C. reinhardtii, was chosen and the metabolic network reconstructed. Intracellular fluxes were then calculated using flux balance analysis (FBA).Photosynthetic organisms convert atmospheric carbon dioxide into numerous metabolites along the pathways to make new biomass. Aquatic photosynthetic organisms, which fix almost half of global inorganic carbon, have great potential: as a carbon dioxide fixation method, for the economical production of chemicals, or as a source for lipids and starch which can then be converted to biofuels. To harness this potential through metabolic engineering and to maximize production, a more thorough understanding of photosynthetic metabolism must first be achieved. A model algal species, C. reinhardtii, was reconstructed using genomic and biochemical information. The reconstructed network accounts for the intracellular localization of enzymes to three compartments and includes 484 metabolic reactions and 458 intracellular metabolites. Based on BLAST searches, one newly annotated enzyme  was added to the Chlamydomonas reinhardtii database. FBA was used to predict metabolic fluxes under three growth conditions, autotrophic, heterotrophic and mixotrophic growth. Biomass yields ranged from 28.9 g per mole C for autotrophic growth to 15 g per mole C for heterotrophic growth.The metabolic network of primary metabolism for a green alga, C. reinhardtii is the first such model for algae and the first model to include three metabolically active compartments. In addition to providing estimates of intracellular fluxes, metabolic reconstruction and modelling efforts also provide a comprehensive method for annotation of genome databases. As a result of our reconstruction, one new enzyme was annotated in the database and several others were found to be missing; implying new pathways or non-conserved enzymes. The use of FBA to estimate intracellular fluxes also provides flux values that can be used as a starting point for rational engineering of C. reinhardtii. From these initial estimates, it is clear that aerobic heterotrophic growth on acetate has a low yield on carbon, while mixotrophically and autotrophically grown cells are significantly more carbon efficient.The flux balance analysis model of central and intermediary metabolism in  However, to harness this potential through metabolic engineering, a deeper understanding of photosynthetic metabolism is required.Algae and other marine organisms are responsible for the fixation of almost half of the inorganic carbon from the atmosphere . With riThere are several widely accepted methods for modelling metabolism, ranging from highly detailed kinetic models to less complex stoichiometric models. One of the more increasingly used methods is flux balance analysis (FBA), which has the ability to predict fluxes using linear programming with the knowledge of reaction stoichiometry, biomass composition and additional constraints, such as limits on uptake/excretion rates and thermodynamic constraints. FBA has been used for a number of model organisms -7 to preSynechocystis [Arthrospira platensis, was reconstructed and fluxes computed [Chlamydomonas reinhardtii was chosen as a representative algal species for this study. C. reinhardtii has been used as a model organism to study numerous cellular functions from photosynthesis research to flagellar function and assembly [C. reinhardtii was the first algal species to have its genome sequenced [C. reinhardtii is that its photosynthetic capability is dispensable; as it can grow heterotrophically on acetate. However, as an acetate flagellate, it can only grow on acetate and similar 2-carbon molecules in the dark. In the presence of light, C. reinhardtii can metabolize pentoses and hexoses (mixotrophic growth) as well as acetate [FBA has been previously used to model photosynthetic metabolism in a model cyanobacteria, hocystis . In an ecomputed . The goaassembly  and mostassembly . It has equenced  and this acetate  and suppC. reinhardtii. The metabolic network was reconstructed using the genomic database [The major contribution of this work is the reconstruction of a compartmental metabolic network for primary metabolism in the green alga, database , biochemdatabase -17, metadatabase ,19, and database ,21. FBA C. reinhardtii consists of 458 metabolites and 484 metabolic reactions. Almost half of the metabolites included in the network are present in the chloroplast  reactions, oxidative phosphorylation and a simplified lipid biosynthesis reaction.In the course of reconstructing the model, several assumptions about the presence or absence of reactions had to be made. Although many reactions were not linked to the EC number in the database, the coinciding gene was determined by performing a protein BLAST  search. The reactions in the network were localized into three compartments; cytosol, mitochondria and chloroplast  were calculated using the reconstructed network and FBA. During autotrophic growth, the cell fixes carbon dioxide by converting light into cellular energy . In this study we defined heterotrophic growth as aerobic growth on acetate in the dark; the cell using acetate for both carbon and energy sources. Another metabolic mode, mixotrophic growth, is the link between the two extremes. In our model, mixotrophic growth has three inputs: light, acetate and carbon dioxide.2. Interestingly, the fluxes for both optimization steps were identical (as reported previously by [Autotrophic growth was simulated using a two-step optimization with a basis of 100 moles COously by ), which ously by .C. reinhardtii is only capable of growing heterotrophically on acetate and other similar 2-carbon molecules. Most of the carbon flux for heterotrophic growth is directed through the TCA cycle, as would be expected H for biomass synthesis during low light conditions, but when light intensity increases enough to send flux through Rubisco, the cell is capable of producing enough NADPH through the non-cyclic ETC to supply metabolism with NADH via transhydrogenases. In the heterotrophic case, C. reinhardtii has an incomplete TCA cycle. This could also be a result of the production of NADPH within the chloroplast and the subsequent indirect transport of reducing equivalents throughout the cell. At a light flux of approximately 0.8 μE/m2/s, flux is directed through the Calvin cycle and the cell enters the second growth regime. In this growth regime, the glyoxylate shunt flux steadily decreases while the Rubisco flux increases rapidly with increasing light. As the light increases, the flux distribution becomes more similar to the autotrophic case. The increase in biomass flux with each increase in light is slightly less than that for the first growth regime. This is due to the higher energetic demand of carbon fixation..Quantitative results for all three growth regimes as well as reaction lists can be found at C. reinhardtii, this is 100% of the carbon taken into the cell. This is of course due to the production of energy from light during photosynthesis, so no net carbon is lost during respiration. In contrast, the heterotrophic biomass yield is 15 g per mole carbon, which implies that almost half of the carbon taken in by the cell is used for energy production instead of biomass formation. The fraction of carbon used for energy production is quite high compared to another photosynthetic organism, Synechocystis [Synechocystis utilizes glucose, which has significantly higher energy content per mole than acetate; glucose has a standard heat of combustion of -2.8 kJ/mole compared to -0.8 kJ/mole for acetate. During mixotrophic growth, the biomass yield of C. reinhardtii increases from 13.5 to 22.9 g per mole carbon. With increasing light flux, the cell can direct more carbon towards biomass and less towards energy production, however, the amount of carbon fixed per photon is constant. Therefore, the maximum yield is lower than the autotrophic yield because it is limited by the energy in the cell. During mixotrophic growth, the cell must utilize acetate and it has to divert some carbon away from biomass and towards energy production.The autotrophic biomass yield is 28.9 g biomass for every mole of carbon taken up Table , based oSynechocystis has a much higher flux through the non-cyclic ETC than C. reinhardtii which is due mainly to the compartmentation in the model; due to a lack of a direct NAD(P)H transporter in C. reinhardtii, the flux through the non-cyclic ETC is constrained to match the need for NADPH in the chloroplast. Any additional NAD(P)H is indirectly transported via shuttles, but these shuttles are also constrained by mass balances and steady state assumptions. In contrast, since Synechocystis is prokaryotic and unicellular, it can use the non-cyclic ETC to produce all the NADPH needed in the cell. Therefore, to make up for the energetic difference of having a lower flux through the non-cyclic ETC, C. reinhardtii must have a larger flux through the cyclic ETC. Cellular compartmentation also comes into play in the total moles of oxygen produced. The only reaction the cell can use to produce oxygen in both organisms is the non-cyclic ETC, which is why the production of oxygen from C. reinhardtii is lower than that of Synechocystis. Comparison of the biomass yields per 100 moles carbon dioxide from both organisms shows yet another difference; Synechocystis has a lower yield than C. reinhardtii, 2.43 kg and 2.89 kg respectively. Part of this difference can be explained by the use of a lumped biomass equation for Synechocystis which specifies the loss of approximately one mole of carbon dioxide per kilogram biomass formed in order to have a balanced reaction. In contrast, the C. reinhardtii model is much more detailed and the carbon dioxide lost during biosynthesis can be fixed because it is not required to be present on the right hand side of the biomass formation equation to balance the reaction. This results in 2.47 moles of carbon dioxide loss for the production of 2.43 kilograms of Synechocystis, which translates to a loss of 0.11 kg of biomass. Another element that contributes to the difference in yield is the carbon content of the 2 organisms; Synechocystis is reported to be 51% carbon [C. reinhardtii was measured to be 48% carbon, which explains at least 0.15 kilograms difference in biomass yield. Due to the nature of the optimization technique employed, which allows the cell to use unlimited energy in the first step, the difference in yields can be attributed to these two factors and it is not due to a lack of energy.Flux estimates for autotrophic growth were compared to estimated fluxes for the cyanobacteria, Synechocystis sp PCC 6803 . One majC. reinhardtii from the genomic database, pathway databases and literature. The network includes all the major pathways in central metabolism  as well as amino acid, nucleotide, chlorophyll, lipid and starch synthesis. Metabolic network reconstruction is a valuable tool to identify gaps in existing knowledge [A stoichiometric model of primary metabolism was constructed for nowledge ,5,29-31.Intracellular fluxes were estimated using FBA for three growth conditions, autotrophic, heterotrophic, and mixotrophic. Yield on carbon and growth rate are factors that need to be considered in choosing the appropriate growth conditions for maximizing the production of desired metabolites. For example, a lower yield for heterotrophic growth is off-set by a faster growth rate, which may be ideal for the production of growth associated products. Along with this, the model provides a more complete picture of photosynthesis in a compartmented organism and can serve as a starting point for models of other photosynthetic algae and more complex models of higher photosynthetic organisms.C. reinhardtii presented here can serve as a starting point for metabolic engineering of lipid or starch production in algae. Future work will use elementary mode analysis [With renewed interest in biofuel production from algae  the recoanalysis  to deterC. reinhardtii was constructed using the genomic database [Chlamydomonas reinhardtii [16 and C18 in the C1 and C2 position on the head group [A stoichiometric model of the primary metabolism of database , pathwaydatabase ,34, biocdatabase -17,35 andatabase . Fatty anhardtii . The synad group . Althougad group  and is sA. thaliana, E. coli, and S. cerevisiae). The amino acid sequence of these known genes were then blasted against the C. reinhardtii database; in most cases, this resulted in a hit which had already been annotated but not linked to the KEGG portion of the genome database. There were a few genes that resulted in hits to proteins that were either listed as having a different function or were not annotated at all (see results). A few enzymes resulted in no hits in the database, but were assumed to be present in order to have a complete network.Despite large efforts to fully annotate genome databases, not all enzymatic functions are listed and therefore gaps exist in the pathways. Gaps in the network were first addressed by searching pathway databases for the missing enzymes and corresponding genes in other organisms whose genome is sequenced (Synechocystis by Shastri and Morgan (2005) as two non-interacting reactions as shown below:Accurate reconstruction of a metabolic network requires the inclusion of reactions for cellular energy production. Two main sources of energy in algae are photophosphorylation and oxidative phosphorylation. Photophosphorylation is the process by which light is converted into energy (ATP) and reducing power (NADPH) via two electron transport chains (ETC). The cyclic ETC is made up of several membrane-bound and membrane associated proteins that are coupled with the light harvesting complex, photosystem I (PSI) which pumps protons across the chloroplast membrane. The non-cyclic ETC uses both light harvesting complexes (photosystem I and photosystem II) to produce NADPH and pump protons across the plastidic membrane. This process has been modelled previously in +/ATP ratio for this reaction is 14/3 or 4.67 [Both the cyclic and non-cyclic ETCs are coupled to the chloroplast ATP synthase complex to synthesize ATP from ADP. This enzyme complex couples the translocation of protons with the production of ATP. Recent studies have shown that the H or 4.67 . The ATP+/ATP ratio for the mitochondria ATP synthase has not yet been agreed upon, it is assumed to be between 3 and 4 [+/ATP ratio of the reaction was assumed to be the same as that used in the genome-scale Saccharomyces cerevisiae model [Oxidative phosphorylation occurs via the mitochondrial ETC, which is made up of 4 complexes  that control the flow of electrons from NADH to reduce oxygen to water. The ETC is also coupled to an ATP synthase which produces ATP from ADP by pumping protons across the mitochondria membrane. Although the exact H 3 and 4 -41. For The reconstructed metabolic network provided the information necessary to develop a stoichiometric model . A stoicij is the stoichiometric coefficient of the ith metabolite in the jth reaction, vj is the flux of the jth reaction, Mi is the set of intracellular metabolites, Mr is the set of reactants other than substrate, and Mp is the set of products excreted.where sA mixed integer linear program was formulated in the GAMS environment  and the optimum solution was found using the ILOG CPLEX 8.100 solver .Unlike heterotrophic organisms that utilize the same substrate as the source of both carbon and energy, photoautotrophic organisms require two substrates, one for energy (light) and one for carbon (carbon dioxide). Due to the input of two substrates, FBA simulations can be run in either light or carbon limitation conditions. To simulate carbon limitation, the model is allowed unlimited light, which calculates an optimal biomass flux. No fermentation products were detected in the media during growth (see maximum uptake rates discussion) therefore, in the absence of carbon overflow products, the yield of biomass is fixed because the only outlet for carbon is biomass. For photoautotrophic metabolism, a more meaningful result is to find the flux distribution that maximizes biomass while minimizing energy usage. Therefore the optimization is done in two steps. The first step is to maximize biomass with no constraint on light and the second is to fix the biomass and minimize light. Flux distributions for the heterotrophic case are the result of a one-step optimization to maximize biomass.Chlamydomonas reinhardtii strain CC-400 cw15 mt+ was acquired from the Chlamydomonas Genetics Center. Cells were cultivated at 25°C in 250 ml flasks with a working volume of 50 ml and an agitation rate of 200 RPM. Heterotrophic and mixotrophic cells were grown in TAP media [2/s. All cells were grown in the presence of atmospheric carbon dioxide levels. Growth was monitored spectrophotometrically by measuring absorbance at 750 nm.AP media  and auto2/s [In order to add constraints on nutrient and light uptake to the model, additional experimental measurements were taken. Maximum growth rates were measured for all three growth conditions from three separate experiments. The results are shown in Table 2/s . For het2/s), the surface area per kilogram biomass must be calculated. Based on experimental measurements, the dry weight of a typical C. reinhardtii was determined to be 0.2 pg. The length and width of cell were assumed to be 10 μm and 3 μm respectively [2kg-1.In order to convert the calculated total photons from the model to a flux .Click here for file


Tumor therapy mainly attacks the metabolism to interfere the tumor's anabolism and signaling of proliferative second messengers. However, the metabolic demands of different cancers are very heterogeneous and depend on their origin of tissue, age, gender and other clinical parameters. We investigated tumor specific regulation in the metabolism of breast cancer.For this, we mapped gene expression data from microarrays onto the corresponding enzymes and their metabolic reaction network. We used Haar Wavelet transforms on optimally arranged grid representations of metabolic pathways as a pattern recognition method to detect orchestrated regulation of neighboring enzymes in the network. Significant combined expression patterns were used to select metabolic pathways showing shifted regulation of the aggressive tumors.Besides up-regulation for energy production and nucleotide anabolism, we found an interesting cellular switch in the interplay of biosynthesis of steroids and bile acids. The biosynthesis of steroids was up-regulated for estrogen synthesis which is needed for proliferative signaling in breast cancer. In turn, the decomposition of steroid precursors was blocked by down-regulation of the bile acid pathway.We applied an intelligent pattern recognition method for analyzing the regulation of metabolism and elucidated substantial regulation of human breast cancer at the interplay of cholesterol biosynthesis and bile acid metabolism pointing to specific breast cancer treatment. Breast cancer is a prevalent disease and a leading cause of cancer death in women . WorldwiChemotherapy and hormonal therapy reduces the risk of distant metastases by approximately one third. However, 70-80% of the patients would have survived without it (five years of follow-up) -4. A morBesides this, over the past decade there have been exciting developments in analyzing large scale gene expression profiles. This improved the understanding of the tumors' composition and behavior to develop new targets for therapy . Many st2 test. In a different approach, a gene-specific statistics, known as the "local" statistics, measures the strength of association between the gene expression and the phenotype for each gene. A global statistics for a gene set is then constructed as a function of local statistics for each gene in it. The significance is assessed by permutation tests [To detect the enrichment of gene sets, commonly, a list of significantly differentially expressed genes is identified and statistical tests applied, such as Fisher's exact test and χon tests . A globaon tests . In anoton tests . In geneTo overcome these and other gene-associated problems, transcriptional data was analyzed using topology information of cellular networks. Topological information derived from the metabolic network was connected by calculating Z-scores of highly correlated sub-networks . Chuang In our study, gene expression profiles of breast tumors having an "unfavorable" prognosis were compared to breast tumors with a "favorable" prognosis. We wanted to track how the aggressive (unfavorable) tumors have specifically regulated their metabolism to optimize their oncogenetic fitness, and to elucidate ways to severely perturb this process. For this, we used an approach that detects orchestrated regulation of neighboring enzymes in the metabolic network. We mapped gene expression data onto optimally arranged grid representations of pathways of the metabolic network and applied Haar wavelet transforms onto defined pathways of the network to combine gene expression values from neighboring enzymes. These combined features were tested using a non-parametric test (Wilcoxon) if they could separate samples from different treatments. Metabolic pathways were selected that had features with the most discriminative gene expression patterns. We detected a substantially higher number of significant gene expression patterns in comparison to commonly used enrichment tests. We revealed 19 significant metabolic pathways including increased purine and pyrimidine biosynthesis which were needed for increased mitosis cycles. Furthermore, we found pathways for increased energy metabolism . Interestingly, we observed the regulation of a possible a cellular switch in the pathway for bile acid biosynthesis redirecting the metabolic flux to the synthesis of steroids while preventing degradation into bile acids.In this study, 250 patients were examined, 196 having a "favorable" and 54 patients an "unfavorable" prognosis. 1826 reactions could be extracted from KEGG  for 1771Most up-regulated reactions were identified in the pyrimidine (P = 2.25E - 04) and purine P = 1.21E - 03) metabolism. These pathways were up-regulated to enable enforced nucleotide biosynthesis for increased cell cycle activity of the aggressive tumors. Nearly all enzymes involved in the biosynthetic pathway for nucleotides were up-regulated, such as enzymes converting substrates to dNTPs and polyribonucleotide nucleotidyltransferases (EC 2.7.7.7), incorporating dNTPs into DNA. Enzymes reversing pyrimidine and purine anabolism, such as enzymes degrading dNTPs, were down-regulated . Reactions involved in RNA synthesis were partially up-regulated to increase protein biosynthesis (EC 2.7.7.8). Furthermore, reactions which were responsible for synthesizing adenosine were up-regulated (EC 2.4.2.1). Adenosine was shown to be angiogenic, cyto-protective and anti-inflammatory in several tissues and contributed to more aggressive behavior and metastasis of cancer cells [E - 03 meWe detected significant differential expression patterns in glycolysis (P = 3.85E - 03), pyruvate (P = 1.20E - 02) and fructose/mannose (P = 1.55E - 02) metabolism. They were mostly up-regulated to generate sufficient energy and metabolites for fast-growing cancer cells. Genes of the glycolysis pathway have been found to be over-expressed in a set of 24 cancers, while other pathways showed less consistent up-regulation so far . GlycolyHowever, the extent of up-regulated genes in glycolysis varies for different cancer types. In our study, all except one differentially regulated reactions were up-regulated, including enzymes such as glyceraldehyde-3-phosphate dehydrogenase (EC 1.2.1.12), phosphor glycerate mutase (EC 5.4.2.1), phosphoglycerate kinase (EC 2.7.2.3), triosephosphate isomerase (EC 5.3.1.1) and fructose-bisphosphate aldolase (EC 4.1.2.13). These enzymes were also described as up-regulated by Altenberg and co-workers . InhibitInhibition of glycolysis was effective even in killing cancer cells with a multidrug resistance (MDR) phenotype. It is known that cells expressing MDR proteins require ATP as their energy source to export drugs out of the cell. Thus, to overcome this drug resistance, depletion of cellular ATP causes the excretion to fail and consequently, cancer cells become more sensitive to anti-cancer therapy .We found a smaller pattern of up-regulated reactions in the pyruvate metabolism. Significantly up-regulated were: pyruvate kinase (EC 2.7.1.40) which is responsible for ATP production in glycolysis, and the conversion of pyruvate to malate via (S)-Malate:NADP+ oxidoreductase . Aldehyde dehydrogenase (EC 1.2.1.3) was down-regulated to prevent degradation of fatty acids. Oxaloacetate was reported to directly induce cell proliferation by increasing DNA synthesis . SurprisThe steroid pathway was mainly up-regulated in breast cancer of unfavorable outcome. 8 out of 10 reactions were significantly up-regulated . Cholesterol is a precursor for the biosynthesis of steroid hormones. It was shown that sex steroid hormones such as estrogen increase the proliferation of breast cancer cells by acting on estrogen receptors . TherefoBesides this, there have been intensive cancer investigations on bile acids as they have very heterogeneous effects on tumor cells and carcinogenesis. They are known enhancers for invasiveness of colon cancers ,32. In tBile acids are normally predominantly produced by hepatocytes which may explain the elevated levels of bile acids in the blood when elevated breast cancer estrogen is decomposed into bile acids in the liver. In conclusion, this regulation may reflect a cellular switch which redirects the metabolic flux from degradation of cholesterol (via bile acids) into the conversion of steroid hormones, suggesting drug targets in the biosynthesis of steroids, such as mevalonate (diphospho) decarboxylase (EC 4.1.1.33) and mevalonate kinase (EC 2.7.1.36).http://www.ebi.ac.uk/microarray-as/ae/) and normalized as described in Methods. We divided the dataset into 250 tumors showing a favorable prognosis and 61 tumors with an unfavorable prognosis following our criteria as described for the other dataset (in Methods). 103 tumors were discarded as they did not fit in any of the prognostic groups. The significance level was again set to P = 0.05. Our analysis revealed 12 pathways with significantly differentially regulated patterns  and steroid hormones (biosynthesis of steroids). An interesting view in breast cancer metabolism was observed in the interplay of biosynthesis of steroids and bile acids, the latter of which was down-regulated possibly to convert cholesterol into proliferative acting steroid hormones. Such a cellular switch would be interesting to compare to other tumors and tissues, also in order to define a tumor specific therapy. Performing Fisher's exact tests as a standard enrichment analysis revealed the lysine biosynthesis pathway to be significantly enriched with differentially expressed genes. The GSEA method yielded pyrimidine biosynthesis. In addition to this pathway, our method yielded eighteen further significant regulation patterns. However, not all pathways detected by such enrichment tests and also our pattern analysis may be relevant for the pathogenesis of the analyzed disease. Some pathways in our results, such as valine, leucine and isoleucine degradation, could not be associated with oncogenesis and may need further examination.Complex regulated pathways which were relevant to breast tumors with unfavorable prognosis were detected and described in a straightforward manner. The global analysis of network patterns offered a good insight into the regulation of metabolism in breast tumors and may support revealing new potential targets for drug design, specifically in the interplay of the biosynthesis of bile acids and steroids.We wanted to identify pathways and regions of pathways that showed patterns of differentially regulated reactions. To find such patterns we applied wavelet transforms on the mapped gene expression data. For the application of wavelet transforms and the subsequent feature calculations we needed to arrange the metabolic pathways onto a 2-dimensional grid  and overall survival were available for all patients. Most of the patients had breast cancer of stages one and two. 165 had received local therapy alone, 20 had received tamoxifen only, 20 had received tamoxifen plus chemotherapy, and 90 had received chemotherapy only. 151 patients were diagnosed as lymph-node-negative and 144 as lymph-node-positive. The tumors were primary invasive breast carcinoma that were less than 5 cm in diameter at pathological examination [Normalized gene expression data was taken from a published study  of breasth, 2009). Two reactions were neighbors if a metabolite existed that was the product of one and the substrate of the other. We defined reactions as the nodes and metabolites as the edges between them. Pathways without any connected reaction were discarded. This resulted in 99 pathways with 1826 different reactions. Each pathway was represented by its adjacency-matrix. An entry at row a and column b was set to one if there existed a metabolite that was produced by reaction a and consumed by reaction b or vice versa. The sizes of the symmetric adjacency-matrices were between 2 × 2 and 92 × 92 reactions.Pathways were defined according to curated pathway maps of the KEGG database   and v =  the distance was given by uv d= |i1 - i2| + |j1 - j2|. This resulted in an NP-hard combinatorial optimization problem. We stated this problem as an integral linear program (IP)  stating whether or not node v has to be placed on grid point . For each pair of nodes  we calculated their distance uvd. For a given lattice grid g, the undirected network graph G =  with node set V, edge set E and adjacency matrix M, the most basic IP was given by finding an optimum forTo apply our feature extraction method we required a 2-dimensional grid arrangement of the metabolic network. We calculated an embedding of the metabolic networks for every KEGG pathway into a 2-dimensional, regular square lattice grid. To preserve neighborhood characteristics of the reactions, we were looking for embeddings in which adjacent nodes of the network were placed onto the grid as close to each other as possible. We wanted to determine an optimal neighborhood in which the total edge length of the graph was minimized according to some metric on the lattice. The network topology was preserved as good as possible. For this purpose the minimization of total edge length is more suitable than a minimization of the longest edge which is widely applied in very large scale integration (VLSI) designs as the latter one allows a variety of optimal solutions in which adjacent nodes are placed unnecessarily far from each other. As a measure of distance in the lattice, we used the natural metric induced by the underlying lattice graph, the so-called Manhattan distance. That is, for any two grid points IP)  ∈ V × V, a <b, wherefor all (a and b is given by |A| + |B| where A and B are computed by Eq. (6) and Eq. (7) as a - ib A = iand a - jbB = j. All variables were enforced to values 0 or 1 by constraint Eq. (8). The problem was solved by CPLEX 8.1  for 99 lattice grids (representing 99 KEGG-maps) with an average optimality of 96% for embeddings on square grids of side length G' ⊂ G with a least objective function contribution of lb(G'), the following inequality was added or dynamically separated byConstraints Eq. (2) and Eq. (3) guaranteed that all nodes (reactions of the pathway) were placed exactly once and that each grid point could be used at most once, thus avoiding multiple placements and stacking of reactions on a single grid point. Constraints Eq. (4) and Eq. (5) ensured that the distance of node lb(G') for the different sub-graph motifs needed to be determined only once as they are independent of G. Furthermore, the motifs were defined in a pre-processing step and could therefore be separated quickly during the optimization process. We considered the sub-graph motifs of star graphs, cliques consisting of up to 10 vertices and odd cycles (2k + 1-cycles) for k = 1,2. Moreover, a certain class of trees with maximum vertex degree Δ(T) ≤ 4 decreased computation time and enhanced separation ability. Furthermore, calculation time was reduced by symmetry breaking constraints eliminating all but a few representative embeddings from each equivalence class of symmetrical embeddings. For this, grid symmetries due to translation, rotation and reflection of the embeddings were considered as well as vertex subsets which inner permutations didn't change the value of the objective function. After solving the optimization problem the values of the variables vij xallowed to construct the embedding of the metabolic pathway on a 2-dimensional grid placing reaction v on the grid point with coordinates . On the grid representations of the pathways we then applied our feature generation method.The right-hand sides Neighboring enzymes on the 2-dimensional grid representation were grouped by combining their gene expression values with wavelet transforms. These transforms yielded combined expression values ("features") of low pass filters to detect similar expression changes and high pass filters to detect contrasting regulation patterns. The wavelet calculation is described in the following. Each cluster-matrix was divided into 2 × 2 pixeled disjoint sub-sections (e.g. a cluster matrix of size 8 × 8 was divided into 16 sub-sections). Clusters with non-fitting sizes  were extended with rows and columns of zeros to yield matrices that could be divided into 2 × 2 pixels sub-sections. For each sub-section, all combinations of row-wise and column-wise mean and differences, respectively, were calculated. This yielded 4 combined values for each 2 × 2 pixels sub-section: 1st: mean of the mean of the upper and mean of the lower row, 2nd: difference of the mean of the upper and the mean of the lower row, 3rd: mean of the difference of the upper and the difference of the lower row, and, 4th: difference of the difference of the upper and the difference of the lower row. All four combined values for each 2 × 2 pixels sub-section were stored and applied as features for the classifier. This was done for all sub-sections of the matrix. All 1st combined values (mean of means) were taken for a new matrix and were again grouped into 2 × 2 fractions that were combined in the same manner, yielding again 4 new features for every fraction. This procedure was repeated until no further grouping was possible. The discriminative behavior of all non-trivial features was tested using Wilcoxon rank tests. Pathways were ranked according to their best discriminating features. Features were regarded as significant if they had p-values ≤ 0.05 after correction for multiple testing using the Bonferroni method ,41. OnlyThe authors declare that they have no competing interests.GS and RK conceptualized and designed the method. GS and EMS analyzed the data. SW, MO and GR provided solutions for the combinatorial optimization problem. GS, EMS and RK wrote the manuscript. RE and RK revised it critically. All authors read and approved the final manuscript.The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1755-8794/3/39/prepubAdditional results and performance assessment. Results for the additional gene expression data set and comparison of our approach with standard enrichment tests using simulated data.Click here for file


Aspergillus nidulans is an important model organism for studies on fundamental eukaryotic cell biology and on industrial processes due to its close relation to A. niger and A. oryzae. Here we identified the gene coding for a novel metabolic pathway in A. nidulans, namely the phosphoketolase pathway, and investigated the role of an increased phosphoketolase activity.phk) improved the specific growth rate on xylose, glycerol and ethanol. Transcriptome analysis showed that a total of 1,222 genes were significantly affected by over-expression of the phk, while more than half of the affected genes were carbon source specific. During growth on glucose medium, the transcriptome analysis showed that the response to phk over-expression is targeted to neutralize the effect of the over-expression by regulating the acetate metabolism and initiate a growth dampening response.Over-expression of the phosphoketolase gene (13C-labelled glucose, showed that over-expression of phosphoketolase added flexibility to the central metabolism. Our findings further suggests that A. nidulans is not optimized for growth on xylose, glycerol or ethanol as the sole carbon sources.Metabolic flux analysis using  Filamentous fungi are prominent users of the sugar xylose, but currently little work has been devoted to study the metabolism of this sugar. This is in sharp contrast to the large and continued commercial interest for xylose utilization in bioethanol production and as cheap raw material in industrial fermentations.It is known that xylose enters the pentose phosphate (PP) pathway, but it is not clear how it interacts with the remaining part of the metabolism. Phosphoketolases  are a class of key enzymes of the phosphoketolase pathway of heterofermentative and facultatively homofermentative lactic acid bacteria, as well as the D-fructose 6-phosphate shunt of bifidobacteria, and xylose fermenting yeast Aspergillus nidulans, which could be induced under certain cultivation conditions. Induction of PHK in Aspergilli increases the carbon flux towards the precursors acetyl-CoA or acetate, and consequently there is a potential to improve the yields and productivities of a long series of industrially important secondary metabolites derived from acetyl-CoA. For a comprehensive evaluation of genes that are transcriptionally modulated during growth in the presence of an active PHK pathway, we constructed a strain that constitutively expressed the gene putatively encoding PHK  and performed a large-scale analysis of gene expression in A. nidulans by using DNA microarrays. Despite the wide use of DNA microarrays, only a few studies have been reported on transcriptome profiling in Aspergilli, e.g. A. oryzaeA. flavusA. nidulansRecently, our group phk on transcription, we grew the cells on a broad range of carbon sources  in well controlled bioreactors. To further understand the effects on glucose, we performed labelling experiments with [1-13C] glucose to quantify the metabolic fluxes in the central carbon metabolism. Quantification of metabolic fluxes is one of the most direct measures on operation of metabolic networks, and it is especially valuable in connection with studies of metabolite production where the aim is to direct carbon from the substrate into the metabolic product, e.g. secondary metabolites In order to accurately determine the effects of over-expressing A. nidulans mutant, which constitutively over-expresses phk (AR1phkGP74), was constructed. The vector that contained the corresponding gene harboured the strong constitutive glycolytic promoter from glyceraldehyde-3-phosphate dehydrogenase (gpdA) of A. nidulans. Northern blot analysis clearly indicated a strong over-expression of phk in the transformant compared to the reference strain (data not shown). To further verify that the over-expressed gene actually is coding for PHK, the wild type (A4) and the mutant (AR1phkGP74) strains were cultivated on glucose in the presence of 1 mM of iodo acetate, a specific and strong inhibitor of glyceraldehyde-3-phosphate dehydrogenase −1) it had only a minor effect on the specific growth rate of the AR1phkGP74 mutant (specific growth rate of 0.19 h−1). However, growth of the AR1phkGP74 mutant ceased after consumption of half the carbon source, probably due to accumulation of glyceraldehyde-3 phosphate or drain of intracellular free phosphate.An A. nidulans wild type (A4) and the A. nidulans AR1phkGP74 strains on various carbon sources . Substrate and product concentrations in the medium were determined for all cultivations as well as the maximum specific growth rate and the biomass yield on carbon source during the fully aerobic growth phase (phkGP74 strain had similar maximum specific growth rates and biomass yields on glucose (Ysx). In contrast, over-expression of phk significantly increased the specific growth rate and Ysx to a lesser extent when the cells were cultivated on xylose and glycerol. In the cultivations on ethanol, over-expression of phk surprisingly led to a significant increase in both the specific growth rate and Ysx. These results show that over-expression of phk significantly improves growth performance on all substrates except from glucose. Growth performance was not expected to be improved on the C-2 compound ethanol since acetyl-CoA is formed as an intermediate during assimilation without the use of phosphoketolase.A set of experiments was carried out to investigate the metabolism of the th phase . When gl13C labelling experiments in three conditions: strains A4, AR1phkGP74, and AR1phkGP74 in the presence of the glyceraldehyde-3-phosphate dehydrogenase inhibitor iodo acetate (1 mM). The mass spectra obtained from the GC-MS analysis of the hydrolysed biomass were converted into summed fractional labellings (SFL)  pathway, an efficient PHK and glyoxylate cycle are required for growth. All metabolites in the lower part of the EMP pathway and the TCA cycle must be formed from acetyl-CoA, and consequently the glyoxylate cycle is needed to form C-4 compounds from acetyl-CoA.The impact of phosphoketolase in glucose cultivations was further studied with L is 60% . It can A. nidulans with the EMP pathway, the PP pathway and the TCA cycle. We also estimated the fluxes with a more detailed metabolic model which included compartmentalisation of acetyl-CoA, pyruvate and oxaloacetate. However, the SFL data were only slightly better fitted to the larger model. In order to avoid over-fitting of the limited number of data points, we chose the simpler but more robust version of the two models . Since the specific growth rate, as well as the biomass yield on glucose, was similar for the two strains, there must be an alternative source of NADPH production in the strain with over-expressed phk (AR1phkGP74). This may be achieved through a switch in isoenzyme preference, e.g. the use of NADP-dependent isocitrate dehydrogenase rather than the corresponding NAD-dependent enzyme or a higher flux through malic enzyme. In either case, the results demonstrate that this A. nidulans strain has a high degree of metabolic flexibility with respect to fluxes in the central carbon metabolism. It is likely that over-expression of phk enhances this metabolic flexibility as it opens for an alternative route from sugars to C-2 and C-3 compounds. The metabolic network analysis demonstrates that NADPH mainly is provided through the PP pathway, but there are alternative sources.The simulation results showed that the wild type strain (A4) had a relative flux into the oxidative branch of the PP pathway of 56.9 compared to 44.4 when xpressed . Despitephk, and consequently a large deviation from the typical flux distribution was anticipated. Initial simulations demonstrated that the flux through glyceraldehyde-3-phosphate dehydrogenase was negligible and could be omitted (results not shown). When glycolysis is blocked, acetyl-CoA must be formed exclusively through PHK, and consequently is a six-fold increase in the flux expected. The flux through the TCA cycle increased from 82 to 99 and the glyoxylate cycle was very active .In conclusion, with over-expression of A. nidulans A4 and AR1phkGP74 were grown on the four carbon  sources in triplicates. From each of the 24 cultivations samples were taken for transcriptome analysis. Statistical analysis of the data was done in order to identify genes that exhibited different expression between the two strains in the four conditions. phk was over-expressed. A total of 1,222 unique genes were affected by the up-regulation of phk. Only four genes were significant on all four carbon-sources , and only 29 genes appeared to be significant between three carbon sources. Indeed, for all carbon sources more than 50% of the regulated genes are specific to that carbon source. On the glucose medium, this percentage is as high as 86%. It is thus apparent that the response to the over-expression of phk, is highly dependent on the carbon source used for growth with glucose having the highest number of responding genes.The strains phk-over-expression. The phk-over-expressing strain had an increased specific growth rate and Ysx compared to the wild type during growth on xylose, glycerol and ethanol. For this reason, one might expect to see a common response between those three sets of experiments. However, these three comparisons only share significant regulation of two genes, both of them being putative dehydrogenases. No common response coordinating the increase in biomass on these carbon sources can therefore be elucidated based on transcriptome data. When examining significantly changed expression level of putative transcription factors  and nine genes were putatively involved in cell growth or cell cycle regulation. The two characterized transcription factors are BrlA, a transcriptional regulator involved in sporulation, inducing the cessation of vegetative growth phk on metabolism, we examined differentially expressed metabolic genes . On glucose, scattered response was found throughout metabolism, including glycolysis, TCA and C5 metabolism, but an especially strong response was found in all steps of the C-2 metabolism pathways connecting acetyl-CoA, acetate, acetaldehyde and ethanol, suggesting strong regulation of the levels of these metabolites , the more profound is the effect of over-expressing phk on the specific growth rate (phk had no effect on the specific growth rate on glucose. While during growth on ethanol the TCA cycle is very active making the extra acetyl-CoA an important source of energy (1 mol of acetyl-CoA yields 4 mol of NADH), the same effect is not expected when cells are growing on glucose. Furthermore, Panagiotou et al A. nidulans on glucose is not limited by ATP and during growth on glucose there is already an efficient supply of all necessary precursors for biomass production and therefore inducing the phosphoketolase pathway does therefore not have a positive effect.More interesting is that the less favorable the carbon source is for growth of wth rate . Consequphk over-expression on the glucose medium seems targeted to neutralize the effect by regulating the acetate metabolism and initiating a growth dampening response. On the other three substrates, we observed that the induction of the PHK pathway increases growth without initiating inhibiting responses, thus supporting that it is a pathway that adds flexibility to the central metabolism as observed in the flux study. It also suggests that A. nidulans is not optimized for growth on glycerol or ethanol as sole carbon sources. As these carbon sources, and especially glycerol and ethanol, are seldom found alone in the dead biomass that the saphrophytic A. nidulans grows on in nature, it is not surprising that the cells have not been evolved to grow fast on these carbon sources. It also suggests that production strains that grow faster on these substrates can be evolved or constructed by phk over-expression. The major difference between growth in nature and growth in aerobic, stirred bioreactors is probably that oxygen can be taken up efficiently in the bioreactor, and consequently respiration is expected to be much more efficient in our experiments compared to nature. If this is the case then less carbon is needed for ATP generation and instead carbon can be used for synthesis of biomass. When A. nidulans is growing on xylose, a pentose sugar, then PHK offers a direct way of generating cytosolic acetyl-CoA. When ATP generation is efficient, then PHK is an efficient way of generating acetyl-CoA since the route via pyruvate decarboxylase results in loss of carbon and a corresponding lower biomass yield. There is no requirement for an efficient PHK when growing on glucose.The above hypothesis was confirmed by the transcriptome analysis, where the response to Aspergillus nidulans A4 was used as wild type reference strain. Aspergillus nidulans AR1 , IBT 27263, was used for the transformation. In order to over-express phk in A. nidulans AR1, the gene was cloned into an integrative vector derived from pBARGPE1 , obtained from the FGSC, USA. For the construction of the plasmid, standard molecular biotechnology techniques were applied according to Sambrook et al. A. nidulans phk (XP_662517) was amplified from genomic DNA with PCR using the Fphk_FW (5′-CGAGTCGGCCGGCCATGCCAGGAGAAGTCATCG-3′) and Fphk_RV (5′-TTGGCGCGCCCTAGCTCCAGTTTCCATCTGC-3′) primers, which introduced FseI and AscI restriction sites. The resulting strain was named AR1phkGP74 (over-expressing phk).3; 0.52 g/L KCL; 0.52 g/L MgSO4; 1.52 g/L KH2PO4; 4·10−4 g/L CuSO4·5H2O; 4·10−5 g/L Na2B2O7·10H2O; 8·10−4 g/L FeSO4·7H2O; 8·10−4 g/L MnSO4·2H2O; 8·10−4 g/L Na2MoO4·2H2O; 8·10−4 g/L ZnSO4·7H2O. Arginine (4 mM) was supplemented in the MM used for the selection of transformants.Minimal medium (MM) for transformation: 10 g/L glucose; 10 mM NaNO−1). Arginine, 0.7 g/L, was added to all bioreactor cultivations by sterile filtration.For bioreactor cultivations a previously described defined medium was used A. nidulans protoplasts was performed as previously described PvuI was used for linearization of the plasmid as only one restriction site is present in the vector and which is located in the ampicillin resistance gene.Genetic transformation of Transformants were purified by streaking out spores to obtain single colonies on selective minimal medium and incubated at 37°C for 3–4 days. The resulting recombinants were further purified twice by streaking out spores on fresh plates with selective medium.To determine the physiological characteristics as well as for sampling for gene expression analysis, cultivations were performed in well-controlled 1.5 l bioreactors with a working volume of 1.2 l. The bioreactors were equipped with two disc-turbine impellers rotating at 350 rpm and sparged with air at a constant flow rate of 1.0 vvm (volume of gas per volume of liquid per minute). The pH was kept constant at 5.5 by addition of 2 M NaOH or HCl and the temperature was maintained at 30°C. For selected experiments, iodo acetate was added by sterile filtration to the sterilized growth medium giving a final concentration of 1 mM.Cell dry weight was determined using nitrocellulose filters . Fermentation samples were immediately filtered and stored at −20°C until analysis. The concentrations of glucose, xylose, glycerol, acetate, succinate, and pyruvate were determined by HPLC as described previously 13C labelling experiments A. nidulans A4 and AR1phkGP74, respectively, were cultivated with 5 g/L of [1-13C] glucose and an aeration rate of 1.0 vvm. In the late exponential phase, biomass samples from the cultivations were harvested, hydrolyzed, derivatized and analyzed by gas GC-MS for determination of labelling patterns of intracellular metabolites. All fragments were derived from either glucose-6-phosphate or proteinogenic amino acids For the A. nidulans was approximated by the biomass composition of A. oryzae (strain A1560) grown in glucose limited, continuous cultivations (specific growth rate of 0.17 h−1) with ammonia as nitrogen source The biomass composition of A modified version of the metabolic model of David et al The fluxes were determined by an in-house software based on the metabolic network analysis framework developed by Wiechert The cultures were harvested in the late exponential phase at a biomass dry-weight concentration of 6–7 g/L with the exception of the cultivation on ethanol, where the biomass concentration was 3–4 g/L. Mycelium was harvested by filtration through sterile Mira-Cloth . The mycelium was quickly dried by squeezing, and subsequently frozen in liquid nitrogen. Samples were stored at −80°C until they were used for RNA extraction. Total RNA was isolated using the Qiagen RNeasy Mini Kit, according to the protocol for isolation of total RNA from plant and fungi Fifteen µg of fragmented biotin-labeled cRNA was prepared from 5 µg of total RNA and hybridized to the 3AspergDTU Affymetrix GeneChip www.R-project.org) version 2.5. The probe intensities were normalised for background noise with the robust multiarray average (RMA) method The scanned probe array images (.DAT files) were converted into CEL data files using the GeneChip Operating Software from Affymetrix, and subsequently pre-processed using the statistical language and environment R . Additionally was added A. nidulans genes found in the SwissProt database  was assigned by comparing PFAM predictions to a manual lookup of the bi-directional best hits in the A. nigerA. nidulans homologues to metabolic genes. p<.05 was employed as a cut-off value for statistical significance.Metabolic pathway analysis was done using an adaptation of a metabolic network map for A. nidulans metabolic network reconstruction was used The statistical significance of regulation around metabolites was assessed using the reporter feature algorithm with default settings Table S1File containing the measured and calculated SFL (%) of 16 fragments(0.04 MB PDF)Click here for additional data file.Table S2File containing the modified version of the metabolic model from Pedersen et al (0.19 MB PDF)Click here for additional data file.Table S3File containing the modified version of the metabolic model of David et al (0.28 MB PDF)Click here for additional data file.Table S4Results of reporter feature algorithm for the examination of phosphoketolase over-expression on glucose.(0.35 MB PDF)Click here for additional data file.Table S5Results of reporter feature algorithm for the examination of phosphoketolase over-expression on xylose.(0.36 MB PDF)Click here for additional data file.Table S6Results of reporter feature algorithm for the examination of phosphoketolase over-expression on glycerol.(0.35 MB PDF)Click here for additional data file.Table S7Results of reporter feature algorithm for the examination of phosphoketolase over-expression on ethanol(0.35 MB PDF)Click here for additional data file.Table S8General functional (KOG/Interpro/PFAM) assignment and SwissProt gene names for 2805 genes from A. nidulans.(0.38 MB PDF)Click here for additional data file.Figure S1Metabolic map of differentially regulated genes in a comparison of wild type and a phosphoketolase over-expressing (PHK) strain on glucose medium.(0.38 MB PDF)Click here for additional data file.Figure S2Metabolic map of differentially regulated genes in a comparison of wild type and a phosphoketolase over-expressing (PHK) strain on xylose medium.(0.38 MB PDF)Click here for additional data file.Figure S3Metabolic map of differentially regulated genes in a comparison of wild type and a phosphoketolase over-expressing (PHK) strain on glycerol medium.(0.38 MB PDF)Click here for additional data file.Figure S4Metabolic map of differentially regulated genes in a comparison of wild type and a phosphoketolase over-expressing (PHK) strain on ethanol medium.(0.38 MB PDF)Click here for additional data file.


Integrative analysis between dynamical modeling of metabolic networks and data obtained from high throughput technology represents a worthy effort toward a holistic understanding of the link among phenotype and dynamical response. Even though the theoretical foundation for modeling metabolic network has been extensively treated elsewhere, the lack of kinetic information has limited the analysis in most of the cases. To overcome this constraint, we present and illustrate a new statistical approach that has two purposes: integrate high throughput data and survey the general dynamical mechanisms emerging for a slightly perturbed metabolic network.kinetic library, which constitutes the base for identifying, statistical and dynamical properties during the relaxation. For the sake of illustration we have applied this approach to the human Red blood cell metabolism (hRBC) and its capacity to predict temporal phenomena was evaluated. Remarkable, the main dynamical properties obtained from a detailed kinetic model in hRBC were recovered by our statistical approach. Furthermore, robust properties in time scale and metabolite organization were identify and one concluded that they are a consequence of the combined performance of redundancies and variability in metabolite participation.This paper presents a statistic framework capable to study how and how fast the metabolites participating in a perturbed metabolic network reach a steady-state. Instead of requiring accurate kinetic information, this approach uses high throughput metabolome technology to define a feasible In this work we present an approach that integrates high throughput metabolome data to define the dynamic behavior of a slightly perturbed metabolic network where kinetic information is lacking. Having information of metabolite concentrations at steady-state, this method has significant relevance due its potential scope to analyze others genome scale metabolic reconstructions. Thus, I expect this approach will significantly contribute to explore the relationship between dynamic and physiology in other metabolic reconstructions, particularly those whose kinetic information is practically nulls. For instances, I envisage that this approach can be useful in genomic medicine or pharmacogenomics, where the estimation of time scales and the identification of metabolite organization may be crucial to characterize and identify (dis)functional stages. Constraints-based modeling represents a paradigm in systems biology with a broad scope of applications ranging from bioengineering to cellular evolution in silico modeling, the data supplied from high throughput technologies has triggered the development of deductive top-down procedures, in order to complement and verify biological predictions obtained from constraints-based models Parallel to these in silico models have provided a successful method for accomplishing the integrative task between high throughput data and genome scale models, the steady-state assumption may oversimplify cellular behavior such that its description is valid only at certain time scales. In order to deal with metabolic mechanism away from a steady-state, it is imperative to develop new genome scale in silico models capable to provide a temporal description of the cell activity and relay it with its physiological behavior Even though constraints-based For instance, a paradigm linking dynamic and physiological behavior is clearly manifested in human red blood cell metabolism (hRBC) kinetic library conformed by all the kinetic parameters which dynamically ensure the existence of a steady-state solution. Subsequently, through this kinetic space, one constructs a library of dynamical models, all of them characterized by the same metabolic network but predicting dynamic behavior with different kinetic parameters. As this paper suggests, a statistical analysis applied over the library of dynamical models allows us to survey general properties even in the absence of accurate kinetic information. The library of dynamical models constitutes a fundamental space required to explore two immediately questions: how and how fast a metabolic network reaches its steady-state after a slightly external perturbation has occurred. The workflow of the method is such that it integrates three main components: metabolome data In this work I suggest a statistical framework to analyze dynamical properties of a metabolic network when its metabolite concentrations are slightly perturbed around a steady-state. To overcome the lack of kinetic parameters, this approach uses high throughput metabolome data for obtaining a k-cone, has been calculated considering three requirements: 1) All biochemical reactions obey law mass action, 2) Steady-state metabolite concentrations are known quantities and potentially obtained from metabolome data k-cone are such that they dynamically ensure the existence of a steady-state solution, see The solution space of feasible kinetic parameters, defined as the k-cone, the statistical nature of this framework emerges when one constructs two additional libraries, Jacobian and ModalHaving defined Jacobian matrix defines the times scales and the Modal matrix specify how metabolites organize to reach its steady-state. As this paper supports, statistical analysis accomplished in both libraries can potentially guide us to identify: 1) robust dynamical properties inherent to the biological systems, 2) scrutinize how dynamic properties depend on specific kinetic parameters, and 3) potentially associate dynamical with functional behavior in cell.More specifically, given certain kinetic parameters, see Table S1 and Table S2 in supporting information. Overall, I believe this approach, schematically represented in In order to illustrate the scope of our method we will apply this to the Human Red Blood Cell (hRBC) metabolic network. In this paper, hRBC metabolic reconstruction is conformed by 33 metabolites participating in 68 biochemical and transport reactions, K-cone analysis is a formalism useful to determine a space containing all candidate values for kinetic parameters of a metabolic network K-cone space for hRBC metabolic network was obtained taking into account the stoichiometric matrix and a set of metabolite concentrations defining a steady-state condition , two assumptions were applied during the analysis. Firstly, the concentration of all the metabolites at a steady-state was supposed to be known, see . This assumption particularly encourages to use accurate data obtained from high throughput metabolome technology k-cone space, see k-cone space, one proceeds to construct a kinetic library simply by randomly selecting some points inside k-cone space. Mathematically, random sampling procedure was accomplished by applying an Artificial Center Hit and Run algorithm see . As a result, numerical distributions associated with the kinetic parameter for each metabolic reaction were obtained. The resulting ranges of values for each biochemical reaction are reported in .Thus, a point inside this space represents a vector with 68 entries, each one defining a kinetic parameter corresponding for the 68 biochemical reactions included in hRBC metabolic network. Having identified kinetic library was obtained, one can proceeded to survey how and how fast the metabolites reaches the steady-state after a slightly perturbation. In general, biochemical reactions integrating metabolic networks occurs over a broad spectrum of time scales, such that some of them are faster than others depending on its kinetic parameters and presumably on its physiology relevance Jacobian matrix, see . In essence the entries in this matrix indicate how fast a metabolic flux changes when the concentration of certain metabolite changes too. Subsequently, a library of feasible time scales was constructed by evaluating each component on kinetic library in the Jacobian matrix, and proceeding as described in , the time scale proper for each set of kinetic parameters were calculated. The resulting distribution of hierarchical time scale was gathered for constructing a hierarchical time scale library. Furthermore, in order to reveal how the metabolites organize between them for recovering its steady-state, we used a modal matrix analysis which was directly obtained from the Jacobian library, see Once Modal matrix analysis is formalism for identifying the metabolites that coordinately moves at a specific time scale, called metabolic pools. According to modal theory, for each one Jacobian matrix (J) it is possible to find a Modal matrix (M) whose rows supply information of the metabolic pools at each time scale, see . Thus, as we did before, a modal library was constructed by storing all Modal matrices obtained for each element inside the Jacobian library, see hierarchical time scales and modal library, next section is devoted to show that one can tackle two interesting issues: to uncover global properties in dynamic metabolic networks and to survey the proper metabolic organization required to induce adequate physiological functions. An overview of the methodology and the relationship between its libraries is schematically represented in Based on a statistical analysis applied to the hierarchical time scale library was accomplished. Thus, proceeding as described in  (Equation 6), the average and the standard deviation for the inverse of each time scale obtained from Jacobian library were calculated and plotted in see . Robustness is a property that has been reported in a variety of biological systems k-cone sample sizes. 10 scale) for the eigenvalues and time scales obtained when one select 4, 600 and 12586 points in k-cone space. Particularly, we note that in all cases the average and dispersion converge according the number of sample size increase. Notably, this approach allows to identify time scales that are closely similar to those obtained by using a detail kinetic model for hRBC To uncover the role that kinetic parameters have onto time scale profiles, a statistical analysis over the modal library was classified separately at each time scale as described in the next section.In summary, fast and intermediate time scales tend to be statistically robust to kinetic parameter variations. Robustness, in this case, may be a consequence that the metabolic network compensates an altered kinetic property by using an equivalent functional metabolic pathway. Conversely, the last three slow time scales are sensitive to variations in kinetic parameters and it may be caused by a reducing number of alternative pathways to replace the effects of kinetic variations. Based in this hypothesis, we postulate that robustness in time scale can be correlated with the number of equivalent functional metabolism pathways. In order to justify this idea, we proceed to explore and quantify the variety of mechanisms underlying the robustness inherent in each time scale. For this purpose, all the possible metabolic organization to reach the steady-state encrypted in the modal library in such a way that first row of a modal matrix identifies the metabolic pools at the first time scale; the second row is associated with the second time scale, and so on. Continuing with our analysis, the modal library was statistically analyzed to survey the metabolic organization by which the cells respond to changes in kinetic parameters. The central aim is to survey the extent to which each metabolite participates in defining metabolic pools and whether some metabolites participate to an equal extent in spite of the selected kinetic parameters. Behind this analysis, I have hypothesized that the metabolites having a robust participation on metabolic pools can be potentially assigned certain fundamental physiological role. With this in mind, we defined two matrices (aveM and N) supplying information referring to the average and the dispersion for each entry along the entire modal library, see Experimental measurements on perturbed metabolic networks have revealed that some metabolites, called metabolic pools, move in a coordinated fashion along time scales i,jM identify the average (dispersion) contribution that the j-th metabolite have to define the metabolic pools at i-th time scale, see . For instances the entry M3,1ave represents the average contribution of glucose 6 phosphate (g6p) at the third time scale, see N.Entries of these matrices aveM reveals the formation of physiological metabolic pools emerging at slow time scales, see nd time scale. It indicates that at that time scale the reaction g6p = f6p driven by glucose 6-phosphate isomerase is at thermodynamic equilibrium. Equivalently, other metabolic pools suggesting an organized movement on its metabolite concentration were identified at subsequently time scales see Visual inspection of N matrix. As previous interpretation, i-th row represents the dispersion of the metabolic pool formed at the i-th time scales and the columns quantify the dispersion of each metabolite. On the other hand, modal library, we classify all the i-th rows along each matrix in modal library to construct a new sub-space called the i-th metabolic pool library. This sub-space have special relevance due that contains informative data referring to the degree of variation of metabolic pools in modal library. For example, the rd metabolic pool3 library is conformed by the collection of all metabolic pools identified at the rd3 time scale along all modal library, so if redundancy does exist it should be hidden in that subspace. This classification allows us to construct 33 subspaces, each one consisting of 12586 rows corresponding to each time scale identified in previous section see Robustness in metabolic networks has been attributed to a set of factors, with redundancy representing one of the most recognized i-th metabolic pool library by applying a hierarchical cluster analysis, whose visual representation reveals the degree of metabolite participation, redundancy and (dis)similarily between them. For instance, th and 32ndmetabolic pool library respectively. In both cases, this graphical representation allows to identify conservative patterns through the space. Thus, for the 6thmetabolic pool library, we note that sedoheptulose 7-phosphate (r7p) participates over the pool formation in most of the situations. The inverse situation occurs with D-glucose 6-phosphate (g6p), fructose-6-phosphate (f6p), Fructose-1,6-diphosphate (fdp), dihydroxyacetone phosphate (dhap) and glyceraldehyde 3-phosphate (g3p) whose participation in metabolic pools would appear to be a function of kinetic parameters. Similarly, pyruvate (pyr), 2 phosphoglycerate (2pg) and phosphoenolpyruvate (pep) represent the predominant metabolites participating in the 32ndmetabolic pool library.Having performed this classification, we studied the metabolic composition for each metabolic pool libraries, one note that metabolites participation vary depending of the selected subspace. However, a frequency study accomplished over each metabolic pool library allows us to identify the potential metabolites that invariantly participate without reference on its kinetic parameters. Proceeding as described in i-th metabolic pool library we identify those metabolites that have contribute with at least with 80% over all the cases, the result is shown in i-th metabolic pool library. For these metabolites, redundancies may postulate them as key components to induce a proper physiological function, a hypothesis that should be experimentally verified through metabolome technology From a global analysis accomplished over the 33 i-th metabolic pool library, however it is needed to know how (dis)similar are the elements conforming each i-th metabolic pool library in order to have a better appreciation of the variability along the entire space. In order to quantify how similar are the elements of each i-th metabolic pool library, we applied Principal Component Analysis (PCA) i-th metabolic pool library, one concludes that the number of independent variables present in the space can be accurately represented by a reduced set of principal components. In fact, the first five principal components are capable to reproduce between the 72%–100% of the complete variability along the metabolic pool libraries, see i-th metabolic pool coverage achieved by the first five principal components for all the 33 libraries of metabolic pools is presented in Previous section has revealed valuable information concerning the redundant participation of metabolites along each i-th metabolic pool libraries, see In summary, along these last sections two observations stand out. Primarily, we have identified some metabolites that play part metabolic pools without reference to of kinetic parameters, this indicating a degree of redundancy of metabolic mechanisms to recover the steady-state condition, see in silico procedures capable of explaining how the metabolism in cell responds to external perturbations. Despite significant advances on dynamic theory k-cone. Instead of following a deterministic description with well defined kinetic parameters, we have opted to consider a statistical procedure which leads to the construction of dynamic libraries for quantifying how and how fast the metabolic networks reached its steady-state, see The advent of high throughput technology and the increasing number of reconstructed metabolic networks constitutes essential components that have encouraged the development of As this paper shows, robustness, redundancy and variability were properties identified at different stages in perturbed metabolisms, all of them combined to give the global phenomenological effect. In general we conclude that robustness in time scale is caused by two types of metabolites: redundant and context dependent. The first classification confers redundancy to metabolic pools, and they are conformed by metabolites that always participate on the mechanics governing the relaxation toward a steady-state independently of the selected kinetic parameters. Conversely, context dependent metabolites are sensible to kinetic parameters and they supply variability to regulate the activity metabolites required to select the specific answer depending on the environment. From a systems biology perspective, there is evidence that different sort of robustness emerges inherently with network complexity Overall, our method constitutes a framework for exploring dynamic behavior of slightly perturbed metabolic networks, where precise knowledge of kinetic information is lacking. Contrasting with others approaches, this method has been constructed such that data from high throughput metabolome technology Finally, I expect that this methodology can provide guidance in a future for exploring the relationship between dynamic and physiological behavior on other metabolic reconstructions. For instances, we envisage that it will contribute to design therapeutic targets in areas such as pharmacogenomics and genome medicine supporting information. In order to develop comparative studies and validate our predictions we use the same independent metabolites as reported in previous works Table S1 and supporting information.The metabolic network of Human Red Blood Cell (hRBC) analyzed in this paper is integrated by 33 metabolites participating in 68 internal and exchange reactions. These reactions integrate glycolysis, pentose phosphate pathway, Rapoport-Liubering and the nucleotides metabolism pathways. A graphical representation of this metabolic network can be found elsewhere K-cone analysis is a useful framework for estimating potential candidates of kinetic parameters underlying a metabolic network and ensuring the existence of a steady-state solution m metabolites and n reactions governed by law of mass action, the set of kinetic parameters (k) that ensure a steady state behavior are defined byS is the stoichiometric matrix, diag(.) represents a diagonal matrix and C is a i-th entry is the product of the reactant concentration at steady-state corresponding to the i-th reaction, i.e.−i,jS denotes the stoichiometric coefficients of reactants in the j-th reaction, in addition ix represents the known steady-state concentration for the i-th metabolite participating as reactant in the j-th reaction. In order to compare the results obtained with the statistical approach presented in this paper with the reported obtained from a detail kinetic model, we have used the same metabolite concentration at the steady-state as in previous reports see Table S1 in supporting information. Given that in general the number of reactions is greater that the number of metabolites, the kinetic solution of Equation 2 is determined by a myriad of points inside the null space of the matrixk-cone was accomplished by an Artificial Center Hit and Run Algorithm (ACHR) Q. Once defined this point the algorithm calculate “warm-up” points from this initial point by an iterative procedure. These warm-up points are stored in a matrix W by which a centroid cx is calculated. Finally the sample points are calculated by selecting one point ny in the W matrix and moving in the direction vector given by (c - yx). The new vector n+1y is substitute by the previous point ny in W. The centroid is recalculated and this process continues iteratively until a desired number of sample points are reached. ACHR was done using the COBRA tool box Jacobian matrix were neglected. Overall, from the 19,000 sampled points in k-cone only 12586 were considered for all the statistic analysis.The identification of kinetic parameters integrating the i) as the informative parameters to estimate how fast a perturbed dynamical system reaches its equilibrium state Jacobian matrix with rank m, one can deduce m time scales, τi, calculated by τi = −1/λi , i = 1..m. Thus, hierarchical time scale library was reconstructed by consecutively calculating the eigenvalue distribution for all matrices integrating the Jacobian library. For each realization, we ranked the eigenvalues, going from higher to lower magnitudes  and the corresponding time scale was calculated. Average and standard deviation for the eigenvalues and the time scales along the entire distribution were calculated.Linear perturbation theory considers the eigenvalues of the Jacobian matrix  shows the average time scales obtained from the statistical analysis. The coefficient of variation associated with each time scale is depicted in (B).(1.06 MB EPS)Click here for additional data file.Table S1Metabolite concentrations. Metabolite concentrations at the selected steady state condition. These data were estimated from references (0.21 MB RTF)Click here for additional data file.Table S2Biochemical Network for Red Blood Cell Metabolism. Biochemical reactions included in the Red Blood Cell metabolic network.(0.28 MB RTF)Click here for additional data file.Table S3Range of Kinetic parameters. Range of the kinetic parameters obtained from k-cone space.(0.30 MB RTF)Click here for additional data file.