Mycobacterium tuberculosis into a single network, which allows many reactions that could not be active in the individual models to become active, and predicts essential genes with a higher positive predictive value.Reconstructed models of metabolic networks are widely used for studying metabolism in various organisms. Many different reconstructions of the same organism often exist concurrently, forcing researchers to choose one of them at the exclusion of the others. We describe MetaMerge, an algorithm for semi-automatically reconciling a pair of existing metabolic network reconstructions into a single metabolic network model. We use MetaMerge to combine two published metabolic networks for  Due to the recent explosion in the number of sequenced genomes of unicellular organisms, it has become possible to systematically analyze their biochemical functionality. Analysis of reconstructed metabolic networks - most commonly through constraint-based approaches, such as flux-balance analysis  - has beBacillus subtilis, Escherichia coli, Haemophilus influenzae, Mycobacterium tuberculosis and Staphylococcus aureus. When experimental data are available, the reconstructed metabolic model is often further refined, as was done for Acinetobacter baylyi [Saccharomyces cerevisiae [Metabolic network models are typically constructed based on a genome's annotated sequence and existing biochemical knowledge . Genome-r baylyi  and for revisiae .The complexity of the reconstruction process and the large number of literature sources on metabolism have often led to the generation of multiple metabolic models for the same organism. Indeed, the 59 metabolic networks currently available  only repTo date, very few works have addressed the problem of reconciling different reconstructions for the same organism. Recent studies have attempted to align metabolic networks of two different organisms . HoweverM. tuberculosis by Beste et al. [et al. [M. tuberculosis: only 21 articles are shared between the 100 articles referenced by Beste et al. [These discrepancies are illustrated in a comparison of the two main existing metabolic networks published for e et al.  and by Je et al. .  user confirmation of the matching in step 2; stage 4, iterative extension, matching additional reactions and metabolites; stage 5, checking the metabolite matching to ensure transitivity and non-transformability ; and stage 6, merging and providing the resulting network in the desired format. We concisely describe each stage below and provide full details in the Materials and methods.MetaMerge begins by parsing and pre-processing each model, augmenting each metabolite and reaction with several features Figure , stage 1M. tuberculosis models trehalose dimycolate is denoted as TREHALOSEDIMYCOLATE in one model [During the merging process  are initialized in stage 2, based on the number of features that the entities have in common. The matrices are possibly cleaned up in stage 3, when the user can choose to either accept or reject any given match. Finally, they are expanded in stage 4, based on the reasoning that reactions that have almost all their metabolites in common are likely to match one another, and that the remaining metabolites in those reactions are likely to match as well. Stages 3 and 4 are then iterated until no further expansion can be proposed, or until every entity in one of the models has been matched (the latter case being unlikely due to the incomplete overlap between any pair of models).During post-processing Figure , stage 5In the final stage Figure , stage 6Specifically, a single new metabolite in the combined model is created by MetaMerge to represent each (matched) class of metabolites from the individual models, according to the matching matrix. Each reaction is then written using the new metabolites, and identical reactions are joined into a single reaction, treating the enzymes or enzyme combinations necessary to catalyze them as isozymes. This approach for combining models ensures that mass-balance constraints on each metabolite in the combined model are no more stringent than the corresponding constraints in the original model, because identifying two metabolites is equivalent to adding the corresponding constraints, and any flux vector satisfying both constraints satisfies their sum.M. tuberculosis models [We applied MetaMerge to the two s models ,14 and g2O), as well as in their stoichiometric coefficients. However, another reason for the relatively low number of reactions that were matched between the two models appears to be the differential coverage of a number of important pathways by the two reconstructions.The combined model has a substantially broader scope than the two original models. It contains 1,400 reactions , with 1,017 metabolites  and 917 genes . Overall, 70% of the genes and metabolites are matched between the two models, but only 45% of the reactions are matched. This is due to the fact that we only considered two reactions to be identical if they agree completely in their metabolites according to the matching matrix , where two reactions are considered to be very similar if they come from different original models and differ by only one metabolite  constraints . In general, a reaction is blocked if the linear program that constrains it to carry one unit of flux is infeasible.We reasoned that combining the two models might provide the particularly important benefit of 'unblocking' some of the reactions that were blocked in the individual models, since previous constraints may be relaxed by additional reactions in the combined model and cannot become more stringent.M. tuberculosis [pncA (Rv2043c), which is required for activation of the antitubercular drug pyrazinamide [Indeed, in the combined model, the total number of blocked reactions decreases by 55%, from 246 to 109 .We next examined the ability of our combined model to assess gene essentiality by comparing its predictions to those determined experimentally using transposon site hybridization (TraSH), a negative genetic selection method . This esin vitro growth of M. tuberculosis on Middlebrook medium 7H10, supplemented with glycerol [M. tuberculosis, we did not include OADC (particularly the oleic acid component) in the computational medium's composition because oleic acid was not present in the original models. This limitation is also present in all previous studies [We approximated these conditions as closely as possible by simulating the glycerol . To thisglycerol ,14: ammoglycerol : carbon  studies ,14.in vitro biomass composition as an indicator of growth. For model 2, we attempted to use the reduced biomass composition. However, the model was unable to produce any biomass on the medium described above when analyzed with any of six different linear programming solvers [in silico experiments.We next predicted gene essentiality in the combined model and its two constituent models. We eliminated the enzymes one at a time from the model and tested the impact on the model's ability to exhibit flux through the biomass reaction, as an indicator of growth . For the combined model and for model 1, we used the  solvers , whetherin vitro essential' . For each of the models, we considered a gene to be essential only when setting the flux through the corresponding reaction to 0 results in no biomass production. This allowed us to avoid imposing an arbitrary cutoff on the growth rate, but gave results for model 1 that differ somewhat from those previously reported for this model [We compared gene essentiality from the TraSH experiments for model 1 and the combined model Figure . Becauseis model .in vitro essentiality , with a positive predictive value of 71% (63 true positives/89) versus 68% (139 true positives/203) at a threshold of 0.2. The negative predictive value, on the other hand, is somewhat lower at both thresholds calculated (0.2 and 0.1), with a negative predictive value of 68% (436 true negatives/637) versus 75% (285 true negatives/381) at a threshold of 0.2. These results are consistent across different thresholds , as expected given the expanded scope and functionality of the combined model . Briefly, all the reactions in a metabolic network can be divided into reaction subsets , such tWe focused on comparison to the targets for two first-line antitubercular drugs, ethambutol (ETH) and isoniazid (INH) . EthambuWe first applied our approach to the proposed drug targets of ethambutol, the enzymes Rv3793 (embC), Rv3794 (embA) and Rv3795 (embB). We found three reactions catalyzed by these enzymes in the combined model. By examining the reaction subsets to which these belong, we found 29 additional enzymes whose inhibition is predicted to yield similar effects to those of known ethambutol targets , we found 14 reactions disabled by isoniazid, and two enzymes, Rv0503c (CmaA2) and Rv0643c (MmaA3), that are predicted to have a similar metabolic effect . In that case, MetaMerge can greatly reduce the time required to build a consensus model. Additionally, MetaMerge could be used to reconcile two networks corresponding to different, but closely related, organisms, although the result may or may not correspond to that of the metabolic network of their closest ancestor. MetaMerge may be best used in combination with a metabolic network alignment algorithm in order to gain evolutionary insights from the comparison of the networks for closely related organisms.M. tuberculosis and used three criteria to assess the success of the combined model. The combined model provides better coverage of the space of metabolic reactions, has fewer blocked reactions (and hence significantly more effectively available reactions), and produces slightly better predictions of gene essentiality in terms of the positive predictive value . However, both the original and the combined model still do not capture the full range of gene essentiality information. The discrepancies between the model's prediction and experimental data can suggest areas where knowledge in the model should be improved, such as potentially missing reactions, missing gene-protein-reaction associations, or unnecessary restrictions on reaction directionality.We applied MetaMerge to two existing network models for Finally, we used the combined model to suggest 31 genes whose inhibition is predicted to result in an effect similar to that of exposure to two known antitubercular drugs, many of which are within similar functional pathways. Notably, a similar, more stringent criterion, previously used by , is baseMetaMerge in its current version results in a combined network that preserves the full metabolic capabilities of the individual networks while providing the possibility of synergistic interactions that lead to novel capabilities. If expertise is available, the resulting model can be further refined, for instance, by resolving the discrepancies between pairs of similar reactions . In that case, MetaMerge can greatly reduce the time required to build a consensus model.One of the main features of the MetaMerge algorithm is its ability to extract features of entities  present in a metabolic model in an automatic way by querying appropriate databases. Even for richly annotated models, this can be an important way of updating the annotation given that new biological information becomes available almost every day. It is conceivable that automated metabolic network reconstruction will become a possibility in the future, and a tool such as MetaMerge will then be crucial to gathering available information on organisms' metabolism, unifying information from disparate sources into a single model, and providing a natural starting point for metabolic network analysis.M. tuberculosis model from the two original models and the production of an SBML (Systems Biology Markup Language) file containing the combined model. It precisely follows the stages that we outline here. We also provide the required scripts and input files as Additional file Additional file ModelParsing.py script contained in Additional file We parsed the models using the get_close_matches method in the difflib module. We considered only perfect matches for the remaining features.The following features were used to compare metabolites: abbreviation, official name, CAS number , Internaurlopen method in the urllib module in Python [The following features were used to compare reactions: reaction name, pathway name, gene name, protein name, enzyme name Table . Unlike n Python .M and N, using the features described immediately above. The features were each given a score of 1, although the code allows for user-defined unequal weights to be provided as well. The various names were considered to be a match if they contained at least one non-function word in common (at least two for the case of protein names and reaction names), and we only considered perfect matches for the remaining features. ijM(respectively ijN) is the total score of the matching features for the pair of metabolites (respectively reactions) i and j. We note that additional unique annotations, such as SMILES or InChi strings for metabolites, would make the reconciliation process less ambiguous, and therefore less error-prone for MetaMerge. We highly recommend their use in annotating genome-scale metabolic network reconstructions.We created two score matrices, BMand BN, initialized to contain a 0 in every position. The entry BijMis 0 if the two metabolites have not been matched and 1 if they have been matched. If the algorithm is being used interactively (with input from the user), these matrices become ternary: an entry of 1 means that the match has been accepted by the user, and -1, rejected, while an entry of 0 means that the match has never been proposed. The matrices BMand BNare then used during the iterative stage to keep track of matching decisions in the previous iterations.We also created two binary matching matrices, i,j) with a total score ijNabove a cutoff of 3. Subsequently, the highest-scoring pairing of the metabolites was computed for each of the reaction pairs in the matching using a greedy algorithm. This algorithm identifies the metabolites k in reaction i and l in reaction j with the largest total score klM, matches these to one another, and then repeats the process with the remaining metabolites until all the metabolites in one of the reactions have been matched or all remaining pairs of metabolites have a total score of 0.To initialize a matching of reactions and metabolites, we used the pairs of reactions  should be matched.Although these interactions could, in principle, be bypassed entirely, we found that they were helpful in steering the algorithm away from possible mistakes in the matching process. For instance, several close matches with similar scores were sometimes available for a given reaction, but only one of them was the correct match, and this could only be detected by using the browsing feature of the interface. Furthermore, the possibility of seeing previous decisions on putative metabolite matches helps to maintain overall consistency in the matching, which prevents violations of transitivity (as discussed below).During the matching of metabolites in matched reactions, new pairs of matching metabolites are usually found. If that is the case, the extension algorithm finds all the pairs of reactions that have not yet been matched, and whose metabolites could be matched almost perfectly . Convergence occurs when no further extension of the current matching is possible.In the postprocessing phase of the algorithm, the matching of the metabolites is cleaned up. This phase is currently performed in a semi-automatic way, although it might be possible to automate it completely. First, transitivity of the metabolite matching needs to be ensured. A matching matrix is said to be transitive if it can be perfectly covered by rectangles. In graph-theoretic terms, this is equivalent to saying that the bipartite graph formed by the matching is a disjoint union of bicliques . The traSecond, non-transformability of the metabolite matching needs to be ensured as well. A transitive matching matrix is said to be non-transformable if there is no rectangle in its covering that contains two metabolites from the same network that participate on different sides of a reaction. This will lead to the undesirable behavior of metabolites canceling out on either side of a reaction in the combined network.A third condition that is not strictly necessary, but which makes the merging process a lot easier and cleaner, is compartmentalization. In the context of a model with only two compartments (the cell and the extracellular space) this simply means that no internal metabolite in one network is matched to an external metabolite in the other network. In the case of more complex models, such as the eight-compartment yeast model , this woM. tuberculosis networks considered in this work, we deleted only protons (H) and water molecules (H2O). Each reaction is then rewritten using the new metabolites. This results in many identical reactions, which are considered to be isozymes of one another. The combined network contains only one reaction from each group of isozymes. To determine the reversibility of a reaction in the combined network, we examine the reactions from the original networks that are represented by it. If at least one of them is reversible or if two of them are oppositely directed, the new reaction is taken to be reversible; otherwise, it is taken to be irreversible. The network created by combining models 1 and 2 [In order to create the combined network, we combined each group of metabolites corresponding to a rectangle in the matching matrix  into a single new metabolite. Optionally, we allow for some of the metabolites that were frequently matched to 'nothing' to be deleted from the combined network. In the case of the two  1 and 2 ,14 is wr 1 and 2  in Additi is said to be topologically blocked if it contains a unique internal metabolite (not present in any other reaction), stoichiometrically blocked if the mass balance condition Sv = 0 implies iv= 0, and thermodynamically blocked if the mass balance condition together with the irreversibility conditions implies iv= 0. In each case, we choose the simplest possible cause for the blockage. This analysis was performed using the MONGOOSE toolbox [For each reaction, we determined whether it is able to sustain a nonzero flux at steady-state, and if not, whether this is due to the topology, the stoichiometry or the thermodynamics of the model. Reaction  toolbox , describet al. [To construct our gold standard for gene essentiality, we used results of the TraSH experiment  and follet al. . We testFor each reaction, we assembled the genes required to catalyze it in conjunctive normal form (OR of ANDs). From this information, we compiled a list of all the reactions disabled by the knockout of each gene. Subsequently, we constrained these reactions to have a flux of 0 and determined that the gene is essential if the resulting metabolic network was unable to exhibit growth, and non-essential otherwise. This analysis was performed using MONGOOSE .S of the network, and then compute the nullspace matrix K and identify sets of proportional columns. Two reactions, i and j, in a metabolic network with stoichiometric matrix S are said to be in a reaction subset if there exists a constant κ ≠ 0 such that Sv = 0 implies vi = jκv. As explained in Additional file S, then all reaction subsets can be identified from the nullspace matrix K of S, regardless of the irreversibility of any of the reactions. In the combined network for M. tuberculosis, the size of such subsets varies between 2 and 38 reactions, and in fact, the largest subset with 38 reactions contains a reaction that is disabled by ethambutol.To find all the reaction subsets, we first identify the blocked reactions, delete them from the stoichiometric matrix CAS: Chemical Abstracts Service; IUPAC: International Union of Pure and Applied Chemistry; KEGG: Kyoto Encyclopedia of Genes and Genomes; OADC: oleic acid: albumin: dextrose and catalase; SBML: Systems Biology Markup Language; TraSH: transposon site hybridization.LC proposed the algorithm, carried out the analyses, and drafted the manuscript. SS and DH controlled the quality of the combined model and suggested the computational experiments for validating it. AR suggested the approach and helped devise a strategy for creating the combined model. BB guided the design of the study and suggested improvements to the MetaMerge algorithm. All authors helped revise the manuscript and approved the content of the final version.Reactions in models 1 and 2 differing by at most one metabolite. There are 29 pairs of reactions (each pair consisting of one reaction from model 1 and one reaction from model 2) that differ by at most one metabolite. These reactions are given in the representation used in the original models. Each pair is followed by a line of dashes.Click here for fileEnzymes predicted to have similar metabolic impact to that of known drug targets. There are 29 enzymes listed for ethambutol and 2 enzymes listed for isoniazid. Each enzyme is given with its gene ID and name, the set of reactions it is essential for in the initial models , its fuClick here for fileM. tuberculosis modelA sample Python session yielding a combined . This file contains the step-by-step transcript of a Python session culminating in the creation of a combined M. tuberculosis model from the two original models and the production of an SBML file containing the combined model.Click here for fileThe full code of the MetaMerge algorithm implemented in Python. The code is divided into 14 modules, each of which contains multiple functions, as follows: ClassDefinitions.py, the code for defining all the formats used by MetaMerge internally; FeatureMatching.py, the code for matching species, reactions based on the available features; FeaturePreparation.py, the code for extracting metabolite and reaction features from text; GeneProcessing.py, the code for processing gene information; MatchProcessing.py, the code for processing the metabolite and reaction matching matrices; MetaboliteMatching.py, the code for generating and processing closely matching metabolites; MetaMerge.py, an initializer for the other modules required by the MetaMerge algorithm; MetaMergeCore.py, the user interface of MetaMerge for preparing the matching matrices; ModelParsing.py, the user interface for parsing a metabolic model in Excel or SBML format; NetworkMerging.py, the code for merging two networks based on their matching matrices; OutputProcessing.py, the code for processing the output of the MetaMerge algorithm; ReactionMatching.py, the code for generating and processing closely matching reactions; Unrelated.py, the code for analyzing a metabolic network, not directly related to MetaMerge; Utilities.py, the code of miscellaneous auxiliary functions used by the MetaMerge algorithm. Additionally, the zipped directory contains a shelve file called Mappings with KEGG and Biocyc identifiers for the metabolites in both M. tuberculosis models extracted by Jeremy Zucker, and the cleaned-up and extended Excel files Mycobacterium tuberculosis 1.xls and Mycobacterium tuberculosis 2.xls for models 1 [models 1  and 2 [1Click here for fileM. tuberculosis modelsA list of errors corrected in the original . This file contains a list of errors detected in the original M. tuberculosis models [s models ,14 and cClick here for fileet al. Model 1 (Beste [) in SBML. The model contains 873 reactions and 753 metabolites. Each reaction is annotated with lower and upper bounds on its flux, the EC numbers for the enzymes catalyzing it, the Boolean expression containing the genes it requires, the name and chemical equation of the reaction, and the pathway to which it belongs, whenever these are known. Each metabolite is annotated with its abbreviation, official name, molecular formula, IUPAC name, CAS number, and BioCyc and KEGG database identifiers, whenever these are known.e et al. ) in SBMLClick here for fileModel 2  in SBML. The model contains 937 reactions and 825 metabolites. Each reaction is annotated with its confidence score, the proteins needed to catalyze it, the Boolean expression containing the genes it requires, the name and chemical equation of the reaction, and the subsystem to which it belongs, whenever these are known. Each metabolite is annotated with its abbreviation, official name, molecular formula and charge, IUPAC name, CAS number, and BioCyc and KEGG database identifiers, whenever these are known. Palsson ) in SBMLClick here for fileM. tuberculosis model in SBMLThe combined . The model contains 1,400 reactions and 1,017 metabolites. Each reaction is annotated with the corresponding information from the reactions in the original models that it corresponds to. Each metabolite is similarly annotated with the corresponding information from the metabolites in the original models that it corresponds to. In case a reaction or metabolite in the combined model represents two or more reactions or metabolites from the same original model, the annotations are separated by 'or', while if those reactions or metabolites that come from different models are separated by 'OR'.Click here for fileThe MONGOOSE toolbox. The MONGOOSE (MetabOlic Network Growth OptimizatiOn Solved Exactly) toolbox [ toolbox  is a sof toolbox .Click here for file


Parkinson’s disease (PD) is a multifactorial disease known to result from a variety of factors. Although age is the principal risk factor, other etiological mechanisms have been identified, including gene mutations and exposure to toxins. Deregulation of energy metabolism, mostly through the loss of complex I efficiency, is involved in disease progression in both the genetic and sporadic forms of the disease. In this study, we investigated energy deregulation in the cerebral tissue of animal models (genetic and toxin induced) of PD using an approach that combines metabolomics and mathematical modelling. In a first step, quantitative measurements of energy-related metabolites in mouse brain slices revealed most affected pathways. A genetic model of PD, the Park2 knockout, was compared to the effect of CCCP, a complex I blocker. Model simulated and experimental results revealed a significant and sustained decrease in ATP after CCCP exposure, but not in the genetic mice model. In support to data analysis, a mathematical model of the relevant metabolic pathways was developed and calibrated onto experimental data. In this work, we show that a short-term stress response in nucleotide scavenging is most probably induced by the toxin exposure. In turn, the robustness of energy-related pathways in the model explains how genetic perturbations, at least in young animals, are not sufficient to induce significant changes at the metabolite level. Two important cellular hallmarks of this disease are the formation of cellular inclusions named Lewy Bodies, and the degeneration of dopamine-containing neurons of the ventral midbrain, mainly within the Toxins used in farming, such as paraquat (herbicide), rotenone (pesticide) and maneb (fungicide) are known to induce specific PD-related symptoms in animal models carbonyl cyanide m-chloro phenyl hydrazone). The genetic model of Parkinson’s disease selected for the present study was Parkin KO mice that present mitochondrial efficiency reduction. This gene is situated on locus 6q25.2–q27 In this work, we have studied the effect of PD-related perturbations on brain cells metabolism. Metabolites were measured in brain tissue from Parkin KO (knockout) mice, as well as in brain tissue exposed to the complex I antagonist CCCP  cutting-solution ) containing (in mM): NaCl, 125 mM; KCl, 2.5 mM; KH2PO4, 0.3 mM; NaHCO3, 26 mM; CaCl2, 2.4; GLC, 10 mM; MgSO4, 1.3 mM; at 300 mOsm. The olfactory bulbs and cerebellum were removed and the rest of the brain sliced using a vibrating microtome (Leica VT1000S®) in order to make 300- µm thick coronal slices. During slice preparation, the tissue was always maintained immersed in 4°C ACSF. Each slice was delicately transferred to a Petri dish continuously perfused with oxygenated ACSF. After preparation, brain slices from both mice were allowed to recover for about 30 min.Mouse brain slices were prepared and rapidly transferred in Petri dishes. Two slices were evaluated each 10 min  and homogenised in an alcohol extractor to arrest cellular metabolism. In two experiments, a control group (wild type mouse) was compared to either the genetic model or the toxin-induced model. Mice were anaesthetized with halothane and immediately killed by decapitation. The brain was rapidly removed and placed in ice-cold carboxygenated (95% OTwo brains (a control and a test sample) were sectioned and processed in parallel for each experiment. Individual slices were processed at a rate of one per 10 min for a total of about 75 min. Parkin KO mice on a C57bl/6 background were used as a genetic model of PD, and their oxidative phosphorylation capacity was taken to be 90% of that of the wild-type (WT) The understanding of cells metabolic activity in response to perturbations requires the simultaneous evaluation of many compounds involved in the cellular metabolic network. Several extraction methods for metabolite analysis have been reported, and based on previously reported results g at 4°C for one min; the ACSF supernatant was then removed using a flame-pulled Pasteur pipette. The pre-weighted centrifuge vial was then reweighted to deduct the collected fresh brain mass and 200 µL of an 80% v/v mixture of methanol and water, cooled on dry ice, was added. The tissue was then homogenized using a motorised pillar, vortexed and sonicated to disrupt cell membranes, precipitate proteins and arrest metabolic reactions. An additional 200 µL of methanol/water was next added and the homogenization, vortexing and sonication steps were repeated. The samples were maintained at −80°C for further analyses.The two slices selected for each extract were transferred using a brush from a Petri dish to a centrifuge tube, which was then centrifuged at 21 000 g for 7 min at 4°C. The resulting supernatant was collected and considered as the first extract. After the addition of 0.2 mL of ice-cold 50% v/v methanol/water to the pellet, the sample was again vortexed, cooled in an ice-water bath and sonicated for three rounds. The sample was then micro-centrifuged at 21 000 g and 4°C for 5 min to produce the second extract; the latter was added to the first. Next, 0.2 mL of ice-cold water was added to the pellet and the vial was vortexed and micro-centrifuged at 21 000 g and 4°C for 3 min to give the third extract. Finally, the vial contained the pooled extracts was micro-centrifuged at 21 000 g and 4°C for 5 min. The supernatant was then filtered in a syringe with a 0.2 µm filter (Millipore) and stored at −80°C until LCMS analysis.The sample was resuspended and vortexed after addition of 0.2 g of sand to improve homogenisation, and micro-centrifuged at 21 000 The samples were thawed and vortex mixed before analysis. Samples were kept at 4°C during LCMS autosampling. Minimal LCMS autosampling loading was performed since it has been reported that metabolites degrade faster at higher temperatures, compared to −80°C.Nucleotide and organic acids together with sugar phosphates quantification was performed as described in Hammami et al. Nucleotides in extracts were analyzed using a 1290 UPLC system coupled to a 6460 triple quadrupole mass spectrometer (Agilent Technologies®). Nucleotides were separated by a Symmetry C18 column (Waters®) equipped with a Security C18 guard-column (Waters®) using ion-pair method. DMHA  was used as an ion-pair reagent to improve the signal-to-noise ratio with positive ionization mode.Organic acids and phosphate sugars concentrations were assessed using the aforementioned UPLC-MS/MS system using a Hypercarb® column and a Hypercarb pre-column (Thermo Fisher®).ACSF cellular environment samples were taken directly from the Petri dish. The four major extracellular components such as glucose, lactate, glutamine and glutamate were measured with a blood analyser . Two modules were used in parallel; glucose and lactate were measured simultaneously on an analyser, while another measured glutamine and glutamate simultaneously.n = 3 independent experiments from brain slices prepared from three mice. Outliers were removed using box-plot analysis.Data are shown as mean ± SEM (standard error of mean) of In the present study, complete brain slices were homogenized. It was therefore not possible to distinguish between metabolites originating from the different cell types . Considering that cell populations are not homogeneous throughout the rostro-caudal extent of the brain, we were careful to select comparable sets of slices from control and test samples. In addition, although PD is associated with the degeneration of a limited number of brain regions including the locus ceruleus and the substantia nigra pars compacta, in the present study, brain tissue was collected from the whole brain. We did not attempt to collect only the ventral mesencephalon, where the substantia nigra is localized, as this would have lead to insufficient quantities of cells and thus of metabolites; an experimental limitation determined from the detection limit of the LCMS and UPLCMSMS equipments used. Although in these mice the Parkin gene was knocked out from all cells, it is possible that by analysing whole brains, we missed perturbations in cell metabolism that were more specific to the affected nuclei.The metabolic pathways investigated in this study are presented in BioCyc.orgT”, as T_glc for the transport of GLC). As the main influx, glycolysis is described with a high level of detail. The modelling is focused on highly controlled enzymatic reactions (e.g. V_pfk for the flux of phosphofructokinase) and important branch point. The pentose phosphate pathway (PPP), which is the major pathway for anti-oxidative action, is represented with its two glycolytic connecting points. Even if the latter pathway is extensively simplified to a single state, the by-products stoichiometry (regeneration of 2 NADPH for each GLC cycling through PPP) is consistent with the full pathway. Pyruvate from the glycolytic pathway is either converted to lactate through reversible lactate dehydrogenase, or transferred to the mitochondria and consumed in the TCA cycle. While some intermediates (such as AKG) can be used as branch point to amino acids (GLT) consumption/production, the cycle’s main function is to perform reduction of NAD shuttles to NADH. This in turn allows ATP regeneration from ADP by oxidative phosphorylation in the mitochondria matrix. Although this pathway involves many enzymatic complexes and sub-compartments, a simple one-step reaction with parallel proton leakage is considered here.In this work, we have limited our scope integrating central carbon metabolism and energetic pathways. Pathways represented in the model originate from a database of combined information from literature as well as the web-database The two major energetic buffers are considered: phosphocreatine and glycogen. Creatine kinase transfers the high energy phosphate link from ATP to Cr and the resulting molecule PCr can in turn be used to directly regenerate ATP during periods of high demand. Glycogen is considered as a single state with a reversible reaction from G6P. Although energy is used to obtain G6P, glycogen can in turn be used temporarily if GLC transport becomes limiting during periods of high-energy demand, thus creating a buffer effect between low and high energy demand periods TOT – PCrCr = PCr”. In those cases, the unique assumption is that the total pool of metabolites is constant over the time frame of the experiment. This approach reduces the number of differential equations and computing time. In energy metabolism, some enzymatic activities reach an extremely rapid equilibrium and this can also be used to reduce the number of differential equations, while still describing the associated state variables with algebraic equations. As an example, even if uridine-triphosphate (UTP) is necessary for glycogen storage, the enzyme nucleoside diphosphate kinase covers the use immediately and stabilises the UTP pool with ATP. In the model, we thus only represent ATP as the global energy currency and its dynamics will be representative of the overall energetic state.Most model states are determined as a distinct mass balance with a rate of change equal to the difference between production and consumption fluxes. Alternatively, moiety conservation is used to reduce the number of differential equations, when possible. For example, the sum of PCr and Cr is constant and Cr can be expressed as “brenda-enzymes.infoAlthough the model presented here could eventually be used to estimate confidence intervals on the parameters, this was not the immediate objective of the present work. Our objective was rather to develop a kinetic-metabolic model structure that can be challenged with experimental data. Along with this process of model calibration, we tested its usefulness to retrieve various fundamental informations  that can hardly be obtained experimentally, with regards to energetic regulation during the early events of PD pathogenesis. The parameters of the model were first estimated from the available literature, as detailed below, and then calibrated minimizing the error between simulations and experimental data, as previously described The affinity of protein-substrate interactions has not been measured for all organisms or cell types. In this work we thus gathered the most relevant values from the databases. When possible, the affinity values were taken for mouse brain proteins  GLC uptake rate and LAC excretion rate, as measured from the extracellular GLC and LAC concentrations. The rate of GLC intake imposes a global limit on the glycolytic fluxes and also on its branchpoints; the sum of fluxes at a branchpoint has to balance when in the ‘baseline’ steady-state. The rate of LAC excretion indicates, indirectly, the proportion of GLC that underwent complete oxidation, which in turn is an estimate for the TCA fluxes. Thus, with known values for the Krameters , if we hAnother addition was also made to the model to allow a sudden change linked to the addition of CCCP to the media . Because this ionophore uncouples the respiration chain as it increases proton leakage across the membrane barrier, the stress is represented in the model as an increase of the natural mitochondrial leakage process. As the proton gradient has a direct effect on the efficacy of the oxidative phosphorylation pathway, and considering that pH gradients are not represented in the model, the leakage is modeled as oxidizing directly NADH to NAD without ADP phosphorylation to ATP. As the stress was implemented as a pulse, such mathematical description is added to the model using a sigmoidal-shape function. Since the toxin diffuses easily into the brain slice, a fast acting sigmoid is imposed in the opening pulse function. Finally, since the CCCP was washed out of the slice relatively slowly, a slow acting sigmoid is added for the pulse function closing term.in-vitro calculated values and 46 in-silico defined parameters  is not due to GLC excretion from the slices. The Petri dish being open to unsaturated air and sparged with dry gases, significant evaporation is likely to have happened during the experiment. Effective metabolites flows were then corrected by estimated evaporation measurements and analysis of simulated fluxes; results showed that the effect of evaporation was slightly stronger than GLC consumption by the slices and thus had to be considered.2-to-GLC consumption ratio.On the other hand, in the case of LAC, the increase was much more significant (+50% in 75 min) and most of the increase is likely to have arisen from LAC excretion from the slices. This indicates an imbalance between glycolysis and oxidative phosphorylation, which is coherent with previous work on brain physiology. Furthermore, the basal unstressed consumption ratio of oxygen-to-glucose indicator, as calculated by V_hk), 36 (V_pfk), 38 (V_pk) and the ADP-on-ATP ratio as considered in reaction 32 (V_op) in Results show that ATP profile for the wild-type tissue did not exhibit any clear trend, and that experimental and measurement noise may dominates. In the model, a consistent result (i.e. no trend) is achieved because the negative feedback on various steps of energy metabolism produces a homeostatic response in terms of ATP. More specifically, hexokinase, phospho-fructokinase and pyruvate kinase enzymes are activated when ATP is low, and oxidative phosphorylation is inhibited when ATP is high  could be as severe, with a significant drop in ATP, but without causing immediate cell death. In the longer term (days or weeks), the lack of complete metabolic recovery would however certainly lead to necrosis and loss of dopaminergic neurons, which agree with the literature on MPTP usage V_pdh) and CIT dehydrogenase (V_cdh) from TCA cycle are up-regulated. Hence, the global unbalancing of the TCA cycle could be described in a more complete way if all connected pathways were considered. However, based on the measurements of extracellular lactate, its rate of production after 60 min is not significant. Thus the model is in accordance with this observation as shown in The only discrepancy between the modelling and experimental data is the slower LAC increase in the simulation with CCCP -A. This Furthermore, the reduction of NADPH allows such a “turbo” mode for the overall metabolism as seen in Model simulations are in agreement with extracellular measurements of cell energetics markers . In the V_ldh) is negative, the reaction rate is approximately doubled. This result is probably a metabolic adaptation following genetic modification. In fact, the deletion of the parkin gene is likely leading to the accumulation of a number of damaged proteins, such as misfolded alpha-synuclein, which could lead to increased oxidative stress, as described by Cloutier and Wellstead Although all profiles are generally similar to the genetically unaltered model, a slight adaptation can be observed. While lactate production is still positive, as the flux of lactate dehydrogenase , the modelling, supported by experimental evidences, suggests that the biochemical regulation of energy metabolism increases metabolic flows without affecting the metabolite concentrations in order to allow the system to adapt to a certain level of stress. Although the experiments and simulations are on a relatively short timescale, the results suggest how energy can be rapidly deregulated by strong environmental stresses relevant to PD. In the long term, a certain level of adaptation could certainly occur, but over time, some damage (i.e. protein misfolding or oxidative stress) would accumulate, leading to cellular disorganisation and cell death Table S1In silico model mass balances.(DOCX)Click here for additional data file.Table S2Fluxes kinetics description.(DOCX)Click here for additional data file.Table S3Fluxes functions description.(DOCX)Click here for additional data file.Table S4State variables and initial conditions.(DOCX)Click here for additional data file.Table S5Maximal fluxes rates, affinity, inhibition, threshold, stoichiometric ratios and other constants.(DOCX)Click here for additional data file.Table S6Model Matlab® code.(DOCX)Click here for additional data file.


Saccharomyces cerevisiae.Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of  Genetic manipulation of microorganisms for obtaining improved strains involves expensive and time consuming experiments that have typically relied on trial-and-error mutagenesis and selection of promising variants. Nowadays, mathematical models of cell metabolism and gene regulation circuits have become reliable enough for metabolic engineering applications The selection of an appropriate mathematical model is a crucial step towards success in this field. Two main strategies can be followed at this stage. On the one hand, one can choose mathematical simplicity and a genome-wide scope. In this context, flux balance analysis (FBA) provides an appropriate solution  calculate the Pareto front of the kinetic metabolic model in this multi-objective problem and (ii) identify from it a small enough set of the most promising changes in enzyme activity to be tested in the laboratory. In other words, the goal of this analysis is to determine a set containing the preferred enzymatic profiles that optimize the synthesis rate of a metabolite at minimum cost  and minimum increase in the concentration of intermediate metabolites.Note that there are two main difficulties associated with the identification of such set. First, we need to solve a high dimensional non-convex multiobjective optimization problem in which several criteria must be simultaneously minimized. This problem is challenging not only because of the high number of objectives, but also due to the existence of non-convexities. Second, even if a sufficiently large number of Pareto solutions can be identified, there is still the issue of analyzing and interpreting them, in order to keep the most promising for further evaluation in the laboratory. Deb and Saxena In particular, our strategy relies on the combined use of multiobjective global optimization and Pareto filters, which are both applied to metabolic networks described using the GMA formalism. The method presented builds upon our global optimization framework for single-objective models of metabolic networks Note that our methodology shares some common features with that presented by Saccharomyces cerevisiae considering 14 objectives. This process has been already studied in the past by several authors. For instance, Sendín et al. The capabilities of the proposed methodology are illustrated in the optimization of the fermentation of Saccharomyces cerevisiae. For this, steps 2 and 4 of the algorithm proposed (refer to the Methods Section for further details) were coded in GAMS 23.2.0, while the normalization step 3 was implemented off-line using Microsoft Excel. Numerical experiments were performed on an Intel 1.2 GHz. The GMA model (Step 1) was retrieved from In order to illustrate the capabilities of our approach we solved a case study that optimizes the ethanol production in the fermentation of Note that we assume that the GMA model is given. If this was not the case, a previous step would be necessary to construct such a model from dynamic profiles using parameter estimation methods. We should note also that the modeling software GAMS is a versatile tool that allows implementation of all the framework's steps, offering standard coding capabilities and interfacing with powerful optimization solvers.The MOO problem was solved using the epsilon constraint method, which was enhanced through a heuristic procedure based on generating solutions for all possible bi-criteria subproblems. We defined 10 epsilon parameters for each objective, which gave rise to 910 single iterations  assuming a normal distribution for all objectives. We further assumed that the mean and standard deviation are the same as those of the samples . Note that this brings the data to the  range. The Smart filter was applied next in order to remove indistinguishable solutions from the pool. The application of this algorithm has also the effect of providing a more uniform spread of points. Note that choosing larger values of tolerance We next resort to the second type of Pareto filter: the order of efficiency filter. We started by imposing a Particularly, the lower and upper limits of the 214 solutions efficient of order 13 are quite close to the bounds corresponding to the 611 solutions of the Pareto set obtained using the Smart filter, showing a small decrease (about 2%) in the ethanol synthesis rate with respect to the maximum possible value. There are 14 solutions efficient of order 12 with a curve rather close in most objectives to that of the 611 original solutions. In this set, however, the ethanol synthesis rate drops by an additional 69%, which is consistent with the trend observed in Remarkably, the only solution efficient of order 11 , illustrating the usefulness of the approach in the post optimal analysis of the candidate solutions. In different test problems, the outer approximation algorithm integrated in our systematic framework efficiently solved problems with up to 30 independent metabolites and 60 reactions in short CPU times . Hence, we expect the method to scale up smoothly when tackling more complex models, even though we have yet to explore its limits. Note, however, that genome-wide scale problems are still beyond the capabilities of current deterministic global optimization methods. First, there is a lack of kinetic data to build realistic genome scale models. Second, assuming the existence of a detailed enough kinetic model, there is still the issue of solving it to global optimality in short CPU time. For these reasons, genome scale models are usually solve via FBA, despite the known limitations of this method. Nevertheless, we think that advances in deterministic global optimization theory and software applications will pave the way for more efficient algorithms leading to significant CPU savings, which will make it possible to tackle complex genome scale kinetic models.In summary, our approach allows for the global optimization of metabolic networks on different objectives simultaneously. The method presented reduces the computational burden associated with the generation of solutions, and facilitates the post-optimal analysis of these alternatives by systematically identifying the best ones  for subsequent experiments in the laboratory. Hence, our method is particularly suited for problems of moderate size. Larger kinetic models could be tackled with stochastic methods, but even if they are the method of choice, it will be still possible to use the Pareto filters introduced in our work. However, we will not have any information on the quality of the solution found. Finally, for genome-wide scale models, FBA might be the method of choice, despite having some limitations already discussed in the literature.Our systematic framework comprises the following steps see :Model building and parameter estimation : construct a GMA model for the targeted metabolic network.Global optimization of the GMA model on several biological criteria.Normalization of the solutions obtained in step 2.Application of Pareto filters to identify the preferred subset of alternatives.The sections that follow describe in detail each of these steps.The optimization of the metabolic network is posed in mathematical terms as a multiobjective NLP  that embeds GMA equations. Note that there are different possible ways to obtain this GMA model. Particularly, we can follow a top-down approach, that is, find the parameters of a GMA model that make it consistent with dynamic data by solving a parameter estimation problem. On the contrary, we might be interested in following a bottom-up strategy and acquire the GMA model of interest from the literature. In what follows, we describe briefly the GMA formalism before presenting the details of the moNLP.We assume that the concentration Since we are interested in solving the steady state, the time dependence can be dropped from the formulation:For demonstrative purposes, we assume that the main objective is to maximize the synthesis rate of a desired product. This rate is calculated by summing up the velocities of those processes contributing to its synthesis, as illustrated in Two additional criteria are appended to the objective function. The first is the minimization of the metabolites concentrations, proposed as an optimality principle for metabolic networks The optimization problem takes the form of a nonconvex NLP, in which multiple local optima may exist. We employ global optimization techniques to ensure global optimality within a desired tolerance.In general, the Pareto set of a GMA model may be nonconvex due to the nonlinear kinetic equations. Different MOO algorithms could be used to calculate this set Click here for additional data file.


Higher plants and algae are able to fix atmospheric carbon dioxide through photosynthesis and store this fixed carbon in large quantities as starch, which can be hydrolyzed into sugars serving as feedstock for fermentation to biofuels and precursors. Rational engineering of carbon flow in plant cells requires a greater understanding of how starch breakdown fluxes respond to variations in enzyme concentrations, kinetic parameters, and metabolite concentrations. We have therefore developed and simulated a detailed kinetic ordinary differential equation model of the degradation pathways for starch synthesized in plants and green algae, which to our knowledge is the most complete such model reported to date.cat and KM are substantial, whereas those for cytosolic glucose are not, consistent with a kinetic bottleneck due to transport. Response coefficient norms show stromal maltopentaose and cytosolic glucosylated arabinogalactan to be the most and least globally sensitive metabolites, respectively, and β-amylase kcat and KM for starch to be the kinetic parameters with the largest aggregate effect on metabolite concentrations as a whole. The latter kinetic parameters, together with those for glucose transport, have the greatest effect on stromal glucose, which is a precursor for biofuel synthetic pathways. Exploration of the steady-state solution space with respect to concentrations of 6 external metabolites and 8 dynamic metabolite concentrations show that stromal metabolism is strongly coupled to starch levels, and that transport between compartments serves to lower coupling between metabolic subsystems in different compartments.Simulation with 9 internal metabolites and 8 external metabolites, the concentrations of the latter fixed at reasonable biochemical values, leads to a single reference solution showing β-amylase activity to be the rate-limiting step in carbon flow from starch degradation. Additionally, the response coefficients for stromal glucose to the glucose transporter kWe find that in the reference steady state, starch cleavage is the most significant determinant of carbon flux, with turnover of oligosaccharides playing a secondary role. Independence of stationary point with respect to initial dynamic variable values confirms a unique stationary point in the phase space of dynamically varying concentrations of the model network. Stromal maltooligosaccharide metabolism was highly coupled to the available starch concentration. From the most highly converged trajectories, distances between unique fixed points of phase spaces show that cytosolic maltose levels depend on the total concentrations of arabinogalactan and glucose present in the cytosol. In addition, cellular compartmentalization serves to dampen much, but not all, of the effects of one subnetwork on another, such that kinetic modeling of single compartments would likely capture most dynamics that are fast on the timescale of the transport reactions. Insolation is the dominating contributor to a sustainable terrestrial energy balance, whether directly captured or transformed into secondary sources such as wind or biomass. Plants have evolved to use this resource to provide themselves with the low-potential carbon necessary for growth by splitting water and fixing carbon dioxide, a known greenhouse gas. During the light photosynthetic reactions, more carbon can be fixed than can be productively marshalled for growth, and cells store this excess carbon in compact polymers such as starch. Chloroplastic starch is stored in the form of granules  that conet al. have proposed a pathway of starch degradation in Arabidopsis thaliana leaves, whereby starch is released from the granule in a soluble form, then debranched to yield soluble linear glucans in the chloroplast stroma . The value of -1 using the maximal maltose consumption rate for a given residual maltose concentration and the mass concentration of cells in anaerobic sugar-limited yeast (Saccharomyces cerevisiae CBS 8066) chemostat cultures  is the concentration of metabolite i, and C carries units of (μM/s) μM-1. Final metabolite vectors at convergence cutoffs of 10-2 and 10-8 were clustered by the k-means algorithm (as implemented in the SciPy package). Each row of the data matrix comprised a final point in the logarithm of metabolite concentration space. The variance of each column was normalized to 1.0, then the data clustered with a seed cluster estimate of 64 . Cluster centroid distances were checked to be greater than the sum of their respective cluster standard deviations. Establishing unit variance for the most tightly converged metabolite vectors was problematic, and so data in this case were clustered sequentially in the direct space of concentrations, using a distance threshold of 10-8 μM. For this latter case, a cluster could be defined by the position of the first point added, rather than the centroid, due to the relatively tight bunching observed.where [The authors declare that they have no competing interests.AN developed and encoded the starch degradation model, ensured model self-consistency, simulated the model behavior, analyzed results from serial and parallel simulations, and drafted the manuscript. ML implemented the parallel parameter sampling routines and carried out parallelized simulations. PG wrote the sequential clustering routine, supervised the software design and implemented the core simulation components. CHC developed the modeling strategy, wrote and ran the k-means clustering routine and analyzed the results, co-drafted and edited the manuscript, and supervised the research. All authors have read and approved the final manuscript.AN is a research associate in the Computational Science Center at the National Renewable Energy Laboratory (NREL) with research interests including mathematical biology and theoretical immunology. His current explorations include metabolome representation and expression for potential biofuel-producing organisms, enzymatic hydrolysis of biomass particles containing multiple polysaccharide types, flux balance analysis, and modeling regulatory networks using data-mining, bioinformatics analysis and correlation of multiple types of high-throughput "omics" data.ML is a research associate in the Computational Science Center at NREL. His research interests are numerical search, high performance computing (HPC) and uncertainty quantification. In addition to supporting systems biology, Monte is also working on exploring more efficient building designs using parallel computing.PG is a senior scientist in the Computational Science Center at NREL. His research interests center on the application of mathematics and HPC to renewable energy challenges, particularly optimizations involving expensive simulations. In addition to developing kinetic simulation software for HPC, he studies multi-scale device simulation and optimization and high-throughput materials screening, inverse material design by electronic structure data mining and optimization, and computational battery modeling.CHC is a senior scientist in the Computational Science Center at NREL. His research focuses on systems biochemistry and computational chemistry from molecular to cellular scales. His current projects touch on dynamical properties of chemical and biochemical systems, electron and energy transfer, and homogeneous transition metal catalysis.Clustering analysis. A single Excel 2008 file containing statistics about k-means clusters for 10-2 convergence cutoff with 63 clusters, and 10-8 convergence cutoff with 45 clusters. Correlation coefficients are also contained as separate sheets within the file, color-coded by magnitude of coefficient: gray (1.0), orange (0.5-0.99), green (0.2-0.49), and white (< 0.2).Click here for fileSBML Model File. A single Systems Biology Markup Language file representing the reference model in this study. This model is automatically transformed to C++ by the translation utility of the High-Performance Systems Biology Toolkit and compiled into high-performance executable programs for sampling and optimization tasks, as well as simple forward integration. This model may also be found in the BioModels database under accession number MODEL1106030000.Click here for fileSummary graphics and enzyme kinetic models. Integration timecourse for the reference model, close-up of debranched stromal starch evolution, a graphical summary of the response coefficients and norms for the 8 states detailed in Table Click here for file


E. coli was discussed from the points of view of enzyme level  regulation, and gene level  regulation. Then the effects of the specific pathway gene knockout such as pts, pgi, zwf, gnd, pyk, ppc, pckA, lpdA, pfl gene knockout on the metabolism in E. coli were overviewed from the systems biology point of view with possible application for strain improvement point.Recent metabolic engineering practice was briefly reviewed in particular for the useful metabolite production such as natural products and biofuel productions. With the emphasis on systems biology approach, the metabolic regulation of the main metabolic pathways in  The concept of metabolic engineering has been proposed back in 1991 Bailey, .Escherichia coli, Saccharomyces cerevisiae, Corynebacterium glutamicum, Bacillus subtilis etc.; (4) metabolic pathways available in the strains from the available carbon source(s) to the target metabolite(s), (5) introduction of the heterologous pathways by recombinant DNA technology; (6) reduction of the flux to undesirable by-products; (7) enhancement of precursor metabolites production together with necessary cofactors production; (8) modulation of transporters for exporting the target metabolite(s) to the extracellular medium; (9) understanding the metabolic regulation mechanism by both allosteric regulation of enzymes and transcriptional regulation by global regulators; (10) robust and responsive genetic control system for the desired pathways and the host microbe, (11) methods for debottlenecking the chosen pathways; and (12) ways to maximize yields, titers, and productivities  available raw materials such as cellulosic biomass, algae, and waste materials, which can be converted to glucose, xylose, fructose, galactose, mannitol, and glycerol etc. by the appropriate saccharification methods and their processing costs; (2) enhancement of the substrate uptake rate and co-consumption of multiple carbon sources (for the enhancement of the target metabolite production rate); (3) appropriate host microbes such as E. coli by probably considering the advantages of high cell growth rate and well-known characteristics etc. In the field of biofuel production, much interest has centered on S. cerevisiae. Corynebacterium glutamicum is also frequently employed as platform cell factories in industry in particular for amino acid production. An overview of the recent advances in engineering the central carbon metabolism of such industrially important bacteria as E. coli, C. glutamicum, B. subtilis, Streptomyces sp., Lactococcus lactis has been reported  Fell,  may be ain silico gene knockout simulations for succinic acid fermentation. Trinh et al.  system and the MglBAC system  for the case of using a mixture of multiple carbohydrates, an early attempt was to knockout  Gosset, . Thus Gapgi gene, which codes for the first enzyme of Embden-Meyerhof-Parnas (EMP) pathway, was knocked out, the glucose catabolism occurs exclusively through the oxidative pentose phosphate (PP) pathway. As a result, NADPH is overproduced, and inhibits allosterically the activity of G6PDH, thereby reducing the glucose uptake rate, resulting in the low growth rate  pathway is activated, and the flux through G6PDH is reduced for the gnd mutant .The effect of d mutant  , PEP is accumulated, which causes the activation of Ppc and increases the Ppc flux. This in turn causes the increased fluxes through MDH (reverse direction) and Mez, and the reduced PYR (caused by Pyk disruption) could be backed up by these alternative pathway fluxes  both activate the aromatic amino acid biosynthetic pathways  is regulated by the phosphorylation /dephosphorylation of ICDH by aceBAK, and the decrease in OAA becomes dominant for the activation of glyoxylate pathway due to the importance of cell synthesis.If either the  pathway  . The metabolic flux analysis of lpdA gene knockout mutant indicates that glyoxylate pathway was activated, while glycolysis, the oxidative PP pathway, and the TCA cycle activities were down-regulated  accumulates and in turn glycolysis intermediates accumulate, and thus the glucose consumption rate decreases. Moreover, the accumulation of PYR activates Pox pathway producing acetate, and in turn AcCoA is backed up by ACS pathway from acetate (aceBAK operon was induced to activate glyoxylate pathway. If sucA gene, which codes for subunit of αKGDH, was knocked out, the metabolism is a little different from the case of lpdA gene knockout (Li et al., If  acetate  (Li et apflA, B gene knockout caused overproduction of lactate (Zhu and Shimizu, pfkA and pykF gene expressions, and thus the glucose uptake rate was increased (Zhu and Shimizu, ldhA gene was knocked out, the fluxes toward the production of acetate, formate, and ethanol were increased as expected (Kabir et al., Under anaerobic or microaerobic conditions, NADH balance and the substrate level phosphorylation for the production of ATP may control the metabolic fluxes at the branch points such as PEP, PYR, and AcCoA (Zhu and Shimizu, E. coli. The metabolisms of other microorganisms have also been investigated by Fuhrer et al. (13C-metabolic flux distributions, where the changes in the metabolic flux distributions are caused by the regulation of enzymes and the intracellular metabolite concentrations. In addition to allosteric regulation, the enzyme activities are controlled by their corresponding gene expressions. Since gene expressions are under control of global regulators or transcription factors, it is quite important to understand how these control the metabolism for metabolic engineering (Matsuoka and Shimizu, The above explanation is for r et al. . The aboAlthough most of the metabolic pathway engineering practices have focused on the modulation of the metabolic pathways of interest, the present analysis indicates the importance of understanding the overall main metabolic regulation in response the specific pathway mutation for the efficient metabolic engineering. It may be also considered to modulate transcription factors for the significant strain improvement.


Medicago, such discrepancies were partly reconciled by the recent finding that certain biosynthetic enzymes may be spatially organized into two independent channels for the synthesis of guaiacyl (G) and syringyl (S) lignin monomers. Nevertheless, the mechanistic details, as well as the biological function of these interactions, remain unclear. To decipher the working principles of this and similar control mechanisms, we propose and employ here a novel computational approach that permits an expedient and exhaustive assessment of hundreds of minimal designs that could arise in vivo. Interestingly, this comparative analysis not only helps distinguish two most parsimonious mechanisms of crosstalk between the two channels by formulating a targeted and readily testable hypothesis, but also suggests that the G lignin-specific channel is more important for proper functioning than the S lignin-specific channel. While the proposed strategy of analysis in this article is tightly focused on lignin synthesis, it is likely to be of similar utility in extracting unbiased information in a variety of situations, where the spatial organization of molecular components is critical for coordinating the flow of cellular information, and where initially various control designs seem equally valid.Lignin is a polymer in secondary cell walls of plants that is known to have negative impacts on forage digestibility, pulping efficiency, and sugar release from cellulosic biomass. While targeted modifications of different lignin biosynthetic enzymes have permitted the generation of transgenic plants with desirable traits, such as improved digestibility or reduced recalcitrance to saccharification, some of the engineered plants exhibit monomer compositions that are clearly at odds with the expected outcomes when the biosynthetic pathway is perturbed. In  The organization of cooperating enzymes into complexes is a pervasive feature of metabolism. In particular, this phenomenon has been shown to participate in the regulation of flux through the networks of both primary and secondary metabolism in plants. It remains a challenging task to unravel the organizing principles of such “metabolic channels,” which can be temporary or persistent, and to understand their biological function. In this article, we analyze metabolic channels in the biosynthetic pathway of lignin, a complex polymer that stiffens and fortifies secondary cell walls within woody tissues. This system is well suited because the present analysis can be based on a computational, experimentally validated model demonstrating that several enzymes are spatially associated into channels specific for the production of two lignin monomers. To characterize the functioning of these channels, we develop a novel computational approach that is capable of identifying interesting structural and regulatory features of metabolic channeling and permits the formulation of targeted and readily testable hypotheses. Since the spontaneous or controlled assembly of molecules into functional units is known to occur in many biological contexts where information flow is tightly coordinated, the proposed approach might have broad applications in the field of computational systems biology. The development of lignin biosynthesis is considered to be one of the key factors that allowed vascular plants to dominate the terrestrial ecosystem Lignin is a phenolic heteropolymer in the secondary cell walls of vascular plants. It is derived mainly from three hydroxycinnamyl alcohol monomers, namely In addition to lignin, the secondary cell walls of vascular plants contain several polysaccharides, such as cellulose and hemicellulose. Extraction of these polymers from lignocellulosic biomass for biofuel production has attracted extensive interest partly because exploitation of this source of fermentable sugars could minimize the competition for food, which has been criticized in the case of corn- or sugarcane-based biofuel production. However, the natural resistance of lignocellulosic biomass to enzymatic or microbial deconstruction has rendered the task of generating sustainable and cost effective biofuels from lignocellulosic feedstocks very challenging. While impressive advances have been made toward the reduction of biomass recalcitrance Medicago truncatula, where the characterization of two distinct cinnamoyl CoA reductases, CCR1 and CCR2, has suggested parallel routes from caffeoyl CoA to coniferyl aldehyde , an important forage legume. Medicago is particularly suited for these studies, because comparatively extensive information is available. For instance, a detailed dataset was established that characterized different lines in which seven lignin biosynthetic enzymes were independently down-regulated, and the resulting lignin content and monomer composition were determined in several stem segments The focus of this article is an assessment of such a regulatory system associated with lignin biosynthesis in in vivo? Are they sufficient to explain all available data in Medicago? Is there crosstalk between them, and if so, how is it organized? Exploring all pertinent scenarios associated with such questions would be experimentally intractable because they are simply too numerous.Although these earlier results provided significant insights into the mechanisms of regulation in this pathway, several critical questions, especially regarding the biological function as well as the operating mode of the channels, remain unanswered: For instance, are these channels always active permanent in a sense that the component enzymes are persistently assembled into a complex; such a complex could be realized through membrane co-localization, thereby ensuring that the corresponding alcohol is always synthesized. As an alternative, the channels could be facultative, thereby displaying a functionality that depends on the sub-cellular localization of the component enzymes and the metabolic milieu. This hypothesis, in turn, leads to 19 possible topological configurations  and ferulate 5-hydroxylase (F5H) were suggested to form an analogous complex contributing specifically to the synthesis of S lignin. These two complexes, which we called G and S lignin channels, are represented in The base scaffold on which the different topological variants were built is shown in e.g. kinetic orders), but also at the level of steady-state fluxes. For instance, the ratio of fluxes leading to S and G lignin was fixed at a value observed in the wild-type Medicago species  models by randomly sampling loosely-constrained parameter combinations from a parameter space that was deemed biologically realistic. A notable feature of this approach was that the parameter space was not only constrained at the level of individual parameters  and feruloyl CoA (0.40 µM−1•min−1) Medicago might be competitively inhibited by feruloyl CoA  that is 60 times lower than that for feruloyl CoA (1.14 µM−1•min−1) In the case of lignin biosynthesis, two regulatory mechanisms could arise from substrate competition. First, recombinant O-methyltransferase (OMT) activity against caffeoyl CoA in extracts from internodes 6 to 8 of CCoAOMT-down-regulated alfalfa was reduced by 4.2-fold compared with the empty vector control line, about ∼25% of OMT activity remained Second, the methylation of caffeoyl CoA by the combined activity of COMT and CCoAOMT may be subject to weak competitive inhibition by caffeyl aldehyde  had at least one valid model , the increase in mean CCoAOMT activity became less. Assays using lower concentrations of the substrate caffeoyl CoA  and the putative activator caffeyl aldehyde  showed no increase in CCoAOMT activity compared to the reaction without caffeyl aldehyde (data no shown). The maximal activation achieved in vitro was only 16%, which may not be biologically significant.To examine whether caffeyl aldehyde indeed activates CCoAOMT, we expressed alfalfa CCoAOMT in O-methylation of caffeyl aldehyde (Lolium perenne) points to the possibility of COMT being inhibited by different substrates, such as caffeyl aldehyde and 5-hydroxyconiferyl aldehyde Selagniella moellendorffii COMT Medicago as well; direct evidence supporting this hypothesis in Medicago remains to be determined.Since a direct activation of CCoAOMT by caffeyl aldehyde was not observed with recombinant enzymes, we tested other regulatory mechanisms by themselves and in combination with known mechanisms. According to one possible mechanism, based again on the concept of substrate competition, caffeoyl CoA could be a competitive inhibitor for the 3-4 = 16 different crosstalk patterns that can result from the combination of four independent regulatory mechanisms  connects one to the other. In the most extreme case, the graph would consist exclusively of isolated nodes. Second, the graph is fully connected, so that any pair of topological configurations is connected by at least one evolutionary path. As shown in The spatial organization of cooperating enzymes, known as metabolic channeling, has long been recognized as an effective means of regulation in primary and secondary plant metabolism Using the lignin biosynthetic pathway as a model system, we propose here a novel strategy for studying metabolic channeling in unprecedented detail. Specifically, we consider all possible modes of action for both the G lignin and S lignin channels, and these can be mapped into 19 different topological configurations . MetabolIdeally, the comparative assessment of design features would be entirely symbolic and independent of specific parameter values. However, systems of a realistic size are rarely analyzable in such fashion. As a reasonable alternative, we analyzed the possible design space comprehensively with widely varying parameter values, which resulted in a computational analysis of millions of models from hundreds of designs. This analysis yielded several interesting findings.Medicago CCoAOMT, which failed to provide evidence confirming the putative role of caffeyl aldehyde as an allosteric activator. It might still be possible that activation exists in vivo, but it seems more likely that the activation is indirect rather than direct.Importantly, it predicted that CCoAOMT is directly or indirectly activated by caffeyl aldehyde. This piece of information by itself is essentially unbiased, but insufficient to explain the exact mechanism of regulation. Nevertheless, it offered a specifically targeted hypothesis and was therefore experimentally testable. However, the hypothesis of a direct activation was refuted by subsequent experiments using the recombinant O-methylation of both caffeoyl CoA and itself. Several lines of evidence, although not exclusively from Medicago, support this computational prediction. Most importantly, the same six topological configurations were identified in the indirect design analysis and in the initial analysis of a putative activation mechanism. However, the two most parsimonious mechanisms differ in their proposed control strategies. The original analysis suggested just one activation mechanism, while the second analysis proposed two inhibition mechanisms. To some degree, these two mechanisms have the same ultimate effect. If ccr2 is knocked out, the flux entering the CCR2/COMT pathway and the subsequent synthesis of S lignin decline. The only possibility to increase the S/G ratio is to reduce the flux entering the CCoAOMT/CCR1 pathway. This task can be accomplished either through a diminished activation, as suggested for the single activation mechanism, or through an enhanced inhibition, as suggested for the dual-inhibition mechanism. The latter mechanism seems sufficient to restore consistency with the data, but it is of course possible that more complicated control patterns are present.As a possible mechanism, the design analysis suggested that caffeyl aldehyde inhibits the 3-Arabidopsis NST1/SND1 double knockout mutant that shows a complete suppression of secondary cell wall thickening in woody tissues, including interfascicular fibers and secondary xylem, but otherwise grows quite well as compared to the wild-type plants The computational analysis suggests that the G lignin channel is necessary for the system to respond correctly and robustly to certain genetic perturbations. By contrast, the S lignin channel appears to be dispensable. This theoretical deduction is indirectly in line with the fact that S lignin has arisen much later in the evolution of higher plants than G lignin Medicago population use the same or different designs, or whether the response to selected perturbations is an adequate phenotypic feature. Further investigation of the protein-protein interactions between lignin biosynthetic enzymes is thus necessary to confirm that a G lignin channel is indeed necessary for optimal functioning.Within an evolutionary context, the multiplicity of robust solutions can be represented with a graph representation that connects any two (robust) topological configurations differing by a single edge. This graph is reminiscent of the “neutral network” concept that was initially proposed in genotype-phenotype models for RNA secondary structures The work in this article describes a novel computational approach that shows promise in deciphering the principles of channel assembly in a biosynthetic pathway when relevant information is limited. It also provides a clear direction in which to proceed with more targeted experiments. Beyond the application described here, the proposed strategy might be beneficial in entirely different biological contexts, such as gene regulatory and signaling networks, where the task is to analyze how information flow is controlled by the spatial organization of molecules in the cell.a priori specification of a biological mechanism iγ that represents the turnover of reaction i, and kinetic orders i,jf, each of which characterizes the effect of a variable jX on a reaction i. A kinetic order can take any real value, and the sign of its value has a directly interpretable meaning: a positive value indicates an activating effect, a negative value an inhibiting effect, and zero no effect.Since the two metabolic channels of interest are assumed to affect only the relative amounts of G and S lignin, the analysis is restricted to those critical steps within the lignin biosynthetic pathway system that govern the flow of material either toward G or S . For eacX1, has two representations  and X3 (feruloyl CoA), as well as two independent variables, Xn+1 (CCR2) and Xn+2 (CCoAOMT). In GMA representations, n typically denotes the number of dependent variables, so that n+1 and n+2 refer to the first two independent variables. At the steady state, the derivative on the left-hand side becomes zero, thereby turning the differential equation into a linear equation of fluxes As a typical example, the differential equation for caffeoyl CoA, defined as X3 and X2 are included in the power-low representations of V2 and V3, respectively, because they potentially modulate the two consuming fluxes of X1. Applying the rules for kinetic orders described above, we can immediately impose bounds on the values of f2,3 and f3,2 for different regulatory mechanisms , where m equals the number of reactions. The sampled steady-state fluxes can be thought of as possible representatives of a wild-type Medicago species, while P defines the boundaries within which the system is able to operate. Biologically, these boundaries are given by many linear equality or inequality constraints with physiological meaning, such as the reaction stoichiometry (e.g.P is a bounded polyhedron (or polytope) and therefore has a concise parametric descriptionm-dimensional vectors iu can be identified using first principles iu have been called “extreme pathways” To address this issue of insufficient data, we sample parameter values from relatively wide, biologically realistic ranges. The procedure involves the following steps. First, we sample the steady-state fluxes try e.g., the rati,jf) from their respective ranges , compared to the wild-type value.Qualitative correctness for the simulations of ad hoc fashion: We applied more lenient, qualitative criteria to the predictions of S/G ratios for ccr1 and ccr2 knockout mutants because the experimental data were only available in Medicago truncatula, but not in our model organism alfalfa . However, when we relaxed the criteria for screening the predictions of S/G ratios for CCoAOMT and COMT down-regulated lines to allow a percentage error as large as 25%, we obtained the exact same set of pathway designs that are consistent with the data, suggesting that the main conclusions are quite robust to the choice of thresholds.These criteria for success of a model instantiation were initially determined in an E. coli Rosetta strains containing the constructed plasmid were cultured at 37°C until OD600 reached 0.6–0.7, and protein expression was then induced by adding isopropyl 1-thio β-galactopyranoside (IPTG) at a final concentration of 0.5 mM, followed by 3 h incubation at the same temperature. Cell pellets from 25 ml induced medium were harvested and frozen at −80°C for further use. Induced cell pellets were thawed at room temperature, resuspended in 1.2 ml of extraction-washing buffer , and sonicated three times for 20 s. Supernatants were recovered after centrifugation , and incubated at 4°C for 30 min with equilibrated Ni-NTA beads  under constant inversion to allow the His-tag protein to bind to the beads. The beads were washed three times with 1 ml of extraction-washing buffer, and the target protein was eluted with 250 µl of elution solution . The concentration of the eluted target protein was determined using the BioRad protein assay  and its purity was verified by SDS-PAGE.The cloning of the alfalfa CCoAOMT cDNA into the expression vector pET15b was as described previously 2 and 2 mM dithiothreitol. The substrate (caffeoyl CoA) concentration was 20, 30 or 40 µM and the putative activator  concentration was 0, 2, 5 or 10 µM. Since caffeyl aldehyde was in dimethyl sulfoxide solution, the final concentration of dimethyl sulfoxide in the reaction was 4% and the final volume of the reaction was 50 µl. The reactions were stopped by adding 10 µl of 24% w/v trichloroacetic acid. Reaction products were analyzed by reverse-phase HPLC on a C18 column  in a step gradient using 1% phosphoric acid in water as solvent A and acetonitrile as solvent B. Calibration curves were constructed with authentic standard of the product feruloyl CoA. Activity assays using lower concentrations of the substrate caffeoyl CoA  and the putative activator caffeyl aldehyde  were performed using a sensitive radioactive assay method as described previously Caffeoyl CoA for the enzyme assays, and feruloyl CoA for the calibration curve, were synthesized as described previously Figure S1Simulation results for CCR1 and CCR2 down-regulation using only Mechanism 1. As with (TIF)Click here for additional data file.Figure S2Simulation results for CCR1 and CCR2 down-regulation using only Mechanism 2. See legend of (TIF)Click here for additional data file.Figure S3Simulation results for CCR1 and CCR2 down-regulation using Mechanisms 1 and 2. See legend of (TIF)Click here for additional data file.Figure S4Model formulation and nomenclature. (A) Definition of all dependent and independent variables for a system that implements configuration A in iY to values that represent the degree of down-regulation as observed in prior experiments.(TIF)Click here for additional data file.Table S1Number of valid model instantiations as judged by two different robustness measures (Q and Q′). Statistics with a non-zero value of Q or Q′ are marked in bold. The first number is from simulation with Mechanism 3 only, whereas the second number is from simulation with both Mechanisms 1 and 3.(DOCX)Click here for additional data file.Table S2Upper and lower bounds for kinetic orders.(DOCX)Click here for additional data file.Text S1Details regarding the selection of target tissue and the definition of physicochemical constraints. A supplementary text for (DOCX)Click here for additional data file.