inputs including essential amino acid uptake rates. To overcome these limitations, a team led by Michael Betenbaugh at Johns Hopkins University estimated the essential amino acid inputs for Chinese hamster ovary (CHO) cells from readily measured growth rates. These predictions are then combined with the implementation of an unconventional approach for solving metabolic models based on minimization of uptake rates. Solutions predicted by this approach successfully distinguished metabolic differences between CHO cell lines that are not directly observable using conventional approaches and managed to identify the correct cell line from metabolic flux data. Implementation of this systems approach will enable users to better utilize genome-scale models of mammalian cells for improved understanding and control of biotechnology processes. Besides a value of the optimized objective function, the resulting solution also provides information about intracellular fluxes within the system.2 A conventional objective function often used for biological entities is maximization of the growth rate, known as the biomass objective function (BOF), giving the underlying assumption that the “goal” of an organism is to maximize its reproduction, from a perspective of adaptive evolution.3 This optimization approach has been well-studied and validated for many prokaryotic organisms such as Escherichia coli5 and B. subtilis.7 However for a more complex metabolic system such as mammalian cells, fewer successful constraints-based and FBA-related models have been published.8 Chinese hamster ovary (CHO) cells represent the most widely used host cell for therapeutic recombinant protein production and have been gaining increased attention for in-silico modeling to better understand the metabolism. Prior to the development of CHO genome-scale models, constraint-based modeling work done on CHO cells included studies using metabolomics and FBA to investigate key metabolism such as energy consumption and lactate production,10 using a non-specific mammalian cell genome-scale model and Mus musculus metabolic model.Constraint-based genome-scale models and flux balance analysis (FBA) have been widely used to investigate metabolic systems of various organisms. By connecting genotype to phenotype, genome-scale metabolic models (GeM) provide detailed information about biochemical reactions networks that compose cellular metabolism.11 The model was validated by predicting growth rates using sets of metabolic flux data from the literature, and was then applied to study the tradeoff between growth and recombinant protein production.11 The published CHO GeM has demonstrated its value in facilitating the studies of CHO metabolism. For example, one study tailors the generic CHO GeM into host and recombinant cell-specific models and integrated with multi-omics data to understand the differences of genotypic and phenotypic traits between wild-type and recombinant CHO cells.12 Another study perturbed the constraints of a CHO GeM to mimic the variation of medium composition and found that CHO cells stop growing when CHO-specific essential amino acids availability decreases, and limitations in non-essential amino acids can be overcome by enhancing amino acid biosynthesis reactions.10 Besides understanding intracellular physiology and predicting metabolic engineering consequences, constraint-based models can be useful for other applications such as model predictive control,15 for various organisms including yeast and mammalian cells.19A recent CHO-specific genome-scale model contains information on 1766 genes, 6663 reactions, and has led to the generation of three cell line-specific models .Computational models are useful tools typically because of their capability to describe multiple or hard-to-measure outputs from fewer or easy-to-measure inputs. However, current constraint-based modeling approaches do not fully exploit the value of detailed metabolic models, in particular for mammalian cells with complex, numerous and distinct nutrient inputs. Although intracellular fluxes can be estimated, required inputs are considerable and may be challenging to quantify rapidly. These represent some of the principal difficulties in extending constraint-based models to mammalian cell bioprocesses, eliciting the need for a modeling approach specifically tailored for mammalian cells.14 which can be useful for bioreactor monitoring and control. In this study, we introduce an unorthodox FBA approach based on a set of uptake-rate objective functions (UOFs), which utilizes the measured growth rate as a constraint and independently minimizes the uptake rate of each individual non-essential nutrient. We demonstrate that the UOFs approach reveals insights concerning metabolic differences between mammalian cell line variants not evident from traditional BOF methodologies. Furthermore, sensitivity data derived from the UOFs solution provides a direct visualization of metabolic relationships between nutrients in the networks, providing enhanced characterizations of CHO physiology with applications ranging from cell line evaluation, metabolic engineering to media optimization and biomanufacturing control.In particular, mammalian cell growth predictions by FBA suffer from a significant complication due to the input requirement of numerous essential amino acids exchange fluxes as part of the constraints. Even slight disagreement between these uptake rate constraints and biomass composition in the model can result in optimization solutions being overly restrictive or even dictated by a single or a few potentially underestimated essential amino acid uptake rates. However, direct estimation of these essential amino acid uptake inputs is possible based on measured growth rates and a “essential nutrient minimization” (ENM) approach which solves for the absolute minimal consumption requirements. These rate estimations can be used to adjust the FBA constraints in order to resolve problematic mass balance constraints. Also, they can be transformed into real-time concentration predictions via a static optimization approach,20 Reported cell-density specific exchange rates of each replicate were converted to dry-weight specific rates assuming cell dry weight equaling 216.1 pg/cell.11 The FBA-predicted growth rates using metabolomics data of all the seven replicates as well as a prediction using all averaged flux data were compared against experimental measurements as illustrated in Fig. We initially demonstrated how the presence of essential amino acids can exert a negative impact on the FBA of a mammalian cell model due to their values being rate-limiting factors for the conventional BOF, using a case study containing published CHO-K1 specific growth rates, 23 metabolites production and consumption rates for 7 cell culture replicates.In order to elucidate which metabolites or fluxes limit the growth prediction for each individual replicate, we evaluated the dual price  of each metabolite for the BOF, which indicates how maximized growth rate changes in response to increasing the flux value of a particular metabolite under pseudo steady-state conditions. Shown in Supplementary Table To illustrate how predictions are biased by deviation in the lysine and histidine flux measurements, the growth rates were predicted with individual lysine and histidine flux constraints replaced by the replicate average. Averaged lysine or averaged histidine fluxes both result in increases of uptake flux constraints and growth rate predictions for multiple replicates see Fig. , in whicGiven that essential amino acids can independently control the final FBA solution as essential elements of the BOF, it is possible that these amino acids can be rate-determining factors of cell growth. Since essential amino acid uptake rates may be directly related to growth, their consumption rate values can be estimated by finding the uptake requirements needed to sustain the observed growth rates, and one way to evaluate this approach is to compare measured amino acid uptake rates to model-predicted levels. Therefore, we began by revisiting the standard BOF and instead implementing a minimization approach in which the cells are assumed to incorporate nutrients at the minimal uptake rates with respect to the growth rate. This inversion of the objective function can provide a useful strategy to address the challenges in estimating the utilization rates for essential amino acids and other metabolites and eventually reduce the model inputs for FBA.22 These growth and metabolomics datasets collected for various culture conditions were originally used to validate the CHO GeM.11 Shown in Fig. 11 Minimal amino acid flux predictions match closely to the experimental data except for phenylalanine and threonine, and among the two, the measured threonine uptake is much lower than prediction and has the same level of error as growth prediction, meaning that the growth prediction is directly dictated by the low measured threonine uptake flux for this particular case.First of all, one can solve for the “essential minimal” nutrient uptake rates for a particular growth rate after unbounding all nutrient uptake rates in order to permit unrestricted consumption of other nutrients while constraining growth and protein productivity, if available Fig. . The obj11 Specific productivity was assumed unchanged to be the model’s “default number”, originally measured in another study.9 Since the flux magnitude through recombinant protein production is relatively small compared to the flux through biomass function, productivity does not have a significant impact on flux prediction results for this model. Flux predictions for the eight measured essential amino acids  obtained by this approach agree with the experimental values for all cases  were minimized individually one at a time. Measured growth rates, IgG productivity and all measured metabolite exchange rates (except for the one to solve for) were set as constraints. Essential amino acid exchange inputs were corrected with the ENM-predicted uptake rates  and furthermore provides enhanced sensitivity in predicting insights into metabolic variability as described below.Nonetheless, this rate prediction approach can refine existing problematic constraints for FBA by preventing mass balance conflicts between constrained growth rates and essential nutrient exchange fluxes. This enables the implementation of the alternative UOFs objective function described here involving minimization of the uptake rate of non-essential nutrients. Previous studies have examined different objective functions that are potential candidates for representing the metabolic goal of organisms and considered selection of minimizing substrate utilization. Knorr, Jain, and SrivastavaIndeed, for a network including “macro-reactions” such as biomass generation which requires a combination of multiple elements such as energy sources and building blocks for protein, minimizing individual elements is distinct from maximizing biomass generation and is more capable of demonstrating metabolic differences between networks. This minimization approach takes into account the availability and excess of each single element and the metabolic connections among them, while classic maximization solutions may ignore some of these. As a simple example, FBA problems for 2 different hypothetical networks shown in Fig. Such a difference indicates the UOFs to be a more suitable choice for selecting cell lines or clones by providing information about nutrient consumption efficiency and, potentially, viability in specific media environments. From the perspective of intracellular flux analysis, the FBA-derived flux profile is likely to be reliable only if the optimized objective function is consistent with the experimental data. Compared to BOF, linear program solutions based on UOFs are more sensitive to “system-level” variations, not only because UOFs calculate every single uptake flux, but also due to the reason that the BOF optimization does not consider other additional fluxes that do not contribute or detract from to the optimal solution of biomass generation . Thus an accurate prediction by UOFs may be more reliable for intracellular flux analysis than one obtained from a BOF. This advantage of being more sensitive increases the capability of identifying cell line variants from metabolomic flux data, leading to increased potential to obtain physiological or genomic insights from metabolomics data. However, the selection between BOF and UOFs approach is a trade-off between sensitivity and flexibility, where the UOFs may strictly necessitate certain measurement inputs as constraints which may not be required by the BOF to generate a solution. Moreover, the fact that UOFs uses growth rate as a constraint enables a robust analysis of intracellular flux profiles when the realistic cell growth rates can be reliably measured. The biomass generation reaction (growth rate) is the most important factor in FBA models which often drives the intracellular flux distribution since this reaction involves the greatest number of metabolites and its value largely determines the overall nutrient consumption and energy generation requirements. As mentioned before, BOF predictions may exhibit challenges in cases where nutrient constraints limit the range of possible growth solutions and hence lead to varied intracellular flux predictions. In contrast, the UOFs approach fixes growth rates as constraints; in cases where the uptake rate of a nutrient is inaccurately predicted, the impact on the intracellular flux profile may be more restricted to fluxes within that particular nutrient and its derivatives. Thus, the UOFs method is likely to still generate reasonable flux profiles for many of the metabolites involved in cell growth as long as the growth estimates are reliable.30 This sensitivity data will also carry information regarding the energetics of metabolism.31 Dual prices calculated based on UOFs allow researchers to visualize the sensitivity of a metabolite uptake requirement with respect to changes in availability, providing useful information about metabolic relationships between metabolites such as inter-conversion, nutrient substitution as well as cost-benefit responses to metabolite pool perturbation. A previous study calculated the cost of synthesizing intermediates of glucose/glutamine consumption in hybridoma cells under different oxygen availability, by minimizing glucose/glutamine uptake rates after fixing glutamine/glucose exchange flux to minimum flux needed for biosynthesis and removing the catabolic pathways of essential amino acids.32 However, these sensitivity data were generated with artificial exchange constraints that will affect the optimization results and the optimization was not validated by experimental measurement, thus these values may not represent the actual metabolic cost of metabolites in hybridoma cells. Also, ignoring the catabolism of essential amino acids does not permit analysis of cases in which essential amino acids are over-consumed as shown in Fig. Dual prices provide information on how the objective can increase/decrease relative to the change in a specific factor. In FBA, dual prices are commonly used to analyze the sensitivity of growth in response to a metabolite pool change and identify growth-limiting factors.33 due to the fact that methionine catabolism in mammalian cells demands serine and ATP.34The results in Fig. As a result, this study introduces an alternative approach to predict the metabolic characteristics and performance for complex systems such as mammalian cells, for which conventional FBA approach are limited due to multiple overly restrictive or conflicting constraints. Prediction of essential amino acid consumption through the ENM approach prevents problematic rate-limitations by ensuring consistency between flux constraints and biomass composition, making our non-traditional UOFs approach feasible. The UOFs approach improves the capabilities and sensitivity of mammalian FBA with the underlying dual prices providing additional information about nutrient consumption, metabolic variations, and differences across cell lines. In addition, straightforward estimation of hard-to-measure amino acid concentration data from easy-to-measure cell counts and recombinant protein productivity may also enhance optimization of biomanufacturing  in incubators operating at 37 °C and constant 5% CO2 level. Direct mixture of two chemically defined media purchased from GE HealthCare Life Science and MilliporeSigma were used to generate different media compositions. 6 mM of glutamine was supplemented to the media before using. Culture aliquots were collected daily for analysis. Viable cell density was counted using hemocytometer and cell viability was estimated via trypan blue staining method. Glucose and lactate levels were measured using a YSI 2700 D select biochemistry analyzer (Yellow Spring Instruments). Concentrations of alanine, glycine, valine, leucine, isoleucine, proline, methionine, serine threonine, phenylalanine, aspartate, glutamate, lysine, glutamine, and tyrosine were measured using a GC-MS based method as described in a previous publication.35A CHO-K1 suspension cell line provided by National Institute of Health was used to perform amino acid consumption study. CHO cells were seeded at 0.3 × 10Nx,0 is the number of cells (counted in millions of cell) at initial time, Nx is the number of cells after culture time t (hour), and μ is the specific growth rate (1/hour). Specific growth rates were estimated by fitting the time and cell counts data to the exponential equation , ΔCi (mmol/L) is the concentration difference of metabolite i between two time points . Specific exchange rates were converted to genome-scale model inputs, in the unit of millimole per gram dry weight per hour with an assumed cell dry weight.Growth rates of CHO cells were assumed to follow exponential growth behavior:37 was used to conduct constraint-based modeling studies, running in MATLAB 2016b environment (The MathWorks Inc.). CHO global and cell-line specific genome-scale models (available from http://bigg.ucsd.edu/ and11) were used to perform analysis.COBRA toolbox v3.030 Such kind of dual problems study the marginal worth of a specific resource with respect to the optimization target. For FBA problems in this article, the dual price (λi) of a specific uptake rate (ri) can be defined by the following formula:Z is the objective function for specific problems, which is, growth rate for BOF and non-essential nutrient uptake rate for UOFs. Dual prices in Fig. In linear programs, dual price, also known as shadow price, is defined as the change in objective function as a result of a unit incremental change of a specific constraint.mentclass2pt{minimFurther information on research design is available in the Supplementary Information.Supplementary Data.Reporting Summary