The storage of photosynthetic carbohydrate products such as starch is subject to complex regulation, effected at both transcriptional and post-translational levels. The relevant genes in plants show pronounced daily regulation. Their temporal RNA expression profiles, however, do not predict the dynamics of metabolite levels, due to the divergence of enzyme activity from the RNA profiles.Unicellular phytoplankton retains the complexity of plant carbohydrate metabolism, and recent transcriptomic profiling suggests a major input of transcriptional regulation.Ostreococcus tauri. Measured RNA expression datasets from microarray analysis were integrated with a detailed stoichiometric reconstruction of starch metabolism in O. tauri in order to predict the optimal flux distribution and the dynamics of the starch content in the light/dark cycle. The predicted starch profile was validated by experimental data over the 24 h cycle. The main genetic regulatory targets within the pathway were predicted by in silico analysis.We used a quasi-steady-state, constraint-based modelling approach to infer the dynamics of starch content during the 12 h light/12 h dark cycle in the model alga O. tauri directly from time-series gene expression data.A single-reaction description of starch production is not able to account for the observed variability of diurnal activity profiles of starch-related enzymes. We developed a detailed reaction model of starch metabolism, which, to our knowledge, is the first attempt to describe this polysaccharide polymerization while preserving the mass balance relationships. Our model and method demonstrate the utility of a quasi-steady-state approach for inferring dynamic metabolic information in  Twenty-four hour biological rhythms are known to pervade the transcriptomes of the several organisms tested, for example, human, mice and higher plants -3 Diurna targets ,9.M. tuberculosis. Although did not take post-transcriptional regulation into consideration, it was enough sufficient for analysis of the steady state reached by bacteria in response to environmental and genetic perturbations. The alternative Boolean-like tri-value mapping of gene expression states used to reveal tissue-specific enzyme activity, reported by Shlomi et al [Additional information available from transcriptome data can significantly improve the results obtained by FBA. A few successful approaches to incorporate the gene expression data into the flux model to infer the metabolic information have been made during the last decade. Among them is the method called E-flux has been proposed recently . It opermi et al , which a2 fixed during the day in the form of starch, which is remobilised to sucrose during the night to avoid carbon depletion in plant cells [In higher plants diurnal expression patterns are evidently demonstrated by the genes encoding the central metabolic pathways including those involved in the carbohydrate storage metabolism ,12. Manynt cells . Transcrnt cells ,14, but nt cells . Among tnt cells -18. TranChlamydomonas reinhardtii that has been used as a model organism for plant biology for the last half century, [Ostreococcus spp tauri and lucimarinus and two Micromonas species, have been sequenced [Eukaryotic green microalgae from the picophytoplankton (cells with a size <2 μm) shares the main photosynthetic functions with higher plants. However, the gene redundancy is reduced in these small genomes, thus making them attractive models for investigating the general properties of photosynthetic physiology. In addition to century,  recentlyequenced ,21., Ostreococcus tauri [Ostreococcus demonstrates a structural complexity comparable to higher plants [C. reinhardtii, with multiple enzyme forms for each pathway step  time series for O. tauri and integrated them to the flux model in a similar fashion as [By accomplishing a full metabolic reconstruction of the shion as  in orderO. lucimarinus and is partially incomplete. Nevertheless, based on the results of the EST transcriptome analysis from [We started from the exploration of the Kyoto Encyclopedia of Genes and Genomes databases (KEGG) to obtain the necessary information about the proteins that comprise the starch pathway. Information in KEGG is available for sis from  and BLASWe used microarrays to obtain the expression profiles of genes encoding enzymes of the starch metabolic pathway. For starch synthesis, we included genes annotated as encoding chloroplastic phosphoglucoisomerase (PGI) and phosphoglucomutase (PGM), a small subunit of ADP-glucose pyrophosphorylase (AGPase), starch synthase , and starch branching enzyme . For the starch degradation pathway, we include glucan, water dikinase (GWD), α-amylase , β-amylase , isoamylase (ISA1 and ISA3 isoforms), pullulanase, starch phosphorylase, glucose and maltose (MEX1) transporters. In total we incorporated expression profiles for 29 out of the 43 genes annotated as starch-related into the analysis, which uniformly cover the whole pathway.Single genes for PGI and PGM show very similar profiles, reaching their maximum level in the first 3 hours of light, and decreasing throughout the next 12 hours with a minimum during the early night , annotated as SSI and SSIII- A and B  has a different profile, staying relatively stable for most of the time with rapid changes connected to the light-dark transitions. Granule-bound starch synthase GBSSI Ot06g03200) demonstrate the shape similar to the small AGPase subunit , β-amylase (Ot02g06960), pullulanase (Ot01g03030), starch phosphorylase (Ot04g02110), MEX1 (Ot09g03160) and SEX4 (Ot13g02940). All of them peak at the subjective dusk and decrease during the night achieving the minimum level before dawn . Only those genes that were annotated as chloroplast-located were connected to the corresponding fluxes. The process of starch degradation is described up to the departure of glucose and maltose to the cytosol  from the Calvin cycle, so that we used 16 enzymes and 43 genes in total . PhosphoAlthough the overall starch metabolism constitutes a multistep polymerisation process, it is still possible to simplify the complexity by reducing the number of metabolites to a presentable minimum, enabling one to illustrate the most essential biochemical features . Introducing a certain gene expression profile, we simulated the situation in which all the genes, except the chosen one, were expressed at their maximum level. Thus, we interrogated how the flux limitation obtained from single gene regulation influenced the overall starch production flux  and AGPase Ot07g02930) strongly affect the 'light' part of the starch flux pattern, while GWD (Ot03g01510), both ISA1 and ISA3 (Ot12g00310 and Ot14g02550), and α-amylase (Ot07g02010) have an influence upon the 'dark' region  by allowing the uptake of CO2 from time 0 until time 12 .Additional file At time 12 the starch flux leaves the positive region, and the process of degradation starts to dominate. The fluxes of the reactions for starch granule phosphorylation are brought to the forefront; meanwhile, the flux for maltose export attains its maximum value . This is caused by a zero value for maltose export flux, which, in turn, results from a zero value for the expression level of MEX1. In our procedure, this value is directly applied as the upper flux bound for the reaction of maltose translocation from the chloroplast. However, the real flux distribution at the time point time 21 merits further experimental investigation.To obtain the diurnal dynamics of the starch content from the flux, we estimated the cumulate of the starch flux at each time point. We also measured the actual starch content dynamics during the 12/12 light-dark cycle experimentally . Figure Ostreococcus nor for Chlamydomonas has full starch deprivation been demonstrated, even after prolonged incubation in darkness [While simulating the longer-term behaviour of starch content, we observed the tendency for its baseline to increase . After this, the simultaneous effect of the substitution of all genes was calculated as in the previous simulation  (AGPase), which removes the oscillatory pattern completely when deleted Figure . This isThe deletion of the maltose transporter MEX1 (Ot09g03160) increases the rate of starch production as it decreases the maltose efflux. Interestingly, starch phosphorylase (Ot04g02110) gene deletion changes the local pattern for the light-dark transition causing a noticeable decrease in the starch degradation rate during the dark period.2 to the pathway.From the last 5 genes we can observe the deletion of fructose-1,6-bisphosphatase (Ot03g00330) gene, decreasing the starch synthetic flux Figure . As in tFor the maltose flux the results of the simulation of single gene deletion are presented in Additional file Glucan, water dikinase Ot13g01510) defines the kinetics of 'dark' maltose region . Previous reaction models for carbohydrate metabolism usually present starch synthesis as ADP-glucose being converted to starch without intermediate stages [We developed a detailed reaction model of starch metabolism, which, to our knowledge, is the first attempt to describe the polysaccharide polymerization while preserving the mass balance relationships e stages . AlthougO. tauri in our experimental observations.We analysed the dynamics of starch during the light/dark cycle as a sequence of metabolic quasi-steady states, each of them corresponding to particular genetic state within the 3 hour interval. This approximation correctly predicted the diurnal pattern of starch content in Obviously, neither mRNA nor even protein abundance itself may be sufficient for prediction of true flux through a reaction, but it could be the effective indicator of the relative strength of the flux over a time course. At the same time, modification of the upper bounds of reaction fluxes is an effective way to model genetic knockout experiments using FBA and combining FBA with boolean gene models.The model structure and the constraints applied are sensible and biologically plausible for they are based on the actual pathway structure and describe the main features of starch metabolism. The model starch "phenotype" on the whole matches the data from , taking Arabidopsis and Chlamydomonas. The list also includes GBSSI, β-amylases, glucan, water dikinases GWD (R1) and the maltose transporter MEX1. As we observed, the main regulation targets are concentrated at the linear entrance to the system, within the actual topological bottleneck of the system . Some of the events of high importance, corresponding to synthesis and degradation, are located at the granule surface. Here GBSSI and GWD appear as the main potential targets for genetic regulation. The final set of targets deals with the production of maltose and its withdrawal from the system. The main target enzymes identified for this location are β-amylases and the maltose transporter MEX1.We identified the set of potential targets of transcriptional regulation , we checked whether enzymes of the starch metabolic pathway in O. tauri contain the target sequences reported as responsible for the redox-related modifications for plant species, namely, for AGPase, GWD and β-amylase enzymes [O. tauri [C. reinhardtii [O. lucimarinus nor both Micromonas species contain the redox-target sequences  and demonstrates low sensitivity to inhibitor (PPi). On the other hand, the large subunit, being fully catalytically competent, is assumed to be the only one that undergoes the allosteric regulation at subsaturated concentrations of effectors [O. tauri enzymes likely contribute to the pre-eminent role of transcript regulation over much of the day. Including post-translational regulation in future models might further improve the model's performance at the light-dark transitions.Allosteric regulation is also important in the control of starch metabolism in higher plants, but here again, according to , the regffectors . As our Ostreococcus cell division at the end of the light phase seems to dictate the local time of elongation and division of the starch granule and, therefore, the overall timing for the starch synthesis and degradation cycle [C. reinhardtii the cell cycle is also clearly gated by the circadian clock [Saccharomyces cerevisiae [In on cycle ,27,38. Ian clock , influenan clock . Regulatrevisiae . This miOstreococcus [O. tauri would be a valuable system for modelling metabolic networks based on transcriptomic data.It has been proposed recently that in addition to the transcriptional regulation of the cell division cycle , many oteococcus . Thus, OChlamydomonas, Micromonas, or other unicellular algae, which are becoming of great interest as unicellular factories to produce metabolite of interest such as lipids for biofuels. Furthermore, in the absence of detailed kinetic information about the regulation of a metabolic network, such an approximate phenomenological model could be a useful tool for suggesting genetic-metabolic interactions.The modelling approach presented requires further development before it will be applicable in detail to any plant system, due to the strong differences in the degree of post translational regulation and redox regulation between higher plans and unicellular algae. It is, however, applicable to the systems of similar complexity, such as http://bioinformatics.psb.ugent.be/blast/public/?project=ostreococcus). 6369 genes were represented by at least one probe. Cell culture conditions, RNA extraction, labelling, hybridization and raw analysis have been previously described [-3 using a 3 factor  ANOVA. Genes in the final KOG based genome annotation (June 2006) corresponding to O. tauri probe sequences were also searched (BLASTX) against the Arabidopsis non redundant database to identify the closest orthologue of Arabidopsis. Putative genes involved in starch metabolism were identified in the dataset based on the annotations, but also on protein sequence conservation (BLASTP). The complete dataset is available in the Gene Expression Omnibus (GEO) public database at NCBI under the accession number: GSE16422. (Processed data: http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?token=jbmhpwkyccmuwvu&acc=GSE16422).Microarray design and analysis have been previously described ,38. Brieescribed . Technic2 uptake rate and the defined starch composition, the maximum possible rate of starch synthesis can be predicted in silico. FBA is based on linear optimization of the objective function.The model was developed in COPASI , convertv has 69 fluxes, including 6 exchange fluxes (b1-b6):The stoichiometric matrix for the system is of size 38 substrates x 69 reactions. The vector -5-10-6 mmol/h, which is difficult to analyse, as it is prone to rounding errors during computations. To avoid this problem, we set all the boundaries for our model reaction rates as a proportion of the maximum starch production rate. This enables us to operate with a solution space in which most of the flux values are greater than one.Since a starch polysaccharide has an enormous molecular mass, the normal flux value for starch production will be in the range of 10We used linear optimization ,49 for fvi,min  ≤ i v≤ vi,max, and bi,min  ≤ i b≤ bi,maxA linear objective function to define has a form:w is a vector of weights (iw) on the internal flux (iv) and the external flux (jb). Z then has to be minimized , depending on the problem posed. Because equations are linear, the linear programming (LP) method has been used for this constrained-based optimisation problem.where In the initial setup when the upper bound was defined as a ratio of maximum starch production, the model could either produce starch (if optimized to maximum), or maltose (optimized to minimum). To make the model work in both directions (produce and degrade the starch) simultaneously, with starch production dominating during the day, we introduced the specific cost components for the maltose and glucose transporters and adjusted the upper bounds for the respective reactions appropriately.Since we aim to model the diurnal cycle in starch production and degradation, and having in mind that starch is generally produced during the day when the carbon source is available, we used the step function (+1 during the day and -1 at night) to fit the starch production rate by simultaneous modification of the maltose transport rate upper bound and the coefficient of that reaction in the cost function. The optimum has been achieved with the values for the export reactions' upper bounds equal to 166.5 and 122.45 for maltose and glucose respectively, which is slightly less than the respective stoichiometric values. Therefore, we assume a kind of competing relationship between starch production and maltose export for carbon fixed by the photosynthetic machinery, with a given privilege for starch synthesis under light exposure.2 uptake flux in the objective function to one. As a result, nightfall could be easily simulated by switching it to zero, assuming saturating light.We introduced light into the system by equating the weight coefficient for the CO2 fixation, starch production, and glucose and maltose export from the chloroplast:The resulting general linear objective function includes the COTo summarize, the stoichiometric analysis presented above gives us the general representation of the capacity of the system and potential variability of its behaviour, depending on applied constraints. In particular, the extreme pathway analysis sheds light on how the system may behave if it is not constrained by the objective function. The sampling of the solution space and, especially, the robustness analysis are extremely useful as they both provide the idea for the each reaction's "importance" in terms of the overall system performance and uncover the existing relationships between the reactions. The latter should be taken into account in experimental design.Details of analysis are presented in Additional file All reactions in our model are gene associated. This means that each enzyme responsible for the certain reaction has one or several genes whose function has been annotated correspondently. Each gene has a characteristic pattern of diurnal expression that can be correlated to its specific physiological function.We assume that all regulatory feedback influences will be equilibrated rapidly enough to treat the flux system as being in a quasi-steady state on a time scale of three hours. Thus, the behaviour of the system of interest could be approximated as a set of steady states with rapid transitions between them. These steady-states will correspond to the genetic states at different time points available through the microarray data.Variation of gene expression could lead to a deviation of the reaction flux upper bounds from their value defined by the stoichiometry of the system. To represent such a deviation we scaled RNA abundance from the microarray data and multiplied the flux upper bound by the value obtained. We have chosen the simplest method, which gives us a value in a range between 0 and 1, thus assuming that at the lowest point flux through reaction is blocked, while at the highest level of expression flux is saturated. We understand that aforementioned approximation is quite strong and requires further theoretical investigation, but we have shown in this paper that application of such assumption allowed direct incorporation of gene expression time series into FBA model and, together with analysis of other mechanisms of starch metabolism regulation, described time course of starch content.Thus, we represent the dynamics of starch content as a set of steady states corresponding to genetic states available through microarray data. Each steady state corresponds to a certain time point of the 12/12 light-dark cycle with an interval of 3 h between the neighbouring points. For those genes from the list with expression profiles that are not available we set the RNA abundance to the minimum level of 0.01 at each time point as there is no reaction controlled by unavailable gene only. For cases where we have more than one gene associated with the same reaction we sum up the gene data for each reaction and multiply the current reaction upper flux bound by the obtained sum.As mentioned above, expression profiles of some genes involved in starch production and generation are not correlated with a starch dynamics itself. Generally, such discrepancy is explained by post-transcriptional and posttranslational regulation of the protein and metabolic regulation within the pathway. We have shown that in some cases, like O. tauri, when transcriptional regulation has a pronounced effect  while th-2.sec-1). In these conditions cells are synchronised and achieve one division per day. Cells were inoculated at low density (4 × 105 cell/ml and 8 × 105 for cells grown in antiphase with the day/night cycle), 400 ml were dispatched in flasks and further grown for 4 days to reach the approximate density of 3 × 106 cell/ml and 6 × 106 cell/ml for antiphase grown cells). Pluronic acid  was added to 800 ml of cells that were collected by 8000 g, 8 min, 4°C centrifugation [Ostreococcus cultures grown in natural sea water supplemented with Keller enrichment  were splfugation  every 3 fugation .OS designed and performed the modeling, analyzed data and wrote the paper; FC and DD designed and performed experiments, participated in interpretation of results and drafting the manuscript; AS contributed to model design and data analysis; FYB contributed to the design of the study and the experiments, participated in interpretation of results and drafting the manuscript;SB, IG and AJM contributed to the design of the study and revised the paper. All the Authors read and approved the final manuscript.Figure S2. The optimal flux distribution for the objective function. Figure S3 and 4 Results for flux variability and robustness analysis. Figure S5 Some results of sampling flux distribution. Figure S6 Transcripts encoding the enzymes of starch metabolism in O. tauri. Figure S7 Investigation of effect of single gene rhythmic expression on the overall diurnal starch pattern. Figure S8 Simulation of effect of flux upper bounds constraining on the resulting starch flux pattern. Figure S9 The log flux distribution at ZT0, ZT3, ZT6 and ZT9. Figure S10 The log fluxes distribution at ZT12, ZT15 and ZT18. Figure S11 The weekly pattern of the starch content dynamics. Figure S12 The effect of the in silico single gene deletion on the pattern of diurnal maltose production. Figure S13 GWD1  from A. thaliana, S. tuberosum, C.reinhardtii, O.tauri, O.lucimarinus , M.pusilla and M.CCMP490. Figure S14. Multiple alignment for Beta-amylases from Arabidopsis, Maize, Brassica, C.reinhardtii, O.tauri, O.lucimarinusClick here for fileFigure S1. Full map for the starch metabolic pathway considered in the flux balance model.Click here for fileTable S1. The starch pathway reactions described in the model. Table S2. Summary of targets for genetic regulation indentified in different analyses.Click here for fileDetailed model assumptions and structure. Flux balance analysis. Evidence of the moderate redox regulation of starch pathway in O. tauri.Click here for file


Purple nonsulfur bacteria (PNSB) are facultative photosynthetic bacteria and exhibit an extremely versatile metabolism. A central focus of research on PNSB dealt with the elucidation of mechanisms by which they manage to balance cellular redox under diverse conditions, in particular under photoheterotrophic growth.Rhodospirillum rubrum, Rhodobacter sphaeroides and Rhodopseudomonas palustris). Using flux variability analysis, the model reveals key metabolic constraints related to redox homeostasis in these bacteria. With the help of the model we can (i) give quantitative explanations for non-intuitive, partially species-specific phenomena of photoheterotrophic growth of PNSB, (ii) reproduce various quantitative experimental data, and (iii) formulate several new hypotheses. For example, model analysis of photoheterotrophic growth reveals that - despite a large number of utilizable catabolic pathways - substrate-specific biomass and CO2 yields are fixed constraints, irrespective of the assumption of optimal growth. Furthermore, our model explains quantitatively why a CO2 fixing pathway such as the Calvin cycle is required by PNSB for many substrates (even if CO2 is released). We also analyze the role of other pathways potentially involved in redox metabolism and how they affect quantitatively the required capacity of the Calvin cycle. Our model also enables us to discriminate between different acetate assimilation pathways that were proposed recently for R. sphaeroides and R. rubrum, both lacking the isocitrate lyase. Finally, we demonstrate the value of the metabolic model also for potential biotechnological applications: we examine the theoretical capabilities of PNSB for photoheterotrophic hydrogen production and identify suitable genetic interventions to increase the hydrogen yield.Given the complexity of the central metabolism of PNSB, metabolic modeling becomes crucial for an integrated analysis of the accumulated biological knowledge. We reconstructed a stoichiometric model capturing the central metabolism of three important representatives of PNSB  explains various redox-related phenomena of the versatile metabolism of PNSB, (ii) delivers new hypotheses on the operation and relevance of several metabolic pathways, and (iii) holds significant potential as a tool for rational metabolic engineering of PNSB in biotechnological applications. PNSB possess the well-known Calvin-Benson-Bassham cycle  which is essential for autotrophic but partially also for photoheterotrophic growth Rps. paluIn order to analyze functional properties of the three proposed acetate assimilation routes, we first summarize their overall stoichiometries. For simplicity, we balance only carbon metabolites and reducing equivalents. In addition, we assume in these net balances that electrons carried to ubiquinone via membrane-bound enzyme complexes such as succinate dehydrogenase will be shuttled to NADH via reverse electron flow (consuming proton motive force (pmf) ). StartiRps. palustris):i) glyoxylate cycle (Rba. sphaeroides/Rs. rubrum):ii) citramalate-cycle Rba. sphaeroides/Rs. rubrum):iii) ethylmalonyl-CoA-pathway . Consequently, the EMCoA pathway can still not serve as a redox sink in the overall stoichiometry. Again, this result follows when assuming that electrons carried to ubiquinone in intermediate steps of the pathway will be further conveyed to NADH via reverse electron flow. It is reasonable to take the electrons in the electron transport chain into account in the overall redox balance as they are neither consumed during cyclic photosynthesis nor do we assume that there are other external redox sinks such as oxygen .As starting point for simulating growth on acetate we used again scenario S2 as in the previous section but re-enabled (separately) the three proposed assimilation pathways .2 net release per substrate taken up (Table 2) during the reductive carboxylation of crotonyl-CoA with NADPH . Under physiological conditions, each reaction will have a limited maximal flux due to thermodynamic constraints. The exact k) reaction rates m1, ..., mk ∈ {1,..., q} are known, e.g. because their flux values Equation (1) and inequalites (2) usually define an underdetermined system and, hence, no flux can be calculated uniquely. However, additional constraints arise when some -(3). The corresponding optimization problem readsSome of the unknown rates might then become calculable. For calculating uniquely determined reaction rates or for identifying feasible ranges of the fluxes we will use is , an appu optimizations (u = number of unknown fluxes) is the physiologically feasible flux range for the unknown reactions. Moreover, if the computed minimal and maximal rate of a reaction coincide, ri,min = ri,max, the reaction rate follows to be uniquely determinedThe information we get from the 2·Note that FVA as described above does not make any assumption about biological objectives, in contrast to flux balance analysis . The objCellNetAnalyzer [http://www.mpi-magdeburg.mpg.de/projects/cna/cna.html and the network project files will be made available on this site (within the CNA model repository). CNA has its own FVA functionality and uses the glpk solver for flux optimization.All computations presented in this study were performed with our software Analyzer , a MATLAConceived and planned the study: SK. Carried out the study: OH, SK. Interpretation of the results: OH, HG, SK. All authors read and approved the final manuscript.Network model of PNSB. Full definition of the stoichiometric network model.Click here for fileNetwork model of PNSB in SBML format. Network model of PNSB in SBML format.Click here for file


Bacillus anthracis, Francisella tularensis and Yersinia pestis. Nine metabolic enzymes- belonging to the coenzyme A, folate, phosphatidyl-ethanolamine and nucleic acid pathways common to all strains across the three distinct genera were identified as targets. Antimicrobial agents against some of these enzymes are available. Thus, a combination of cross species-specific antibiotics and common antimicrobials against shared targets may represent a useful combinatorial therapeutic approach against all Category A bioterrorism agents.The 2001 anthrax mail attacks in the United States demonstrated the potential threat of bioterrorism, hence driving the need to develop sophisticated treatment and diagnostic protocols to counter biological warfare. Here, by performing flux balance analyses on the fully-annotated metabolic networks of multiple, whole genome-sequenced bacterial strains, we have identified a large number of metabolic enzymes as potential drug targets for each of the three Category A-designated bioterrorism agents including  Bacillus anthracis (anthrax), Yersinia pestis (bubonic plague), Francisella tularensis (tularemia), and the botulism toxin of Clostridium botulinumBacterial Category A agents include Bacillus anthracis, the Gram-positive agent causative of anthrax is naturally found in animals and in soil worldwide. They can survive both under aerobic and anaerobic conditions and can form heat resistant spores that make it an ideal agent for biological warfare. B. anthracis exhibits high genetic homogeneity, as determined by partial genome DNA microarray hybridization experiments and by genome sequencing. However, using variable number tandem repeats (VNTR) and multiple locus VNTR analyses researchers have identified genomic variation among diverse geographical isolates of B. anthracis. Based on historical, DNA analysis, SNP variations, molecular signatures and microbiological methods, they have been grouped into A, B, and C clusters and sub-lineages in each of the major clusters  Francisella tularensis, a Gram negative, facultative, intracellular mammalian pathogen, is a causative agent of zoonotic infections F. tularensis can be grouped into four distinct subspecies; F. tularensis sub spp. tularensis, F. tularensis sub spp holartica, and F. tularensis sub spp mediasiatica, and F. tularensis spp novicida. F. tularensis (Biovar type A) is highly virulent and occur predominantly in North America. F. tularensis sub spp holarctica (Biovar type B) is the primary cause of tularemia in Europe and is relatively non-pathogenic to humans F. tularensis sub spp novicida, there is no systematic identification of essential genes as targets for drug discovery among this group of bacteria F. tularensis sub spp holarctica emphasizes the need for newer targets and drug identification. There is also an increased effort for human vaccine development, as the current F. tularensis sub spp holarctica LVS (Live Vaccine Strain) strain is ineffective in certain populations.Yersinia pestis, the causative agent of the plague, is a Gram-negative enteric bacterium th century. Y. pestis is significantly diverse and is divided into three major branches, Branch 0 (Microtus and Pestiodes isolates), Branch 1 , and Branch 2  et alY. pestis CO92 isolate. However, the sequence diversity among various Y. pestis geographical isolates is high, which is reflected in their metabolic capabilities and demonstrates the need for strain specific target identification. Despite the successful use of antibiotics such as streptomycin or gentamycin as primary therapeutic choice in the treatment of infection, doxycyline, ciprofloxacin or chloramphenicol is also administered as prophylactic drug of choice.S. aureus strains B. anthracis, F. tularensis, and Y. pestis.In the past few years, there has been a significant effort in genome sequencing and molecular diagnostics studies for diverse strains of the three Category A bioterrorism agents. Despite sequencing of diverse geographical isolates, there has been only very limited new target discovery and virtually no specific drug development. Identifying gene essentiality by experimental approaches either using transposon mutagenesis or RNA silencing is time consuming and expensive, and the results are strain-specific. In contrast, computational methods provide an alternate approach for the identification of single essential and synthetic lethal metabolic enzymes E. coliS. aureusE. coli and S. aureusB. anthracis, F. tularensis and Y. pestis strains for common target identification.Bacterial genome variations are manifested in the metabolic or physiological characteristics of a given organism. Identification of these variations defines unique biochemical capabilities that allow growth and survival in a specific ecological niche. However, recognizing common core metabolic capabilities allow enzymatic target identification for anti-infective discovery. Using this logic and computational approaches for B. anthracis and Y. pestis compared to F. tularensis, which is attributed to the size of the genome, number of ORFs, etc.  were also identified as essential in B. anthracis  were also identified as essential. Only two enzymes involved in the purine (guanosine) nucleotide biosynthesis (guanylate kinase Gmk) and thymidine nucleotide biosynthesis  were identified as essential for biomass production.Among vitamins, enzymes involved in the folate biosynthesis pathway, enzymes such as PabC DfrA, FolB, FolC, FolE and FolP were identified to be essential. Other enzymes involved in cofactors synthesis such as coenzyme A biosynthesis , pantothenate (Dfp) and E. coliN-acetyl-D-glucosamine biosynthesis, an essential precursor of peptidoglycan. A third UDP-glucose 4-epimerase , which is involved in galactose, amino sugar and nucleotide sugar metabolism, was also identified as essential enzyme in the cell wall biosynthesis. UDP-D-galactose is a building block for colonic acid and mycolyl-arabinogalactan-peptidoglycan complex biosynthesis. Phosphoglucosamine mutase (GlmM) involved in cell-wall peptidoglycan and LPS biosyntheses was determined to be essential. It is interesting to note that enzymes involved in fatty acid metabolism, specifically in β-oxidation  are essential for growth. This conservation implies that the β-oxidation of fatty acids has an indispensable function under certain physiological conditions. In fact, the fadNA-E operon encoding the β-oxidation catalyzing enzymes is induced at the onset of sporulation. This induction requires the yvbA protein involved in cannibalism by sporulating cells In lipid metabolism, enzymes involved in the glycerolipid (diglucosyldiacyl glycerol) biosynthesis (UgtP) that catalyzes the formation of mono-, di- and triglucosyldiacyl glycerol were identified as essential. Diglucosyldiacylglycerol is a predominant glycolipid used as a membrane anchor for lipoteichoic acid. A second essential enzyme, cytidylyl-transferase (CdsA), which is involved in CDP-diglyceride biosynthesis, a major component for phosphatidyl group of phospholipids was also identified as essential. Another key enzyme, phosphatidylserine decarboxylase (Psd) involved in phospholipid (phosphatidylethanolamine) biosynthesis was found to be essential. Phosphoethanolamine head groups of phosphatidylethanolamine are transferred and attached to the LPS core sugars and to periplasmic membrane-derived oligosaccharides. Among the enzymes involved in cell wall biosynthesis, phospho-N-acetylmuramoyl-pentapeptide-transferase (MraY) involved in peptidoglycan biosynthesis is essential, as in Francisella species are in the order of 3–5%, there is a significant variation in the number of unique enzymes and metabolic reactions among the F. tularensis sub species. The single essential enzymes for individual strains of the diverse isolates of F. tularensis are given in Although the genome wide sequence variations of B. anthracis, fewer enzymes in amino acid biosynthesis were identified as essential for growth in F. tularensis. These include methionine adenosyltransferase (MetK) involved in cysteine/methionine metabolism, which has been shown to be essential for the growth of E. coli K-12 gltX1) and L-glutaminyl-tRNA were determined as essential under the conditions tested  and tmK (thymidine) nucleotides biosynthesis was also identified as essential in all the Y. pestis genomes. Surprisingly, only two enzymes, phosphatidylserine decarboxylases (Psd) and CDP-diacylglycerol-serine O-phosphatidyltransferase (PssA) were determined as essential for growth.The enzymes identified as essential by computational approaches were in the cofactor pathways including folate , coenzyme A , riboflavin  (FMN) biosynthesis, pantothenate biosynthesis (Dfp) and nicotinate/nicotinamide biosynthesis (PpnK). Seven enzymes involved in the lipid A and peptidoglycan biosynthesis was identified . The specific reactions associated with these enzymes are given in Y. pestis. These enzymes may have evolved to play a specific role in metabolism in insect or human hosts under specific conditions. Finally, arabinose 5-phosphate isomerase (KdsD), which is involved in the synthesis of ribulose −5 phosphate that is necessary for nucleotides, was also identified as essential.Three enzymes in the carbohydrate metabolism, starch synthase (GlgA) involved in bacterial glycogen, ramnulokinase (RhaB) involved in pentose degradation, and L-xylulokinase (Lyx) involved in the breakdown of pentose sugars such as L-lyxose and L-xylulose were identified as essential for biomass and growth in http://tubic.tju.edu.cn/deg/) E. coliV. cholera, H. influenzae, S. pneumoniae, and others. Phosphatidyl serine decarboxylase (Psd), which is involved in the synthesis of phosphatidyl-ethanolamine was also found to be essential in other Gram-negative bacteria, including F. tularensis sub spp novicida, E. coli, and S. enterica , which has two distinct enzymatic activities in some bacteria in vivo it is only effective against Y. pestisB. anthracis and F. tularensis are fully and partially resistant against it, respectively S. aureus strains The development of antibiotics only against Category A bioterrorism agents may not be economically feasible. An alternative solution would be the development of combinatorial treatment protocols using current antibiotics that are used to treat common bacterial infections. A potential approach toward this goal is to combine the use of common antibiotics already used to treat The treatment and/or prevention of infections with Category A bioterrorism agents in case of an epidemic or deliberate outbreak remains challenging E. coliE. coliS. aureusThe identified nine common essential enzymes in the three Category A organisms are shared among several metabolic pathways, but three of them are clustered in the dihydrofolate and tetrahydrofolate biosynthesis pathway that provide the only target (FolC: dihydrofolate synthase) that is affected by existing antimicrobials . The othB. anthracis, Y. pestis, or F. tularensis represents on such combinatorial therapy.Of note, these common essential enzymes can only be viewed as potential targets for at least two reasons. First, they should display sufficient structural similarity in all strains, especially in their catalytic sites, so a common inhibitor can potentially be developed against them. Secondly, their human orthologs should have sufficient dissimilarity and/or not be essential in order to avoid potential toxicity B. anthracis, seven F. tularemia, and four Y. pestis strains. These genomes, which were fully sequenced and analyzed by various research groups provided input data on which we performed the annotations and metabolic reconstruction using the ERGO bioinformatics suite For comparative metabolic analyses we included eight http://www.genome.jp/kegg/ ligand.html) to identify all the metabolic reactions in the genomes. Briefly, ORF callings, which were originally (by the sequencing organizations) performed by using either GLIMMER or CRICITA, were imported into the ERGO schema of annotations and pathway analysis. The protein similarities were computed by BLAST ‘all against all’ with over 8.1 million protein sequences being present in the non-redundant ERGO database for over 2,232 genomes We used the updated KEGG ligand/reaction database (http://www.genome.jp/kegg/ligand.html). The metabolic reactions were classified into three categories: cellular (reactions in the cytoplasm), transport reactions (involving both the intra and extracellular metabolites), and exchange reactions (either uptake or excretion metabolites) similar to our recent studies in S. aureusB. anthracis, F. tularensis, or Y. pestis were considered “unlikely reactions” and were excluded from the flux balance analysis (FBA) computations. Individual transport reactions were added from the ERGO pathway collection. All the reactions and their corresponding KEGG identifiers (reaction IDs and compound IDs) were used in the FBA computations The associated biochemical reactions for each of the enzymes were selected from the KEGG reaction database  for generating network diagrams. We used open source software Gephi (http://gephi.org/) to arrange the nodes and used modified perl/python scripts for data analysis and extraction to create svg format files.For essentiality test, we used the mapping between genes and EC numbers. A gene may be mapped to multiple EC numbers  and an EC number may be mapped to multiple genes . Accordingly, gene deletion may disable multiple reactions associated with multiple EC numbers or no reaction (when multiple genes are associated with the reaction). We used Omnigraffle . In addition, we remove the metabolites that belong to the biomass components. The essential genes were compared to the experimentally identified essentials using the DEG database Table S1Metabolic essential enzymes and their gene identifiers of the individual strains of Category A pathogens.(XLS)Click here for additional data file.


Archaea and Eubacteria. Our results provide evidence for limits to the contingency of evolution.There is an acute need for better tools to extract knowledge from the growing flood of sequence data. For example, thousands of complete genomes have been sequenced, and their metabolic networks inferred. Such data should enable a better understanding of evolution. However, most existing network analysis methods are based on pair-wise comparisons, and these do not scale to thousands of genomes. Here we propose the use of weighted graphs as a data structure to enable large-scale phylogenetic analysis of networks. We have developed three types of weighted graph for enzymes: taxonomic (these summarize phylogenetic importance), isoenzymatic (these summarize enzymatic variety/redundancy), and sequence-similarity (these summarize sequence conservation); and we applied these types of weighted graph to survey prokaryotic metabolism. To demonstrate the utility of this approach we have compared and contrasted the large-scale evolution of metabolism in  Biology is undergoing a revolution due to the remarkable increase in the availability of DNA sequence data. This data is replete with biological knowledge. An increasingly important scientific challenge is therefore how best to extract this knowledge. This depends on the development of better data-structures and algorithms.One area that has been transformed by the sequencing revolution is the area of prokaryotic metabolism. The complete genome sequences of over a thousand prokaryotic species are now known. These have been used to infer the compliment of enzymes available to these prokaryotic species, and hence their full metabolic competences — though of course caution must be used in interpreting such predictions.nodes connected by edges. A number of different ways have been used to represent metabolic pathways using graphs  to form weighted graphs for the large-scale analysis of metabolic pathways.taxonomic. Such graphs summarize the phylogenetic importance of enzymes: enzymes with high weights occur in many species, and those with low weights rarely occur.The first approach is to define the enzyme weights to be the proportion of genome instantiations where a gene for the enzyme is found. We call this type of weighted graph isoenzymatic. Such graphs summarize the enzymatic variety/redundancy of metabolism: a high number indicates more isoenzymes.The second approach is to define the enzyme weights to be the average number of protein sequences of that enzyme in a genome. We call these weighted graphs sequence similarity weighted graphs. Such graphs summarize the sequence conservation of metabolism: a high number indicates high sequence conservation.The third approach is to define the enzyme weights to be the average sequence similarity of that enzyme in the genome instantiations. These are termed To the best of our knowledge weighted graphs have not been used in any of these ways before.Archaea and the EubacteriaArchaea and the Eubacteria.We wished to test the utility of our weighted graphs for large-scale metabolic analysis. For this we selected the problem of investigating the diversity of prokaryotic metabolic pathways. Specifically we investigated the oldest and most fundamental split in the evolution of life, that between the two prokaryotic domains: Archaea Eubacteria divide. However, we hypothesize that this effect is insufficient to obscure the main signal from evolutionary descent.We recognize that because of gene transfer prokaryotic species/enzyme evolution does not have a pure tree topology (it is a directed acyclic graph). Genes have jumped between species, and across the Eubacteria and Archaea there is also the problem that Eubacteria genomes outnumber Archaea by an order of magnitude. It is unclear how much this imbalance is due to the fact that Eubacteria have been studied more , and how much it is due to there being more species of Eubacteria. These biases mean that we had to be careful how we used the sequenced genomes. We therefore decided to sample genomes uniformly across evolutionary space. By this we mean that if you envisage prokaryotic species as leaves of the tree of life with the branches evolutionary distance, then we will sample leaves uniformly distant from each other.Any conclusions that we draw regarding prokaryotic metabolism should be generally true for prokaryotic genomes. However, only a limited number of genomes have been sequenced. If these sequenced genomes were an unbiased sample from all existing sequenced and non-sequenced prokaryotic genomes, then one could argue that the sample is representative of the whole. But unfortunately this is not the case. (1) The sequenced genomes are very biased towards prokaryotic groups that are of special interest to humans , and also towards groups that are easy to cultivate in the lab. (2) When comparing http://www.genome.jp/kegg/http://www.genome.jp/kegg/) . This produced a graph with 2,365 enzymes with complete EC codes, and 43,627 metabolite edges .To generate our super-metabolic graph we selected the 192 pathways that occur in prokaryota from Kyoto Encyclopedia of Genes and Genomes (KEGG) Archaea and Eubacteria) species with complete genomes from this release of KEGG. This gave 108 Archaea species and 1,287 Eubacteria species.We selected all prokaryotic  to cluster species based on their 16S ribosomal RNA sequences similarities at 0.8 level in each domain. We obtained 15 clusters of Archaea and 114 clusters of Eubacteria species. The different number of clusters reflect the difference in sampling (and possibly a difference in genomic diversity). To fairly compare sampling from the two domains, we sampled the same number of genomes from both domains. To generate the sampling datasets: for Archaea we randomly chose one species from each cluster; for Eubacteria we first randomly chose 15 clusters, then from each cluster randomly chose one species. We repeated the sampling process 100 times uniformly from both domains to provide 200 datasets each containing 15 genomes. We argue that this procedure produces datasets sampled uniformly across evolutionary space.To sample genomes we first applied CD-HIT  For intra-domain correlations we included all enzymes that exist in at least two genomes in the selected data set. For the inter-domain correlations we examined all enzymes that have weights in either kingdom. We used Spearman's rank correlation to calculate correlations as it is robust. The correlations between datasets were calculated by using cor.test function in the R program, and values of pWe wished to investigate the correlation between weights in the metabolic graphs. We first deleted non-informative regions of the graph: 1,112 enzymes have zero taxonomic weight in all 200 sampled datasets.  if its mean weights are above a specified high threshold in both domains.Let pathways, and these pathways have proven useful in analysis. We therefore used pathway information from KEGG. Our construction of a weighted metabolic pathway Traditionally sub-parts of metabolism have been classified into different Because of limited availability of enzyme taxonomic data, nearly half of enzymes have zero weight in all sampled datasets. For analysis, we selected pathways that averagely contain at least 10 weighted enzymes in both domains. To examine the importance of each selected pathway to a domain, we calculated the ratio of specific (or ubiquitous) enzymes the pathway contains to the enzymes that averagely have non-zero weights in the pathway.We further analyzed the weighted metabolic graphs using graph compression techniques. The model we applied is the extended version of the work, proposed by Toivonen et al A graph is compressed iteratively through executing a series of operations. There are two basic operations: individual edge removal and node-pair merge. In the edge deletion operation, a single edge is removed, and if the removal leaves an edge endpoint isolated then the endpoint is removed as well. In the merge operation, a pair of nodes are merged into a new super-node, and the new super-node links with the neighbors of the merged nodes, and the weights on the super-edges re-assigned. Whether the new super-node links with their neighbors or not depends on whether the omission of the super-edge produces smaller error with respect to the extra saved space. In each iteration the effect of two operations are computed, and the one that produces a more compressed graph with smaller error is executed. An illustrated example is in Compression may cause four types of error: a) a superedge may represent edges that do not exist in the original graph; b) edges in the original graph may not be represented by any superedge; c) nodes in the original graph may not be preserved in the compressed graph; and d) edge weights may be changed. The quality of the compressed graph is measured by computing the distance between the original graph and the decompressed graph of the compressed graph with respect to node weights, that is,The weights on the superedges are set to minimize the distance between the original and the compressed graphs. However, the minimization problem is computational hard. Since the distance metric  satisfieThe goal of weighted graph compression is to produce a compressed graph Archaea and Eubacteria domains. We also calculated the similarity between the original and the compressed pathways. Suppose for the pathway To investigate the conservation of evolution, we computed the average enzyme weights in the compressed graphs with respect to different compression ratios, and the average enzyme weights in the compressed part that exist in both Eubacteria and Archaea. In order to better illustrate the differences of weights intuitively we have adjusted the thickness of nodes according to their node weights. We selected glycolysis because it is the proto-typical pathway, and because it is found in most prokaryota. Yet even in glycolysis large differences in weight are observed.To illustrate the result of processing of the sampled metabolic networks into weighted graphs, Eubacteria and Archaea, e.g. pyruvate kinase (EC 2.7.1.40); while other enzymes occur more frequently in one domain or the other, e.g. pyruvate synthase (EC 1.2.7.1) occurs much more frequently in Archaea than Eubacteria; other enzymes are uncommon in both domains, e.g. PEP carboxylase (EC 4.1.1.32).The taxonomic weights are in Eubacteria and Archaea. Enolase (EC 4.2.1.11) has relatively high sequence similarity in both Eubacteria and Archaea, while Pyruvate synthase (EC 1.2.7.1) has relatively low sequence similarity. In contrast PEP carboxylase (EC 4.1.1.32) has a high sequence similarity in Archaea and low similarity in Eubacteria. Such differences do not seem to be explainable by technical problems with alignment or sampling.The sequence similarity weights are in Eubacteria and Archaea. PEP carboxylase (EC 4.1.1.32) has the lowest isoenzymatic weights in both Eubacteria and Archaea, while Pyruvate synthase (EC 1.2.7.1) has the highest weights. The most notable difference between Eubacteria and Archaea is Acetate—CoA ligase (EC 6.2.1.1).The isoenzymatic weights are in Archaea and Eubacteria there is a statistically significant and moderate negative correlation between sequence-similarity and isoenzymatic weights  between taxonomic and isoenzymatic weights . Their significance test results  is highly significant . The correlation of 0.19 in isoenzymatic weights between domains is also significant but at a much lower level . There is however no significant correlation . The significance test results  occurs in every genome examined.  The commonest enzyme that isn't associated directly with macromolecule processing is ribose-phosphate diphosphokinase (EC 2.7.6.1). Other extremely ubiquitous enzymes are phosphoglycerate kinase (EC 2.7.2.3) and glycine hydroxymethyl-transferase (EC 2.1.2.1).Eubacteria. However, others are more surprising, such as the comparatively frequent occurrence of L-lactate dehydrogenase (EC 1.1.1.27) in Eubacteria, but not Archaea. Examples of enzymes that occur much more frequently in Archaea are mevalonate kinase (EC 2.7.1.36), and nicotinamide-nucleotide adenylyltransferase (EC 2.7.7.1).Some enzymes occur much more frequently in one domain than the other. Some of these enzymes are expected, for example UDP-N-acetylmuramate dehydrogenase (EC 1.1.1.158) is involved in peptoglycan metabolism and is much more common in Eubacteria Archaea divide, and we may speculate they are perhaps the oldest of all pathways. The pathways that contain the highest ratio of specific enzymes are: terpenoid backbone biosynthesis, and pantothenate and Co-A biosynthesis. It is also noteworthy that both glycolysis/gluconeogenesis has quite a high ratio of specific enzymes.To examine the importance of each pathway to the domain we calculated the ratio of special enzymes (e.g. specific or ubiquitous enzymes) to the size of enzymes with non-zero weights in each pathway . The patEubacteria and Archaea.To further investigate the conservation of evolution we applied weighted graph compression to abstract the metabolic networks into smaller ones utilizing taxonomic enzyme weights. The idea of using compression is that with increased compression more and more nodes and edges with lower weights are removed; therefore the compressed graphs may also be informative about the common ancestor of Archaea in the dashed-line in Eubacteria in We calculated the average taxonomic enzyme weight in the compressed graphs as a function of compression ratio, and plotted the results of We further investigated how similar the compressed pathways are to the original ones. The correlations of compression results of pathways across domains are significant and very strong positive in three types of weights .We ranked pathways based on the descending similarity between the original and the compressed graphs . The patThe weighted graphs, in By comparing different types of weighted graphs we can also get some useful understandings of the correlation among sequence-similarity weights, isoenzymatic weights and taxonomic weights. For example, when an enzyme is common in a domain it is more likely to have a higher number of isoenzymes .Another useful analysis is about how many specific or ubiquitous enzymes each pathway contains . If a paWonderful LifeOne of the most fundamental questions in evolutionary biology is to what extent the paths that evolution has taken are stochastic, and to what extent they are determined by constraints imposed by the environment and biochemistry. Eminent evolutionary biologists have taken radically different views on this question of stochasticity. Stephen Jay Gould in many essays, and most notably in his book Archaea and Eubacteria.The central problem with investigating this question is that it is generally impossible to repeat the experiment — evolution. However, it is possible to get some understanding of the stochasticity of the problem by looking at cases where evolution started from the same starting points, i.e. the Archaea and Eubacteria is highly significant . This means that knowing the phylogenetic importance of an enzyme in one domain is informative about its importance in another domain. Our interpretation of this result is that as the process of evolution proceeded and new species of prokaryota were formed, evolution was constrained to use enzymes similarly in both domains. We argue that these results are evidence for limits to the contingency of evolution, however it is difficult to quantify the extent of contingency.Our most relevant results regarding this question are A similar but weaker pattern is seen for isoenzymatic weights. However, there is no correlation in the case of sequence-similarity weights. Our interpretation of this is that most sequence changes are neutral and not selective The correlation of compression results of pathways between domains  is statiWe have demonstrated the use of weighted graphs as a way of efficiently analyzing large amounts of genomic information about metabolic networks. Similar weighted graphs could also be applied to other types of network: regulatory genetic, protein interaction, etc. The definitions of taxonomic and sequence similarity weighted graphs are directly applicable to other regulatory genetic and protein interaction graphs, and the definition of isoenzymatic weighted graphs could be adapted to be isofunctional. This would open up an interesting range of types of analysis for application to large numbers of genomes.Table S1The list of removed compounds taken from the article “Using a Logical Model to Predict the Growth of Yeast,” authored by K. E. Whelan and R. D. King, published in BMC Bioinformatics in 2008.(PDF)Click here for additional data file.


Network reconstructions at the cell level are a major development in Systems Biology. However, we are far from fully exploiting its potentialities. Often, the incremental complexity of the pursued systems overrides experimental capabilities, or increasingly sophisticated protocols are underutilized to merely refine confidence levels of already established interactions. For metabolic networks, the currently employed confidence scoring system rates reactions discretely according to nested categories of experimental evidence or model-based likelihood.Escherichia coli. The model is adjusted to the observations to derive connection probabilities between individual metabolite-reaction pairs and, after validation, to assess the reliability of each reaction in probabilistic terms. This network-based scoring system uncovers very specific reactions that could be functionally or evolutionary important, identifies prominent experimental targets, and enables further confirmation of modeling results.Here, we propose a complementary network-based scoring system that exploits the statistical regularities of a metabolic network as a bipartite graph. As an illustration, we apply it to the metabolism of We foresee a wide range of potential applications at different sub-cellular or supra-cellular levels of biological interactions given the natural bipartivity of many biological networks. A crucial milestone to understand and control cellular behavior is the building up of reliable reconstructions of the interactions spanning different functional levels. Such reconstructions find a natural abstraction in the form of complex networks -3, whereAt present, the information for complex network representations of cellular systems comes primarily from web-based databases, oftentimes manually curated with information from multiple sources, like annotations from the literature or new experiments . It is cIn this scenario, prediction of interactions in probabilistic terms is possible on the basis of the structure of the network alone and could serve to better characterize network-based descriptions of biological systems and as a guide for new experiments. In particular, the likelihood of biochemical reactions in cellular metabolisms can be assessed in terms of a scoring system that assigns a probability of occurrence to every reaction. This claims for a new interpretation, since canonically a chemical reaction either exists or does not. For network analysts, scoring a biochemical process in terms of its likelihood is a computational challenge. Starting from the assessment of individual links, as it has been done for instance for protein-protein interaction networks ,17, the E. coli. We introduce a link prediction method that exploits the complex hierarchical structure and the statistical regularities of metabolic networks [Here, we propose a computational network-based reaction-scoring system and, subsequently, apply it to the metabolism of networks ,23 and tnetworks ,25. Our networks -28 betwenetworks . HoweverBeyond experimental evidence, it is possible to assess the likelihood of reactions in genome-scale metabolic reconstructions using theoretical models. Given an experimentally derived metabolic reconstruction, a score can be computed for each reaction on the basis of a suitable stochastic network-based model, as we propose in the next section. In the context of bipartite network representations ,25, the m has a probability mr pof being associated to a reaction r. Once the connection probabilities between metabolites and reactions are estimated from the model, and assuming their mutual independence, the probability that a certain combination ν of metabolites co-occur in a reaction r isTo define the network-based scores in quantitative terms, we interpret that a reaction is equivalent to the univocal combination of its associated metabolites, and that every metabolite m corresponds to metabolites in the predefined set ν and m' to those not included. The average number of co-occurrences can be calculated as the sum over all reactionswhere the subindex ν nthat the model associates to its particular combination of metabolites ν. Defined in this way, these scores break the degeneracy of reactions with identical experimental evidence.A network-based reaction score can then be defined as the average number of occurrences In the following, we introduce and discuss a stochastic network-based model to estimate the connection probabilities between metabolites and reactions. Taking advantage of their natural bipartite nature, we consider network representations where metabolites and reactions appear as two different classes of nodes, and metabolites are connected by edges to the reactions they participate in. We consider the simplest unweighted undirected representation, where substrates and products are not differentiated. See Figure mr pbetween metabolites and reactions. Network-based models are usually defined in terms of connection rules between the nodes. These laws are usually stated independently of observed systems to produce simulated networks that summarize their topological structure. Notice that here, in contrast, we compute the set of connection probabilities that has the maximum likelihood to reproduce the observed patterns in empirical metabolic networks, so we are solving the inverse problem.Previous works have shown that the complex organization of metabolic networks displays characteristic features shared by other complex networks: short topological diameter , steady M metabolites and R reactions . Our results are based on intensive numerical simulations that average a large number of samples in the stationary state when changes in the form of the dendrogram do not modify the likelihood function beyond fluctuations.Our first step is to assume a metric space underlying the structure of the empirical metabolic network. To this end, we fit to it a hierarchical random graph , once remr dis associated to a metabolite-reaction pair, we correct for heterogeneity in the degrees of metabolites. We compute estimated connection probabilities mr pbetween all possible combinations metabolite-reaction asOnce a distance m kis the degree of the metabolite and μ = 1/R ensures that network realizations with these connection probabilities have the same number of links as the observed network. From this equation, it is clear that the closer a pair is, the higher will be its connection probability. A Tree Distance Bipartite (TDB) score for every specific reaction can then be computed by applying Eq. (1) and Eq. (2).where iAF1260 version of the K12 MG1655 strain of E. coli [rk, follows a nearly homogeneous distribution with mean <r k> = 4.82 and mode 5. In contrast, the number m kof reactions in which a metabolite participates displays a heterogeneous degree distribution very close to a scale-free with m k> = 7.30 .As an application of the methodology, we analyzed the  E. coli  provided E. coli ,34. Frommr pwere validated using standard tools in medical decision making and signal-detection theory [The TDB probabilities n theory , and comn theory ,36,37 , the TDB model has more discriminatory power over a wide range of values as compared to other alternatives.To calculate the ROC curves we ranked the TDB probabilities from highest to lowest. We took every value in the rank as a threshold, and for each threshold we computed the fraction of true connections and the fraction of false connections above the threshold, the True Positive Rate (TPR) and the False Positive Rate (FPR) respectively, understanding that a true connection is an observed link in the empirical network and a false connection is an absent link. When representing the TPR in front of the FPR, a completely random guess would give a point along the diagonal line and points above the diagonal represent improved classification results. In relation to this, the area under the ROC curve (AUC) is a scalar measure of accuracy . In the The second test helps to evaluate robustness against noise. Links were removed from the empirical network in order to see whether our algorithm was able to distinguish those from non-existing links. After removing a subset of links uniformly at random in the original network, a new set of connection probabilities was calculated on the basis of the remaining part of the network. The new probabilities associated to the removed connections were compared one by one to that of non-existing links. This statistic ranges from 0.5 to 1 and indicates how much better our method performs as compared to a by chance baseline accuracy of 0.5. We calculated this accuracy statistic, that is shown in Figure inorganic diphosphatase, which hydrolyzes the pyrophosphate anion into inorganic phosphate; the hydrolase of ATP into ADP, which appears in the Nucleotides Salvage pathway and as a reaction for ATP maintenance requirement according to flux balance analysis, and mediates also the uptake of phosphate; and the ATP synthase in the Oxidative Phosphorylation pathway that takes four protons in periplasm to produce one ATP in cytosol from ADP. These non-specific reactions are at the end of catabolic chains and are likely to be shared by many different organisms. For instance, we checked that, according to the BiGG database [S. cerevisiae iMM904) and that inorganic diphosphatase and ATP synthase appear in human metabolism as well, where the hydrolase of ATP into ADP mediates the active transport of different metabolites across compartments. Even very simple organisms like Mycoplasma pneumoniae [inorganic diphosphatase reaction and the hydrolase of ATP into ADP in their metabolism. In [inorganic diphosphatase is reported in 101 out of 107 organisms spanning a wide taxonomical range, and the hydrolase of ATP into ADP is found into 25 of those. At the other extreme of the spectrum, low values of TDB Sscores are associated with very specific reactions involving rare metabolites, in the sense that they enter a small number of reactions, or with unlikely reactions, like those involving a large number of metabolites. As an example, the thiazole phosphate synthesis is the largest reaction in the database involving twelve metabolites and has the lowest TDB Sscore, seventeen orders of magnitude below the maximum. In between, TDB Sscores adopt a broad distribution of continuous values.In both tests, the TDB model outperforms all other strategies. Furthermore, TDB probabilities are well calibrated, meaning that the distributional forecasts and the observations are statistically consistent  is annotated with a confidence score assessing its level of experimental evidence. These values are discrete and range from 4 at the top, when there is direct biochemical proof, to 0 at the bottom, if the reaction is included with no experimental evidence but only because it improves modeling results. In between, values of 3 correspond to genomic evidence, level 2 refers to sequence homology evidence, and 1 stands for physiological evidence. This confidence scoring system presents some shortcomings, one being the degeneracy implicit in the use of only five discrete values for lists of hundreds or thousands of reactions, another the fact that different categories are not disjoint but nested, meaning that one backs the other. An additional worth remarking feature concerns the mean degree of the metabolites participating the reactions in each scoring level. Quite unexpectedly, we found a strong bias as this measure monotonously increases when decreasing rank from 4 to 1. More specifically, the average degree of metabolites entering into reactions with high level of confidence score is, on average, smaller than the average degree of metabolites associated to reactions with low level of confidence score.FMNH2-dependent monooxygenase reactions in the Inorganic Ion Transport pathway, the Pyridoxine 5'-phosphate synthase reaction in the Cofactor and Prosthetic Group Biosynthesis pathway, or the Taurine dioxygenase reaction in the Alternate Carbon metabolism. Conversely, a weak experimental evidence, scores 2 or 1 in the database, but a high value of the TDB Sscore, qualifies the reaction as a good target for further experimental verification in standard conditions. Many examples are found within the transport subsystems, like reactions of transport via ABC system (iron (II) and (III), phosphatidylglycerol, phosphatidate). If the TDB Sscore is low, the reaction could be difficult to be observed experimentally except for very specific environments. Finally, high TDB Sscores for reactions that where required for modeling, score 0 in the database, denote consistency between our model and steady-state flux optimization solutions. It is worth remarking that these reactions involve more than one carrier metabolite and stand out as potential experimental targets in standard conditions. However, a variety of reactions manifest discrepancies between both model-based likelihoods. More specifically, we differentiate two situations. The first does not entail contradiction and refers to very specific reactions with low TDB Sscores involving rare metabolites that, on the other hand, seem to be essential for the viability of the bacteria according to flux balance analysis. This points out to potential experimental targets in non-standard conditions. Reactions in the subsystem of Cofactor and Prosthetic Group Biosynthesis are, for instance, in this category. In contrast, the second situation involves reactions like those with the highest number of participating metabolites, which according to confidence scores in the database were included in the reconstruction on the basis of modeling reasons while our methodology predicts very low scores. For them, we believe that low TDB Sscores point indeed to insufficient ne detail resolution in the database and we are suspicious that new experiments may show a split of the high degree reactions into a set of coupled lower degree ones.It is not completely surprising, as the just mentioned test seems to suggest, that absolute indices based on the architecture of the empirical network may go differently as compared to qualitative indicators assigned from updated experimental information. We, thus, aim at complementing the potentialities of both scoring systems by cross-comparing them. In this respect, first we look for reactions with strong experimental evidence  that at the same time score low in the TDB system. Those correspond to very specific reactions that could be functionally or evolutionary important. Examples are the five CMB Sscore of a reaction represents its probability of occurrence according to the configuration model and we use this value to compute the relative score as the ratio ∑ = TDB S/CMB S points to the presence of tree distance correlations (anticorrelations) in the bipartite network, which are absent in the random case. In other words, a ratio higher  than one for a certain reaction indicates that its metabolites have a tendency to aggregate (avoid each other) as compared to the random case.Along with absolute scores, we also analyzed relative scores defined on the basis of the Configuration Model for bipartite networks (CMB) ,36,37 .The ranking of relative scores is shown in the bottom graph of Figure Relative scores conform better than absolute scores to the idea of pathways as functional modules, since they accentuate the e ect of tree distances that we expect to be related with the modular organization of the network. This topic will be explored in depth in future work.The computational network-based TDB scoring system is able to assess, in probabilistic terms, the likelihood of reactions in metabolic reconstructions solely on the basis of the structure of the bipartite interactions between metabolites and reactions. It relies on a link prediction method adjusted to the observations that exploits the statistical regularities of the empirical network to estimate connection probabilities, that afterwards are integrated at the level of reactions. As a result, our TDB scoring system is able to break the degeneracy of currently employed scores that only use a discrete number of integers to label different levels of empirical evidence or model-based likelihood. We stress the main advantages of our procedure. First, our system permits to single out those reactions, well confirmed experimentally, that turn out to be highly specific as a potential signature of functional or evolutionary impact. Conversely, our analysis can help experimentalists to choose, among their potential targets, those reactions that appear, according to our scheme, more probable as compared to metabolic processes more prone to operate under non-standard conditions. In addition, our scoring system may provide information for unranked databases, and can be contrasted with other model-based alternatives such as steady state flux optimization solutions. When compared with a random null model that just accounts for heterogeneity in the number of connections per element, relative scores detect and quantify the tendency of groups of metabolites to aggregate or disaggregate. These distance-based correlations or anticorrelations in the underlying tree metric space raises a question worth exploring in the future in relation to functional modules.In a broader context, many biological interactions find a natural representation in the form of bipartite networks. The ubiquity of these bipartite structures in cellular networks foretells a wide range of potential applications of the present methodology, from the estimation of gene-reaction associations in metabolic network reconstructions to the assessment of codon-gene association probabilities and of protein complexes.M + R - 1 internal nodes at its bifurcation points and M + R leaves corresponding to the nodes of the metabolic bipartite network, M metabolites and its R reactions. Each internal node t has an associated tree probability t ρthat we transform into a distance t d= 1 - tρ. Each pair metabolite-reaction having as lowest common ancestor t is then separated by a distance mr d= td. Given a dendrogram, the internal probabilities t ρare only dependent on the structure of the empirical bipartite network and can be calculated as the fraction of observed connections between leaves in each branch of the internal node over the total possible. To find the dendrogram that best fits the real data in terms of likelihood, we assume that all trees are a priori equally probable and explore the space of possibilities using a Markov chain Monte Carlo method [We adjust a binary tree to the observed data. The tree has o method  combinedo method .tρ, and taking into account the underlying tree, the likelihood function becomesIn statistical inference, the likelihood ℒ of a statistical model for a certain set of observed data is the probability that the model is a correct explanation, and allows us to estimate its unknown parameters. For a set of connection probabilities t Estands for the number of actual edges in the empirical bigraph, in our case those that connect metabolites and reactions in the bipartite graph with t as their lowest common ancestor in the tree. The variable t εcorresponds to the total possible number of such edges given reactions and metabolites in the different branches of the common ancestor t, discounting internal combinations. In the unipartite case, t ε= tRtL, being t Land t Rthe number of leaves in the left and right subtrees rooted at t. In our scheme for bipartite networks, t ε= tmRtr L+ trRtmL, counting possible combinations between metabolite leaves in the left subtree and reaction leaves in the right subtrees and vice versa. Then, t ρ= tE/t εmaximize ℒ.As for unipartite graphs, the variable logℒ) .Starting from a random configuration, we move among all possible sets of dendrograms by performing random swaps between one of the branches of a randomly chosen internal node and the alternative branch at its father level. This exploration is appropriate because it is ergodic and fulfils detailed balance. The likelihood of the new dendrogram produced in this way is computed and the dendrogram is accepted or rejected according to the standard Metropolis-Hastings rule : the tra3 dendrograms at regular intervals to produce an average measure of t ρand so of mr ρfor each possible metabolite-reaction pair. This model, the Hierarchical Random Bipartite Graph (HRBG), is a generalization for bipartite networks of the model introduced in [mr d(mr d= 1 - mrρ) for heterogeneity in the degrees of metabolites. We renormalize the distances according to Eq. (3) to produce the connection probabilities mr pthat we use in the construction of the probabilistic reaction scores.After a transient period when ℒ reaches its equilibrium value  the system reaches a stationary state where we sample over 10duced in . As explR, a certain number of metabolites M, and their degree distributions P(rk) and P (mk), which should fulfill the requirement 〈rk〉 R = 〈mk〉 M, where 〈rk〉 is the average number of metabolites in the reactions and 〈mk〉 is the average number of reactions in which metabolites participate. Metabolites and reactions are partitioned into two different classes and each element in each class is assigned an expected degree from the corresponding distribution, which is attached in the form of stubs. Two stubs, one in each partition, are selected at random and the link between the metabolite and the reaction is created avoiding multiple connections. For the CMB model, r k≈ 〈rk〉, it becomesThe Configuration Model for bipartite networks ,36,37  is iAF1260 version of the K12 MG1655 strain of E. coli [mn2, ca2, na1, ag, and cl) because they do not enter in any reaction involving chemical transformation. See Additional File The  E. coli  provided E. coli ,34 comprAll authors contributed equally to this work. Both authors have read and approved the final manuscript.Supporting figures and text for E. coli metabolism bipartite network representation and further validation of the model.Click here for fileDatabase with reaction probability scores for E. coli metabolism and bipartite network representation in edge list format.Click here for file


The world's oceans are home to a diverse array of microbial life whose metabolic activity helps to drive the earth's biogeochemical cycles. Metagenomic analysis has revolutionized our access to these communities, providing a system-scale perspective of microbial community interactions. However, while metagenome sequencing can provide useful estimates of the relative change in abundance of specific genes and taxa between environments or over time, this does not investigate the relative changes in the production or consumption of different metabolites.We propose a methodology, Predicted Relative Metabolic Turnover (PRMT) that defines and enables exploration of metabolite-space inferred from the metagenome. Our analysis of metagenomic data from a time-series study in the Western English Channel demonstrated considerable correlations between predicted relative metabolic turnover and seasonal changes in abundance of measured environmental parameters as well as with observed seasonal changes in bacterial population structure.Gammaproteobactaria, Plantcomycetes, and Betaproteobacteria, chitin degradation to Actinomycetes, and potential small molecule biosynthesis pathways for Lentisphaerae, Chlamydiae, and Crenarchaeota. The PRMT method can be applied as a general tool for the analysis of additional metagenomic or transcriptomic datasets.The PRMT method was successfully applied to metagenomic data to explore the Western English Channel microbial metabalome to generate specific, biologically testable hypotheses. Generated hypotheses linked organic phosphate utilization to  Environmental parameter data from the WCO have been continuously monitored for over a century. More recently, microbial metagenomic data collected from this site have shown that the abundance and relative composition of genes and taxa change over time, demonstrating seasonal structure and predictable community responses to environmental parameters .The PRMT-scores for phosphonate compound, 3-Phosphonopyruvate, had strong correlations with PRMT-scores for COphonates . Anotherphonates . MeasureChitin catabolism: The highly insoluble, nitrogen-containing compound chitin is the most abundant polymer in the ocean [he ocean -43. Yet,he ocean . Marine he ocean -48. TherThese reactions were all represented in the Western English Channel metagenomes. In the KEGG metabolic pathways, Fructose-6P metabolism leads to KEGG pathways for Glycolysis/gluconeogenesis (map00010) and Fructose and mannose metabolism (map00051), where both acetate and ammonia are generated.When considering PRMT-scores for the metabolites on the pathway for chitin degradation Figure , a patte2, Iron, orthophosphate, nitrate, and chlorophyll with marine primary production. Specific, testable, biological hypotheses regarding the utilization of organic phosphorus and chitin were made, some of which are currently being actively investigated. The predictions made by PRMT are consistent with the hypothesis that bacterial population diversity is linked to the metabolic capacity of the community. While we have restricted our analysis to the metagenome, PRMT calculations are equally applicable to metatranscriptomic data. Ongoing environmental monitoring projects such as the Global Ocean Survey, TARA Oceans, Hawaiian Ocean Time Series, Bermudan Ocean Time Series, the Long Term Ecological Research sites, NEON, and the extended application of the Earth Microbiome Project http://www.earthmicrobiome.org are generating vast amounts of metagenomic and experimental metadata that can readily be investigated by further PRMT analyses.We have presented a novel computational approach, Predictive Relative Metabolic Turnover (PRMT), for making predictions of the relative change in the production or consumption of a metabolite by a microbial community. The set of all PRMT-scores for all the metabolites predicted to be present in an environmental metabolome provides a system-scale representation of the environmental metabolome derived from metagenomic sequence analysis that changes in response to fluctuations in the structure of its bacterial community. The approach was supported by comparing predicted relative turnover of metabolites to relative abundance of the biological measurements for those same metabolites. PRMT also provided the expected relationships between COPRMT: Predicted Relative Metabolomic Turnover; EMM: Environmental Metabolomic Matrix; EAC: Enzyme Activity Count; nEAC: Normalized Enzyme Activity Count; TOC: Total Organic Carbon; TON: Total Organic Nitrogen; SRP: Soluble Reactive/Phosphate; PCC: Pearson Correlation Coefficient.The authors declare that they have no competing interests.Conceived and designed the experiments: PEL, JAG. Performed the experiments: JAG, DF, PEL. Analyzed the data: PEL, JM, JQ, JAG. Contributed reagents/materials/analysis tools: FRC, FM, JAG. Wrote the paper: PEL, FRC, JAG, KPK, CSH, JM, JQ, DF. All authors read and approved the final manuscriptTable S1. This file contains a list of all enzymatic reactions in the predicted environmental metabolome for the Western L4 Station. Each line in the tab-separated file is a metabolic reaction in the format: Reactant, unique enzymatic function, product.Click here for fileFigure S1. The network and calculated PRMT-scores.Click here for fileTable S2. This file contains all calculated PRMT-scores, all PCC-scores between PRMT and relative abundances of Taxa, and between PRMT and relative abundances of measured environmental metabolites for the Western English Channel L4 Station environmental metabolome.Click here for file