The Warburg effect - a classical hallmark of cancer metabolism - is a counter-intuitive phenomenon in which rapidly proliferating cancer cells resort to inefficient ATP production via glycolysis leading to lactate secretion, instead of relying primarily on more efficient energy production through mitochondrial oxidative phosphorylation, as most normal cells do. The causes for the Warburg effect have remained a subject of considerable controversy since its discovery over 80 years ago, with several competing hypotheses. Here, utilizing a genome-scale human metabolic network model accounting for stoichiometric and enzyme solvent capacity considerations, we show that the Warburg effect is a direct consequence of the metabolic adaptation of cancer cells to increase biomass production rate. The analysis is shown to accurately capture a three phase metabolic behavior that is observed experimentally during oncogenic progression, as well as a prominent characteristic of cancer cells involving their preference for glutamine uptake over other amino acids. Cancer cells, as opposed to normal cells, produce a substantial amount of energy inefficiently via aerobic glycolysis, even in the presence of sufficient oxygen to support mitochondrial respiration. Despite the fact that this phenomenon, called the Warburg effect, has already been discovered back in 1924, its causes remain poorly understood. Here we utilize a genome-scale human metabolic network model and show that by accounting for cellular capacity for metabolic enzymes, the Warburg effect is a direct consequence of cancer cells' adaptation to fast proliferation. We demonstrate that our model accurately captures several metabolic phenotypes observed experimentally during cancer development, as well as the preference of cancer cells to glutamine uptake over other amino acids. They found that aerobic glycolysis enables maximal palmitate production yield due to specific reducing power requirements. In another recent study, Vazquez et al. employed a schematic model of ATP production in human cells (considering two lumped reactions representing aerobic glycolysis and oxidative phosphorylation), elegantly showing that a switch to aerobic glycolysis should result from cellular maximization of ATP production macromolecular crowding constraint E. coliet al., where the production costs of the metabolic enzymes involved were accounted for in a self-replicating model Previous computational investigations of the Warburg effect studied the role of either energy or biomass production in causing the Warburg effect, focusing solely on central carbon metabolism. For example, the study of Vander Heiden In this paper, we study the causes of the Warburg effect by accounting for both energy production and anabolism of essential biomass constituents, in a genome-scale stoichiometric network model biomass reaction that represents the production of a pre-defined set of essential biomass precursors required for cellular proliferation, as conventionally done in Flux Balance Analysis  optimal yield metabolism at a growth rate that is below 43% of the maximal possible rate, characterized by low glycolytic vs. high oxidative phosphorylation (OXPHOS) flux . (ii) Intermediate yield metabolism at growth rate between 43-92%, characterized by increased glycolytic and oxidative phosphorylation flux ((iii) Low yield metabolism at a growth rate above 92% of the maximal possible growth rate, characterized by a sharp increase in glycolytic flux and a decrease in oxidative phosphorylation (and hence of O2 uptake). The increase in aerobic glycolysis flux (We applied the approach described above (FBA with solvent capacity constraint) to predict human cellular flux distributions that maximize the biomass production rate. To simulate varying growth rates we performed the optimization across a wide range of different glucose uptake rates. Indeed, under these combined sets of constraints we find that biomass yield does decline at high growth rates – in accordance with the Warburg effect OS) flux , phase IOS) flux , phase Iion flux . NeitherTo further validate the plausibility of the model, we examined the correlation between its enzyme concentration predictions  and high ‘cost’ in terms of the required enzyme concentrations per unit of glucose uptake (AC), and, on the other hand, a flux distribution B with a lower growth yield (BY) and lower cost (BC). Considering a bound on the total enzyme concentration cost, one can observe that when the glucose uptake is unlimited flux distribution B will provide a higher growth rate if its growth yield normalized by its cost is higher than that of flux distribution A . Flux distribution B stands for a typical metabolic state at phase III, which involves a high rate of aerobic glycolysis, with a low growth yield of 0.035 and a low cost of 0.050 (yield to cost ratio  =  0.7). These values indeed transcribe to a higher growth yield per unit of concentration cost of the enzymes participating in B, as alluded above. et al.Concretely, analyzing the results of our model, flux distribution i.e. by considering only the network stoichiometry in the vanilla FBA model) fails to predict the preference for glutamine (The role of glutamine in cancer has been a topic of major interest as cancer cells are known to have a significant high glutamine uptake rate lutamine .We carefully examined the flux distribution obtained with glutamine in the growth medium (achieving a growth rate of 0.062 1/h) vs. the one obtained with glutamate (growth rate  =  0.056 1/h). Interestingly, when glutamate is present in the medium, a large quantity of it is transformed into glutamine in an ATP consuming reaction catalyzed by the enzyme glutamine synthetase (EC 6.3.1.2). This satisfies the glutamine biomass requirement as well as the production of nucleotide precursors, among others. When removing the ATP requirement from this reaction, the growth rate achieved with glutamate in the medium increases to 0.059 1/h, which explains 50% of the growth rate difference. Notably, while this provides some intuitive explanation for the predicted preference for glutamine, we cannot identify a simple explanation for the entire effect due to the high complexity of the network model employed.Metabolic adaptation to elevated growth requirements during cancer development has been recently suggested as the possible cause of the Warburg effect, a long-standing enigma of cancer metabolism. In this work we rigorously study this hypothesis using a genome-scale human metabolic model and demonstrate that stoichiometric considerations solely are insufficient to explain the shift to inefficient metabolism, in difference from recent claims et al.E. coli model improved phenotypic predictions. In their work, however, Beg et al. assumed an upper bound on the total cell-volume occupied by metabolic enzymes, as opposed to the method introduced here where we assume a bound on the enzyme mass per cell mass . In order to account for enzyme volumes, Beg et al. estimated enzyme volumes by assuming a uniform specific volume parameter (representing the ratio between enzyme mass and volume) for all enzymes. Here, we employed a simpler approach that does not depend on specific volume estimations, and explicitly constrains the total sum of enzyme mass. Notably, we further tested the effect of accounting for volumes instead of masses, and obtained results which are very similar to those obtained with masses only  already pointed to the significance of the solvent-capacity constraint in explaining the Warburg effect et al. work introduces a schematic model of ATP production in central metabolism including just a handful of variables. Furthermore, similarly to the work of Pfeiffer et al., their work does not explicitly account for the entire biomass composition and the associated energy requirements. In contrast, here we study a genome-scale biomass producing human model that, despite the scores of alternative biomass and energy production pathways existing in the human network, successfully shows that highly proliferating cells such as cancer cells are forced to display Warburg related phenotypes at high growth rates (phase III). Additionally, and in contrast to the small-scale models, our genome-scale model correctly predicts an experimentally observed transitional phase (II). Furthermore, on a mechanistic level, the genome-scale metabolic description provided by our analysis is significantly correlated with the gene expression patterns across the wide array of NCI-60 cancer cell-lines , a result which could not have been predicted by the Vazquez et al. model. Lastly, the model was able to predict the marked contribution of glutamine to rapid cellular growth. As a further demonstration of the robustness of our results, we repeated the analyses using a model accounting for maintenance ATP production, obtaining qualitatively similar results  subject to steady-state, thermodynamic and growth medium constraints:The Duarte Equation 2 imposes the steady state constraints on the system, assuming that the metabolite concentrations remain constant in time. Thermodynamic constraints determining the reaction directionalities are accounted for via the flux limits A constraint on the total enzyme concentration was added to the biomass production FBA model: iv [mmol/(mgDW*h)]) is given by the product of iv and the enzyme's molecular weight (iMW [mg/mmol]) divided by its turnover number (C = 0.078 [mg/mgDW]) was estimated based on dry cell weight protein biomass measurements .The enzyme mass (per mg dry weight (DW) of cells) required to maintain the flux in the i-th reaction . For each phase, the median flux distribution across 1000 different uniform samples was calculated using ACHR sampling v, for each reaction i, the enzyme concentration v) was calculated as the product ofi.e. reactions catalyzed by enzymes encoded by this gene), based on a gene-to-reaction mapping given in the human metabolic model. The Spearman correlation between the gene expression vector and inferred enzyme concentration vector was calculated for the two models in each of the 60 cell lines. The robustness of the results was validated against 1,000 uniformly sampled flux distributions from the solution spaces of the two models using ACHR sampling Gene expression readouts for 1,269 metabolic genes across 60 cell lines from the NCI-60 collection Each of the 20 amino acids was added, in turn, to the growth media, resulting in 20 different maximal biomass production rates calculated based on (i) the stoichiometric model, and on (ii) a model additionally accounting for the solvent capacity constraint. The maximal amino-acid uptake rate was set to the same uptake rate as glucose; the results are shown to be robust to the choice of this value .Dataset S1Human biomass composition.(XLSX)Click here for additional data file.Dataset S2Enzyme molecular weight data for the reactions in the model.(XLSX)Click here for additional data file.Dataset S3Enzyme turnover number data for the reactions in the model.(XLSX)Click here for additional data file.Text S1Validating the robustness of the results to various model parameters and exploring additional changes in the model.(DOC)Click here for additional data file.


Shewanella oneidensis MR-1 sequentially utilizes lactate and its waste products (pyruvate and acetate) during batch culture. To decipher MR-1 metabolism, we integrated genome-scale flux balance analysis (FBA) into a multiple-substrate Monod model to perform the dynamic flux balance analysis (dFBA). The dFBA employed a static optimization approach (SOA) by dividing the batch time into small intervals , then the Monod model provided time-dependent inflow/outflow fluxes to constrain the mini-FBAs to profile the pseudo-steady-state fluxes in each time interval. The mini-FBAs used a dual-objective function  to capture trade-offs between optimal growth and minimal enzyme usage. By fitting the experimental data, a bi-level optimization of dFBA revealed that the optimal weight in the dual-objective function was time-dependent: the objective function was constant in the early growth stage, while the functional weight of minimal enzyme usage increased significantly when lactate became scarce. The dFBA profiled biologically meaningful dynamic MR-1 metabolisms: 1. the oxidative TCA cycle fluxes increased initially and then decreased in the late growth stage; 2. fluxes in the pentose phosphate pathway and gluconeogenesis were stable in the exponential growth period; and 3. the glyoxylate shunt was up-regulated when acetate became the main carbon source for MR-1 growth. S. oneidensis MR-1). The modeling results reveal that MR-1 metabolism is suboptimal for biomass growth, while MR-1 continuously reprograms the intracellular flux distributions in adaption to nutrient conditions. This innovative dFBA framework can be widely used to investigate transient cell metabolisms in response to environmental variations. Furthermore, the dFBA is able to simulate metabolite-labeling dynamics in 13C-tracer experiments, and thus can serve as a springboard to advanced 13C-assisted dynamic metabolic flux analysis by using labeled proteinogenic amino acids to improve flux results.This study integrates two modeling approaches, a Monod kinetic model and genome-scale flux balance analysis, to analyze the dynamic metabolism of an environmentally important bacterium ( Cell metabolisms are highly dependent on environmental conditions, so the metabolic state often shifts during the cultivation period in situ bioremediation and microbial fuel cell applications This study developed an FBA framework that integrates Monod kinetics and FBA to decipher the dynamic metabolism of MR-1 . MR-1 ismax) was much higher than that for either pyruvate or acetate, indicating that lactate was the major carbon substrate for biomass growth at the early growth stage. plk, apk and alk) for waste products (pyruvate and acetate) synthesis and reuse, which indicates that MR-1 quickly consumed lactate, producing significant metabolic overflows to the waste products. Such a strategy illustrates an advantageous ecological niche for MR-1 in competing for favorable carbon sources. Finally, although our standard Monod model reasonably well described MR-1 growth data, its results showed some lack-of-fit with statistical analysis (MR-1 growth displayed an apparent lag phase (∼7.1 h) in 30 mM lactate medium (0.1% inoculation). By incorporating a time delay function for the lag growth phase, a standard Monod model consisting of four ordinary differential equations was built to describe the extracellular metabolite curves and growth kinetics . The paranalysis . Such a To resolve the flux dynamics, the static optimization approach (SOA) divided the cultivation phase into numerous pseudo-steady states so that a conventional genome-scale MR-1 framework  was able to calculate the flux distributions 2 production by diverting the carbon flow into a shorter metabolic route. The glyoxylate shunt activity was further confirmed by in vitro enzyme assays at both the mid-log phase  and the late-log phase .The dynamic flux distributions in MR-1 were calculated using the bi-level optimization . The car13C-labeled tracer experiments, dFBA can be used to predict the isotopomer dynamics in slow turnover metabolites, such as proteinogenic amino acids. During MR-1 growth with [3-13C] lactate, the dynamic metabolism led to variations of labeling patterns in intracellular metabolites (biomass precursors) so that the isotopic labeling in proteinogenic amino acids was continuously changing during cell growth in vivo reactions could be bi-directional, we implemented exchange coefficients for four pathways  in the model to improve the simulation of 13C-labeling  to the oxidative TCA cycle (represented by fumarase activity) when acetate started to be used as the main carbon substrate  and late-log phase .The dFBA model can also simulate time-dependent isotopomer enrichment in proteinogenic amino acids. In turn, the isotopomer results  can be u13C-metabolic flux analysis (MFA) offer analytic insight into the cell metabolisms in fermentation processes 13C-MFA is useful only for analyzing the steady-state central metabolism. To perform 13C-MFA of dynamic flux distributions, the fast turnover metabolites have to be extracted and analyzed at multiple time points 13C-MFA cannot resolve the flux distributions in a large-scale metabolic network. To overcome these difficulties, this study illustrates a proof-of-concept approach that exploits the synergy between proteinogenic-amino-acid-based 13C-MFA and genome-scale dynamic flux balance analysis.Proteinogenic amino acids are abundant in biomass and can easily be measured by GC-MS. Complementing this instrumental data, In our dFBA, the Monod model is solved first independently of the FBA. As an alternative approach, we also tested to integrate the kinetic models with FBA . iFBA simultaneously optimizes the kinetic model parameters and solves the dynamic cell metabolism in MR-1 (Supplementary max) on intracellular flux distributions. Furthermore, dFBA can identify the objective functions that are possibly used by microorganisms in adaption to environmental variations. Finally, by simulating and comparing the isotopomer labeling patterns of different metabolites, the proposed dFBA framework can potentially improve dynamic flux resolutions by incorporating the isotopomer data from labeled proteinogenic amino acids.In conclusion, as in other FBA studies, the dFBA framework proposed in this study links macroscopic bioprocess variables (such as nutrient concentrations) to microscopic intracellular metabolism analysis. It predicts metabolic responses under dynamic culture conditions, and reveals the impact of the kinetic parameters (such as μS. oneidensis MR-1 (ATCC 70050) was first grown in LB medium in shake flasks overnight. A 0.1% inoculum volume was then cultured into modified MR-1 defined medium 2 were mixed with water. The mixture was then added with 20 µL 100 mM glyoxylate. The difference in absorbance at OD412 before and after glyoxylate addition reflected the activity of malate synthase, in which one unit ΔOD412 corresponded to 70.6 nmol of TNB produced (in a 1 mL reaction solution). Furthermore, the activity of malic enzyme was detected based on increased absorbance at 340 nm due to the reduction of NAD+ to NADH 2, 25 µL 40 mM NH4Cl, 100 µL 1 M KCl, 50 µL 20 mM NAD+, 100 µL 100 mM malate, and 50 µL cell extract were mixed with water (1 mL reaction solution). The change in absorbance at OD340 reflected the activity of malic enzyme.To analyze the activity of malate synthase and malic enzyme, samples were taken at early middle log phase (biomass of MR-1 ∼0.08 g/L) and late log phase (biomass of MR-1 ∼0.23 g/L). The harvested cells were centrifuged and re-suspended in 100 mM Tris buffer. The samples were then ultra-sonicated for 5 min to release the enzymes. Malate synthase activity was gauged based on the reaction of CoASH with DTNB , as described by Dixon and Kornberg 13C] lactate (purity>98%) purchased from Cambridge Isotope Laboratories, Inc. . The biomass was harvested at ∼24 h (before lactate was depleted) and ∼30 h (after the substrate had switched from lactate to waste products). To analyze the labeling pattern of proteinogenic amino acids, we hydrolyzed the biomass with 6 M HCl at 100°C. The isotopic analysis of proteinogenic amino acids was performed using a GC-MS based TBDMS method, as previously described + (unfragmented amino acid) were used for the 13C-simulations In the labeling experiment, MR-1 was first grown overnight in the LB medium in shake flasks. A 0.1% inoculum volume was then cultured into 100 mL of modified MR-1 defined medium at 30°C, with the initial carbon source as 30 mM (DOC)Click here for additional data file.Figure S2Shewanella oneidensis MR-1. Blue ▪: time profiles of flux ratio using “maximizing growth rate” as the objective function in dFBA; red ▴: time profiles of flux ratio using dual-objective function in dFBA: a combination of “maximize growth rate” and “minimize overall flux”. The entire growth of MR-1 was divided into three phases. In phase I, lactate was mainly used as the carbon substrate. In phase II, lactate, acetate and pyruvate were used as the carbon substrates. In phase III, acetate was used as the carbon substrate.Flux ratio of malate synthase (MALS) and fumarase (FUM) in dynamic metabolism of (DOC)Click here for additional data file.Figure S3Histogram of normalized Monod model residuals.(DOC)Click here for additional data file.Table S1Lack-of-fit test for the Monod model.(DOC)Click here for additional data file.Text S1Framework of integrative Flux Balance Analysis (iFBA).(DOC)Click here for additional data file.Text S213C-labeling simulations.Reactions involved in (DOC)Click here for additional data file.Text S3Shewanella oneidensis MR-1.SBML file of the metabolic model for (DOC)Click here for additional data file.


Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a “cycle of knowledge” strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought.We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in  These isoenzymes may play an especially important role in S. cerevisiae whose metabolism has evolved through whole-genome duplication and subsequent gene loss In kinetic modelling, the potential for alternative isoenzymes catalysing each metabolic reaction step is generally overlooked. For prokaryotic systems this is likely to be relatively unimportant since a given activity is more commonly controlled by a single gene/protein. However, in eukaryotes, there are often multiple gene/protein isoforms that may act separately and with different activities under different environmental conditions, or may occur in different cellular compartments. For example, Gu et al. S. cerevisiae and identical growth conditions. Furthermore, we characterise individual isoforms of enzymes involved in the biochemistry of central carbon metabolism and their differential roles.In this paper, we introduce a novel strategy that addresses the above sources of heterogeneity by producing complete sets of experimentally-derived data using the same parental strain of As with any system, parameters are distinguished from variables. In a given metabolic network, the parameters are the concentrations of enzymes and their kinetic properties, while the variables are represented by fluxes and concentrations S. cerevisiae as a model system to develop and validate our approach. We stress a number of features of this approach:1The external conditions for the biological system (the cell culture) are well defined, and these act as a source for the metabolites that are taken up by the system.2A topological description of the network is then constructed, in which all metabolic reactions are defined and associated to all isoenzymes known to catalyse the reaction. This process is performed by extracting a sub-network from larger, genome-scale metabolic networks, or by compiling literature data 3A kinetic model is built upon the metabolic map defined in point 2. Rate laws and parameter values are either taken from pre-existing models or estimated from published data.4The model is evaluated through software packages such as COPASI 5The control properties of the system are evaluated computationally and the reaction step exerting the major control over the system fluxes is identified.6catk), concentration and affinity constants of each of the corresponding isoenzymes are measured and their value is used to refine the model.The kinetic properties of the most controlling reaction step are experimentally measured. More particularly, the turnover number  problems, it is appropriate to calibrate or validate it by applying it to a well-understood system. Glycolysis represents an excellent test-case S. cerevisiae is also a particularly suitable organism in which to perform such a study from a number of other perspectives: it is well-characterised genetically, and it can be grown under conditions of continuous culture in which its metabolism can adopt a steady state This article describes the overall strategy set out above and illustrates the accuracy of systems biology modelling that is currently achievable with such a strategy. This is also the first time that the individual contributions by different isoenzymes have been accounted for in such detail, whether in a model or experimentally.22.1S. cerevisiae strains that contain either an overexpression plasmid with the open reading frame of interest, which was under control of the GAL1 inducible promoter and in fusion to a multiple tag at the C-terminus . The expressions and purification of proteins was performed as described by Malys et al. Enzymes were expressed in S. cerevisiae proteins.Although the overexpression of proteins with tags provides significant advantages by increasing throughput and protein recovery from the cell extract, it also brings some limitations related to the function and structure of enzymes. The position of the tag on the protein may interfere with its folding, multimeric complex formation, or functionality. Therefore, in some cases, as for example, enolase 2  an alternative construct with an N-terminal tag had to be used. The use of Yeast MORF and Yeast GST-Tagged collections PFK1 and PFK2 were co-expressed and their protein products co-purified as a heterooctamer from the Yeast TAP-Tagged collection. The activity of this complex was significantly higher than that of each isoenzyme purified alone.Applying a standardised approach of using a single yeast expression collection did not allow the reconstitution of fully active phosphofructokinase (EC 2.7.1.11) from individual Pfk1 and Pfk2 subunits. Therefore, in the second round of the experimental cycle, 2.2To determine the kinetic parameters for individual enzymatic reactions, spectrophotometric assays were performed for the glycolytic isoenzymes measuring the consumption or production of NADH or NADPH by using one or more coupling reactions when needed. All assays were carried out in medium-throughput measurements with a BMG Labtech NOVOstar plate reader  in 384-well format plates with a 60 μl reaction volume −1 cm−1, unless the reaction of a particular enzyme consumes or produces NADH or NADPH in which case no coupling enzymes were used. Some assays were modified by altering the concentration of coupling enzymes or other reagents to ensure that the rate measured is the rate of the reaction of interest (fully rate limiting). This is a critical step that needs special care to be taken when using coupling enzymes in assays All assays were coupled with enzyme(s) in which NAD(P) or NAD(P)H is a product or substrate so that its formation or consumption could be followed spectrophotometrically at 340 nm using an extinction coefficient of 6.62 mMAll measurements are based on at least duplicate determination of the reaction rates at each substrate concentration. Control experiments were run in parallel to check and correct for any background activity. For each isoenzyme, the initial rates at various substrate concentrations were determined and the data obtained were analyzed by the KineticsWizard Not all enzymes were found to exhibit these kinetics. As reported previously 2.3S. cerevisiae strain Y23925  were established in a turbidostat-like approach in which the biomass was monitored by measuring the electrical capacitance of the culture Continuous cultures of 2.4S. cerevisiae cells from 50 ml cultures were harvested by centrifugation for 5 min at 4000 g, and the cells mechanically disrupted using a mini bead-beater  yielding the cellular cytoplasmic soluble fraction for analysis. The latter was combined with known amounts of the recombinant labelled QconCAT protein (containing diagnostic peptides for the glycolytic enzymes 2.5http://www.thermofisher.com/)) and the standard addition method for accurate quantification. Other metabolites were quantified applying GC–MS ) and the external calibration method for accurate quantification. The concentrations determined in the extracted samples were reported as the number of molecules per cell.For metabolomics, a quenching method was applied The gas chromatographic separation of 2-phosphoglycerate and 3-phosphoglycerate is technically demanding and was not achieved during this study. Therefore, the combined concentration of both metabolites was reported rather than separate concentrations for each metabolite.2.6An existing model of yeast glycolysis At each of 17 iterations, flux control coefficients All models are provided in standard Systems Biology Markup Language format  of these reactions – a function of both protein concentration and turnover number – was now too low (i.e. was lower than the estimated in vivo flux). By contrast, using all expression data simultaneously provides substantial constraints in which non-systematic noise cancels out effectively For some iterations, the addition of experimental data led to a significant decrease in both fit to our data and flux through the pathway. This was because the limiting rate  were purified and assayed in isolation. A subsequent assay combined the α and β subunits, that had been purified separately, in equimolar amounts, but this still produced a low catk value. Finally the two subunits were co-expressed, co-purified and then assayed, resulting in a catk value of 200 s−1.For phosphofructokinase a catk of Eno1p was 0.8 s−1 and Eno2p was inactive. Since these enzymes had been previously purified and stored at −70 °C, the new experiment assayed them immediately after purification. In this case Eno1p had a catk of 8 s−1 but Eno2p was still inactive, and the activity of Eno1p alone was not enough to explain the flux. A hypothesis was formulated that the tag in the C-terminus of Eno2p (which is left on in the MORPH strain proteins) could be interfering with its active site. Published evidence for the role of the C-terminus of enolase in enzyme activity and in binding Mg2+ were found ENO2 with a tag in the N-terminus, it was expressed, purified and assayed fresh, resulting in a catk of 20 s−1, which is more than twice as active as Eno1p.The reaction catalysed by the enolases was also deficient in total capacity relative to the observed physiological flux: the catk values determined were: Pdc1p 3 s−1, Pdc5p 2 s−1, and Pdc6p was inactive. These enzymes had been stored at −70 °C following purification. We re-purified them and performed the assay immediately after the purification. This time, the catk values for the three enzymes were all 10 s−1, which leads to the conclusion that the storage had caused loss of activity.The calculated limiting rate of the reaction catalysed by the pyruvate decarboxylases, EC 4.1.1.1, was also below the physiological flux. The 5–4 × 106 molecules per cell, after reinterpretation of the proteomics data. Lysine acetylation occurred on an internal lysine residue of an analyte peptide from Fba1p. This led to division of the analyte signal between the modified and unmodified forms, present in our data, and resulted in an underestimation of the total analyte signal The enzyme concentration of fructose bisphosphate aldolase  was updated from 5 × 10It is important to note that experimental problems such as those described above only came to light upon modelling of the entire system. Since this project included iterative modelling and experimental components, replicate experiments could be carried out when needed. This contrasts with previous modelling approaches that typically relied upon third-party experimental data. It also highlights that the iterative and integrative modelling approach followed here has an important role in quality control for the experimental data, which would not be applicable to dedicated experimental studies that do not contain a modelling element.In 3.3Whilst many parameters were measured under standardised conditions, some were nonetheless estimated from the literature. The relative contribution of each unmeasured parameter to the quality of fit to data may be ranked using sensitivity analysis . Given estimates of cell volume of 40 fl V from 1.1 mM s−1 to 5.3 mM s−1) and the succinate branch was turned off (k from 0.005 s−1 to 0).The other two changes in parameter values required were both related to bulked reactions: the ATPase rate was increased  in the direction of 3-phosphoglycerate (P3G) to 2-phosphoglycerate (P2G) revealed an interaction between the substrate P3G and the coupling enzymes system . This made it difficult to determine the kinetic properties of GPM for the forward reaction, and hence only the kinetics for the reverse reaction could be determined.catk = 5.07 s−1 ± 2.9% and m K= 0.617 mM ± 10.2%), producing phophenolpyruvate (PEP). Multiple batches from different sources were tested and 31P NMR spectra of the P3G material showed no evidence for the presence of P2G, hence this observation is not due to P2G contamination. There is some evidence In studying this interaction, it was found that P3G acts as a substrate for Eno1p  and catk (using enzyme kinetics). Here the default assumption is that the catk of enzymes is not changed by the processes of protein purification; since we purify proteins that have tags in their C-terminus, we also assume that the catk (and other kinetic parameters) are not changed by the presence of the tag. The latter condition is more likely to be violated in some cases, so we checked for this. Indeed, we have found that Eno2p activity was affected by C-terminus tags (see above).In this work, we constructed a model based on three data sources: metabolomics, proteomics and enzyme kinetics. In contrast to earlier work, we separated the limiting rates into two terms representing (the product of) the enzyme level and its maximal turnover number: The benefits of this separation are twofold. First, it allows one to investigate the effects of the different isoenzymes within the system. For example glucokinase  has lower activity than the two hexokinases ; however it also has a higher affinity for its substrate glucose see , allowinSecondly, the kinetic characteristics of enzymes remain fairly constant under different growth conditions. Rather, cells respond to cues through changing enzyme levels, validating the assumptions stated above. As such, knowledge of enzyme levels under different physiological conditions may be combined with a specific set of kinetic data to create a suite of mathematical models of a system.3.6Trypanosoma brucei, control over glycolytic flux was found to be almost uniquely determined by the glucose transporter In 4For over a decade, modern systems biology has been seen as a crucial strategy and methodology for biological research. It pays particular attention to the way in which molecules interact inside cells in a quantitative way. Within systems biology there are two fundamentally distinct approaches, one uses data from large-scale measurements  to reverse engineer models directly from those data; the other approach is based on combining enzyme kinetic data to build mechanistic biochemical network models. The latter approach, sometimes referred to as “bottom-up”, is a descendent of the work of Michaelis and Menten, and at one level uses essentially the same methodology to assess the properties of each of the component enzymes in the system. It has thus been common to re-use, in systems biology models, the enzyme kinetic parameters previously estimated inenzymology studies (e.g., Ref.


Lactococcus lactis MG1363, for which actual time-series data of metabolite concentrations are available. The results indicate the usefulness of our approach and suggest a probable pathway for the production of lactate and acetate. The results also indicate that the approach pinpoints a probable strong inhibition of lactate on the glycolysis pathway.Recent development of high-throughput analytical techniques has made it possible to qualitatively identify a number of metabolites simultaneously. Correlation and multivariate analyses such as principal component analysis have been widely used to analyse those data and evaluate correlations among the metabolic profiles. However, these analyses cannot simultaneously carry out identification of metabolic reaction networks and prediction of dynamic behaviour of metabolites in the networks. The present study, therefore, proposes a new approach consisting of a combination of statistical technique and mathematical modelling approach to identify and predict a probable metabolic reaction network from time-series data of metabolite concentrations and simultaneously construct its mathematical model. Firstly, regression functions are fitted to experimental data by the locally estimated scatter plot smoothing method. Secondly, the fitted result is analysed by the bivariate Granger causality test to determine which metabolites cause the change in other metabolite concentrations and remove less related metabolites. Thirdly, S-system equations are formed by using the remaining metabolites within the framework of biochemical systems theory. Finally, parameters including rate constants and kinetic orders are estimated by the Levenberg–Marquardt algorithm. The estimation is iterated by setting insignificant kinetic orders at zero, i.e., removing insignificant metabolites. Consequently, a reaction network structure is identified and its mathematical model is obtained. Our approach is validated using a generic inhibition and activation model and its practical application is tested using a simplified model of the glycolysis of  Thus, it may be difficult to apply this technique to a large-scale metabolic system. On the other hand, time-dependent changes of metabolite concentrations can be determined in vivoUnderstanding metabolic pathways allows us to control metabolism, design a better metabolic system and optimise productivity. In vitro, in vivo and in silico research has been used to reconstruct the set of reactions that compose metabolic networks and their regulatory structure. However, it is still challenging to predict an unknown metabolic reaction network both experimentally and theoretically. For example, an in vitro experimental constraint mentioned above. Biochemical systems theory (BST) is an alternative method of analysing enzymatic reactions in network systems Because of the experimental constraints, systems biology approaches are recently considered to be one of the alternatives for handling metabolomics data and analysing metabolic systems. Specifically, the mathematical modelling approaches have been exploited to analyse metabolic reaction networks To overcome these difficulties, therefore, the present study explores a new approach for identifying a metabolic reaction network and simultaneously constructing a mathematical model. The approach consists of statistical and mathematical modelling techniques. The main concept of this approach is to employ time-series data to determine the structure of the metabolic reaction network. In principle, metabolites probably relate to others in a complicated network. A perturbation of a metabolite concentration causes changes in other metabolite concentrations. Thus, if changes in the time courses of metabolite concentrations are analysed, it becomes possible to predict and understand their metabolic reaction network. The present work therefore proposes such a new approach based on this idea.The proposed algorithm is presented in 1–X4 were generated at 51 time points by using the mathematical model with parameter values described in iX are metabolite concentrations. iα and iβ are rate constants of net influxes and effluxes, and ijg and ijh are their kinetic orders.To validate if the algorithm is applicable, we start the study using a known metabolic reaction network, i.e., the generic inhibition and activation model . This moin silico generated are plotted in p-value<0.05), and the Spearman's rank correlation coefficient should be used to calculate the correlation coefficient. However, to broadly observe correlations among metabolite concentrations, we simply calculated both the Pearson's correlation coefficient and Spearman's rank correlation coefficient according to common methods for acquiring correlations of metabolite concentrations. The results, shown in Table S1, S2 in Information S1, indicate good positive and negative correlations between several metabolites. However, this finding does not indicate causal relationships between metabolites and effects of one metabolite on the other.The time-series data u) in u = 1, implying that the present data point was used for predicting the value at the next time point. On the other hand, changes in the values of the time lag may have an effect on the Granger causality result. However, the p-values are still lower than the significance level of 0.01, although their value increases as the time lag increases . Thus, we consider the time lag that maximises significance and set this lag to unity throughout the simulations. Only the data point at time t-1 was considered for predicting the value of the data point at time t. Furthermore, the Granger causality may give some false positive interactions if a network is very large, but it is not considered to be a serious problem here, since we perform this calculation only for finding the highest causality and removing unnecessary metabolites.To obtain more information on network properties, the bivariate Granger causality test was executed to investigate relationships among metabolites. From The performance of LMA for estimating parameters in a well-known model was investigated before it is used in our algorithm. The results are given in Table S8 in Information S1. LMA finds only a local minimum, not a global one. It is therefore necessary to verify whether this non-linear regression method can successfully converge when power-law equations are used. Exact slope values from S-system equations were selected for this validation. The initial values for both rate constants and kinetic orders were set at unity. The results show that the parameters that converge using the exact slopes (estimated parameters b) are identical to their respective actual parameter values. This indicates that convergence behaviour of our parameter estimation procedure performs very well, especially for this system. In contrast, when the slopes were calculated from neighbouring data points, the converged parameter values (estimated parameters c) are slightly different from their true values. This is natural because these slopes were directly calculated and are not a function of other metabolites, unlike in the former case. In actual experiments, however, such exact slopes are not obtained and only the metabolite concentrations are available. Nevertheless, both sets of estimated parameters provide similar characteristics in terms of the behaviour of metabolite concentrations.X1, X2, X3 and X4 with the exact slope values were 0.119, 0.176, 0.319 and 0.087 s, respectively, whereas those with the slope values calculated from neighbouring data were 0.120, 0.169, 0.382 and 0.090 s, respectively.LMA provided fast convergences although the initial parameter values which were set to be unity are far from the true parameter values. The convergence times were calculated using GNU octave version 3.2.4 on Windows 7 platform with 2.93 GHz CPU. The convergence times of X1, X2, X3 and X4 were 6.08, 11.9, 5.28 and 3.85 s, respectively. The convergence times also decreased with a decrease in the number of parameters.Once the performance of LMA was successfully elucidated, we exploited it to our algorithm. Assuming that the network is unknown, the S-system equations  were setThe significantly large kinetic orders in Although there is a constraint for using the bivariate Granger causality and also the parameter estimation using slopes may give slight calculation errors in the model construction, the above result clearly shows that our approach is theoretically consistent. Furthermore, it can provide a mathematical model for system analysis, although most of the systems biology approaches focus on either data analysis or model construction. On the other hand, actual experimental data contain biological and analytical errors and it may be difficult to obtain a large amount of time-series data. To evaluate the performance of our approach in practical application, therefore, the number of the time-series data for each metabolite concentration in the generic inhibition and activation model was decreased to 11 points and each data was allowed to include a noise in the range of 0–5% (Information S3). The result shows that it is still possible to estimate the metabolic reaction network if the time-series data set possesses clear characteristics and behaviours. It is therefore clear that our approach more depends on the quality of data than the quantity of data.Lactococcus lactis because a number of metabolite concentrations have been reported for several types of micro-organisms genetically modified or perturbed both in vitro and in vivoLactococcus lactis MG1363 were taken from a number of studies We next discuss the glycolysis pathway of According to these studies, several metabolite concentrations, such as phosphoenolpyruvate and phosphoglyceraldehyde, contain significant experimental errors, and it is difficult to validate the results. Consequently, these experimental data were neglected. In contrast, metabolites that have clear metabolic behaviours despite containing large experimental errors were considered here. The current system thus consists of five metabolites, including three extra- and two intra-cellular metabolites.We fitted the measured time-series data of metabolite concentrations obtained in Neves et al. X2 to X1, X4 to X2, X1 to X3, X2 to X4 and X3 to X5.The bivariate Granger causality for these estimated time-series data was calculated. The results are listed in X1 (glucose) is not considered because it is the starting compound. Second, effluxes from X4 (lactate) and X5 (acetate) are also not considered because they are end products. Third, the metabolites that have insignificant Granger causalities are removed. Fourth, the metabolites having first and second Granger causalities are considered. As a result, it is possible to predict a pathway from the Granger causality, as illustrated in A procedure to construct a metabolic reaction by Granger causality is as follows. First, the influx to To more accurately predict the metabolic network structure, the mathematical modelling approach was repeatedly used right after the time-series data were statistically analysed. S-system equations  were setiX are metabolite concentrations. iα and iβ are rate constants of total influxes and effluxes, respectively, and ijg and ijh are their kinetic orders. Yi represent unknown parameters assigned for both rate constants and kinetic orders.Identification of the probable metabolic reaction network automatically leads to the formulation of a mathematical model in the S-system. As shown in To further verify whether the mathematical model is appropriate, we calculated the instantaneous bottleneck ranking (BR) indicator defined asL and the metabolite concentration iX and provides the time-transient response of the dependent variable iX to an infinitesimal percentage change in the independent variable jYThis indicator is a product of the logarithmic gain 4) and acetate (X5) after the individual rate constants and kinetic orders . Overall, the BR indicators for the lactate concentration increase or decrease more significantly than do those for the acetate concentration, suggesting that lactate is more easily formed than acetate. The difficulty in the formation of acetate arises because the flux for lactate formation is higher than that for acetate formation. Moreover, ranking of enzymes based on the BR indicators reveals that the bottleneck enzyme for lactate formation is Y2 when it is increased and Y7 when it is decreased, while that for acetate formation is Y3 when it is increased and Y8 when it is decreased. These finding are supported by the previously reported experimental data c orders  increaseUnlike other statistical approaches using correlation or causality, our approach can not only identify a metabolic reaction network but also provide a mathematical model simultaneously. Furthermore, it provides kinetic parameters which allows us to straightforwardly analyse the metabolic system using the obtained mathematical model.The present study investigated an approach to identify a metabolic reaction network structure from time-series data of metabolite concentrations and simultaneously obtain its mathematical model in the S-system equations within the framework of BST. The Granger causality test was used to statistically identify interactions among metabolites and then remove metabolites which have insignificant causality to the considered metabolite. This result was used to form a mathematical model in the S-system representation. The parameters, namely, rate constants and kinetic orders in this mathematical model, were estimated by the Levenberg–Marquardt method. This estimation process was iterated to remove the least significant metabolite of each total influx and efflux according to the magnitudes of the kinetic orders. Consequently, the final form of the mathematical model was used to predict a probable structure for the metabolic reaction network system. A series of theoretical analyses clearly show that our approach is effective in identifying a metabolic reaction network. In the future, an in vitro experiment for measuring individual enzyme activities may also be performed on the basis of the prediction to reconstruct a newly possible metabolic pathway.To efficiently identify a metabolic reaction network using time-series data of metabolite concentrations, we use statistical and mathematical modelling techniques as described below.iy is the ith measurement of the response y, ix is the corresponding measurement of predictors, g is the regression or the smooth function and iε is the random error. The weights are given by the tricube function:The locally estimated scatter plot smoothing (LOESS) method is a non-parametric statistic which does not require any specific function to fit a mathematical model. Hence, it is very flexible in fitting experimental data containing noise or experimental errors. The regression function is locally approximated by the value of a function in some specified parametric class kx is distant from ix. If its value is increased, the influence from the data points located in the neighbourhood will be increased. This results in increased smoothness of the smoothed points. A piecewise function is used to handle the data that cannot be properly fitted.The value of weight function is low when x and y are the stationary time series for testing the null hypothesis that x does not Granger-cause y. Appropriate lagged values of y are found and included in a univariate autoregression of y. The symbol m denotes the largest lag length for which the lagged dependent variable is significant, u is the shortest lag length and v is the longest length for which the lagged value of x is significant. The time lag was set to be unity, denoting that the value at the present data point was used to predict the value at the next time point.The Granger causality test is a statistical hypothesis test used to determine whether one time series causes another. It is widely used in economics and has recently been employed to integrate omics data, i.e. transciptomics and metabolomics RSS1 and RSS2 are the sums of squared residuals of tresidual and tresidual', respectively.An F-test for equality of variances is used to verify whether the residuals are significant. An index measuring the strength of the causal interaction is defined asThe null hypothesis is rejected if the F calculated from the data is greater than the critical value of the F distribution for some desired false rejection probability; the present study used 0.01 for the significant value.iX  are the metabolite concentrations for n dependent variables and iα and iβ are the rate constants of influxes and effluxes, while ijg  and ijh  are kinetic orders of influxes and effluxes, respectively. The S-system describes a metabolic reaction network by individually aggregating influxes and effluxes for each metabolite pool, reducing the number of parameters.Biochemical systems theory (BST) provides a powerful procedure for characterising biochemical systems Non-linear least-squares methods use parameter estimation iterations to reduce the sum of the squared errors between each function value and a measured data point. LMA is a combination of the gradient descent method and the Gauss–Newton method y(it) is the measured value, y is the curve fitting function and iw is the measure of error in measurement y(it).The chi-squared error criterion is given asW is diagonal with W = 1/iw2The gradient of the chi-squared objective function with respect to the parameters is given as follows:The Gauss–Newton method denotes the perturbed model parameters that are locally approximated by first-order Taylor series expansion asλ represents the algorithm parameter.The Levenberg algorithm adaptively varies and updates the parameters between the gradient descent method and Gauss–Newton asLMA implemented here uses the following modified equation λ lead to a Gauss–Newton update, whereas large values of λ lead to a gradient descent update.Small values of Our proposed algorithm is illustrated in Lactococcus lactis MG1363 Two mathematical models were used in the present study. One is the generic inhibition and activation model Information S1Evaluation of correlations, bivariate Granger causality and Levenberg-Marquardt Algorithm (LMA) performance.(DOC)Click here for additional data file.Information S2Additional information for the generic inhibition and activation model.(DOC)Click here for additional data file.Information S3Evaluation of the performance of our approach in practical application.(DOC)Click here for additional data file.Information S4Additional information for the Lactococcus lactis model.(DOC)Click here for additional data file.


Metabolic network reconstructions formalize our knowledge of metabolism. Gaps in these networks pinpoint regions of metabolism where biological components and functions are "missing." At the same time, a major challenge in the post genomic era involves characterisation of missing biological components to complete genome annotation.We used the human metabolic network reconstruction RECON 1 and established constraint-based modelling tools to uncover novel functions associated with human metabolism. Flux variability analysis identified 175 gaps in RECON 1 in the form of blocked reactions. These gaps were unevenly distributed within metabolic pathways but primarily found in the cytosol and often caused by compounds whose metabolic fate, rather than production, is unknown. Using a published algorithm, we computed gap-filling solutions comprised of non-organism specific metabolic reactions capable of bridging the identified gaps. These candidate solutions were found to be dependent upon the reaction environment of the blocked reaction. Importantly, we showed that automatically generated solutions could produce biologically realistic hypotheses of novel human metabolic reactions such as of the fate of iduronic acid following glycan degradation and of N-acetylglutamate in amino acid metabolism.The results demonstrate how metabolic models can be utilised to direct hypotheses of novel metabolic functions in human metabolism; a process that we find is heavily reliant upon manual curation and biochemical insight. The effectiveness of a systems approach for novel biochemical pathway discovery in mammals is demonstrated and steps required to tailor future gap filling algorithms to mammalian metabolic networks are proposed. These properties have resulted in widespread applications of metabolic models in microbial bioengineering, contextualisation of high-throughput data, and biochemical pathway discovery [An dge base ,2. It isiscovery . While tiscovery , fewer hiscovery ,6. To daiscovery -9, boviniscovery , and humiscovery -13 genomiscovery , to creaiscovery , to prediscovery , and to iscovery . Their phttp://bigg.ucsd.edu[E. coli by employing a systems approach [RECON 1 accounts for 1496 ORFs, 2004 proteins, 2766 metabolites, and 3311 metabolic reactions. It represents one of the most comprehensive biological network reconstructions published to date [.ucsd.edu. Second,.ucsd.edu. These lapproach . Consideapproach -24 and oapproach , it appeE. coli on various substrates [Multiple computational algorithms have been devised to address gaps in metabolic network models in an automated manner . These mbstrates .Because of the difference between humans and microorganisms in terms of the number of related organisms for which biological, biochemical, and genetic information exists, it was not known whether an automated approach to gap-filling of RECON 1 could yield biologically plausible hypotheses. Here we investigated the potential of RECON 1 for discovery of novel reactions involved in human metabolism. We used FVA to identify dead-end metabolites and blocked reactions in RECON 1 and SMILEY to propose reactions capable of restoring flux through the identified dead-end metabolites. We then characterised the metabolic pathway distribution of identified gaps and their solution types in order to get an idea of how gaps are distributed within RECON 1 and in what manner these gaps are resolved by SMILEY. Finally we validated the automatically generated metabolic reaction hypotheses by manual literature review in order to assess the biological relevance of the proposed solutions with the goal of identifying suitable experimental targets.S) from universal reaction databases  to enable flux through a blocked reaction . Nearly half of the blocked reactions had more than one solution indicating that flux could be restored through these reactions in multiple ways  quantitative assignment of blocked reaction directionalities based on estimates of their Gibbs free energy changes  and ii) abolites . These vabolites -38. The abolites . Furtherabolites . This imIn order to validate the category III solutions, we investigated whether the metabolites to which the transport solutions applied have been detected in biofluids by querying the Human Metabolome Database . The 67 As opposed to category I and III SMILEY solutions, category II solutions involve adding resolving reactions to RECON 1 to restore flux through the dead-end metabolites. Of the 45 blocked reactions with category II solutions we found that seven had solutions composed of resolving reactions associated with human genes. Of those, five were part of peroxisomal beta-oxidation of long chain unsaturated fatty acids Figure . These bPlasmodium vivax shows 42-53% sequence similarity to eukaryotic ornithine transaminases and is known to accept both acorn and orn [The majority of category II solutions were composed of resolving reactions not associated with any known genes (19 solutions) or resolving reactions associated with enzyme activities encoded for by non-human genes (19 solutions) Figure . These r and orn . We suggThe investigation of large complex systems on a global scale makes it impractical and maybe even impossible to know details about all involved metabolites, genes, and proteins. At the same time, a high level of knowledge about metabolic subsystems and or enzyme activities is necessary in order to come up with hypotheses of particular metabolic fates and novel reactions. In this study we used a systems biology approach to characterise and fill gaps in human metabolism. The key results include i) many dead-end metabolites affect reaction cascades, ii) computationally predicted solutions require thorough manual curation and biochemical insight, and iii) four biological plausible hypotheses were identified. This work highlights that finding gene candidates for metabolic functions in the human genome is not a trivial issue and the extensive manual effort to curate the computational predictions of candidate reactions highlight the overall quality and quantity of data included in Recon 1.We characterised knowledge gaps of human metabolism, represented by blocked reactions and dead-end metabolites identified in RECON 1 , to whicWe highlighted four examples of missing knowledge in human metabolism Figures , 7 and 8Multiple gap finding and gap filling algorithms exist, including GapFind/GapFill  and GrowIdentification of genes associated with biological plausible hypotheses as suggested by SMILEY was a major challenge. Relatively few knowledge gaps were resolved using known metabolic functions Figure , and theUbiquitous unknowns e.g. genes with unknown function and orphan enzymes belonging to orthologous families, have been identified as top targets for functional elucidation in terms of biological knowledge payoff as these are ancient in origin and therefore likely to be involved in essential metabolic processes ,25,76. WThe results presented here show that RECON 1 allows the identification of specific metabolic pathways and reactions for which knowledge is lacking; thereby focusing the search for unknown metabolic functions by putting them into context with previously gathered metabolic information. Following identification and characterisation of RECON 1 network gaps, we showed that gap solution hypotheses can be generated automatically and successfully but require detailed, time consuming manual investigation in order to validate their biological plausibility. In this manner we have derived multiple hypotheses, which we intend to use to direct our knowledge-driven approach towards novel metabolic discoveries.RECON 1 was obtained from Duarte et al. . It cont-5 mmol/gdw/hr and |Vmin, i |≤ 10-5 mmol/gdw/hr for all i reactions in the network. All exchange reactions were unconstrained permitting free uptake and secretion of respective metabolites. A total of 285 reactions were identified.As a next step, all blocked reactions present in Recon_1_decomp were identified using flux variability analysis (FVA)  as reactU. Furthermore, we constructed a transport matrix, X, by defining a transport reaction from cytosol to extra-organism and an exchange reaction for each metabolite occurring Recon_1_decomp (S) and U .The SMILEY algorithm has been described previously by Reed et al.  and implb, i was chosen as objective function, requiring the SMILEY algorithm to find reactions in U and/or X to be added to S such that |vb, i| could carry a flux greater than 10-5 mmol/gdw/hr. SMILEY is designed to find the shortest possible solution consistent with this requirement [In the next step, each blocked reaction vuirement . For eacSMILEY generated a total of 1335 solutions for the 175 blocked reactions. We filtered the solutions such that: i) only category II solutions with the least number of resolving reactions were investigated, and ii) if no category II solution was found, the solution involving the least number of resolving reactions was investigated. In cases where a blocked reaction had multiple solutions with the same number of resolving reactions, a random solution was picked. These criteria generated the S1 SMILEY solution output that is reported in the results.http://bigg.ucsd.edu/[http://www.genome.jp/kegg/[http://blast.ncbi.nlm.nih.gov/Blast.cgi and using the STRING database [http://www.hmdb.ca/[in vivo pH (pH = 5.5-8.0), temperature (37°C), ionic strength (0.25 M) and electrical potential (-150 - 30 mV) was used to predict the upper and lower bounds on standard transformed reaction Gibbs energy. The upper and lower bounds are dependent upon in vivo metabolite concentration ranges which were set to 10-7 - 10-2 M. When the transformed reaction Gibbs energy range spans zero the reaction is predicted to be quantitatively reversible. Spontaneous reactions proposed by SMILEY were assessed in a similar manner as enzyme catalysed reactions. All gap filling hypotheses can be found in Additional files Biochemical and genetic information concerning each blocked reaction identified by FVA was obtained from the Bigg database ucsd.edu/. The rea.jp/kegg/, which adatabase . The loc.hmdb.ca/. Resolvi.hmdb.ca/ and by q.hmdb.ca/ an exten.hmdb.ca/. The deterature 3°C, ionicThe authors declare that they have no competing interests.OR carried out the experiments, analysed the data and wrote the manuscript. IT designed study, carried out experiments, analysed the data and contributed to the writing of the manuscript. BØP contributed to the design and writing of the manuscript. All authors read and approved the final manuscript.Metabolic subsystem distribution of the 175 blocked reactions. The distribution of the blocked reactions identified in RECON 1 within metabolic subsystems.Click here for fileDead-end metabolites can cause multiple blocked reactions. In the majority of cases, dead-end metabolites only cause one blocked reaction. When a dead-end metabolite is at the end or beginning of a reaction cascade however, it inhibits flux through all reactions, which are part of the reaction cascade. The figure shows the number of blocked reactions found in the reaction cascades. For example, there is one reaction cascade, which has 14 blocked reactions.Click here for fileThe SMILEY solution distribution is not dependent upon the metabolic pathway. Blocked reactions can have multiple SMILEY solutions independent of the metabolic pathway, of which the blocked reaction is a part.Click here for fileCharacterisation of alternative SMILEY solution. The figure shows the solution categories of the alternative SMILEY solutions to blocked reactions, which had a category I (A), category II (B) or a category III (C) S1 solution. A) 30% of the blocked reactions with a category I S1 solution had alternative category III solutions. The remaining 70% had either an alternative category I solution or none at all. B) 61% of the blocked reactions, which had category II S1 solution, had alternative category II or III solutions. C) None of the blocked reactions, which had category, III S1 solutions had alternative category solutions as expected.Click here for fileThe pathway distribution of blocked reactions and their SMILEY S1 solutions categories. The figure shows the SMILEY S1 solution category as a percentage of the total number of blocked reactions found within a particular metabolic pathway. The number of blocked reactions within each metabolic pathway and their SMILEY solution type is also shown. Some blocked reactions, such as those involved in amino acid metabolism, are easily bypassed using functionalities already described in the KEGG, represented by category I and II SMILEY solutions. Others, such as those involved in glycan biosynthesis, can only be solved by transport of their causative dead-end metabolite out of the system.Click here for fileThe filtered S1 SMILEY output. The table contains the filtered SMILEY S1 output as described in materials and methods. The identified blocked reaction is given in column A. Columns B-J report properties of the blocked reactions i.e., causative dead end metabolites, BiGG confidence scores, cellular compartment, whether or not the blocked reaction is in a cascade, blocked reaction components, associated genes, the metabolic subsystem and the metabolic pathway the blocked reaction occurs in. Columns K-O report properties of the S1 solution i.e. the solution category, the experimentally reported directionality and computed directionalities of blocked reactions having category I reversal solutions, the number of resolving reactions composing the solution and the KEGG identifiers of each resolving reaction. The remaining columns report properties of each individual resolving reaction comprising the SMILEY solution i.e. KEGG identifiers, resolving reaction components, metabolic pathway and subsystem and any associated enzyme commission numbers or known human genes.Click here for fileThe complete SMILEY output. The table contains the complete SMILEY output with up to twenty solutions for each identified blocked reaction. The identified blocked reaction is given in column A. In columns B-D the properties of the blocked reaction are reported . In column E the resolving reactions comprising the complete SMILEY solution for the blocked reaction is reported with KEGG reaction identifiers. In the following columns the properties of the resolving reactions are reported .Click here for file


Streptomyces that harbour the highest diversity of secondary metabolite biosynthetic gene clusters in their genomes do not necessarily have the metabolic network topology most suitable for compound overproduction. Secondly, multi-objective analysis of biomass production and natural product biosynthesis in these actinobacteria shows that the well-studied occurrence of discrete metabolic switches during the change of cellular objectives is inherent to their metabolic network architecture. Comparative and multi-objective modelling can lead to insights that could not be obtained by normal flux balance analyses. MultiMetEval provides a powerful platform that makes these analyses straightforward for biologists. Sources and binaries of MultiMetEval are freely available from https://github.com/PiotrZakrzewski/MetEval/downloads.Comparative metabolic modelling is emerging as a novel field, supported by the development of reliable and standardized approaches for constructing genome-scale metabolic models in high throughput. New software solutions are needed to allow efficient comparative analysis of multiple models in the context of multiple cellular objectives. Here, we present the user-friendly software framework Multi-Metabolic Evaluator , built upon SurreyFBA, which allows the user to compose collections of metabolic models that together can be subjected to flux balance analysis. Additionally, MultiMetEval implements functionalities for multi-objective analysis by calculating the Pareto front between two cellular objectives. Using a previously generated dataset of 38 actinobacterial genome-scale metabolic models, we show how these approaches can lead to exciting novel insights. Firstly, after incorporating several pathways for the biosynthesis of natural products into each of these models, comparative flux balance analysis predicted that species like  Living cells owe their existence to complex metabolic networks, in which large numbers of chemical conversions occur to allow the cells to harvest energy, sustain themselves and reproduce. In the past decades, methodologies have been developed to systematically describe and quantitatively analyse (parts of) the metabolic network of a cell in computational models Genome-scale constraint-based metabolic models are reconstructions of metabolism that comprise the stoichiometries of all reactions predicted from whole genome sequences based on the presence of enzyme-coding genes. Accordingly, they can be used to model the steady-state behaviour of the metabolism of a whole organism The resulting metabolic models can be used to perform several kinds of analyses Recently, high-throughput methods have been developed to generate and gap-fill metabolic models for multiple species in a rapid and standardized way The standardization offered by automation opens up the road for comparative modelling, as little model reconciliation is needed, in contrast to what is usually the case for manually reconstructed models As well as studying multiple models at the same time, it can also be very revealing to optimize models for multiple objectives simultaneously A pair of objective functions (such as a biomass objective function and the objective function of production of a specific compound) can be balanced to find the so-called Pareto front Here, we describe a new software package, Multi-Metabolic Evaluator , a simple framework that provides an efficient and user-friendly interface for the comparative study of multiple models and the use of multiple objective functions. The software has been conveniently linked up to the SurreyFBA package for metabolic modelling In a case study, we show how the principles of comparative modelling can be applied to a concrete biological problem with our software, in a comparative study of the metabolic networks of 38 actinobacteria. Based on the 38 genome-scale models, we predict the suitability of different bacterial strains for the heterologous production of a range of different secondary metabolites and use multi-objective analysis to study the dynamic balance between the biomass objective and the compound production objective. We find that the maximally attainable fluxes to a natural product vary greatly between species as well as between the chemical classes of compounds. Moreover, we observe discrete switch-like behaviour in the models when the priority of the compound production objective function is gradually increased compared to the biomass objective function; this provides a possible systems-level explanation for the metabolic switches observed in the onset of secondary metabolism in such organisms The MultiMetEval comparative analysis framework was written in Java 6 Standard Edition with an interface handled by the Swing framework and integrated plot generation handled by the JFreeChart library. It is functional in both Windows and Linux operating systems. The program was built upon the SurreyFBA framework Incompatibility of SBML models coming from different frameworks has been a major drawback for comparative studies Existing FBA frameworks make use of their own parsers enforcing usage of their own SBML format variety. In order to make SBML files from different frameworks cross-compatible in our tool, we generated a parser that can convert any major SBML format variety into the SurreyFBA format. As we show in MultiMetEval provides a user-friendly facility to perform comparative analysis of multiple metabolic models, by combining batch runs of the single model analysis functionalities provided by SurreyFBA with new features that allow for convenient multi-model input and output.The basic units analysed by the comparative analysis module are “model collections”, which are sets of models selected by the user for analysis and parsed into the same format by the universal SBML parser.A specific menu allowing user-friendly construction of such collections is available via the File menu. To allow reuse of models in different collections, the collections can be created as subsets of a main model repository that holds all models that were imported to the program. Models can easily be added to the main repository and then moved to any collection in the same window.For every model, the number of reactions, metabolites, orphan reactions and orphan metabolites are detected and displayed in MultiMetEval’s main overview table when a collection is opened. FBA can be performed on the entire collection at once by clicking a simple menu button, and results are output in a single spreadsheet table Figure 1Our framework also offers a growth medium editor, which allows comparative analysis not only of different models, but also in different growth conditions. In order to make sure that the medium is compatible with the models, the medium description format used in our framework operates only on the metabolites present in a given collection and restricts the choice of medium ingredients to those which were defined in any of its models as external. The motivation for this is, of course, that these are the only metabolites that can be consumed by at least one model.MultiMetEval allows performing multi-objective analysis by calculating the Pareto front In this analysis, MultiMetEval calculates the tradeoff between two objectives. Often, the first objective will be the biomass production reaction, but, in principle, MultiMetEval can calculate a Pareto front for the optimization of any combination of two fluxes of reactions that co-occur in the same model.n times (were n represents the resolution), and with each simulation step the constraint put on the reaction by the first objective will decrease unless its value reaches zero.In the Pareto front calculation, first the maximal possible flux of the first objective is calculated. This value will be used in the following steps as a constraint that is iteratively decreased at each step. So after calculating the maximal flux of objective one, the program will carry out optimizations for the second objective The results of the multi-objective analysis are output to a results table as well as in a visual plot Figure 2In addition to the implementation of the Pareto trade-off routine in the MultiMetEval framework described here, we also implemented it in the SurreyFBA command-line interface as well as in JyMet, the single-model analysis framework from SurreyFBA Comparative and multi-objective metabolic modelling has many exciting applications in systems and synthetic biology Tropheryma models, but including models for Bifidobacterium adolescentis ATCC 15703, Bifidobacterium longum NCC2705 and Kineococcus radiotolerans SRS30216). We then reconstructed biosynthetic pathways for 15 secondary metabolites of different classes that were present as annotated pathways in the KEGG database. These included polyketides , aminoglycosides , aminocoumarins , nonribosomal peptides  and a beta-lactam (clavulanic acid). Such types of compounds are highly relevant biotechnologically, because they often have antimicrobial or anti-cancer activities In our comparative FBA analysis, we constructed a model collection in MultiMetEval from the 38 genome-scale metabolic models of actinobacteria that were recently constructed and curated by Alam et al. Bifidobacterium and Propionibacterium). However, these differences clearly do not account for all the variation observed. Among the most interesting exceptions is the severely genome-minimized Mycobacterium leprae, which still reaches surprisingly high predicted fluxes. Members of the same class of secondary metabolite  are usually predicted to be most efficiently produced in the same hosts. An exception is formed by two nonribosomal peptides, cephalosporin and enterobactin, for which fewer species are able to obtain the maximum observed flux towards compound production than for two other nonribosomal peptides, pyochelin and penicillin. This is probably due to the requirement of additional precursors, 2-oxoglutarate and 2,3-dihydroxybenzoic acid, respectively, for these two molecules, which are not required for penicillin and pyochelin.As no regulatory and kinetic information is used in the constraint-based models, one should note that the variation observed between the species only represents the difference due to differences in network topology given the medium composition used. Still, it is intriguing that substantial differences in theoretical production capacities are observed between the actinobacterial species. As expected, we observe some correlation with general topological properties of the metabolic networks such as the numbers of reactions and metabolites: minimalistic genomes generally tend to be less efficient predicted production hosts  achieve the highest predicted production rates for secondary metabolites in the simulations, although they have only about 15 secondary metabolite gene clusters per genome. The difference with the pathogenic Mycobacterium species, such as M. tuberculosis, M. bovis and M. leprae, may be explained by the further genome minimization of the pathogenic species, which may have led to a loss of flexibility in the metabolic networks and consequently an increase in pathway competition.On the other hand, models representing species from the taxonomic branch of free-living mycobacteria  the presence or absence of pathways directed towards the necessary precursors , 2) efficiency of ATP generation from the used carbon source glucose, and 3) the ability of models to re-utilize the (sometimes quite exotic) side products of biosynthetic pathways to generate more precursors.As expected, similar patterns of theoretical maximal production rates across organisms were observed for compounds with similar chemical structures, such as the aminocoumarins novobiocin, coumermycin and clorobiocin. Also notable is that the metabolic networks of some organisms appear more fit for the production of certain compounds than others. For example, Of course, it should be kept in mind that this study used only mildly curated automatically generated metabolic network models to illustrate the main concepts of comparative flux balance analysis, and a more careful manual curation will be needed before committing substantial experimental resources to testing the hypotheses suggested here. Additionally, more systematic analysis of the specific differences between topologies associated with high and low production capacities of the different compound types may offer specific leads for metabolic engineering, by revealing topological bottlenecks. Another interesting follow-up study would consist of designing several additional media to study the dynamic interactions between network topology and medium composition or environmental niche.Biotechnological optimization of natural product biosynthesis often suffers from pathway competition with fluxes leading to the synthesis of biomass components In The predictions suggest that the overlap between network resources needed for biomass production and compound production differs notably between species, even without taking into account the organism-specific biomass compositions. It is likely that this has to do with the rate with which the network topology of a species enforces pathway competition between the two objectives, and to which extent alternative pathways are available for both processes.The applied multi-objective analysis thus characterizes organism-specific relationships between biomass production and compound biosynthesis. Methods such as OptKnock 3 were the limiting medium ingredients, respectively. When medium influx bounds of these compounds were increased by 100% each, the horizontal plateau disappeared.In the simulations for pyochelin, biomass production at biomass maintenance levels  hardly competes with compound production. It appears that in this case the production of biomass components from the medium leaves several metabolic resources unused at the point where the first nutrient limitation from the medium prevents higher biomass production. We confirmed this by recalculating the trade-off under several different medium conditions. Indeed, we observed that pyochelin production and biomass production were constrained by different nutrient limitations: orthophosphate and NHIn that sense, there is a “free lunch” for compound production as long as it is limited by a different nutrient than biomass production is. Remarkably, this suggests that production titers of industrial strains can sometimes be optimized without costs to the biomass maintenance.In most plots, a single transition point is observed, at which the production titre starts to drop much more drastically when biomass production is increased. This might signify that the metabolic networks of these microbes have at least two distinguishable states in which a different nutrient is limiting for compound production given the fixed biomass production flux at that point. A “metabolic switch” seems to operate at this point, at which the regulation of metabolism probably needs to be drastically changed to maintain optimal levels of both biomass and compound production . Of course, switch-like behaviour would be expected given that FBA is based on linear programming, and different linear constraints will be limiting at different points in the graph. Nonetheless, the fact that the switches corroborate observations from experimental microbiology, in which a carefully regulated switch has been observed at the onset of secondary metabolite biosynthesis Comparative metabolic modelling is a new field, and as with any recent advance in biology, new software solutions are needed to achieve its full potential. With MultiMetEval, we provide an easy-to-use software framework to analyse large collections of metabolic models in parallel and to perform multi-objective analysis, coupled to the SurreyFBA framework. Although this is just a starting point for further software development, the tool already allowed us to study secondary metabolism in actinobacteria in novel ways. Most interestingly, comparative analysis of their genome-scale models predicts that the organisms whose genomes encode the largest numbers of biosynthetic gene clusters do not necessarily have the metabolic network topology most suited for industrial production of these compounds, suggesting an interesting line of enquiry for future experimental work. Additionally, results from multi-objective analysis suggest that bacterial metabolic switches are not just enforced by regulation, but are grounded in the very architecture of the metabolic system in which they occur. We expect that further experimental analysis will likely give exciting definitive insights into these phenomena.Table S1Used methods for integration of KEGG pathways towards the biosynthesis of secondary metabolites. To integrate the KEGG pathways for secondary metabolite biosynthesis in all 38 actinobacterial models, compound-specific Python scripts were written which used our in-house PyModelEditor to edit the models in such a way that they would allow simulation of compound biosynthesis. For the fifteen compounds chosen, different modifications had to be made to the models, as indicated in this table. The minimal medium used for flux balance analysis (FBA) consisted of H2O (influx upper bound 10000), O2 (10000), glucose (10), NH3 (10), PO43− (10), SO42− (10), CO2 (10), H+ (10), Cu2+ (10), Pb2+ (10), Zn2+ (10), Mn4+ (10), CrO42− (10), Mg2+ (10), K+ (10), Co2+ (10), Ca2+ (10), Fe2+ (10), Fe3+ (10), Cl− (10), Ni2+ (10), Na+ (10), Cd2+ (10). Also, low influx of octadecanoic acid (0.001) was allowed, which was necessary to ‘start up’ some essential biosynthesis reactions.(DOCX)Click here for additional data file.Table S2Correlation between reaction presence/absence and maximum fluxes. For each compound, this table shows the squared correlation coefficient (r2) of the absence/presence of reactions in a metabolic model and the maximum flux obtained during flux balance analysis. The reaction name is the name as it is given in the SEED database, and the reaction formula corresponding to each reaction is given in the third column.(XLSX)Click here for additional data file.