The appearance of planetary oxygen likely transformed the chemical and biochemical makeup of life and probably triggered episodes of organismal diversification. Here we use chemoinformatic methods to explore the impact of the rise of oxygen on metabolic evolution. We undertake a comprehensive comparative analysis of structures, chemical properties and chemical reactions of anaerobic and aerobic metabolites. The results indicate that aerobic metabolism has expanded the structural and chemical space of metabolites considerably, including the appearance of 130 novel molecular scaffolds. The molecular functions of these metabolites are mainly associated with derived aspects of cellular life, such as signal transfer, defense against biotic factors, and protection of organisms from oxidation. Moreover, aerobic metabolites are more hydrophobic and rigid than anaerobic compounds, suggesting they are better fit to modulate membrane functions and to serve as transmembrane signaling factors. Since higher organisms depend largely on sophisticated membrane-enabled functions and intercellular signaling systems, the metabolic developments brought about by oxygen benefit the diversity of cellular makeup and the complexity of cellular organization as well. These findings enhance our understanding of the molecular link between oxygen and evolution. They also show the significance of chemoinformatics in addressing basic biological questions. Elucidating the link between the rise of planetary oxygen and biological evolution is a challenging topic in evolutionary biology. Previous studies in this area were dominated by biological investigations. The recent simulations of metabolic networks under anaerobic or aerobic conditions revealed that aerobic metabolism gave rise to 1,000+ new reactions. Since metabolites are small molecules and metabolic reactions are basically chemical reactions, we think that the impact of oxygen on metabolic evolution can be well studied by chemoinformatics. In this paper, we use chemoinformatic methods to perform a comprehensive comparative analysis of the chemical structures, properties and reactions of anaerobic and aerobic metabolites. It was found that aerobic metabolism has considerably expanded the structural space of metabolites by inventing 130 novel molecular scaffolds. Moreover, aerobic metabolism also helped organisms to explore a new chemical space by increasing the hydrophobicity and rigidity of metabolites. Since hydrophobic metabolites are fitting to modulate membrane functions and to serve as transmembrane signaling factors, these metabolic innovations definitely benefit the establishment of complex cellular organizations. The present findings not only help to understand the molecular link between oxygen and evolution but also suggest that chemoinformatics is of special value in addressing some basic biological questions. Accumulating biological and geological evidence indicates that oxygen has had a great impact on biological evolution Elucidating the molecular link between the rise of oxygen and biological evolution has been one of the most challenging topics in evolutionary biology. A straightforward explanation to this link is that aerobic respiration is much more efficient than anaerobic respiration in generating ATP Since metabolites are small molecules and metabolic reactions are basically chemical reactions, they could be best dissected by chemoinformatics The aerobic and anaerobic metabolic networks simulated by Raymond and Segrè consist of 1,145 anaerobic and 454 aerobic reactions, from which 1,326 anaerobic metabolites and 538 aerobic metabolites can be identified An analysis of metabolic network structure reveals the existence of some predominant modules in the aerobic and anaerobic pathways. For example, 48 and 19 major modules account for 80.2% and 80.8% of anaerobic metabolites and aerobic metabolites, respectively  and S2. e.g., NAD(H), NADP(H) and FAD) were more prevalent than metallic counterparts , while in aerobic enzymes, metallic redox cofactors were more popular. This mirrors the poor bioavailability of copper and molybdenum in the anaerobic world At protein level, prior studies revealed that at least 31 folds are exclusively used by aerobic enzymes, most of which (90%) use oxygen explicitly Thus, anaerobic and aerobic metabolic networks are remarkably distinct and must exhibit marked differences in their chemical space. This includes the structural, chemical and reaction properties of their metabolites.In order to explore the impact of oxygen on metabolic evolution in structural space, we first calculated the scaffolds  for 1,174 anaerobic metabolites and 520 aerobic metabolites with clearly defined structures. Since different molecules can share the same scaffold, scaffolds are much more conserved than overall chemical structures To intuitively illustrate the structural space expansion of aerobic metabolism, we constructed a ‘structural cluster map’ consisting of anaerobic and aerobic metabolites. This map is a two-dimensional scatter plot that characterizes the structural similarity patterns of compounds. In this map, each compound is represented with a dot and the position of the dot is determined by its Tanimoto similarity to other compounds  e.g., gibberellins), polyphenols , alkaloids  and macrocyclic lactones , most of which are secondary metabolites and are important for aspects of life that are known to be evolutionarily derived, such as transmembrane export and import (steroids), signal transfer , defense against biotic factors  and organism protection from oxidation (polyphenols).Analysis of the major clusters (big dots) of anaerobic and aerobic metabolites  shows thTo explore the impact of oxygen on metabolic evolution in chemical space, some commonly used chemical property descriptors were calculated for anaerobic and aerobic metabolites . Since pAlthough anaerobic and aerobic metabolites are similar in some bulk characteristics, such as molecular weight, total molecular surface area and total molecular volume, they are much different in other properties . First, i.e., polar molecular surface area and polar volume, hydrogen bond acceptor count and oxygen atom count) (in bold). In comparison, the second factor, explaining 38.2% of the variance, contains important contributions (with loadings >0.85) from constitutional properties   in catalytic sites more frequently (P<0.05), while aerobic enzymes use non-polar residues  more often (P<0.05)  (P<0.05) . PatternIn evolution, metabolic networks expand as new chemistries and enzymes are made available to the cell The chemical features of aerobic metabolites raise an interesting question. Oxygenation reactions usually introduce hydroxyl groups and these groups are hydrogen donors/acceptors and are hydrophilic. Given this fact, how can we explain the observation that aerobic metabolites contain less hydrogen donors and acceptors and are more hydrophobic than anaerobic compounds? To address this question we investigated features that describe anaerobic and aerobic metabolic reactions.Based on KEGG metabolic maps, 1,114 anaerobic reactions (covering 938 anaerobic metabolites) and 630 aerobic reactions (covering 480 aerobic metabolites) were identified as irreversible. During assignments, the “augmented reactions” defined in ref. 13 were not considered. We extracted 1342 anaerobic reaction pairs and 656 aerobic reaction pairs from these irreversible reactions, discarding enzyme cofactors and metabolites with molecular weights <70 Da. We then calculated net changes (from reactants to products) for some properties associated with polarity and averaged values . RemarkaOur calculation shows that the average logarithm of the partition coefficient (AlogP98) of the initial anaerobic reactants (−1.63)  is much In summary, the present chemoinformatic analysis reveals two major impacts of oxygen on metabolic evolution that unfold in chemical space. First, the new reaction types of aerobic metabolism embody a large number of novel molecular scaffolds. In particular, the epoxidation of squalene by oxygen and subsequent oxygen-dependent reactions generate a series of steroids, which are most popular scaffolds in aerobic metabolites. Since the hydroxyl group is directly attached to the ring structure at C3, the polar layout of steroids contrasts with their anaerobic counterparts, the hopanoids. This layout enables steroids to play crucial roles in endo- and exocytosis of unicellular and multicellular eukaryotes http://prelude.bu.edu/O2/networks.html) consist of 1,326 anaerobic metabolites (blue nodes) and 538 aerobic metabolites (red nodes) The metabolic networks simulated by Raymond and Segrè , adopting default parameters. The plotting procedure is as follows. First, we conducted a principal component analysis of substructural fingerprints (UNITY 2D fragments embedded in Benchware DataMiner) and used the first two components as the initial coordinates for the first batch of compounds (randomly selected from the dataset). Second, all compounds were added to the plot of already projected compounds using Tanimoto similarities of shared UNITY 2D substructural fragments. Similar compounds (with Tanimoto similarity >0.85) were pooled together into clusters. Finally, the distances were collapsed over the horizon. The non-linear mapping method (NLM) was used to minimize the overall fractional error and preserve the actual distances in many dimensions when plotting in fewer dimensions.Tanimoto coefficient (TC) has been widely used to characterize the structural similarity of molecules The commonly used chemical property descriptors, including Molecular weight, Total molecular surface area, Total molecular volume, Total atom count, Polar molecular surface area, Polar molecular volume, H-bond acceptor count, H-bond donor count, Hydrophobic fragment count, Ring count, Total bond count, Rotatable bond count and Chiral center count, were calculated with Sybyl 7.0. Carbon atom count, Oxygen atom count, Nitrogen atom count, Sulfur atom count, Phosphorus atom count and Aromatic ring count were calculated by Pipeline Pilot. Logarithm of partition coefficient (AlogP98) was calculated by Cerius 2 . All of the statistical analyses were performed with SPSS .Figure S1Illustration of anaerobic and aerobic metabolic networks.(DOC)Click here for additional data file.Figure S2Chemical property distribution patterns in the anaerobic and aerobic metabolite datasets.(DOC)Click here for additional data file.Table S1Basic information for the 48 major anaerobic modules.(DOC)Click here for additional data file.Table S2Basic information for the 19 major aerobic modules.(DOC)Click here for additional data file.Table S3Descriptors of chemical space consisting of anaerobic and aerobic metabolites and corresponding loadings  for the first two factors.(DOC)Click here for additional data file.Table S4Basic information for the additional aerobic metabolic reactions.(DOC)Click here for additional data file.Table S5Property comparison between early and late anaerobic metabolites.(DOC)Click here for additional data file.


Experimental evidence shows the existence of multiple steady states in mammalian cell culture with distinct cellular metabolism . DiffereChanges on the cell culture’s metabolic state have been found to be related to the amount of residual glucose in a reactor . ExperimThe problem of providing an optimized strategy for glucose feeding in order to achieve a specific metabolic state is yet to be studied. We propose a model based strategy for designing a control system for metabolic state regulation that considers the biological complexity of the regulation of the cellular system.A detailed metabolic model for mammalian cell metabolism was formulated (complete model); a system of ordinary differential equations for the main metabolic variables of the following form:S is the stoichiometric matrix, is the reaction rate vector, and wherein is the metabolite concentration vector, i and where The model’s parameters were obtained from literature and through a fitting process to experimental data; said fitting process was by the least squares method using the Nelder-Mead simplex method .Once the experimental curves were obtained with the detailed model a simplified model was traced that includes the main metabolic reactions in CHO cells, and the same fitting process was carried out. Stability analysis was carried out on both the detailed and the simplified model in order to establish the number of feasible steady states for both models.F, which varies between 0 and 1:Enzyme kinetic for lactate dehydrogenase was weighted with an enzyme factor ΔL/ΔG with low values of F. Based on the estimated F values, a Hill activation function that depends on the residual glucose concentration was adjusted to obtain the experimental curves of the culture with metabolic shift.The objective of the same was to associate low The results of the curve fitting of the detailed and simplified models are depicted in Figure Stability analysis confirmed that both the simplified and detailed metabolic models exhibit only one steady state. The existence of only one stable attractor supports the idea that metabolic regulation alone cannot explain the metabolic shift. Therefore, gene regulation is an element that should be considered in a model that correctly describes this phenomenon.- : Simulated Glucose, (a) Simulation results for complete model without metabolic shift, (b) Simulation results for unregulated simplified model without metabolic shift, (c) Simulation results for unregulated simplified model with metabolic shift, (d) Simulation results for regulated simplified model with metabolic shift. The implemented regulation model consists of a Hill activation function that depends on the residual glucose concentration, which modifies the enzyme kinetic for lactate dehydrogenase in the following manner:β = 1 is the maximal expression level, glcK = 1.24 [mM] is the activation coeficient, n = 14.64 is the Hill coeficient, and Ceglc is the glucose concentration within the bioreactor. The result of the implementation of the above function is presented in Figure wherein ΔL/ΔG ratio is accompanied by a variation in the expression levels of certain genes that participate in glycolisis, which justifies the use of a regulation function that varies from 0 to 1. Stability analysis concludes that the current metabolic models are capable of reproducing only one steady state, making explicit the need to implement a regulation model. Moreover, the immediate response capability to glucose feed pulses indicate that said regulation model must be continuous. A Hill activation function was for supplying the gene regulation due to its structure; glucose concentration has been noted experimentally to be the main factor that produces a metabolic shift in mammalian cells and the modification of enzyme kinetics leads to a different ΔL/ΔG ratio, thus to a different steady state.Metabolic shift is caused by regulation at gene expression and metabolic levels. A reduction of the The final objective of said model is to design a model based controller capable of maintaining a low metabolic state (ΔL/ΔG ratio under 0.5) under continuous operation. The tentative input variables are the glucose and lactate concentrations as well as the ΔL/ΔG ratio. The controller will modify the response of the system by manipulating the dilution rate and the glucose feed concentration of the culture.


A metabolism is a complex network of chemical reactions that converts sources of energy and chemical elements into biomass and other molecules. To design a metabolism from scratch and to implement it in a synthetic genome is almost within technological reach. Ideally, a synthetic metabolism should be able to synthesize a desired spectrum of molecules at a high rate, from multiple different nutrients, while using few chemical reactions, and producing little or no waste. Not all of these properties are achievable simultaneously. We here use a recently developed technique to create random metabolic networks with pre-specified properties to quantify trade-offs between these and other properties. We find that for every additional molecule to be synthesized a network needs on average three additional reactions. For every additional carbon source to be utilized, it needs on average two additional reactions. Networks able to synthesize 20 biomass molecules from each of 20 alternative sole carbon sources need to have at least 260 reactions. This number increases to 518 reactions for networks that can synthesize more than 60 molecules from each of 80 carbon sources. The maximally achievable rate of biosynthesis decreases by approximately 5 percent for every additional molecule to be synthesized. Biochemically related molecules can be synthesized at higher rates, because their synthesis produces less waste. Overall, the variables we study can explain 87 percent of variation in network size and 84 percent of the variation in synthesis rate. The constraints we identify prescribe broad boundary conditions that can help to guide synthetic metabolism design. Among the most important goals of synthetic biology and biotechnology is to engineer organisms with novel properties Blochannia floridanusCarsonella ruddiifree-living organism.To be able to synthesize new life, one needs to understand life’s minimal needs. Considerable effort has thus focused on understanding and creating minimal organisms A second, complementary line of research starts from a complex genome, successfully eliminates genes from it without affecting viability, and thus creates a genome that is (close to) minimal. This is possible because free-living organisms have many genes that are dispensable in any one environment One indispensable feature of any living organisms is its metabolism. A metabolism is a complex network of chemical reactions, catalyzed by enzymes that are encoded in genes. It uses sources of energy and chemical elements – nutrients – to synthesize molecules that an organism needs, including precursors of biomass and various secondary products, such as molecules for defense and communication Metabolic engineering has multiple applications. They include the large-scale, fast, and efficient synthesis of pharmaceuticals, chemical reagents, and biofuels Current metabolic engineering approaches typically manipulate one or a few enzyme-coding genes While contemporary metabolic engineering focuses on altering existing pathways, future engineering will design metabolisms and minimal organisms de novo R needed to synthesize a given number B of (biomass) molecules from a given spectrum N of nutrients. The ideal network has few reactions and can synthesize many molecules using a broad spectrum of nutrients. However trade-offs between these properties exist, which do not allow all these requirements to be met.To be able to design a metabolism, one needs to be able to predict system-wide metabolic properties. In recent years great strides have been made towards such prediction. Especially noteworthy are constraint-based modeling approaches, which can predict the spectrum of biosynthetic properties of a metabolism from knowledge about the reactions that its enzymes catalyze, and from the nutrients available in its environment N, that is, the number of different carbon sources a metabolic network can utilize as sole carbon sources. The second is a network’s biosynthetic ability B, that is, the number of biomass molecules that it can synthesize. The third is the number of reactions R in a network. We then extend our analysis to further properties, such as the biosynthetic flux S, the rate at which biomass molecules are synthesized, and the amount W of waste produced.We here take a first step towards a quantitative understanding of these and other trade-offs using constraint-based methods. To this end, we study the properties of not just one metabolic network, but of multiple networks that differ in these properties. Experimental techniques are not yet suitable to do that, but computational approaches are Due to the presence of alternative metabolic routes that connect many pairs of molecules, most metabolic systems are able to tolerate genotypic changes, such as the deletion of enzyme coding genes. For instance, 80% of single gene deletions in budding yeast have no detectable phenotypic effect in standard laboratory environments minimal networks (see Methods) with a given nutrient flexibility N, that is, networks that can use N sole carbon sources to synthesize all biomass components, but in which every single reaction is essential, such that no reaction can be removed without abolishing viability of the network on at least one of the carbon sources. More specifically, we created 50 random viable networks that can use N = 20, 40, 60, and 80 carbon sources as sole carbon sources , and that could synthesize all B = 63 E. coli biomass components. We then studied the relationship between N and the number of reactions in these minimal networks (R to depend on N as R = (1.9±0.1)N +234, where the number 0.1 indicates the 95 percent confidence interval of the regression coefficient B +195. We then asked again how this relationship between biosynthetic ability and number of reactions depends on N, and thus repeated this analysis for networks viable on N = 20, N = 40, and N = 60 sole carbon sources. The slope of the regression line was indistinguishable for the different values of N . Overall, variation in the two independent variables explains 87 percent of the variation in the number of reactions of a metabolic network.The results of pairwise regression analysis are easy to display graphically and to interpret intuitively, which is why we use it here. However, where more than two quantities vary, pairwise regression analysis is insufficient to study dependencies among all of them. We thus also carried out a multiple regression analysis using all 800 minimal networks, where nutrient flexibility and biosynthetic ability were independent variables, and where the reaction number was the dependent variable. Not unexpectedly, the pairwise regression coefficients estimated from the multiple regression analysis were statistically indistinguishable from those estimated from the pairwise analysis above  of viable networks to answer this question (see Methods).Engineered metabolic networks that produce one or more desired products at a high rate are a key goal of biotechnology. For our purpose, it is therefore important to ask whether the maximal rate at which biomass can be synthesized by a network depends on 4 random viable networks that are not minimal and that differ in size between R = 400 and R = 800 reactions.  We found that network size does not influence biosynthetic flux for networks able to synthesize all B = 63 E. coli biomass molecules. That is, the regression coefficient describing their relationship is statistically indistinguishable from zero . The same holds for networks that can synthesize B = 20, B = 30, and B = 40 biomass molecules. . That is, the greater the number of active reactions, the lower the biosynthetic flux of a network.We just showed that the number of reactions in a network does not affect its biosynthetic flux. However, it is well-known that only a subset of a network’s metabolic reactions are usually R itself influences the number of active reactions AR. The answer is no. Network size has no statistically significant influence on the number of active reactions for any combination of values of N and B. This observation is in agreement with earlier results by Nishikawa et al. We next used linear regression to ask whether network size We subsequently asked whether synthesis of each additional biomass molecule also needs more active reactions. The answer is yes, as shown by linear regression analysis .−300). Each molecule to be synthesized decreases biosynthetic flux by 0.05 mmoles per g DW per hour, equivalent to a 6 percent decline relative to E.coli’s computed biosynthetic flux. Next, we analyzed networks viable on 80 different sole carbon sources that were able to synthesize B = 20, 30, 40, or 63 randomly chosen biomass components . Biosynthetic flux under these conditions also decreased approximately linearly with biosynthetic ability (S = -(0.05±0.001)B +3.5). Similar relationships also hold for networks viable on N = 20, N = 40, and N = 60 sole carbon sources . This correlation is significantly negative  and that can synthesize B = 63 biomass molecules. (S =  (0.01±0.0001)N +0.6 mmoles of biomass per g DW hour, n = 1000 networks) for every additional carbon source that a network is viable on. This is equivalent to 1 percent of increase relative to E. coli's biosynthetic flux on glucose. Quantitatively similar relationships hold for networks able to synthesize B = 20, B = 30, and B = 40 biomass components .4 random viable networks on glucose as the sole carbon source. This relationship is strongly negative (Pearson's r = -0.66) That is, the greater waste production is, the lower the biosynthetic flux.We first wanted to know if waste has any influence on biosynthetic flux. The answer is yes, based on an analysis of all our 1.6×10N on waste production W. To this end, we first analyzed random viable networks that vary in N and that can synthesize all B = 63 molecules E. coli biomass molecules N +24, n = 1000 networks) for every additional carbon source that a network is viable on. Statistically indistinguishable relationships exist for networks with B = 20, B = 30, and B = 40 biomass components. .Thus far, we have considered five variables and how they influence biosynthetic flux. These are network size −10, Mann-Whitney U-test, n = 100) In our analysis of how required reaction numbers depend on a network’s biosynthetic abilities, we have purposely focused on randomly chosen biomass precursors, as they give us an unbiased view of this dependency. However, this relationship may change if one considers biochemically related biomass molecules. To obtain some insights how it changes, we next studied a group of molecules whose known biosynthesis pathways share several reactions. These are the 20 proteinaceous amino acids −13, n = 80, Mann-Whitney U-test) In minimal networks every reaction is active under the conditions we study. Our observations in the last paragraph thus also show that amino acid biosynthesis needs fewer active reactions than biosynthesis of arbitrary biomass molecules. One of our analyses above showed that fewer active reactions also imply higher biosynthetic flux, which raises the question whether the 20 amino acids can be synthesized at higher rates. The answer is yes . Minimal−16, one sample t-test, for n = 105 sets of 20 random biomass molecules). This means that low amino acid cost cannot explain a higher rate of amino acid production.We next hypothesized that these dependencies might be explicable as a by-product of a lower cost of amino acid synthesis. If amino acids have fewer carbon molecules than the average biomass molecule, both fewer steps would be needed to synthesize them and a higher synthesis rate could be achieved. To test this hypothesis, we computed the average carbon content of all 20 amino acids, weighted by each amino acid’s stoichiometry in biomass, as 1.28±0.60 mmoles of carbon per mmole biomass. This molecular weight turned out not to be smaller but significantly larger than the carbon content of 20 random biomass molecules, also weighted by their stoichiometry in biomass  We next asked whether lower waste production might be responsible for the lower biosynthetic flux we observed. We therefore analyzed the quantity of secreted waste products in 80 networks that synthesize 20 amino acids, and in 80 networks that synthesize 20 random biomass compounds. Waste production is indeed significantly lower in networks that synthesize amino acids  To provide a concrete example of a prominent waste molecule, consider the amount of secreted carbon dioxide. For each mole of carbon entering a network in the form of glucose, amino acid synthesizing networks excrete 0.18±0.12 (mean ± one standard deviation) moles of carbon per g DW hour as carbon dioxide, whereas networks synthesizing 20 arbitrary molecules excrete 0.31±0.06 mmoles of carbon per g DW hour as carbon dioxide  molecules B it can synthesize, the rate S at which it can synthesize these molecules, the number of reactions R in the network, the number of active reactions AR, that is, reactions that have nonzero metabolic flux, and the amount of waste W the network produces.We here studied typical properties of metabolic networks with recently developed techniques to create random and unbiased samples of metabolic networks from a vast space of such networks R depends on N and B, because this number of reactions is an important design variable. Smaller networks would be easier to design and smaller genomes would be easier to synthesize We focused first on how the number of minimally needed reactions In a related analysis, we focused on nutrient flexibility. The ability of a metabolic network to sustain life on multiple sources of chemical elements and energy is highly desirable in industrial production processes E. coli where N = 54 and R = 1396 and Bacillus Subtilis where N is smaller (N = 41) and so is R (R = 769). We also compared the computationally predicted number of carbon sources that can be utilized by metabolic models of seven organisms  needed to synthesize B = 20 molecules to an average of 381 reactions (29% of the E. coli network) to synthesize all B = 63 biomass molecules of E. coli. For networks that can use 80 alternative carbon sources, the largest number we studied, it increases from 398 (27%) to 518 reactions (37% of the E. coli network) as B increases from 20 to 63.As a result of dependencies between N and B can explain the vast majority (87%) of the variance in R, in a relationship that is close to linear. Note that the proportions in which biomass molecules are to be synthesized are immaterial, as long as the metabolic reactions to synthesize each required molecule are present. This is why the stoichiometry of biomass composition would not influence the relationships we observe. The remaining 13% of variance is unexplained by linear relationships among the variables we considered. Such unexplained variance could have multiple sources, and especially nonlinear relationships among the variables. For example, as the number of biomass molecules to be synthesized increases, fewer and fewer additional reactions might be required, because most precursors of the additional biomass molecules may already be synthesized by existing reactions.We showed that the reactions needed to utilize an additional carbon-containing molecule or to synthesize an additional biomass molecule typically involve the additional molecule. For example, the utilization of an additional carbon source requires a reaction that catabolizes that molecule. The synthesis of an additional molecule requires a reaction that produces that molecule. We emphasize that the numbers of reactions required for an additional carbon source or biomass molecule reflect statistical patterns, averages over multiple networks. Some additional carbon sources or biomass molecules need more reactions than the average we identified, whereas others need fewer. . Our approach has the advantage of allowing us to make quantitative statements about the number of active reactions required to synthesize additional molecules that are not just based on few, well studied organisms, as in We also studied the number of active reactions – reactions with nonzero flux on a given carbon source. Quantitatively, we found that the number of active reactions increases by 3.6–4 reactions for each additional biomass molecule to be synthesized. Qualitatively, this tendency – increasing synthetic ability requires more active reactions – is not surprising, it is also corroborated by empirical data. efficiently in multiple chemical environments.The identity of active metabolic reactions can depend strongly on the nutrient environment S. These analyses are motivated by the fact that high synthesis rates of one or more target molecules are important goals of metabolic engineering S. In stark contrast, the number of active reactions – reactions with nonzero flux – shows a strong negative association with biosynthetic flux. That is, the higher the biosynthetic flux is, the smaller is the number of active reactions.  This observation is consistent with earlier work based on four microbial metabolic networks A second major set of analyses focused on how metabolic network properties influence biosynthetic flux S is the number of biomass molecules to be synthesized. Specifically, every additional such molecule reduces S by approximately 5 percent. This influence is stronger than the influence of nutrient flexibility, where each additional carbon source changes biomass synthesis flux by 1 percent. That nutrient flexibility influences biosynthesis rates is known from experiment A second important influence on biosynthetic flux W that a network produces is a third, and the most important influence on biosynthetic flux S. Metabolic networks generally excrete waste, for example, in the form of carbon dioxide S shows a strong negative correlation with waste production W in the form of excreted carbon. This observation is in qualitative agreement with experimental observations E. coli, Weber et alN on flux S. Experimental support for this observation exists as well. For example, Wisselink et al. et al. The amount of waste B. Networks seem to produce indistinguishable amounts of waste products regardless of how many biomass molecules they synthesize.We also found that an analogous association does not exist for S we observed. This means, that these quantities account for most of the variation in the biosynthetic flux, and are thus important factors in the design of a synthetic metabolism.Overall, the quantities we examined can explain 84 percent of the variance in biosynthetic flux In our final analysis, we showed that the nature of the molecules to be synthesized can influence biosynthetic flux. For example, in biotechnological applications, a metabolic network may need to synthesize molecules that are closely related, and whose biosynthetic pathways are therefore similar, in the sense that they share many reactions. Examples include vitamins and coenzymes We conclude with some caveats and limitations of our analysis. First, we are well aware that there is still a gap between current metabolic engineering and synthetic biology experiments on the one hand, and theoretical studies such as ours on the other. We see the value of studies like ours as providing quantitative reference points for future experimental work in this area.Second, flux balance analysis, on which our approach rests, assumes a metabolic system that is in a steady-state, such as might be achieved by a microbial population growing under a constant nutrient supply. This assumption ignores possible additional constraints that regulation and enzyme kinetics exert on a metabolism typical network properties, that is, properties of metabolic networks sampled at random from a large space of such networks. Optimization procedures that search metabolic networks space systematically may be able to identify individual networks whose properties deviate from those we identified as typical. For example, they may identify networks that are able to synthesize biomass with even fewer reactions or at higher rates. Such procedures have been successful in other combinatorial optimization problems. They include simulated annealing Third, we focus on Fourth, the expression of enzymes itself has a metabolic cost. This cost may be reduced by regulating enzyme expression depending on the nutrient environment (through a regulatory machinery whose expression may itself be costly.) We did not consider costs like these here, because they are poorly understood on a quantitative level. Their analysis also remains an important goal for future work.E. coli with a large genome, fewer than 75 percent of genes exert metabolic functions Buchnera, Wiggleswothia glossinidia and Thiomicrospira crunogena more than 80 percent of genes are devoted to metabolic functions, and in yet others, such as the gamma proteobacteria, Blochmanni floridanus and Wolbachia pipientis more than 95 percent have metabolic functions Finally, we note that an organism’s genome encodes more than metabolism. Nonmetabolic genes, even in small genomes serve roles in systems that allow cell motility, signaling, secretion, and defense metabolic genotype of an organism comprises all genes that encode metabolic enzymes. This genotype can be compactly represented through a list of reactions that can take place in the organism and that are catalyzed by enzymes genotype space that contains all possible metabolic networks – all possible combinations of reactions drawn from a set of biochemically feasible reactions – that could take place in a living system. According to our current knowledge, there are more than 5000 such reactions, which means that metabolic genotype space comprises 25000 possible metabolic networks. The metabolic genotype or metabolic network of any one organism can be viewed as a point in this space. Two genotypes differing from each other in a single reaction are neighbors in this space. We refer to a network’s metabolic phenotype as the spectrum of chemical environments – defined by nutrients these environments contain – on which the network can synthesize a predetermined spectrum of molecules, as well as the rate at which it can synthesize these molecules. We call a network viable in a given environment if it can synthesize all these molecules in the environment.The E. coli and S. cerevisiaeS of dimensions m×n, where m denotes the number of metabolites, and n is the number of reactions in a network v of metabolic fluxes – the rates at which a network’s metabolic reactions convert substrates into products – must satisfy the equation.Flux balance analysis (FBA) is a constraint-based modeling approach that predicts steady state metabolic fluxes – rates of substrate to product conversion – for all metabolic reactions in a metabolic network. It can thus also predict the biomass yield and other complex metabolic attributes of a metabolic network ZcT stands for a transposed (T) array c of scalar coefficients that define the objective function. Vectors a and b contain lower and upper limits of reaction fluxes in the flux vector v, respectively. A particularly important quantity to be maximized is the rate of synthesis of a given set biomass molecules. We refer to this quantity as the biosynthetic flux (in units of mmol per g DW per hour) of a metabolic network. We used the software packages CPLEX  and CLP  to solve all linear programming problems that arise in this study.This equation typically has a large solution space of allowable fluxes. The size of this space can be reduced somewhat by placing biochemically motivated constraints on the irreversibility of some reactions and on maximal flux magnitudes E. coliE. coli’s biomass composition is well studied, and many of its components – amino acids, nucleotides, etc. – also occur in most other free-living organisms. In addition, E. coli and its biomass molecules are highly relevant to biotechnological applications E. coli biomass molecules, we allowed all but four molecules to vary. These four molecules are the “currency metabolites” adenosine 5′-diphosphate (ADP), phosphoric acid (Pi), pyrophosphoric acid (PPi), and hydrogen ions. A complete list of the biomass molecules we used can be found in The starting point of our analysis was a set of 67 biomass molecules from Any one metabolic network can only synthesize biomass if its chemical environment contains specific nutrients We computed the biomass growth of a network by taking the average of its biomass growth rates on each carbon source that the network is required to be viable on, except where mentioned otherwise.E. coli (iAF1260), which contains 1397 non-transport reactions Some of our analyses use a “global reaction network”. This global network contains a comprehensive set of known biochemical reactions from multiple organisms, and it has universal biosynthetic abilities. We are fully aware that no such network is likely to exist in any one organism. We use this global network merely as a starting point for successive elimination of reactions, as described in the next section. We generated this global network by merging reactions from two sources, as described in more detail in essential gene. Analogously, an essential reaction in a metabolic network is a reaction that cannot be removed without abolishing the organism’s viability in a given environment. A minimal metabolic network is a network from which not a single reaction can be removed without abolishing viability in a given environment. In other words, all reactions of a minimal network are essential in that environment. We emphasize that a minimal network is not the smallest possible viable network, which would be difficult to find in a vast space of metabolic networks. We note that there may be multiple minimal networks, which contain different pathways among a set of possible alternate pathway from a nutrient to a biomass precursor. These networks need not have the same size. We also note that the number of essential reactions in any one non-minimal network may be smaller than the size of a minimal network, because non-minimal networks may contain alternate pathways able to by-pass any one reaction.A gene whose deletion abolishes the viability of an organism is called an B of biomass molecules on (ii) each of N different carbon sources, we created and analyzed many minimal networks with different values of B and N. Because there are astronomically many combinations of different values of B and N, and because the FBA approach we use is computationally expensive, we focused on subsets of such combinations, which we created as follows.To analyze the smallest number of reactions that a network needs to have in order to (i) synthesize a given number B = 40, B = 30, and B = 20 randomly chosen biomass molecules from the set of 63 E. coli biomass molecules  B. To arrive at identical sample sizes for subsequent analyses, we also included 10 “sets” with B = 63, that is, each of these sets contained all 63 biomass molecules. In total, we thus created a total of 40 (10×4) sets of biomass molecules.First, we created 10 different sets each of N = 20, N = 40, N = 60, and N = 80 carbon sources. Thus, up to this second step we had generated a total of 160 (40×4) combinations of sets of biomass molecules and nutrients.Second, for each of these 40 sets we determined 4 different sets of nutrients, where each set contained a different number of randomly chosen carbon sources from the list of carbon sources we used (see Section Carbon Sources). Specifically, these sets of nutrients contained B biomass molecules in the set – when each of the N nutrients was provided as the sole carbon source, that is, the network was required to be viable on each carbon source. If that was not the case, we reversed the reaction elimination and removed a different, randomly chosen reaction, until the resulting network was viable. We continued this procedure until no further reactions could be removed from the network without abolishing viability. In this fashion, we generated 800 (160×5) minimal networks. Note that carrying out this procedure repeatedly may not arrive at the same minimal network, because reactions are removed at random. That is, different minimal networks may contain different numbers and different sets of reactions. What unites them is that all their reactions are essential.Finally, for each of these 160 combinations, we created 5 minimal metabolic networks. To create each minimal network, we used the following procedure. We started from the global network and sequentially removed individual randomly chosen reactions from it. After each reaction removal we verified that the network was still viable – able to synthesize all cT in the biomass growth function of Equation 1 to a value of one. We used the same combinations of sets nutrients and biomass molecules as described above, except that we generated only 2 minimal networks (instead of 5) for each combination, in order to reduce computational cost. In total, we thus analyzed 320 minimal networks with isostoichiometric biomass composition.We asked whether the stoichiometric composition of biomass, that is, the relative amounts of different biomass molecule in biomass, influences the relationships we explore here. To this end, we generated minimal networks synthesizing given biomass compounds, as described in the previous section, with the difference that these networks synthesized these compounds in equal molarities, that is isostoichiometrically. In other words, for the purpose of this analysis we changed the stoichiometric coefficients N = 20, N = 40, N = 60, and N = 80 randomly chosen carbon sources, and analyzed 8 minimal networks for each set, for a total of 320 networks.To study examples of networks that synthesize biochemically related biomass molecules, we studied minimal networks synthesizing only the 20 proteinaceous amino acids. We generated these networks as described in ‘Generation of Minimal Networks’, except that we did not choose the biomass molecules to be synthesized at random. More specifically, we created 10 sets each of 3 swaps, the autocorrelation of two genotypes becomes negligible E. coli metabolic network and after 2.5×106 reaction swaps, we sampled networks every 5×103 steps in a sequence. Overall, the network samples we created comprise 1000 networks for each condition we study. We did not subject transport reactions to the reaction swap procedure.As we mentioned earlier, changing the genotype of a network does not necessarily cause a change in its phenotype. One can take advantage of this property to generate arbitrarily large and unbiased random samples of metabolic networks with any desired property see , such thE. coli, because E. coli is able to survive in multiple different environments To compare our observations from randomly sampled metabolic networks to a reference from biology, it is useful to use a network from a well-studied organism. For this purpose, we used the metabolic network of R, nutrient flexibility N, and biosynthetic ability B. To this end, we started with the same 160 sets of N nutrients and B biomass molecules described in ‘Generation of Minimal Networks’. We created for each set 5 viable networks that differ in their number of reactions, that is, they had 400, 500, 600, 700 and 800 reactions. To create these networks, we used the same procedure as for the production of minimal networks, except that we stopped removing reactions when a network with the desired number of reactions had been reached. At the end of this procedure, we had 800 networks (160×5) with various combinations of the 3 network properties. We used each of these networks as starting networks for MCMC sampling, and generated 20 random viable networks from each of the 800 starting networks, for a total of 16000 random networks. This amounts to 200 networks for each different combination of N, B, and R.To initiate the MCMC procedure that generates random samples of networks with a given set of properties, we needed starting networks that have these properties. Specifically, we needed to create networks with a given number of reactions We performed all our analyses using MATLAB  and R .Figure S1Biomass stoichiometry does not affect the number of reactions in a minimal network. The vertical axis shows the number of reactions in minimal networks as a function of a) biosynthetic ability and b) nutrient flexibility. Dots and lengths of error bars correspond to means and one standard deviation. Each blue dot of size 200 indicates networks with the biomass stoichiometry of E. coli (TIF)Click here for additional data file.Figure S2Biosynthetic flux distribution. The flux distributions in units of mmoles per g DW per hour are shown for each combination of biosynthetic ability  and nutrient flexibility  that we examined. Data are based on 16,000 random viable networks, as described in methods (1000 networks per panel).(TIF)Click here for additional data file.Figure S3Distribution of number R of reactions. The distributions of R are shown for each combination of biosynthetic ability  and nutrient flexibility  that we examined, and for in total 800 minimal viable networks (50 Networks per panel).(TIF)Click here for additional data file.Table S1List of E. coli’s Biomass Compounds (DOC)Click here for additional data file.Table S2List of carbon sources used in this study.(DOC)Click here for additional data file.Table S3Examples of reactions required to synthesize additional biomass molecules. The table contains 20 arbitrary biomass molecules (left), and a list of reactions that are required to synthesize the molecule in a random minimal network (in addition to the reactions that the network needed to synthesize other biomass molecules). The analysis is based on minimal networks that are required (i) to synthesize 62 E. coli biomass molecules and (ii) to be viable on glucose. The Table illustrates that the number of additional reactions needed depends on the biomass molecule. (DOC)Click here for additional data file.Table S4Examples of reactions required to utilize additional carbon sources. The table contains arbitrary carbon sources (left) and a list of reactions that are required to utilize the carbon source in a random minimal network (in addition to the reactions that the network needs to utilize other carbon sources). The analysis is based on minimal networks that were required (i) to synthesize all E. coli biomass molecules and (ii) to be viable on 30 other carbon sources. The Table illustrates that the number of additional reactions needed depends on the carbon source. (DOC)Click here for additional data file.Text S1Confidence Interval Calculation.(DOC)Click here for additional data file.Text S2Examples of reactions needed to metabolize new carbon sources.(DOC)Click here for additional data file.Text S3Examples of reactions needed to synthesize additional biomass molecules.(DOC)Click here for additional data file.


Saccharomyces cerevisiae undergoes mitosis in glucose-rich medium but enters meiosis in acetate sporulation medium. The transition from mitosis to meiosis involves a remarkable adaptation of the metabolic machinery to the changing environment to meet new energy and biosynthesis requirements. Biochemical studies indicate that five metabolic pathways are active at different stages of sporulation: glutamate formation, tricarboxylic acid cycle, glyoxylate cycle, gluconeogenesis, and glycogenolysis. A dynamic synthesis of macromolecules, including nucleotides, amino acids, and lipids, is also observed. However, the metabolic requirements of sporulating cells are poorly understood. In this study, we apply flux balance analyses to uncover optimal principles driving the operation of metabolic networks over the entire period of sporulation. A meiosis-specific metabolic network is constructed, and flux distribution is simulated using ten objective functions combined with time-course expression-based reaction constraints. By systematically evaluating the correlation between computational and experimental fluxes on pathways and macromolecule syntheses, the metabolic requirements of cells are determined: sporulation requires maximization of ATP production and macromolecule syntheses in the early phase followed by maximization of carbohydrate breakdown and minimization of ATP production in the middle and late stages. Our computational models are validated by in silico deletion of enzymes known to be essential for sporulation. Finally, the models are used to predict novel metabolic genes required for sporulation. This study indicates that yeast cells have distinct metabolic requirements at different phases of meiosis, which may reflect regulation that realizes the optimal outcome of sporulation. Our meiosis-specific network models provide a framework for an in-depth understanding of the roles of enzymes and reactions, and may open new avenues for engineering metabolic pathways to improve sporulation efficiency.The diploid yeast  Saccharomyces cerevisiae to the mouse. Multiple lines of evidence suggest a tight link between meiosis and metabolism C. elegans and the fruit fly Drosophila melanogaster, ablation of the germline leads to profound alternations in lipid metabolism Meiosis is a strongly conserved cell division program that generates haploid gametes from a diploid parental cell. Successful meiosis is the fundamental basis of sexual reproduction. Meiosis has been studied extensively in multiple model systems, ranging from the budding yeast The diploid yeast undergoes mitosis in glucose-rich medium. When cells are transferred to acetate sporulation medium, a developmental switch from mitosis to meiosis occurs to generate four haploid spores Conspicuous differences have been observed in metabolism between mitosis and meiosis. In mitosis, glucose is consumed by fermentation or respiration via the tricarboxylic acid (TCA) cycle. In meiosis, acetate serves as the sole carbon source and five metabolic pathways are active at different stages: glutamate formation, TCA cycle, glyoxylate cycle, gluconeogenesis, and glycogenolysis  [8], [9]in silico perturbations such as gene or reaction knockout Although the pathways are well characterized from biochemical studies, the optimal principles responsible for the dramatic metabolic changes accompanying meiosis are poorly understood. The cellular objectives, i.e., the metabolic requirements of cells, are undetermined. We construct a meiosis-specific metabolic network in yeast and apply a constraint-based modeling approach—flux balance analysis (FBA) A meiosis-specific metabolic network is reconstructed based on the literature and databases However, metabolic pathways and macromolecule syntheses are not constitutively active throughout meiosis. Instead, each has a unique dynamic profile based on experimental studies To determine the metabolic requirements of sporulating yeast, we systematically evaluate ten objective functions relevant to meiosis: ATP production, ATP consumption, net ATP production (production minus consumption), acetate uptake, glutamate synthesis, carbohydrate synthesis, carbohydrate breakdown, nucleotide synthesis, amino acid synthesis, and lipid synthesis. Not all enzymes are expressed at any given time during meiosis. To reflect the dynamic profile of the metabolic network, we constrain the upper bound of reactions using time-course ribosome profiling data on SK1 sporulating cells The ten objective functions are individually maximized or minimized at each of the 18 time points; this is equivalent to evaluating 360 FBA models. The optimal solution of network fluxes is determined for each model. We calculate the Pearson correlation between predicted fluxes and biochemical data  on eightAt 0.033 hour immediately after yeast cells are transferred to the acetate medium, net ATP production maximization is the best objective function. When using expression data at 0.5, 1, and 1.5 hours as reaction constraints, the metabolic requirement is best described by glutamate synthesis maximization. This is in accordance with the report that glutamate is the major metabolite produced early from acetate utilization Although the solution space has been constrained by network structures, reaction stoichiometry, reaction bounds, and objective functions, linear optimization often leads to multiple optimal flux distributions with an identical objective value. To determine whether the optimal solution identified using our method is an artifact of one single optimum or a representative of multiple optima, we sample the solution space of meiosis-specific network models for each objective function while constraining the objective value to its optimum. The sampling is performed at each time point during sporulation using expression-based constraints. We find that alternative optima exist for carbohydrate breakdown maximization  and acetate uptake maximization , both having only one reaction in the objective function. Pearson correlations are calculated between alternative optima and biochemical data on pathways to obtain the distribution of correlations at each time point. The correlation value of optimum identified by our method falls within the range of sampled correlations for carbohydrate breakdown maximization at all eight time points  and for To provide further proof of best objective functions identified along the time series, we implement four alternative methods to deduce objectives. First, instead of using the Pearson correlation, we calculate the Spearman correlation between predicted fluxes and biochemical data. All best objective functions except those during 6.5–8 hours reproduce as using the Pearson correlation . Second,We use independent data—data distinct from those used for model building—to evaluate the meiosis-specific network models. High-throughput screens of ∼4,000 yeast deletion strains have identified 267 genes required for sporulation, i.e., sporulation-deficient genes, as well as 102 genes that enhance sporulation proficiency in silico and obtain the optimal fluxes for a gene knockout (KO) using the identified best objective function and expression-based constraints at every time point. The Pearson correlation between in silico fluxes of a KO and biochemical data on eight pathways is calculated in a similar way as that for wild-type (WT). The KO effect is quantified by a z-score that measures the difference in correlation coefficient between a KO and WT. This allows us to assess each KO's change in correlation with experimental values in units of standard deviation, a form of the z test. A negative z-score indicates that the KO causes pathway fluxes less correlated with biochemical data compared to WT for a given time point. Using the criterion of having a z-score less than -2 for at least one time point, our models validate 12 out of 16 sporulation-deficient genes , glyoxylate cycle , acetate uptake (ADY2), and others (MDH2), thus affecting sporulation at an early stage.All 12 validated KOs exhibit reduced correlation with biochemically determined pathway data during the first 1.5 hours of sporulation when net ATP production maximization and glutamate synthesis maximization are the most relevant objective functions. These genes have essential functions in TCA cycle  or in combination with an increased flux in glyoxylate cycle . Between 0.5 and 1.5 hours, when glutamate synthesis maximization is the most favored objective, reduced flux is observed in glutamate formation, TCA cycle, and glyoxylate cycle .We further examine the flux difference between validated KOs and WT on eight pathways . At 0.03in silico and find 32 out of 69 KOs are predicted to affect sporulation as defined by having a z-score less than −2 for at least one time point, the same criterion used for the validation experiment. Among the 32, 12 are known sporulation-deficient genes and the remaining 20 are potential novel genes required for meiosis  and acetate transport (ACS2) are predicted to be required for sporulation. These KOs result in reduced TCA activity or both enhanced glyoxylate cycle flux and reduced TCA activity, as we have seen in deletions of known sporulation-deficient genes (GDH3), TCA cycle , and acetate metabolism (ACS2) cause reduced correlation of predicted pathway fluxes with experimentally determined values. In these KOs, in silico fluxes in glutamate formation, TCA cycle, and glyoxylate cycle are reduced compared to WT, similar to the pattern seen for the KOs of known sporulation-deficient genes at the same time frame . ACC1 converts cytoplasmic acetyl-CoA to lipids; the ACC1 KO exhibits reduced fluxes in lipid synthesis. Deletions of the other seven genes lower fluxes in both glycogenolysis and lipid synthesis. At 11 hours of sporulation, carbohydrate breakdown maximization becomes the best objective function again. PGM2, GPH1, and INO1 are predicted to be required for sporulation. INO1 converts glucose-6-phosphate into lipids, while PGM2 and GPH1 catalyze initial reactions in glycogenolysis to produce glucose-6-phosphate. These gene KOs completely shut down the lipid synthesis and decrease the glycogenolysis activity.In contrast to known sporulation-deficient genes that impact SDH3, UGP1, ACC1, ACS2) LPD1, ZWF1, PFK1, FBA1, PGI1) GPH1 still permits sporulation The meiosis-specific network models predict 20 genes that potentially affect sporulation, among which four are essential for cell viability , the maximum net ATP production is achieved at 800. FBA1 KO results in the deletion of two reversible reactions, reducing the net ATP production to 500. With such amount of ATP production, the cell is unable to meet the energy requirement for viability. Similarly, PGI1 KO decreases net ATP production from the maximum value to 500 that is predicted to be deleterious to cells at a late phase of sporulation.Both To evaluate whether the identified metabolic requirements of sporulating yeast are network-dependent, we repeat the analysis using iMM904, a genome-scale yeast metabolic network consisting of 1,577 reactions catalyzed by 904 enzymes We compare the performance of meiosis-specific and genome-scale network models in predicting KO sporulation deficiency . Among 6To further assess the performance of network models, we implement two alternative approaches to estimate KO effects . The firYeast meiosis is a reproductive process producing four haploid spores from one diploid cell. Shifting from a mitotic to a meiotic state requires multiple adjustments within the cell. Indeed, cells constantly tailor their metabolic machinery to meet new energy and biosynthesis requirements, and this is no less true in the meiotic process. Decades of biochemical research have identified most enzymes that catalyze metabolic reactions. However, the optimal principles that drive the dynamic adaptation of metabolic pathways are poorly understood.in silico fluxes and in vivo fluxes is performed using quantitative metrics—the Pearson correlation coefficient. It measures the overall agreement between computational and experimental pathway values and allows direct comparison of the performance of all objectives. Our results from the meiosis-specific network suggest that the metabolic requirements of cells evolve during sporulation, starting with ATP production maximization followed by glutamate and nucleotide synthesis maximization. Carbohydrates in the form of glycogen are subsequently broken down to supply energy. At the end, under nutrient scarcity, cells reduce all pathway activities by limiting ATP production, which leads to the dormant stage of spores. Similar objective functions are determined from a genome-scale network: ATP production maximization at the early phase and ATP production minimization at the late stage. Consistent metabolic requirements revealed by two networks of different scales suggest the robustness of optimal flux solutions on pathways. These best objective functions reflect the cellular adaptation to the acetate environment by switching from glycolysis to gluconeogenesis, using ATP efficiently, and producing macromolecules for spore formation.FBA can be utilized to predict flux distribution in a metabolic network when the objective function is known. Because metabolic requirements are uncharacterized in yeast meiosis, we test a total of ten probable objective functions to uncover the optimal principles for different phases of meiosis. Although FBA predicts flux distribution at a steady state, the use of time-course expression data for reaction bounds allows us to change constraints, generating dynamic fluxes over the entire period of yeast meiosis. The ribosome-protected mRNA levels measured by deep sequencing The meiosis-specific network model is validated using genes known to be required for sporulation in silico perturbations pinpoint specific enzymes essential for sporulation, allowing for the prediction of novel sporulation-deficient genes that have not been identified by high-throughput screens The meiosis-specific network model is key to manipulating reactions or genes to determine their contribution to cell metabolism. We delete each gene in the network to study the effects of knockouts. These in silico experiments on any reaction or multiple reactions simultaneously, or on over-expression, knockdown, or knockout of any enzyme or combinations of multiple enzymes. Such analyses will provide insight into the metabolic machinery of yeast meiosis, and may open new avenues for engineering pathways to increase sporulation efficiency.In summary, this study provides an in-depth knowledge of metabolic mechanisms during yeast meiosis. Further, the meiosis-specific network model offers a theoretical framework to investigate the contribution of enzymes and reactions to the sporulation phenotype. The model is powerful with respect to performing Saccharomyces Genome Database, iMM904, and Yeast4.0 http://www.ebi.ac.uk/biomodels/, MODEL1303140001).We manually construct a meiosis-specific metabolic network by including reactions known to be active during yeast meiosis. The network comprises pathways involved in the uptake of acetate from the external environment; the use of acetate for synthesizing carbohydrates, amino acids, nucleotides, and lipids; and, later, the breakdown of stored carbohydrates We also investigate a genome-scale metabolic network–iMM904, which contains 1,228 metabolites and 1,577 reactions catalyzed by 904 unique enzymes m rows as metabolites and r columns as reactions. The entries in the matrix correspond to coefficients of metabolites for each reaction. Constraints are imposed for reactions: a and b define the lower and upper bounds of allowable flux V for a reaction, respectively. An objective function defines a particular goal of cells, and can be represented as a linear combination of flux: C is a vector of weights on flux V. FBA seeks to maximize or minimize an objective function using linear programming by carrying out a steady-state analysis on Flux is the rate at which metabolites are consumed or produced in a reaction. Flux in the metabolic networks of yeast meiosis is calculated using FBA at a steady state. Specially, all reactions in a metabolic network are mathematically represented as a stoichiometric matrix, C is a vector of zeros with a value of one at the positions of reactions relevant to the objective function. The exceptions are three ATP objectives: positive numbers of yielded ATPs are coefficients for reactions participating in ATP production, positive numbers of used ATPs are coefficient for reactions participating in ATP consumption, and positive numbers of yielded ATPs and negative numbers of used ATPs are entered as coefficients for the objective function of net ATP production  ATP production, 2) ATP consumption, 3) net ATP production, 4) acetate uptake, 5) glutamate synthesis, 6) carbohydrate synthesis, 7) carbohydrate breakdown, 8) nucleotide synthesis, 9) amino acid synthesis, and 10) lipid synthesis. Each objective function, oduction .For the meiosis-specific metabolic network, the lower bound for all reactions is 0, implying irreversible reactions. The upper bound is determined by deep sequencing of ribosome-protected mRNA levels (GSE34082) One optimal solution of network flux is obtained using GLPK (GNU Linear Programming Kit) supported by the COBRA Toolbox for Matlab x and y are computational and experimental data, respectively, n is the number of pathways. Computational data on pathways are obtained by averaging optimal fluxes of reactions included in each pathway  glutamate formation, 2) TCA cycle, 3) glyoxylate cycle, 4) gluconeogenesis, 5) glycogenolysis, 6) nucleotides, 7) amino acids, and 8) lipids. The Pearson correlation quantifies the linear relationship between two datasets and is defined as  pathway . Biochem pathway . ExperimHigh-throughput screens of yeast deletion strains have identified 267 sporulation-deficient genes (pre-sporulation/sporulation≥1.5 in two independent experiments) To determine whether known sporulation-deficient genes are enriched among model-predicted deficient genes, we calculate the P-value from a hypergeometric distribution: Figure S1The optimum identified by our method for carbohydrate breakdown maximization is consistent with multiple optima derived from sampling the solution space of meiosis-specific network models. For each of 18 time points with expression-based constraints, the sampling is performed with 2,000 points while constraining the objective value to its optimum. Multiple optimal solutions are identified for 8 time points. Pearson correlations are calculated between alternative optima and biochemical data on pathways. The quartiles of the distribution of correlations are displayed: maximum, 75 percentile, median, 25 percentile, and minimum. The Pearson coefficient calculated from one optimum, as shown in (PDF)Click here for additional data file.Figure S2The use of Spearman correlation to evaluate objective functions for the meiosis-specific network models. The Spearman correlation is calculated between predicted fluxes and biochemical data on eight pathways when maximizing or minimizing each of the ten objective functions at each of the 18 time points. The best objective function for each time point is the one with the maximum Spearman correlation coefficient. Eleven out of 18 best objective functions during 0.033–3 and 8.25–11 hours are consistent with those determined by the Pearson correlation as the first, second, or third ranked objective. Close circle: maximization of an objective function; open circle: minimization of an objective function. Undefined correlation coefficients due to zero variance of predicted pathway fluxes are not shown in the figure.(PDF)Click here for additional data file.Figure S3The use of microarray data to evaluate objective functions for the meiosis-specific network models. Reaction constraints are defined by gene expression from time-course Affymetrix data on SK1 sporulating cells at 1, 2, 3, 4, 6, 8, and 10 hours. The Pearson correlation is calculated between predicted fluxes and biochemical data on eight pathways when maximizing or minimizing each of the ten objective functions at each of the seven time points. The best objective function for each time point is the one with the maximum Pearson correlation coefficient. Five out of seven best objective functions at 1, 2, 3, 4, and 10 hours are consistent with those deduced from ribosome profiling. Close circle: maximization of an objective function; open circle: minimization of an objective function. Undefined correlation coefficients due to zero variance of predicted pathway fluxes are not shown in the figure.(PDF)Click here for additional data file.Figure S4The use of uniform bounds to evaluate objective functions for the meiosis-specific network models. A uniform constraint of 1,000 is imposed for all reactions. The Pearson correlation is calculated between predicted fluxes and biochemical data on eight pathways when maximizing or minimizing each of the ten objective functions at each of the 18 time points. The best objective function for each time point is the one with the maximum Pearson correlation coefficient. Three out of 18 best objective functions at 0.033, 2, and 3 hours are consistent with those deduced from ribosome profiling. Close circle: maximization of an objective function; open circle: minimization of an objective function. Undefined correlation coefficients due to zero variance of predicted pathway fluxes are not shown in the figure.(PDF)Click here for additional data file.Figure S5Evaluation of objective functions using the genome-scale network models. The Pearson correlation is calculated between predicted fluxes and biochemical data on eight pathways when maximizing or minimizing each of the ten objective functions at each of the 18 time points. The best objective function for each time point is the one with the maximum Pearson correlation coefficient. Close circle: maximization of an objective function; open circle: minimization of an objective function. Optimal solution does not exist regardless of objective functions at 2 hours of sporulation, thus does not shown in the figure.(PDF)Click here for additional data file.Model S1The yeast meiosis-specific metabolic network in the Systems Biology Markup Language format.(XML)Click here for additional data file.Table S1Reactions in the yeast meiosis-specific metabolic network.(PDF)Click here for additional data file.Table S2A comparison between the meiosis-specific network and iMM904.(XLSX)Click here for additional data file.Table S3Biochemical data on metabolic pathways and macromolecule syntheses during yeast meiosis.(PDF)Click here for additional data file.Table S4Interpolated biochemical data on metabolic pathways and macromolecule syntheses at 18 time points.(PDF)Click here for additional data file.Table S5Context-specific networks determined by iMAT for incorporating expression data with the meiosis-specific network.(XLSX)Click here for additional data file.


Enterobacteriaceae diversified from an ancestral lineage ~300-500 million years ago (mya) into a wide variety of free-living and host-associated lifestyles. Nutrient availability varies across niches, and evolution of metabolic networks likely played a key role in adaptation.E. coli/Shigella (~10 mya), E. coli/Shigella/Salmonella (~100 mya), and all enterobacteria (~300-500 mya). Using these models we analyzed the capacity for carbon, nitrogen, phosphorous, sulfur, and iron utilization in aerobic and anaerobic conditions, identified conserved and differentiating catabolic phenotypes, and validated predictions by comparison to experimental data from extant organisms.Here we use a paleo systems biology approach to reconstruct and model metabolic networks of ancestral nodes of the enterobacteria phylogeny to investigate metabolism of ancient microorganisms and evolution of the networks. Specifically, we identified orthologous genes across genomes of 72 free-living enterobacteria (16 genera), and constructed core metabolic networks capturing conserved components for ancestral lineages leading to This is a novel approach using quantitative ancestral models to study metabolic network evolution and may be useful for identification of new targets to control infectious diseases caused by enterobacteria. Enterobacteriaceae are distributed worldwide and are found in soil, water, agronomic crops and produce, plants and trees, and in animals ranging from insects to humans. Pathogenic enterobacteria cause biomedically and agriculturally significant diseases, and historically have resulted in numerous pandemics, foodborne outbreaks, and nosocomial infections, arguably impacting human health more than any other microbial family. Enterobacteria have been extensively studied in the laboratory due to their importance to human health and as standard laboratory strains for molecular biology. The family includes 44 distinct genera and 176 named species [Initially named for a group of intestinal bacteria, members of the family E. coli K-12 numerous types of genome-scale biological networks have been constructed including metabolic, regulatory, and transcriptional and translational machinery [Computational modeling of bacterial metabolism offers a promising approach to predict strain-to-strain variation in metabolic capabilities and microbial strategies used in different environments, including host tissues. The number of available genome-scale metabolic models (GEMs) has grown in the last ten years to over 50 GEMs, and they capture the metabolic capabilities of numerous microbial taxa important to human health, biotechnology and bioengineering ,3. Systeachinery -9, and aachinery ,10-15.E. coli strains [E. coli strains [Salmonella strain [Klebsiella strain [Yersinia strains [Buchnera[E. coli strains [E. coli genomes were used to construct models from the combined genomic content of these E. coli strains, representing the intersection  and union (pangenome) and revealed new insight into the evolution of this species [To date, GEMs of enterobacteria have been constructed for three standard laboratory  strains ,6-8,10,  strains , one Sala strain ,16, one a strain , two Yer strains , and one[Buchnera. These G[Buchnera-22, to c[Buchnera, to iden strains , and to  strains -25. In a species .Enterobacteriaceae diversified from a common ancestor ~300-500 million years ago (mya) into a wide variety of free-living and host-associated lifestyles [E. coli/Shigella ancestral core (~10 mya), the E. coli/Shigella/Salmonella ancestral core (~100 mya), and the enterobacterial ancestral core (~300-500 mya). Using these metabolic models we have analyzed the metabolic capacity for carbon, nitrogen, phosphorous, sulfur, and iron utilization in aerobic and anaerobic conditions and have identified conserved and differentiating catabolic phenotypes and validated these predictions by comparison to experimental data. Apart from our previous publication on E. coli, this is the first study to use constraint-based modeling to examine the metabolic properties of ancestral bacteria and provides new insight into the evolution of metabolism for the family Enterobacteriaceae.Members of the family festyles ,27, yet festyles . Here thE. coli K-12 MG1655, was developed 10 years ago and has undergone numerous improvements and updates. It is now a sophisticated compartmentalized model containing over 1,300 genes and 2,400 reactions [Enterobacteriaceae from a E. coli K-12 MG1655 GEM [in silico carbon source utilization predictions to experimental data spanning 36 extant strains from 16 genera to examine the shared metabolic capabilities of modern-day enterobacteria and the impact of changes in the metabolic network on phenotypic traits.The first GEM for eactions . It has Dickeya and Pectobacterium, as well as the Erwinia-Pantoea clade, suggesting ancient speciation events for these genera. The clade including Escherichia, Salmonella and other animal-associated organisms shows relatively shorter intra-clade branches length, indicating their relatively recent speciation. This phylogenetic tree for the enterobacteria was used to determine the order of genomes used in subsequent analysis for ancestral core metabolic gene determination.A total evidence tree was constructed for the enterobacteria with available genome sequence data Figure . The totE. coli and Shigella strains are thought to have diverged from a common ancestor ~10 mya [E. coli strains differing by as much as 25% of their gene content [E. coli strains. From the 16 E. coli and seven Shigella spp. genomes we identified a collection of 2,073 conserved genes to construct iEcoli_core  [E. coli/Shigella ancestral core was made by removing reactions from the iEco1339_MG1655 network if orthologs to the associated gene(s) were absent in one or more of the 23 genomes and if the reactions did not have any isozymes. If removing a reaction prevented biomass production  then the reaction was added back to the metabolic model without a gene associated with it and the reaction was classified as an orphan reaction (i.e. a reaction without any associated genes). Using this approach 549 ORFS associated with 454 reactions were removed from iEco1339_MG1655 resulting in an E. coli core metabolic network (iEcoli_core) consisting of a total of 790 ORFs and 1,674 reactions (Table  ~10 mya . Althoug content . It is o_MG1655) . As prev_MG1655) , a metabE. coli and Salmonella strains are thought to have diverged from a common ancestor ~100 mya [E. coli and Salmonella strains. We assume that genes conserved across all strains represent a conservative estimate of the core genome of the ancestor of modern E. coli and Salmonella strains and from these 16 E. coli, seven Shigella spp., and 16 Salmonella spp. genomes the collection of 1,703 conserved genes were used to construct the ancestral metabolic model iSalcoli_core  [E. coli/Shigella/Salmonella ancestral core was made as before by removing reactions from the iEco1339_MG1655 network if orthologs for the associated genes were absent in one or more of the 39 genomes. Reactions were added back as orphan reactions if they were essential for biomass production during growth simulation in minimal media with glucose as the sole carbon source. Using this approach 657 ORFS associated with 527 reactions were removed from iEco1339_MG1655 resulting in an E. coli/Salmonella core metabolic network  consisting of a total of 683 ORFs and 1,601 reactions  . A metabE. coli K-12 MG1655 GEM (iEco1339_MG1655) [All members of the family of enterobacteria are thought to have diverged from a common ancestor ~300-500 mya . The met_MG1655) . A metabTo evaluate the accuracy of three ancestral core GEMs, we predicted if these ancestral strains could use 190 different carbon sources under aerobic and anaerobic conditions. These predictions were then compared to experimental growth phenotypes for current strains measured using Biolog phenotypic arrays or published carbon source utilization data for 38 enterobacteria spanning 23 genera listed in Table in silico carbon source utilization using FBA, predictions were generated for utilization of sole nitrogen, phosphorous, iron, and sulfur compounds. As the number of genomes used for the generation of the three ancestral core models increased, the number of metabolites decreased that were predicted as useable nitrogen, phosphorous, iron, or sulfur source under aerobic  of these predictions matched non-essential gene predictions from orthologous genes contained in GEMs generated from genomes of extant enterobacteria.To further explore the metabolic similarities between all enterobacteria, we determined reaction essentiality predictions of the enterobacterial core metabolic network (iEntero_core) for conditions simulating aerobic and anaerobic growth in glucose containing minimal media Table . Of the structed ,11,12,14structed ,34, and structed )   of gene essentiality predictions, 76% (241/325) when compared to experimental data from enterobacterial members, and 70.4% (229/325) when compared to “superessential” gene predictions. In summary, essential gene predictions from the enterobacterial ancestral core were 80.3% in agreement with essentiality data determined previously in one or more published studies from individual enterobacterial members  were in agreement with the experimentally determined essential genes for E. coli and Shigella (~10 mya), the second represents the ancestor of Ecoli/Shigella and Salmonella (~100 mya), and the third represents the ancestor of all enterobacteria (~300-500 mya). Each model includes all identifiable metabolic reactions from a previous GEM for E. coli K-12 that are linked to genes conserved among  descendants of the phylogenetic node, plus orphan reactions from the E. coli K-12 model that must be retained because removal would prevent production of biomass. Thus, these three models are progressively smaller subsets of the E. coli K-12 model. The models were created in a step-wise fashion by deleting reactions missing from one taxon at a time selected approximately in order of increasing phylogenetic distance from E. coli K-12. Figure This study describes the generation of three computational models designed as a first approximation of the metabolic capacity of ancestral enterobacteria. We selected three nodes in a well resolved phylogenetic tree of enterobacteria with complete genome sequences Figure . The firFor the model representing the ancestor of all enterobacteria, over 600 of the approximately 1,200 reactions in the model are orphans .Here, we focus on these models representing core absolutely conserved reactions to examine a conservative estimate of the metabolic capacity of each ancestral lineage. We compared the reactions retained in each ancestral model to the total set of reactions in the mature y Figure . Some suE. coli Biomass equation from iAF1260 [E. coli (23), Salmonella (8), Klebsiella (12), and Yersinia (6). As more enterobacterial members have GEMs constructed with strain-specific biomass equations, a future direction may be to generate an average biomass composition from all modern-day GEMs of enterobacteria to use in the enterobacterial ancestral core metabolic model, or to use parsimony-based ancestral state reconstruction to estimate node-specific ancestral biomass composition. Future studies are warranted to investigate whether and how these alternative approaches impact insights gained through simulations.Since the biomass of ancestral cells is impossible to determine empirically, we used the  iAF1260 ,12,14, wE. coli/Shigella, Ecoli/Shigella/Salmonella, and the enterobacteria core model reconstructions, the total number of experimentally reported carbon sources utilized by all relevant strains in anaerobic conditions were 81, 65, and 33, and in anaerobic conditions were 77, 46, and 16, respectively  or anaerobic (81.5% ± 4) conditions is within the range of accuracy for all 16 GEMs (86% ± 7.5) that have been published , and one sulfur source (sulfate SO4) predicted to support growth of the ancestral core of enterobacteria  and incubated at 37°C or 28°C overnight aerobically or anaerobically in sealed Whirl-Pak® Long-Term Sample Retention Bags  saturated with an anaerobic gas mixture (95% N2 and 5% CO2) as described [E. coli, Salmonella, and Shigella strains, and up to 72 h for the Erwinia, Pantoea, Dickeya, and Pectobacterium strains.Six dy Table . Frozen escribed . Cells wescribed , and BioEnterobacteriaceae[Vibrio cholerae and Pseudomonas syringae were designated as outgroup taxa, because they are members of phylogenetically closely related families from the order of gamma proteobacteria. Genome-wide orthologous genes among selected genomes were retrieved in two steps. We first generated all-against-all BLASTP reciprocal (best or nearly best) matches for all investigated sequences, using an E-value ≤ 0.000001 cutoff. We then use a threshold based on a metric that is defined as the minimal number of pair-wise comparisons consistent across a putative orthologous sequence cluster, in order to preserve a genome-wide dataset with maximal phylogenetic informativeness. Alignment of each retrieved orthologous data among all strains under investigation was performed in AMAP  [Genomes used in this study for phylogenetic reconstruction, their sources, dates of isolation, and hosts are listed in Additional file teriaceae, there ateriaceae. For allnealing)  with 0.5nealing) ,39 and mnealing)  for bothnealing)  is used nealing)  and gammE. coli K12 MG1655 (Table E. coli/Shigella (genomes #1-23), Ecoli/Shigella/Salmonella (genomes #1-39), and the enterobacterial core (genomes #1-72). The GEMs for these ancestral core models were made by removing orthologous ORFs and their associated reactions from the iEco1339_MG1655 GEM if one or more of the enterobacteria genomes leading up to the phylogenetic branching point did not have a gene assigned. If removing a reaction prevented biomass production for anaerobic growth on glucose (predicted using FBA) then the reaction was added back to the metabolic reconstruction without a gene associated with it. Gene-to-protein-to-reaction associations representing the metabolic models of the E. coli/Shigella (iEcoli_core),E.coli/Shigella/Salmonella , and the Enterobacterial (iEntero_core) ancestral core are provided  was used. FBA was also used to predict essential reactions by constraining reactions to have zero flux and maximizing growth rate. If the resulting maximum predicted growth rate (using FBA) was zero then the reaction and the associated genes were considered to be essential. Reaction deletion simulations were evaluated under both aerobic and anaerobic conditions.Fluxes through metabolic network reactions can be predicted using flux balance analysis (FBA) . In FBA,The authors declare that they have no conflict of interest.in silico analyses. DB obtained all of the experimental data. DB and JR analyzed and interpreted the data and performed the statistical analysis. All authors helped draft and edit the final manuscript. DB generated all SBML model files. All authors approve the content of this manuscript. All authors read and approved the final manuscript.NP conceptualized and DB designed the study. BM conducted all phylogenetic analysis, and NP and BM analyzed the results. DB constructed all three ancestral core metabolic network reconstructions and performed all Aerobic experimental carbon source utilization for 38 enterobacterial strains.Click here for fileAnaerobic experimental carbon source utilization for 38 enterobacterial strains.Click here for fileDataset 1. A list of experimental carbon source utilization data of enterobacteria.Click here for fileList of genomes used for the phylogenetic analysis of the enterobacteria.Click here for fileDataset 2. A list of orthologous genes from 72 genomes of enterobacteria to those from E. coli K-12 MG1655, and to genes contained in the metabolic models of the E. coli/Shigella (iEcoli_core),E.coli/Shigella/Salmonella  , and the enterobacterial (iEntero_core) ancestral core.Click here for fileDataset 3. Gene-to-protein-to-reaction associations representing the metabolic models of the E. coli/Shigella (iEcoli_core), E.coli/Shigella/Salmonella , and the enterobacterial (iEntero_core) ancestral core.Click here for fileComputational Model 1. SBML format of iEcoli_core for distribution and use in other modeling environments.Click here for fileComputational Model 2. SBML format of iSalcoli_core for distribution and use in other modeling environments.Click here for fileComputational Model 3. SBML format of iEntero_core for distribution and use in other modeling environments.Click here for file