Phaeodactylum tricornutum to changing atmospheric carbon concentrations on an ocean-wide scale. By integrating an available genome-scale metabolic model and a newly developed transcriptional regulatory network inferred from transcriptome sequencing expression data, we demonstrate that carbon metabolism and nitrogen metabolism are strongly connected and the genes involved are coregulated in this model diatom. These tight regulatory constraints could play a major role during the adaptation of P. tricornutum to increasing carbon levels. The transcriptional regulatory network developed can be further used to study the effects of different environmental perturbations on P. tricornutum’s metabolism.Using a systems biology approach, we studied the response of the marine diatom  Phaeodactylum tricornutum to explore the connectivity of the regulatory network and shared metabolites. The integrated regulatory and metabolic model revealed highly connected modules within carbon and nitrogen metabolism. P. tricornutum’s response to rising carbon levels was analyzed by using the recent genome-scale metabolic model with cross comparison to experimental manipulations of carbon dioxide.Diatoms are eukaryotic microalgae that are responsible for up to 40% of the ocean’s primary productivity. How diatoms respond to environmental perturbations such as elevated carbon concentrations in the atmosphere is currently poorly understood. We developed a transcriptional regulatory network based on various transcriptome sequencing expression libraries for different environmental responses to gain insight into the marine diatom’s metabolic and regulatory interactions and provide a comprehensive framework of responses to increasing atmospheric carbon levels. This transcriptional regulatory network was integrated with a recently published genome-scale metabolic model of IMPORTANCE Using a systems biology approach, we studied the response of the marine diatom Phaeodactylum tricornutum to changing atmospheric carbon concentrations on an ocean-wide scale. By integrating an available genome-scale metabolic model and a newly developed transcriptional regulatory network inferred from transcriptome sequencing expression data, we demonstrate that carbon metabolism and nitrogen metabolism are strongly connected and the genes involved are coregulated in this model diatom. These tight regulatory constraints could play a major role during the adaptation of P. tricornutum to increasing carbon levels. The transcriptional regulatory network developed can be further used to study the effects of different environmental perturbations on P. tricornutum’s metabolism. DIC is a combination of CO2, HCO3, and carbonate. The relative amounts of the three DIC species are set by the pH. At modern seawater pHs, the most dominant form of DIC is HCO3. Under bloom conditions, the pH increases, resulting in a rising carbonate content but also a lower total DIC content. Under ocean acidification conditions, there is a higher total DIC level but also the percentage of CO2 increases, essentially resulting in ocean carbonation. Overall, future atmospheric increases can be expected to facilitate higher CO2 diffusive uptake through decreased pH and active HCO3 uptake through increased total DIC.Here, we investigated the metabolic response of sporters . Rising 2 levels. Here, we exploited a genome-scale metabolic network recently developed for the model diatom P. tricornutum to understand its metabolic response to rising CO2 concentrations  inferred from transcriptome sequencing (RNA-Seq) data in order to gain a comprehensive understanding of the interconnection between metabolic and regulatory mechanisms that could drive the adaptation to increased CO2 concentrations.Within this study, the genome-scale metabolic network for P. tricornutum that allows detailed insights into its physiology and provides a framework to analyze and predict genotype-phenotype relationships  and the reaction catalyzed by one of the genes and the corresponding information in the genome-scale model (right) are shown. The TRN consists of coexpressed genes and experimental conditions organized into biclusters. The metabolic network contains information about the metabolic reactions and the gene products (GPRs) by which they are catalyzed. Both networks interact via the metabolic genes. By using the information included in the genome-scale model, subsystems are associated with the genes in the TRN. Download Copyright © 2017 Levering et al.2017Levering et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the 2 or iron levels , as well as whether they are enriched in genes involved in carbon and/or nitrogen metabolism, are listed. Download Copyright © 2017 Levering et al.2017Levering et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the 10.1128/mSystems.00142-16.2TABLE S2 TABLE S2, XLSX file, 0.5 MB.Annotations associated with the regulon for each cluster. For each cluster, the genes and the reaction association and annotation , as given in the genome-scale model, as well as the Ensembl or NCBI database (for genes located on organelle genomes) annotation, are listed. Download Copyright © 2017 Levering et al.2017Levering et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the 10.1128/mSystems.00142-16.3TABLE S3 TABLE S3, XLSX file, 0.02 MB.Abbreviations used for the experimental conditions in Table S1. Download Copyright © 2017 Levering et al.2017Levering et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the P. tricornutum. To investigate this strong correlation between carbon metabolism and nitrogen metabolism more precisely, we performed a GO enrichment analysis and associated each significant GO term with carbon or nitrogen metabolism. By using the subsystems given in the model, genes associated with reactions involved in amino acid metabolism, nitrogen metabolism, nucleotide metabolism, or the urea cycle were categorized into nitrogen metabolism. Genes associated with reactions involved in aldehyde degradation, ascorbate metabolism, butanoate metabolism, the Calvin-Benson cycle, carbon fixation, galactose metabolism, nucleotide sugar metabolism, oxidative phosphorylation, photosynthesis, pentose interconversions, the pentose phosphate pathway, or pyruvate metabolism were categorized as carbon metabolism. Genes associated with reactions involved in the tricarboxylic acid cycle were classified as both carbon metabolism and nitrogen metabolism. On the basis of this mapping, 48 clusters were enriched or purified in genes involved in carbon metabolism and 40 clusters contain enriched or purified genes taking part in nitrogen metabolism. Twenty-two clusters are enriched in genes involved in both carbon metabolism and nitrogen metabolism. Of the 18 clusters containing nitrogen but not carbon metabolism genes, 9 are not enriched in genes belonging to any other subsystem, 1 is also enriched in genes involved in transport, 1 is also enriched in genes belonging to glycan metabolism, 3 are also enriched for genes involved in cofactor metabolism, and 4 also contain enriched or purified genes involved in lipid metabolism.On the basis of the TRN see , genes t2. However, they exhibit different expression patterns indicated by their clustering into different modules. Not surprisingly, the two clusters share two predicted regulatory proteins, J49099 and J47726, that provide a tangible link between transcriptional regulation and metabolite exchange between different pathways and subcellular compartments. Metabolite exchange between subcellular compartments has been shown to be important to diatom metabolism . Note that we used the biomass objective function (BOF) and the constraints previously determined experimentally , product secretion, and biomass composition were used under low- and high-carbon conditions. The biomass function accounts for all known biomass components, i.e., DNA, RNA, protein, pigments, carbohydrates, membrane lipids, and the storage lipids triacylglycerols (TAGs), as well as energetic requirements and their fractional contributions to the overall cellular biomass. As depicted in 3 levels. Thus, the reaction fluxes are increased to meet the larger demand of biomass components accounting for P. tricornutum’s increased growth at increased HCO3 levels.To simulate the effect of rising HCO2 concentrations. Half of the genes (93 genes) were downregulated at high CO2 concentrations, whereas the other half (94 genes) were upregulated. By using the P. tricornutum genome-scale model, the genes were mapped to 1,323 metabolic reactions belonging to 63 model subsystems, which were further categorized into nine groups   . Note th2 concentrations, whereas this group does not show up in the sampling results. Although N-glycan biosynthesis is included in the genome-scale model, glycans are not accounted for in the biomass reaction. Instead, a demand reaction was included in the model  to account for the missing knowledge of the fraction of glycans present in the biomass. This demand reaction was blocked prior to the solution space sampling and thus cannot be accounted for in the sampling result.Compared to the genome-scale model solution space sampling results, where increased reaction fluxes were identified at higher carbon levels  are identified by the sampling and differential expression analysis, the reactions within these groups are different between the two analyses, as shown in 2 levels, as observed between the metabolic model predictions and the differential expression analysis, might be explained by the different types of data exploited for the two analyses. The differential expression analysis is based on RNA-Seq data, whereas the metabolic model predictions are based on simulated reaction fluxes and thus protein activities. The differential expression analysis takes into account regulation by TFs but not posttranscriptional and -translational modifications, as well as allosteric regulation on the enzyme level. In contrast, the metabolic model does not include any regulatory effects and the predicted flux distributions are based on the mature enzyme activities, i.e., after modifications. However, random sampling of the metabolic model’s solution space identifies all possible flux distributions and, combined with further physiological data such as transcriptomics, more complete insights into the organism’s metabolism can be gained.The discrepancy in the metabolic response to rising COP. tricornutum  supply, NO3 becomes limiting and is not stored internally with increasing HCO3 concentrations, as shown in 3 is used for biomass production to enable maximal carbon fixation into biomass. Consequently, biomass production stagnates because of limiting NO3 availability. Since HCO3 further increases and the cell is forced to take it up, 3-(dimethylsulfonio)propanoate (DMSP) is secreted, which is the only reaction allowing the release of excess carbon.According to the predictions of scenario 1 with stepwise increasing HCO3, is indeed the limiting factor constraining biomass production using scenario 2 with stepwise increasing HCO3 uptake and allowing the NO3 supply to increase by 0.1 mM with each carbon uptake increase when the HCO3 uptake is ≥5.5 mM. The available NO3 is incorporated into biomass for HCO3 levels below 5 mM. The supplied rising nitrogen is sufficient to enable nitrogen storage and fixation of all presented carbon into biomass; thus, no DMSP is secreted.3 uptake is constrained and constant throughout the simulation, nitrogen storage decreases with increasing HCO3 concentrations. At an HCO3 uptake of 5 mM, the biomass production increase is slowed down before it finally stagnates when the HCO3 uptake reaches 5.5 mM. NO3 storage shows a similar pattern and vanishes at HCO3 levels higher than 5.5 mM. With HCO3 uptake higher than 5.5 mM, excess carbon is stored as TAG, which increases with HCO3. In this scenario, excess carbon is not stored as chrysolaminarin.In scenario 1, excess carbon was released in the form of DMSP. This reaction (DM_dmsp_c) was introduced into the model because of a knowledge gap in DMSP metabolism and to prevent its accumulation . In the 3 levels until P. tricornutum encounters nitrogen limitation. A strong connection between carbon metabolism and nitrogen metabolism was also observed in the TRN, where we showed that genes involved in nitrogen and carbon metabolism are often coregulated. It should be noted that temperature, nutrient deprivation, and other factors are also known to influence the growth of P. tricornutum but were not taken into account in this study. Our work describes for the first time which genes are coexpressed and coregulated upon different environmental perturbations and provides insight into the effect the limitation of a nutrient such as carbon or nitrogen has on the phenotype. The integration of the regulatory network developed here and the published metabolic model offers new insights into the model diatom P. tricornutum’s metabolic and regulatory interactions and provides a comprehensive framework of responses to increasing atmospheric carbon levels.Using the genome-scale metabolic network, we demonstrated that biomass production increases with elevating HCOhttps://www.r-project.org), scaled by using DESeq scaling factors (2 transformed (a constant +1 was added prior to log2 transformation), and adjusted for batch effects introduced by the utilization of different sampling platforms with the ComBat software  by using an in-house mapping table. The expression profiles of 196 known TFs in P. tricornutum  and high  COge limma . The Ben2 algorithm discovers coregulated modules in transcriptome profiles by integrating additional information, such as the genome sequence, protein-protein interactions, and the de novo detection of cis-regulatory DNA sequence motifs, and aggregates it into a combined score to improve clustering  was obtained from Ensembl Protist (http://protists.ensembl.org/Phaeodactylum_tricornutum/Info/Index). Chloroplastic and mitochondrial genomic information was obtained from NCBI   , 21. Thecornutum . Proteincornutum  and repl2 H, protons, oxygen, inorganic phosphate, pyrophosphate, and CO2, were removed from the cluster-substrate-product list.On the basis of the clustering result and the le model , a clustHighly connected clusters were identified on the basis of substrates or products. The connectivity of two clusters was defined as the number of common substrates (or products) divided by the total number of substrates (or products) in both clusters. Here, two clusters are strongly connected if their connectivity is >0.9.Modeling simulations were performed with the Gurobi Optimizer version 5.6.3  solver in MatLab  with the COBRA Toolbox . NutrienP. tricornutum metabolic network iLB1027_lipid (3 uptake was set to 1.57 mM and doubled to 3.14 mM for the simulations of high-carbon conditions. All other constraints were identical between the two sampled conditions (2 conditions. Corresponding reactions and their gene-reaction associations were extracted from the genome-scale model. However, this analysis did not result in any reaction knockout. The reduced metabolic model contains 3,904 reactions and 1,734 metabolites. Both networks, representing low- and high-carbon conditions, were sampled by using 50,000 sample points with a step count of 7,808, which is double the number of reactions in the model.To uniformly sample the solution space of the 27_lipid , optGpSa27_lipid  for MatLnditions . Before 3 levels are significantly different, the minimal distance between the histograms was determined for each reaction in the metabolic model by randomly permuting the flux vectors and subtracting them from each other. To get a representative distance, this procedure was repeated 100 times, yielding 100 distance vectors for each histogram comparison. The mean of the minimum number of positive and negative entries in each distance vector was used to calculate the P value for the two-sided test. To correct for multiple-hypothesis testing, a false-discovery rate correction was applied, setting the significance threshold at 0.05.To determine if the flux distributions at low and high HCO


E. coli. This work demonstrates that the topology of a metabolic network can shape kinetic parameters of enzymes and lead to seemingly wasteful enzyme usage.A set of chemical reactions that require a metabolite to synthesize more of that metabolite is an autocatalytic cycle. Here, we show that most of the reactions in the core of central carbon metabolism are part of compact autocatalytic cycles. Such metabolic designs must meet specific conditions to support stable fluxes, hence avoiding depletion of intermediate metabolites. As such, they are subjected to constraints that may seem counter-intuitive: the enzymes of branch reactions out of the cycle must be overexpressed and the affinity of these enzymes to their substrates must be relatively weak. We use recent quantitative proteomics and fluxomics measurements to show that the above conditions hold for functioning cycles in central carbon metabolism of DOI:http://dx.doi.org/10.7554/eLife.20667.001 Many bacteria are able to produce all the molecules they need to survive from a limited supply of nutrients. This allows the bacteria to thrive even in harsh environments where other organisms struggle to live. The bacteria act as miniature chemical factories to convert nutrients into the desired molecules via a series of chemical reactions. Some molecules are made in sets of reactions termed autocatalytic cycles. These reaction sets require a molecule to be present in the cell in order to produce more of that molecule; like how a savings account needs to contain some money before it can generate more via interest.Bacteria have many different enzymes that each drive specific chemical reactions. In order for an autocatalytic cycle to work properly, the cell needs to maintain adequate supplies of the molecule it is trying to make and all of the “intermediate” molecules in the cycle. If less of an intermediate molecule is produced, for example, the cell needs to reduce the demand for that molecule by controlling later chemical reactions in the cycle. Bacteria control chemical reactions by regulating the activities of the enzymes involved, but it is not clear exactly how they regulate the enzymes that drive autocatalytic cycles.E. coli. The experiments suggest several core principles allow autocatalytic cycles to work smoothly in the bacteria. The next step is to apply these principles to different kinds of molecules produced in bacterial cells. A future challenge is to search for other structures that regulate chemical reactions in E. coli and other bacteria. Extending our understanding of autocatalytic cycles and other pathways of chemical reactions is essential for designing and engineering new reactions in bacteria. Such knowledge can be used to modify bacteria to produce valuable chemicals in environmentally friendly ways.Barenholz et al. combined two approaches called proteomics and fluxomics to study autocatalytic cycles in a bacterium known as DOI:http://dx.doi.org/10.7554/eLife.20667.002 An essential trait of living systems is their ability to reproduce. This fundamental ability makes all living organisms autocatalytic by definition. Moreover, autocatalytic metabolism is considered to be one of the essential components of life .In this work, we focus on autocatalytic cycles in chemical reaction systems, in the context of metabolic networks. The components we consider are the metabolites of the system, with autocatalytic cycles being formed using the reactions of the metabolic network. An illustrative example for a metabolic autocatalytic cycle is glycolysis. In glycolysis, 2 ATP molecules are consumed in the priming phase, in order to produce 4 ATP molecules in the pay off phase. Therefore, in order to produce ATP in glycolysis, ATP must already be present in the cell. Subsequently, autocatalysis of ATP in glycolysis  results in sensitivity to mutations in seemingly irrelevant enzymes . AutocatMetabolic networks often require the availability of certain intermediate metabolites, in addition to the nutrients consumed, in order to function. Examples of obligatorily autocatalytic internal metabolites in different organisms, on top of ATP, are NADH, and coenzyme A . We find2 while transforming five-carbon compounds into two three-carbon compounds, serves as the main gateway for converting inorganic carbon to organic compounds in nature (2 molecules). Beyond the CBB cycle, we show that most of the reactions and metabolites in the core of central carbon metabolism are part of compact (i.e. consisting of around 10 reactions or fewer) metabolic autocatalytic cycles. Some of the autocatalytic cycles we find are not usually considered as such. The span of autocatalytic cycles in central carbon metabolism suggests that the constraints underlying their stable operation have network-wide biological consequences.A key example of an autocatalytic cycle in carbon metabolism is the Calvin-Benson-Bassham cycle (CBB) . The carn nature . The autIn this study, we present the specific requirements metabolic autocatalytic cycles must meet in order to achieve at least one, non-zero, steady state which is stable in respect to fluctuations of either metabolites or enzyme levels close to the steady state point. The mathematical tools we use are part of dynamical systems theory . We idenWe use recent fluxomics and proteomics data to test the predictions we make. We find them to hold in all cases tested where autocatalytic cycles support flux. Our analysis demonstrates how the requirement for stable operation of autocatalytic cycles results in design principles that are followed by autocatalytic cycles in-vivo. The results and design principles presented here can be further used in synthetic metabolic engineering applications that require proper functioning of autocatalytic cycles.Different definitions exist for autocatalytic sets in the context of chemical reaction networks . Here weE. coli  shows the ubiquity of compact autocatalytic cycles. On top of the previously discussed CBB cycle  in bacteria. This transport system imports a glucose molecule using phosphoenolpyruvate (pep) as a co-factor. The imported glucose is further catabolized, producing two pep molecules via glycolysis ), two conditions must be satisfied:The first requirement states that the maximal flux of the biomass generating, branching reaction should be higher than the maximal flux of the autocatalytic reaction. This requirement ensures a stable solution exists, as large concentrations of Interestingly, these conditions imply that if In the model above, to keep the analysis concise, we neglected the bisubstrate nature of the autocatalytic reaction. We extend the analysis to the most common classes of bisubstrate reaction mechanisms in the Materials and methods, sections "Connecting bisubstrate reaction kinetic constants with simple Michaelis-Menten constants", "Constraints on concentration of assimilated metabolite and kinetic constants of bisubstrate reactions", and "Dependence of steady state concentration on assimilated metabolite". All bisubstrate reaction schemes analyzed take a Michaelis-Menten like form once the concentration of the assimilated metabolite is kept constant  of autocatalytic cycles. When an input flux is present, an autocatalytic cycle can always achieve a non zero, stable steady state by tuning the expression levels of the enzymes forming the cycle.Interestingly, we find that in the two autocatalytic cycles shown in The simple model assumed both the autocatalytic and the branch reactions are irreversible under physiological conditions. Assuming the branch reaction, If If The simple model assumed both the autocatalytic and the branch reactions are irreversible under physiological conditions. The autocatalytic reaction in the simple model represents an effective overall reaction for all of the steps in autocatalytic cycles found in real metabolic networks. In order for the combined autocatalytic reaction to be physiologically reversible, all of the reactions in the real metabolic network must be reversible under physiological conditions. We note that this is not the case in any of the cycles we identify in central carbon metabolism. Nevertheless, this case can be mathematically analyzed.If the autocatalytic reaction is reversible, then it must be driven by the displacement from thermodynamic equilibrium of the concentration of This condition can always be satisfied by high expression of the autocatalytic enzyme, increasing Even the most compact real-world autocatalytic cycles are composed of several reactions. It is thus useful to extend the simple criteria we derived to more complex autocatalytic cycles. In such cycles the criteria for the existence of a steady state become nuanced and detail specific. We therefore focus on evaluating stability of such cycles, under the assumption that a non-zero steady state exists, which is usually known based on experimental measurements.We analyze the stability criteria for the autocatalytic cycles depicted in Using the connection between derivatives of reactions and saturation levels , we conclude that if This condition also dictates that the affinity of the branch reaction to the intermediate metabolite of the cycle it consumes must be weaker than the affinity of the corresponding recycling reaction of the cycle.While having a single branch point at which Although we utilized the widely-used irreversible Michaelis-Menten kinetics equation to model enzyme kinetics, our results can be extended to different kinetic equations. Generally, two conditions must be met for a stable flux through an autocatalytic cycle to exist: (A) there should be a positive concentration of the intermediate metabolites for which the outgoing fluxes balance the autocatalytic fluxes, resulting in a steady state, and, (B) at the steady state point at least one derivative of an outgoing reaction out of the cycle should be higher than the derivative of the corresponding cycle reaction, as is implied by E. coli from To evaluate the validity of our analysis of autocatalytic cycles we searched for growth conditions under which the autocatalytic cycles we identified in central carbon metabolism carry substantial flux in-vivo. We used recent in-vivo flux measurements in As noted above, we predict a design principle for functioning autocatalytic cycles: that at least one branch reaction should have a steeper response than the corresponding autocatalytic reaction at steady state. This requirement is sufficient, but not necessary, for the autocatalytic cycle to be at a stable steady state point. Moreover, having more than one branch point at which the branch reaction has a steeper response than the autocatalytic reaction increases the robustness of the steady state flux in the cycle as shown in the Materials and methods section "Multiple unsaturated branch reactions increase convergence speed and dampen oscillations". An outcome of the relationship between the steepness’s of responses is a reverse relationship between the saturation levels of the corresponding reactions . In ordeThe maximal flux capacity of the reaction under the given condition, The actual flux through the reaction at the steady state, To estimate the maximal capacity of a reaction we followed the procedure described in  see Mat to identOur results show that for any of the four functioning autocatalytic cycle cases, in at least one branch point the biomass generating branch reaction has a larger maximal flux capacity, and is considerably less saturated than the respective autocatalytic reaction, in accordance with our predictions. Moreover, out of nine branch points analyzed, in six branch points the branching reactions were significantly less saturated than the autocatalytic reactions, in two branch points the saturation levels were similar, and only in one branch point the autocatalytic reaction was less saturated than the branching reaction.The branch point at which the autocatalytic reaction is less saturated than the branch reaction is the branch point from fructose-1,6-bisphosphate in growth on fructose as the carbon source. The high saturation of the branch reaction arises as a large flux is reported for the fbp reaction, whereas the corresponding enzyme is not highly expressed under this condition. The large reported flux through fbp arises due to assuming a single transport pathway for fructose, entering the cycle as fructose-1,6-bisphosphate. However, an alternative fructose transport pathway is known to occur for the concentration at which the measurements were made . The altWe made two negative control analyses to examine whether other reasons do not underlie the trend we find. First, we compared the saturation levels at the same branch points in growth conditions at which the autocatalytic cycles do not function, but the reactions carry flux. We find that for these cases, only 4 out of 9 cases satisfy the low branch saturation condition . Second,The consistently lower saturation values of biomass generating branch reactions demonstrate that the expressed enzymes have enough capacity to prevent the autocatalytic cycle from increasing the concentration of intermediate metabolites infinitely. Moreover, the lower saturation values of the biomass generating reactions suggest that at the steady state point their derivatives are higher, ensuring stable operation of the cycle.E. coli, and for which no flux measurements are available. This cycle has been recently introduced synthetically into E. coli and was shown to carry flux in it, given further metabolic engineering of central carbon metabolism , the regulated reaction , and the direction of the regulation (activation or inhibition). One interaction, the activation of fba by pep, does not follow our expectation.For the glyoxylate cycle, we find that there are a total of 13 interactions, 12 inhibitions and one activation. Out of these 13 interactions, 8 interactions follow our expectations and 5 do not. The lack of significant agreement between the expected regulation direction and the actual regulation found for this cycle is consistent with the observation in It is important to note that allosteric regulation serves many roles, and that the metabolic network faces many more challenges than just the support of stable autocatalysis. Therefore, the agreement we find between existing allosteric interactions and the expected regulation scheme supporting autocatalysis does not suggest that the autocatalytic nature of the PTS is the only, or even main underlying reason for these allosteric interactions.Our study into the dynamics and stability of autocatalytic cycles suggests design principles applicable to both systems biology, that aims to understand the function of natural networks, and in the context of synthetic biology, in the effort to express novel heterologous cycles.While autocatalytic cycles are often overlooked in the study of metabolism, we find that such cycles are at the heart of central carbon metabolism. Our autocatalytic modeling framework gives concrete predictions on saturation levels of branch reactions for operating autocatalytic cycles. We find these predictions agree well with empirically measured fluxomics and proteomics data sets. Given that there are other suggestions  that mayA common concept in synthetic biology is that the successful implementation of novel pathways requires the expression of functional enzymes in the correct amounts in the target organism. Here we show that in the context of autocatalytic cycles, such expression modulation may not suffice. Specifically, changes to the substrate affinity of enzymes at branch points of the cycle may be required in order for the novel pathway to function.Another aspect of our findings is that while it is common to assume that strong affinity and high catalytic rate are desirable traits for enzymes, such seeming improvements may actually lead to instability and thus to non functional metabolic cycles. Furthermore, for reactions branching out of autocatalytic cycles, weaker affinities increase the steady state concentration of intermediate metabolites, resulting in higher fluxes both through the cycle, and through the branch reaction, suggesting an unconventional strategy for optimizing fluxes through such reactions. We note that because allosteric regulators modify the affinity of the enzymes they target, such regulators can potentially be used to restrict the affinity of branch reactions only when the autocatalytic cycle functions.E. coli by introducing the two genes missing for its function , non-caGiven a metabolic network composed of a set of reactions and metabolites, the following criteria can be used to define a subset of the network that is an autocatalytic cycle: First we define a metabolic cycle. A set of irreversible reactions (for reversible reactions only one direction can be included in the set) and metabolites forms a cycle if every metabolite of the set can be converted, by sequential application of reactions in the set (where two reactions can be chained if a metabolite in the set is a product of the first reaction and a substrate of the second reaction), to every other metabolite in the set. A cycle is autocatalytic if the reactions of the cycle can be applied, each reaction at an appropriate, positive number of times, such that the resulting change in the amount of each of the metabolites forming the cycle is non-negative, with at least one metabolite of the cycle having a strictly positive change.n, such that the The same definition can be stated in terms of reaction vectors and a stoichiometric matrix. If a metabolic network has With this notation, a set of metabolites: Every row and every column of the stoichiometric matrix have at least one positive and one negative number.There is a set of positive integers, The condition that the total reaction vector E. coli  mechanism . As thisRearranging to get the dependence of the flux on which gives apparent Michaelis-Menten kinetic constants of:The second bisubstrate reaction mechanism we consider is the ternary enzyme complex with random binding order of the two substrates. As this equation is also symmetric with respect to the two substrates, we can again arbitrarily decide which of the two substrates is the assimilated metabolite, and which is the internal metabolite. We get that the flux through the reaction is:Rearranging to get the dependence of the flux on which gives apparent Michaelis-Menten kinetic constants of:The other equation describing a ternary enzyme complex bisubstrate reaction assumes ordered binding of the substrates. Because in ordered binding the equation is asymmetric with respect to the two substrates, analyzing this reaction is further split according to which of the two substrates is assumed to be the assimilated metabolite with constant concentration.If the first binding metabolite is assumed to be the assimilated metabolite we get that:which gives apparent Michaelis-Menten kinetic constants of:If the first binding metabolite is assumed to be the internal metabolite we get that:which gives apparent Michaelis-Menten kinetic constants of:To summarize, the most common equations describing bisubstrate reactions reduce to equations of the same form as Michaelis-Menten equations, under the assumption that one of the metabolites maintains a constant concentration. The apparent kinetic constants of the Michaelis-Menten equivalent equations depend on the kinetic constants of the bisubstrate reactions, as well as on the concentration of the assimilated metabolite.In Here, we map the same constraints from The case of substituted enzyme mechanism is the simplest case to analyze. We can substitute As In the case of a random binding order, we can substitute We first note that from the second inequality we get that:Giving a lower bound on the concentration of the assimilated metabolite for which a stable steady state is attainable.We now wish to obtain a lower bound on We note that for positive Substituting this inequality in the second inequality of We have therefore obtained a lower bound on the affinity of the branch reaction, For the random binding order we can thus conclude that, like in the single-substrate case, a lower bound exists on the affinity of the branch reaction, below which a positive steady state is not attainable, even if the expression levels of the enzymes, and the concentration of the assimilated metabolite are modified. Furthermore, for any set of kinetic parameters, there is a lower bound on the concentration of In the case of ordered binding, with the assimilated metabolite binding first, we can substitute As the second inequality is identical to the one in the random binding order case, we can immediately conclude that the same lower bound on the concentration of Regarding a lower bound on Therefore, we can deduce, by using the first inequality from which immediately yields:setting an absolute lower bound on We thus arrive at the same conclusions in this case, as we have arrived to in the previous case, namely that a lower bound exists on the affinity of the branch reaction, and that, for any set of kinetic parameters, there is a lower bound on the concentration of the assimilated metabolite, below which a positive stable steady state cannot be obtained.In the case of ordered binding, with the internal metabolite binding first, we can substitute As in the previous two cases, the second inequality can be used to obtain a lower bound on the concentration of However, unlike in the previous two cases, in this case if Assuming the kinetic parameters satisfy the stable steady state conditions derived in The simple model assumed both the autocatalytic and the branch reactions are irreversible. Here we assume the branch reaction is reversible, and let We assume that a third reaction, We start by deriving the necessary conditions for steady state existence. Because at steady state Furthermore, as at the steady state Substituting Which is satisfied when Albeit intimidating, this quadratic equation can be used to derive the conditions for the existence of a positive steady state. Only if both of the roots of this equation are negative, no positive steady state exists. We recall that the two roots of a quadratic equation of the form As in the irreversible case, the sign of Under the assumption that If If We now turn to analyze the stability of the steady state. For a steady state to be stable, the eigenvalues of the Jacobian matrix must have negative real values. In our system it holds thatWe use the following notation:We can use this notation to write the Jacobian matrix as:which gives a characteristic polynomial of:In order for the real values of the roots of the characteristic polynomial to be negative it must hold that We denote by First, we note that if If For this equation, As this that is constant. Therefore, rearranging c such that:we note that as On the other hand, when Therefore, for small values of Our conclusions are therefore as follows: As in the irreversible case, Qualitatively, the cases we analyze show that, on top of the required We analyze the stability criteria for the autocatalytic cycles depicted in We note that in steady state, where Solving for the characteristic polynomial gives:that has two negative roots when:which is satisfied if The two-metabolites cycle case can be easily extended to a larger number of intermediate metabolites and reactions, as is depicted in In this case, steady state implies that the concentration of each intermediate metabolite is conserved, meaning that for all  implying that for all We stress that To conclude, for the straightforward extension of the simple model to multiple reactions with a single autocatalytic reaction, steady state implies that for all Where the left inequality is due to A sufficient condition for such a steady state point to be stable is that at the steady state point there exists at least one branching point Stability analysis of a model complex autocatalytic cycle with The characteristic polynomial of this matrix is given by:To extract the conditions under which all the roots of the characteristic polynomial have negative real parts we use Rouche’s theorem. Our strategy will be as follows: We will define a contour that contains only numbers with negative real parts. We will show that all the roots of the polynomial We pick a large parameter noting that it is constant over all of ℂ and specifically over noting that all of For the arc segment we note that, as for complex numbers it holds that From the triangle inequality we know that As we picked and thereforeconcluding that over the arc, For the part of and, as before, thatTo meet the condition that Simplifying this inequality gives:A sufficient condition to satisfy this inequality, given that all the We therefore get that if there exists Using the Jacobian matrix from We denote by It therefore follows that any increase in It turns out that for the Michaelis-Menten kinetics equations, the following useful lemma can be used to connect theoretical observations on the relationships of derivatives to physiological observations on affinities and saturation levels.We define the saturation level of a reaction as the ratio between the flux it carries, and the maximal flux it can carry, given the expression level of the relevant enzyme, that is:Given this definition we can show that if two Michaelis-Menten reactions consume the same metabolite, then it follows that:Proof: expanding the condition that Expanding the premise of the lemma in Because setting the affinity of the autocatalytic enzyme as a lower bound for the affinity of the branch enzyme. Finally, given this relation of affinities it follows that:concluding the proof.We note that a multiple reaction autocatalytic cycle at a stable steady state point satisfies To evaluate the maximal flux capacity of a reaction under a prescribed growth condition, given expression level and flux data for a set of conditions, we follow the procedure described in In this section we touch upon the potential (in somewhat simplified and naively non-rigorous terms) of allosteric regulation to improve the properties of autocatalytic cycles. The constraint on the affinity of the branch reaction imposed by the stability requirement  may be sFrom the perspective of the simple model, we recall that The assimilated metabolite can also allosterically regulate the reactions of the cycle. We assume that the desired steady state, denoted Another possible class of regulators are the products of the branch reactions. Taking a somewhat simplistic view, if the level of Finally, we note that in the autocatalytic cycles we identify in central carbon metabolism, there are also reactions that operate in the reverse direction to the branch reactions, such that they consume products of the cycle and produce intermediate metabolites of the cycle. As such reactions are mirror images of branch reactions, we expect them to be oppositely regulated to branch reactions.We find that these predictions hold for the cycle using the PTS, that is known to be allosterically controlled, but not for the glyoxylate cycle, which is known to be transcriptionally controlled . In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.eLife. Your article has been reviewed by four peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Aviv Regev as the Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Frank Bruggeman (Reviewer #2).Thank you for submitting your article "Design principles of autocatalytic cycles constrain enzyme kinetics and force over-expression at flux branch points" for consideration by The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.Summary:This article addresses a very interesting and fundamental question about the nature of autocatalytic cycles within cellular metabolic networks, namely whether the existence and stability of steady states in such cycles imposes constraints on the kinetic parameters of the reactions involved. Starting from simple reactions, and gradually looking at slightly more complicated cases, the authors identify general rules that enzymes should follow in order for the autocatalytic cycles to support a stable flux.eLife. However, they also requested a number of important clarifications and revisions, as listed cumulatively below:All four reviewers agreed that the article is well written and original, and that it provides insightful and valuable results that would be in principle worth presenting to the audience of Essential revisions:1) In the equation for "fa", there is no mention of the bisubstrate nature of the reaction. It is understood that the authors consider A constant, which seems a reasonable assumption to start with . However, it is not completely obvious that, even if the kinetic parameters relative to A in the M.M. equations are incorporated into the constants of the equation as shown, the bisubstrate nature of the reaction would not affect the generality of the conclusions drawn throughout the paper.2) Both in the simple model, and in the extended ones, the authors consider A to be constant. This can be a convenient assumption for the simple model, but makes conclusions for realistic models less relevant, since consumption of A  can be an important part of the system's dynamics. The authors should either explore this alternative possibility, or provide a justification for why this would not be expected to affect significantly the main conclusions.3) Even though the simple example that is treated in the paper nicely sets the stage and helps the reader in understanding the analytical approach, it is based on irreversible enzyme kinetics only. How do the requirements for proper functioning change when the reactions are catalysed by product-sensitive and reversible kinetics? Does product sensitivity prevent loss of stability? How does the displacement from thermodynamic equilibrium of the enzymes at the branch point influence the stability?4) Allosteric regulation, within or onto, the autocatalytic subnetwork can also improve the robust functioning of the autocatalytic subnetwork. Have the authors analysed this? What did they find? This is particularly relevant in relation to the remark, which suggests that enzyme expression adjustment -- so, in fact rate adjustment -- can always lead to a non-zero, stable steady state. If so, then is it true that allosteric regulation could always lead to a steady state? Could one then make predictions about the kinetic design of autocatalytic cycles based on their allosteric control?5) In subsection “Stability analysis for multiple-reaction cycles”, the authors mention that the affinity of the branch reaction to the intermediate metabolite of the cycle it consumes must be lower than the affinity of the corresponding recycling reaction of the cycle. Is this statement really correct, given that it is based on either a unscaled sensitivity (dv/ds and not dlnv/dlns) or a saturation degree, which generally also depend on the expression levels of the enzymes, i.e. their Vmaxs?6) The theoretical predictions could and should be tested more strictly. Although the experimental results that are discussed are consistent with the predictions from the mathematical analysis, they could have alternative explanations. Low saturation of enzymes with their substrates is not uncommon in metabolic networks, and a number of hypotheses have been put forward to explain the apparently wasteful investment in high enzyme concentrations. See for instance refs. [1-6], not to mention some from this manuscript's authors. In fact, while according to the theory a single branching enzyme being less saturated than the cycle enzyme consuming the same substrate would warrant stability, the experimental data point to most of the branching enzymes being less saturated than the cycle enzymes, which makes the concern about alternative explanations pertinent. The authors may thus wish to discuss these potential alternative explanations, and explain why they eventually don't apply. As a negative control, the authors may wish to examine if enzymes branching from non-autocatalytic cycles tend to be more saturated with substrates from the cycle than those branching from autocatalytic cycles.7) If lower expression of the enzymes catalyzing reactions that branch out from autocatalytic cycles leads to higher production rates of metabolic precursors, one would expect a negative correlation between the cellular abundance of some of these enzymes and growth rate. This prediction should be relatively straightforward to test based on published quantitative proteomics datasets. Again, a comparison with enzymes branching from non-autocatalytic cycles could be made as control.8) An examination of the regulation of the branching enzymes may also provide additional support for the theory. E.g., these enzymes may be subject to competitive inhibition (to increase the apparent KM) under conditions where there is a higher demand for the cycle's intermediates.9) It would also be very useful to have experimental data showing that forcing a lower activity or higher saturation of key branching enzymes would cause instability as predicted. However, this may require dedicated experiments, and should not be viewed as a necessary condition for acceptance.10) While most of the paper seemed clearly written and unambiguous, several statements in the Introduction are imprecise or unclear. (a) One confusing aspect is the ambiguity between collectively autocatalytic systems and autocatalysis of their components. The component of a system that is collectively autocatalytic is in general not autocatalytic. Thus the statement in the second sentence of the Introduction is inaccurate. In fact, the authors themselves contradict that statement in paragraph two of the Introduction. (b) The authors mention that "autocatalytic systems have an inherent potential to be unstable as their operation changes the amount of their components". This last part of the sentence could be true for many other non-autocatalytic dynamical systems, so it is not clear that this statement is justified. (c)The concept of a system being catalytic "with respect to something" is not clearly defined ; (d) It is not clear how the statement at the end of paragraph two ("Therefore….") follows as a logical consequence of the prior statement.11) In the interest of reproducibility, the authors should provide supplementary material tables containing the data used for deriving References[1]. Weiss, S.L., Lee, E.A. & Diamond, J. (1998) Evolutionary matches of enzyme and transporter capacities to dietary substrate loads in the intestinal brush border. Proceedings Of The National Academy Of Sciences Of The United States Of America, 95, 2117-2121.[2]. Suarez, R.K., Staples, J.F., Lighton, J.R.B. & West, T.G. (1997) Relationships between enzymatic flux capacities and metabolic flux rates: Nonequilibrium reactions in muscle glycolysis. Proceedings Of The National Academy Of Sciences Of The United States Of America, 94, 7065-7069.[3]. Staples, J.F. & Suarez, R.K. (1997) Honeybee flight muscle phosphoglucose isomerase: Matching enzyme capacities to flux requirements at a near-equilibrium reaction. Journal of Experimental Biology, 200, 1247-1254[4]. Salvador, A. & Savageau, M.A. (2003) Quantitative evolutionary design of glucose 6-phosphate dehydrogenase expression in human erythrocytes. Proceedings Of The National Academy Of Sciences Of The United States Of America, 100, 14463-14468[5]. Salvador, A. & Savageau, M.A. (2006) Evolution of enzymes in a series is driven by dissimilar functional demands. Proceedings Of The National Academy Of Sciences Of The United States Of America, 103, 2226-2231Drosophila melanogaster. Proceedings Of The National Academy Of Sciences Of The United States Of America, 103, 19413-19418[6]. Eanes, W.F., Merritt, T.J.S., Flowers, J.M., Kumagai, S., Sezgin, E. & Zhu, C.T. (2006) Flux control and excess capacity in the enzymes of glycolysis and their relationship to flight metabolism in [7]. Tibor Gánti (2003) "The principles of life" Oxford, Oxford University Press[8]. Semenov, S.N., Kraft, L.J., Ainla, A., Zhao, M., Baghbanzadeh, M., Campbell, V.E., Kang, K., Fox, J.M. & Whitesides, G.M. (2016) Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions. Nature, 537, 656-660. Essential revisions:1) In the equation for "fa", there is no mention of the bisubstrate nature of the reaction. It is understood that the authors consider A constant, which seems a reasonable assumption to start with . However, it is not completely obvious that, even if the kinetic parameters relative to A in the M.M. equations are incorporated into the constants of the equation as shown, the bisubstrate nature of the reaction would not affect the generality of the conclusions drawn throughout the paper.We thank the reviewers for this (and the following) important points. The reviewers correctly point at an important gap in the paper regarding the bisubstrate nature of the autocatalytic reaction.We updated the manuscript  to include, beyond the uni-substrate case, also four cases of bisubstrate reactions: substituted enzyme (Ping-Pong) scheme, random binding order, ordered binding, with the assimilated metabolite binding first, and ordered binding with the internal metabolite binding first . We show that in all four cases, keeping A constant results in a M.M. like equation, with kinetic parameters relative to A, maintaining the main result of the paper. In three cases a critical amount for A exists, below which a positive stable steady state cannot be attained .In the first three cases of bisubstrate binding, bounds on the affinity of the bisubstrate enzyme to the internal metabolite X, exist , supporting the conclusions drawn throughout the paper. In the last bisubstrate case  the expression levels of the autocatalytic and branch enzymes can be modified to achieve positive stable steady state for any set of affinity parameters.We therefore conclude that the generality of the conclusions drawn throughout the paper hold also with bisubstrate reactions, with a modification in the case of ordered binding with the internal metabolite binding first. Even for this case the conclusions apply, but do not impose constraints on the affinity of the bisubstrate reaction.2) Both in the simple model, and in the extended ones, the authors consider A to be constant. This can be a convenient assumption for the simple model, but makes conclusions for realistic models less relevant, since consumption of A  can be an important part of the system's dynamics. The authors should either explore this alternative possibility, or provide a justification for why this would not be expected to affect significantly the main conclusions.As noted in the previous comment, we find that  a critical amount for A exists, below which the system loses the positive stable steady state. Interestingly, under some circumstances, an upper bound on the level of A also exists, but this upper bound can be removed by lowering the expression level of the bisubstrate enzyme. The exact critical level of A depends on the bisubstrate reaction scheme and on the specific kinetic parameters and expression levels of the bisubstrate enzyme and the branch enzyme. Nevertheless, qualitatively, the system’s dynamics is identical in all of the reactions schemes we analyze . The concentration of the intermediate metabolite, X, at the st.st. decreases as the level of A decreases , and reaches 0 when A hits its critical amount . Thus, the effect of draining A does not affect the main conclusions, but does add another observation regarding the system’s dynamics when the assimilated metabolite is depleted. We have updated the text to reflect these observations.3) Even though the simple example that is treated in the paper nicely sets the stage and helps the reader in understanding the analytical approach, it is based on irreversible enzyme kinetics only. How do the requirements for proper functioning change when the reactions are catalysed by product-sensitive and reversible kinetics? Does product sensitivity prevent loss of stability? How does the displacement from thermodynamic equilibrium of the enzymes at the branch point influence the stability?The reviewers address a biologically important extension to the simple example treated in the paper. We added analysis of the requirements for proper functioning under two cases of product-sensitive, reversible kinetics:1) When the branch reaction is reversible , the system behavior depends on the assumptions made regarding the consumption of the product of the branch reaction, Y. If Y is removed rapidly, the branch reaction operates far from thermodynamic equilibrium and the same requirements as in the simple example hold. If Y is removed slowly, then we show that the requirements from the irreversible case are ‘forwarded’ to the reaction that consumes Y, requiring its maximal flux to be higher than that of the autocatalytic reaction, and its flux for small values of Y to be smaller than the autocatalytic flux for small X .2) When the autocatalytic reaction is product-sensitive  we find that the level of X for which the reaction proceeds in the autocatalytic direction is bounded (regardless of the exact bisubstrate reaction mechanism). Therefore, in this case the only requirement for proper functioning is that, for constant A, the initial rate of the autocatalytic reaction for small X is larger than the rate of the branch reaction for the same X, a requirement that can always be satisfied by increasing the expression level of the autocatalytic enzyme. Therefore, in this case, product sensitivity prevents loss of stability.4) Allosteric regulation, within or onto, the autocatalytic subnetwork can also improve the robust functioning of the autocatalytic subnetwork. Have the authors analysed this? What did they find? This is particularly relevant in relation to the remark, which suggests that enzyme expression adjustment -- so, in fact rate adjustment -- can always lead to a non-zero, stable steady state. If so, then is it true that allosteric regulation could always lead to a steady state? Could one then make predictions about the kinetic design of autocatalytic cycles based on their allosteric control?We thank the reviewers for highlighting this important aspect of metabolic control, overlooked in our work. We find allosteric regulation to be valuable in optimizing native autocatalytic cycles enabling both faster convergence to st.st. and modulation of affinities such that branch enzymes can be more efficient, by having higher affinity, when the corresponding autocatalytic subnetwork is not functioning . We note that, as our work also targets synthetic design and metabolic engineering leading to the introduction of novel autocatalytic cycles, we find allosteric regulation implementation to be more complicated in such contexts and thus less appealing a strategy compared with, for example, the introduction of external input fluxes.E. coli (the PTS using cycle and the glyoxylate cycle). Briefly, for the PTS using cycle we find good agreement between our predicted direction of regulation and the regulation found (11/12 interactions agree with our prediction). For the glyoxylate cycle, the agreement is much weaker (8/13 interactions agree with our prediction). We note that this finding is in agreement with the work of Gerosa et al. (Cell Systems 2015) that suggests that TCA cycle fluxes are mostly regulated by transcription and not reactant levels.We added two sections to the paper analyzing allosteric regulation. One section  describes the allosteric regulation interactions (inhibitions or activations) that are expected to improve the function of autocatalytic cycles. Another section  compares the predicted interactions with the actual direction (activation or inhibition) found for the two autocatalytic cycles we identify and find to be functional in the central carbon metabolism of native Clearly, allosteric regulation serves many more roles and the metabolic network faces many more challenges than just the support of stable autocatalysis. We do not therefore suggest that proper autocatalytic function is the underlying reason for the interactions that agree with our predictions.5) In subsection “Stability analysis for multiple-reaction cycles”, the authors mention that the affinity of the branch reaction to the intermediate metabolite of the cycle it consumes must be lower than the affinity of the corresponding recycling reaction of the cycle. Is this statement really correct, given that it is based on either a unscaled sensitivity (dv/ds and not dlnv/dlns) or a saturation degree, which generally also depend on the expression levels of the enzymes, i.e. their Vmaxs?We thank the reviewers for showing us we did not make this delicate point clear. We now address the issue of the connection between the unscaled sensitivities of reactions, their saturation degrees, and their affinities in the Materials and methods, section "Inverse relationship between derivatives, affinities, and saturation levels". According to the lemma we prove, we conclude that if f_a(X*)>f_b(X*) and β>α, then it holds that S_a(X*)>S_b(X*) and K_<K_, which correspond to the statements we make in subsection “Analysis of a Reversible autocatalytic cycle reaction”.6) The theoretical predictions could and should be tested more strictly. Although the experimental results that are discussed are consistent with the predictions from the mathematical analysis, they could have alternative explanations. Low saturation of enzymes with their substrates is not uncommon in metabolic networks, and a number of hypotheses have been put forward to explain the apparently wasteful investment in high enzyme concentrations. See for instance refs. [1-6], not to mention some from this manuscript's authors. In fact, while according to the theory a single branching enzyme being less saturated than the cycle enzyme consuming the same substrate would warrant stability, the experimental data point to most of the branching enzymes being less saturated than the cycle enzymes, which makes the concern about alternative explanations pertinent. The authors may thus wish to discuss these potential alternative explanations, and explain why they eventually don't apply. As a negative control, the authors may wish to examine if enzymes branching from non-autocatalytic cycles tend to be more saturated with substrates from the cycle than those branching from autocatalytic cycles.We thank the reviewers for this point. We agree that alternative explanations may underlie the lower saturation of branching enzymes from autocatalytic cycles.We added references to the excellent works the reviewers pointed at.We address this issue in three independent ways:1) We show that having multiple unsaturated reactions increases the robustness of the cycle to perturbations, as is suggested in minor point 7 below .2) We compare the saturation levels of the same branch points as those presented in 3) We consider branching points from two non-autocatalytic cycles – the TCA cycle and the PP + gluconeogenesis cycle . For each such cycle we identify the major branch points (akg consumption from the TCA cycle and r5p consumption from the PP cycle). We find that out of 6 branch cases, in 3 cases the branch reaction is less saturated than the cycle reaction, and in 3 cases, the situation is reversed  If lower expression of the enzymes catalyzing reactions that branch out from autocatalytic cycles leads to higher production rates of metabolic precursors, one would expect a negative correlation between the cellular abundance of some of these enzymes and growth rate. This prediction should be relatively straightforward to test based on published quantitative proteomics datasets. Again, a comparison with enzymes branching from non-autocatalytic cycles could be made as control.The reviewers suggest an interesting, additional validation of the findings of the paper. However, we do not find this suggestion to be straightforward to test. In order to be tested, it requires multiple conditions with different growth rates, under all of which the same autocatalytic cycle functions and the expression levels of the branch or cycle reactions differ. Glucose-limited chemostat data may seem to be an adequate candidate, but there are a few caveats for using it:1) The level of the assimilated metabolite, glucose, changes dramatically between the different chemostat conditions.2) Different transporters exist and function under different concentrations of glucose, not necessarily following the autocatalytic properties of the PTS.3) As noted in our response to the points regarding allosteric regulation, it may play a major role in controlling fluxes in the PTS-using autocatalytic cycle, which is the cycle used in growth on glucose.Indeed, evaluating the correlations for two data sets  shows that the branch and corresponding recycling enzymes display various dependencies on the growth rate, mostly even non-uniform . We believe a specific experimental system, titrating the expression levels of various enzymes along the cycle while maintaining the level of external metabolite fixed, is probably the best way to investigate this phenomenon, but find it to lie outside the scope of this work.8) An examination of the regulation of the branching enzymes may also provide additional support for the theory. E.g., these enzymes may be subject to competitive inhibition (to increase the apparent KM) under conditions where there is a higher demand for the cycle's intermediates.We thank the reviewers for highlighting this potential additional support. We address this issue together with addressing point 4 above and find that, in the PTS-using cycle, such evidence indeed exists. In the glyoxylate cycle such regulation is not statistically significant, suggesting other control mechanisms may be at play  It would also be very useful to have experimental data showing that forcing a lower activity or higher saturation of key branching enzymes would cause instability as predicted. However, this may require dedicated experiments, and should not be viewed as a necessary condition for acceptance.We agree with the suggestion the reviewers make here, and find such a system to also be useful for investigating point 7 above further.10) While most of the paper seemed clearly written and unambiguous, several statements in the Introduction are imprecise or unclear. (a) One confusing aspect is the ambiguity between collectively autocatalytic systems and autocatalysis of their components. The component of a system that is collectively autocatalytic is in general not autocatalytic. Thus the statement in the second sentence of the Introduction is inaccurate. In fact, the authors themselves contradict that statement in paragraph two of the Introduction. (b) The authors mention that "autocatalytic systems have an inherent potential to be unstable as their operation changes the amount of their components". This last part of the sentence could be true for many other non-autocatalytic dynamical systems, so it is not clear that this statement is justified. (c)The concept of a system being catalytic "with respect to something" is not clearly defined ; (d) It is not clear how the statement at the end of paragraph two ("Therefore….") follows as a logical consequence of the prior statement.We thank the reviewers for pointing out these confusing points regarding the general introduction to autocatalysis. As we found this part of the Introduction does not contribute to the main theme of the paper, we removed it from the revised version.11) In the interest of reproducibility, the authors should provide supplementary material tables containing the data used for deriving The reviewers correctly point at the missing tables, which we added in the revised version.


Decades of biochemical, bioinformatic, and sequencing data are currently being systematically compiled into genome-scale metabolic reconstructions (GEMs). Such reconstructions are knowledge-bases useful for engineering, modeling, and comparative analysis. Here we review the fifteen GEMs of archaeal species that have been constructed to date. They represent primarily members of the Euryarchaeota with three-quarters comprising representative of methanogens. Unlike other reviews on GEMs, we specially focus on archaea. We briefly review the GEM construction process and the genealogy of the archaeal models. The major insights gained during the construction of these models are then reviewed with specific focus on novel metabolic pathway predictions and growth characteristics. Metabolic pathway usage is discussed in the context of the composition of each organism's biomass and their specific energy and growth requirements. We show how the metabolic models can be used to study the evolution of metabolism in archaea. Conservation of particular metabolic pathways can be studied by comparing reactions using the genes associated with their enzymes. This demonstrates the utility of GEMs to evolutionary studies, far beyond their original purpose of metabolic modeling; however, much needs to be done before archaeal models are as extensively complete as those for bacteria. Since their discovery and classification in the late 1970s and early 1980s  archaea Despite the significant progress in sequencing archaeal genomes, a systematic understanding of the metabolism of archaea is still lacking. This is especially true for peripheral metabolic pathways and mechanisms of adaptation to extreme environments . It has For this reason, systematic databases of the metabolic properties of the archaea are highly desirable; the field of systems biology is uniquely positioned to provide useful insight into the diversity and evolution of metabolic capabilities. To date, fifteen genome-scale metabolic models  have been constructed for ten archaeal species. However, these models represent primarily members of the Euryarchaeota with almost three-quarters representatives of methanogens. An examination of the phylogenetic tree demonstrates a lack of well-curated metabolic reconstructions in many of the archaeal taxa see . Methanosarcina acetivorans.Despite the limited representation, much can already be learned from the GEM “knowledge-bases”. Here, we review the GEMs constructed to date and the knowledge gleaned from them. We begin by briefly reviewing the construction process for GEMs and general predictions made by metabolic models. We also give a historical perspective of the construction of the archaeal GEMs. We then review the models and specific insights gained from model constructions, including novel metabolic enzymes/pathways. Finally, we demonstrate the utility of these metabolic models to the study of evolution of diversity in archaea. We do this by computing the conservation of reactions (based on genetic association of the enzymes) across the archaea and visualizing the extent of conservation on a comprehensive map of the metabolism of the methanogen Haemophilus influenzae Rd. Through comparative genomics they showed that 68% of the known E. coli proteins had homologs in the H. influenzae Rd genome, enabling a hypothesis of which metabolic pathways exist in H. influenzae Rd. Since then, the pioneering work of Thiele and Palsson [Metabolic networks are invaluable tools for qualitatively understanding an organism's metabolic behavior under given conditions and have a long history of use in biology. Systematic construction of metabolic models which couple metabolic networks with genetic associations, reactions that exchange metabolites with the environment, and the organism's biomass composition only began to take shape in the mid-1990s when Fleischmann et al.  fully se Palsson  has esta Palsson .A GEM can best be described as a knowledge-base containing all the biochemical information describing an organism's metabolic network. They are typically presented as Systems Biology Markup Language (SBML)  files thHere, we will briefly summarize the GEM construction process and highlight the most important characteristics of GEMs that one typically encounters. The de facto standard GEM construction protocol is that published by Thiele and Palsson  and shouThe construction process is divided into four broad stages: (1) automated construction of a draft model, (2) manual refinement of the draft model, (3) conversion of the model into a mathematical model, and (4) quantitative evaluation and refinement of the model. The first stage involves identifying all the potential reactions and pathways that the organism harbors based on its annotated genome. This process can be automated as it is essentially a bioinformatics problem requiring the comparison of the genome with databases that document known genes and their associated metabolic enzymes and pathways  and the corresponding nongrowth associated ATP maintenance (NGAM) reaction, and the Boolean gene-protein-reaction associations (GPRs).Quantitative prediction using GEMs is typically framed as a linear programming problem in which one feature of the model is optimized under a given set of constraints. This feature is typically the model's biomass production rate  which is described by a single pseudo-reaction that produces a “biomass” pseudo metabolite by consuming all the metabolites that the organism requires to grow . Ideally, this reaction is constructed using the experimentally characterized biomass composition of the organism. However, this data is often difficult to obtain, leaving curators to either estimate biomass compositions from the organism's genome or adopt the compositions available from other organisms. M. barkeri model by Feist et al. [The GAM and NGAM reactions consume ATP. The GAM reaction reflects the ATP consumption required for the organism to grow whereas the NGAM reaction reflects the organism's basal ATP consumption required to survive but not necessarily to grow . Since both reactions reflect the organism's energy requirements in the model, the choice of stoichiometric coefficients for these two reactions greatly influences the model's growth predictions. Ideally, the stoichiometric coefficients of these two vital reactions should be determined from a chemostat experiment in which the growth rate is tracked alongside ATP consumption . In prat et al. ).The GPRs are Boolean expressions containing the genes that code for metabolic enzymes facilitating the reactions. By piecing the genes together in series of AND and OR operations, a GPR encodes which genes are necessary for an enzyme to be synthesized by the cell and therefore which genes are required for a metabolic reaction to exist. Predictions of gene knockout effects are commonly computed with GEMs. Not all reactions in the model will have GPRs due to either the lack of experimental gene characterizations, the use of nonphysical “gapfill” reactions , or the Once this manual curation is complete, one can proceed to the third stage of converting the GEM into a quantitatively predictive model. This is done by defining the “objective” reaction to be optimized in the model and constraining the flux ranges on all model reactions. These flux ranges must reflect a specific growth condition to which the organism is subject. During model construction, most internal reaction fluxes will likely be unbounded, due to the relatively limited biochemical and proteomics data available for most reactions and organisms; it is the exchange reaction fluxes that must be constrained to reflect the nutrient availability of the organism's environment. Exchange reactions are nonphysical external reactions of the model that introduce compounds into the system, thereby simulating the organism's growth environment. These constraints  will hav Methanococcus jannaschii by Tsoka et al. [ Methanosarcina barkeri (iAF692) which was first constructed by Feist et al. [ iAF692 was the first manually curated methanogen GEM thoroughly verified against experimental growth data. M. barkeri is also one of the most metabolically diverse methanogens in the Euryarchaeota kingdom, capable of consuming acetate, methylamines, methanol, CO, and CO2/H2. Two models, iVS941 [ iMB745 [ M. acetivorans and published in 2011 by the Maranas and Price research groups, respectively. M. acetivorans is equally diverse and similar in metabolism and thus inherited much of the M. barkeri GEM characteristics. iMB745 was then used as the base model from which to draft the more recent methanogen GEMs, Methanobrevibacter smithii (iMsi385) [ Methanospirillum hungatei (iMhu428) [ M. acetivorans models include iMAC868 [ iST807, which are both independent updates to iMB745. The GEM for M. maripaludis (iMM518) was constructed in 2014 by Goyal et al. [The genealogy of all the published archaeal GEMs to date is shown in a et al.  in 2003,t et al.  in 2006., iVS941  and iMB7[ iMB745 , were iniMsi385)  and MethiMhu428) , both of iMAC868  and our l et al. , 80 inde Halobacterium salinarum R-1 (iOG478) [ Natronomonas pharaonis (iOG654) [ H. salinarum model. The only other nonmethanogenic archaeal GEM to our knowledge was independently constructed in 2012 for the Sulfolobus solfataricus by Ulas et al. [Nonmethanogenic archaeal GEM construction has been largely dominated by the work from Dieter Oesterhelt's research group. In 2008, they released the first manually curated GEM for(iOG478) . This wa(iOG654) , which is et al. .Although archaea had been established since the 1980s as the third domain of life by the pioneering work of Carl Woese and collaborators –5, 7, 102 is reduced to methane in a series of steps. Although this basic framework is well conserved among methanogens, the key difference lies in the exergonic-endergonic reaction couplings in the pathway. The first step of CO2 reduction is an endergonic reaction that oxidizes ferredoxin and produces formylmethanofuran. In simple hydrogenotrophic methanogens that lack cytochromes, this energy is typically recovered by the methyl-H4MPT:CoM methyltransferase (Mtr) reaction and the heterodisulfide reductase (Hdr) reaction. Mtr expels Na+ ions in the process of transferring the methyl group onto coenzyme M (CoM) and thus establishes the electrochemical gradient responsible for driving ATP synthesis. Electrons are extracted from formate or H2 by Hdr which then uses these electrons to split the CoM-CoB heterodisulfide and reduce ferredoxin, thus replenishing the ferredoxin pool that is required to run the very first step of CO2 reduction. This oxidation of formate or H2 to reduce the heterodisulfide and ferredoxin is called the electron bifurcation reaction. This is in contrast to cytochrome-containing methanogens which are almost exclusively found within the Methanosarcinales. In these substrate-diverse methanogens, the Hdr enzyme evolved to harbor a cytochrome and can utilize methanophenazine as another electron carrier. Instead of directly reducing and replenishing the organism's supply of ferredoxin, Hdr expels hydrogen ions to establish a proton-based electrochemical gradient that is used by a membrane-bound energy conserving hydrogenase (Ech) to regenerate the reduced ferredoxin. This system is best exemplified by the M. barkeri model (iAF692) in which the Ech reaction was of particular interest during model construction because the ratio of protons translocated to electrons extracted was unknown at the time. Using experimental growth yield data, a stoichiometry of 1 proton/2e and GAM/NGAM of 70/1.75 mmol/gDWT/hr enabled the model to predict growth yields consistent with experimental data for growth on methanol, acetate, H2/CO2, and pyruvate. This Ech stoichiometry was later updated in iMG746 to 2 protons/2e−. Although very closely related to M. barkeri, M. acetivorans has significant differences as a marine methanogen. Within methanogenesis, it substitutes Ech with the ferredoxin:NAD+ oxidoreductase complex (Rnf) which interestingly translocates sodium ions instead of hydrogen ions [+ dominated electrochemical gradient and helps explain why M. acetivorans inhabits a marine environment [ M. barkeri [ M. acetivorans is not able to consume CO2, it would not be carrying out the endergonic first step of reducing CO2 and thus justifies the absence of an Ech.As the most defining metabolic pathway within methanogens, methanogenesis has been well characterized by numerous biochemical studies over the years. Therefore, the most significant and notable differences between the methanogen models will be found in the methanogenesis pathway and supportive pathways producing novel cofactors for different substrates. The basic framework is shown in gen ions . This esironment  in contr barkeri . Since M M. barkeri model iAF692 and the M. acetivorans model iMB745. Both models describe seven major metabolic subsystems: vitamins and cofactor biosynthesis, amino acid metabolism, nucleotide metabolism, central metabolism, lipid and cell wall biosynthesis, and methanogensis. iMB745 inherited most of the reactions in iAF692 but also incorporated various additional pathways. The most notable changes include a modification of the methanofuran biosynthesis pathway based on homology of enzymes to those from the same pathway in M. jannaschii, a modified electron transport chain reflecting the aforementioned substitution of Rnf for Ech, and an updated biomass reaction that incorporated new carbohydrate, lipid, and nucleotide composition data. Although an attempt was made to estimate the GAM purely from genomic data, the model had to retain and optimize iAF692's original value in order to fit experimental growth data. The biomass reaction was more systematically constructed in iMB745 than iAF692. The general components of the biomass reaction  were taken from a typical bacterial cell instead of an average methanogenic archaea cell, most likely due to the lack of experimental data. This practice is quite common when reconstructing archaeal GEMs and can have serious consequences because the biomass composition has significant influence over metabolic flux distributions throughout the network. These computed flux distributions may be biased by the use of bacterial biomass compositions rather than archaeal biomass compositions  in whic iMB745 despite the fact that iVS941 was independently published at the same time. This inheritance trend is most likely due to the more complete model documentations and availability of a readily testable GEM provided for iMB745 in contrast to iVS941. Given that metabolic modeling for archaea is still a developing effort, this practice of providing poorly assembled GEM files that are ill-prepared for quantitative assessment is still, unfortunately, common in the field. In order to alleviate this problem, we provide in the supplementary information  of this review all the currently available M. acetivorans models standardized to use BIGG IDs (http://bigg.ucsd.edu/data_access) and proper compartment tags such that the models can be conveniently handled within COBRApy. We also compare their growth characteristics as shown in From the methanogenic GEMs geneology, it is clear that most of the methanogenic GEMs are inherited fromiVS941 predicts unrealistic growth rates, growth yields, and no methane efflux, which indicates the model's deficiency. This growth characteristic assessment shows that, besides proper documentation, iMB745 also demonstrates better predictive ability over iVS941 and thus serves as a more reliable parent model for M. acetivorans. This is also evidenced by the predictive performances of iST807 and iMAC868 which are updated versions of iMB745. Across all growth substrates and growth characteristics, iMAC868 predictions showed a median deviation of 36% from experimental values. In contrast, iST807 demonstrated only a median deviation of 12% which is a marginal improvement over the 14% median deviation of iMB745. Although these statistics may seem to suggest that iMB745 and iST807 are more reliable models overall, it is important to keep in mind that growth predictions are heavily dependent on each model's allowed uptake reactions and their respective rates. In this assessment, each model's uptake reactions were set to the defaults that were provided within their respective publications. The uptake rate for the growth substrate being tested was uniformly set to the experimental value across all the models, and all other major growth substrate uptake reactions were turned off. Halobacterium salinarum R-1 capable of growing on 15 different carbon/energy sources was developed by the group of Dieter Oesterhelt [ H. salinarum was missing all or portions of these pathways. An alternate pathway using the partial Entner-Doudoroff (ED) pathway was connected to the partial oxidative branch of the PPP by a semiphosphorylated 6-phosphogluconate. This pathway thus described why the organism retained parts of the oxidative PPP and part of the ED pathway even though it is incapable of growing on sugars. During the reconstruction the authors also noted that shikimate production was incomplete and thus proposed that hexose and L-aspartate-4 semialdehyde were used, consistent with 13C labeling data from tryptophan degradation. Additionally, draft pathways for synthesis leucine, isoleucine, and valine could be generated in the model.While only four GEMs have been developed for only three nonmethanogenic archaea, they provided significant insight into the metabolism and growth of the organisms. A reconstruction of the halophilic archaeumsterhelt . During  H. salinarum primarily produces isoprenoid lipids using leucine (~10%) while isoleucine was primarily degraded entering the TCA as acetyl-CoA and succinyl-CoA. Valine was the only amino acid that was primarily incorporated into biomass. Because the uptake rate of amino acid far outpaced the biomass incorporation they hypothesized that degradation pathways for all amino acids exist and proposed six enzymes to facilitate some of these reactions. However, it was only later that they determined the biosynthetic pathways for aromatic amino acids which they shared in common with M. jannaschii; during the discovery they used the metabolic model to identify uptake rates in auxotrophs [To calibrate the model, they measured the amino acid composition and content using experiments and found that protein mass constitutes 49% of the dry mass, much less than in the other archaea. Using dynamic simulations with experimentally measured uptake rates for amino acids they predicted internal fluxes from which they drew a number of conclusions. Most strikingly, only 15% of amino acid carbons ended up in biomass with the majority being used to produce energy in the TCA cycle. They found that all amino acids were simultaneously used, though arginine, aspartate, leucine, and isoleucine were taken up most quickly, even the essential amino acids methionine, lysine, isoleucine, leucine, and valine which the cells are incapable of producing. Using flux balance analysis, they found thatxotrophs . Most imxotrophs  and indiThe model was later updated to include a refined description of the respiratory chain as well as phototrophic growth leading to additional insights into metabolism . Several H. salinarum led to the conclusion that the organism evolved its metabolic behavior to maximize growth during blooms, which can occur sporadically with many years in between [By fitting uptake rates of amino acids to aerobic growth experiment measurements, they identified isoleucine, leucine, and valine as the preferred energy sources, while others such as alanine, proline, and ornithine had distinct periods of different uptake rate . Thus, t between , 14. It  Natronomonas pharaonis was developed [ H. salinarum. The network is significantly larger, with nearly 30% more genes associated with reactions, mostly due to additional amino acid and carbon degradation pathways. As N. pharaonis is capable of growth on a single carbon source the reconstruction complements that for H. salinarum which requires a complex broth for growth. For this reason, the reconstructions could be used to investigate questions regarding the metabolic objective of halophiles that are subject to different evolutionary pressures and answer questions about optimality of energy production.The metabolic network for the polyextremophile eveloped  using th H. salinarum, that it made up about 75% of organic mass [μmol/ΔOD·mL. A wide range of maintenance energies and acetate:oxygen ratios gave near optimal growth, indicating that growth of N. pharaonis is robust to environment and the biological objective is to maximize growth and energy production [2 production and oxygen consumption) the authors were able to demonstrate that about 10% of carbon is neither incorporated in biomass nor respired, suggesting that the organism uses some form of overflow metabolism [The authors measured the amino acid content to define the biomass composition and found, similar tonic mass , 25. Per Sulfolobus solfataricus [The final nonmethanogen model developed for an archaeon is for the hyperthermoacidophileataricus . The mod S. solfataricus uses a reverse ribulose-monophosphate pathway (RRMP) instead of the pentose phosphate pathway. Specifically, they found that the organism was missing a transaldolase and thus they allowed accumulation of sedoheptulose 7-phosphate. They found that accumulation of sedoheptulose 7-phosphate in their simulated media accounted for ~3% of all carbon atoms and thus is a significant portion of the overall carbon available for biomass. Simulations indicated that on glucose growth about 22% of carbon flux was fed into the RRMP pathway while the rest was metabolized to pyruvate via the Entner-Doudoroff (ED) pathway to be subsequently used in TCA cycle. Flux variability analysis of the metabolic model demonstrated that both the semiphosphorylative and nonphosphorylative branches of the ED pathway were possible and indicates that further studies are required to understand the growth of the organism. Similarly, the TCA cycle showed significant variability, primarily due to the glyoxylate shunt. Finally, variability in the production of amino acids such as histidine, tryptophan, alanine, and glutamate indicates different routes of synthesis.During the model reconstruction, the authors identified the fact that Sulfolobus sp. VE 6 could grow autotrophically fixing bicarbonate, the authors searched for the hydroxypropionate-hydroxybutyrate cycle. They found 11 of the 16 enzymes and performed BLAST searches to identify putative homologs of the 5 remaining enzymes. Thus, they predicted that S. solfataricus is able to grow autotrophically and suggested that experiments should be performed. It is important to note, however, that autotrophic growth of S. solfataricus had already been verified by Zillig et al. [2S. Regardless, this gives a hint about the possibility of syntrophic interactions with sulfate reducing bacteria.Because a related organismg et al. . During  S. solfataricus is metabolically versatile. Although S. solfataricus is naturally a thermophile and therefore likely possesses a large repertoire of thermostable enzymes, it has been suggested [ S. solfataricus' metabolic versatility is potentially advantageous in high-temperature environments, allowing the organism to circumvent the potential issues of decreased enzyme catalytic activity and higher mutation rates. Overall, these results suggest that S. solfataricus can preferentially consume certain carbon sources and regulate alternative pathways to support beneficial symbiotic relationships. Alternatively, one can also argue that S. solfataricus can take advantage of its metabolic versatility to outcompete other organisms.The authors went on to compare the growth of the organisms on the 35 different carbon sources. To do this they fixed the carbon uptake rate and compared biomass flux. Overall, the organism grew significantly faster when growing on glycerol and propanol and marginally better on oligosaccharides. They also grew significantly more slowly on carbon sources than on compounds that enter the TCA cycle at points other than 2-oxoglutarate. Gene deletion assays indicated that over 50% of all single gene knockouts were nonlethal and an additional ~25% allowed limited growth, suggestinguggested  that theWell-curated metabolic models function as comprehensive databases of the knowledge about organisms; thus, they are potentially useful tools for studying evolution and diversity of metabolism. Three properties of the metabolic models are of particular utility for comparative studies: (1) metabolic models connect gene function with metabolic function via their gene-protein-reaction rules, (2) the metabolic network is topologically defined by metabolites and the reactions that interconvert them, rather than the genes that facilitate those interconversions, and (3) metabolic networks coupled with modeling techniques allow for the identification of function redundancy/degeneracy. The first of these properties allows direct comparison of gene content based on metabolic function and the application of traditional evolutionary tools . The second of these properties allows networks to be compared by function rather than gene content; for example, the network could be used to identify convergent evolution. The final of these properties could be used to provide insight into the selective pressures of the organism; specifically, duplicated functionality might suggest a critically important function for the organism. M. acetivorans model iST807 were used as input to the db_evaluateReactionsFromGpr.py function to assess the conservation in other organisms. The “or” option to the function was used to assess whether any genes for each M. acetivorans reaction existed in the other archaea. Doing this for each organism, we computed the extent of conservation for each reaction . The results can be seen in  M. acetivorans, it is not surprising that the extent of conservation is relatively low (blue) across the network. Nevertheless, it is interesting to note that the most visible conservation (red) occurs within Nucleotide metabolism, coenzyme synthesis-related reactions, and various amino acid biosynthesis reactions. This suggests that the underlying transcription and translation machinery of archaea are fairly similar.To demonstrate the utility of metabolic models to evolutionary analyses we computed the conservation of genes facilitating metabolic reactions. An ITEP database  of 221 a iST807 computed by ITEP lends more specific insight into conservation of metabolism in these archaea  or very lowly conserved (high reaction uniqueness). This is not a surprising observation as it has long been known that metabolic networks have a bowtie topology [Categorizing the homologous genes by metabolic subsystem as annotated inhaea see . Amino ahaea see . Prolineentified . Althougtopology  and are topology . Cross cWe have presented an overview of genome-scale metabolic models and discussed the defining metabolic features among the few GEMs available for archaea. In these discussions, we have also highlighted some much-needed improvements to model building practices in order to facilitate the development of archaeal models. By using the gene-protein-reaction associations in these archaeal GEMs, we also demonstrate the invaluable utility of these metabolic models as they can be extended beyond flux analysis to gain significant insight into evolutionary patterns among organisms. Visualizing the known archaeal metabolic models on a phylogenetic tree see  leads toThe supplementary data includes modified versions of the four previously published models for Methanosarcina acetivorans where reaction and metabolite identifiers have been standardized so as to allow direct comparison. These models were used for the comparative study of M. acetivorans presented in the review. Models are presented in the SBML format which is compatible with COBRAPy and COBRA Toolbox software packages. Models were originally published as: 1) iVS941 in Kumar et al. 2011, 2) iMB745 in Benedict et al. 2012, 3) iMAC868 in Nazem-Bokaee et al. 2016, and 4) iST807 in Peterson et al. 2016.