The incongruity of metabolome coverage by typical metabolite profiling approaches and genome-scale metabolic reconstruction was solved by the design of superpathways to define a metabolic interaction matrix. A differential biochemical Jacobian was calculated using an approach which links this metabolic interaction matrix and the covariance of metabolomics data satisfying a Lyapunov equation. The predictions of the differential Jacobian from real metabolomic data were found to be correct by testing the corresponding enzymatic activities. Moreover it is demonstrated that the predictions of the biochemical Jacobian matrix allow for the design of parameter optimization strategies for ODE-based kinetic models of the system. The presented concept combines dynamic modelling strategies with large-scale steady state profiling approaches without the explicit knowledge of individual kinetic parameters. In summary, the presented strategy allows for the identification of regulatory key processes in the biochemical network directly from metabolomics data and is a fundamental achievement for the functional interpretation of metabolomics data.High-throughput molecular analysis has become an integral part in organismal systems biology. In contrast, due to a missing systematic linkage of the data with functional and predictive theoretical models of the underlying metabolic network the understanding of the resulting complex data sets is lacking far behind. Here, we present a biomathematical method addressing this problem by using metabolomics data for the inverse calculation of a biochemical Jacobian matrix, thereby linking computer-based genome-scale metabolic reconstruction and  Arabidopsis thalianaGenome-wide analysis of transcript levels, protein abundance and metabolite concentration has evolved as a central strategy in biology. Numerous studies based on techniques like next-generation sequencing and metabolic phenotyping using liquid chromatography coupled to mass spectrometry (LC-MS) and gas chromatography coupled to mass spectrometry (GC-MS) have significantly contributed to our current knowledge about the molecular organisation of cells, tissues and whole organisms up to the analysis of ecosystems if with respect to metabolite concentrations iM (Eq. 1).However, results from many studies also indicated the need to further analyse dynamical behaviour of metabolism in order to understand how a stable metabolic homeostasis can evolve and is sustained under changing environmental conditions Arabidopsis thaliana. This strategy allowed for the calculation of a differential biochemical Jacobian directly from metabolomics data. We analysed regulatory strategies in primary metabolism of leaves of Arabidopsis thaliana induced by conditions of energy deprivation, which is a substantial challenge for a plant due to restricted energy resources and a complex reprogramming of metabolism One central parameter defining these functions in a biological metabolic system is enzyme activity for which experimental data are available only to a limited degree when compared to high-throughput measurements of metabolite content or protein abundance. To overcome this limitation a parametric representation of the Jacobian matrix is possible to allow the characterisation of a metabolic system of interest Arabidopsis thalianahttp://www.arabidopsis.org/biocyc/index.jsp; MetaCyc, http://metacyc.org/) we developed a metabolic superpathway model of leaf primary metabolism in Arabidopsis thaliana :1, 102, 103, 104 and 1.6×104 times and found the interquartile distance of calculated Jacobian entries to be robust after at least 103 calculations in all data sets . Stationary solutions of (Eq. 3) are linked to the covariance matrix by a corresponding Fokker-Planck equation, finally resulting in (Eq. 2) ata sets . MediansThe next step was to analyse whether the finding of differential regulation of pyruvic acid metabolism is sufficient to explain the differences in metabolic homeostases. Metabolic changes were classified according to underlying pathways and measured metabolite abundances were summarized in metabolic clusters . This reif. These functions if represent the abstract summary of metabolite functions, which are defined by parameters, for example like temperature, enzyme abundance or substrate affinity. To test whether the information about relative changes in PDC activity is applicable to the solution of a system of ODEs describing relative levels of metabolite pools, an optimization procedure was applied providing information about the contribution of every single interconversion function if to the best solution of the ODEs. The optimization procedure was designed as described in the following: an arbitrary solution of the system of ODEs was calculated allowing for the simulation of the metabolic steady state in Col-0 under normal light conditions resulting in a set of i,Col-0f. Starting from these identified values of i,Col-0f,L a local solution for the system of ODEs was searched which allows the simulation of the metabolic homeostasis of Col-0 under conditions of extended darkness. To evaluate the contribution of each if to the best solution, different optimization runs were performed only allowing one or two of the if to be varied. For example, in the first optimization run only f7, the function which describes the turnover of pyruvic acid, was set as a decision variable in the optimization procedure. Here, the solution only depended on variation of f7. In the next run, an additionally function, e.g. f8, was defined as a decision variable, too; hence the solution now depended on variation of f7 and f8. In this way, all combinations of functions were analysed to evaluate the most efficient function combination for yielding the best solution. The landscape showing the relative contribution of each if in combination with another function to the best solution indicated the most significant contribution by 7f (turnover of pyruvic acid) and 9f   .Af describes the time-dependent concentration change of metabolite A which is predominantly catalysed by an enzyme following the Michaelis-Menten kinetics under conditions C1 and C2, this would result in a characteristic diagonal Jacobian entry iidJ:Metabolism is organized in a highly complex manner being attributed to a vast variety of interlaced regulatory loops between different levels of molecular organisation, e.g. metabolite-protein interaction, and a high level of cellular compartmentation. This makes it hardly possible to intuitively conclude regulatory strategies from large experimental data sets, which have become a central part of systems biology and are provided by various omics technologies Arabidopsis thaliana wildtype Col-0 under control conditions as well as under low energy stress if grown in an extended night period. We found the diagonal Jacobian entries depending on pyruvic acid to be significantly lower in extended darkness. According to our hypothesis of a dominating effect of enzyme kinetics for definition of metabolite functions, the differential Jacobian entries were predicted to be due to a differentially regulated activity of PDC. The PDC enzymatic activity was measured in vitro and was found to be significantly higher in the control plants than in the samples of extended darkness. However, the multivariate Gaussian distribution of the stationary solution of the Langevin-type equation significantly affects the fluctuation matrix D Based on this equation in context of Arabidopsis thaliana. The central components of a mathematical optimization procedure are decision variables, an objective function and constraints 7f) is set to be a decision variable. Additionally, the reactions of amino acids to polyamines (9f) were found to be a pre-requisite for the best solution of the optimization problem. In context of this finding it is interesting to note that the diagonal entry of the differential Jacobian for arginine interconversion was greater than zero which is directly related to 9f as it describes the polyamine biosynthesis. Thus, we provide evidence that inverse calculation of a differential Jacobian based on metabolomics data provides a framework for evaluation of optimization strategies which have to be applied to ODE-based models of complex metabolic networks.The representation of a biochemical system by ODEs has been focused by many approaches of mathematical and kinetic modelling To summarize the findings of the present study, we could demonstrate how metabolomic data from different homeostasis can systematically be linked to large-scale models allowing for the identification of perturbed pathways. Because the calculations of the Jacobian matrix are based on genome-derived stoichiometry of the metabolic network and metabolomics data, this matrix now provides a comprehensive platform for estimating the impact of genetic or environmental impact on regulatory mechanisms in complex biological systems.Arabidopsis thaliana Col-0 were sown on soil, stratified at 4°C for 2 days, and plants were grown in a growth cabinet in a 12 h light/12 h dark cycle. Light intensity was 80 μmol m−2s−1, and temperature was set to 20/16°C during the light/dark period. Whole rosettes of 35 days old plants were harvested 6 h after light on and after 18 h of darkness, i.e. 6 h of extended darkness. Samples were frozen immediately in liquid nitrogen. Plant material was ground to a fine powder in a ball mill  and stored at −80°C until further experimental processing.Seeds of 2O  was added to 80 mg of plant material. Samples were vortexed, incubated on ice for 8 – 10 min and centrifuged for 4 minutes at 14000 g. 500 μl H2O were added to the supernatant, followed by brief vortexing and 2 minutes centrifugation. The polar phase was split equally into 2 aliquots and C13 labeled Sorbitol was added to a final concentration of 10 mg/l as an internal standard. Samples were dried and for derivatisation, the dried pellets were dissolved in 10 μl of a 40 mg ml−1 solution of methoxyamine hydrochloride in pyridine by shaking at 30°C for 90 minutes. 40 μl of N-methyl-N-trimethylsilyltrifluoroacetamid (MSTFA), spiked with 60 μl/ml of a mix of even-numbered alkanes, were added and the samples were incubated at 37°C for 30 minutes under constant shaking, followed by 2 minutes of centrifugation at 14000 g. The supernatant was transferred into a glass vial for measurement. GC-MS measurements were carried out on an Agilent 6890 gas chromatograph coupled to a LECO Pegasus 4D GCxGC-TOF mass spectrometer . Setup, methods and raw data processing were applied as previously described Metabolite extraction and derivatisation was done as described in 1, 102, 103, 104 and 1.6x104 times, and medians as well as interquartiles of calculated Jacobians were determined. Medians were normalised to the square of interquartiles to include fluctuation of calculations in the data interpretation. Differential Jacobian matrices were built as the log2-ratio of Jacobian entries from data sets recorded under conditions of light (L) and extended night (EN)  :(5)Arabidopsis thaliana was assayed by the formation of NADH at 340 nm as described by Yu and co-workers with slight modification The activity of PDC in crude extracts of leaf samples of Programming and global optimization of ODEs was performed in MATLAB 7.12.0 (R2011a) using the ‘Systems Biology Toolbox 2’ and the ‘SBPD Extension Package’ Figure S1Interquartile distance of calculated Jacobian entries derived from n replicates. Each interquartile of samples under conditions of light (A) and extended night (B) was normalised to the interquartile distance of 10 replicates.(PDF)Click here for additional data file.Table S1Metabolomics data. GC-MS data, mean and cluster-analysis results.(XLSX)Click here for additional data file.Model S1Metabolic reconstruction of genome-scale superpathways adapted to metabolite profiling data for Arabidopsis thaliana .(XML)Click here for additional data file.Model S2ODE model global optimization procedures .(XML)Click here for additional data file.


Saccharomyces cerevisiae growing in rich media supplemented with either glucose or ethanol as the main energy source. The resulting models comprise about 50% of the reactions in the original model, and predict environment-specific essential genes with high sensitivity. By minimizing the sum of fluxes while forcing our predicted active reactions to carry flux, we predicted the metabolic states of these yeast cultures that are in large agreement with what is known about yeast physiology. Most notably, our method predicts the Crabtree effect in yeast cells growing in excess glucose, a long-known phenomenon that could not have been predicted by traditional constraint-based modeling approaches. Our method is of immediate practical relevance for medical and industrial applications, such as the identification of novel drug targets, and the development of biotechnological processes that use complex, largely uncharacterized media, such as biofuel production.The large size of metabolic networks entails an overwhelming multiplicity in the possible steady-state flux distributions that are compatible with stoichiometric constraints. This space of possibilities is largest in the frequent situation where the nutrients available to the cells are unknown. These two factors: network size and lack of knowledge of nutrient availability, challenge the identification of the actual metabolic state of living cells among the myriad possibilities. Here we address this challenge by developing a method that integrates gene-expression measurements with genome-scale models of metabolism as a means of inferring metabolic states. Our method explores the space of alternative flux distributions that maximize the agreement between gene expression and metabolic fluxes, and thereby identifies reactions that are likely to be active in the culture from which the gene-expression measurements were taken. These active reactions are used to build environment-specific metabolic models and to predict actual metabolic states. We applied our method to model the metabolic states of  Saccharomyces cerevisiae grown with glucose or ethanol as main energy source. Our modeling enables the prediction of genes that are essential for growth in either environment. We also show that our method predicts aspects of the energy metabolism of these cultures that are in large agreement with what is known about yeast physiology. Our method is of direct practical importance in the fields of biotechnology and medicine, such as in vivo drug target identification, where nutrient conditions are largely unknown.Metabolic fluxes are steady-state rates of metabolite interconversion within living cells. They determine the rates of growth and product formation, and are of biotechnological and medical importance. An important and pressing question is how to identify the actual distribution of fluxes in living cells among the manifold possibilities that complex metabolic networks allow. One way to address this question is to constrain the space of possibilities using gene-expression measurements. Here we present a method that uses gene-expression measurements to infer the metabolic state of cells growing in uncharacterized environments. We applied this method to model the metabolism of  The metabolic state of a cell is defined by the distribution of all its metabolic fluxes. It constitutes a significant aspect of cellular phenotype and is of both medical and industrial relevance. There are, for instance, striking differences in the metabolic states of healthy and cancer cells. Healthy cells rely predominantly on oxidative phosphorylation as a means to drive ATP synthesis, but cancer cells ferment profusely, converting the majority of the glucose and glutamine they consume into lactate The advent of genome-scale constraint-based models of metabolism enables the study of metabolic fluxes in whole-cells. The large size of these metabolic models, however, entails the challenge of identifying the actual metabolic state of cells among the myriad possibilities allowed by stoichiometric and thermodynamic constraints. To illustrate this point, Nutrient availability places an enormous constraint on the space of possible flux distributions. For instance, in our toy model, there are only two flux distributions compatible with the absence of the two-carbon substrate . HoweverSaccharomyces cerevisiae, fluxes have been reported to correlate poorly with both transcripts and protein levels Escherichia coli were analyzed in the light of a genome-scale model of metabolism, evidence for a coordinated expression of metabolic genes became apparent It is reasonable to expect gene expression to be a major determinant of the cell's flux distribution. However, the understanding of the relationship between transcript levels and metabolic fluxes has been challenged by the confounding observations that, for both prokaryotes and eukaryotes, transcript levels correlate poorly with protein concentrations Several methods for integrating transcript measurements and genome-scale models of metabolism have been proposed e.g. . We highS. cerevisiae growing on yeast-extract peptone media, supplemented with either glucose or ethanol. Our modeling predicts, with high sensitivity, genes that are essential for growth specifically on glucose or on ethanol. Remarkably, we predict the Crabtree effect Here we present a method that uses gene-expression as the sole source of information to build environment-specific metabolic models. We introduce a novel exploration of the alternative optimal solutions to the optimization problem proposed by Shlomi et al S. cerevisiae growing on two different media, uncovering essential aspects of yeast energy metabolism.The study of metabolic fluxes is enormously aided by genome-scale reconstructions of metabolic networks. The large size of these networks, however, entails the challenge of identifying the actual metabolic state of living cells among a very large number of possibilities. Here we present a method that integrates gene-expression measurements with genome-scale models of metabolism to: i) identify reactions that are likely to be active, ii) constrain the space of possible flux distributions, and iii) predict the metabolic states of cells growing in completely uncharacterized environments. We applied this method to model the metabolism of In this study we used genome-scale constraint-based model of yeast metabolism by Mo et al. The first step into constraining the space of possible flux distributions using gene-expression measurements is to translate these measurements into reaction-expression calls. Gene expression measurements for yeast cultures growing on YPD  and YPEtOH  were obtained from Gasch et al Gene-expression calls defined as described above were translated into reaction-expression calls using the metabolic model's detailed Boolean gene-to-reaction mapping . The numWe formulated predictions of which reactions are likely to be active or inactive in YPD or YPEtOH by integrating gene-expression measurements with a model of yeast metabolism. First we used iMAT Our method to predict reactions that are likely to be active or inactive, stems from the realization that the flux distribution obtained by iMAT is one among many that maximize the agreement score. For example, in our toy model, three of the eight possible flux distributions maximize the agreement score . In ordeAs a means to predict which reactions are likely to be active or inactive in the condition of interest, we counted the number of times that each reaction was found to be active among the alternative optimal flux distributions. Reactions that were active in all alternative optimal solutions defined a set of high-frequency reactions (HFR) and are predicted to be active. Reactions that were always inactive defined a set of zero-frequency-reactions (ZFR) and are predicted to be inactive. The number of ZFR in YPD and YPEtOH  was lower than that of HFR . It is important to note that HFR and ZFR sets comprise different reactions than the rH and rL sets. For instance, not all highly expressed reactions are within the HFR set. Moreover, the HFR set includes some reactions that are lowly expressed . The resulting sets of ZFR and HFR for yeast cultures growing on YPD or YPEtOH are reported in the Supplementary We built environment-specific metabolic models hypothesizing that HFR and ZFR are likely to be active and inactive, respectively, in the condition of interest. To this end we first deleted all ZFR, and thereafter used MBA to minimize the size of the network with the constraint that all HFR must be able to carry flux. We call our method ‘EXploration of Alternative Metabolic Optima’ (EXAMO), and summarize it in Genome-wide measurements of essential genes have been used frequently as a means to validate constraint-based models of metabolism e.g. . MoreoveICL1 gene in S. cerevisiae, is essential for growth on minimal medium when acetate or ethanol are provided as carbon sources, but is dispensable for growth on sugars or three-carbon substrates However, it is well known that nutrient availability determines the essentiality of genes S. cerevisiaeS. cerevisiae. Single-gene deletion mutants that failed to grow on YPD were identified as essential for growth in this medium. The second study, by Snitkin et al To address this issue, we contrasted our model predictions with the results of two large-scale gene essentiality studies in Using FBA-based gene essentiality analysis By building environment-specific models of metabolism, we predict drastically reduced spaces of possible flux distributions available to yeast cultures growing on YPD of YPEtOH. We then asked whether we can use these models to infer the actual metabolic state of these cells and, thereby, reveal aspects of yeast physiology. As a means of predicting a specific flux distribution, a point within the flux distribution space, we minimize the sum of all fluxes Supplementary all ATP is produced by oxidative phosphorylation. The main sources of electrons feeding the electron transport chain, and thus maintaining the proton motive force, are the reactions catalyzed by: aldehyde dehydrogenase (25%), malate dehydrogenase (26%) and succinate dehydrogenase (45%), with minor contributions by isocitrate dehydrogenase and pyruvate dehydrogenase. Our modeling predicts that acetaldehyde, which can be produced from ethanol via a single reaction, serves as the main energy source. In stark contrast with our predictions for YPD cultures and in line with what is known about yeast physiology, for YPEtOH cultures we predict that in vivo. It may also be used to predict which nutrients are being consumed in complex industrial substrates, and contribute in research efforts towards the development of biofuel producing processes where many incompletely characterized media are tested.In summary, we developed a method that used gene-expression measurements and genome-scale models of metabolism to infer the metabolic states of cells living in completely uncharacterized environments. Our method yields predictions about the essentiality of genes in specific environments with higher sensitivities than alternative methods. The metabolic states predicted by our method are in large agreement with what is known about yeast physiology with the prediction of the Crabtree effect as a prominent example. The consideration of the quality of gene-essentiality and metabolic state predictions together, encourages us to suggest that our method contributes to the decoding of the way the transcriptome represents the metabolic state of cells. Our method is also of immediate practical value, as it can be used to identify potential drug targets against infection that would be specifically effective within the host, where nutrient availability is largely unknown, or to distinguish metabolic states of health and diseased tissues We used the genome-scale constraint-based model of yeast metabolism by Mo et al. Our objective is to use gene-expression measurements to infer the metabolic state of cells growing in uncharacterized environments. To this end, we classified the reactions in the model as highly (rH) or as lowly (rL) expressed, based on gene-expression, using the constraint-based model's detailed Boolean gene-to-reaction mapping  or ethanol (YPEtOH), were taken from Gasch et al. S is an n is the number of metabolites and m is the number of reactions, and v is the flux vector. Thermodynamic  and capacity constraints are enforced by lb and ub are the vectors containing lower and upper flux boundaries, respectively. For each reaction in the highly expressed set (rH), y forces the flux through the reaction to zero when equal to 1  refer to correctly predicted essential genes, false negatives (fn) refer to genes predicted to be dispensable that are actually essential, and false positives (fp) refer to genes predicted to be essential but that are actually dispensable. Because the mutant library was constructed in YPD, mutants that would be essential for growth in YPD but dispensable for growth in some other medium are not available. For this reason, the scope of the gene essentiality study on YPEtOH excludes genes that are essential for growth in YPD. Thus, genes that are essential for growth on YPD were excluded in the prediction sensitivity and positive predictive value of YPEtOH.We used our environment-specific metabolic models to predict essential genes using FBA To further appraise the usefulness of our method, we compared its predictions to those of two other methods that integrate gene-expression with constraint-based models of metabolism: Jerby et al. 's MBA S is a n is the number of metabolites and m is the number of reactions, and v is the flux vector. Thermodynamic  and capacity constraints are enforced by lb and ub are the vectors containing lower and upper flux boundaries, respectively. For each reaction in the HFR set we defined an integer variable y. If the We hypothesized that HFR are likely to be active in the condition of interest. To investigate whether this hypothesis yields meaningful predictions for the metabolic state of the cells, we computed flux distributions for cells growing on YPD or YPEtOH by minimizing the sum of all fluxes in the environment-specific models subject to the constraint that HFR must carry flux. Minimizing the sum of fluxes requires that each reversible reaction is separated into a forward Click here for additional data file.Dataset S2EXAMO scripts. Scripts for running the EXAMO software are provided. The user's manual lists the necessary dependencies and explains how to run the scripts and what input and output files are used and generated by each script.(ZIP)Click here for additional data file.Figure S1Gene essentiality predictions varying gene expression thresholds. The sensitivities and positive predictive values (PPV) of the predictions of essential genes are shown for YPD and YPEtOH for three different thresholds used to define highly and lowly expressed genes (see main text). The methods compared are: EXploration of Alternative Metabolic Optima (EXAMO –red circles), Shlomi et al's integrative Metabolic Analysis Tool (iMAT –blue diamonds) (EPS)Click here for additional data file.Table S1Gene-expression calls. Based on the gene expression measurements from yeast cells growing on glucose (YPD) or ethanol (YPEtOH) (XLSX)Click here for additional data file.Table S2Boolean gene-to-reaction mapping. The genome-scale constraint-based model of yeast metabolism by Mo et al (XLSX)Click here for additional data file.Table S3Reaction-expression calls. Reactions were classified by expression based on gene-expression calls (Supplementary (XLSX)Click here for additional data file.Table S4Lists of high- and zero-frequency reactions for YPD and YPEtOH. High- and zero-frequency reactions computed by integrating gene expression from yeast cultures grown on YPD or YPEtOH (XLSX)Click here for additional data file.Table S5Metabolic state of yeast cells growing on YPD. Reaction stoichiometries, identifiers, names, associated genes and predicted fluxes are listed. Reactions with absolute fluxes lower than 10E-10 are not shown.(XLSX)Click here for additional data file.Table S6Metabolic state of yeast cells growing on YPEtOH. Reaction stoichiometries, identifiers, names, associated genes and predicted fluxes are listed. Reactions with absolute fluxes lower than 10E-10 are not shown.(XLSX)Click here for additional data file.


G. sulfurreducens is one of the commonest microbes used in microbial fuel cells (MFCs) for organic-to-electricity biotransformation. In MFCs based on this microorganism, electrons can be conveyed to the anode via three ways: 1) direct electron transfer (DET) mode, in which electrons of reduced c-type cytochromes in the microbial outer membrane are directly oxidized by the anode; 2) mediated electron transfer (MET) mode, in which the reducing potential available from cell metabolism in the form of NADH is targeted as an electron source for electricity generation with the aid of exogenous mediators; and 3) a putative mixed operation mode involving both electron transfer mechanisms described above (DET and MET). However, the potential of G. sulfurreducens for current output in these three operation modes and the metabolic mechanisms underlying the extraction of the reducing equivalents are still unknown.G. sulfurreducens for current output that is compatible with reaction stoichiometry, given a realistic nutrient uptake rate. We also developed a method, flux variability analysis with target flux minimization (FATMIN) to eliminate futile NADH cycles. Our study elucidates the possible metabolic strategies to sustain the NADH for current production under the MET and Mixed modes. The results showed that G. sulfurreducens had a potential to output current at up to 3.710 A/gDW for DET mode, 2.711 A/gDW for MET mode and 3.272 A/gDW for a putative mixed MET and DET mode. Compared with DET, which relies on only one contributing reaction, MET and Mixed mode were more resilient with ten and four reactions respectively for high current production.In this study, we performed flux balance analysis (FBA) of the genome-scale metabolic network to compute the fundamental metabolic potential of The DET mode can achieve a higher maximum limit of the current output than the MET mode, but the MET has an advantage of higher power output and more flexible metabolic choices to sustain the electric current. The MET and DET modes compete with each other for the metabolic resource for the electricity generation. Geobacter sulfurreducens has been extensively studied for microbial fuel cell (MFC) applications since discovered in 1994 . In. In62]. The reaction CYOR1m makes the model suitable for studying direct electron transfer in the case of MFC. The availability of the c-type cytochrome for extracellular electron transfer is determined by the flux of this reaction. It is assumed that one round of this reaction cycle produces two quotients of the reduced c-type cytochrome for the extracellular electron transfer reaction (FERCYT), equivalent of two quotients of electrons for the electric circuit.For modelling the maximum metabolic potential for the current production and the pertinent metabolic behaviours in the MET mode, the cells were tested for their capabilities to convert low energetic co-substrates (NAD) to their highly energetic counterparts (NADH). For the DET mode, the oxidation rate of c-type cytochrome by the exogenous electron acceptor  was maximized. For the Mixed mode, the maximization of the rates of the MET and DET were equally combined. Hence, the Mixed mode was just a special case of the MET mode with the reduced type c cytochrome as an additional electron supplier.The present study used an optimization based framework based on a hypothesized objective function produced by a weighted combination of fluxes Table . CharactA high COI implies that the corresponding flux is preferentially maximized by the network, whereas a low COI indicates the converse . In the present modelling, COI can also be considered as the degree of NADH perturbation caused by the mediators of MFCs. A high COI magnitude associated with NADH is used to model NADH drain in MFCs, while the COI assigned to the biomass production by default is 1 in the network model.The use of COI is also a way to represent regulatory mechanisms of the cell to increase the electron transfer rate in DET and MET for MFCs while trying to maximize the cellular growth rate. The mediator in MFCs deprives the cell of the electrons, and the cell metabolism reacts to the deprivation by regulating the metabolism to increase NADH production because the cell requires NADH for growth. In other words, we use the growth objective to model the normal cell metabolism. Then we introduce the COI to model the regulation process of the cell Table .The growth-coupled product flux ensures that the metabolic network is forced to produce the desired reaction flux while still supporting a functional state of the network for a biologically meaningful goal, i.e., to grow (to survive). The predictions of these models on growth rate have been verified by the experimental studies where the original network was published .The values of the COI’s in this study should not be directly interpreted as specifications of the relative priorities of the two objective functions, because due to the different units of measurement of biomass and reduction equivalent objectives, they also contain a unit conversion factor. The value of this factor is not easily determined because it is related to the “molecular weight” of the biomass, but it is not clear what meaning to attach to one “molecule” of biomass.18 electrons, and 1 mol = 6.02 × 1023 electrons (Faraday's constant 96485 C/mol). Therefore, one flux unit (mmol/g/h) can be converted into A/g as follows:Current (in amperes) was integrated over time and converted to electrons recovered by using the following conversions: 1 C = 1 A × 1 s, 1 C = 6.24 × 10One of the parameters commonly used to quantify the performance of MFCs is the Coulombic efficiency (CE); the CE is defined as the ratio of electrons transferred to the anode to that in the starting substrate. For the characterization of the energy efficiency of the metabolism, the full oxidation of acetate with oxygen as the oxidant (see as follows) will be used as the reference reaction.-) [Based on such stoichiometric information, 1 mol of acetate was converted into 8 mol of electrons (1 mol of acetate = 8 mol e-) .The calculations in the present study are only based on a flux balance viewpoint and thus do not take into account ohmic resistances, concentration polarization and kinetic constraints during a MFC operation. For the sake of simplification the calculations of cell voltage  are based on formal potentials (at pH 7) of the involved biological and electrochemical redox processes. Therefore, this calculated Electromotive force (EMF) provides an upper limit for the cell voltage and the actual potential derived from the MFC will be lower due to various potential losses :Where The formal potentials of the anode and cathode used for calculation of power density in the three operation modes were summarized in Table The calculation of standard cell potential of MFC Table  shows thSeveral modelling works assumed 1% of the maximum theoretical biomass yield as the viability threshold for computational identification of lowest growth rate ,70. Neve4+ uptake rates were set to 568 mmol/g/h and 0.468 mmol/g/h respectively [2, H2O, K+, Mg2+, PO43-, and SO42- were allowed to freely enter and leave the network [The flux values in the simulations were in units of mmol/gDW (dry weight)/h. The maximum acetate uptake rate was constrained to 18 mmol/gDW/h . Non-groectively . The exc network .G sulfurreducens PCA strain [in silico analysis. The original network model in Excel format was parsed into SBML using the converter integrated in the NetSplitter [An updated metabolic network model of A strain ,63 was uSplitter ,74. The Splitter ,76. CompSplitter  in MATLASplitter . FATMIN MFC: Microbial fuel cell; NAD: Nicotinamide adenine dinucleotide; NADH: Nicotinamide adenine dinucleotide (reduced form); DET: Direct electron transfer; MET: Mediated electron transfer; BG: Bromocresol green; NR: Neutral red; COI: coefficient of importance; AOS: alternate optimal solutions; FATMIN: Flux variability analysis with target flux minimization; FBA: Flux balance analysis; FVA: Flux variability analysis.The authors declare that they have no competing interests.in silico modelling and modelling analysis. WV supervised the work. Both authors read and approved the final manuscript.LM and WV conceived of the study, developed the method and wrote the manuscript. LM performed A simple method to eliminate encountered futile cycle reactions during FBA modelling.Click here for fileFlux profiles and FATMIN results.Click here for fileSBML file of the G sulfurreducens network model.Click here for file


Escherichia coli K-12 and facilitates computational exploration of this important model organism. We have analysed the occurrence of dead end metabolites within the database – these are metabolites which lack the requisite reactions (either metabolic or transport) that would account for their production or consumption within the metabolic network. 127 dead end metabolites were identified from the 995 compounds that are contained within the EcoCyc metabolic network. Their presence reflects either a deficit in our representation of the network or in our knowledge of E. coli metabolism. Extensive literature searches resulted in the addition of 38 transport reactions and 3 metabolic reactions to the database and led to an improved representation of the pathway for Vitamin B12 salvage. 39 dead end metabolites were identified as components of reactions that are not physiologically relevant to E. coli K-12 – these reactions are properties of purified enzymes in vitro that would not be expected to occur in vivo. Our analysis led to improvements in the software that underpins the database and to the program that finds dead end metabolites within EcoCyc. The remaining dead end metabolites in the EcoCyc database likely represent deficiencies in our knowledge of E. coli metabolism.The EcoCyc database is an online scientific database which provides an integrated view of the metabolic and regulatory network of the bacterium  Symbolic systems biology is the application of logic-based computational methods to the systems-level analysis of an organism. Previously, several types of symbolic systems biology approaches have provided novel biological insights. For example, metabolic pathway analysis of genomes can be used to identify reactions within metabolic pathways that have no associated enzyme (“pathway holes”) , thus moA dead-end metabolite (DEM) is defined as a metabolite that is produced by the known metabolic reactions of an organism and has no reactions consuming it, or that is consumed by the metabolic reactions of an organism and has no known reactions producing it, and in both cases has no identified transporter . DEMs arEscherichia coli K-12 MG1655 was conducted using EcoCyc (http://EcoCyc.org), an online encyclopedia of E. coli K-12 biology that provides an integrated view of the genome, genes and gene products, and the metabolic and regulatory networks of this important model organism [E. coli K-12, along with detailed summaries from manual literature curation. In release version 17.0 , EcoCyc contained 1497 metabolic enzymes and 268 transporters catalysing a total of 2175 reactions. The database contains 2392 compounds of which 995 are directly involved in reactions . EcoCyc version 17.0 also cites 24,391 publications from the literature. In addition to being a comprehensive reference resource, EcoCyc also provides tools that can be used for computational exploration within the database including multiple search tools and the identification of DEMs [Our DEM analysis of organism . EcoCyc E. coli K-12.This project was undertaken to identify and analyse the dead end metabolites within the EcoCyc database. Our analysis led to the improved curation of many compounds within the database and also to improvements within the Pathway Tools software that underpins the database. We were able to resolve the dead end status of a large number of compounds through the addition of previously missing metabolic or transport reactions. As a result we are able to more accurately define the true DEMs within the EcoCyc database and by extension the ‘known unknowns’ within the metabolic machinery of the model organism DEMs within the EcoCyc database were identified using the DEM finder tool. In EcoCyc, metabolites may be reactants or products of reactions that occur within metabolic pathways defined within the database, or metabolites may form part of isolated reactions that are not contained within defined pathways. The DEM finder tool in EcoCyc can be customised to identify only those compounds that exist within metabolic pathways (pathway DEMs) or to include DEMs that come from reactions occurring outside pathways (non-pathway DEMs). Participation in metabolic pathways may make pathway DEMs rare, but also more likely to be physiologically relevant. A search of 271 metabolic pathways yielded 32 DEMs while a search of 393 isolated reactions within EcoCyc returned a further 123 compounds. 28 of these compounds were lacking proper classification within the EcoCyc database and could be resolved by correcting this omission. For example, correct classification of the compound “methylphosphonate” as a child of the class “alkylphosphonates” meant that it was recognised by the EcoCyc software as a substrate of the phosphonate ABC transporter, thus resolving its dead end status. The remaining 127 compounds  were thehttp://www.metacyc.org/META/NEW-IMAGE?type=PATHWAY&object=PWY-6432) and tetrahydrocurcumin are considered to be pathway DEMs in EcoCyc because the database contains no other reactions for these molecules – it does not describe the production nor transport of curcumin, nor the fate of tetrahydrocurcumin. In contrast, the compound 3α,12α-dihydroxy-7-oxo-5β-cholan-24-oate  is a DEM from an isolated reaction in EcoCyc. HdhA acts on cholate, which is thought to cross the inner membrane of E. coli [E. coli cell is unknown although it is known to be further metabolised by other anaerobic and facultative anaerobic bacteria in the human intestine (see http://metacyc.org/META/NEW-IMAGE?type=PATHWAY&object=PWY-6518).Examples of DEMs and the EcoCyc reactions from which they derive are shown in The 127 DEMs identified in the EcoCyc database encompass a wide variety of compounds. As a necessary first step to understand the biochemistry of each compound and its metabolic context, the reactions containing the DEMs were identified within EcoCyc and any associated literature was reviewed. Extensive literature searches were then conducted to see if further information relating to the compound could be uncovered.E. coli K-12 carried out in 1967 [E. coli K-12 to use acetoacetate as a sole carbon source was reported by Pauli and Overath in 1972 [38 DEMs were resolved through the addition of transport reactions to the database . 29 new Salmonellatyphimurium, which can synthesize adenosylcobalamin de novo, unlike E. coli K-12, which can synthesize cobalamin only when supplied with the intermediate compound cobinamide [E. coli are homologous to those from Styphimurium.  and our DEM analysis revealed that the final steps of the pathway in Styphimurium.  had recently been experimentally characterised [http://ecocyc.org/ECOLI/NEW-IMAGE?type=PATHWAY&object=COBALSYN-PWY) and in the process resolve the dead end status of adenosylcobinamide-5-phosphate.The number of metabolic reactions added to EcoCyc as a result of DEM analysis was small. One case worth mentioning involved the DEM adenosylcobinamide-5-phosphate, whose presence alerted us to inaccuracies in our representation of the pathway of adenosylcobalamin (coenzyme B12) salvage in EcoCyc. Experimental work on this pathway is largely carried out in binamide . Despitecterised . Based oE. coli K-12), revealed a deficiency in our link between two related pathways, oleate β-oxidation and fatty acid β-oxidation. This was remedied by the addition of the following two metabolic reactions [Another DEM, 3-hydroxy-5-cis-tetradecenoyl-CoA i) 3-hydroxy-5-cis-tetradecenoyl-CoA + NAD → 3-keto-5-cis-tetradecenoyl-CoA + NADH + H+ ii) 3-keto-5-cis-tetradecenoyl-CoA + coenzyme A → 3-cis-dodecenoyl-CoA + acetyl-CoA  and thus the two reactions provide the direct link between oleate β-oxidation and fatty acid oxidation that had previously been lacking in the EcoCyc database.cis-aconitate; EC 5.3.3.7), representing formation of the DEM trans-aconitate from the citric acid cycle intermediate cis-aconitate [One spontaneous reaction  is used to assay glutathione S-transferase activity (EC 2.5.1.18) in vitro but CDNB is not membrane permeable [E. coli cell. In many cases an enzyme catalysing a reaction containing non-physiological DEMS is also associated with a reaction that has physiological relevance to E. coli. For example, D-cysteine desulfhydrase (encoded by dcyD) is a cysteine-specific carbon-sulfur lyase with a role in the utilization of D-cysteine as a source of sulfur and is associated in EcoCyc with the physiologically relevant reaction EC4.4.1.15. However, the purified enzyme is also an effective 3-chloro-D-alanine dehydrochlorinase (EC 4.5.1.2) in vitro although it does not contribute to detoxification in vivo [E. coli proteins encoded by ygeX, solA and hyuA are examples of enzymes with associated reactions in EcoCyc, whose physiological role has not been characterised. One enzyme (AzoR) which had been characterised as an azoreductase in vitro was reannotated after a literature search revealed its physiologically relevant role to be an NADH: quinone reductase with a role in the protection against thiol stress [A large number of DEMs were associated with reactions that are not part of the normal physiology of elevance . These r in vivo . Associal stress .The identification of non-physiological DEMs has resulted in improvements to the Pathway Tools software, which now enables reactions to be tagged as non-physiological in order to clarify their role . In addiE. coli open reading frames reported in the literature [E. coli [E. coli acs as an hydroxycinnamate-CoA ligase (E.C 6.2.1.12) was removed, as no evidence for the presence of the common plant metabolites 4-coumarate and 4-coumaroyl-CoA in E. coli could be uncovered.A small number of compounds identified as DEMs were deleted from EcoCyc. In several cases, enzyme-catalysed reactions had been added to EcoCyc based on putative functional assignments for terature . For exa[E. coli . The reaE. coli metabolism. 9 of these compounds lack reactions accounting for their production within the network while a further 17 compounds lack reactions that would account for their consumption. 5 compounds  are possible nutrient sources in E. coli K-12. Sulfinoalanine, quinate and urate are included on Biolog phenotype assay plates [E. coli K-12; literature references are available on the EcoCyc website under the enzyme of interest.The physiologically relevant DEMs remaining in the EcoCyc database are listed in fdrA [E. coli K-12 are annotated with this activity. Early research showing that the extremely slow degradation of linear dimeric GMP to GMP in E. coli K-12 was unlikely to be relevant in vivo [E. coli AidB protein  is uncovering a role in the protection from alkylating agents [For a number of DEMs the literature record provides some hint as to possible solutions for resolution. For example, it has recently been suggested that the dead end metabolite oxamate may be further degraded by a pathway that begins with the action of an oxamate:CoA ligase encoded by the gene fdrA . SimilarfdrA . Several in vivo  has led  in vivo . Likewisg agents .E. coli K-12 metabolism – known as iJO1366 [E. coli K-12. In iJO1366 the reaction producing 2-aminomalonate-semialdehyde is specified as reversible whereas in EcoCyc the reversibility is unspecified, although the text summary in EcoCyc notes that kinetic analysis [dosP (a cyclic-di-GMP phosphodiesterase in EcoCyc and a 3’ 5’ cyclic nucleotide phosphodiesterase in iJO1366) and nudC .The DEMs remaining at the completion of this study were also queried within the latest version of the Palsson group’s model of  iJO1366 . Six metanalysis  suggestsE. coli K-12 as represented in the EcoCyc database. Using this program, we identified 127 DEMs within the database, analysed their context and undertook a literature search to see if any could be further resolved. The model organism E. coli K-12 is an intensively studied bacterium, much of its biochemical network has been experimentally elucidated, and many of the biochemical pathways represented in EcoCyc are complete – this is reflected in the considerably smaller number of DEMs derived from within pathways  compared to those derived from isolated reactions . Our analyses resulted in the direct resolution of the dead-end status of just under half these metabolites.The DEM finder tool is able to identify dead end metabolites in the biochemical network of E. coli K-12 but are lacking known transport proteins (E. coli K-12 can use phenylethylamine as a sole carbon and energy source [tynA) converts phenylethylamine to phenylacetaldehyde which is the substrate of a cytoplasmic dehydrogenase (encoded by feaB) but an inner membrane transport system for phenylacetaldehyde has not been characterised. Transport proteins specific for aromatic compounds such as hydroxyphenylpropionic acid and 3-phenylpropionate and for aromatic amino acids have been characterised in E. coli K-12, and perhaps one of these also transports phenylacetaldehyde. The existence of an uncharacterised open reading frame - ydbH – predicted to contain beta-barrel structure [38 new transport reactions were added to the EcoCyc database. Over half of these could not be assigned to a specific transport protein. In the majority of cases where a transporter was identified, the transport capability reflected an expanded substrate range for a previously characterised protein rather than the assignment of new function to a transporter of unknown substrate specificity. The identification of compounds that are imported into proteins  may be oy source  and a patructure  and locaE. coli can salvage the compounds 4-methyl-5-(β-hydroxyethyl)thiazole (THZ) and hydroxymethylpyrimidine (HMP) for use in thiamine synthesis (http://metacyc.org/META/NEW-IMAGE?type=PATHWAY&object=PWY-6897). A predicted thiamine transporter encoded by the genes tbpA, thiP and thiQ exists in E. coli K-12 but has not been functionally characterised and thus its substrate range is unknown. Similarly, biotin-d-sulfoxide can be used as an alternative source of biotin by E. coli mutant strains that are unable to synthesize biotin [E. coli but no transporter has been identified [Several compounds with unknown transport systems are substrates of scavenging reactions. e biotin . Active entified ,29.E. coli metabolism, however their inclusion in EcoCyc provides useful data regarding enzyme specificity and kinetics. Again, the status of E. coli K-12 as a model organism is a contributing factor to the large number of non-physiological compounds that are included in the EcoCyc database. Many of its enzymes have been purified and characterised in vitro, sometimes using standard assays that are not relevant in vivo or in other cases focusing on enzyme activity and compounds that may be of industrial importance. Our DEM analysis indicated a clear need to better identify these reactions in EcoCyc and to modify the software program that is used to identify DEMs in order to exclude these reactions from future analyses.Our analysis identified reactions within the EcoCyc database that are not physiologically relevant; these reactions and compounds are not part of normal E. coli under that substrate, and correction of a DEM in the EcoCyc pathway for adenosylcobalamin (coenzyme B12) salvage will allow that pathway to carry flux.DEMs have the potential to affect metabolic modelling, for instance DEM-driven corrections to a metabolic database will improve the accuracy of flux-balance analysis (FBA) models  derived E. coli K-12. The improvements and insights we have gained by analysing the DEMs within EcoCyc are likely to prove useful when applied to Pathway/Genome Databases of other organisms. Manual curation of the EcoCyc database is an ongoing process and thus the list of dead end metabolites is not static. As new enzyme functions are characterised and biochemical pathways elucidated, the output of the dead end finder will vary. Evaluation of the DEMs in the database will thus be an ongoing task and an important check on the quality and overall coherence of the information in EcoCyc.In theory, DEMs reflect areas where our knowledge of metabolism is lacking and thus may be a useful tool for identifying potential research targets. Achieving this goal relies on accurate identification of physiologically relevant DEMs and our analysis of the output of the DEM finder in EcoCyc has enabled us to improve on the ability to do that for The computational definition of DEMs used by the EcoCyc DEM finder is given below. The definition references a specified compartment, including the reactions and transporters present in that compartment, which for the purpose of this study was always the cytoplasm. Substrates in EcoCyc reactions can be specific compounds or they can be compound classes. The term “C” refers to a specific compound while “a parent of C” refers to a compound class to which compound C belongs. For example, the specific compound “cytosine” belongs to the compound class “a pyrimidine base”.A compound C is a DEM if1C or a parent of C is only produced by small-molecule metabolic (SMM) reactions in Compartment, and C or a parent of C is not transported out of Compartment, OR2C or a parent of C is only consumed by SMM reactions in Compartment, and C or a parent of C is not transported into CompartmentThe DEM finder was also instructed to ignore compounds that are recorded in EcoCyc as enzyme cofactors, since we would expect synthesized cofactors to be used by the cell but not necessarily consumed by metabolic reactions.E. coli-related literature were done using the text mining system, Textpresso [E. coli (see EcoCyc website command Search → Search Full-Text Articles) a user can search, via specific keywords and/or categories, a literature database that currently contains just over 30,000 full text articles and 7000 abstracts. More general searches were also undertaken using publicly available internet search engines.Compounds returned by the DEM finder were initially analysed within the context of the EcoCyc database in order to locate the reactions (and associated enzymes) producing or consuming them and to review the literature that led to their inclusion in the database. Comprehensive literature searches were then undertaken to see if further information relating to the metabolism or transport of the compound of interest could be uncovered. Specific searches of xtpresso . In TextTable S1Transport reactions representing the import of a metabolite added to EcoCyc.(DOCX)Click here for additional data file.Table S2Transport reactions representing the export of a metabolite added to EcoCyc.(DOCX)Click here for additional data file.


Some of these organisms, including the lactic acid bacterium Lactococcus lactis, downregulate their high-yield pathway in favor of the low-yield pathway. Other organisms, including Escherichia coli do not reduce the flux through the high-yield pathway, employing the low-yield pathway in parallel with a fully active high-yield pathway. For what reasons do some species use the high-yield and low-yield pathways concurrently and what makes others downregulate the high-yield pathway? A classic rationale for metabolic fermentation is overflow metabolism. Because the throughput of metabolic pathways is limited, influx of glucose exceeding the pathway's throughput capacity is thought to be redirected into an alternative, low-yield pathway. This overflow metabolism rationale suggests that cells would only use fermentation once the high-yield pathway runs at maximum rate, but it cannot explain why cells would decrease the flux through the high-yield pathway.Low-yield metabolism is a puzzling phenomenon in many unicellular and multicellular organisms. In abundance of glucose, many cells use a highly wasteful fermentation pathway despite the availability of a high-yield pathway, producing many ATP molecules per glucose, Saccharomyces cerevisiae and L. lactis that downregulate the high-yield pathway at increasing glucose concentrations, and E. coli, which keeps the high-yield pathway functioning at maximal rate. FBAwMC correctly predicts the metabolic switching mode in these three organisms, suggesting that metabolic network architecture is responsible for differences in metabolic switching mode. Based on our analysis, we expect gradual, "overflow-like" switching behavior in organisms that have an additional energy-yielding pathway that does not consume NADH . Flux decrease through the high-yield pathway is expected in organisms in which the high-yield and low-yield pathways compete for NADH. In support of this analysis, a simplified model of metabolic switching suggests that the extra energy generated during acetate production produces an additional optimal growth mode that smoothens the metabolic switch in E. coli.Using flux balance analysis with molecular crowding (FBAwMC), a recent extension to flux balance analysis (FBA) that assumes that the total flux through the metabolic network is limited, we investigate the differences between Maintaining redox balance is key to explaining why some microbes decrease the flux through the high-yield pathway, while other microbes use "overflow-like" low-yield metabolism. This effect is known as the Crabtree-effect in the baker's yeast Saccharomyces cerevisiae. S. cerevisiae turns glucose into CO2 in aerobic, glucose-limited conditions. But in abundance of glucose, glucose is converted into ethanol [Escherichia coli [Bacillus subtilis [e.g., Lactobacillus plantarum and Lactococcus lactis [One of the key steps in energy metabolism is to transfer the energy carried by sugars, including glucose, to the biological "energy currency" adenosine triphosphate (ATP). The number of ATP molecules generated by metabolizing one molecule of glucose—the ATP yield—is one of the most basic measures of an organism's energy efficiency. One would perhaps expect that evolution has selected organisms for the ability to extract energy from their food at optimal efficiency by maximizing ATP yield. Yet surprisingly, many organisms switch between a high-yield pathway,  ethanol , even ifsubtilis  and lacts lactis ,5. The es lactis . Muscle s lactis , ferments lactis -12.E. coli uses high-yield metabolism, aerobically converting glucose into CO2 and water. At higher glucose concentrations and fast growth rates, it redirects part of the glucose influx into a low-yield fermentation pathway, keeping oxidative phosphorylation fully active [S. cerevisiae uses high-yield, aerobic respiration at slow growth rates; at fast growth rates it ferments most glucose into ethanol, and downregulates aerobic respiration, keeping aerobic respiration active at a much lower rate. Although L. lactis does not have an aerobic respiration pathway, it still performs a metabolic switch. At fast growth rates it makes a full switch to lactic acid fermentation [Microbial species show remarkable differences in their metabolic switching strategies. At low glucose concentrations and low growth rates, entation , which yE. coli. However, a problem with overflow metabolism is that it does not explain why organisms like S. cerevisiae or L. lactis would partly switch off their high-yield pathways at high growth rates.A plausible explanation for metabolic switching is "overflow metabolism". It assumes that organisms only switch to low-yield metabolism if the high-yield pathway is operating at maximum rate and cannot process any more molecules ,14. The Saccharomyces clade [Recent studies have suggested that the limited amount of metabolic enzymes fitting inside the cell may be key to low-yield metabolism ,17,18. Ses clade  and in ces clade .E. coli? We address this question by comparing the optimal metabolic switching strategies of L. lactis, S. cerevisiae, and E. coli as predicted by a genome-scale computational model. These three organisms use different pathways to metabolize glucose. In Figure E. coli can use oxidative phosphorylation, lactate fermentation, ethanol fermentation and acetate fermentation. L. lactis can use mixed-acid fermentation, producing formate, acetate and ethanol, or lactate fermentation. S. cerevisiae can use oxidative phosphorylation, ethanol fermentation and acetate fermentation.If cells need to trade off fast metabolism and high-yield metabolism, then why do we still observe overflow metabolism, as in yield (defined as the growth rate divided by the glucose uptake rate) is effectively maximized [To predict the metabolic switches these three organisms can perform, we make use of a variant of Flux Balance Analysis (FBA), a method that calculates fluxes through metabolic networks given constraints on the network and given an objective function to maximize. By maximizing growth rate, FBA often correctly predicts cellular metabolism, including uptake, excretion and growth rates of cells ,21. Howeaximized . Therefocatk), molecular crowding naturally results in a constraint on the total metabolic flux through the network:For this reason, we use an extension of FBA, Flux Balance Analysis with Molecular Crowding (FBAwMC) ,22. In ci fbeing the flux through reaction i, prot Vthe volume fraction of macromolecules devoted to metabolic enzymes and i cthe "crowding coefficient" of reaction i. The crowding coefficient of reaction i is defined as the volume that needs to be occupied with enzymes to reach unit flux through reaction i and is given by M is the cell mass, V the cell volume, i vthe molar volume of the enzyme catalyzing reaction i, and i ba variable describing the proportionality between enzyme concentration and flux through reaction i [e.g., growth curves of E. coli [with action i . Intuiti E. coli ,22, and  E. coli . Therefoet al. [et al. [et al. [Because crowding coefficients for most metabolic enzymes are unknown, previous studies proposed a range of strategies to estimate them. Beg et al.  fitted a [et al.  obtained [et al.  sampled Although the study of an estimated, specific set of crowding coefficients or an average can provide some insight, in reality metabolic networks may operate under an entirely different set of crowding coefficients. Therefore, in the absence of accurate, experimental estimates of crowding coefficients, FBAwMC cannot decide on one real situation. Studying growth yield predictions for large samples of biochemically-plausible sets of crowding coefficients can give more robust insights into the metabolic network than studies with single crowding coefficient estimates, because it reveals what growth yields are most plausible and what are the alternative behaviors of the network.+/NADH ratio are key to the metabolic differences between the two types of metabolic switches. Organisms in which both the high-yield and low-yield pathways reduce NADH may downregulate high-yield metabolism at high growth rates. If organisms have an additional energy-yielding pathway that does not consume NADH , it is optimal to keep both the low-yield and high-yield pathways active at high growth rates.Our analysis suggests that mechanisms to maintain NADL. lactis [E. coli [S. cerevisiae [S. cerevisiae and L. lactis and the overflow metabolism of E. coli. Following Vazquez and coworkers [E. coli, 44% for L. lactis and 32% for S. cerevisiae. As reflected by the growth curves' large variation, the optimal growth curve that FBAwMC predicts depends strongly on the particular sample of crowding coefficients used. Because a crowding coefficient i creflects the enzymatic cost of producing a metabolic flux if, we asked if the relation between crowding coefficient selections and the predicted optimal fluxes could yield new biological insight.Using genome-scale stoichiometric networks of . lactis , E. coli[E. coli , and S. revisiae  we firstoworkers , crowdinoworkers ) and turoworkers ). Thus tL. lactis and S. cerevisiae distribute bimodally, with only few simulations predicting intermediate growth yields. By contrast, the predicted growth yields of E. coli are distributed more uniformly. Strikingly, the predicted growth yield distributions for a random sampling of crowding coefficients correlate well with the organisms' switching strategies: L. lactis and S. cerevisiae, which downregulate their high-yield metabolism, display a bimodal distribution of predicted growth yields, whereas E. coli, which has overflow-like metabolism, displays a uniform distribution of predicted growth yields.Figure E. coli we observe that most sets of crowding coefficients lead to little flux decrease through the high-yield pathway  or further metabolize pyruvate to yield extra ATP. L. lactis converts two acetyl-coA into acetate and ethanol in parallel to retain redox balance, gaining (at most) one additional ATP per mole glucose. S. cerevisiae feeds pyruvate into the citric acid cycle and oxydative phosphorylation, gaining (at most) twenty-eight additional ATP and two GTP per mole glucose. Interestingly, E. coli has three choices: it can convert pyruvate into the waste product ethanol, it can metabolize pyruvate in the citric acid cycle, or it can gain one extra ATP in the conversion of acetyl-coA into acetate.A key difference that sets E. coli. During formation of waste products  the NADH produced in glycolysis or in the conversion from pyruvate to acetyl-coA is reduced back to NAD+. Thus such waste product formation is a "fast" way to restore a sufficiently high NAD+/NADH-ratio. Acetate production does not restore the NAD+/NADH-ratio, so acetate production might deplete the available NAD+ in the cell. So, E. coli might keep oxidative phosphorylation running at fast growth rates (and consume oxygen) in order to profit from the extra ATP yield in acetate formation and restore the NAD+/NADH ratio.Although acetate production is a "cheap" way—in terms of the number of enzymes required—to produce additional ATP from pyruvate, it poses an additional challenge to E. coli ferments glucose into lactate or ethanol, its oxygen consumption will be reduced. We therefore studied the excretion patterns belonging to different sets of crowding coefficients more carefully. We found that, if a set of crowding coefficients results in acetate fermentation, without any ethanol or lactate fermentation, the cells continue to consume oxygen consumption during the switch. If a set of crowding coefficients results in lactate or ethanol fermentation, the consumption of oxygen is often reduced , it needs dissolved oxygen to grow [This analysis suggests that, if d Figure . Of the DH ratio . If E. c to grow .E. coli due to acetate excretion, we blocked acetate excretion in the FBAwMC model of E. coli (by setting the maximum efflux to zero) such that acetate production stalled, and recalculated the distribution of optimal growth yields. As Figure E. coli can switch bimodally. Also, there are more sets of crowding coefficients that result in a decrease in flux through the high-yield pathway  or ethanol formation (for AOX) were diminished. In another study, Vemuri et al. [E. coli and studied the effect on overflow metabolism. They found that overexpression of NOX strongly diminished acetate fermentation.Our model results suggest that restoring the redox balance is key in metabolic switching, agrees with experimental observation. Vemuri et al.  overexpri et al.  increaseE. coli and S. cerevisiae. We introduced the reactions that NOX and AOX catalyze to the metabolic model and enforced a lower bound on their fluxes to mimic the effect of overexpression. We performed simulations of S. cerevisiae with ten thousand sets of crowding coefficients, of which only 110 crowding coefficient selections resulted in excretion of both ethanol and glycerol. We went on with these sets of crowding coefficients, because they best mimicked the wild-type phenotype that Vemuri et al. [S. cerevisiae suggests that excessive NADH breakdown reduces ethanol and glycerol fermentation. In the FBAwMC model of E. coli we found that increased oxidation of NADH could either result in a decreased or in an increased production of acetate, depending on the selection of crowding coefficients. Thus, the experiments of Vemuri et al. [E. coli, during acetate fermentation some NADH is formed in the conversion of pyruvate to acetyl-coA. During NOX overexpression, the cells must boost NADH production to maintain optimal growth; this can be done either using the TCA-cycle or using acetate fermentation. Depending on the crowding coefficients, either way is optimal.To check whether our model is consistent with these experiments, we mimicked them in the FBAwMC models for i et al.  used. Thi et al.  do not ci.e., the number of enzymes "fitting" inside the cell) puts selective pressure on cells to evolve mechanisms to rapidly produce or remove enzymes for alternative metabolic pathways [The computational results presented in this paper are contingent on two underlying, biological assumptions of FBAwMC that may limit the applicability of our approach to strains growing in well-mixed, nutrient-rich lab conditions: a) evolution optimizes cells' growth rates instead of yields, and b) a solvent constraint  representing the volume fraction of macromolecules devoted to metabolic enzymes. We fit prot Vto the experimentally observed growth rate and glucose uptake rate. Additional file prot Vvalues are very similar across different organisms, ranging from 0.15-0.2. Note that Vazquez et al. [prot V= 1, which we believe is unrealistic, because not only metabolic enzymes fill the cell's cytoplasm. Linear programming efficiently solves this problem, but the solution is not necessarily unique.Here g et al. . Vprot iz et al.  assumed i cwe adopted the approach of Vazquez et al. [i vcan be estimated from the molar masses of the enzymes using a specific protein volume of 0.73 ml/g. i bdepends on the concentration of metabolites and on the turnover numbers of the enzymes . Following Vazquez et al. [To obtain the crowding coefficients z et al. . The molz et al. , we consz et al. , enzyme z et al. . The disL. lactis we used E. coli crowding coefficients for this organism as well. The turnover numbers, both for E. coli and S. cerevisiae varied over orders of magnitudes. Importantly, a few enzyme-substrate combinations had extremely low turnover numbers that effectively stopped the reactions. Because these turnover numbers typically occurred for non-metabolic reactions  or for non-typical substrates of metabolic enzymes, we only used turnover numbers of metabolic enzymes and for each enzyme we only kept the highest available turnover number and left out enzymes with turnover number smaller than 0.01/s. We used wild-type turnover numbers if reported. The resulting distribution of crowding coefficients for E. coli was similar to the distribution found by Vazquez et al. [S. cerevisiae we found a similar distribution as for E. coli  maximal growth rate. In this way, the maximal amino acid uptake rate suffices for twice the experimentally observed growth rate.The Matlab code to reproduce the simulations are included in Additional file 2: Carbon dioxide; COBRA: COnstraints Based Reconstruction and Analysis; FBA: Flux-balance analysis; FBAwMC: Flux-balance analysis with molecular crowding; GTP: Guanosine-5'-triphosphate; NAD+: Nicotinamide Adenine Dinucleotide; NADH: Reduced form of NAD+; NOX: NADH oxidase.AOX: Alternative oxidase; ATP: Adenosine triphosphate; BiGG: Biochemical Genetic and Genomic knowledgebase of large scale metabolic reconstructions; COThe authors declare that they have no competing interests.MvH designed the model and performed the simulations. RM and MvH conceived of the study and drafted the manuscript. All authors read and approved the final manuscript.Figure S1. Histogram of decrease in oxygen uptake for E. coli, when acetate excretion is allowed (black) and knocked out (red). When acetate excretion is knocked out, there are more simulations that become fully high-yield, but also more that stop consuming oxygen.Click here for fileTable S1. Table describing the summary of fitting prot Vto experimental growth rate and glucose uptake rate. For every organism, we varied prot V(volume fraction of macromolecules devoted to metabolic enzymes) between 0 and 1 and performed, for each value of protV, 1000 simulations with random sets of crowding coefficients. For the simulations described in this paper, we used the value of prot Vthat minimized /max, obsμ)2+/max, obsGup)2. Here, max, fitμ, max, obs μare the fitted and observed maximal growth rate and max, fitGup, max, obs Gupare the fitter and observed maximal glucose uptake rate. In this table, ineff Pindicates the fraction of the 1000 simulations that exhibits low-yield metabolism, which was defined as having a growth yield < 0.3 gr/gr glucose. Experimental data is from Hoek et al. [et al. [k et al. ; Thomas  [et al. ; Varma aClick here for fileFigure S2. Excel file with turnover numbers and enzyme masses used to calculate the crowding coefficients.Click here for fileFigure S3. Histograms of turnover numbers (1/s) (A) and crowding coefficients (gram DW hr/mmol) (B) of E. coli. A. All turnover numbers of E. coli in BRENDA ; B. Crog et al. ); C. Turz et al. ; F. Crow [et al. .Click here for fileFigure S4. Histograms of turnover numbers (1/s)  and crowding coefficients (gram DW hr/mmol)  of S. cerevisiae. A. All turnover numbers of S. cerevisiae in BRENDA ; B. Crog et al. ); C. TurClick here for fileTable S2. Excel file describing, for every reaction, the lower and upper bounds used in the simulations.Click here for fileMini-website with Matlab code and instructions for reproducing the simulations.Click here for file