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.


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


To understand complex biological systems such as cells, tissues, or even the human body, it is not sufficient to identify and characterize the individual molecules in the system. It also is necessary to obtain a thorough understanding of the interaction between molecules and pathways. This is even truer for understanding complex diseases such as cancer, Alzheimer’s disease, or alcoholism. With recent technological advances enabling researchers to monitor complex cellular processes on the molecular level, the focus is shifting toward interpreting the data generated by these so-called “–omics” technologies. Mathematical models allow researchers to investigate how complex regulatory processes are connected and how disruptions of these processes may contribute to the development of disease. In addition, computational models help investigators to systematically analyze systems perturbations, develop hypotheses to guide the design of new experimental tests, and ultimately assess the suitability of specific molecules as novel therapeutic targets. Numerous mathematical methods have been developed to address different categories of biological processes, such as metabolic processes or signaling and regulatory pathways. Today, modeling approaches are essential for biologists, enabling them to analyze complex physiological processes, as well as for the pharmaceutical industry, as a means for supporting drug discovery and development programs. Over the last decade, DNA-sequencing technologies have advanced tremendously, culminating in the deciphering of the complete human genome in 2001 . This acIn the meantime, further technological advances have led to a considerable increase in the understanding of the workings of the human body under normal conditions and in various disease states. For example, transcriptomicThis article summarizes the challenges associated with the study of complex biological systems, the benefits of systems biology approaches, and the ways in which computational models can help consolidate and interpret the experimental data obtained using these approaches. These principles are exemplified by some concrete examples from current research projects.14 individual cells, each of which is itself a complex system comprising thousands of different proteins and other biomolecules. The information specifying the composition and structure of virtually all of these molecules is encoded in the DNA. Although researchers now have information on all genes at hand, they still lack a deeper understanding of many seemingly common biological effects. The reason for this can be exemplified by an analogy with a modern passenger jet, another complex, yet man-made, system. Modern passenger jets consist of thousands of individual components, such as screws, wheels, cables, and other components that perform a specific function in a specific technical context. However, knowledge of those individual components does not reveal functions that arise through interactions with other components, such as those related to takeoff, navigation, communication, or landing. To understand how a plane flies, one must know the interplay of the various components of the plane’s controls and the dynamic regulatory feedback loops that control this interplay. Similarly, the processes that occur in living organisms during growth, metabolism, and regulation of cell functions also are interrelated and require equally tight and coordinated control mechanisms.The human body consists of approximately 10The characteristics of a complex system that arise from the interaction of various components are referred to as the emergent properties of the system. Because they are the result of interactions between the different parts, these emergent properties cannot be attributed to any single part of the system. Thus, the ability of a passenger jet to fly is not the consequence of one particular screw (even though this particular screw may be necessary for the plane to function). Similarly, the development of a complex disease  likely is not caused by a single gene, although a particular gene may be one of the elements necessary for the disease to develop. Such a system is considered irreducible—that is, the system is unlikely to be fully understood by taking it apart and studying each part on its own. To understand irreducible systems and fully appreciate their emergent properties, one must study the systems as a whole.The publication of the human genome sequence provided biological scientists with a list of all the individual parts that make up the human body. However, just like having a pile of all the pieces of a passenger jet does not allow a technician to put together a functional plane without having a blueprint of the wiring scheme, this genome sequence is not sufficient to understand the interactions between the genes and their products. Advances over the last few years in transcriptomics, proteomics, and metabolomics that allow investigators to monitor the biological response of cells, however, will allow studies of physiological systems as a whole in order to identify higher-level biological mechanisms encoded in the human genome  see fig.A major reason for the advent of systems biology activities is that only recently analyses at the molecular level of the cell have become technically feasible on a larger scale. With the development of these new, large-scale technologies to identify and quantify molecules on the DNA, mRNA, protein, and metabolite level, researchers for first time are in a position to gather comprehensive data on the molecular state of a given biological system in a systematical manner. These technologies are sometimes collectively referred to as “–omics” technologies see . In addiThe new –omics technologies are characterized by three distinct features. First, they allow for analyses on different molecular levels, such as the DNA, RNA, protein, or metabolite level. These different molecular levels sometimes behave asynchronously—that is, although some proteins are highly abundant in a cell, the levels of the corresponding mRNAs from which they are produced may be very low or vice versa. Because asynchronous behavior can indicate the effects of complex regulatory interactions, it is important to examine the role and degree of synchronization of the transcriptome, proteome, and metabolome. For example, metabolites produced in certain biochemical pathways sometimes exert a feedback on key enzymes in the pathway by modifying the expression of the genes that encode these enzymes. The –omics technologies allow researchers to systematically discover such interactions and incorporate them into models aiming to capture the essential regulatory features of a pathway.Second, –omics technologies are highly parallelized. This means that for a single biological sample many different biological “readouts” can be measured simultaneously. For example, with today’s microarrays researchers can simultaneously measure the expression of virtually all genes of the organism being studied rather than having to perform numerous separate experiments focusing on different genes. This parallelization enables scientists to detect not only the expected but also unforeseen responses of an organism. For example, microarrays in toxicology research allow for a broad screen for unexpected biological side effects caused by new drugs . The higThird, –omics technologies are highly standardizable and thus amenable to a high degree of automation, allowing researchers to handle and process large numbers of biological samples. The ease of sample processing and experimentation has a huge impact on how experimental studies are performed today. For instance, comparison of larger numbers of replicate experiments allows researchers to validate biological effects with a greater statistical certainty. The ease of use of –omics technologies is particularly relevant for clinical studies, in which large patient populations must be tested to obtain a sound statistical basis for confirming drug efficacy and identifying potential side effects.The huge amounts of data gathered require tools to automatically process, compare, and interpret the data in a manner that identifies the most relevant pieces of information and which can be used to generate models of, for example, regulatory or metabolic pathways. These tools include computerized data analysis strategies that result in the formulation of mathematical models of the biological systems analyzed.Biological systems are inherently complex, and many of their emergent properties result from the interplay of numerous molecular components. Moreover, biochemical reactions often obey nonlinear reaction kinetics—that is, an increase in the amount of the starting material of the reaction does not necessarily lead to a proportional increase in the amount of the reaction product. Finally, other complexities, such as cell structure and compartmentalization or random  effects, also often result in unexpected behavior of the entire system. Mathematical models that take these factors into consideration allow researchers to capture the features of complex biological systems and to understand how biological systems respond to external or internal signals and perturbations, such as different growth or development conditions or stress triggered by agents such as alcohol.Mathematical models have the big advantage of being amenable to computer simulations. Models describing biological systems generally are too complex to be solved analytically  and therefore typically are solved numerically—that is, using computers to solve the mathematical equations that help predict the response of a biological system. With the availability of computer-based techniques for solving mathematical equations, the response of a biological system to different conditions can be relatively easily simulated in silico once a mathematical model is available. These computer simulations  in many cases require much lower investment and much less time compared with the typically more time-consuming and expensive biological experiments (sometimes referred to as “wet experiments”).The general approach for creating and using mathematical models in biological sciences is similar to the one followed in other scientific disciplines such as physics and provides the basis for communication between experimental and theoretical scientists. Thus, the theories and mathematical formulas developed by theoretical biologists on the basis of existing experimental data can be tested by experimentalists and used to predict the behavior of biological systems under as-yet-unexplored conditions. Any discrepancies between the predicted and measured results then need to be resolved, either by extending the theoretical framework  or by refining the experimental setup or data interpretation.Mathematical models for biological systems and the associated computer simulations offer numerous benefits. First, discrepancies between systems behaviors predicted by a mathematical model and actual behaviors measured in experiments can point to components that still are missing from the mathematical model, thereby assisting in developing a more comprehensive picture of a biological process. And even if it is not clear which components are missing from the system under investigation, the results obtained with the mathematical model may help to guide the design of additional experiments to clarify the issue see .Second, mathematical models provide a systematic approach for investigating systems perturbations—for example, those induced by drug administration, genetic alterations, developmental signals, or other factors. To this end, scientists can modify the values of the model parameters  and re-run the computer simulations. This approach is relatively straightforward once a reasonable base model is available.Third, mathematical simulations are not as limited by experimental constraints as wet experiments. Computer simulations can quickly investigate different experimental conditions for the biological system of interest, and only the most relevant cases can be assessed afterwards in the laboratory. This allows researchers to investigate novel scenarios and to develop hypotheses to guide the design of new and promising experiments. This approach is particularly helpful if the wet experiments are difficult and expensive to perform. The combination of dry and wet approaches is at the heart of systems biology and already is being used widely in the metabolic engineering industry, which uses live cells  to produce complex chemicals  based on fermentation processes. In these cases, mathematical models are used to suggest directed genetic modifications that may improve the productivity of the microorganisms.Fourth, mathematical models can be very helpful for systematically determining the relevance of a specific molecule or pathway for the overall behavior of the system. Not all components of a reaction or pathway are equally important, and many biological processes are controlled by relatively small subsystems. Comparison of computer simulations and actual experimental data may help the researcher to readily identify such simpler subsystems that are sufficient to understand the features of the much more difficult-to-treat full biological system.For choosing the optimal modeling approach it is essential to understand the nature of the biological process of interest because different mathematical frameworks have been developed for modeling the behavior of different types of biological systems. For example, most cellular phenomena are governed by dynamic processes so that the cell can adapt to environmental changes or control inherently dynamic cellular functions, such as periodic cell division. For describing such time-dependent phenomena, it is imperative to choose mathematical equations that can capture these dynamic effects. For other biological processes, however, it often is not necessary to describe all the details of the underlying dynamics because some molecules’ concentrations do not change over time . For most types of applications, appropriate modeling methods have been developed. Two examples are described below—modeling of metabolic processes and modeling of signaling and regulatory pathways.Metabolic processes are essential for all living organisms and provide the cell’s energy, deliver building blocks for the synthesis of larger molecules, or degrade toxic substances. Although biological research has focused on metabolism for several decades, many metabolic processes still are not fully understood, and, in particular, the regulatory mechanisms controlling even well-investigated metabolic pathways often are unknown.A key parameter in any metabolic study is the metabolic flux—that is, the conversion rate of metabolites along a metabolic pathway. For many research and industrial applications, it is crucial to predict the metabolic flux patterns that indicate which biochemical routes are utilized . Modeling techniques are widely used in the field of metabolic engineering to identify any steps in the production of a desired molecule by cultured cells or bacteria that limit the overall rate with which the process occurs . The results of these analyses can guide researchers on how to genetically modify the cells or bacteria to optimize the yield of the desired end product  to the sugar glucose, yielding a compound called glucose-6-phosphate. This reaction must be balanced in terms of atoms and electrical charges. In a chemical notation, the balanced reaction is written as C13C-method)   that wilSignaling pathways serve as the cell’s central control machinery, which tightly regulates the cell’s response to external and internal stimuli. These pathways involve the transmission of external and internal signals through the cell’s membrane and interior into the cell’s nucleus, where they activate or deactivate specific sets of genes. All of these processes are inherently dynamic events that require different mathematical modeling strategies than the quasi-stationary (metabolic) processes discussed above.Many signaling pathways are triggered by the binding of extracellular biomolecules  to a docking molecule  embedded in the membrane surrounding the cell. Receptors are proteins, often spanning the membrane, which expose one part of their structure to the exterior environment  and one part to the cell’s interior . If a signaling molecule binds to the extracellular region of the receptor, the receptor’s three-dimensional structure may change—a process that can trigger cascades of biochemical reactions within the cytoplasm. These cascades often involve specialized signaling molecules such as enzymes known as kinases, which transfer phosphate groups from one molecule (the donor) to a specific target molecule (the substrate) and which are used extensively to transmit and integrate signals to control complex cellular processes. In many cases, kinases act on and modify the activity of specific proteins. The addition of the phosphate group changes the substrate protein’s biochemical behavior so that it, in turn, can modify additional signaling molecules in the signaling cascade. Ultimately, this chain reaction results in the activation of proteins called transcription factors that bind in the cell nucleus to DNA, triggering expression of distinct sets of target genes. It is this gene activation that alters the cell’s behavior and represents the cell’s response to the initial stimulus.56.Obviously, signal transduction is an inherently dynamic phenomenon, as the cell has to be able to flexibly respond to changes within the organism and in the environment. To model the dynamics of signaling cascades such as those described above, researchers primarily rely on so-called differential equations . Such differential equations are used to model the dynamic behavior of, for example, the changes in the concentration of signaling molecules over time as well as the signaling molecules’ distribution across different cellular compartments. Modeling of even relatively simple signaling networks has revealed that signal transmission through the cell often shows unexpected behaviors, such as periodic activation patterns or enhancement  of the initial signals . A speciAny equation in a mathematical model will contain one or more parameters that describe certain biophysical characteristics of the molecules involved in the reaction or pathway being studied. For example, when modeling the dynamics of a network of biochemical reactions, the mathematical equations must incorporate parameters that reflect the kinetic properties of the involved enzymes—for example, the number of reactions the enzyme can perform during a given period of time . Researchers must know these kinetic parameters before they can set up well-defined systems of differential equations representing appropriate models of biological processes.In principle, the kinetic parameters for all the relevant enzymes can directly be experimentally determined. In practice, however, many kinetic parameters, even for otherwise well-investigated enzymes, still are unknown, primarily because the relevant experimental data are lacking . But even if the kinetic parameters have been measured, these data often are based on experiments performed in a test tube with purified enzymes , and it is unlikely that the enzymes behave similarly under the conditions found in a living cell . To overcome this limitation, one can use dynamic measurements of the overall system. Computational procedures are available to estimate the appropriate model parameters by testing different parameter sets until they fit the available experimental data. However, this process is critically dependent on the quality of the experimental data, and unreliable experimental data will lead to unreliable predictions of kinetic parameters and therefore to models of very limited value . The lacIt must be pointed out that some biological phenomena cannot be described by using models that are just based on continuous concentration fields , ignoring the existence and relevance of individual molecules. For instance, on a molecular scale random molecular movements can have a major impact on cellular processes. The molecules in a cell are closely packed, and thermally induced random movements of these molecules as well as interactions between them can strongly affect the transmission of signals. To account for such effects, a random  component must be integrated into the mathematical equations of the model. Particularly for rare signaling molecules, of which only a few copies may be present in the cell, the effects of such a stochastic component are significant and must not be neglected.Another issue that complicates modeling of biological systems is that the different components of a pathway often act over different time and distance scales. For example, metabolic reactions can happen within seconds or minutes, whereas genetic regulatory processes that are induced by these metabolic reactions may occur over several hours or even days. Similarly, some regulatory reactions occur over small distances , whereas others involve greater distances . To couple relevant effects occurring on very different length and time scales, researchers use so-called multiscale models as a compromise to avoid making the model overly complex.One important signaling factor is nuclear factor kappa B (NFκB), which regulates numerous processes relevant for inflammatory reactions, immune responses, cell proliferation, and survival of the cell. NFκB is a transcription factor—that is, it activates specific genes required for these processes by binding to the DNA in front  of these so-called target genes.Because of its important functions in the cell, the levels and actions of NFκB must be tightly regulated. NFκB normally is found in the fluid filling the cell  and must move to the nucleus to exert its effects on its target genes. To prevent inappropriate movement of NFκB to the nucleus, the molecule normally is linked to a phosphate group  and interacts with proteins called inhibitory molecules of NFκB (IκBs). When the NFκB pathway is activated by another signaling molecule, IκBs are degraded, allowing NFκB to move to the nucleus and activate its target genes. One of these target genes codes for one of the inhibitory molecules, IκBα. Thus, NFκB activation leads to production of new IκBα, which can then bind to NFκB and shut off the NFκB pathway. This is known as a negative feedback loop. Continuous cycles of IκBα degradation and synthesis give rise to regular changes  in NFκB activity that can be observed experimentally. Mathematical models have been used to investigate these oscillations in more detail, and comparisons between “dry” and “wet” experimental results generally have shown good agreement. The mathematical equations for modeling NFκB activation also have been used to identify potential contributions of other molecules that are thought to modulate the NFκB/IκB-mediated regulatory process. For example, modeling approaches using experimental data derived from mice in which specific IκB genes had been inactivated  demonstrated that certain IκBs had a damping effect on cyclic NFκB/IκBα oscillations  .Finally, it is important to recognize that any model can be only as good as the assumptions upon which it is based. By definition, any model is an abstraction and simplification of reality. All currently available, tractable mathematical models of biological systems neglect the majority of the molecular players in an organism. Moreover, all models make assumptions about relevant time and length scales. For example, the discussion in this article focuses on modeling approaches for cellular pathways that neglect molecular details . It is essential to keep these limitations in mind when discussing the value and validity of mathematical models or when developing a specific model to capture the characteristics of a given biological process.Systems biology approaches have great potential for enhancing the drug discovery and development process. Currently, the productivity of the pharmaceutical industry is lagging behind its investments in research and development. The output of new chemical entities , which is considered an indicator of the innovation potential of pharmaceutical research, is only slowly growing . The whoSystems biology is expected to play an increasingly important role in the establishment of innovative drug discovery strategies. Today, the industrialized drug discovery process relies, to a large degree, on highly automated processes for screening the biological activity of large chemical libraries in order to identify new drug candidates. These screening assays enable a systematic assessment of candidate compounds by testing their activity on therapeutic targets—that is, biomolecules that are causally involved in disease outbreak or disease progression .Systematic compound screening provides the starting point for further chemical development to optimize the drug-like features of the lead compound. Computational models of disease-relevant pathways that allow for dry experiments to support the assessment of a candidate molecule’s safety and efficacy most likely will play an increasingly important role in this process, and the pharmaceutical industry is greatly interested in establishing new predictive, computer-supported methods to systematically identify the most promising drug candidates. In this context, a number of pharmaceutical companies recently have initiated dedicated systems biology programs to support their in-house drug discovery and development programs .58). One of the pioneering systems biology programs is the publicly funded German HepatoSys initiative, in which more than 40 German research centers cooperate in a joint program investigating the systems biology of the liver cell using numerous complementary approaches. The liver is an organ of great medical interest with relevance to many disease areas, including alcohol-related diseases. The different groups participating in HepatoSys apply a broad spectrum of technologies, ranging from classical cell biological methods to imaging, transcriptomics, proteomics, and metabolomics; in addition, several groups conduct dry experiments by applying pathway modeling to liver cell pathways. Within the overall consortium, different technology platforms are organized into subgroups, or networks, which focus on specific medically relevant themes, such as liver regeneration or detoxification processes. In a first step, the researchers seek to reconstruct liver-specific pathways using wet and dry methods. Later, liver metabolism and liver-specific signaling and their roles in liver regeneration and drug metabolism will be investigated.At the same time, an increasing number of publicly and privately funded initiatives and consortia aim at establishing systems biology in different domains of biological research to elucidate, for example, the functions of specific cell types relevant for medical applications or to develop comprehensive systems biology applications for metabolic engineering. In most cases, multiple research centers or companies are integrated in a decentralized research network to which investigators from numerous disciplines  contribute see , p. 58. For HepatoSys and other systems biology consortia and research centers, it is essential that the different research groups are connected via a central, dedicated data transfer and exchange infrastructure to facilitate the close collaboration among groups and disciplines. Such an infrastructure must include a specialized data management system that allows the participating groups to deposit their wet and dry data in a central location, which is accessible to the experimentalists as well as to the modelers. Although the focus of publicly funded systems biology consortia primarily is on basic research, the results produced will likely also be critical for applications in the healthcare and biotechnology sectors.In summary, the various systems biology approaches developed in recent years provide an extraordinary amount of new information on many functions of human and other organisms relevant to research and biotechnology applications. Only with the help of computerized modeling efforts, however, can researchers make sense of all the different bits and pieces of information that are accumulating at an ever-increasing pace. Just as an engineer can turn a heap of metal pieces, wires, screws, and bolts into a jet plane only if he has a comprehensive blueprint, biomedical scientists can understand the workings of living organisms only if they have comprehensive models that enable them to connect the often disparate pieces of information derived from experimental approaches. The Greek philosopher Aristotle said more than 2,000 years ago, “The whole is more than the sum of its parts,” and today, systems biology research and modeling efforts are helping to obtain a more comprehensive understanding of life.


Escherichia coli, Corynebacterium glutamicum, Bacillus licheniformis, and Saccharomyces cerevisiae during well-controlled bioreactor cultivations. Most surprisingly, in all cases a great diversity of central metabolic intermediates and amino acids is found in the culture medium with extracellular concentrations varying in the micromolar range. Different hypotheses for these observations are formulated and experimentally tested. As a result, the intermediates in the culture medium during batch growth must originate from passive or active transportation due to a new phenomenon termed “extended” overflow metabolism. Moreover, we provide broad evidence that this could be a common feature of all microorganism species when cultivated under conditions of carbon excess and non-inhibited carbon uptake. In turn, this finding has consequences for metabolite balancing and, particularly, for intracellular metabolite quantification and 13C-metabolic flux analysis.Overflow metabolism is well known for yeast, bacteria and mammalian cells. It typically occurs under glucose excess conditions and is characterized by excretions of by-products such as ethanol, acetate or lactate. This phenomenon, also denoted the short-term Crabtree effect, has been extensively studied over the past few decades, however, its basic regulatory mechanism and functional role in metabolism is still unknown. Here we present a comprehensive quantitative and time-dependent analysis of the exometabolome of  Saccharomyces cerevisiae.13C-MFA) is the standard method for quantifying intracellular fluxes + mode at an electron energy of 70 eV. The source temperature was set to 180°C. The MS was tuned and calibrated with the mass fragmentation pattern of Heptacosa (heptacosafluoro-tributylamine). During analysis, the accurate masses were corrected to a single point lock mass of CPFB (chloropentafluorobenzene) as an external reference at 201.9609 m/z. Data acquisition was done in centroid mode at a scan rate of 0.09 s and an interscan delay of 0.01, i.e. 10 scans s-1. For the identification of known metabolites a baseline noise subtracted fragment pattern was used and compared to the in-house database JuPoD, the commercial database NIST and the freely available database GMD. Unknown peaks were identified by a structural combination of elemental compositions and verified by virtual derivatization and fragmentation of the predicted structure.Prior to analysis, 13 μl aliquots of the samples were lyophilized overnight in a Christ LT-105 freeze drier and then stored at −20°C. The dried samples were consecutively derivatized with 50 μl MeOX (20 mg mlThe authors declare that they have no competing interests.NP, AN and TL conducted the experiments and analyzed the data; JG performed GC-TOF-MS analysis; SN wrote the paper with substantial input from NP and WW. All authors read and approved the final manuscript.Supplementary Information. Click here for file