Leishmania infantum, causative agent of visceral leishmaniasis in humans, illustrates a complex lifecycle pertaining to two extreme environments, namely, the gut of the sandfly vector and human macrophages. Leishmania is capable of dynamically adapting and tactically switching between these critically hostile situations. The possible metabolic routes ventured by the parasite to achieve this exceptional adaptation to its varying environments are still poorly understood. In this study, we present an extensively reconstructed energy metabolism network of Leishmania infantum as an attempt to identify certain strategic metabolic routes preferred by the parasite to optimize its survival in such dynamic environments. The reconstructed network consists of 142 genes encoding for enzymes performing 237 reactions distributed across five distinct model compartments. We annotated the subcellular locations of different enzymes and their reactions on the basis of strong literature evidence and sequence-based detection of cellular localization signal within a protein sequence. To explore the diverse features of parasite metabolism the metabolic network was implemented and analyzed as a constraint-based model. Using a systems-based approach, we also put forth an extensive set of lethal reaction knockouts; some of which were validated using published data on Leishmania species. Performing a robustness analysis, the model was rigorously validated and tested for the secretion of overflow metabolites specific to Leishmania under varying extracellular oxygen uptake rate. Further, the fate of important non-essential amino acids in L. infantum metabolism was investigated. Stage-specific scenarios of L. infantum energy metabolism were incorporated in the model and key metabolic differences were outlined. Analysis of the model revealed the essentiality of glucose uptake, succinate fermentation, glutamate biosynthesis and an active TCA cycle as driving forces for parasite energy metabolism and its optimal growth. Finally, through our in silico knockout analysis, we could identify possible therapeutic targets that provide experimentally testable hypotheses. Leishmania infantum is the causal agent of visceral leishmaniasis, a systemic disease that is transmitted by female phlebotomine sandflies [Leishmania parasites have been extensively scrutinized for the carbon sources that it prefers during its lifecycle [Leishmania amastigote metabolism is more or less fragmented and incomplete [L. infantum achieves in both the physiological states still needs to be accomplished. With the aid of transcriptomic and proteomic analyses, it is speculated that certain metabolically crucial enzymes display characteristic stage-specific regulation, both in mRNA and protein levels aiding the parasite in adapting to changing environments [andflies . The disandflies . The parandflies –5. Theseifecycle . But, incomplete . Also, aronments , 5, 8–10Sequencing of parasite genomes has paved way to the reconstruction of metabolic pathways from genome data . MetabolLeishmania, a genome-scale model of L. major metabolism was reconstructed using heterogeneous information and was analyzed using flux balance analysis to understand whole cell metabolism in the cutaneous species and predict genes essential for its growth [Leishmania species and to be essential for either survival or virulence [L. infantum parasite. With the objective to study the energy metabolism of the visceral species Leishmania infantum, we here de novo reconstructed a constraint-based model iAS142 that accommodates the pathways related to glucose metabolism, energy metabolism and biosynthesis of non-essential amino acids. The iAS142 model encompasses a total of 237 total reactions, out of which 115 reactions could be associated with a total of 142 genes. The reactions were distributed across 5 different model compartments: four subcellular–the glycosome, the mitochondrion, the mitochondrial intermembrane space and the cytosol, and an extracellular for exchange of metabolites. We adopted a similar strategy for metabolic reconstruction as other reconstruction studies [Previously, a number of constraint-based models have been published on Trypanosomatids –17. Specirulence , 19. Addirulence –24. Ther studies . But, weLeishmania species; and also by ii) enumerating model conditions so as to capture the secretion of experimentally observed overflow metabolites in Leishmania. We compared our Leishmania specific biomass objective function with the biomass previously used in the iSR215 Trypanosoma cruzi constraint-based FBA model [From our model, we explored many scenarios of parasite growth and attempted to capture the changes in energy metabolism with respect to the changing environmental conditions. To analyze the model, we presented a novel biomass equation from formerly published 13C isotopic enrichment data . The bioLeishmania species, identification of novel drug targets in an early discovery phase has become increasingly important so as to design new small molecule inhibitors that can serve as potential drug candidates against the parasite [Leishmania have been proposed previously, only few of them could be validated through experiments [As a part of rational drug design in parasite , 24. TheLeishmania infantum energy metabolism substantiating the strength of suitable in silico metabolic reconstruction strategies in creating biologically feasible predictions. Additionally, the model reaction knockout analyses along with simulation of chemotherapeutic interventions give a larger applicability of a constraint-based model in predicting and categorizing chemotherapeutic targets.Thus, our simple modeling approach could reveal many important cellular consequences of the Leishmania infantum, here we reconstructed the GPR considering the reactions involved in energy generation (ATP) and production of critical metabolites by following a stringent reconstruction strategy considering heterogeneous data, tools and supporting analyses  updated as of 16/12/2011. The reactions considered in the model and the corresponding Enzyme Classification numbers (E.C Nos.) were curated from databases like BRENDA [Leishmania infantum. Each enzyme was annotated for its molecular function, its associated pathway, and its subcellular location within the cell.The genes considered for model reconstruction were obtained for e BRENDA , Expasy e BRENDA . The resThe molecular function of each protein was annotated through primary sequence search against databases like NCBI GenBank , UniProtLeishmania and other Trypanosomatids were referred for curating the subcellular location of the enzymes considered in the model  was unavailable, subcellular location was explicitly assigned by in silico identification of subcellular localization signals within each protein sequence. TargetP was used for predicting the presence of a mitochondrial target peptide within a protein sequence [Most of the reactions were assigned to a particular cellular compartment on the basis of direct literature evidence, which could suggest the subcellular location of the enzyme catalyzing that particular reaction. Reaction information from odel see . Hence, sequence . A similsequence . For trasequence –40. Scansequence  was usedsequence . PTS-2 wsequence .in silico using the ProtParam Tool [Almost all glycosomal proteins have isoelectric point (pI) in the range of 8.8–10.2 , 42, 43.ram Tool . For exaLeishmania, obtained through sequence search were also scanned for the presence of mitochondrial targeting peptide or peroxisomal targeting signal. If these selected homologues also displayed the presence of targeting signals, then a higher confidence was given to the probable location assigned. If not, then the assignment of function was made purely based on the results acquired from sequence-based prediction of subcellular location with low confidence. For certain reactions, the subcellular location was not clearly identified through experiments, and is rationally assumed to occur in a particular subcellular location. One such reaction is glycosomal triose phosphate isomerase (TPIg), which is assumed from experiments to occur in the glycosome although the sequence-based subcellular location analysis does not indicate presence of any subcellular signals. For such reactions, a score of 2 was assigned so as to account for the uncertainty of its subcellular location through experiments. Thus, TPIg was assigned to the glycosome with a score of 2 and then included in the network.Based on all the above mentioned analysis, a confidence score was evaluated for the location of every reaction. The confidence score is designed in such a way that prediction of an enzyme’s location when supported by literary evidence is given more importance and the assignment of location solely based on sequence analysis is considered to be less significant see . The reaTrypanosoma and Leishmania and their associated substrates was collated. Protein sequences with considerable sequence similarity to the above given transporter protein sequences were then associated with transport of the particular substrates considered in our model  followed by the number of genes that are part of the model (142).According to the previously established convention of naming d models , the comS, a mathematical representation of the reconstructed network. The S matrix comprises of m reactions and n metabolites (dimensions of S are m x n). Each element in Sij represents the stoichiometric coefficient of metabolite i in reaction j. The coefficients are positive if the concerned metabolite i is a product in reaction j and negative if a reactant. The metabolic iAS142 model comprises of 237 reactions and 231 metabolites highly interconnected between 5 distinct model compartments. The stoichiometric matrix S for this system is of size 231 x 237. The vector v has 237 fluxes, including 27 exchange fluxes. Note that each reaction flux in the flux vector is constrained between bounds a and b. All reversible reactions considered in the model were given bounds as a = -1000 and b = 1000, the default considered in rBioNet toolbox [a = 0 and b = 1000. For metabolite exchange reactions, exchange specifically considering release of a particular metabolite from the cell were bounded between a = 0 and b = 1000, whereas exchanges considering uptake of a metabolite were bounded between a = -1000 and b = 0. After applying the required constraints, the model was analyzed using Flux Balance Analysis (FBA) [The list of reactions along with the metabolites was transformed into a stoichiometric matrix  toolbox . The bouis (FBA) .Bacillus and Tetrahymena respectively, to construct the objective function [L. mexicana developmental stages, where glucose in the medium was labeled with 13C isotope [The objective function used in previous studies was constructed using biochemical data of cellular composition, available in the literature for various organisms , 17, 51.function , 17. In  isotope . See SecLeishmania is performed in a completely defined medium (CDM) which is majorly composed of glucose when compared to the other carbon sources [Leishmania [Leishmania as compared to other carbon sources, the biomass objective function based on the 13C isotopic enrichment data attained from a CDM containing 13C labeled glucose, would be as close to the actual metabolic demand reaction of L. mexicana. As a proof of concept, this derived biomass objective function can possibly be applied to L. infantum, considering it to be an evolutionarily close relative of L. mexicana. It is important to note here that, none of the previous metabolic reconstructions have considered radio-labeled isotopic enrichment data for deriving the objective function. Further, it can be observed that the biomass reaction accounts for precursor metabolites of different pathways related to energy and non-essential amino acid metabolism in Leishmania. Further, other energy and amino acid metabolic reconstruction studies of Trypanosomatids also considers precursor metabolites in their biomass reaction [Trypanosoma cruzi [The cultivation of the different developmental stages in  sources . Glucoseishmania . Additioishmania , 53–55. reaction . Also, Areaction , 17, 51 ma cruzi ) we simuModel simulations were performed by changing the bounds of different reactions and validating them with existing biological observations. Exchange for glucose was constrained such that there will be uptake of glucose. Exchanges of non-essential amino acids were selectively opened along with glucose to understand their fate. The exchanges of essential amino acids have been constrained to zero, to ensure that the model simulations are dependent only on glucose as an essential substrate. Also, exchange of overflow metabolites were constrained to be excreted outside the cell. The default model simulations correspond to the situation where glucose is abundant and the sole carbon source in the environment. Flux balance analysis of the network was performed using the COBRA toolbox . For skeai = bi = 0), sequentially one reaction at a time, and FBA was performed subsequent to each reaction knockout in a medium containing only glucose. Further, to perform double reaction knockouts, the bounds of different reaction pairs were constrained to be zero and FBA was performed subsequent to each combination knockout keeping glucose as the sole carbon source. In each of these knockout simulations, the transport fluxes of glucose and oxygen were fixed to their optimal flux value attained from the wild type simulation (the default FBA run devoid of reaction knockouts). Glucose is present as its anomers—alpha-D-glucose (Aglc-D) and beta-D-glucose (Bglc-D) in the model which interconvert by the reaction catalyzed by aldose-1-epimerase. Accordingly, transports for alpha-D-glucose and beta-D-glucose have also been considered separately in the model. Therefore, in order to avoid degeneracy of glucose uptake from either of these transports, one of them was closed during reaction knockout study. For both the single and double reaction knockout studies, a reaction proved to be essential  when biomass reaction flux became zero after applying the aforementioned constraints; else it was deemed to be non-essential .To identify the reactions essential for parasite growth and to simulate the effect of the single reaction deletions, the upper and lower bounds of all the reactions were constrained to be zero  and T. cruzi (iSR215 model) have been reconstructed and analyzed using flux balance analysis [L. infantum iAS142 model has been curated de novo for the L. infantum genome with respect to updated information obtained from literature, it became important to identify the significant differences with respect to energy metabolism between the three models. The differences in reaction subcellular locations and metabolites used in the three models were compared and enlisted. These differences can help to understand the differences between behaviors of the metabolic networks.Previously, among the Trypanosomatids, the metabolic networks of ruzi iSR2 model haanalysis . As the L. major iAC560 were extracted separately. The bounds of the individual reactions were also fixed to the same values in both the models. FBA was performed using the iAS142 biomass function; both for the iAS142 metabolic network and for the corresponding subset of reactions from the L. major iAC560 genome scale metabolic network. To quantify the differences, fluxes through the exchange reactions and biomass reactions from each of the models were monitored. To understand the degree of association between the L. major iAC560 and L. infantum iAS142 flux profiles, the non-parametric Spearman correlation was used. Students’ t-test was used to compare the magnitude of fluxes of reactions related to glycosomal lactate fermentation between the two models [Further, to assess the effects of these model differences on network behavior, reactions representing the glucose and non-essential amino acid network of the o models .The stoichiometry of amino acid uptakes in the model is from cytoplasm to extracellular space. Hence to impose constraints such that the amino acids are only taken up by the network, the upper bound of the exchange flux of aspartate, glutamate, proline and alanine amino acids was fixed to 0 (zero) and the lower bound to -1000. FBA was performed under these constraints for measuring each amino acid uptake flux value. The flux profiles were saved and the important reactions shown in the heatmap were grouped according to the pathway they belong. In order to understand the effect of all amino acid uptakes when coupled with glucose uptake, the upper bounds of all four of these amino acid exchange fluxes were simultaneously fixed to 0 (zero) and the lower bound to -1000. In all the simulations, exchanges of essential amino acids have been kept zero as pathways involved in catabolizing them have not been considered in the iAS142 network.L. mexicana developmental stages were previously shown to co-utilize glucose and a few, selected non-essential amino acids like glutamate, aspartate, alanine and proline, when cultured in a CDM containing a range of carbon sources [L. infantum identified preferential expression of hexokinase, ATP-dependent phosphofructokinase/6-phospho-1-fructokinase, glycosomal glyceraldehyde-3-phosphate dehydrogenase, and PAS-domain containing phosphoglycerate kinase in promastigotes as compared to amastigotes [L. major was used elsewhere [ sources , 19. Henstigotes . Thus, flsewhere . FBA waslsewhere .To simulate intervention by chemotherapeutics in the amastigote stage, we varied the optimal flux values of the previously determined targets in the model-presumed amastigote stage and attempt to monitor the corresponding growth and ATP synthesis rates. For this simulation, the upper/lower bound of each target (with respect to its default bounds) was evenly varied from its optimal flux value observed in the amastigote stage presumed in the model up to zero. For every change in the bounds of the target reactions, a separate FBA simulation was performed by maintaining glucose as the only carbon source, to capture the steady state growth and ATP synthesis.L.infantum genome , and an ATP maintenance reaction constitute the iAS142 network. A total of 115 reactions could be associated with 142 genes from the m genome . NotablyL. infantum, by virtue of which the percentage of the reactions occurring in the cytosol, mitochondria and the cytosol appear to be nearly equal , are explicitly available for any Leishmania species  is used as a substrate for GLUDy and TRPAS1a reactions. Without ammonium transport, the GLUDy and TRPAS1a reactions would be affected creating an imbalance in NADP-NADPH ratios which would be deleterious to the cell. Hence, ammonium transport also governs a lethal phenotype. Further, mitochondrial membrane ATP synthase (ATPSmm) that is responsible for ATP production also governs a lethal phenotype suggestive of its coupling with growth  whereas the cytosolic ATPase reaction (ATPS) that represents a continuous drain of ATP is not dependent on growth maximization and hence, is not predicted to be lethal.NADPH cytochrome oxidoreductase (NADPH_CYOR) a reaction that was not considered in previous Trypanosomatid core energy metabolism reconstructions  is requiIn addition to single reaction deletions, we also performed double reaction deletions of all possible paired combinations of reactions considered in the model . A totalTrypanosoma species, we restricted ourselves to the insect-stage procyclic T. brucei phenotype information, as the promastigote and T. brucei insect stages exist in fly midgut. Comparison with every known growth phenotype in the insect stage Trypanosoma species further revealed that few growth phenotypes in Trypanosoma show substantial difference with the iAS142 model predictions  and mitochondrial  counterparts respectively. This produces a sink for the pyruvate that is produced from mitochondrial alanine aminotransferase, pyruvate dehydrogenase reactions and extracellular pyruvate uptake. This cycle causes fermentation of lactate to be preferred over succinate. This requirement of lactate production leads to a corresponding higher activity of the pentose phosphate pathway (PPP) reactions to maintain redox balance within the glycosome in the iAC560 model. This leads to an over production of CO2 from the 6-phopshogluconate dehydrogenase reaction which is released outside the cell to the extracellular , an objective function (Tryp_biomass) derived from the biochemical data of Bacillus subtilis was used for performing flux balance analysis on the model [In a previous study that modeled the energy metabolism in ruzi iSR2, an objeLeishmania parasite is able to persist in two extremely opposite environments, the sandfly gut and the human macrophage by switching between the promastigote and amastigote developmental stages, each stage adapted to survive in a particular environment. In order to identify the metabolic routes by which L. infantum achieves this feat, we recreated model scenarios that might represent the promastigote and amastigote metabolic states , the mitochondrion, the mitochondrial intermembrane space and the cytosol and an extracellular for exchange and transport of metabolites from the cell to the environment. The main point to note here is that none of the previous constraint-based models have considered the mitochondrial intermembrane space compartment [In this paper, we present the first constraint-based model reconstruction and analysis of energy metabolism in partment , 17, 51.L.mexicana promastigotes grown in medium containing 13C labeled glucose [L. infantum metabolism could be fairly demonstrated. Further, the iAS142 biomass was compared with the biomass objective obtained from a previously published Trypanosoma cruzi iSR215 model to enlighten the influence of biomass objective on reaction flux distribution [The iAS142 metabolic network was analyzed using flux balance analysis with respect to a novel metabolic demand/biomass reaction; developed using 13C isotopic enrichment data acquired from  glucose . None of glucose –17 have in silico reaction knockout analysis and comparison with experimentally known phenotypes. With respect to available knockout phenotype information in Leishmania, the model could predict the corresponding known growth phenotypes associated with 7 reaction knockouts with an absolute accuracy of 100%. Apart from validation purposes, the reaction knockout study gave a distinct biological insight into the crucial role played by every reaction in L. infantum energy metabolism. Even though it is inappropriate to compare the model predictions with Trypanosoma species that show stage specific differences in metabolism and reside in different environments than Leishmania, the model predictions were compared with available non-stage specific Trypanosoma knockout phenotype data only to further stress on the fact that the model was indeed Leishmania specific giving biological reasoning behind every single gene deletion phenotype predicted from the model. A total of 61 lethal reactions were identified through single reaction deletions in the network and 55 non trivial lethal reaction pairs were proposed to be essential through double reaction deletions. Each one of these deletions constitutes a promising drug target and an experimentally testable hypothesis, which we considered further to show the chemotherapeutic intervention scenarios for 9 reactions predicted to be essential for parasite growth from the model reaction knockout analysis.A two-tier validation of the model was performed to assess its importance in predicting the actual metabolic aspects as perceived from various experimental studies. The first stage of model validation was performed through prediction of growth phenotypes using L. infantum, many knockout validations were not made from L. infantum data alone, but also considering data obtained from other Trypanosomatid species. Second, as the model considered here is not a genome-scale model, there might be other essential pathways that might be connected to core energy metabolism but not considered in the model. Hence, it is possible that the model might predict a reaction to be non-lethal, even though in the whole genome scale context it might be lethal or vice versa. Third, the experimental knockout data for validation purposes were collected from heterogeneous studies that might have considered different experimental conditions or media to generate knockouts, which are not explicitly implemented in our model. Hence, we prefer to use the model reaction knockout analysis as a predictor of essential genes required for parasite growth rather than a basis for validating our model.Even though the model predictions are usually validated through reaction knockouts, there are three important shortcomings in validating a constraint-based model through reaction knockout studies . First, Leishmania is known to exhibit an overflow metabolism during which it secretes substantial amount of succinate, acetate, pyruvate, CO2 and small amounts of lactate [Leishmania specific. Sequence analysis and experiments indicate absence of a functional D-lactate dehydrogenase in Trypanosoma species [Trypanosoma species have been shown to demonstrate L-lactate secretion instead of D-lactate, the pathway for this mechanism is still unknown [Leishmania specific overflow metabolites, the model could be appropriately validated.In order to overcome the limitations of validation through reaction knockout studies, by performing a robustness analysis with respect to changes in oxygen uptake in our model, we attempted to validate the model by identifying model conditions to discern the secretion of overflow metabolites.  lactate , 58. Thi species , 72, 74. unknown . Thus, wL. infantum. 13C isotope resolved metabolomics in L. mexicana developmental stages revealed a reduction of glucose uptake, glutamate uptake and secretion of overflow metabolites in axenic amastigotes as compared to promastigotes [Promastigote and amastigote specific metabolic scenarios were created from the model so as to observe the stage specific differences in the energy metabolism of stigotes . SimilarL. mexicana promastigotes [L. infantum energy metabolism as implemented in the iAS142 model that governs this metabolic behavior. Also, it is through the same metabolic route that the cellular energy maintenance of the parasite is met. This particular route was also, preferred in both the promastigote and amastigote scenarios of energy metabolism that were recreated in the model. Fascinatingly, model reaction knockout studies also predicted cytosolic NADPH–dependent glutamate dehydrogenase to be crucial for Leishmania infantum. All this information point towards the role played by succinate fermentation and glutamate biosynthesis in driving energy metabolism further establishing the fact, that the enzymes of succinate fermentation and glutamate biosynthesis could possibly be novel therapeutic targets for the L. infantum parasite.The reaction knockout studies could predict the enzymes of succinate fermentation as essential for the organism’s growth suggesting the role of succinate fermentation pathway in maintaining a redox balance within the glycosome by regenerating the NAD molecules consumed by the enzymes of upper glycolytic pathway , 18. FurLeishmania species, identification of novel drug targets in an early discovery phase has become increasingly important so as to design new small molecule inhibitors that can serve as potential drug candidates against the parasite [in silico chemotherapeutic intervention scenarios within our model-presumed amastigote stage for 9 essential reactions predicted by in silico reaction knockout analysis carried out in the iAS142 model. By partially reducing the optimal flux value of each of these individual reactions in the amastigote scenario, a minimum inhibition threshold a chemotherapeutic needs to exert on each reaction to achieve zero parasite growth was identified through this simulation. Accordingly, the predictions indicated that for glutamate dehydrogenase and phosphoglucomutase reactions in comparison to the other 7 reactions, a minimal reduction in enzyme activity/reaction flux brought about an immediate decline in the parasite growth suggesting their choice as an important drug target.As a part of rational drug design in parasite , 24. Theparasite , 75–77. Leishmania infantum. As compared to other metabolic reconstruction studies in Trypanosomatids, our model accounts for a unique compartment like the mitochondrial intermembrane space and 36 novel intracellular reactions assigned to appropriate subcellular locations. In the process of model reconstruction, annotation of certain genes was refined and corresponding reactions to their appropriate subcellular locations were dispensed. The model was analyzed using a biomass objective function based on 13C isotope enrichment data; this also, being unique to the iAS142 model. With the aid of reaction knockouts, robustness analysis of overflow metabolites and observations in the effects of different amino acids on parasite energy metabolism, innumerable features of parasite metabolism could be extensively explored.In this study, we presented a reconstructed metabolic network for in silico therapeutic intervention scenarios created in the model specific for the amastigote could reveal an application of a FBA-based model in categorizing drug targets predicted to be essential from reaction knockout analysis for a parasite. Thus, from our simple but conceptually intensive model-based study, we could explore the different facets of the Leishmania infantum energy metabolism and substantiate the importance of such integrative metabolic reconstruction studies in unearthing the diverse features of parasite metabolism.Analyses of the model revealed important roles of succinate fermentation, an active TCA cycle, and glutamate biosynthesis on parasite survival and growth. Also, single and double reaction deletions in the model led to identification of promising drug targets that can be experimentally validated in the future. The promastigote and amastigote specific metabolic states created from the model suggest that amastigotes display a glucose-sparing metabolism by reducing the uptake of glucose from the environment. The S1 FigThe bar plots show the differences in flux profiles of amino acids supplemented with glucose. A) Bar plot showing absolute flux values of amino acid uptakes when supplemented with glucose for which we get optimum biomass B) Bar plot showing growth rates when glucose uptake is supplemented with corresponding amino acids.(TIF)Click here for additional data file.S2 FigFlux distributions are overlaid on pathway map. The map distinctly shows that glycolysis, pentose phosphate pathway, TCA cycle and glutamate biosysnthesis reactions are constitutively activated in promastigote metabolism with high flux through every reaction. Also, there is an increased rate of ATP synthesis, glucose uptake and uptake of non-essential amino acids.(TIF)Click here for additional data file.S3 FigFlux distribution overlaid on pathway map. The map distinctly shows that glycolysis, pentose phosphate pathways and glutamate biosysnthesis reactions are constitutively activated in amastigote metabolism but, the reaction fluxes are considerably reduced as compared to promastigote metabolism. Also, there is reduced rate of ATP synthesis, glucose uptake and uptake of non-essential amino acids.(TIF)Click here for additional data file.S4 FigBar plots showing differences between the amastigote and promastigote specific metabolism at the pathway level. A) differences observed in the glycolytic reactions in the amastigote and promastigote stages B) differences observed in the TCA cycle reactions in the two stages C) differences in the pentose phosphate pathway observed between the two stages D) differences between other important reactions in both the stages(TIF)Click here for additional data file.S1 FileL. infantum energy metabolism reconstruction saved in both SBML and.mat file formats.This is a zip file that contains the iAS142 (ZIP)Click here for additional data file.S1 TableThis excel file contains the information curated for the iAS142 model reconstruction. It contains information about the reactions considered in the model along with the information about the genes and proteins associated with the reactions and their subcellular locations. A column for the confidence score for every reaction has also been included. The PubMed ID of the references is provided beside every reaction entry. The list of references curated are listed at the end of the excel file.(XLS)Click here for additional data file.S2 TableLeishmania.This excel file contains the set of enzymes whose subcellular localizations were confirmed by detection of cellular signals in their homologous protein sequences obtained as a result of performing BLAST against the RefSeq database excluding sequences from Genus (XLS)Click here for additional data file.S3 TableThis excel file contains the detailed information of the growth phenotypes predicted from the model by keeping bounds of glucose and oxygen fixed to their optimal values. The predictions have been compared with the experimentally observed growth phenotypes listing their references beside growth phenotype prediction of every reaction considered in the model.(XLS)Click here for additional data file.S4 TableThe flux profiles of every non-essential amino acid  supplemented with glucose separately and in combination are given in separate columns in the excel file. In order to give a comparison, the flux profile generated for the only glucose situation as a control has also been given.(XLS)Click here for additional data file.S5 TableThe excel file contains the flux distributions obtained from the model by considering the two biomass objective functions. This was done to explain the importance of choosing a biomass objective and how it might affect the model predictions.(XLS)Click here for additional data file.S6 TableFlux profiles generated in the promastigote and amastigote specific scenarios have been given in the excel file. The model was constrained for the uptake of glucose and non-essential amino acids in both the scenarios and flux profiles were generated using FBA.(XLS)Click here for additional data file.S1 TextSection A discusses about the formulation of the biomass objective function from 13C isotopic enrichment data. The other sections relatively support the results of the model described in the main article. It also contains three tables, Table SB, Table SC and Table SD, which are relevant to support the model analyses discussed in the methods and results section of main article.(DOC)Click here for additional data file.


We perform the theoretical analysis of a gene network sub-system, composed of a feed-forward loop, in which the upstream transcription factor regulates the target gene via two parallel pathways: directly, and via interaction with miRNA.As the molecular mechanisms of miRNA action are not clear so far, we elaborate three mathematical models, in which miRNA either represses translation of its target or promotes target mRNA degradation, or is not re-used, but degrades along with target mRNA. We examine the feed-forward loop dynamics quantitatively at the whole time interval of cell cycle. We rigorously proof the uniqueness of solutions to the models and obtain the exact solutions in one of them analytically.We have shown that different mechanisms of miRNA action lead to a variety of types of dynamical behavior of feed-forward loops. In particular, we found that the ability of feed-forward loop to dampen fluctuations introduced by transcription factor is the model and parameter dependent feature. We also discuss how our results could help a biologist to infer the mechanism of miRNA action. An important role in regulation of gene expression in higher eukaryotes, plants and animals belongs to miRNAs, the endogeneous small non-coding RNAs that bind to partially complementary sequences in target mRNAs. The miRNAs are involved in regulation of development, differentiation, apoptosis, cell proliferation -4, as weHowever, it should be noted that the mechanisms of miRNA action are not unanimous. There are experimental evidences that miRNAs regulate gene expression through translational repression, mRNA deadenylation and decay, however the contribution and timing of these effects remain unclear ,15. AlthCaenorhabditis elegans showed that targets can also protect miRNAs from active degradation [Mathematical modeling is often used to discriminate between these tentative mechanisms. It was shown that variability in the miRNA action on protein production in different experiments could be due to differences in rate-limiting steps . Morozovradation ,23The role of miRNA in gene regulatory networks becomes currently a subject of wide speculations. In general, it is expected that motifs with miRNA can buffer the consequences of noise action in gene expression in order to confer a robustness to environmental perturbation and genetic variation ,24. The direct regulation path coincides with the overall sign of the indirect regulation path, and "incoherent" otherwise.The transcription networks contain several biochemical wiring patterns called network motifs, and one of the most significant recurring motifs is the feed-forward loop (FFL) -32, in wRecent computational analysis demonstrated that FFL with TF and miRNAs are overrepresented in gene regulatory networks, assuming that they confer useful regulatory opportunities . There aalgebraic equations only, obtained by trivial reduction of the coupled 1st order ordinary differential equations (O.D.E.) to a steady state. For stochastic statement of the problem in [A simple mathematical modelling was used recently to explore the capability of FFLs with miRNA to buffer fluctuations in gene expression. Osella et al.  introducoblem in  O.D.E. wis not reached before the cell division. As a consequence, quantities per cell are not only defined by synthesis and degradation, but also by an initial number of protein molecules at the beginning of cell cycle. Secondly, an absence of time derivatives (as in the steady state approximation) is provided by simple replacement of the initial coupled kinetic non-linear equations with corresponding algebraic equations, avoiding any information about the temporal behaviour of cell components. A variety of the cell process models usually demonstrate versatile dynamics at early stages even in case of coincidence of stationary values. For these reasons it is much more faithful and informative, however difficult, to study coupled ODEs at every time moment, aiming to decipher mechanisms underlying its dynamics. It is worth to mention the importance of analytical solutions, which provide a genuine 'check point' for any numerical simulation often obtained by means of different methods.There is a critical imperfection in any mathematical model based on the steady state data analysis. Firstly, latter measurements ,36 of prIn general, it is not simple to derive  differential equations, describing a biological system and obtain an analytic solution to them. Fortunately, many biological systems demonstrate the module structure, and therefore, at least, in theory, they can be decomposed in segregated subsystems, and, with luck, the equations can be solved in closed form.the non-uniqueness of solutions. This non-uniqueness is partly caused by imperfections of current experimental methods, which are often unable to provide the measurements of all the parameters required to describe the system dynamics. As a result the parameter values have usually to be found by numerical fitting of the solutions to data. This task, called "an inverse problem", is, in a way, tricky, because there are usually several parameter sets in good agreement with data. It means that within a given accuracy there are several models, which are, in a sense, equivalent in the data description. Non-uniqueness provided by numerical simulations represents a crucial problem for contemporary mathematical modelling in biology, and usually an appropriate solution may be found by invoking additional information from complicated experiments. On the other side, an intrinsic non-uniqueness may have transparent biological reasons, as biological subsystems are robust and can tolerate large parameter variation, as long as the core network topology is retained [Another challenge in mathematical modeling of biological systems consists in retained ,38. TherHere we consider a gene network sub-system composed of a FFL mediated by TF and miRNA. We perform the analysis of three mathematical models, which describe temporal dynamics of gene expression in FFL under an assumption of different mechanisms of miRNA action. In contrast to  we examiNew computational experiments ,22 justiw of mRNA molecules transcribed from the TF gene, the number q of TF molecules, the number s of miRNA molecules, the number r of mRNA molecules transcribed from the target gene, and the number p of target protein molecules.The biological system under study will be described with 5 variables, representing the number We deal with the models proposed in  and consAs molecular mechanisms of miRNA action are not clear so far we consider three different models:Stop model,• the model, in which miRNA represses translation of its target - Target degradation model and• the model in which miRNA promotes target mRNA degradation - Dual degradation model.• the model in which miRNA is not re-used but degrades along with target mRNA - 'working titles' for the models introduced above will be used for brevity.and the Let us write five coupled differential equations proposed in  for a few kand q kare rates of TF mRNA and TF synthesis, ks(q) and r k(q) are rates of transcription of the regulated gene, pk(s) is the rate of target protein synthesis; wg, qg, sg, s gand p grepresent the degradation rates of the corresponding species.Here Before we shall specify the types of production functions in equations (1-4) let us remind that various dynamic processes in a complex system can be described as a progression from an initial quantity that accelerates (or decelerates in case of repression) and approaches a plateau over time. When a detailed description is lacking, a sigmoid function is used, that is based on an idea by A.V. Hill (1910) to describe the sigmoidal oxygen binding curve of haemoglobin. The general form of the Hill function is written as:α, β are arbitrary given parameters of the process. The rate c represents either production (c ≥ 2) of a quantity x or repression of it (c ≤ −2) in time. Consequently, the Hill function will be represented by either uprising or falling down graph, and its slope depends on the value of c. The easiest way to get a nontrivial regulation type is to prescribe the rate values c = 2 and c = −2 for activation and repression, respectively, however, even in this case the mathematical problem becomes the non-linear one.where both sk(q) and rk(q) are assumed to be the classical Hill functions in the form k(q) = (maxqck)/(c h+ cq). The parameters s hand r hspecify the amount of TF, at which the transcription rate of the miRNA or target gene reaches one half of its maximal value (s kor rk), and c is the Hill coefficient, representing the steepness of the regulation curve, see (2).In the problem considered the production functions Therefore for the type 1 coherent FFL  to be a repressive Hill function of the number of miRNA molecules: h specifies the quantity of miRNAs, at which the translation rate reaches one half of its maximal value pk, and c = −2 is again the Hill coefficient.We shall consider three different mechanisms of the miRNA action, following , and to r g(in absence of miRNAs), a term, which represents an increasing Hill function of a copy number of miRNAs, where max gis the maximal value of the degradation rate in case of high miRNA concentration, deg his the dissociation constant of miRNA-mRNA interaction, and c = 2 is the Hill coefficient.To model miRNA action in the destabilization of target mRNA we add to the basal rate of mRNA degradation rsk, and the resulting non-linear (due to the multiplicative term rs) equations will have a form:As in  we discuStop model we obtained the exact solutions to the non-linear ODE, which coefficients explicitly depend on initial values. Main advantage of exact solutions to corresponding non-linear differential equations is that they do not require any parameter fitting and provide also a reliable basis for verification of numerical results. For the Target and Dual degradation models the numerical solutions to the problem are obtained. For each model considered we proved also the uniqueness of solutions, i.e., the one-to-one correspondence between given parameters and solutions.Details of mathematical analysis of the coupled ODE are given in Additional file The mechanisms underlying miRNA-mediated repression are not clear so far, and for this reason we consider three models of the miRNA action described above.Four different topologies of FFLs mediated by TF and miRNA are possible in theory, as in Figure 1C will mean the type 1 coherent loop, 1In - type 1 incoherent loop, 2C - type 2 coherent loop and 2In - type 2 incoherent loop, resp. We assume that the initial number of molecules in a loop is equal to one half of that obtained just before cell division, which often  corresponds to the steady state level. The results for the Stop model are based on exact and explicit solutions obtained to the non-linear O.D.E. 1 , but with continuous repression of the miRNA synthesis, the target protein begins to rise up to the steady state level  at steady state, and the steady state level is reached later (about 4000 sec vs. 3000 sec) in comparison with 2In loop.Contrary to the Stop model in the Target degradation model the temporal dynamics of both target mRNA and protein is similar. In this model the target protein production is a linear function of the target mRNA molecules number, and miRNA promotes the degradation of target mRNA. In 1s Figure . In both1In and the 2C loops has a form of increasing function, tending to a constant value  than in 2C loop, that can be explained by promotion of the target mRNA degradation by miRNA in the 1In loop.The dynamics of target mRNA and protein in both the e Figure . The looC and 2In loops shows pulse-like behaviour , than in 1C loop. The target protein molecules number at steady state in 21n loop is also higher than in 1C loop (1800 molecules vs 1400 molecules). Moreover, all these numbers in the Dual degradation model are higher than in Target degradation model  and the level of target protein at steady state is lower (3000 molecules vs. 4000 molecules) than in 2C loop. Again, in the Dual degradation model these numbers are bigger than in the Target degradation model.In both 1Next step is to describe the behaviour of each type of FFL in the framework of each model under consideration. We should demonstrate that FFLs mediated by miRNA and TF may have many possible outcomes, depending on the nature of the relationships between the loop elements.The study of dynamical behaviour of FFLs is based on the variation of initial conditions, and model coefficients with subsequent analysis, how these changes affect the target protein molecules number. To simplify comparison in each numerical experiment we used one and the same parameter set, described in the Section above, except of the coefficient value, which effect on the loop behaviour will be analyzed. The dynamical analysis is important not only for the noise buffering ability, but also for demonstration of how sensitive are the control pathways to parameters and initial state.w kand qk), the number of miRNA copies , as well as the strength of the miRNA action. In the Stop model the strength of repression of mRNA translation by miRNA is defined as 1/ph. In the Target degradation model the degradation of the target mRNA is described by a term, which represents an increasing Hill function of a copy number of miRNAs, while 1/g hrepresents the strength of miRNA action. In the Dual degradation model the degradation constant of the mRNA-miRNA complex rs kis introduced. Therefore, in short, the idea of an analysis given below is to fix a type of FFL and investigate how the target protein molecule number p will vary in all models considered.The efficiency in control of the target protein synthesis in all three models depends upon the quantity of TFs  loop only. For other FFL subjected to parameter variation we have to refer to corresponding Figures and captions; the descriptive analysis will be similar to the one made for 1In loop.However, the detailed description of each FFL behaviour under variations of every parameter is quite lengthy, and for lack of space we shall do it for the type 1 incoherent  the variation of g hor rs kcoefficients has little influence on target protein production. In all models the difference in target protein production at different values of coefficients increases with time, as shown in Figure Mathematical analysis showed that the increase of y Figure . The difs hleads to increase in the target protein quantity  the target protein production does not depend on s hvariation; at later times the difference between two bounding s hvalues in the Target degradation model is much smaller than in other models. In all models the largest difference in target protein production is observed for large s hvalues  than in the Stop model (around 5000 seconds) , the number of miRNA copies (depending on s kand sh) and the strength of miRNA action on target mRNA . We studied the ability of FFLs to buffer noise as a function of each of these three quantities, changing a corresponding coefficient and keeping fixed all others. For each combination of a model, loop and coefficient value we performed 100 numerical simulation runs to estimate the average value of the parameter e and the number of experiments with positive value of this parameter as described in section. Positive values of ε mean that a loop cannot dampen noise introduced by TF, and vice versa negative values of this coefficient testify the ability of the loop to reduce TF noise.Consequently, we decide to investigate the ability of all FFLs with miRNA to buffer a noise caused by TF at all time moments and in all models. At each time moment we introduce the random fluctuations in TF quantity and measure how these fluctuations affect the target protein molecule number. We also consider how the variation of model coefficients influences the ability of the loops in noise damping. The efficiency of the FFLs in controlling the fluctuations of the target protein in response to noise introduced by TF depends on the number of TF molecules , has large variation. In the Stop model the maximal effect is achieved at intermediate values of the p hcoefficient.The 1In loop to decrease noise introduced by TF essentially depends on the q kcoefficient values: all the models are not able to efficiently buffer noise for large values of this coefficient (at q k= 0.16 the ε coefficient was positive in 9 - 14% of experiments), however, in the Stop and Target degradation models this effect becomes evident at larger q kvalues that in the other model  exposes to the ability of these loops to buffer noise weaker than in the Stop model   and in both the Target and Dual degradation models this loop loses the ability to efficiently reduce noise and starts to deal with the noise as in the Stop model.In the Stop model the 14) Table . For larC loop is able to effectively buffer noise only for very small values of s hand s kcoefficients in the Stop model: the larger are these coefficients, the less efficient is the noise reduction  decrease  the TF noise was reduced in all numerical simulations. In two other models the TF noise is always dampen . In the Stop model the ability of 2C loop to buffer noise decreases with the growth of sk: at small s k≤ 0.25 values the noise damping was observed in all simulations, while for higher s kvalues the fluctuations of the target protein molecules number are not reduced in many simulation runs , at larger coefficient values this loop starts to efficiently buffer noise ,- fast degradation of miRNA (when miRNA is degraded two times faster than TF or its mRNA) and- very fast degradation of miRNA (when miRNA is degraded three times faster than TF)  points among all others. By virtue of the uniqueness theorem this graph will correspond to most feasible regulation type in the FFL among all models considered.However FFLs are subjected to noise influence, and for this reason we studied the noise buffering in both coherent and incoherent FFLs, that led to conclusion that incoherent FFLs are better noise buffers than coherent ones Figure . MoreoveThe FFL dynamic behaviour analysis performed for different models and parameter sets shows that an extremal value of target protein quantity  may be accomplished for intermediate values of coefficients. This is valid also for the noise buffering problem, that required a simple analysis of the Hill sigmoid behaviour, see Additional file not be suppressed by a loop.In general, an action of any disturbance, e.g., a noise, having sufficiently small amplitude,  depends on the Hill function type and can be described as follows. For the Hill sigmoid functions, governing either an activation or a repression, the noise will be recognizable for intermediate molecule quantity. By virtue of analysis in the whole time interval we found that when the noise amplitude is high, but the total amount (the regular one plus the noise associated fluctuations) of miRNA is intermediate , then the noise is translated directly into the protein production process and will be suppressed by a loop.When the noise amplitude is still high, however, the total amount of miRNA is sufficiently high, too (the Hill function is close to any of limits), then the noise level is relatively small to disturb the protein production and will Many details of mathematical analysis are given in Section and in the Supporting Information files; here we briefly describe the numerical simulations. The coefficients used in mathematical modeling were mostly taken from , and forThe other coefficients used in both the Degradation and the Dual degradation models are:t = 5000 seconds. The initial numbers of components in each loop were equal to one half of their steady state values. The dynamics of solutions at early stages depends not only on coefficients, but on initial values, too. To analyze how the quantity of target protein molecules depends on the numbers of TF and miRNA molecules at initial time moment these numbers were changed from 0 to one quarter and one half, as well as to the values of two and four times higher, than at steady state .Numerical simulation of dynamics in each loop was made for the time period of z with the correlation function For the noise simulations we introduced a vector ξ is another vector, obtained by the MATLAB procedure, which contains the Gaussian white noise. The vector z represents the model of a stationary Markov process, and we may add its values at the moments i tto the number of molecules of TF, which is used in equations for the quantities of miRNA and target mRNA, and solve these equations numerically. In fact, the procedure mentioned is based on the Uhlenbeck-Ornstein process (1930), the only one, which is stationary random, Gaussian and Marcovian simultaneously. The process is widely used now in mathematical modelling of noise instead of any numerical version of the so called "white noise". The particle velocity in this process is finite, and taking into account the difference between a random force and the idealised white noise, one may provide a finite acceleration of the particle, too.where q of TF molecules, of miRNA (s), of the target mRNA (r) and of target protein (p) with the noise component and without it, and afterwards we found the values q(t),p(t) are the numbers of molecules of transcription factor and target protein without the noise component, respectively, while nq(t), np(t) are corresponding quantities with noise. Therefore we may find the value of the estimation parameter ε:We calculated the numbers ε < 0 means that the noise level in target protein is lower than in TF, and the noise is buffered in the loop.to conclude whether the relative noise level in target protein quantity is higher or lower, than in TF. Consequently, z for each loop and each model, estimated ε in every calculation, studied and calculated an average value of ε, as well as the number of calculations with positive ε value. We used the Wilcoxon test for these averaged values of ε to compare results for the same loops and same models under variation of the model coefficients.We performed calculations with 100 different noise vectors The authors declare that they have no competing interests.AS and MS proposed and designed the study, MD and AS obtained all the mathematical solutions to the problem, MD and MS analyzed the modeling results. AS and MS wrote and typeset the manuscript with considerable input from MD.contains details of mathematical analysis of the coupled ODE.Click here for filecontains additional figures useful for better understanding the results presented in the main text.Click here for file


T. pallidum, the syphilis-causing pathogen, performs very differently in metabolism compared with other bacterial pathogens. The desire for safe and effective vaccine of syphilis requests identification of important steps in T. pallidum's metabolism. Here, we apply Flux Balance Analysis to represent the reactions quantitatively. Thus, it is possible to cluster all reactions in T. pallidum. By calculating minimal cut sets and analyzing topological structure for the metabolic network of T. pallidum, critical reactions are identified. As a comparison, we also apply the analytical approaches to the metabolic network of H. pylori to find coregulated drug targets and unique drug targets for different microorganisms. Based on the clustering results, all reactions are further classified into various roles. Therefore, the general picture of their metabolic network is obtained and two types of reactions, both of which are involved in nucleic acid metabolism, are found to be essential for T. pallidum. It is also discovered that both hubs of reactions and the isolated reactions in purine and pyrimidine metabolisms play important roles in T. pallidum. These reactions could be potential drug targets for treating syphilis. T. pallidum, the causative agent of syphilis, is analyzed as a successful demonstration.As data for molecular interactions and sequenced genomes in microorganisms are increasing rapidly, network analysis provides a novel perspective for studies on the metabolism of microorganisms. When it comes to human beings, the study of pathogens is highly related with the treatment of and drug development for infectious and inflammatory diseases. Recent studies have revealed important facts about the metabolisms that microorganisms, especially pathogens, have developed mechanisms to escape from the prevention process of the elaborate network of the human immune system , 2. In tT. pallidum is a spirochete as well as a phylogenetically ancient and distinct bacterial group. Despite its discovery almost a century ago, T. pallidum continues to be an enigma. The problem confronted by syphilis researchers is their failure in cultivating T. pallidum in artificial medium [ T. pallidum that utilizes glycolysis for energy production. It lacks the tricarboxylic acid cycle and oxidative phosphorylation pathways. In addition, it is unable to synthesize enzyme cofactors, fatty acids, and most amino acids [ Treponema denticola (T. denticola) and T. pallidum reveals that many genes and metabolic capabilities present in T. denticola, which enable this bacterium to replicate in vitro, are absent in T. pallidum rendering the latter incapable of sustained replication under similar conditions. Due to these frustrating facts, it is aspiring to perform an analysis of T. pallidum's metabolic network in silico.l medium . For yeal medium , 4. It ino acids . Further T. pallidum. Recently, many studies have found numerous important properties of the metabolic networks such as the scale-free topology [Systems biology, which provides us with an efficient way to exploring the biological mechanisms, would facilitate the study oftopology , networktopology , and a htopology . Howevertopology –14 and ctopology , among wtopology  because  T. pallidum by cellular metabolic network analysis. Previous work only identifies a small number of virulent determinant genes based on the biological functions related to pathogen-host interaction [ T. pallidum metabolic enzymes genes are not annotated to be virulent factors because the traditional angle for virulent genes is more focused on housekeeping and pathogen-interaction processes. However, accumulated evidences link the metabolic enzymes as virulence factors in the pathogens [ T. pallidum metabolome by comparative genomics strategy may provide further insight into the metabolic virulent factor [It is promising to identify the virulence determinants ineraction . Interesathogens , 18. Thut factor , 5, 19. T. pallidum and H. pylori together [ T. pallidum in gastric lesion to confirm the diagnosis [ H. pylori as a comparison to find out differences between organisms, especially the factors which are important to their artificial cultivation.Syphilitic gastritis is the case of chronic active gastritis which involvestogether . In cliniagnosis . So, in  T. pallidum and group them into different types based on both the Flux Balance Analysis and topological analysis. By computing the stoichiometry matrix's null space, reactions are represented quantitatively and further classified. In addition, critical reactions are identified through minimal cut set calculation. Analysis of H. pylori follows as a comparison. This paper closes with a discussion.In this paper, we cluster all reactions in T. pallidum obtained from KEGG database, the network has a “hub-structure” (shell-type ordering): there is one or two clusters consisting of a large number of reactions (more than 85 reactions) while the other clusters have only a few reactions (less than 8 reactions)  . This tyThe role type distributions in  T. pallidum. Here, reactions that take part in minimal cut sets are considered to be crucial to the metabolism [It is known that reactions in nucleotide, purine, and pyrimidine metabolisms play an important role intabolism . AccordiThe degree distribution for the subnetwork shown in  H. pylori, is analyzed.To further explore the functions that the reactions of each role type perform, another microorganism, T. pallidum and H. pylori  take part in purine metabolism and the others (circular nodes) participate in pyrimidine metabolism  but synthesized DNA from uridine nucleotides [ T. pallidum possesses the necessary enzymes to synthesize DNA. Among these genes, TP0667 and TP0354 are responsible for 16 reactions  in the minimal cut sets, giving strong evidence that both genes and reactions found here are critical in the metabolism of T. pallidum.It is worth noticing that all the 28 reactions which are essential totabolism . This dileotides , 24. BotThe purine and pyrimidine metabolism are indispensable constituents critical for synthesis of DNA and RNA and relevant metabolic regulation to all organisms. The mutations of these enzymes often cause lethal effect on the newborn. In total, at least 19 inborn disorders are related to purine and pyrimidine metabolism in human . Accordi Trypanosoma brucei find out that all three modes obtained are in agreement with experimental observations. Klamt and Gilles have verified the relationship between elementary modes and minimal cut sets [ T. pallidum is expressed during testicular infection of rabbits [ T. pallidum takes the least part of its DNA sequence. So, once destroyed or interrupted, it is less likely that T. pallidum could repair its DNA or RNA to survive [ H. pylori [ T. pallidum and H. pylori.This method leads us to view the metabolism of microorganism in a new perspective. Topological analysis has been used for drug target selection . Calculacut sets . However rabbits . Previou survive . Moreove survive  discover. pylori . All theOne of the great current challenges in bioinformatics is to correlate the simple linear world of nucleotide sequence with the nonlinear world of cellular function . In this T. pallidum results from its “complex” metabolism. The problem is extended to questions about the importance of reactions and the roles of reactions in the metabolism. This paper is concerned with the related questions. The first question is addressed by calculating the minimal cut sets under the frame of whole metabolism. In concordance with the previous biological findings, nucleotide metabolism contains all 28 reactions in minimal cut sets. The question regarding the reaction role is harder since we do not have a universal definition or classification about the reactions. Here, we use a novel way to deal with the difficulty. The reactions are first quantified by Flux Balance Analysis. Then they are clustered through hierarchical clustering analysis. Given the cluster structure of the reactions, different reaction patterns show up with respect to the within-cluster and out-cluster distances. We associate the reactions in minimal cut sets with their role types and thus extend the concept of essential reactions to essential role types. Furthermore, by analyzing H. pylori as a comparison, we discover that different types of reactions have various importance in diverse microorganisms.The failure in identifying virulent determinant or drug targets ofData used here were obtained from Kyoto Encyclopedia of Genes and Genomes (KEGG) LIGAND database . For eacFor each organism, only reactions catalyzed by enzymes were considered.In most metabolic network analysis, metabolites are treated as nodes while two metabolites are connected if a biochemical reaction exists. However, to explore the connection between reactions directly, we treated each reaction as a node. Reactions are linked by reaction compounds.m metabolites with concentrations , r reactions with fluxes , and N is the m∗r stoichiometry matrix with element nij to be coefficient for metabolite j in reaction i:Flux Balance Analysis (FBA) , 34 provC is r∗1 defining the weights of fluxes: fluxes that produce glucose, acetate, glycerol, and ATP have weight 1, fluxes that consume glucose, acetate, glycerol, or ATP have weight −1, and the others have weight 0. Combining these constraints, FBA can be presented as a linear programing problem:N is the stoichiometry matrix and C defines the weights of fluxes in the objective function. To solve this linear programming problem, it is noticed that all stationary flux distributions lie in the right null space of stoichiometry matrix. It can be further derived that the null space could be spanned by its kernel which is indicated by r∗k matrix K, assuming that the rank of kernel is k. Thus, the kernel represents the basis of the steady states of an organism [ci's are coefficients. Among all the fluxes which satisfy the steady state condition, those with the largest growth rate are the desired states. In other words, the boundary surface of the null space depicts the fluxes that achieve the cellular objective. Depending on the collinearity between the weight matrix and the stoichiometry matrix, the boundary surface could be a set of fluxes or a subspace of the null space. In the latter case, the subsets of the orthogonal basis that span the subspace are the fluxes that quantify the reactions.The mass balance equation above represents the principle constraint of FBA. Additional constraints or objectives are added to maximize the growth in terms of glucose, acetate, glycerol, and so forth, with excess energy production in form of ATP. The physicochemical constraints represent a set of linear equations: organism . In addiAs the flux of a reaction is correlated with its reaction rate, the value of the flux could be used to cluster reactions based on their reaction rates. Here, hierarchical clustering is used to group the reactions.xr =  and vector xs = , respectively, the distance is defined bellow: Firstly, find out the similarities between each pair of reactions according to their “distance.” If two reactions are associated with vector drs reaches the maximum value of 2; when the two reactions are positively correlated implying that correlation between associated vectors is 1, distance drs reaches the minimum value of 0.Therefore, when the two reactions are negatively correlated, meaning that the correlation between associated vectors is −1, distance nr reactions in cluster r and ns reactions in cluster s. Denote by xir the ith reaction in cluster r and denote by xjs the jth reaction in cluster s. The distance between clusters r and s isxir, xjs) is defined above  is the vector associated with reaction i belonging to cluster c, Rc is the average of ri for all n reactions in cluster c; that is, Rc = (1/n)∑i=1nri = . The within-cluster distance of reaction i is defined as di = ∑j=1k(rij − Rcj)2. Moreover, if there is only one reaction in the cluster, the within-cluster distance is defined to be 0, which is in concert with the former definition.If s clusters in all and the average for each cluster is R1,…, Rs, respectively. The out-cluster distance for reaction i is defined as Di = ∑c=1s∑j=1k(rij − Rcj)2.Suppose there are di and Di. To classify the reactions, assume that reactions of the same type have similar connectivity in the subnetwork. Reactions in the clusters that only contain one reaction are isolated reactions which form a stand-only type. The other reactions are classified by the order of magnitude of the within-cluster distances. As seen in the left panel of K-means would classify the reactions into three groups: one with the order around −30, one with the order around −5, and one with the order above −4. For clusters with within-cluster distances larger than 1e − 4 or equivalently with the order larger than −4, the order of within-cluster against the out-cluster distances relationship is shown in the right panel of di = 0, reaction i belongs to type 1; if 1e − 10 > di > 0, reaction i belongs to type 2; if 1e − 10 > di > 1e − 4, reaction i belongs to type 3; if 1e − 1 > di > 1e − 4, reaction i belongs to type 4; if di > 1e − 1 and Di < 1, reaction i belongs to type 5; if di > 1e − 1 and Di > 1, reaction i belongs to type 6.Then each reaction is classified according to their scores: T. pallidum and H. pylori in the KEGG LIGAND database. Each reaction identifier represents a chemical reaction occurs in the microorganism. For example, R00086 is ATP phosphohydrolase which defined by ATP + H2O ⟺ ADP + Orthophosphate.Below is a list of reaction identifiers of


Mining the relationship between environmental and genetic factors and metabolic fluxes hidden in existing fluxomic data will lead to predictive models that can significantly accelerate flux quantification. In this paper, we present a web-based platform MFlux (http://mflux.org) that predicts the bacterial central metabolism via machine learning, leveraging data from approximately 100 13C-MFA papers on heterotrophic bacterial metabolisms. Three machine learning methods, namely Support Vector Machine (SVM), k-Nearest Neighbors (k-NN), and Decision Tree, were employed to study the sophisticated relationship between influential factors and metabolic fluxes. We performed a grid search of the best parameter set for each algorithm and verified their performance through 10-fold cross validations. SVM yields the highest accuracy among all three algorithms. Further, we employed quadratic programming to adjust flux profiles to satisfy stoichiometric constraints. Multiple case studies have shown that MFlux can reasonably predict fluxomes as a function of bacterial species, substrate types, growth rate, oxygen conditions, and cultivation methods. Due to the interest of studying model organism under particular carbon sources, bias of fluxome in the dataset may limit the applicability of machine learning models. This problem can be resolved after more papers on 13C-MFA are published for non-model species. 13C-MFA can quantify microbial physiology at the level of metabolic reaction rates. To speed up microbial characterizations and fluxomic studies, we hypothesize that genetic and environmental factors generate specific fluxome patterns that can be recognized by machine learning. Aided by constraint programming and quadratic optimization, our platform based on machine learning (ML) can predict meaningful metabolic information about bacterial species in their environments. Further, it can offer constraints to improve the accuracy of flux balance analysis. This study infers that the bacterial metabolic network has a certain degree of rigidity in allocating carbon fluxes, and different microbial species may share common regulatory strategies for balancing carbon and energy metabolisms. As a proof of concept, we demonstrate that the use of data-driven artificial intelligence (AI) approaches, e.g., ML, may assist mechanistic based models to elucidate the topology of microbial fluxomes.Metabolic information is important for disease treatment, bioprocess optimization, environmental remediation, biogeochemical cycle regulation, and our understanding of life’s origin and evolution.  Since the last term We adopted a quadratic programming method similar to minimization of metabolic adjustment (MOMA) , to tuneMaxi and Mini, we used the maximal and minimal values observed in multiple datasets as the default values. Users can manually set desired values for the upper/lower bound of any specific flux in MFlux webpage, or they can opt to not use any boundaries. For instance, users can simply set the boundary of a certain flux as zero if this specific gene is knocked out.For the upper and lower boundaries of each flux, i.e., To ensure user inputs, e.g., growth rates, oxygen usage, and substrate uptake rates, are biologically meaningful, MFlux first checks the satisfiability  of input values . The bioDifferent parts of MFlux mentioned above are put together as illustrated in 13C-MFA to precisely resolve the anaplerotic pathway fluxes [13C-MFA anaerobic metabolisms , because of lacking sufficient samples for machine learning. The omission of those fluxes can also partially explain the high prediction error in some fluxes .The core metabolism of bacteria is summarized into a pathway map in y fluxes . Informa13C-MFA dataset. The average value, the range, and the 95% confidence interval for each flux are shown in 13C-MFA is based on the glucose metabolism). All 29 fluxes are found to have a relatively narrow confidence interval compared to possible flux ranges, suggesting that fluxes of different bacteria species varies in a relatively small range. This is because most 13C-MFA studies are focusing on models species  and glucose based metabolism, while there are much less MFA efforts to study non-model species or metabolism of carbon substrates other than sugars .By statistical analysis, we determined the variation between each flux profile and the average flux profile from our To decide the most suitable ML algorithm, we first performed a grid search in the parameter space, using a dataset of wild type (WT) samples only. The best results of three different algorithms  are presented in v11 (the second step of the oxidative PP pathway) and v24 (the glyoxylate shunt) have relatively large variations. Two factors may contribute to this fact. Both v11 and v24 have relatively narrow ranges  [E. coli. To resolve this problem, the MFlux platform allows the users to manually set the boundaries of central fluxes to improve prediction quality .Better cross validation was expected from the SVM models trained on the WT dataset, rather than on the WP dataset, while sophisticated genetic variations are not included in the WT dataset. However, cross-validation results refuted our initial thought: the models from the WP dataset demonstrated significantly better performance than those trained on the WT dataset (data shown in nges see  and consknockout ) and v24knockout ) signifipathway) . Howeverv24 may have a negative value). To address those issues, we employed quadratic programming for flux correction as described in the Methods section. More rational results with improved accuracy are expected after flux correction. An essential assumption of this step is that ML predictions are relatively close to real values reported in the literature. This hypothesis is backed by our cross-validation results further validated in the following case studies.After parameter optimization, the SVM models of the best parameter sets can predict with relatively small error. However, the flux profile predicted by the ML method does not necessarily satisfy the inherent stoichiometric constraints of metabolic networks because the ML methods do have big enough dataset at this stage to reflect this. The situation could get even worse where specific fluxes predicted by the ML algorithm may go beyond a biologically meaningful range  is illustrated in 13C-MFA flux profiles with Root Mean Squared Error (RMSE) under 5. For ML, the predictions have large variation on specific fluxes . Quadratic programming can further adjust flux profiles and reduce deviations of flux predictions. The corrected flux profiles also meet the basic stoichiometric relationship of the metabolic network. The final prediction from MFlux shows improvement with RMSE reduces to 3.2.In Case 8, v et al. . MicrobiG. thermoglucosidasius strain M10EXG grows under microaerobic conditions. G. thermoglucosidasius is a thermophilic and ethanol tolerant bacterium which can convert both hexose and pentose into ethanol [13C-MFA fluxes with ML-only fluxes and MFlux results. The results are encouraging: ML-only prediction gives an RMSE of 4.0, while MFlux uses both ML and quadratic programming to improve the prediction to an RMSE of only 3.0. Among the 20 case studies, the average flux set has very large variations (RMSE of 33.5) from actual 13C-MFA fluxes , MFlux predictions have an RMSE between 5 and 10, higher than the RMSE for prediction of wild type strains. Since MFlux is currently unable to capture complex regulatory mechanisms of flux reorganization, human-computer interaction can be employed by manually tuning boundary values of certain fluxes to improve flux prediction quality. For example, knocking out ppc on E. coli may activate the glyoxylate shunt [For species with genetic modifications in major pathways  was used [E. coli fluxomes: one case for glucose based 13C-MFA via parallel labeling experiments [13C-MFA results as the control, MFlux results apparently have smaller RMSEs than FBA predictions. In the first case, the FBA has an RMSE of 11.3, while MFlux has an RMSE of 6.5  is an important mechanistic tool to predict unknown cell metabolism . Accuratwas used . Two comeriments  and the E of 6.5 . In the E of 6.5 . To circE of 6.5 . In gene2 generation). Without proper flux constraints and objective functions, it is more challenging for FBA to narrowly determine intracellular fluxomes in suboptimal metabolisms, especially for co-metabolism dual substrates because of the large solution space for the cell metabolism to optimize biomass growth using two substrates. As a complementary tool, MFlux may offer a quick metabolic overview and provide biologically meaningful flux boundaries to reduce FBA solution spaces when proper constraints for FBA are unavailable.FBA alone has given good predictions of growth rate as well as input and output fluxes, but not of intercellular fluxes. It is difficult to obtain actual P/O ratios, the ATP maintenance cost, the oxygen flux, and the transhydrogenase activities . These e“Robustness” was originally defined as the closed-loop process stability under perturbations in the control field. This definition is applicable to biochemical networks. To maintain the physiological output  within a desired range, microorganisms employ sophisticated control disciplines at different architecture levels, from the genome to the phenotype. In contrast to chaotic transcriptional profiles, the microbial fluxome shows robustness so that cells can survive in constantly-altering environments or in response to genetic mutations –58. MetaP. aeruginosa, P. fluorescens, and P. putida have been studied by 13C-MFA in the past decade [Pseudomonas species employ remarkably identical fluxomics types: they employ a highly active ED pathway for glycolytic metabolism and keep a low flux on the PP pathway for biomass synthesis, due to the lack of the pfk gene [Pseudomonas species have slow cell growth rates and their aerobic metabolisms do not yield by-products. They also demonstrate a very active pyruvate shunt (MAL → PYR) and NADPH overproduction flux (a benefit for counteracting oxidative stress). On the other hand, the TCA cycle in Pseudomonas species show plasticity under genetic and environmental variations [Flux pattern recognition enables MFlux to predict metabolism of new species by learning from a small set of fluxome information from the same genus. For example, the metabolisms of t decade –65. The pfk gene . The ED pfk gene , 68. Pseriations , and canriations .E. coli and Bacillus), their fluxomes  can be similar, because central fluxes in catabolism are regulated by energy and building block requirements that show much smaller variations than genome or transcriptional differences. On the other hand, change of carbon substrates may alternate flux distributions. For example, co-utilization of glucose and glycerol in E. coli cause significant re-organization of fluxomes. In a same microbial strain, different fluxome patterns can be employed for metabolizing different substrates . Recognizing these metabolic patterns allows the use of a relatively small training set to perform a decent metabolic prediction of diverse metabolic types. Consequently, these common principles of certain classes of microorganisms can be captured by machine learning for fluxome predictions.For different bacterial species , and thus our current ML cannot predict fluxomes well in certain cases. Such problem (model bias) can be resolved after more 13C-MFA papers for non-model species are included in the database and more constraints are implemented by our platform.There are several major challenges regarding MFlux. First, the 13C-MFA has not widely used by synthetic biology community yet. In future versions of MFlux, new metabolic knowledge and rules should be applied for flux corrections.Second, the predictability of ML is limited to species and pathways that are already included in learning. More information and efforts are required to deal with cases of genetically modified strains with engineered pathways that hijack flux for synthesis of diverse commodity chemicals . CurrentE. coli when both glucose and glycerol are available, E. coli, Bacillus and Corynebacterium).Third, it is still difficult to incorporate regulation mechanisms into the current model. For instance, various catabolite repression mechanisms regulate the cell fluxome in the presence of multiple substrates  to produce complicated overflow metabolites . This meCO2 fixation pathway (such as the reversed TCA cycle). Therefore, our MFlux platform could not make ML predictions but only reports a general description of metabolic features of these species.Fifth, our current dataset is still unable to support ML studies on phototrophic bacterial fluxomes. For phototrophic metabolism, its energy generation  may not be controlled by substrate catabolism. Some phototrophic bacteria  have versatile autotrophic and photomixotrophic metabolism that is highly sensitive to light and substrate availability. Other phototrophs may even have Lastly, ML cannot directly estimate fluxes for carbon sources which are not part of the learning dataset. To predict fluxomes for new substrates, users need to assume that similar entry-points of carbon sources into the central metabolic network may cause similar flux distributions .13C-MFA is a very small field of just hundreds of MFA research papers on microbial species published in the past two decades. In the long term, ML methods may solve this problem: with a large and reliable fluxomics dataset and more information from 13C-MFA and AI scientists, the future MFlux model can make broad-scope metabolism predictions. To sum up, MFlux presents the first platform introducing ML in the field of fluxomics and it will be continuously updated and improved. It will inspire the development of similar computational tools to advance omics and metabolic engineering fields [This proof-of-concept study demonstrates that AI methods can facilitate fluxomics research with reasonable precision. g fields .S1 ProgramPython scripts in a ZIP file.(ZIP)Click here for additional data file.S1 Table13C-MFA flux, the flux profiles predicted by ML, and the flux profiles predicted by MFlux with additional constraints.Detailed information for 20 cases studies using MFlux, including literature references, input conditions, (XLSX)Click here for additional data file.S2 TableThe information of constraints, objective function, and simulation results.(XLSX)Click here for additional data file.


Aquilegia genus has been used as a key model for speciation studies. In this study, we defined the metabolomic profiles of flower samples of two Aquilegia species, A. Canadensis and A. pubescens. We identified a total of 75 metabolites that were classified into six main categories: organic acids, fatty acids, amino acids, esters, sugars, and unknowns. The mean abundances of 25 of these metabolites were significantly different between the two species, providing insights into interspecies variation in floral chemistry. Using the PlantSEED biochemistry database, we found that the majority of these metabolites are involved in biosynthetic pathways. Finally, we explored the annotated genome of A. coerulea, using the PlantSEED pipeline and reconstructed the metabolic network of Aquilegia. This network, which contains the metabolic pathways involved in generating the observed chemical variation, is now publicly available from the DOE Systems Biology Knowledge Base .To date, variation in nectar chemistry of flowering plants has not been studied in detail. Such variation exerts considerable influence on pollinator–plant interactions, as well as on flower traits that play important roles in the selection of a plant for visitation by specific pollinators. Over the past 60 years the  Nectar plays an essential role in the interaction between animal- and insect-pollinated plants and their pollinators . Plant–pAquilegia genus consists of 70 species[Aquilegia canadensis and Aquilegia pubescens, exhibit extensive variation in flower morphology [A. canadensis, which is native to eastern and central North America, has petals that are prolonged backwards into a tubular spur; the petals are primarily yellow, but redden toward the tip of the spur, which is red. Sepals are petal-like. Plants grow from early spring, bloom from March to July, and set fruit in mid-to-late summer. A. pubescens, which is native to the South Sierra mountains in California, grows only in alpine and subalpine climates; both the sepals and spurs of the flowers are yellow. Flower positioning also differs between A. canadensis and A. pubescens: the A. canadensis flower faces downwards, whereas A. pubescens flowers are erect rather than drooping. Flower morphology and positioning may be essential determinants of pollinator visitation . All instruments and the column were obtained from Agilent Technologies. The GC-MS protocol is described in in details in [To isolate the metabolites and for the GC-MS analysis, we followed the methods described by the Metabolomics Standards Initiative. More sptails in . The GC t.test function with the confidence interval set at 0.95. For principal component analysis (PCA), we used the built-in prcomp function with the default settings. For visualization of the principal components, we used the R package ggplot2. We performed Pearson correlation analysis using the cor function.Upon analysis and transformation of analyte peaks to numerical values, we implemented filtering of the data. Specifically, values of metabolites detected in three flower samples from a species were selected for further analysis. All statistical analysis was performed on iPlant’s cloud-computing resource, Atmosphere , using aAquilegia metabolic network was constructed by annotating the reference genome of A. coerulea v1.1; sequence data were produced by the US Department of Energy Joint Genome Institute. Specifically, the annotation originated from the PlantSEED database [Aquilegia sequence. Once the annotation was complete, a metabolic model was generated from the annotation, using the plant template created by the PlantSEED project. The plant template consists of curated reactions involved in plant primary metabolism and an extensive plant biomass. When the template is used, the annotation in the genome is linked to the reactions in the template, which are then used to create a metabolic reconstruction. Finally, the plant biomass is added to the reconstruction to allow it to function as a model of plant primary metabolism in Aquilegia. A gap-filling algorithm was used to find and fill gaps in the reconstruction that would ensure that the metabolic network could generate the same plant biomass using metabolic flux-analysis methods such as flux balance analysis . Each step in the generation of the metabolic network was performed within the DOE Systems Biology Knowledgebase environment and framework . The annotated genome and metabolic reconstruction are available for public use in the KBase workspace named “Acoerulea”, which can be accessed by users via a free KBase account . The same workspace contains results obtained by simulating heterotrophic growth using flux balance analysis, allowing users to browse reaction activity.The database , which cdatabase . All pro–5 for A. canadensis and 5.14•10–5 for A. pubescens; ribitol: 9.35•10–5 for A. canadensis and 9.29•10–5 for A. pubescens). Using t-test, we ended up with a list of 75 metabolites, including 21 organic acids, 1 fatty acid, 5 amino acids, 4 esters, 25 sugars, and 19 chemically undefined compounds  that were present only in A. canadensis, suggesting that the two species exhibit qualitative as well as quantitative differences in sugar metabolites.Sugars constituted over 90% of all metabolites that differed significantly between the two species. Of the 15 different sugar metabolites identified, the mean levels of 10 differed significantly between the two species, including the three most abundant: fructose, glucose and sucrose. Notably, fructose and glucose were more abundant than sucrose in A. canadensis, whereas quinolinic acid was only detectable in A. pubescens. The qualitative and quantitative variation in organic acids, in addition to that of sugars, suggests that nectar composition is a complex trait.The second major category of metabolites we detected was organic acids. Of the 21 organic acids we identified, the levels of only three were significantly different between the two species . SpeciesA. pubescens. Glycine and cytosine levels did not differ significantly. In addition to amino acids, we also found esters; two out of four esters were present only in A. pubescens. Moreover, a sizable fraction of 17 unknown metabolites was detected, only two of which (Unknown #28 and Unknown #29) differed significantly between species; these compounds remain to be identified. The variation in metabolite identities and concentrations prompted us to look for correlations between flower spur length and the levels of metabolites that differed significantly between the two species. With some exceptions, metabolites tended to be positively correlated with spur length in one species and negatively correlated in the other,  differed significantly between the two species, while a third amino acid, serine, was present only in e other, . The mosIn addition, we performed principal component analysis(PCA) to define the metabolites that contributed the most to differentiation between the two species . The PCAWe mapped all of the identified metabolites to known pathways in the PlantSEED database. Of the 75 metabolites, we were able to map 21. Each metabolite mapped to between 4 and 281 pathways . BecauseAquilegia genome resulted in assignment of metabolic annotations to 1,202 different features, and the resulting working metabolic model consisted of 1,573 reactions Click here for additional data file.S2 TableThe loading are reported for each of the metabolites. In column two there is an ID number for each of the metabolites shown in (XLSX)Click here for additional data file.S3 TableMetabolites vary to the number of pathways they belong to. We mapped 22 out of our 79 metabolites(XLSX)Click here for additional data file.S4 TableIn column F we mention an Arabidopsis exemplar that belongs to each of the pathways. Most of the metabolites belong to cytosol some to the rest of the compartments.(XLSX)Click here for additional data file.S5 TableThere is large variation on the number of KEGG pathways each of our identified metabolites belongs to.(XLSX)Click here for additional data file.