Computational identification of new drug targets is a major goal of pharmaceutical bioinformatics.Escherichia coli (KEIO collection). We yielded very reliable results with high accuracy (93%) and precision (90%). We show that topologic, genomic and transcriptomic features describing the network are sufficient for defining the essentiality of a reaction. These features do not substantially depend on specific media conditions and enabled us to apply our approach also for less specific media conditions, like the lysogeny broth rich medium.This paper presents a machine learning strategy to study and validate essential enzymes of a metabolic network. Each single enzyme was characterized by its local network topology, gene homologies and co-expression, and flux balance analyses. A machine learning system was trained to distinguish between essential and non-essential reactions. It was validated by a comprehensive experimental dataset, which consists of the phenotypic outcomes from single knockout mutants of Our analysis is feasible to validate experimental knockout data of high throughput screens, can be used to improve flux balance analyses and supports experimental knockout screens to define drug targets. In particular, metabolic enzymes have been successfully targeted by specific drugs to inhibit essential processes of pathogenic organisms in the human host . Analyziorganism ,3. A genorganism . The terorganism . Furtherorganism ,3. Load organism . Choke pke point .Escherichia coli, the essentiality of virtually all open reading frames was observed by a comprehensive knockout screen  is a widely used and well established method to assess the essentiality of genes ,8. Howevllection ). This d toolbox  and a neems view .In this paper we propose an integrative machine learning approach applying a broad list of the described tools. The machine learning system was supplied with qualitative and quantitative descriptors derived from biochemical knowledge, genomic and transcriptomic data, and flux balance analyses. Using the KEIO collection  as the gThe data for the metabolic network was taken from a previous study and reconstructed in the same way . Basicaet al. [In order to demonstrate the efficiency of our approach we used data from the KEIO collection  as the get al. . The reaA list of relevant features was obtained from three different aspects: network topology, genomics and flux balance analyses. Table We set up a breadth first algorithm to investigate the network when a single reaction was blocked. We defined a reaction as essential for survival when basically the mutated network could not yield the products of the reaction from upstream substrates of the reaction. Hence, features were defined to describe if the knocked out reaction was substantial for producing its downstream metabolites or if these products could still be produced by other pathways. The investigation for each tested knocked out reaction was performed by the following algorithm.i. All metabolites acting as input nodes (substrates) and output nodes (products) of the knocked out reaction were selected. The set of substrates S defined the input nodes and the set of products P defined the output nodes. To get a broader list of available substrates we integrated several other substrates into S. We included the substrates of the upstream reactions and the products of the downstream reactions into the sets S and P, respectively. Substrates of reactions that had at least one of the substrates S as a substrate was included into S. Further, substrates of reactions that had a metabolite out of P as a substrate were also included into S.ii. Reactions were selected which used only available compounds as substrates.iii. These selected reactions and their products were incorporated into the network. These products were set as new available metabolites in the network.iv. Steps ii and iii were repeated until no further reactions could be identified for incorporation.v. The output nodes that could be produced were counted (reachable products P).After finishing the process, we used the number of defined output nodes that could be produced within the mutated network for two features, i.e. a quality feature defining if at least one product could not be produced , and the percentage of products that could not be produced .We again run a breadth first search on the network to estimate possible deviations. This time we focused on relevant pathways by using the similarity measure from the SIMCOMP software . SIMCOMPA reaction that uniquely consumes or produces a certain metabolite in the metabolic network is considered a choke point. Such a reaction shows high potential for essentiality ,3. We chThe number of substrates and products of the knocked out reaction were counted . Further, we defined features for the number of neighbouring reactions , the number of neighbours of neighbouring reactions  and the clustering coefficient  ,17 of thE. coli with four different e-value cutoffs, i.e. 10-3, 10-5, 10-7, and 10-10 yielding the features H3, H5, H7 and H10, respectively. The method of the flux balance simulations is described in Results and discussion .For our case study, we collected gene expression data from a study observing the regulation during oxygen deprivation . This dan, n = -4, -2, 0, 2, 4). The same range was taken for the kernel width γ. This optimization was realized by training with a grid search over all combinations of these parameters [We applied Support Vector Machines from the R package e1071  to classrameters . The sizThe feature selection was done by a top-down approach. We trained the Support Vector Machines in terms of maximizing the overall accuracy using all features. Each single feature was discarded from the data set and the performance of the machine was observed. Testing the performance of the machine was done by a leave-one-out cross validation. The accuracies of the machines missing one feature were compared and the best machine kept for the next iteration. This was repeated until the accuracy did not increase. The machine with the best accuracy was selected as the best classifier and its features as the optimized feature set.E. coli strain MG1655 on 1% agarose gels.Knockout mutations were verified by PCR amplification of genomic loci expected to contain the 1327 base pair gene replacement cassette with specific primers . For obtaining different stringencies, we weighted the positive instances by a factor ranging from 0.1 to 5.0 with a step size of 0.1 Figure . The senWe compared the enzymes of our predictions and the results from the KEIO collection to a comprehensive list of valid drug targets from the Drugbank database  Figure . SurprisWe performed a single reaction deletion on the network and calculated flux values by FBA using the Cobra Toolbox  to assesFigure or an error within the experimental knockout screen. We examined our lists of false positives and false negatives by two experimental set-ups. Our list of false negatives contained 71 genes which our algorithm predicted to be non-essential under glucose minimal condition in contradiction to the outcome of the KEIO experiment [Predicting a different outcome from experimental high throughput screen (KEIO) may be due to either an error in our algorithm, periment . For 33 E. coli from KEIO [E. coli wild-type and single knock out strains. The single knock outs were regulators for respiration effecting a large number of genes and also the treatment was rather unspecific (growth in oxygen rich and deprived conditions). Hence, a large portion of network pathways of the metabolic network was differentially expressed [Defining drug targets is a challenging task. Many experiments rely on a conditional essentiality screen of genes to define the associated enzymes as possible drug targets. Machine learning methods can help to validate this experimental data. Our approach used the experimental knockout data for rom KEIO . The macxpressed . Within E. coli we benefited from a rich data pool including a well elaborated metabolic network, a genome wide knock out viability screen, the genome sequence and a feasible gene expression dataset. Nowadays, the genomic sequence may not be the limiting factor for most applications as a remarkable number of genomes has been sequenced or will be sequenced in the next future. As our approach uses unspecific gene expression data also this can be obtained from publically available resources or obtained by rather straightforward experiments. Very well elaborated metabolic networks have been assembled for some organisms  to whicrevisiae  and Keggrevisiae . It willKP, J–PM, RE and RK put up the general concept and design of the study. KP carried out the data analysis. MO and KP conceptualized and implemented the breath first search algorithm. FS and VS validated the model predictions experimentally in the lab. KP and RK drafted the manuscript. All authors read and approved the final manuscript.Supplementary tables. Tables S1, S3 and S4.Click here for fileSupplementary Table S2. Results of all Reactions.Click here for file


Whole genome duplication (WGD) occurs widely in angiosperm evolution. It raises the intriguing question of how interacting networks of genes cope with this dramatic evolutionary event.Arabidopsis metabolic network, we assigned each enzyme (node) with topological centralities  to measure quantitatively their centralities in the network. The Arabidopsis metabolic network is highly modular and separated into 11 interconnected modules, which correspond well to the functional metabolic pathways. The enzymes with higher in-out degree and between-ness  tend to be more conserved and preferentially retain homeologs after WGD. Moreover, the simultaneous retention of homeologs encoding enzymes which catalyze consecutive steps in a pathway is highly favored and easily achieved, and enzyme-enzyme interactions contribute to the retention of one-third of WGD enzymes.In study of the Our analyses indicate that the hub and bottleneck enzymes of metabolic network obtain great benefits from WGD, and this event grants clear evolutionary advantages in adaptation to different environments. Arabidopsis [Populus [Arabidopsis, a genome-wide similarities search (Blast) was done among protein-coding genes and strong evidence for a whole genome duplication event was demonstrated by phylogenetic analysis. The analysis of the genomic duplication blocks revealed that about 80 percent of genes lost their sister genes following WGD [Poales from the Liliales and Zingiberales [Populus genome sequences revealed evidence for a whole-genome duplication event in the genome, where about 8000 pairs of homeologs survived after the event [Whole genome duplication is one of the most important evolutionary events in plants  and manybidopsis , rice [3bidopsis  and Popu[Populus  genomes.wing WGD ,6. In riiberales . Analysihe event .Paramecium [Arabidopsis, dosage effects were suggested to be an important factor influencing the retention of homeologs. For example, transcription factors, which have roles in regulating other genes, normally show strong dosage sensitivity and genes encoding transcription factors were over-represented amongst WGD-homeologs as shown by GO analysis [Research on the genome data from vertebrates and yeast has shown that factors, such as gene expression intensity ,8, proteramecium , showed analysis . Althouganalysis -15, the Graph theory provides paradigms to study networks . The plaArabidopsis metabolic network according to the recently updated Aracyc data [Arabidopsis.In this study, we reconstructed the thaliana). By usinArabidopsis enzyme-enzyme metabolic network was constructed using the recently updated Aracyc database [Arabidopsis metabolic network indicates the existence of bottleneck enzymes, which tend to connect different modules/pathways. Between-ness (see Methods), which refers to the centrality of the considered enzymes in control of substrate-product fluxes in the network, was used to quantify this propensity.The database  . Since the genome duplication event in Arabidopsis occurred 20-40 million years ago [Arabidopsis and Populus [Arabidopsis. The enrichment of WGD-enzymes in the hubs and bottlenecks in the metabolic network were not significantly influenced by the phylogenetic ages.Previous research ,22 indicArabidopsis was retrieved from the TIGR database, http://www.tigr.org/tdb/e2k1/ath1/TandemDups/TandemGenes.html . Of the 478 metabolic network enzymes, we identified genes encoding 25 metabolic enzymes which retained tandem-homeologs  were obtained  to (b) were repeated 10000 times, and resulted in a normal distribution N  of k  = N . (b) By randomly assigning m edges to the network, nodes connected by the selected edges were marked, and then the number of nodes, f, was recorded. Repeating two steps from (a) to (b) 10000 times, f followed a normal distribution as N, This indicates that this type of interactions render about 62 enzymes to be WGD-enzymes with the standard error of 16. In total, approximately one-third (62/173) of the WGD-enzymes were attributable to the impact of metabolic interaction.The simulation analysis indicated the retention of genes encoding enzyme-homeologs was not independent of the retention of the genes encoding their interacting enzyme-homeologs. For a metabolic interaction Arabidopsis were also likely connected by WGD enzymes in Populus. The datasets of Populus enzymes from http://genome.jgi-psf.org/Poptr1_1/, and the Populus WGD-homeologs were retrieved from http://chibba.agtec.uga.edu/duplication/[Populus genes encoding 226 enzymes which retain at least one pair of WGD-homeologs  were found to be connected by WGD-enzymes in Populus. Of the 255 Arabidopsis IBWE, 32 ortholog interactions also are connected by WGD-enzymes in Populus. , indicating that the interactions connected by WGD-enzymes in Arabidopsis indeed also tend to be connected by WGD-enzymes in Populus.We applied comparative genomics to explore whether the interactions connected by WGD enzymes in lication/. Our anaArabidopsis and Populus. The seven enzymes locate in the inter-connected positions of three pathways, the fructose metabolism, gluconeogenesis and the pentose phosphate pathways. Phylogenetic analysis revealed that the seven genes were preferentially retained as parallel paralogs in the process of WGD after the two species split (see Methods). Genes encoding these important enzymes were simultaneously duplicated in the process of WGD, hence metabolic flux has simultaneously increased, maintaining the balance of the metabolite flux.Figure Finally, in the process of WGD, genes encoding hub and bottleneck enzyme can be easily retained their homeologs, providing not only one extra copy of individual enzymes but also another set of interconnected enzymes for the consecutive steps in the pathways.Arabidopsis [Arabidopsis metabolic network tend to be highly expressed and more conserved. This results support the previous observations that highly expressed genes evolve slowly in yeast [The gain/loss of homeologs was an important event in the evolution of the plant genome. Previous analysis in bidopsis  showed tin yeast  and genein yeast .Arabidopsis metabolic network tend to preferentially retain homeologs after WGD and the simultaneous retention of WGD-homeologs encoding enzymes which catalyze consecutive steps in a pathway is highly favored. This phenomena can be best explained by the dosage-sensitive relationship in the gene balance hypothesis which has been demonstrated in yeast and humans [Drosophila [Arabidopsis metabolic network, genes encoding hub enzymes are in the important positions and usually connected with many other enzymes, forming a sub-network, and are very likely to be more sensitive to the dosage effects and indeed preferentially retained after WGD.Our further analysis revealed that genes encoding hub and bottleneck enzymes in the d humans , maize aosophila  and alsoosophila . In brieosophila -30. In tArabidopsis are connected by WGD-enzymes in Populus. The results indicate that genes involving in this type of subnetwork-subnetwork connections tend to form an large evolutionary unit, requiring simultaneous retention of interconnected genes. We assume that the metabolism intermediates between the upstream and downstream enzymes are the key biological driving force. Maintaining balanced metabolic flux is important for the survival of plants. Recent experimental data [OSC-Cyp708 operon-like gene cluster resulted in the abnormal development of the Arabidopsis plant. Clear dosage effects were observed in the genetic analysis of saponin biosynthesis pathway in oats [Sad1 encodes 2,3-oxidosqualene to produce β-Amyrin, which eventually is used to produce avenacin A-1 by Sad3 and Sad4. Double mutant analysis revealed that Sad1Sad1-sad3sad3, Sad1Sad1-sad4sad4 and Sad1sad1-sad3sad3 have abnormal root development, while Sad1sad1-sad4sad4 has the normal root development. In many cases, accumulation of metabolic intermediates would be toxic to plants and simultaneous duplication of consecutive steps in the metabolic pathways is required and favoured.The simulation analysis revealed that about one-third of the WGD-enzymes were attributable to the impact of metabolic interaction, the comparative genomics analysis demonstrated that 12% of interactions connected by WGD-enzymes in tal data  demonstr in oats . Sad1 enAt1g52570-At5g57190 and At3g15730-At4g25970 have both coordinately diverged and express in different developmental stages for the benefit of the interaction. The other three divergently connected enzymes showing co-expression are EC2.3.1.12 and EC1.8.1.4, which were found in the gluconeogenesis pathway, EC2.3.16 and EC2.3.3.1, which mediate fatty acid metabolism and the citrate cycle, and EC2.6.1.2 and EC2.3.1.1 which mediate glutamate metabolism and metabolism of amine groups. The concerted divergence of WGD-enzymes may provide an easy route for the retention of consecutive steps. Since only four such interacting enzyme pairs were found, this mechanism seems to make only a small contribution to the retention of enzyme-homeologs.Apart from the potential dosage sensitivity of metabolic interaction, simultaneous expression divergence  of bothArabidopsis metabolic network prefer to retain homeologs through WGD but are not preferentially enlarged in their copy number by tandem duplication.The gene balance hypothesis also predicts that more "connected" genes are less likely to be retained as a tandem or transposed duplicate and are more likely to be retained postpaleotetraploidy . It is iArabidopsis is a good model for plant polyploidization studies. Many economically important plants such as cotton, Brassica rapa, potato, soybean, maize and wheat are polyploids. Through millennia of hybridization and domestication, wheat cultivars that are diploid, tetraploid and hexaploid have been produced. After the divergence from the ancestral sorghum genome, the tetra-ploidization of the progenitor genomes of maize occurred about 5~12 million years ago [Arabidopsis metabolic network shows that both its robustness has been enhanced by the process of WGD. We predicted that the polyploidizations of these main agricultural plants would have increased their environmental adaptability and provided human-needed traits for domestication. Hence, polyploid breeding might be worth more attention in plant breeding programs. Also in transgenic-based plant breeding, the simultaneous engineering of a set of hub and bottleneck genes/enzymes would be a better strategy than manipulation of a single gene/enzyme. As more plant genomes are sequenced, a deeper view of the evolutionary impact of WGD can help us to develop better breeding strategies in modern agriculture.ears ago . PolyploArabidopsis metabolic network by assigning the enzymes with three topological measures, in-degree, out-degree and the between-ness. Comprehensive analyses were carried out between the three centralities and the characteristics of the encoded genes, such as expression intensity, evolutionary rate, and retention of homeologs through WGD. Our results revealed that genes encoding hub and bottleneck enzymes in the metabolic network are preferentially retained after WGD. Furthermore the finding suggested that the retention of metabolic genes was influenced by their interactions and validated that the preferential retention of WGD homeologs encoding hub and bottleneck enzymes is due mainly to the potential dosage effect among interacted genes encoding enzymes if exist). Our results could help us get a deeper view of the evolution of plant metabolic network.In this study, we analyzed the Arabidopsis metabolic network: (a) an expert-curated list of Arabidopsis encoded enzymes and the corresponding genes from Aracyc  [ftp://ftp.genome.jp/pub/kegg/ligand/reaction/reaction/ to scan all catalyzed reactions of Arabidopsis enzymes [ftp://ftp.genome.jp/pub/kegg/ligand/reaction/reaction_mapformula.lst to obtain the information of metabolites in reactions. The reactions between metabolites were used to determine the interactions among enzymes. In the Figure Three files were downloaded to reconstruct the updated) , (b) a " enzymes , (c) a "j in the network as B(j) = 0. (b) Starting from vertex i, a breadth-first tree http://en.wikipedia.org/wiki/Breadth-first_search was built with i on the top, those that were nearest to i directly below and those that were farthest from i at the bottom. Each node was placed at a certain level of the tree based on its shortest metabolic reaction step. (c) P(n) = 1 was assigned to every vertex j in the tree. For every vertex j k is the set of nodes that directly connect ("provides substrates") to j. (d) B(j) = 1 was assigned to every vertex j in the tree. (e) Starting from bottom vertex j of the tree, B(j) was added to the corresponding variable of the predecessor of j. If j had more than one predecessor ("enzyme k provides more than one substrate to the enzyme j"), each predecessor k was assigned the value of (e) was performed for every vertex in the tree. (g) Steps (b)-(f) were repeated for every vertex in the network. Finally, every vertex in the network was assigned with a between-ness value which is the sum of its between-ness of every sub-tree involved.The in-degree was calculated by the number of enzymes providing substrates for the considered enzyme, whereas the out-degree was calculated by the number of enzymes using the products of the considered enzyme as substrates. The between-ness was calculated by the "breath-first tree" based algorithm as following steps ,37. (a) p(k)∞kt -for log-transformed data . Since the estimated power-law exponent was 1.67, methods for study of scale-free structure was applied in analysis the Arabidopsis metabolic network. The algorithm of Guimera and Amaral [The node distributions of P <In> and P <Out> were used to investigate the frequency of the in-degree and out-degree. The least-squares method was used to estimate power-law exponent of d Amaral , with pad Amaral  was usedArabidopsis genes. After filtering the mixture of RNA pools or measurement of the same developmental stages, 59 datasets of ME00319, which measured the developmental stages of Arabidopsis, were selected for downstream analysis  . The rawVi was used to measure the variations of gene i in expressional level across developmental stages [The Expression Variation index l stages .Sij is the expression signal of gene i in tissue j, Si, max)  . The expression variation of enzymes were calculated by n was the number of genes annotated with this enzyme, νi) (was Expression Variation index gene i).The expression maximum density of enzymes were calculated by Pij) was used to measure the co-expression between gene i and gene j as following formula:The Pearson correlation coefficient , were also analyzed with the same procedures.Arabidopsis and Populus. The proteomes of Arabidopsis thaliana, Populus trichocarpa and Oryza sativa japonica were downloaded from http://www.tigr.org/tdb/e2k1/ath1/, http://genome.jgi-psf.org/Poptr1_1/ and http://rice.plantbiology.msu.edu/index.shtml. The sequences of three species were used an all-against-all BLAST with an cutoff of 1e-10, by transforming the E-values with the absolute values of their logarithm[Arabidopsis metabolic genes were used for phylogenetic analysis.The phylogenetic tree approach was used to infer orthologs between logarithm, the scologarithm. The proArabidopsis thaliana, Populus trichocarpa), Oryza sativa japonica)) with Notung [Arabidopsis and Populus.The protein sequences of members in each cluster were aligned with ClustalW  and the h Notung , the ortArabidopsis and Populus, and the corresponding coding sequences were realigned with the gaps in the alignment trimmed. The Ka was estimated from the codon-based nucleotide sequence alignment by using the Yang-Nielsen maximum-likelihood method implemented in the yn00 program of the PAML package[Arabidopsis genes 5' 1000bp upstream and 3' 1000 bp downstream region were calculated against that of Populus orthologs. The Clustalw software [Ku 5and Ku 3with the Kimura two-parameter model were calculated by dismat program of the EMBOSS package [Arabidopsis gene i with more than one orthologs in Populus, the smallest of calculated Ka, Ku 5and Ku 3were selected as Kai) 5and Ku(i)3.The Clustalw was used to globally align two amino acid sequences of orthologs between L package. To calcsoftware  were use package . For a An was the number of genes annotated by this enzyme, Kai) 5and Ku(i) 3was the substitution rate in coding, upstream and downstream non-coding regions of Arabidopsis gene.The average divergence in coding regions, 5'upstream and 3'downstream region of enzyme could be calculated by the formula http://perl.org and R http://www.r-project.org/ scripts were used for analysis, and can be obtained on request.Spearman's rank correlation coefficients were estimated to evaluate the correlations between three topological centralities and expression intensities, expression variation, substitution rates of coding regions of gene encoding enzymes. The p-values were FDR-corrected by using the Q-value program in R package . The comKa: non-synonymous substitution rates of coding region; K5u: substitution rate of 5'UTR; K3u: substitution rate of 3'UTR; WGD: whole genome duplication; WGD: enzyme, the enzyme retaining paralogs through whole genome duplication; IBWE: the interaction between WGD-enzymes.XW and XQ performed the experiments and analyzed the data, XQ directed the project and contributed the materials and analysis tools. XW and XQ wrote the paper. All authors read and approved the final manuscript.Table S1. 478 enzymes in the largest network and their topological centralities.Click here for fileTable S2. 11 topological modules and their major functions.Click here for fileArabidopsis microarry datasets.Table S3. The description of Click here for fileArabidopsis and Populus by phylogenetic trees.Table S4. The identified ortholog groups between Click here for fileArabidopsis and rice by phylogenetic trees.Table S5. The identified ortholog groups between Click here for fileArabidopsis WGD-enzymes and their coding homeologs.Table S6. 173 Click here for fileArabidopsis tandem-enzymes and their coding tandem homeologs in the Arabidopsis metabolic network.Table S7. 25 Click here for fileFigure S1. Comparison of three topological centralities between enzymes retaining tandem-homeologs and the other enzymes.Click here for filePopulus WGD-enzymes and their coding homeologs.Table S8. 226 Click here for fileFigure S2. The expression profiles of four connected enzyme-homeologs in the 59 developmental stages.Click here for file


Drosophila flies was experimentally selected over several generations to survive a chronically hypoxic environment. NMR-based metabolomics, combined with flux-balance simulations of genome-scale metabolic networks, can generate specific hypotheses for global reaction fluxes within the cell. We applied these techniques to compare metabolic activity during acute hypoxia in muscle tissue of adapted versus "naïve" control flies.Cellular hypoxia is a component of many diseases, but mechanisms of global hypoxic adaptation and resistance are not completely understood. Previously, a population of 1H NMR spectroscopy. Principal Component Analysis suggested that the adapted flies are tuned to survive a specific oxygen level. Adapted flies better tolerate acute hypoxic stress, and we explored the mechanisms of this tolerance using a flux-balance model of central metabolism. In the model, adapted flies produced more ATP per glucose and created fewer protons than control flies, had lower pyruvate carboxylase flux, and had greater usage of Complex I over Complex II.Metabolic profiles were gathered for adapted and control flies after exposure to acute hypoxia using We suggest a network-level hypothesis of metabolic regulation in hypoxia-adapted flies, in which lower baseline rates of biosynthesis in adapted flies draws less anaplerotic flux, resulting in lower rates of glycolysis, less acidosis, and more efficient use of substrate during acute hypoxic stress. In addition we suggest new specific hypothesis, which were found to be consistent with existing data. Hypoxia is a component of many diseases and can have devastating effects on the cell. A major goal of medical research is to design therapies to enhance cellular defenses to hypoxic insult, but more basic research on the mechanisms of hypoxic cell death and defense systems is needed as a prerequisite.Metabolically, the primary effect of reduced oxygen levels is a dramatic drop in respiratory activity in the mitochondria. The cell is forced to depend on glycolysis for ATP, though glycolytic ATP production is only a fraction of mitochondrial output, and acidosis occurs as mitochondrial consumption of protons slows . The losSystems biology seeks to build quantitative computer models of biological networks, in order to derive testable hypotheses from large and complex datasets . RecentlDrosophila melanogaster has been a common model organism both for systems biology approaches and for hypoxia research because of the well-known genome, useful tools for genetic manipulation, fecundity and short lifespan of the fruitfly, as well as for its innate tolerance to extreme fluctuations in oxygen levels  and pH must be maintained and energy supply should be conserved in any hypoxia tolerant organism. However, biosynthesis and other metabolic demands require carbon intermediates to be taken out of the TCA cycle. To make up for this, glycolysis is increased and pyruvate carboxylase replenishes the carbon at the start of the cycle. The increase in glycolysis is an uncoupling from the TCA cycle that causes greater use of Complex II, and less efficient ATP production (by the above measures).C. elegans is improved when protein translation is suppressed  for subtracting random variables for concentration C1 and C2) and converted to the same units. A list of 10 "NMR fluxes" was chosen for constraining the flux-balance simulations, based on magnitude of the fluxes and presence of a feasible pathway within the metabolic reconstruction. Virtual "sinks" with unlimited capacity were created for each of these compounds in order to represent metabolite pools, allowing intracellular accumulation and depletion in case substrates and end products did not perfectly balance. The rates of exchange from these "sinks" into/out of the system of reactions were forced to the flux rates calculated from the data. The models with flux constraints are provided [see Additional file Metabolic fluxes in control and adapted flies were modeled using flux-balance analysis within a genome-wide reconstruction, as described previously ,13. MetaFlux-balance analysis was used to simulate system flux distributions during acute (4-hour) hypoxia for each group. The objective function for the system in all simulations was the reaction representing utilization of ATP via hydrolysis.Flux constraints from the NMR data were applied to the model with their respective error distributions. Pseudo-random sets of fluxes were created by sampling from normal distributions with mean and standard errors equal to those of each NMR flux applied to the model. A set of 100 different pseudo-random flux constraints were generated and simulated for each experiment. Simulating each of the 100 constraint conditions generated a statistical distribution for each reaction flux output, from which p-values were calculated. Comparisons of individual fluxes across groups were by one-way ANOVA followed by Tukey's multiple comparison test.The SimPheny software platform  was used for building the model, visualizing fluxes superimposed on the metabolic network, and mapping the network to microarray data. The model was exported to Matlab  for more detailed flux analysis and statistical testing.We used Matlab to analyze the sensitivity of flux distributions to variance in the data. The publicly available COBRA toolbox for constraint-based analysis , running2: molecular oxygen; CO2: carbon dioxide; PYK: pyruvate kinase; ACS: acetyl-CoA synthase; ALAT: alanine transaminase (cytosolic); LDH: lactate dehydrogenase; PC: pyruvate carboxylase; PDH: pyruvate dehydrogenase; PDHK: pyruvate dehydrogenase kinase; MDH: malate dehydrogenase ; GPDH: glycerol-3-phosphate dehydrogenase shuttle; Complex II: succinyl CoA dehydrogenase (electron transport chain); Complex I: NADH dehydrogenase.NMR: nuclear magnetic resonance; PCA: principal component analysis; PC: principal component; TCA: tricarboxylic acid (cycle); ATP: adenosine triphosphate; OJDF carried out all computational and statistical analysis and drafted the manuscript. LC prepared samples, gathered NMR spectra and calculated metabolite concentrations. DZ cultured the fly populations and carried out the hypoxia stimulus experiments. GGH, GP, and ADM conceived of the study, participated in its design and coordination and helped to draft the manuscript. All authors read and approved the final manuscript.Supplementary Figures. A text file including Supplementary Figures is included in pdf format.Click here for fileMetabolomics data. All NMR concentration data are provided in the Excel file "NMR_data.xls"Click here for fileModels. The genome-scale model of Drosophila central metabolism is provided in SBML format in the file "fly_model.xml" and will be submitted to the Biomodels database at .Click here for fileMatlab scripts. M-files for normalization and principal component analysis of metabolite profiles, and for running and visualizing simulations, are provided in the zipped file "m-files.zip". Model files suitable for Matlab import are included. The COBRA Toolbox version 1.3.3 is required. The top-level script for the analysis is named "adapted_analysis.m." These scripts have not been tested for distribution and are provided without support for informational purposes only.Click here for file


Saccharomyces cerevisiae glycolysis as a case study. We show that given the limited solvent capacity constraint, the optimal enzyme activities and the metabolite concentrations necessary to achieve a maximum rate of glycolysis are in agreement with their experimentally measured values. Furthermore, the predicted maximum glycolytic rate determined by the solvent capacity constraint is close to that measured in vivo. These results indicate that the limited solvent capacity is a relevant constraint acting on S. cerevisiae at physiological growth conditions, and that a full kinetic model together with the limited solvent capacity constraint can be used to predict both metabolite concentrations and enzyme activities in vivo.The cell's cytoplasm is crowded by its various molecular components, resulting in a limited solvent capacity for the allocation of new proteins, thus constraining various cellular processes such as metabolism. Here we study the impact of the limited solvent capacity constraint on the metabolic rate, enzyme activities, and metabolite concentrations using a computational model of  Saccharomyces cerevisiae glycolysis as a case study. Our results indicate that metabolite concentrations attain optimal values, minimizing the intracellular space occupied by metabolic enzymes. And, at these optimal concentrations, glycolysis achieves the maximum rate given the intracellular volume fraction occupied by glycolysis enzymes. Taken together with previous studies for Escherichia coli, our results indicate that macromolecular crowding is a general constraint on cell metabolism.The concentration of enzymes and metabolites is continuously adjusted in order to achieve specific metabolic demands. It is highly likely that during evolution global metabolic regulation has evolved such as to achieve a given metabolic demand with an optimal use of intracellular resources. However, the size of enzymes and intermediate metabolites is dramatically different. Enzymes are macromolecules that occupy a relatively large amount of space within a cell's crowded cytoplasm, while metabolites are much smaller. This implies that metabolite concentrations are likely to be adjusted to minimize the overall “enzymatic cost” (in terms of space cost). In this work, we explore this hypothesis using  Understanding an organism's metabolism at a system level and obtaining quantitative predictions for the different metabolic variables requires the identification and modeling of the physicochemical and regulatory constraints that are relevant at physiological growth conditions. Recently, there has been a surge of interest on how macromolecular crowding, i.e., the crowding of the cytoplasm by various molecular components, affects cellular function, including cell metabolism Escherichia coliE. coli cell metabolism, hindering our ability to investigate the impact of the solvent capacity constraint on in vivo metabolite concentrations and enzyme activities.At the local scale it is well known that molecular crowding affects the rate of biochemical reactions, diffusion, protein folding and protein-protein association/dissociation During cellular metabolism the concentration of enzymes and metabolites are continuously adjusted in order to achieve specific metabolic demands. It is highly likely that during evolution global metabolic regulation has evolved such as to achieve a given metabolic demand with an optimal use of intracellular resources. However, the size of enzymes and intermediate metabolites are dramatically different. Enzymes are macromolecules that occupy a relatively large amount of space within a cell's crowded cytoplasm, while metabolites are much smaller. This implies that metabolite concentrations are likely to be adjusted to minimize the overall “enzymatic cost” (in terms of space cost).Saccharomyces cerevisiae, for which a kinetic model is available. We show that the maximum glycolysis rate determined by the limited solvent capacity is close to the values measured in vivo. Furthermore, the measured concentration of intermediate metabolites and enzyme activities of glycolysis are in agreement with the predicted values necessary to achieve this maximum glycolysis rate. Taken together these results indicate that the limited solvent capacity constraint is relevant for S. cerevisiae at physiological conditions. From the modeling point of view, this work demonstrates that a full kinetic model together with the limited solvent capacity constraint can be used to predict not only the metabolite concentrations, but in vivo enzyme activities as well.Here we study the validity of this hypothesis by focusing on the glycolysis pathway of the yeast, iv only a finite number of them fit in a given cell volume V. Indeed, if in is the number of moles of the ith enzyme, thenV0 accounts for the volume of other cell components and the free volume necessary for cellular transport as well. Equation 1 can be also rewritten asiρ = imin/V is the enzyme density (enzyme mass/volume), iμ is the molar mass vspec is the specific volume, and φ = V0/V is the fraction of cell volume occupied by cell components other than the enzymes catalyzing the reactions of the pathway under consideration, including the free volume necessary for diffusion. The specific volume has been assumed to be constant for all enzymes, an approximation that has been shown to be realistic at least for globular proteins iC = in/V (moles/volume) because the specific volume is approximately constant across enzymes, while the molar volume can exhibit significant variations. For example, according to experimental data for several globular proteins The cell's cytoplasm is characterized by a high concentration of macromolecules ith reaction per unit of cell dry weight (mol/time/mass) is given byiA is the specific enzyme activity, iC is the enzyme concentration in molar units, ik is the catalytic constant and M is the cell mass. The coefficient ix is determined by the specific kinetic model: it takes values in the range of 0≤ix≤1, and it is a function of metabolite concentrations. For example, if the ith reaction is described by Michaelis-Menten kinetics with one substrate then ix = iS/(iK+iS), where iS is the substrate concentration and iK is the equilibrium constant. More generally, ix is a function of the concentration of substrates, products and other metabolites regulating the enzyme activity. The fact that the reaction rates are proportional to the enzyme densities (Equation 3) suggests that the limited solvent capacity constraint (Equation 2) has an impact on the reaction rates as well. Indeed, from Equations 2 and 3 we obtainR is the cell metabolic rate (or pathway rate), ir = iR/R is the rate of reaction i relative to the metabolic rate, andρ = M/V is the cell density. We refer to ia as the crowding coefficients i increases with increasing the enzyme's molar mass iμ and decreases with increasing catalytic activity ik. It is also a function of the metabolite concentrations through ix.The solvent capacity constraint (Equations 1 and 2) thus imposes a limit to the amount of catalytic units  that can be allocated in the cell cytoplasm. In the following we show that this in turn leads to a constraint for the maximum metabolic rate. The rate of the To illustrate the impact of the limited solvent capacity constraint, we first analyze a hypothetical example, in which we use the relative reaction rates as input parameters, and the metabolite concentrations are the variables to be optimized. Given the reaction rates and the “optimal” metabolite concentrations, the enzyme activities are determined by Equation 3. Finally, the maximum metabolic rate is computed using Equation 4.1 into M2 (reaction 1) and M2 into M3 (reaction 2), catalyzed by enzymes e1 and e2, respectively  in the steady state, where R is the pathway rate. When reaction 1 is close to equilibrium [M2]≈[M1]K1eq = 3 mM, the first term in the right hand side becomes very large, resulting in a small pathway rate  to their experimentally determined values. By doing so the predicted glycolysis rate is an implicit function of the free metabolite concentration alone, through Equation 4. For example, R as a function of the concentration of fructose-6-phosphate (F6P). R is predicted to achieve a maximum around a F6P concentration of 0.4 mM, close to its experimentally determined value of 0.5 mM R and, more importantly, that this concentration is very close to the experimentally determined metabolite concentrations. In all cases the measured metabolite concentrations are within the range of 50% or more of the maximum glycolysis rate.In analogy with the three metabolites case study , first wS. cerevisiae glycolysis are close to the predicted optimal values maximizing the glycolysis rate given the limited solvent capacity constraint.To further test the optimal metabolite concentration hypothesis, we perform a global optimization and simultaneously compute the optimal concentrations of the glycolysis intermediate metabolites. In this case we fix the concentrations of external glucose and co-factors and all relative reaction rates to their experimentally determined values. By doing so the predicted glycolysis rate is an implicit function of the glycolysis intermediate metabolite concentrations, through Equation 4. The optimal intermediate metabolite concentrations are those maximizing Equation 4. ir are obtained from experimental data, while ix are obtained after substituting the predicted optimal metabolite concentrations on the reaction's kinetic models. pfk), for which the measured enzyme activities are significantly overestimated. Of note, for pyruvate kinase (pk) the predictions are significantly affected by the model parameters, as indicated by the wide error bars.Using the optimal intermediate metabolite concentrations we can make predictions for the enzyme activities as well. Indeed, from the first equality in Equation 3 it follows thatR = (1−ϕ)/ΣNi = 1 (iria)H, parametrized by the exponent H. Although this objective is not inspired by a biological intuition, it allows us to explore other possibilities beyond the original case H = 1. H = 0.1 (red symbols) and H = 10 (blue symbols), representing a milder and a stronger dependency with the crowding coefficients ia, respectively. For H = 0.1, 1.0 and 10 the predicted metabolite concentrations are in good agreement with the experimental values. Furthermore, when we allow sub-optimal metabolite concentrations resulting in a glycolysis rate below it s maximum our predictions are also in the range of the experimental values .This is not, however, the case for the enzyme activities. For R = (1−ϕ)×12.5 mmol/min/g dry weight. Taking into account that about 30% ϕ∼0.03. Therefore, given that glycolysis enzymes occupy only 3% of the cell volume, we obtain R∼0.38 mmol/min/g dry weight. This prediction is in very good agreement with the experimentally determined glycolysis rate of S. cerevisiae, ranging between 0.1 to 0.4 mmol/min/g dry weight Finally, we use Equation 4 to compute the maximum glycolysis rate as determined by the limited solvent capacity constraint. The global optimization predicts the glycolysis rate E. coli we have reported results indicating that the limited solvent capacity is an important constraint on cell metabolism, especially under nutrient-rich growth conditions E. coli cells' growth rate The successful modeling of cell metabolism requires the understanding of the physicochemical constraints that are relevant at physiological growth conditions. In our previous work focusing on S. cerevisiae), and (ii) a full kinetic model of glycolysis. Using the full kinetic model of S. cerevisiae glycolysis, we have demonstrated that the predicted optimal intermediate metabolite concentrations and enzyme activites are in good agreement with the corresponding experimental values. Discrepancies were only observed in association with two different steps in the glycolysis pathway, namely the reaction catalyzed by pfk and the reactions between BPG and PEP. The experimental values measurements from cell extracts Here we have extended the study of the impact of the limited solvent capacity by (i) considering a different organism  kinetic model from an irreversible to a reversible model.We use the Saccharomyces carlsbergensisEidolon helvumE. coli, ρ = 0.34 g/ml The catalytic constants were obtained from experimental estimates for ir) were taken as input parameters, using the values reported in The optimal metabolite concentrations are obtained maximizing Equation 4 with respect to the free metabolite concentrations. In the case of To analyze the sensitivity of our predictions to the model parameters we have generated random sets of kinetic parameters, assuming a 10% variation of the fixed metabolite concentrations and all kinetic constants except for the catalytic activities. For the latter we assumed a larger variation of 50%, because they were estimated from a different organism. For each set of parameters we make predictions for the metabolite concentrations and enzyme activities. Protocol S1Details on the rate equation model used, the utilized model parameters, and the glycolysis rate and optimal metabolite concentrations.(0.10 MB PDF)Click here for additional data file.