Saccharomyces cerevisiae consensus model and large-scale knock-out experiments. Our comparative approach is particularly useful in scenarios where the quality of available sequence data is lacking, and when reconstructing evolutionary distant species. Moreover, the reconstructed networks are fully carbon mapped, allowing their use in 13C flux analysis. We demonstrate the functionality and usability of the reconstructed fungal models with computational steady-state biomass production experiment, as these fungi include some of the most important production organisms in industrial biotechnology. In contrast to many existing reconstruction techniques, only minimal manual effort is required before the reconstructed models are usable in flux balance experiments. CoReCo is available at http://esaskar.github.io/CoReCo/.We introduce a novel computational approach, CoReCo, for comparative metabolic reconstruction and provide genome-scale metabolic network models for 49 important fungal species. Leveraging on the exponential growth in sequenced genome availability, our method reconstructs genome-scale gapless metabolic networks simultaneously for a large number of species by integrating sequence data in a probabilistic framework. High reconstruction accuracy is demonstrated by comparisons to the well-curated  Saccharomyces cerevisiae to the manually curated, high-quality consensus network. We also provide an easy-to-use implementation of the method, usable both in single computer and distributed computing environments.Advances in next-generation sequencing technologies are revolutionizing molecular biology. Sequencing-enabled cost-effective characterization of microbial genomes is a particularly exciting development in metabolic engineering. There, considerable effort has been put to reconstructing genome-scale metabolic networks that describe the collection of hundreds to thousands of biochemical reactions available for a microbial cell. These network models are instrumental in understanding microbial metabolism and guiding metabolic engineering efforts to improve biochemical yields. We have developed a novel computational method, CoReCo, which bridges the growing gap between the availability of sequenced genomes and respective reconstructed metabolic networks. The method reconstructs genome-scale metabolic networks simultaneously for related microbial species. It utilizes the available sequencing data from these species to correct for incomplete and missing data. We used the method to reconstruct metabolic networks for a set of 49 fungal species providing the method protein sequence data and a phylogenetic tree describing the evolutionary relationships between the species. We demonstrate the applicability of the method by comparing a metabolic reconstruction of  The ability to reconstruct high-quality genome-scale metabolic models is crucial in metabolic modeling and engineering, drug discovery and understanding human disease, such as cancer Trichoderma reesei, still lack high-quality genome-scale metabolic networks. Also for other fungal species including major plant pathogens Ustilago maydis and Magnaporthe grisea, and major human pathogens Aspergillus fumigatus and Candida glabrata, no curated metabolic models exist. It is thus important to produce metabolic network models for these species that are able to carry out analyses such as flux balance analysis Although metabolic networks have been reconstructed for many microbial species Comparative ReConstruction) for simultaneous genome-scale metabolic reconstruction of multiple related species that leverages on the growing availability of sequenced genomes. Importantly, we assume that all species in the phylogeny — present and ancestral — must have a gapless metabolic network, and use this assumption to reconstruct metabolisms that parsimoniously explain the observed sequence data In this work, we address these challenges by introducing a novel computational method  for simultaneous reconstruction of multiple, related species with a known phylogeny. In addition to a phylogenetic tree, the method requires as input a set of protein coding sequences for each species. The method consists of two phases, illustrated in In the first phase, sequence data is used to quantify evidence towards existence of known enzymes in each species. To achieve this, the method identifies sequences homologous to input sequences by two distinct techniques, protein BLAST and Global Trace Graph GTG; . The latBayesian network topology is derived from the phylogenetic tree. Conditional probability distributions specify the probability of appearance and disappearance of an enzyme at each ancestral species. These species-specific probabilities are estimated from InterProScan enzyme predictions for present species assuming parsimonious phylogeny. Furthermore, conditional probability distributions are estimated for enzyme existence given BLAST and GTG data. Due to the resulting tree topology of the Bayesian network, exact probabilistic inference can be performed efficiently atom mappings to accurately find biosynthetic pathways In CoReCo second phase, a gapless metabolic network is assembled for each present and ancestral species. Utilizing the posterior probabilities computed in the previous phase, our algorithm reconstructs a highly probable network using reactions with low probability only when an addition of a reaction with a high probability would leave the network gapped. The algorithm iterates through reactions meeting with specified probability threshold, and adds the reaction if a gapless biosynthesis pathway producing the reaction substrates can be found. Here, the method takes advantage of precomputed reaction The framework allows efficient parallelization of both phases, thus scaling up to massive datasets. Input protein sequences can be split into arbitrary small sets of sequences to be processed separately by BLAST and GTG. Furthermore, the posterior probability of each enzyme in all species is computed independently of other enzymes. Since the metabolic network for each species is reconstructed separately, also this phase can be parallelized efficiently. In practice, homolog detection with BLAST and GTG is the most time-consuming and also the part of the method where parallelization can be done to an arbitrary degree.The method produces networks that are gapless in the network connectivity sense: substrates of each reaction in a reconstructed network can be traced to a predefined set of nutrients along reactions in the reconstructed network. Thus networks produced by CoReCo can be utilized with minimal effort in computational analyses requiring structural connectivity such as flux balance analysis. Furthermore, the reactions in the reconstructed models are carbon-mapped, enabling 13C flux analysis S. cerevisiae, T. reesei, and P. pastoris  prediction performance. To understand the contribution of individual CoReCo components, we predicted enzyme content also by using BLAST and GTG data separately, as well as a naive Bayesian classifier combining the two. In these classifiers, phylogeny was not used at all. Finally, we performed prediction by CoReCo phase I only, that is, integrating sequence data in the Bayesian network but not doing gapless reconstruction. To compute true and false positive rates for CoReCo phase II, we varied the acceptance threshold parameter. For CoReCo phase I and the naive classifier, different posterior probability thresholds see  were conS. cerevisiae models was compared to the yeast consensus network by counting the number of shared complete EC numbers. A complete EC number specifies all four digits , whereas an incomplete or partial EC number leaves one or more unspecified . Our comparison disregarded reactions that had no EC number, such as non-enzymatic or spontaneous reactions. Enzyme-level comparison is invariably inaccurate due to the well-known ambiguity of EC classification. However, we preferred this approach to reaction-level comparison, where the stoichiometries of the two models must be first curated before identical reactions can be accurately identified. A summary of prediction performance in the these settings is given in The enzyme content of the resulting Saccharomycotina subphylum species. From this perturbed input data, our reconstruction method was able to reconstruct the S. cerevisiae network accurately, displaying clearly increased performance over individual sequence data sources . Accuracy after CoReCo phase I and II was similar. In phase II, reactions that have not been reliably associated with sequences can be added to the network to ensure gaplessness. While producing connected metabolic networks, addition of gapfilling reactions also slightly increases false positive rate of phase II over the phase I result, where gapfilling is yet to be performed. The result demonstrates the benefit of our comparative analysis, where sequence evidence is propagated from neighboring species that are better sequenced and annotated.Poor sequencing quality was emulated by randomly removing 50% of protein sequences from the four S. cerevisiae reconstruction against the yeast consensus network. Specifically, we modified the BLAST and GTG scores of enzymes in S. cerevisiae, K. lactis, A. gossypii and C. glabrata by replacing all BLAST scores over 600 and all GTG scores over 0.99 with scores below these thresholds randomly chosen from E. cuniculi data. This process resulted in enzyme scores in the above species closely resembling a typical poorly characterized organism.We next considered the second setting where the phylogeny includes a small group of species that are closely related to each other but are poorly annotated and have large evolutionary distances from all the other species. In such a scenario, we would expect a large fraction of enzymes in our data to have a low degree of sequence similarity to known enzymes, thus complicating the discovery of correct homologs and functions. To estimate the effect of missing correct annotations would have on reconstruction accuracy, we produced a modified dataset from our fungal dataset by artificially lowering the scores of high scoring sequence matches and comparing the quality of the resulting We then computed the true and false positive rates as previously for CoReCo phases I and II, and naive, BLAST and GTG classifiers. Here we observed that our phase II algorithm was able to reconstruct a network much more accurately than the underlying probabilistic model (phase I) alone . This isS. cerevisiae CoReCo phase II reconstruction performance in terms of F1 score  than those of other species . Interestingly, Eurotiomycetes models had fewer gapfilling reactions than many species with similar sized models, which probably reflects the fact that many Aspergillus species have extensive manual annotation in public databases In CoReCo phase II, metabolic network models were reconstructed based on KEGG stoichiometry data for each present and hypothetical ancestral species. Prior to reconstruction, we balanced 7076 KEGG reactions by allowing addition of protons and water, and a single C1 group. We then computed atom mappings for balanced reactions using a recent algorithm  species . As expeA. fumigatus, A. gossypii, A. nidulans, B. cinerea, C. albicans, C. immitis, D. hansenii, F. graminearum, K. lactis, M. graminicola, N. fischeri, P. blakesleeanus, P. graminis, P. stipitis, S. cerevisiae, U. reesii and Y. lipolytica.We next investigated the metabolic capabilities of reconstructed fungal models after minimal manual curation see . For eacS. cerevisiae model was 0.7388 whereas the growth rate of yeast consensus model on the same media and biomass was 0.7418 E. cuniculi. Reconstruction of five Saccharomycotina including P. pastoris proved difficult and resulted in up to 32 unproducible components. However, in other Saccharomycotina such as K. lactis and C. tropicalis all or nearly all biomass components could be produced.For instance, max growth rate in our S. cerevisiae model to predict the effects of gene knock-outs on growth. In a recent work, S. cerevisiae gene deletion mutants and compared observations to steady-state model predictions. Here, we compared their results against growth predictions of our final reconstructed S. cereivisae model.Lastly we studied the ability of our We modified the set of 16 growth media used by in silico gene knockouts, resulting in 7440 growth prediction cases, and compared our prediction against growth observed in the previous study. To determine the KEGG reactions to remove for each knockout, we mapped S. cerevisiae genes to reactions via EC numbers using Saccharomyces cerevisiae Genome Database (SGD) and KEGG annotations. A total of 1071 S. cerevisiae genes were mapped to 370 EC numbers. We considered the gene associations in protein complexes specified in the yeast consensus model (v4.02) Gene knockouts in our reconstructed model were simulated according to Identically to We described a computational method for reconstructing metabolic networks from sequence data for related multiple species and their hypothetical ancestor species. The method is able to exploit shared evolutionary history and alleviate problems caused by lacking sequence data by propagating enzyme evidence from related species. Our reconstruction method allows comparative reconstruction of an arbitrary number of species from sequence and phylogenetic data, and thus can be used to shed light into the evolution of metabolism and predict metabolic phenotypes, for example.The increasing availability of microbial genomes sequenced individually from cell cultures, or identified in metagenomics experiments has made the rapid and accurate analysis and interpretation of the data the rate-limiting step of biological discovery instead of data acquisition. In metabolic modeling, scaling up metabolic network reconstruction to cope with emerging big sequence data has so far been hindered by the large amount of manual work that goes into curating metabolic models. This problem can be alleviated by enforcing gaplessness in reconstruction Comparative analysis offers a promising direction for development of metabolic network reconstruction techniques. In this study, we observed significant reconstruction accuracy gains from integration of sequence data from multiple species. Although we used only two distinct sources of sequence information, the Bayesian network framework introduced here can be easily extended to integrate other sequence features as well, or condition- or cell-type specific data S. cerevisiae network by comparing our results against the high-quality yeast consensus network. Further, our S. cerevisiae model was able to accurately predict effects of gene knockouts observed in a previous study We discussed here 49 genome-scale metabolic networks of fungal species constructed with our method from protein sequence data. As a proof of concept, we demonstrated high reconstruction accuracy of We developed an algorithm for finding plausible gap-filling metabolic pathways extending our previous work Evolution of fungal transcriptional networks has been previously studied CoReCo takes as input the full complement of protein sequences for each reconstructed species. We computed reciprocal alignments of the 501619 protein sequences from the 49 fungi against UniProt Swiss-Prot Release 15.15 sequences with BLAST  yielding for each alignment of sequences To evaluate the sequence data support for an enzyme in a single species, we computed a score Reactions contained in the KEGG metabolic database (February 2012 version) were filtered by removing all 191 reactions designated as “general reactions”. In KEGG, general reactions do not specify the reactants fully, instead referring to general categories of molecules, such as KEGG reaction R00056 “Dinucleotide+H2OWe computed species-wise posterior probablities whether an enzyme is encoded by the genome given observed sequence data and phylogeny of the related species. To this end we constructed a Bayesian network model with three groups of nodes . In the S. cerevisiae.To estimate the conditional probability distributions from data, we performed InterProScan (version 1.6) analysis of fungal protein sequences The EC numbers identified with InterProScan in each species served as reference models when estimating the conditional probability distributions. For evidence nodes, a total of four distributions identical to all species and enzymes were estimated. Probability distribution Conditional probability distributions for species and non-root ancestral nodes were estimated from the InterProScan reference models by first estimating ancestral reference models by parsimony. To do this, we used Fitch's algorithm and estimated ancestral models explaining the reference models such that the number of enzyme additions and deletions were minimized. We then obtained distributions Finally, we computed the posterior probabilities To assemble a connected metabolic network from posterior probablities, we developed a novel iterative algorithm, extending our previous work The algorithm assembles each a metabolic network for each individual species complete atom mapping is a bijection from substrate atoms to product atoms. We require that a valid biosynthesis pathway is able to transfer atoms from nutrients to all metabolites involved on the pathway The crucial input parameters to the CoReCo reconstruction algorithm are acceptance threshold Heuristics are employed to decrease running time. First, reactions are enumerated in an increasing order of estimated cost of adding the reaction to the network. Addition cost is estimated by finding the shortest reaction path from nutrients and products of already added reactions to each substrate atom of the reaction, and summing the costs of all such paths. Thus reactions that are potentially inexpensive to add to the network are considered first. Addition costs are re-estimated after each iteration, because reaction additions change the cost estimates. Second, the partial pathways are maintained in a priority queue and visited in increasing order of cost estimate for completing the pathway similarly to the first heuristic.When no complete gapfixing pathways are found for a reaction S. cerevisiae model and added reactions that were required for growth and were not included in the reconstruction. These omissions, described in Following the automatic reconstruction of fungal metabolic models with CoReCo, we manually inspected the central pathways in the reconstructed Reaction direction constraints for the reconstructed genome-scale metabolic model were derived from Gibbs reaction energy change estimates obtained by the group contribution method S. cerevisiae model and modified to account for stoichiometry differences between KEGG database and iMM904 model. The minimal media used contained glucose as carbon source Bicarbonate was added to the media, with the restriction that CO2 production would not exceed the intake of bicarbonate. Biomass and media compositions are described in detail in Biomass definition was derived from the iMM904 Appendix S1Description of the reconstruction algorithm, manual model curation steps, biomass and growth media composition used in experiments, evaluation of the effect of the size of phylogenetic tree to reconstruction accuracy, and posterior probability thresholds used to compute ROC curves.(PDF)Click here for additional data file.Table S1Lower and upper bounds for reaction fluxes used in flux balance analysis experiments.(TXT)Click here for additional data file.


E. coli can be severely affected by the inactivation of metabolic genes that are required to catabolize a nutrient . We hypothesized that the resulting accumulation of small molecules can yield local as well as systemic effects on the metabolic network. Analysis of metabolomics data in wild-type and D-galactose non-utilizing mutants, galT, galU and galE, reveal the large metabolic differences between the wild-type and the mutants when the strains were grown in D-galactose. Network mapping suggested that the enzymatic defects affected the metabolic modules located both at short- and long-ranges from the D-galactose metabolic module. These modules suggested alterations in glutathione, energy, nucleotide and lipid metabolism and disturbed carbon to nitrogen ratio in mutant strains. The altered modules are required for normal cell growth for the wild-type strain, explaining why the cell growth is inhibited in the mutants in the presence of D-galactose. Identification of these distance-based dys-regulations would enhance the systems level understanding of metabolic networks of microorganisms having importance in biomedical and biotechnological research. The metabolic network in  E. coli has been under active research of system biology using genomics, transcriptomics, proteomics and metabolomics. Genome-scale reconstruction of E. coli metabolism suggests 1366 genes, 2251 reactions and 1136 metabolites in the metabolic network of E. coli [The metabolic network of  E. coli ,5. For a E. coli . ElucidaE. coli [E. coli [galE, galT and galU mutant strains of E. coli grown in galactose containing media were analyzed by a non-targeted metabolomics using mass spectrometry. The data were mapped into a metabolic network using the MetaMapp biochemical mapping approach [E. coli metabolic network. The altered modules are required for normal cell growth for the wild-type strain, explaining why the cell growth is inhibited in the mutants in the presence of D-galactose. Systems level properties of metabolic networks, such as organization, robustness, topology, evolvability and global flux balancing are being actively studied in the wild-type. as well as in mutant strains of E. coli ,9. Flux-[E. coli . Althoug[E. coli  leading [E. coli ,13, knocapproach . We repoE. coli and the constituent enzymes are shown in E. coli mutants, galT, galU and galE, encoding the enzymes Galactose-1-phosphate uridylyltransferase, UDPG synthatase, and Epimerase, respectively, in D-fructose minimal media are retarded in the presence of D-galactose, compared to the wild-type control [E. coli using the combined approach of GCMS and LCMS . The detected compounds cover a range of metabolic pathways including energy, nucleotide, lipids and amino acid metabolism  between mutants demonstrate profound metabolic alterations, in addition to the disturbance in the D-galactose metabolism.To assess the global metabolic variability among all the strains, we calculated an unsupervised principal component analysis (PCA) model , which sgalE mutant, suggesting that metabolic response in this mutant was different from the other two strains, as observed in the PCA model. Up to 60% of the compounds that were decreased in the galT mutant were also found to be altered in the galU mutant, pointing to the common metabolic pathways that were affected by galU and galT mutations. A total of 23 metabolites were found to be altered in all three mutants, pointing toward common metabolic pathways disturbed in different mutants. Detailed results of ANOVA analysis is provided in Whereas PCA provided a global view of metabolic variability among samples, the identification of significantly altered metabolites revealed the metabolites in different metabolic modules that were affected following the accumulation of D-galactose metabolic intermediates, which created cellular stress from within . Welch’sE. coli were present in the metabolomics datasets, and 2) that several detected metabolites were not present in the reconstructed metabolic network of E. coli. Since the metabolomics survey covers a variety of metabolites, five major clusters of metabolites were visually observed in the MetaMapp graph, similar to the modules observed previously [E. coli metabolic network, which are described in the next section. Direct biological interpretation of the list of altered metabolites was difficult because of the large number of metabolic changes. Therefore, organizing the metabolites into metabolic modules was chosen as an approach to assist the interpretation of the results of ANOVA analyses. To do so, metabolites were mapped into a metabolic network using a recently developed biochemical mapping approach, MetaMapp . The appeviously  , which is an indicator of glutathione biosynthesis, was also decreased. Glutathione is a major anti-oxidant agent in cell [E. coli. In the presence of D-galactose, erations  that can in cell , and itsgalU and galE mutants. Increase in the levels of ribose (M075) in the mutants augments the UTP biosynthesis. Increase in ribose in all three mutants is likely caused by activation of riobnucleosidases in salvage pathways of purine and pyrimidines, because we have observed low levels of nucleosides including inosine (M135), adenosine (M138), guanosine (M140) and adenosine 5’ diphosphoribose (M087). The salvage of ribose from nucleosides resulted into a decrease in the levels of methylthioadenosine (MTA), which is an essential intermediate in methionine salvage and sperminine biosynthesis. Accumulation of ribose was highest in galU mutants as UTPs were not being utilized in this strain. However, in the galT mutant, UTPs are not utilized as shown [galT mutants, leading to a large decrease in the levels of orotate (M142), dihydroorotate (143) and N-carbamylaspartate (M006), the key intermediates of pyrimidine biosynthesis. The salvage of substrates for biosynthesis is an important metabolic mechanism in adaptation to changing nutrients [We identified an UTP-mediated relationship between pyrimidine biosynthesis and D-galactose metabolism. Higher pools of UDP-glucose were consumed to metabolize the higher amount of galactose that was imported in mutant strains. Increased biosynthesis of UTP from ribose, ATP and uracil is required to elevate the levels of UDP-glucose. For this reason, levels of uracil were maintained by reducing the catabolism of uracil as indicated by lower levels of dihydrouracil (M148) in as shown  for the utrients . Since, E. coli under nutrient stress [E. coli tries to maintain the amino acids levels at the cost of some other nitrogen compounds. However, GABA is also an osmotic stress protectant and diaminopimelate is required for proper cell wall biosynthesis, indicating mechanisms that can inhibit the cell growth of the mutants. Recently it was discovered that GABA can also enter the TCA cycle as an energy source in nutrient starvation conditions [E. coli. Accumulation of asparagine is a marker of protein degradation [galU mutant, suggesting that this mutant was under severe stress conditions, which is also reflected by the large fold changed in other metabolite levels  is not metabolized further, and the ATP/ADP ration will be imbalanced. This will transiently affect the other ATP-dependent reactions 1 of them is glucokinase, which phosphorylate glucose is the first step to glycolysis. Consequently, accumulation of glucose was observed in galT mutant. Strikingly, the accumulated unphosphorylated glucose was converted into maltose (M055), maltotriose (M059) and mannose (M056) in galT mutants. We have increased levels of these sugars, as has been shown previously [galE mutants the levels of these sugars were lower compared to the controls, indicating the activation of maltose system by the accumulation of UDP-galactose and galactose. Levels of glucose and the diasacharides were unaffected in the galU mutant. E. coli mutants have imported the fructose in the media and converted it into fructose-6-phosphate (M072), which was converted into fructose 1,6, biphosphate (M073). Both compounds were increased in galE and galT mutants. Interestingly, galU consumed more fructose (M054) and low levels of fructose were observed in this mutant. Downstream metabolite in glycolysis, 3PGA (M070) was reduced in galT and galU mutants, indicating that glycolytic flux was rerouted toward pentose-phosphate pathway for the synthesis of ribose sugar (M075), which was found to be alleviated in all the mutants. 3-PGA is a precursor for synthesis of serine, glycine and the glycerol moiety in membrane lipids. Levels of serine were unaffected and lipids were increased in galU and galT mutants, suggesting the utilization of 3-PGA for anabolic reactions. In the galU mutant  for cellular growth, from which the highest number of shortest paths are passing through. Using graph theory algorithms, computational identification of choke-points have been undertaken in microorganisms , and theE. coli mutants.In summary, inactivation of a single gene function can cause enormous metabolic changes outside the know biochemical neighborhood of the encoded enzymes consistent with our global transcription analysis that showed dys-regulation of genes near and far from the function of the inactivated genes. Natural selection eliminates the mutants that have failed to survive in a changed environment . But theE. coli deletion mutants were used to transduce galT (UniProt ID : P07902), galE (UniProt ID : Q14376) and galU (UniProt ID : P0AEP3) mutations carrying kanamycin markers into BW25113 wild-type strain to make isogenic mutant strains. Subsequently, the pCP20 [gal gene expression in the operon. After removing the kanamycin marker, the temperature-sensitive pCP20 plasmid was cured at 42°C. P1 transduction was also carried out to introduce glpR mutation into the galT mutant cells to make the galT glpR double mutant.Bacteriophage P1 lysates of Keio collection of 600 of 0.6, the cultures were divided into two flasks. D-galactose  was added to one and cells were further grown for 0.5h. Cells were then placed on ice and harvested. The pellet was gently washed and re-suspended with PBS solution. The cell pellet was collected and stored at -80°C. Each sample is accessioned into a LIMS system, assigned a unique identifier, and stored at -70°C. To remove protein, to dissociate small molecules bound to protein or trapped in the precipitated protein matrix, and to recover chemically diverse metabolites, proteins are precipitated with methanol by vigorous shaking for 2 minutes in a Glen Mills Genogrinder 2000. The samples were centrifuged, supernatant removed (MicroLab STAR® robotics), and split into equal volumes for analysis on the LC+, LC-, and GC platforms by Metabolon, Inc . One aliquot was retained for backup analysis, if needed. Raw data matrix is provided in Bacterial cells were grown in 125-mL corning flasks containing 30 mL of M63 minimal medium plus 0.3% fructose at 37°C. At ODwww.metamapp.fiehnlab.ucdavis.edu. A single-step metabolic reaction network was calculated using KEGG RPAIR computations. Chemical similarity and KEGG RPAIR networks were merged into a single graph, which was visualized in Cytoscape. The Cytoscape Session file is provided in Welch’s two sample T-tests were used to identify the significantly altered metabolites. R and Statistica data miner Version 10 were used for statistical analysis. Mole-file encoded chemical structures of the identified metabolites were retrieved from the PubChem database. A pair-wise Tanimoto chemical similarity matrix was calculated for the structures on the PubChem website. We downloaded the similarity matrix and used it as an input for MetaMapp software  availablFigure S1galT, galU, and galE strains in the presence or absence of D-galactose.Principal component analysis of metabolome profiles of wild-type, (TIF)Click here for additional data file.Figure S2Cytoscape Session file (no title).(XML)Click here for additional data file.Table S1E. coli strains.List of compounds detected by GCMS and LCHS in wild-type and mutant (XLSX)Click here for additional data file.Table S2p<0.05) metabolites in wild-type strain of E. coli cultured in galactose supplemented media.Significantly altered Click here for additional data file.Table S3p<0.05) metabolites in galT mutant strain of E. coli cultured in galactose supplemented media.Significantly altered Click here for additional data file.Table S4p<0.05) metabolites in galE mutant strain of E. coli cultured in galactose supplemented media.Significantly altered Click here for additional data file.Table S5p<0.05) metabolites in galU mutant strain of E. coli cultured in galactose supplemented media.Significantly altered Click here for additional data file.


Plasmodium is the causal parasite of malaria, infectious disease responsible for the death of up to one million people each year. Glycerophospholipid and consequently membrane biosynthesis are essential for the survival of the parasite and are targeted by a new class of antimalarial drugs developed in our lab. In order to understand the highly redundant phospholipid synthethic pathways and eventual mechanism of resistance to various drugs, an organism specific kinetic model of these metabolic pathways need to be developed in Plasmodium species.Plasmodium knowlesi. In vitro incorporation dynamics of phospholipids unravels multiple synthetic pathways. A detailed metabolic network with values of the kinetic parameters (maximum rates and Michaelis constants) has been built. In order to obtain a global search in the parameter space, we have designed a hybrid, discrete and continuous, optimization method. Discrete parameters were used to sample the cone of admissible fluxes, whereas the continuous Michaelis and maximum rates constants were obtained by local minimization of an objective function.The model was used to predict the distribution of fluxes within the network of various metabolic precursors.Fluxomic data were used to build a quantitative kinetic model of glycerophospholipid pathways in The quantitative analysis was used to understand eventual links between different pathways. The major source of phosphatidylcholine (PC) is the CDP-choline Kennedy pathway.In silico knock-out experiments showed comparable importance of phosphoethanolamine-N-methyltransferase (PMT) and phosphatidylethanolamine-N-methyltransferase (PEMT) for PC synthesis.The flux values indicate that, major part of serine derived phosphatidylethanolamine (PE) is formed via serine decarboxylation, whereas major part of phosphatidylserine (PS) is formed by base-exchange reactions.Sensitivity analysis of CDP-choline pathway shows that the carrier-mediated choline entry into the parasite and the phosphocholine cytidylyltransferase reaction have the largest sensitivity coefficients in this pathway, but does not distinguish a reaction as an unique rate-limiting step.P. knowlesi. This model has been used to clarify the relative importance of the various reactions in these metabolic pathways. Future work extensions of this modelling strategy will serve to elucidate the regulatory mechanisms governing the development of Plasmodium during its blood stages, as well as the mechanisms of action of drugs on membrane biosynthetic pathways and eventual mechanisms of resistance.We provide a fully parametrized kinetic model for the multiple phospholipid synthetic pathways in  Plasmodium, is one of the most prevalent diseases in the world, with approximately 50% of the world’s population at risk with several cases of malaria worldwide causing a million deaths, mostly children under 5 years old  denotes several external concentration values F gives the predicted metabolite concentrations. Here ||x|| stands for the Euclidean norm of the vector x.where the index Vmax in Michaelis-Menten kinetics) by the same constant, does not change the steady state and preserves the value of the objective function Φ. In order to fix this multiplicative constant, we used the values of the influxes, that were estimated by dividing the cumulated quantity of end products by the time needed for their accumulation.Of course, steady state data do not uniquely determine steady state parameters. Indeed, multiplying all the flux parameters  we find that the steady state fluxes satisfy the equation Ker(S) of the stoichiometric matrix S. The rank-nullity theorem provides the number of independent steady state flux profiles, dim(Ker(S))=n−rank(S), where n is the number of reactions in the network, and rank(S) is the rank of the matrix S, i.e. the number of reactions that have linearly independent stoichiometries. According to the rank-nullity theorem, if there are n reactions in the network, there are n−rank(S) linearly independent, distinct flux profiles, compatible with the constraints. We call admissible fluxes, the solutions of Eq. (5) such that Ri≥0, for any irreversible reaction.Although it constrains the flux values, Eq. (5) has not an unique solution. The number of independent steady state flux profiles is equal to the dimension of the kernel Ri≥0 for all fluxes. This condition is fulfilled by all reactions in our model, with the exception of the passive ethanolamine influx that is reversible. The later does not represent a problem, because in our data there is no ethanolamine incorporation and the corresponding reaction functions unidirectionally to evacuate internal ethanolamine excess. The generalization of the method to networks with reversible reactions is straightforward. In this case a bidirectional reaction can be replaced by two unidirectional reactions, each one having positive rate.In order to sample the set of admissible fluxes, we need a convenient parametrization of the admissible flux values. For simplicity, we present such a parametrisation for the case when the network contains only monomolecular reactions, i.e. each reaction has only one substrate and only one product. Our kinetic model satisfies this condition, because we chose not to represent cofactors. We also consider that all reactions are irreversible and impose n1=3, there are three different PL precursors). Similarly, n2=3, the model produces three main PLs, namely PC, PE and PS). Given the influxes, the steady state flux distribution depends on a number of branching parameters j, let us denote by j produced or consumed by the reaction i) are denoted by j whose flux outdegree satisfies {Rjin}j∈,n1 denotThis reasoning also leads to the following formula for the nullity of a monomolecular network, which is the number of independent admissible flux profiles: n1 is the number of influxes. Eqs. (6), (7) show that in a network without branching . This algorithm outputs optimal values of the kinetic parameters, for each initial choice of the branching parameters k is a local minimum of the objective function Φ. By comparing these values of Φ one can find the global minimum.For networks with branching, the parametrization (6) is used to sample admissible fluxes by choosing values of the branching parameters In our method, the sampling of admissible fluxes can be exhaustive (for simple networks this is doable), or stochastic, using, for instance, simulated annealing in the discretized simplex of branching parameters. The flowchart of our optimisation procedure is represented in Figure In order to analyse complex metabolic networks with a large number of parallel pathways one needs several types of fluxomic datasets, obtained in various conditions. In this paper we use two types of data corresponding each to incorporating only one PL precursor, either serine or choline. This leads to two datasets and least-squares objective functions. For simplicity of the calculations we combine the two objective functions by summing them. Because of the small overlap of the two datasets, more sophisticated analysis using Pareto optimality would lead to similar results.Flux Balance analysis (FBA) is an alternate method to compute fluxes, given the reaction network and the biomass definition. It is based on the steady state constraint (5) and optimality of biomass production . ThroughF with respect to the logarithm of the rate constant k: Although very popular among biochemists, the limiting step concept surprisingly lacks a clear definition . Citing k can be either Vmax or Km. Also the flux value can be the steady state value, or, if steady state conditions can not be reached, the value at a given time, suggested by experiment. Let us notice that our sensitivity coefficients become the flux control coefficients from metabolic control theory, only when k=Vmax and F is the steady state flux. In this case only, F is homogeneous in the parameters and the corresponding control coefficients satisfy the usual summation theorems [In our study, the parameter theorems . As disctheorems , the usetheorems . The contheorems . FurtherP. knowlesi parasite at its blood stage is one of the most characterized metabolic network, due to the availability of infected erythrocyte collected from Macaca mulatta or M. fascicularis monkeys and several thorough fluxomic studies [P. knowlesi. The availability of the genome sequence of P. knowlesi and the subsequent genomic annotations brought a considerable amount of information for the existence of biological processes and existing biochemical pathways, offering a global view of the parasite biology.Phospholipid synthesis in  studies ,49,50. FPlasmodium knowlesi takes place to a higher extent in late trophozoite and early schizont stage of asexual (erythrocytic) phase [Lipid metabolism in c) phase ,49.P. knowlesi requires large amount of PC and PE that together constitute the bulk of the malaria membrane lipids [Plasmodium operates at the expense of the fatty acids mainly originating from the plasma and polar heads building units. Choline entry into infected red blood cells (IRBC) involves the erythrocytic choline carrier [The intra-erythrocytic proliferation of e lipids . The ver carrier ,51 and p carrier ,38-40. C carrier ,38-40.Ethanolamine can be supplied from the poorly available plasmatic ethanolamine, which can cross the membrane by passive diffusion, and from serine. Serine is diverted from the serum, host RBC or from hemoglobin degradation in food vacuoles .Both PC and PE may be synthesized denovo by the CDP-choline or CDP-ethanolamine-dependent Kennedy pathways. In the so-called Kennedy pathway, choline is phosphorylated into phosphocholine (PCho), which is subsequently coupled to CTP, thus generating CDP-choline, which is further converted to PC by a parasite CDP-diacylglycerol-cholinephosphotransferase (CEPT). A similar de novo pathway allows the synthesis of PE from ethanolamine. The final stage of both branches of the Kennedy pathway involves the same CEPT enzyme, catalyzing the formation of PC and PE from CDP-choline and CDP-ethanolamine, respectively ,23,33.Plasmodium possesses the CDP-DAG-dependent ancestral pathway, which provides the anionic phospholipids PI, PG, cardiolipid and eventually PS [Additionally, ually PS . Biosyntually PS .P. knowlesi also possess a plant-like pathway that relies on serine to provide additional PC and PE, which is named the serine decarboxylase-phosphoethanolamine methyltransferase (SDPM) pathway. Hereby, serine is first decarboxylated to form ethanolamine, which is then phosphorylated to lead to phosphoethanolamine (PEtn). Serine decarboxylase (SD) enzymatic activity was first described by our group in P. knowlesi and P. falciparum[alciparum. The genalciparum. The resalciparum,31. In talciparum.Plasmodium. However, parasite genomes suggest corresponding hypothetic gene and recent biochemical studies have revealed calcium-dependent base exchanges between serine and PLs in P. falciparum . There is no data measuring their quantitative importance but they would be operational at the erythrocytic stage. In some plants species, in which both CDP-DAG-dependent and base-exchange PS synthesis take place, it has been shown that, these enzymatic reactions have different preferential molecular species as substrates [Base-exchange reactions (PSSbe) between serine and PE or PC were initially not detected in bstrates .Plasmodium, including 17 reactions and enzymes. Biochemical experimental data and quantification experiments, supports that this parasite machinery can provide the bulk of PL composing the P. knowlesi membranes. Genomic studies have confirmed that malaria parasites possess most of the panoply of corresponding genes  shown in Figure In CDP-choline pathway, PC is produced from PCho in two steps. First, PCho gives CDP-choline and then CDP-choline transforms to PC. The intermediate CDP-choline was produced in minute quantity which was difficult to measure experimentally ,53. AgaiSimilarly, in CDP-ethanolamine pathway formation of PE from PEtn takes place in two steps. PEtn forms CDP-ethanolamine and in turn produces PE. Again CDP-ethanolamine is produced in minute quantity which is not possible to quantify experimentally. Formation of PE from CDP-ethanolamine is very rapid with respect to the rate limiting formation of CDP-ethanolamine from PCho . So, we The glycerophospholipid model (PL model) was trained with two datasets, (i) incorporation of serine  (ii) incμM of radiolabelled serine were subjected exogenously to the cell and were incorporated into various metabolites . For serine incorporation, this time is approximately two hours .μM, whereas concentrations of extracellular serine (SerE) and ethanolamine (EtnE) were kept very low. Like for the previous data sets, the influx of precursor was calculated by dividing the total amount of accumulated end product (PC) by the accumulation time (1 h). Though used for influx estimates, the phosphatidylcholine does not reach steady state in this experiment .Radiolabelled experiments were also performed with choline as metabolic precursors. Choline produces different metabolic compounds . We compare the results from two methods. Because FBA does not fix the time scale, in this method fluxes are determined up to multiplication by a constant. In order to compare the two methods, we renormalized the FBA fluxes such that the input fluxes  coincide in the two methods. Although there is no reason to expect that the FBA method provides an absolute reference, this comparison is informative. Agreement will confirm the relevance of the optimal biomass production concept, whereas disagreement will indicate the limitations of the FBA method.in silico experiments with the incorporation of different metabolic precursors.We have performed different μM), fluxes were calculated using the FBA method [μM) is shown in Figure At physiological concentration of exogenous serine (SerE) (0-100 A method  and the Fluxes from FBA (represented with blue bars) are independent of the concentration of the metabolites but they depend on the assigned biomass and on the influxes. The biomass was defined to be (50% PC + 5% PS + 45% PE) ,21.Relative to the influx, the distribution of fluxes from FBA method  . This is an area which remains unexplored in Plasmodium.Base-exchange reactions (PSSbe) between serine and PE or PC were initially not detected in PS could be formed directly from serine via PS synthase R2), or by transformation of PC and PE via (PSSbe), R10 and R11 respectively  but considerable amount from PC (R10) and PE (R11). The flux values of R2 from FBA (blue bars) was much higher than the ODE (green bars), though remained significantly smaller than R3. It means considerable amount of PS was formed from serine via R2 (PSS), which quantitatively contradicts the biochemical findings . HoweverPlasmodium[in vitro growth assays using dialyzed serum indicated that CDP-choline pathway was not essential for parasite intra-erythrocytic development and survival [The major source of PC is thought to be provided by CDP-choline or Kennedy’s pathway ,55. Thuslasmodium,56. Howesurvival ,58. TherP. falciparum PMT (PfPMT), has been revealed by the P. falciparum genome sequencing program [Plasmodium falciparum[Plasmodium knowlesi[i. PMT, which transforms PEtn into PCho, which in turn forms PC via CDP-choline pathway. This is a part of SDPM pathway by which host serine is incorporated into PC. The mechanism is S-adenosyl methionine (SAM)-dependent triple methylation carried out by a plant-like phosphoethanolamine N-methyltransferase (PMT or PEAMT) (EC 2.1.1.103). program . Subsequalciparum. The ort knowlesi.P. knowlesi-infected erythrocyte to methylate PE into PC has been documented in previous studies and clearly indicates PEMT activity [Plasmodium species.ii. PE transmethylase (PEMT or PLMT) pathway  into PC. For this, we compared the fluxes R5 (PMT) and R9 (PEMT/PLMT) from ODE and FBA methods Figure . We founin silico knockout experiments were performed.In order to gain further understanding into the relevance of R5 (PMT) or R9 (PEMT/PLMT) μM, whereas the concentrations of choline and ethanolamine were kept very low. The PC efflux (R12), PS efflux (R13) and PE efflux (R14) were estimated before knockout (BKO) and after knockout (AKO) as shown in Figure The PL Model was simulated for two hours with the knockout of R5(PMT). The exogenous serine (SerE) was kept at 100 The result is a two fold decrease in the efflux R12 and PC concentration . The fluxes before knockout (BKO) and after knockout (AKO) are shown in Figure There was a marked decrease in PC efflux (R12) and concentration. Thus, when R9 (PEMT/PLMT) was knocked out, the rate of incorporation of PC into the membrane decreased in the absence of exogenous choline (ChoE).The behavior of fluxes with R5 (PMT) or R9 (PEMT/PLMT) knockout followed the same pattern. There was a significant decrease in PC efflux (R12), and a small increase in the PE efflux (R14). A marked R9 (PEMT/PLMT) reaction denotes the capacity of the parasite to convert PE to PC.in vivo in particular conditions. Because the corresponding genes coding for PEMT have not been found in any Plasmodium species, deletion of PMT gene in P. falciparum could be equivalent to a double knockout of PMT and PEMT in our model, that completely abolishes the incorporation of ethanolamine into PC.From the knockout studies  and ethanolamine (EtnE) were kept very low. As shown in Figure one of [P. knowlesi membrane or structural phospholipids.We are interested here in detecting rate limiting steps for the major PC synthesis pathway, namely the CDP-choline pathway. The analysis is based on experiments that have been done with choline as unique metabolic precursor . This exe one of , the parKm, Vmax) are the ones obtained from model training and common both to serine and to choline incorporation.We have simulated the ODE model for 1 h starting with vanishing initial metabolite concentrations and computed the resulting fluxes. The kinetic parameters .In order to find limiting steps we use a sensitivity based approach. Parameters As seen in Figure stricto sensu rate limiting steps. As expected, rate constants of reaction 15 (the choline influx) controls all the non-vanishing fluxes and concentrations. In order of importance,follows reaction R8 (CCT: phosphocholine cytidylyltransferase) and to a lesser extent, R16 (CK: choline kinase).Consequently, and contrary to our former study , the modOur former experimental work which finPlasmodium, the reconstruction of metabolic pathways can be particularly challenging. Generic pathways databases provide incomplete or unverified metabolic pathways for Plasmodium. For instance, Kegg database [P. knowlesi, P. berghei, and Bacillus subtilis, in fact based on evidence coming mainly from S. cerevisiae and E. coli. Hagai Ginsburg’s Malaria Parasite Metabolic Pathways  is more specific because based on data from Plasmodium species (without interspecies distinction), but is still incomplete and not quantitative. We have proposed here, for the first time, a complete quantitative model for the glycerophospholipid synthesis in Plasmodium knowlesi. This model is based on several fluxomic experiments of incorporation of radiolabelled phospholipid precursors.Precise quantitative models for essential metabolic functions of pathogens can be used to understand their intricate set of biological process and their regulation. It guides us to determine the specificities of their physiology, improve the action of known drugs and discover new treatments directed against them. Even when the full genome is available, as in the case of database  proposesPlasmodium from radiolabelled precursor fluxomic data. It provides an effective sampling of the parameter space. This method can be generally applied to metabolic networks with Michaelis Menten reactions, functioning at steady state. It can be therefore used for other studies of the same kind, for rate constant identification in isotope labelling experiments.In order to learn the metabolic network from data we have developed a new hybrid optimisation scheme, which is based on the discretization of the simplex that parametrizes the set of directions in the cone of admissible fluxes. The main interest of this method is that it facilitates the global search in the parameter space and can be combined with other global optimization algorithms, such as genetic algorithms or simulated annealing. Our method was specifically designed to understand glycerophospholipid metabolism in P. knowlesi. The main source of PC is the CDP-choline Kennedy pathway, however, SDPM and PE transmethylase pathways could provide part of PC. The values of the fluxes as well as in silico knock-out experiments showed comparable importance of PMT and PEMT/PLMT for PC synthesis in P. knowlesi.The metabolic network model has been used to elucidate the functioning of the multiple phospholipid synthetic pathways in P. falciparum and P. knowlesi[in silico knock-out experiments prove partial dependence of PC production on both PMT and PEMT, meaning that single knock-out of any of these enzymes will reduce but not completely eliminate PC production from serine in P. knowlesi. This prediction can not explain the result of [P. falciparum abolish the incorporation of ethanolamine into PC. Because the corresponding genes coding for PEMT have not been found in any Plasmodium species, altogether these findings could suggest that PfPMT might also have PEMT activity in vivo in particular conditions (which are not met in vitro or in yeast) [These findings confirmed earlier hypotheses about the existence of both PMT and PEMT activity in  knowlesi. Our in esult of  that deln yeast) ,62.Our model also indicate that the major part of serine derived PE is formed by serine decarboxylation. PS is predominantly formed by base-exchange reactions and not by the direct CDP-DAG phosphatidyl-synthase (PSS) mechanism.Sensitivity analysis of CDP-choline pathway in our model, does not identify limiting steps. However, it shows that the carrier-mediated choline entry into the parasite and the phosphocholine cytidylytransferase (CCT) reaction have, in order, the largest sensitivity coefficients in this pathway. This finding is in agreement with previous knowledge, and has been partially exploited in the search for antimalarial drugs. Indeed, choline entry is targeted by a new the class of potent antimalarial drugs ,63,64. IThe authors declare that they have no competing interests.PS, HV, and OR wrote the paper. PS and OR developed and implemented the methodology. All authors read and approved the final manuscript.Proofs of mathematical results and calculation of the parameter confidence intervals.Click here for file


Motivation: Dynamic simulation of genome-scale molecular interaction networks will enable the mechanistic prediction of genotype–phenotype relationships. Despite advances in quantitative biology, full parameterization of whole-cell models is not yet possible. Simulation methods capable of using available qualitative data are required to develop dynamic whole-cell models through an iterative process of modelling and experimental validation.Results: We formulate quasi-steady state Petri nets (QSSPN), a novel method integrating Petri nets and constraint-based analysis to predict the feasibility of qualitative dynamic behaviours in qualitative models of gene regulation, signalling and whole-cell metabolism. We present the first dynamic simulations including regulatory mechanisms and a genome-scale metabolic network in human cell, using bile acid homeostasis in human hepatocytes as a case study. QSSPN simulations reproduce experimentally determined qualitative dynamic behaviours and permit mechanistic analysis of genotype–phenotype relationships.Availability and implementation: The model and simulation software implemented in C++ are available in supplementary material and at http://sysbio3.fhms.surrey.ac.uk/qsspn/.Contact:a.kierzek@surrey.ac.ukSupplementary information:Supplementary data are available at Bioinformatics online. One of the fundamental goals of molecular biology is to delineate the molecular mechanisms by which genetic information is expressed in response to environmental cues, giving rise to a specific phenotype. Given the number of molecular components of a cell and the dynamic non-linear nature of their interactions, mechanistic computational modelling is an indispensable tool. Mechanistic models formally represent the current knowledge about the molecular machinery of cells. The molecules and interactions included into such models reflect the extent of genome sequence annotation, with computer simulation used to predict system behaviour under particular environmental conditions. In systems biology, such unbiased representation of molecular interactions in mechanistic models is referred to as reconstruction .Significant effort has already been dedicated to the formal representation of existing knowledge of the molecular machinery of the cell. The predominant framework is a bipartite graph where nodes representing molecules are connected to nodes representing interactions. This representation underlies established knowledge bases such as Reactome  (Petri net (PN) theory provides a general representation of interacting components in a network . HoweverHere, we describe quasi-steady state PNs (QSSPN), a novel algorithm capable of qualitative dynamic simulation of genome-scale molecular interaction networks including all classes of molecular interactions. We apply the algorithm to simulation of the interplay between whole-cell metabolism and gene regulatory and signalling networks involved in bile acid (BA) homeostasis in human hepatocytes. To our knowledge, this is the first dynamic simulation of a molecular interaction network involving gene regulation, signalling and full genome-scale metabolic network (GSMN) in a human cell. The unique feature that enables QSSPN to perform this simulation is Monte Carlo sampling of the feasible dynamic sequences of molecular transitions in the qualitative quasi-steady state model. In the following sections, we introduce QSSPN method, demonstrate its application to human hepatocyte simulation and compare its features with other approaches.The activities of molecular species represented by PN places are given by an integer number of tokens. In most instances, tokens represent discrete levels of activity, but fully quantitative description is, in principle, possible, with node token status reflecting molecular quantities. QSSF and DT interaction sets are connected by two classes of PN places: constraint places set flux bounds in QSSF, translating place token status in to flux bounds; objective places represent metabolic outputs of the QSSF network.t is a propensity function of transition t, ct is a rate constant, N is the number of pre-places of transition t, xi is the number of tokens at pre-place i and μi is the pre-place activity in the transition depending on the pre-place state. The activity function is a look-up table of T thresholds ti and activities ai allowing general definition of the pre-place contribution to the transition propensity Each molecular interaction in a PN subset is represented by a transition connected to pre-places representing substrates, activators and inhibitors and post-places representing products. Substrates and products are connected to transitions by standard edges, whereas catalytic activators and inhibitors are connected to transitions by read and inhibitor edges, respectively. When a transition fires, tokens from substrate pre-places are consumed and tokens representing products fired to post-places; the states of pre-places connected to transitions by read or inhibitor edges are not changed. In the simplest definition of system dynamics, transitions can fire if each substrate and activator pre-place has at least one token and all inhibitory pre-places have no tokens. To allow formulation of general rules involving token number thresholds, we define transition propensity The interpretation of a transition propensity during simulations is dependent on the transition class: stochastic, continuous or immediate. Stochastic transition propensity is interpreted as the probability density of the transition firing in the next, infinitesimally small, time step. Continuous transitions are updated after each iteration of the simulation, and the number of tokens moved is proportional to the propensity (i.e. the propensity is used as reaction rate). Immediate transition fires once whenever its propensity function is different than 0. To further enhance the power of our method to integrate experimental data, we allow stochastic transitions to be delayed /protein degradation . PN formThe gene expression model is illustrated using a hypothetical gene operating in a human hepatocyte. The ‘Gene’ place is used to represent the presence or absence of the gene in the genome, represented as 0 or 1 token, respectively. The ‘Active_Gene’ place represents the presence of a fully assembled transcription initiation complex for the respective gene, meeting the conditions for transcription. This is modelled by the transition that requires ‘Active_Gene’ to fire and places tokens on the ‘mRNA’ place. The PN read edge is used to ensure that the transition does not consume tokens from ‘Active_Gene’. Translation is modelled in a similar way; it requires the presence of ‘mRNA’ and places tokens on ‘Protein’ place without consuming ‘mRNA’. Degradation transitions remove tokens from both ‘Protein’ and ‘mRNA’ places. The flexibility of the PN formalism is used to express dependency between synthesis and degradation as a set of rules. Transitions and edges exclusively describing model rules are shown in grey to distinguish them from PN elements representing biological processes. The inhibitory edge that connects ‘Active_Gene’ with ‘mRNA’ degradation introduces the rule that there is no net mRNA degradation if transcription is possible. We then introduce a second rule that prevents the unnecessary firing of the transcription reaction, when ‘mRNA’ has two tokens, which is a maximal number of tokens in this model. This rule is implemented as an inhibitory edge, which sets propensity of transcription to 0, if ‘mRNA’ has two tokens. Together, these rules result in ‘mRNA’ place acquiring two tokens when conditions of transcription are satisfied and remaining at this state as long as the transcriptional pre-conditions are met. When conditions for transcription are no longer satisfied, the degradation transition removes tokens from the ‘mRNA’ place. Translation and protein degradation are modelled in the same fashion. Thus, we can describe the rise of a transcript/protein to two functional levels and its subsequent degradation in a rule-based model that uses only a few discrete activity levels and is computationally efficient.−3 . The ‘dNTPs’ and ‘AAs’ are connected to transcription and translation transitions as logical pre-places, modelling the precursor requirement of these processes. Logical PN nodes (depicted as shaded places) are an established feature of extended PN formalism, meaning that every ‘dNTPs’ and ‘AAs’ node has the same token status across a PN network. An additional rule is introduced to trigger net degradation of mRNA/protein if transcription/translation stops because of a lack of precursors.Our PN model of gene expression also includes the metabolic demands of transcription and translation processes. Although the model shown in To complete our illustration of a general gene expression model and its coupling with whole-cell metabolism, we have introduced transcriptional regulation by a transcription factor that senses availability of a small molecular agonist produced by metabolic network and made synthesis of this metabolite dependent on enzymatic activity of a protein produced by the ‘Gene’. We use intracellular cholate as an agonist and cholesterol-7-alpha-monooxygenase (CYP7A1) for enzymatic activity. The agonist is an objective node, the state of which depends on maximal producibility of intracellular cholate. The ‘Protein’ is a constraint node, which sets bounds of CYP7A1 catalyzed reactions in HepatoNet1. We then model interference of the agonist with transcription factor binding at the site controlling transcription initiation. The free and bound state of the binding site is represented by two PN places, with transcription factor and agonist affecting transitions between both forms (i.e. the binding site is bound if transcription factor is present and agonist is absent).We used the model to perform qualitative simulation of gene expression dynamics B, with tSupplementary Materials). The oscillatory behaviour can be modelled with just two activity levels and thus the number of molecular events that need to be simulated is relatively small. This is important, as any change of state may potentially trigger evaluation of objective functions of whole-cell metabolic model, the most computationally expensive step of the QSSPN. Thus, apart from addressing the major challenge of sparse quantitative information, the rule-based approach shown here has a substantial computational advantage over ordinary differential equation (ODE) or stochastic simulation; in quantitative models many state changes would have to be simulated to model the balance between synthesis and degradation, requiring a lot of CBM evaluations. In contrast, our novel rule-based gene expression model generates complex qualitative dynamics with far fewer state updates.The timecourses of gene expression dynamics qualitatively reproduce the major qualitative features of gene expression behaviour and its coupling with whole-cell metabolism. When transcription activation conditions are satisfied, transcript and protein quickly reach their functional steady states. When enzymatic activity of the protein enables synthesis of the agonist, transcription is no longer possible, mRNA and protein degradation processes are no longer balanced by synthesis and both transcript and protein products degrade. This negative feedback leads to oscillations and demonstrates that QSSPN can generate qualitative trajectories exhibiting complex dynamic behaviours. In the following case study, we will demonstrate that these trajectories are directly comparable with readily available experimental data. Moreover, the simulation of these trajectories is computationally efficient and crucial for generation of trajectory samples .Using the QSSPN framework, we have reconstructed a molecular interaction network representing whole-cell metabolism of hepatocyte coupled to the gene regulation and signalling processes known to be involved in BA homeostasis. For the QSSF, we use the published HepatoNet1 whole-cell reconstruction of human hepatocyte metabolism . As suchet al. where cultured human hepatocytes were treated with an FXR-specific agonist and subject to small interfering RNA (siRNA) knock-out of SHP  evaluation of QSSPN predictive power against the complete set of experimental data available in Supplementary Material Section 5). Finally, we argue that further refinement of the model, to reproduce all 14 experimental behaviours available in The experimental data B show thin silico gene knock-out 120 trajectories were run. Subsequently, we calculated the fraction of trajectories showing six behaviours of interest designed to monitor BA homeostasis . The analysis identifies a cluster of three genes, FTF, HNF4α and CYP7A1 that influence all behaviours to maximal extent. Knock-out of any of these genes results in all simulated trajectories exhibiting slow cholesterol clearance and no other behaviours. Our analysis also identifies SHP as a key regulatory molecule in BA homeostasis, as it is the only gene knock-out that significantly decreases the probability of slow cholesterol clearance. Such rapid cholesterol clearance is through the unregulated synthesis of BA, which could result in BA accumulation and toxicity. The mechanistic rationale underlying this observation is the fact that SHP transcription is regulated by FXR, which is activated by primary BAs. As SHP acts at the DR1 binding motif and inhibits production of BA synthesis enzymes, forming a negative feedback loop. Elimination of this feedback loop leads to a physiological imbalance in cholesterol clearance and disrupts the composition and concentration of the BA pool.Simulations with our model also identify the coupling of the chenodiol and cholate branches of the BA synthesis pathway through the regulatory network. Knock-out of CYP8B1 affects both chenodiol and cholate homeostasis, despite only acting in the cholate branch of primary BA synthesis pathway. Simulations of CYP8B1 knock-out with the HepatoNet1 model using conventional CBM alone changes the maximal flux towards cholate from 0.898 to 0.1, without impacting on the maximal flux towards chenodiol. However, in our QSSPN model, CYP8B1 knock-out gene significantly decreases the number of trajectories in which both chenodiol and cholate rise to a maximal level. Examination of simulated trajectories and network connectivity shows that both branches of the BA biosynthesis pathway are coupled through the transcriptional regulatory network of nuclear receptors. Both primary BAs are FXR agonists and FXR activates the bileacyl-CoA synthetase (BACS) enzyme through an IR1 binding site in its promoter region. BACS impacts both chenodiol and cholate synthesis. Therefore, when CYP8B1 is inactivated, the maximal flux towards cholate decreases, decreasing the probability of FXR activation, BACS up-regulation and so affects the synthesis of both primary BAs. This result is a novel mechanistic insight into the clinically important process of BA synthesis, which could not have been obtained by FBA simulation of metabolic reaction network alone.Supplementary material provides the C++ source code and Mac OSX and Linux binaries of command line tool under GNU general public license (GPL). The models are built with Snoopy, a general graphic PN editor available as free software . Samples are generated for WT and perturbed states and the fraction of trajectories exhibiting a behaviour of interest is calculated for each state. QSSPN can be used to test not only simple reachability of a particular node of the network or the producibility of a particular metabolite, but also occurrence of dynamic behaviours (e.g. bursts and oscillations). We use piecewise linear definition of the stochastic transition propensity, where contribution of the pre-place  to the propensity is determined by a lookup table with thresholds  and 2. Tsupplementary material, we present detailed comparison with existing approaches and the remaining part of this discussion summarizes its conclusions. First, the only simulation of human metabolism in a quasi-steady state framework published so far . We show that to faithfully model human cell systems the original rFBA needs to be modified to remove reliance on maximization of biomass and simulation of cell culture growth. Furthermore, we show that even the best adaption of rFBA to simulation of human cell is still not able to achieve the predictive power of QSSPN .Conflict of interest: none declared.


Many approaches utilize metabolic pathway information to reconstruct the phyletic tree of fully sequenced organisms, but how metabolic networks can add information to original genomic annotations has remained open.We translated enzyme reactions assigned in 1075 organisms into substrate-product relationships to represent the metabolic information at a finer resolution than enzymes and compounds. Each organism was represented as a vector of substrate-product relationships and the phyletic tree was reconstructed by a simple hierarchical method. Obtained results were compared with several other approaches that use genome information and network properties.Phyletic trees without consideration of network properties can already extract organisms in anomalous environments. This efficient method can add insights to traditional genome-based phylogenetic reconstruction.Structural relationship among metabolites can highlight parasitic or symbiont species such as spirochaete and clamydia. The method assists understanding of species-environment interaction when used in combination with traditional phylogenetic methods. Understanding the phyletic relationship among living organisms has long been a fundamental challenge since the concept of evolution had emerged. Traditionally, molecular biologists constructed phylogenetic trees based on the sequence similarity of small subunit ribosomal RNA  or otheret al. used a distance computed by the exponential graph kernel, i.e., the weighted sum of similarities between adjacency matrices of 1-step neighbors, 2-step neighbors, and so on for 81 organisms [et al. defined existence/absence of metabolic pathways and computed the network similarity measure for 47 organisms [et al. used sets of EC numbers to define pathway similarity and compared metabolism of 8 bacteria [In parallel with genomic comparisons, many studies focused on the similarity of metabolic processes. Metabolic profiles of a living organism are strongly related to its environment, and metabolism is adapted to balance compounds taken up from its surroundings ,6. Thus,rganisms . The secbacteria .et al. converted each enzymatic reaction to a fully connected bipartite graph between substrates and products to enhance connectivity and defined ‘seed’ compounds for each organism as the union of essential metabolites in all environments [Metabolic data are well standardized in previous approaches because all works depended on the bulk-downloadable KEGG database . Less coronments . This trEnzyme annotations and corresponding EC reactions for 1075 organisms  were obtained from the KEGG database through its application program interface. The number of EC reactions was 3116, covering as many as 154 pathway maps. Metabolic annotations in each species were represented as a set of substrate-product relationships by transforming all assigned EC reactions into a set of metabolite pairs (see the next section). Most EC-numbered entries correspond to multiple enzymatic reactions. For example, alcohol dehydrogenase (EC 1.1.1.1) can catalyze a multitude of compounds with a hydroxyl group. For such generic EC-numbered functions we manually integrated possible reactions to ensure the coverage of biochemical transformation shown in the metabolic maps.substrates) and outputs (products). Although standard metabolic pathway charts are depicted as hypergraphs, substrate-product relationships must be specified for each reaction to transform it into a graph. A standard way is to use a fully connected bipartite graph [An enzymatic reaction usually has multiple inputs  using the Cluster 3.0 software program . Each orWe compared results of our data representation with several recent, well known studies.To compare with the phylogeny reconstruction based on the ‘seed’ metabolites , we recoNanoarchaeum equitans, which is an obligatory symbiont on Ignicoccus. It lacks many essential metabolic pathways and therefore became an orphan branch in our reconstruction. Similarly, the reconstruction reflected more on metabolic phenotypes rather than genetic evolution. For example, Mycoplasma spp. were located far from the other bacteria and closer to eukaryotes in our tree because they lack many metabolic pathways . This defect was also observed in the comparison with the ‘seed’-based tree. Some invertebrate parasites were also grouped with Caenorhabditis elegans due to their metabolic similarity of unknown reason. Note that systematics of C. elegans is contentious and still unresolved because of its high evolutionary rate [As the second comparison, our approach was compared with the golden standard tree, reconstructed by using concatenated alignment of 31 universal protein families covering 191 species  Figure . Our metary rate . In summMycobacterium tuberculosis and M. leprae into Gram-positive bacteria. In addition, parasites and symbionts (spirochaete and clamydia) were classified more correctly in our method. In summary, although overall classification was similar, we could better, or at least equally, classify parasitic or symbiotic species in comparison with the results with another phyletic approach.To investigate the information gain by considering metabolic network connectivity, we carefully compared our approach with the network topology-based approach . There aet al. investigated the relationship among 8 photosynthetic bacteria using pseudo-alignment of over 60 metabolic pathways using the EC hierarchy [Synechocystis (syn) and Synechococcus (syw), both of which belong to Chroococcales together with Thermosynechococcus elongates (tel). The misplacement of Chroococcales was observed in the work by Clemente et al. too and presumably results from the insufficiency of gene annotations in these species  and tel were isolated from rocks and hot springs, respectively, whereas the remaining 6 species were isolated from fresh or sea water. Therefore, the two species should be regarded as metabolic out-groups as in our classification.Clemente ierarchy . Lastly,s Figure . In termWe previously argued that metabolic hubs are better identified in the substrate-product graph than in other graph representations, because the approach does not count the frequency of metabolite names in reactions but the number of structural transformations . The num2 and NH3 is an unavoidable artifact of counting all decarboxylations and amino-transfers. High-degree metabolites are largely conserved. It can be seen that eukaryotes contain more reactions with glucuronate, glutathione, and galactose, which appear in drug metabolism. At the same time, eukaryotes use less L-aspartate- or 5-phospho-alpha-D-ribose 1-phosphate-dependent reactions. Archaea lack malonyl-acyl carrier proteins and coenzyme A, which often appear in lipid metabolism for eukaryotes and bacteria. Archaea also use L-glutamine more often than the other domains.Table To elucidate the metabolic differences between the three domains of life, we created a heat map of the substrate-product relationships in 535 species. In Figure Our reconstruction using substrate-product relationships efficiently extracted metabolically interesting species in comparison with the standard phylogenetic approach. Previous approaches which used metabolic information could also produce informative results -9,12, buOur approach is more robust to pathway gaps (incomplete annotation) or currency metabolites by evaluating each biochemical transformation with an equal weight. It is also robust to biases by the number of genes or their multiplicity. Standard phylogenetic methods can elucidate evolutionary relationship, whereas our approach can locate species of anomalous or interesting metabolism in comparison. Therefore, the method is useful in combination (not exclusive) with existing phyletic/phylogenetic clustering.2VN) time for computing pairwise similarity, where N is the number of organisms and V is the maximum number of reactions in one organism. On the contrary, for example, the exponential graph kernel requires O(NV3+N2V2) time to compute the similarity [et al[Our method is also computationally lightweight and scalable, requiring O and a rare reaction type (e.g. sterol synthase) are given the same weights. For this reason, standard parsimony or evolutionary distance does not properly reflect the distance between species in our scheme. Since we wanted to focus on metabolic differences, the complete linkage method was employed. However, other algorithms should be systematically tested and evaluated for their appropriateness, which is left as our future work.We publicize the substrate-product relationships on a wiki-based site so that readers can check every detail of our analysis. This is especially important in the era of high-throughput data management because more and more research results tend to become irreproducible due to the insufficiency of publicized data or incomplete description of methods. To overcome this difficulty, the traceability and transparency of data and their analysis is important in the evaluation of research.Phylogeny was reconstructed by using structural relationship between annotated metabolites. This method is robust to pathway gaps or gene copy numbers, and can extract metabolically anomalous species by comparing the result with other phyletic or phylogenetic reconstructions. Through several comparisons, our method could highlight metabolic anomaly in clamydia and spirochaete, both of which are well known parasitic species. The metabolic comparison thus assists understanding of species-environment interaction in combination with other gene-oriented strategies.There is no competing interests.MA designed, and CWC conducted research under supervision of PCL. CWC and MA wrote the paper together.