Predicting the distribution of metabolic fluxes in biochemical networks is of major interest in systems biology. Several databases provide metabolic reconstructions for different organisms. Software to analyze flux distributions exists, among others for the proprietary MATLAB environment. Given the large user community for the R computing environment, a simple implementation of flux analysis in R appears desirable and will facilitate easy interaction with computational tools to handle gene expression data. We extended the R software package BiGGR, an implementation of metabolic flux analysis in R. BiGGR makes use of public metabolic reconstruction databases, and contains the BiGG database and the reconstruction of human metabolism Recon2 as Systems Biology Markup Language (SBML) objects. Models can be assembled by querying the databases for pathways, genes or reactions of interest. Fluxes can then be estimated by maximization or minimization of an objective function using linear inverse modeling algorithms. Furthermore, BiGGR provides functionality to quantify the uncertainty in flux estimates by sampling the constrained multidimensional flux space. As a result, ensembles of possible flux configurations are constructed that agree with measured data within precision limits. BiGGR also features automatic visualization of selected parts of metabolic networks using hypergraphs, with hyperedge widths proportional to estimated flux values. BiGGR supports import and export of models encoded in SBML and is therefore interoperable with different modeling and analysis tools. As an application example, we calculated the flux distribution in healthy human brain using a model of central carbon metabolism. We introduce a new algorithm termed Least-squares with equalities and inequalities Flux Balance Analysis (Lsei-FBA) to predict flux changes from gene expression changes, for instance during disease. Our estimates of brain metabolic flux pattern with Lsei-FBA for Alzheimer’s disease agree with independent measurements of cerebral metabolism in patients. This second version of BiGGR is available from Bioconductor. H. sapiens, M. barkeri, S. cerevisiae, H. pylori, E. coli, P.putida, M. tuberculosis and S. aureus. The new version of the metabolic reconstruction for H. sapiens, Recon 2 [Metabolism directly reflects cellular functioning. If the biochemical reactions that operate in a cell type are known together with uptake or release measurements of some metabolites, the distribution of metabolic flux in the metabolic system can often be predicted. Large scale reconstructions of metabolic networks are valuable resources for building models for flux estimation. In recent years, genome-scale metabolic networks have been reconstructed for various organisms, such as microorganisms, animals and humans . Public  Recon 2 , is presConstraint-based modeling has proven to be effective to analyze the functional states of metabolic networks when the structure of the network is known (see e.g. ). The paSeveral FBA software tools support import from databases . The freHere we demonstrate the substantially extended second version of BiGGR which is specifically designed for automated model generation and visualization of FBA results and was recently included in the Bioconductor open source project for bioinformatics. Emphasis is placed on functionality to assess the uncertainty of flux distributions estimated from measurements of metabolite uptake and release from the cells under study. This is accomplished by sampling ensembles of flux distributions using Markov chain Monte Carlo (MCMC) approaches. We further demonstrate incorporation of gene expression changes in metabolic analyses. BiGGR is still a relatively lightweight, low-threshold implementation of constraint-based analysis with direct access to reconstruction databases to import reactions. It links models built from the metabolic reconstructions with linear inverse modeling routines developed by ecologists  which tuWe propose that BiGGR is a relatively easily accessible way to analyze metabolic networks, especially for users of R and Bioconductor. Tools available in R and Bioconductor for handling ‘omics’ data can readily be combined with BiGGR. Below we therefore demonstrate the functionality of BiGGR by estimating metabolic fluxes in brain from measurements of metabolite exchange and gene expression in healthy humans and patients with Alzheimer’s disease. To this end we developed and demonstrate a new algorithm, termed Least-squares with equalities and inequalities Flux Balance Analysis (Lsei-FBA), which predicts changes in metabolic flux distribution from changes in gene expression between health and disease.http://bioconductor.org/packages/release/bioc/html/BiGGR.html. A detailed tutorial is available as a vignette within the package documentation.The R package BiGGR comprises the databases from BiGG  and the BiGGR provides the following functionalities . All reactions with annotations indicating that they belong to a certain pathway can be imported in one go. Further, reactions can be imported by specification of lists of reactions, metabolites or gene identifiers. Irrelevant reactions can also be removed.Models in SBML format can be easily imported into BiGGR for further analysis. Model files exported from the web interface of the BiGG database (bigg.ucsd.edu) can also be imported. Each model created or modified within BiGGR can be exported in SBML format.BiGGR uses linear inverse model (LIM) approaches for flux estimation. The fluxes in an underdetermined system can be calculated based on a linear function (i.e. a weighted sum of the unknown variables) which is either minimized (a “cost” function) or maximized (a “profit” function). The function to be minimized or maximized can be subject to inequality constraints, e.g. due to irreversibility of reactions which cannot carry negative fluxes, and equality constraints which reflect the metabolic steady state assumption. BiGGR can also generate ensembles of parameter combinations with a probability density reflecting the likelihood of explaining measured data.BiGGR provides automatic visualization of a network with hypergraphs using the hyperdraw package . The graAn overview of flux balance and ensemble modeling methods implemented in BiGGR is given below. This is followed by a description of the methods used to predict redistribution of fluxes based on measurement of changes in gene expression during disease. In the results, examples of the application of these methods are given.profit or a cost function for maximizing or minimizing certain (combinations of) fluxes given the constraints. Constraints can be equality constraints, such as the steady state assumption and inequality constraints, e.g. posed by the irreversibility of reactions. FBA is a widely used modeling technique and therefore not explained in detail here. For more information, the reader is referred to a large body of literature on FBA, e.g. [Flux Balance Analysis (FBA) is a constraint-based modeling method which derives the vector of fluxes by optimizing an objective function while subject to given constraints. The objective function can either be a BA, e.g. .x given a cost or profit function with respect to the constraints:In brief, FBA uses a linear programming routine to optimize a flux vector E is the stoichiometry matrix of the given reaction system with the rows representing internal metabolites that should be balanced to zero, but without rows that represent external metabolites which are not balanced to zero. These external metabolites may for instance accumulate or decrease in level in the medium outside the cells in a cell culture, or may be metabolites in the cell which are used in unknown reactions not yet fully accounted for in the model. The entries in the vector f are usually set to zero. The first equation therefore ensures that the optimized flux vector x is in the null space of the stoichiometry matrix and therefore the assumption of metabolic steady state holds. In some cases in an FBA, additional equality constraints are desirable, if for instance the value of a certain flux is known beforehand with great precision. The flux can then be fixed to this reference value using matrix E and vector f.Matrix Gx ≥ h usually constrains fluxes in irreversible reactions. Matrix G therefore indicates irreversible fluxes and the vector h consists of zeroes. In BiGGR, FBA is conveniently performed by interfacing the model with the linear programming routines in the ‘LIM’ package [The inequality constraint  package . EqualitE and G matrix can be combined with a linear function that specifies (a combination of) fluxes to be minimized or maximized. Maximization of ATP production  patients see . Microarlimma . Log2 fob vector of the Ax = b equation and providing a reference in the A matrix to the corresponding flux. In this way the sum of the squares of the differences between the final estimated fluxes and the initial rough estimate of the fluxes is minimized, subject to equations lsei routine from the LIM package [In the following part of the Methods section we detail the computational procedure to calculate changes in metabolic fluxes from changes in gene expression. The rationale for this computational approach is discussed further in the Results. We started from the flux distribution in normal healthy brain, determined using FBA with total ATP production maximized and with the pentose phosphate pathway (PPP) and GABA shunt fluxes constrained to measured values relative to glucose uptake. For the diseased brain, an initial estimate of the fluxes in the AD patients is first computed by multiplying the flux estimate in each reaction in normal brain with the fold change in gene expression for the genes mapped to that reaction. In the second step, this initial rough flux estimate was refined by taking the flux balance  and irreversibility  constraints into account, see equations  package . These fTo demonstrate the functionality of BiGGR, we conducted a flux balance analysis using a metabolic model that was previously used to study the effect of physical exercise on glucose and lactate metabolism in the human brain . The smaThe model consists of 89 metabolites and 71 reactions representing the glycolytic pathway, the pentose phosphate pathway (PPP), the citric acid cycle, malate-aspartate shuttle, the glutamate and GABA shunt and oxidative phosphorylation in the brain and was assembled from the Recon 1 reconstruction database. A list of full reaction equations, metabolites and a model scheme of the whole network is given in With the constraints given above, we optimized the network for maximal ATP synthesis. To this end, the net balance of ATP producing and ATP consuming fluxes is maximized:The resulting maximal net ATP production  given the measured uptake of glucose and release of lactate and pyruvate was calculated to be 8.49 mmol/min with a mitochondrial ATP synthase flux of 7.48 mmol/min. Numerical values for all flux estimates are given in Grey boxes represent metabolites, edges (arrows) represent reactions. Labels for boxes and edges show the Recon 1 identifiers for metabolites and reactions, respectively. Estimated flux values in mmol/min for the whole brain  are plotted together with the reaction identifier. Note that only part of the whole network is displayed. The left hand side of the plot shows the reactions in the glycolysis pathway and a subset of the reactions of the pentose phosphate pathway. The right-hand side shows the citric acid cycle. Edge widths are proportional to the estimated reaction fluxes. Arrows point in the direction of the calculated flux. Negative fluxes (reaction runs in reverse direction relative to the one defined as forward in Recon 1) are plotted in red and the flux values are printed as negative. R_AKGMAL is a transport reaction across the mitochondrial inner membrane exchanging alpha-ketoglutarate for malate. Note that not all metabolites involved in a reaction are always plotted. For instance, R_ASPTAm is a transamination reaction inside the mitochondrial matrix which involves aspartate and glutamate (not in scheme) in addition to M_oaa_m and M_akg_m which are plotted.Experimentally determined exchange fluxes for metabolic systems are subject to measurement error. Internal fluxes in the system can be estimated by model analysis using the exchange fluxes as input. It is desirable to quantify the effect of measurement error on the estimates for the internal fluxes. The uncertainty of estimated parameters can be quantified by sampling an ensemble in parameter space which describes the experimental data within precision limits posed by the measurement error . The resxsample algorithm [in vivo flux measurements [BiGGR provides the functionality to sample a posterior parameter ensemble using the Metropolis-Hastings algorithm in constrained linear systems, implemented in the lgorithm . In the urements  into accWe then sampled an ensemble consisting of 100000 parameter sets, allowing the measured fluxes to deviate according to normal probability distributions with the given standard deviations. As a starting point for the Markov chain, we used the parameter set resulting from the FBA performed above. It is important to note that all parameter sets still satisfy all other constraints posed by the model, such as the steady state and reaction irreversibility constraints  patients against healthy controls  in the hin vivo in the brain, translation of gene expression into enzyme activity, etc., not only preclude an exact calculation of the effect of gene expression changes, but also makes it difficult to prove our assumption. However, we will test whether our simple assumption works reasonably well here by comparing predictions on changes of metabolism during disease with available measurements on patients of actual changes in metabolic fluxes. Please note that the measurements of changed metabolic fluxes during disease are not used in any way for the model prediction. If the comparison between predicted and independently measured fluxes during disease is favorable, this would increase the confidence in predictions of those fluxes in parts of the metabolic network for which no measurement is available.Available methods to predict changes in fluxes from changes in gene expression work best when there are large changes in gene expression, but their assumptions seem less applicable when there are many small, largely congruent changes in gene expression in a pathway see . The latThe fluxes for the normal adult human brain at rest were obtained from the FBA with ATP synthesis maximized (see above). The fold changes in mRNA gene expression are subsequently used to provide an initial rough estimate of the changes in the metabolic network. To this end for each reaction in the network the flux estimate for the healthy brain is multiplied by the fold change of the expression of genes linked to that reaction. This first estimate is then refined by using the balance and irreversibility of fluxes in the metabolic network as additional constraints. To this end we minimize the sum of the squared deviations between the final estimates of the fluxes and the first rough estimates.According to the prediction, the pentose phosphate pathway (PPP) increased twofold from normal during AD.Predictions of flux distributions in normal healthy brain  and during Alzheimer’s disease . Unit for flux is mmol/min for the whole brain. Fluxes in green represent decreases from the normal condition and red increases. Only major reaction fluxes are plotted to simplify network visualization. Metabolite names are according to the Recon1 reaction database. PPP: Pentose phosphate pathway, OxPhos: oxidative phosphorylation.Our flux predictions agree with available experimental measurements. The decrease in metabolic rate in the temporal lobe measured by positron emission tomography (PET) was 77% for oxygen  and 36% We also compared our predictions with the reported analysis of a larger multicellular model of brain metabolism . In thatThe BiGGR open source package is built in R, is part of Bioconductor, and derives its input for model construction from metabolic reconstruction databases. BiGGR can be used to automatically construct mathematical and graphical representations of metabolic networks on the fly.Many constraint based modeling software packages are currently available  and This small model of the core of human brain energy metabolism was compared with a large model of human brain metabolism containing more than a thousand reactions and several brain cell types . This coTests showed that the calculation with our algorithm is feasible on models with the size of the Lewis model (>1000 reactions)  within fAs an example of applying BiGGR, we performed an FBA procedure with the objective to maximize net energy production of the brain cell with the small model. Published measurements of cerebral uptake and release rate of metabolites in the brain of healthy elderly control subjects  were usAn appreciable part of the total energy turnover of the human body at rest takes place in the brain. It seems reasonable to assume that, given a certain uptake of nutrients to support energy metabolism, ATP synthesis is maximized. Several alternative objective functions for models of metabolism in brain have been discussed by Cakir et al.  see the. MaximalThe adult brain is not growing, and therefore the emphasis on biomass components as seen in objective functions for metabolic models of microorganisms is not appropriate. However, to produce a reasonable baseline flux distribution, not only ATP synthesis was considered, but other metabolic functions in the brain were taken into account: the pentose phosphate pathway flux and the GABA shunt flux were set to fractions of glucose uptake that are representative of measurements in normal brain cells. We therefore consider ATP the limiting commodity given a certain level of measured nutrient uptake, while considering additional constraints to take other aspects of brain metabolism into account.Here we introduce an algorithm termed Lsei-FBA to predict changes in metabolic fluxes from measured changes in gene expression. Several algorithms to predict metabolism from gene expression changes have been designed previously . Some ofThe iMAT algorithm  predictsYersinia pestis. In their algorithm use is made of nutritional constraints specific for the test condition, which is not directly compatible with our application area. Reversible reactions are not taken into account in GX-FBA. The upper and lower bounds of reactions are modified, and the upper bound for a reaction may for instance be set lower than original even if gene expression for that reaction is increased. Their cost function maximizes fluxes for which gene expression is upregulated and minimizes fluxes for which gene expression is down regulated, weighted by the logarithm of the ratio of gene expression between test and control. Note that although the weight of a flux in the cost function increases with the logarithm of the fold change of gene expression, the flux is not optimized to be near the fold change times the wild type value as in our algorithm.The GX-FBA algorithm was developed by Navid and Almaas  and applMachado and Herrgard  comparedA further important difference is that Machado tested the algorithms on bacteria and yeast where in several of the algorithms the growth rate was maximized. The results of Machado show that the predictions made by the algorithms for the fluxes in the microorganisms were of limited quality. It is therefore remarkable that the results of our algorithm on brain disease were reasonable.Our application area is to estimate changes in fluxes, including uptake rates, in the disease condition without the availability of measurements of uptake rates during disease. Because the exchange rates during disease have not been measured, we tested two extreme situations: (1) the exchange rates are given as measured in the control condition or (2) the upper bound for the exchange rate was set to an unrestrictive value (2 mmol/min). For test 1 GIMME gives the same result as flux balance analysis under the control condition, despite that the FBA for the control does not take the gene expression for the disease data into account, as opposed to GIMME. For test 2 GIMME gives fluxes and uptake rates that approach the maximum values compatible with the upper bounds imposed in the model, e.g. 2 mmol/min for glucose uptake, which is equal to the imposed upper bound. Given the nature of the GIMME algorithm which tends to maintain metabolic functionality and given the modest changes in gene expression in the AD data set, these results were to be expected.We also tried the implementation in the Machado test suite of the Lee-12 algorithm , which iSimilar observations were made for the E-Flux algorithm which also predicts a very deviant pattern of metabolism. High lactate and pyruvate release was predicted in controls and AD patients . The resWhen multiple genes are associated with a biochemical reaction, we average the fold changes of gene expression. This is perhaps the simplest possible choice to map gene expression to the reactions. One finds a range of approaches in the literature. Lewis et al , for insThe model contains more than seventy fluxes and the flux distribution is estimated based on six measured fluxes (four exchange fluxes and two flux ratios for the pentose phosphate pathway and GABA shunt respectively). The exchange data can of course be precisely fitted by the model. This does not add further proof to the correctness of the model which is based on the extensive biochemical literature, but instead the experimental data are used to calibrate the fluxes in the control condition. Using Flux Variability Analysis we showed that the solution for the internal flux distribution in the control condition is unique.To predict the metabolic flux pattern in the patient group we make use of two distinct sources of data: (1) the flux distribution for the normal brain as described above, and (2) gene expression measurements from Alzheimer’s disease (AD) patients in comparison with a control group. We predict the metabolic fluxes in AD patients based on data source 1 and 2, using the Lsei-FBA algorithm. The final predictions of changes of metabolic fluxes during AD from the control condition are then compared with data source 3: independent in vivo measurements of metabolic changes  in AD patients compared to controls (data source 3). Note that the data from source 3 were not fitted by the model, but used to test the model by comparing with the model predictions.The procedure of sampling posterior ensembles of possible flux distributions that agree with measured input fluxes is based on Bayesian parameter inference. Knowledge of the measurement error of known fluxes is thereby used as prior information. Compared to an FBA analysis based on cost or profit function optimization, sampling a distribution of possible flux vectors has the advantage that uncertainty in the estimated fluxes can be directly quantified. As a result, confidence bounds can be defined on flux estimates that are difficult to measure directly. The method thus allows for assessing the robustness of estimates based on a metabolic model. The incorporation of prior knowledge on measured exchange fluxes helps to better delimit feasible and infeasible regions in flux space. Sampling the multidimensional flux space based on hypothetical exchange fluxes with very permissive upper and lower bounds without providing accurately measured prior values could still be used, e.g. to identify whether reactions are used at all or are correlated. Another approach to assess the range of possible fluxes in constraint based models is Flux Variability Analysis (FVA) ,31. FVA A Bayesian approach to FBA was applied by Heino et al . PosteriThe Bioconductor R package BiGGR facilitates constraint based modeling using metabolic reconstruction databases. Special emphasis was placed on the functionality to query metabolic reconstruction databases for pathways, reactions, metabolites or genes to compile constraint-based metabolic models. Metabolic fluxes can be estimated by interfacing linear programming routines. Further, metabolic models and estimated fluxes can be automatically visualized and integration with Markov chain Monte Carlo methods allows for sampling of possible flux configurations. BiGGR is open-source, free of charge and platform independent. As examples of the application of BiGGR, we predicted the metabolic flux distribution in the normal human brain and derived predictions of changes in metabolic patterns during Alzheimer’s disease using the new Lsei-FBA algorithm based on gene expression measurements.S1 Fig(TIF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.S6 Table(XLSX)Click here for additional data file.S1 Text(DOC)Click here for additional data file.


Genomic, transcriptomic, and metabolic variations shape the complex adaptation landscape of bacteria to varying environmental conditions. Elucidating the genotype-phenotype relation paves the way for the prediction of such effects, but methods for characterizing the relationship between multiple environmental factors are still lacking. Here, we tackle the problem of extracting network-level information from collections of environmental conditions, by integrating the multiple omic levels at which the bacterial response is measured.Escherichia coli that includes underground metabolism and new gene-protein-reaction associations.To this end, we model a large compendium of growth conditions as a multiplex network consisting of transcriptomic and fluxomic layers, and we propose a multi-omic network approach to infer similarity of growth conditions by integrating layers of the multiplex network. Each node of the network represents a single condition, while edges are similarities between conditions, as measured by phenotypic and transcriptomic properties on different layers of the network. We then fuse these layers into one network, therefore capturing a global network of conditions and the associated similarities across two omic levels. We apply this multi-omic fusion to an updated genome-scale reconstruction of https://github.com/maxconway/SNFtool.Our method can be readily used to evaluate and cross-compare different collections of conditions among different species. Acquiring multi-omic information on the topology of the space of experimental conditions makes it possible to infer the position and to build condition-specific models of untested or incomplete profiles for which experimental data is not available. Our weighted network fusion method for genome-scale models is freely available at The online version of this article (doi:10.1186/s12859-016-0912-1) contains supplementary material, which is available to authorized users. As the cost of collecting omic data is likely to decrease in the coming years, methods to integrate different types of biological data are likely to become increasingly important. Biological data is often expressed as network data. As a result, methods to tackle networks with different layers, each representing a different omic, are likely to play a key role to integrate these data types. A common approach in this case is a layer-wide analysis of each layer separately, finally integrating the separate results into a single aggregate measure.However, integrating results collected on single layers separately may cause loss of information, especially in cases where the inter-layer interactions are non-negligible. Intuitively, by analyzing different types of data in isolation we miss the information that is implicit in the coordinated activity of the different layers. For instance, in an application to networks of patients to investigate cancer, this approach resulted in different clusters of patients depending on which dataset was used, therefore causing incorrect subdivision of patients or samples in different molecular cancer subtypes .Genome-scale models of biological organisms are often used to analyze the metabolic potential and to identify the metabolic interventions required to produce metabolites of interest. In this post-genomic era, more than 90 genome-scale metabolic reconstructions have been published to date , for botWith the growing availability of multi-omic databases, model-building and data integration techniques, a number of methods for integration of omic data have been proposed recently  and on the fluxomic layer . The idea is that analyzing growth conditions by focusing only on a single omic level will likely miss complementary information and therefore lead to incorrect evaluations. For instance, considering only gene expression profiles as a response to conditions will miss the actual metabolic response of the bacterium, and will not provide insights into the resulting cellular behavior.Our idea is to integrate multiple data types, collected from a comprehensive set of environmental conditions in which Two main methods have been recently proposed to address the task of integrating multiple data types in an aggregate layer of a multiplex network. iCluster, developed by Shen et al. , proposeEscherichia coli, starting from the iJO1366 reconstruction , e.g. by squaring and dividing by the maximum. For instance, social networks are often natively similarity networks, where edge weights are counts of various friendly events between individuals.However, distance is probably more common than similarity as an edge weight type. When we have distances, we must transform them to similarities, with Wang et al.  suggestiP0 are the starting state of the networks, which will be modified as the algorithm iterates. As such, they start as normalized versions of W. Appropriate normalizations are: where or which is more robust to numerical instabilities.S are local similarity matrices for the networks. These are modified similarity matrices such that only the K nearest neighbors of a node have nonzero similarity. If Ni is the set of neighboring nodes of xi (including xi), then we define local similarity by: The core network integration procedure consists of iteration of the following update equation: v is the index of each of the m layers, k ranges over all layers except for the one under consideration, n is the iteration number, vth layer at the nth iteration.where For a set of networks (layers of a multivariate network), this iteration repeatedly makes each network more similar to the others until they converge to a single integrated network.https://github.com/maxconway/SNFtool/blob/master/R/SNF.R is a good place to start.For those readers who find source code more illuminating than equations, the file To combine the multiple gene expression and phenotype networks together we propose a technique based on SNF . SNF takSince our multi-omic model and trilevel formulation provide phenotypic flux rates from gene expression profiles associated with growth conditions, one may object that the transcriptomic layer should carry no weight in the fusion process. However, we remark that the fluxomic layer is a result of predictions of the metabolic model, and therefore it should not be considered as the only indicator of the response to a given condition. In fact, in applications to genome-scale models (as in this study), we suggest setting the weight as the level of confidence in the model itself.Pij in each layer v by exponential negative squared Euclidean distance In order to perform network fusion, we create a similarity matrix of environmental conditions in two different layers: transcriptomics and fluxomics. First, we remove gene expressions and fluxes for which less than 10 % of values were known and finite. Then, we divide each expression and flux into 20 quantiles, and replace each value by their quantile number, to deal with the high kurtosis; finally, we calculate the Euclidian distances between nodes (conditions), and we find similarities i and j in the vth layer.where P be the multiplex network of similarity between environmental conditions. P is computed, using . However, whether the biomass is the right objective for the analysis of the metabolism is still a matter of debate . FurtherTo enable a multi-objective view of the metabolism, we base our method on a multi-level linear program aimed towards classifying the bacterial response associated with external or growth media conditions in any multidimensional objective space chosen by the researcher. Our pipeline can be used to design environmental conditions that likely lead to a desired phenotype. Due to its real-valued kernel, it is well suited for applications involving various perturbations, such as different codon usage bias or continuous genetic manipulations.E. coli microarray profiles for 2369 measured conditions, to an E. coli model that includes underground metabolism  with raw hybridization of intensities, as well as RNA-seq (Illumina MiSeq) with short read sequences, therefore obtaining homogenized expression profiles. Conditions have been fully annotated through manual curation. In Fig. f,g,h in Eq. .When maximizing for acetate and formate production, The distinction between aerobic and anaerobic conditions is of great metabolic importance, and it is reliably recorded in the Colombos condition database. From Fig. −1 gDW −1 of ethanol, with a biomass of 0.27 h −1). Indeed, the trade-off in anaerobic condition is far from the trade off in aerobic condition especially in the low-biomass and high-biomass intervals. This is not observed in the succinate-biomass phenotypic space, where the aerobic trade-off is close to the aerobic trade-off even at high biomass production rates.Interestingly, only a few conditions are able to produce simultaneously succinate and ethanol. In fact, the succinate-ethanol and biomass-ethanol subspaces are where the difference between aerobic and anaerobic condition is more evident. This is mainly due to the difficulty in producing ethanol and high amount of biomass in anaerobic condition . A comparison between predicted and measured growth rates is reported in Fig. 44R-lim).In order to validate our method for associating a predicted growth rate to each condition, we consider a recent phenomics dataset of 14 growth conditions . On the p-value=0.67) and, surprisingly, to a negative Spearman correlation of −0.19  between predicted and measured values.We report that our method consistently outperforms the methods for integration of gene expression data in FBA that employ a linear map between gene expression values and the multiplicative factors for the flux bounds . For inThe inclusion of the underground reactions causes a relevant effect in the prediction of growth and production of additional objectives performed through flux-balance analysis. This is due to the fact that underground reactions share several metabolites with the iJO1366 reactions. Some underground reactions also take part in pathways leading to biomass precursors.In the transcriptomic layer, a condition is represented by a gene expression array; conversely, in the phenotypic layer, it is represented by a flux rate array. Our phenotypic flux data and, to a lesser extent, Colombos expression data displayed high kurtosis, indicating that both layers display many outliers. We do not remove outliers for two main reasons: first, in some cases this would remove most of the data; second, this represents a biologically reasonable all-or-nothing regulation, as one would see in a bistable system created by positive feedback in regulation (for instance ).K value of 500 (number of nearest neighbors) and a phenotype-transcriptome bias of 2:1. We then assess the resulting network by conducting spectral clustering and plotting a heat map. We find that three clusters best represent the data. While moving to larger numbers of clusters could decompose the center cluster slightly, it sacrifices most of the contrast at the cluster boundaries. Figure After constructing the multi-omic similarity network see , we fuseTo detect those fluxes and expressions that are most indicative of the three configurations, we employed a regression technique based on recursive partitioning . This suMulti-layer networks are increasingly being associated with microorganisms, with a rapidly growing number of applications in systems biology . BacteriWhile single-layer networks are able to model interactions between components, their strongest assumption, i.e. all the interactions between two nodes can be mapped as a single link, does not always hold in biology. Interactions between the same nodes can occur at different levels and in different settings , 45. ForWhen we are interested in classifying similarity among growth conditions, and in finding communities structure within their network, we must account for the different omic levels where the response to these growth conditions can be measured.Escherichia coli that takes into account underground metabolism, we map a set of growth conditions to the biomass-acetate-formate and biomass-succinate-ethanol spaces of flux rates. This allows us to estimate the metabolic potential of E. coli, and to predict regions of the fluxomic space where the bacterium operates in different conditions. As a result, each condition is represented by a gene expression profile in the transcriptomic layer, and by a flux profile in the fluxomic layer. In both layers, a network of conditions is built taking into account similarity between gene expression profiles and predicted flux rates respectively. We then fuse the resulting multiplex network into a single-layer network, by introducing a bias to represent the weight put on the phenotype layer rather than on the gene expression layer. This weight should be related to the accuracy of the genome-scale metabolic reconstruction. For instance, for large and exhaustive models (e.g. the E. coli adopted in this study), the information we gather after taking into account the predicted phenotype is likely to be more detailed than merely considering the gene expression levels.After building a genome-scale reconstruction of Our multi-omic network fusion method builds on SNF to allow us to: (i) specify a bias between layers; (ii) calculate a similarity matrix in a robust fashion despite extremely high kurtosis distributions; and (iii) attribute the clusters in the fused similarity matrix to a subset of dominant reactions.Integrating multiplex networks of omic levels in combination with metabolic models serves as an indicator of the behavior of the phenotype across the phase-space of all possible gene expression profiles, and their associated metabolic networks. This paves the way for the high-level topological understanding of multi-omic and multi-condition models. Assigning a specific metabolic model to each experimental condition proves useful in a number of applications. For instance, using the phase-space of conditions, one can predict and investigate metabolic regions in which the bacterium can work under many experimental settings, as well as unapproachable regimes, or regions in which it can grow only in specific conditions. Furthermore, given topological information on the space of experimental conditions, one can infer the position of non-tested or incomplete expression profiles.Multi-omic data modelling will also provide insights into the complexity of regulatory metabolic mechanisms. However, such complexity could be meaningfully analyzed and used in metabolic engineering only through comparative analysis of the organismal response to thousands of environmental conditions. It is noteworthy that this approach resembles the deep phenotyping techniques used in medicine.https://github.com/maxconway/SNFtool.The datasets supporting the conclusions of this article are included within the article . Our weighted network fusion method for genome-scale models is freely available at


A direct 13C enrichment analysis of intracellular free amino acids (FAAs) is expected to reduce time for labeling experiments of the MFA. Measurable FAAs should, however, vary among the MFA experiments since the pool sizes of intracellular free metabolites depend on cellular metabolic conditions. In this study, minimal 13C enrichment data of FAAs was investigated to perform the FAAs-based MFA. An examination of a continuous culture of Escherichia coli using 13C-labeled glucose showed that the time required to reach an isotopically steady state for FAAs is rather faster than that for conventional method using proteinogenic amino acids (PAAs). Considering 95% confidence intervals, it was found that the metabolic flux distribution estimated using FAAs has a similar reliability to that of the PAAs-based method. The comparative analysis identified glutamate, aspartate, alanine and phenylalanine as the common amino acids observed in E. coli under different culture conditions. The results of MFA also demonstrated that the 13C enrichment data of the four amino acids is required for a reliable analysis of the flux distribution. Continuous culture was performed in a 1 L bioreactor  equipped with temperature, pH, dissolved oxygen, and exhaust gas (O2 and CO2) sensors. The working volume and aeration rate were 400 mL and 400 mL/min, respectively. The temperature was controlled at 37 °C, and pH was set at 7.0 using an NH3 solution. Five hours after inoculation, the continuous culture was started at a dilution rate of 0.2 h−1. The feeding medium containing natural glucose was replaced with one containing 13C-labeled glucose after the continuous culture reached a metabolic steady state. Labeling of glucose in the medium was determined by gas chromatography–mass spectrometry (GC-MS) analysis by a previously described method , [M-85], [M-159], and [f302] derived from each amino acid were determined by using GC-MS ; column, DB-5MS+DG; 30 m × 0.25 mm ID × 0.25 μm; ; carrier gas, Helium; flow rate, 1.0 mL/min; detection mode, selected ion monitoring; ion source temperature, 230 °C; electron impact ionization, 70 eV). PAAs were analyzed under the following conditions: injection volume, 1 μL; split ratio, 1:10; oven temperature, 150 °C for 2 min, increased by 3 °C/min to 270 °C, then increased at a rate of 10 °C/min to 300 °C, and maintained at that temperature for 5 min [The mass isotopic distributions of four type of ion clusters at mass to charge  of the ith measured metabolite,  is the estimated MID of the corresponding metabolite, and N is the number of metabolites used for flux estimation. Optimization was started from 20 sets of random flux distributions. Confidence intervals were calculated by a grid search method as described previously [r is fixed to opt,rv + d and the objective function is re-optimized. Here, opt,rv is the optimized metabolic flux of reaction r and d is the perturbation level. The procedure is iterated with increased or decreased d. The range of fixed metabolic flux whose RSS is less than the threshold level is the confidence interval. The threshold level is determined by:min_fixedRSS is the minimized RSS with one fixed flux, minRSS is the original minimized RSS, n is the number of independent data points used in the fitting, p is the degrees of freedom in the original flux fit, F is the F-distribution, and α is the confidence level.A metabolic model including glycolysis, the tricarboxylic acid (TCA) cycle, glyoxylate shunt, anaplerosis, the pentose phosphate (PP) pathway, the Entner-Doudoroff (ED) pathway, COanalysis . The numanalysis . The effno acids . The fra [et al. . Additio [et al. , which i [et al. . In shoreviously ,31,32. TIn this study, a performance of the metabolic flux analysis using free amino acids (FAAs) was directly compared with that using proteinogenic amino acids (PAAs). An estimation of 95% confidence intervals for the first time demonstrated that the FAAs-based MFA has essentially identical reliability with that obtained from the PAAs-based method . It was


Cyanobacteria are increasingly recognized as promising cell factories for the production of renewable biofuels and chemical feedstocks from sunlight, CO2, and water. However, most biotechnological applications of these organisms are still characterized by low yields. Increasing the production performance of cyanobacteria remains therefore a crucial step.Synechocystis sp. PCC 6803 in combination with CASOP and minimal cut set analysis to systematically identify and characterize suitable strain design strategies for biofuel synthesis, specifically for ethanol and isobutanol. As a key result, improving upon other works, we demonstrate that higher-order knockout strategies exist in the model that lead to coupling of growth with high-yield biofuel synthesis under phototrophic conditions. Enumerating all potential knockout strategies (cut sets) reveals a unifying principle behind the identified strain designs, namely to reduce the ratio of ATP to NADPH produced by the photosynthetic electron transport chain. Accordingly, suitable knockout strategies seek to block cyclic and other alternate electron flows, such that ATP and NADPH are exclusively synthesized via the linear electron flow whose ATP/NADPH ratio is below that required for biomass synthesis. The products of interest are then utilized by the cell as sinks for reduction equivalents in excess. Importantly, the calculated intervention strategies do not rely on the assumption of optimal growth and they ensure that maintenance metabolism in the absence of light remains feasible. Our analyses furthermore suggest that a moderately increased ATP turnover, realized, for example, by ATP futile cycles or other ATP wasting mechanisms, represents a promising target to achieve increased biofuel yields.In this work we use a stoichiometric network model of Our study reveals key principles of rational metabolic engineering strategies in cyanobacteria towards biofuel production. The results clearly show that achieving obligatory coupling of growth and product synthesis in photosynthetic bacteria requires fundamentally different intervention strategies compared to heterotrophic organisms.The online version of this article (doi:10.1186/s12934-014-0128-x) contains supplementary material, which is available to authorized users. As one of their main advantages, many cyanobacteria are able to grow and proliferate also in harsh and extreme environments, including brackish water and in environments with high salinity. The metabolic versatility of cyanobacteria therefore offers the potential to overcome some of the problems associated with plant-derived first generation biofuels, such as the massive requirement for fresh water and the resulting competition of fuel versus food. Correspondingly, there has been considerable interest in biotechnological applications of cyanobacteria [Increasing requirements for food, feed and chemical raw materials constitute one of the grand challenges of the 21st century. To overcome the massive problems associated with the use of fossil resources, products derived from cyanobacteria are increasingly recognized as a promising source for renewable biofuels and chemical feedstocks. Cyanobacteria, the ancestors of modern-day chloroplasts, are evolutionary old organisms and are the only known prokaryotes that perform oxygenic photosynthesis. As primary producers, cyanobacteria are able to directly convert atmospheric CO bacteria , rangingbacteria -8, seconbacteria ,10 and bbacteria -17 to thbacteria -20.Most applications of cyanobacteria for sustainable production, however, are still characterized by low product yield. While proof-of-concept for cyanobacterial biofuel production has been established for a variety of potential fuels, such as hydrogen ,22, ethaSynechocystis sp. PCC 6803 [A systematic study clarifying whether growth-coupled production of biofuels with cyanobacteria is feasible or not by suitable interventions and, if so, revealing the key principles behind such strain designs and clarifying major differences to heterotrophic organisms is thus an urgent need. The purpose of this work is therefore to identify and analyze suitable genetic intervention strategies for the overproduction of biofuels, in particular ethanol and isobutanol, based on a metabolic network model of the cyanobacterial strain PCC 6803 ,39. We ePCC 6803  and ConsPCC 6803 , to deteSynechocystis sp PCC 6803. We enumerate all knockout strategies in a reduced version of the genome-scale network model and apply recently developed methods [Our results demonstrate that intervention strategies exist that enforce coupled biomass and product synthesis with high yields of ethanol and isobutanol in  methods  to identSynechocystis sp. PCC 6803 of Knoop et al. [All computations made herein are based on the genome-scale network model (GN) of p et al. . We tookp et al. ,45 as pup et al.  and the bd quinol oxidase (Cyd) and the aa3-type cytochrome c oxidase (Cox)), the Calvin-Benson-Bassham (CBB) cycle, glycolysis, pentose-phophate pathway, photorespiration, amino acid synthesis, lipid and fatty acid metabolism, biosynthesis of peptidoglycan, chlorophylls, carotenoids, terpenoids, quinones and tocopheroles, thiaminediphosphates, as well as the synthesis of several co-factors, vitamins and several stress related-pathways [To allow exhaustive elementary modes analysis, we derived also a reduced network (abbreviated RN) from the GN model comprising 505 reactions and 487  metabolites. The RN version is a true subnetwork of GN where some futile cycles and alternate electron pathways with presumably lower importance were removed. In contrast to the GN model, all electron transport processes in the RN model take place in a single membrane compartment to avoid duplicate reactions in the cytoplasmic and in the thylakoid membrane. Both the GN and RN model contain all main metabolic pathways, including photosynthetic  electron flows, respiratory pathways . Since much of the computational results will center around electron flows in the membrane, Figure CellNetAnalyzer [An SBML representation of both models, GN and RN, are contained in the Additional files Analyzer .Elementary Modes (EMs) provide a suitable concept for a functional characterization of metabolic reaction networks by means of minimal functional units ,48. Formtarget EMs representing the functionality to be blocked and to compute subsequently the so-called minimal hitting sets which are sets of reactions that hit each target EM in at least one reaction, thereby disabling all target EMs.Minimal cut sets (MCSs) provide a framework for enumerating metabolic intervention strategies disabling certain functions in a metabolic (or stoichiometric) network. Formally, MCSs are (support-)minimal sets of reaction (or gene) knockouts blocking a predefined behavior ,50. The An example is shown in Figure constrained MCSs (cMCSs) goes one step further [target and desired EMs. An cMCS hits all target EMs and keeps at least one of the desired EMs feasible. Coming back to the example in Figure The approach of  further . Since Mconstrained MCSs, each found MCS is tested by a simple optimization problem whether its application does not disable the desired functions [As mentioned above, MCSs and cMCSs for a given intervention problem can conveniently be computed from the corresponding sets of target EMs and desired EMs. However, in large networks, the determination of EMs is often not possible. To compute cMCSs also in the genome-scale model GN, we employ a recently developed algorithm  by whichunctions .target EMs to be blocked by the cMCSs are given by all photoautotrophic EMs with a product yield below the defined threshold.As described above we are interested in strategies that couple under photoautotrophic conditions biomass synthesis with the obligate synthesis of biofuels (here: ethanol or isobutanol). In addition, these strategies must not disable the cell to perform maintenance metabolism in the absence of light. To ensure the latter, we demand that the cMCSs must allow regeneration of ATP from the storage compound glycogen in the absence of light. For the analysis of the reduced model RN , we therefore proceed as follows: We compute the EMs separately for day (photoautotrophic regime) and for night (dark metabolism dominated by ATP regeneration based on intracellular glycogen). Two sets of desired EMs are then selected, one set for the photoautotrophic regime and one for dark metabolism. The desired day EMs are evaluated according to two thresholds, the first specifying the requested minimum biomass yield and the second the minimum requested product yield. The set of desired day EMs comprises all EMs where the biomass and the product yield are above the respective thresholds. The desired night EMs comprise all EMs that allow net production of ATP under night conditions. We note that the set of night EMs also includes the possibility of product synthesis, although this is not enforced by the algorithm. Regarding the undesired behaviors, the constrained MCSs which keep the desired day and night functionalities feasible.With this partitioning, the resulting cMCSs will hit (disable) all target modes and keep at least one EM of each of the two sets of desired (day and night) EMs feasible. When computing the smallest cMCSs in the GN, we calculate first the smallest MCSs blocking the undesired behaviors (via the method described in ) and, inand overexpression candidates, and it seeks to find a balance between high-yield and high-productivity strategies. Briefly, EMs are computed for the wild-type behavior  as well as for the desired phenotype . These two sets of EMs are then compared resulting in a score between −1 and 1 for each reaction. The largest positive scores indicate overexpression candidates whereas negative values expose potential knockout candidates.CASOP  is another EM-based framework for target identification . In cont2 in the CBB cycle consumes 3 ATP and 2 NADPH yielding thus a ratio of 1.5. This imbalance can be resolved by the cell by a number of alternate electron flow (AEF) pathways [The importance of the balance between ATP and NADPH synthesis in photosynthetic organisms for achieving metabolic homeostasis is well-known and its relevance for increased production of certain chemicals has also been discussed . The linpathways ,53 whichpathways  reactionpathways . To the −3 gDW/mmol photons. The maximum ethanol yield (upper left corner on the y-axis) is 0.04167 mmol/mmol photons reflecting the theoretical demand of 24 photons per molecule ethanol. With an estimated maximal photon uptake rate of 100 mmol photons/gDW/h [−1 and 4.167 mmol/gDW/h, respectively. As expected, ethanol production reduces the optimal growth yield leading to the characteristic triangle form of the convex hull.We first computed the EMs in the RN model for photosynthetic growth and ethanol production and found that 100803 such EMs exist. Figure ns/gDW/h , the maxguaranteed yield of ethanol under growth-coupled conditions is 0.0344 mmol/mmol photons; this value is obtained from the EM with largest product yield among all EMs with a non-zero biomass yield.Another important observation that can be made by Figure As described in the To obtain an overview of relevant intervention targets for shifting the cell from wildtype growth behavior to coupled ethanol and biomass synthesis, we applied the CASOP procedure to the EMs under photoautotrophic conditions. As described in the Table 2 export/diffusion is expected to increase ethanol synthesis. In fact, this would again force an energy-consuming pathway by which bicarbonate  as they constitute the path to ethanol production. Less intuitively, CASOP also proposes to enhance the unspecific ATP maintenance demand reaction (R35) thus suggesting to enhance ATP turnover or to waste ATP. The same strategy lies behind enhancing a cycle around cyanophycin , and behind the phosphofructo-1-kinase R34) and sedoheptulose-1,7-bisphosphate (R38) reactions all of which force futile cycling and thus loss of ATP  that will delete all low-ethanol-yield EMs and keep at least some desired EMs exhibiting high product and at least a minimal biomass yield. The threshold for the minimum desired yield is set to 1 Figure  each comAs an example, we pick the first cMCSs in Figure Analyzing the complete set of 124 cMCSs in Figure Generally, the cMCSs confirm the knockout targets proposed by CASOP: all reaction knockout candidates in Table Regarding the night behavior, we found that all cMCSs enforcing the desired day behavior still allow synthesis of ATP from intracellular glycogen. Since respiratory pathways are disabled by all cMCSs, the cell can synthesize ATP only by a fermentative pathway. As a beneficial side effect, ethanol becomes thereby a mandatory fermentation product further increasing its overall yield. As it is known that many cyanobacteria engage in fermentative metabolism in the absence of light and oxygen, such a strategy can indeed be expected to provide sufficient energy for maintenance requirements .In addition to full enumeration of cMCSs in the reduced network model RN, we also enumerated the smallest cMCSs in the genome-scale model GN using the same constraints for the desired minimum yields for ethanol and biomass and with the requirement that the cMCSs must allow ATP synthesis from glycogen under night conditions.We found that the minimum number of required cuts is 14 and we were able to identify all cMCS of size 14 (66), 15 (244) and 16 (1254) yielding in total 1564 cMCSs. We first noticed that all computed cMCSs have seven  reaction knockouts in common: R1, R3, R4, R7, which were already essential in the RN model, and, additionally, the reaction of the NDH2 (NADH-dependent dehydrogenase), the Mehler-like reaction and the reaction ‘Proline + PQ ⇒ 1-Pyrroline-5-carboxylate + PQH2’. These three reactions were not contained in the RN model and give rise to additional AEF pathways and must therefore be blocked to obtain coupled ethanol and biomass synthesis. We also found that reaction R2, which was an essential cut in the RN model, is not necessarily to be removed in the GN model. The reason is that some desired behaviors in the GN model exist that involve this reaction implying that a removal of this reaction is not essential in all strain designs.+ ⇔ Glycerone phosphate + NADH + H +’. These reactions establish another AEF pathway via which electrons from NADPH cycle back to the electron transport chain thereby pumping protons for ATP synthesis without net production of NADPH. Therefore, one of these reactions must be deleted to ensure that the cycle is not functional.Apart from the essential cuts mentioned above, several additional pathways need to be blocked in the GN model because they can potentially increase the ATP/NADPH balance in the cell. Non-essential cuts are replaceable in other cMCSs, for instance, if an AEF pathway involves a cycle with several reactions then one of these reactions need to be blocked. One such example comprises the transhydrogenase reaction together with the two reactions ‘sn-Glycerol 3-phosphate + PQ ⇒ Glycerone phosphate + PQH2’ and ‘sn-Glycerol 3-phosphate + NAD Synechocystis sp. PCC 6803 [Generally, we can conclude that the cMCSs of the GN and of the RN model follow the same fundamental design strategies to achieve coupled product and biomass synthesis. They block all potential AEF pathways or cycles that can potentially increase the ATP/NADPH balance above that of the LEF. Analysis of the GN model revealed that many more such potential pathways  may exist at genome scale. The high number of 8 or even 14 reaction cuts computed for the RN and GN model, respectively, may appear unrealistic for strain construction and several reaction knockouts cannot or not easily be mapped to corresponding gene knockouts, such as photorespiration. However, some of the involved pathways to be blocked might already have a low capacity. For example, it has been reported that cyclic photosynthesis is highly active only under low-light conditions and the Mehler reaction is believed to play only a minor role in PCC 6803 . We therWe now seek to identify suitable intervention strategies that potentially reduce the large number of knockouts suggested by cMCSs analysis. As one of such, we may lower the threshold for the minimum guaranteed ethanol yield, e.g. from 0.03 mmol/mmol photons used in Figure Figure The minimal number of required reaction knockouts for growth-coupled ethanol synthesis is 5 which requires to have an ATPm flux between 8 and 11 mmol/gDW/h. Figure −1. We note that different AEF pathways are available and hence multiple optimal patterns for LEF and AEF fluxes exist that produce the optimal ratio required for maximal growth. In the following, the choice of any of these optimal solutions does not affect the argumentation. To study the effect of enforced ATP consumption we (1) select a growth-optimal solution, (2) freeze the exhibited fluxes of the AEF pathways, (3) increase the ATPm flux from 0 to 5 mmol/gDW/h, and (4) re-optimize again for maximal growth. We then observe that the ethanol production rate rises from 0 to 2.4 mmol/gDW/h (and the yield from 0 to 0.024 mmol/mmol photons) accompanied by a growth rate reduction from 0.185 to 0.072 h −1. Hence, ethanol production becomes again mandatory if the cell cannot optimally re-adjust the fluxes along its AEF pathways upon increased ATP consumption.One may speculate whether an increased ATPm flux could improve the ethanol yield also in the wild type without implementing any knockouts. We know that the wild-type alone cannot guarantee growth-coupled ethanol production. It is realistic to assume, however, that (1) cyanobacteria have optimized the fluxes along the LEF and AEF pathways for optimal growth in a given environment and (2) that an increased ATP consumption could not, or not immediately, be counterbalanced by the cell by re-adjusting the AEF fluxes. To study implications of such a scenario, we simulated optimal growth of cyanobacteria for a maximal photon uptake rate of 100 mmol photons/gDW/h, such that the cells adopt an optimal ratio between LEF and AEF fluxes that facilitates the theoretically maximal growth rate of 0.185 h To check how far the engineering strategies found for ethanol can be translated to other products, we recalculated EMs, CASOP scores, and cMCSs in the RN model with isobutanol as product of interest. The ATP/NADPH ratio of isobutanol is 1.0 (12 ATP/12 NADPH) and thus smaller than for ethanol. We found 126484 EMs and the maximal yield of isobutanol amounts to 0.02083 mmol/mmol photons corresponding to a theoretical demand of 48 photons per molecule isobutanol. The CASOP scores and resulting top knockout and overexpression candidates are similar to those obtained for ethanol overproduction. We also found that the 124 cMCSs calculated for ethanol would in the same manner enforce coupled growth and isobutanol synthesis ensuring for all these cMCSs a minimal isobutanol yield above 0.014 mmol/mmol photons and a minimum biomass yield of at least 0.0001 gDW/mmol photons. Hence, the strain design strategies found for ethanol are relevant for other biofuels as well, the latter acting as obligate redox sinks to adjust the ATP/NADPH ratio for biomass synthesis when AEF pathways are blocked.Synechocystis sp. PCC 6803 [In this work, we investigated promising strain design strategies for the production of biofuels with cyanobacteria based on a genome-scale stoichiometric network reconstruction of PCC 6803 . SpecifiIn addition to knockout targets, we also identified certain fluxes or mechanisms whose upregulation would enhance product synthesis. Both CASOP and cMCS analysis clearly indicated that installing ATP wasting mechanisms could, at least partially, act as a substitute for deletions of AEF pathways. The increased consumption of ATP helps to keep the ATP/NADPH ratio low – again favoring or even demanding synthesis of a biofuel acting as redox sink. However, such an ATP wasting flux needs to be carefully controlled to not exceed certain thresholds.Escherichia coli or Saccharomyces cervisiae coupled biomass and product synthesis is usually achieved by growing the cells on a carbon substrate under anaerobic conditions and by deleting alternative fermentation pathways and fermentation products such that the desired product must be synthesized to balance reduction equivalents. In cyanobacteria, photosynthesis is used to generate ATP and NADPH needed to (i) fix carbon dioxide yielding precursors, and (ii) to produce biomass from ATP, NADPH and precursors. By introducing a disbalance between ATP and NADPH, some of the fixed carbon must be used to readjust the ATP/NADPH balance implying formation of ethanol or other (biofuel) byproducts.Exemplified with ethanol and isobutanol, the identified intervention strategies and key principles of redirecting metabolic fluxes in cyanobacteria should be relevant for a large variety of biofuels and other products. Although our results were determined by a model of one representative of cyanobacteria, we believe that the drawn conclusions hold in an analogous fashion for other species of this bacteria class as well. Our results also suggest that achieving obligatory coupling of growth and biofuel (or other product) synthesis in photosynthetic bacteria requires different intervention strategies compared to heterotrophic organisms. In heterotrophic micro-organisms such as


Previously we have used a genome scale model of rice metabolism to describe how metabolism reconfigures at different light intensities in an expanding leaf of rice. Although this established that the metabolism of the leaf was adequately represented, in the model, the scenario was not that of the typical function of the leaf—to provide material for the rest of the plant. Here we extend our analysis to explore the transition to a source leaf as export of photosynthate increases at the expense of making leaf biomass precursors, again as a function of light intensity. In particular we investigate whether, when the leaf is making a smaller range of compounds for export to the phloem, the same changes occur in the interactions between mitochondrial and chloroplast metabolism as seen in biomass synthesis for growth when light intensity increases. Our results show that the same changes occur qualitatively, though there are slight quantitative differences reflecting differences in the energy and redox requirements for the different metabolic outputs. Genome–scale metabolic modeling (GSM) is a technique for investigating the feasible metabolic states of an organism, taking account of the possibilities and constraints imposed by the structure of the metabolic network. The principal constraint is that of mass balance, dictated by the stoichiometries of the reactions in the network, coupled with the assumption of a metabolic steady state where the production and consumption of all internal metabolites of the network is balanced so that their concentrations remain constant. This defines a space containing all feasible states of the metabolism, from which more specific solutions are extracted with a combination of additional constraints, such as experimentally-observed values of nutrient uptake and growth rates, with an objective function that is intended to define an optimal state of the metabolism. The most common objective function, particularly for the models of micro-organisms that constitute the majority of genome–scale models, is optimization of the growth yield  . In brief, it was based on the genome annotation recorded in the“RiceCyc” database, version 2.01, downloaded from http://www.gramene.org/pathway/ricecyc.html  and interrogating BioCyc flat-file databases. The package, and further information, can be obtained from http://mudshark.brookes.ac.uk/ScrumPy or by contacting MGP.All computation was achieved using the software package ScrumPy–metabolic modeling in Python Poolman . This in2, nitrogen as NH3 and NO3, phosphate and sulfate, implemented as transport reactions bringing the species into the cell. Similarly, the outputs of metabolism are also formally expressed as transporters to an external sink, even for cellular constituents such as biomass, starch, and vacuolar sucrose that are in reality intracellular. In contrast to common practice in flux balance modeling, we do not include within the model a reaction equation that takes all the monomers needed for biomass as reactants in amounts proportional to their occurrence in measured biomass. This is in order to maintain the distinction between the structure of the network model and the experimental data and constraints that are applied in its analysis, which is especially relevant in this case where we want to change the metabolic output to something other than biomass. Other issues with the standard biomass equation formulation, causing imprecision in the FBA solutions, have recently been identified  up to the point beyond which all flux responses remain linear. The minimum flux below which no solution is possible was identified from a simple bisection search. However, in this case we also carried out a second scan whereby the proportion of biomass in the output went from 100% to zero, whilst the phloem output went from 0 to 100%. The 100% phloem output rate was set to contain the same amount of fixed carbon as the maximum biomass output, so that the amount of carbon fixed did not change along this second scan axis. The reason for carrying out a 2-D scan of light intensity and fraction of metabolic output to the phloem was two-fold. Firstly, it seems likely that output to the phloem will increase gradually as growth slows, so that a mixed output will exist for a certain period during maturation of a mesophyll cell. Secondly, given that scans of a single parameter give discontinuities in the set of reactions involved in the solution . The second is an arbitrary limit set on the sum of the rubisco carboxylase and oxygenase reaction rates, to implement a limit on the Calvin cycle flux. This is not based on a presumption that rubisco alone implements an upper limit to the Calvin cycle, only that such a limit exists; as this is not a kinetic model, the limitation could be equally applied to any of the enzymes in the same enzyme subset as rubisco to the same effect. We also assumed a fixed ATP requirement for growth-associated and non-growth associated maintenance. In all these cases, the value associated with the constraint affects the photon flux at which transitions in metabolism occur, but does not change the existence or the nature of the transition.D, any reaction flux Ji,r measured at light intensity i and fraction of phloem output r was expressed as a relative difference to the same flux at the same light intensity for r = 0.5, i.e.,:To calculate plots of relative flux differences, 2 is utilized by mitochondrial respiration, whilst the CO2 evolved by respiration is refixed in the chloroplast. In region A, most mitochondrial flux is accounted for by generation of ATP through oxidation of NADH supplied primarily from the operation of a mitochondrial malate-oxaloacetate shunt driven by export for reductant from the chloroplast. Region B is characterized by complete oxidation of pyruvate by the conventional operation of the citric acid cycle and the mitochondrial electron transport chain with increased CO2 fixation in the chloroplast as the respiratory products are recycled . However, the transition extends over a greater range of light flux for phloem production, reflecting the larger amount of reductant that has to be made in order to use 100% NO3. It is probably this increased demand for reductant that contributes to the more abrupt drop in mitochondrial malate dehydrogenase flux mentioned above.A clear quantitative difference is seen in the nitrogen uptake flux, which is larger for phloem sap production on account of the higher proportion of nitrogen than in biomass, as can be seen at the low end of the light range scanned in Figure 2 fixed per O2 released). For the source leaf, AQ is 1.02 at minimal light where NH3 is the sole nitrogen source used, but falls to 0.74 at higher light levels where NO3 is being used instead. The corresponding figures for the expanding leaf are 0.97 and 0.88, as observed previously (Poolman et al., 3 to NO3 use occurs. It is interesting that the nitrogen source has a bigger impact on the AQ for a source leaf than for an expanding leaf, presumably a reflection of differences in redox state and nitrogen content of the outputs. We should reiterate that in neither case is there any further change in AQ as light intensity and photorespiration increases (notably in regions C and D of Figure 2 released by photorespiration is linked to photosynthetic production of sufficient O2 to compensate for that used in the photorespiratory cycle.Another quantitative difference between the growing leaf and the source leaf is in the values of the Assimilatory Quotient (AQ, COOur results have shown that the occurrence of transitions in the flux solutions for our rice leaf cell metabolism model at different light intensities are not peculiar to the production of a specific metabolic output, but are relatively insensitive to the nature of the output. Differences in the redox and energy demands for making different outputs do, however, cause small quantitative changes in the points at which the transitions occur.2 to give the required proportions of metabolites. Part of that difference comes from the known difference in redox state between the two mixtures, reflected in the Assimilatory Quotient values. Another component is in the amount of ATP required for synthesis, and we do not know this value with any certainty. In both cases, there will be a non-growth associated maintenance energy value, which might be assumed to be more or less constant. However, in the case of biomass formation, there is the ATP cost of polymerization that is not fully accounted for explicitly in our model, whereas in the case of phloem sap production, there is the ATP cost of export of sucrose and amino acids, which again is not explicitly represented. Given the uncertainties in estimating both of these values, we have effectively assumed they are equivalent, so any differences in ATP requirement reflect those of biosynthesis of the required mixes of small metabolites. In any case, the small difference in the minimum light input required in the two cases is of no significance compared to the light needed to satisfy the cell's maintenance ATP needs, which itself is a very uncertain figure, though the value we have used results in a minimum quantum demand figure that is in the range of experimental measurements.Some of the quantitative differences in flux between production of biomass and production of phloem constituents arise because there is a small difference in the minimum amount of light needed to fix CO3 and NO3 as N source (Searles and Bloom, 2 is recovered, O2 consumption, and evolution are balanced for the complete cycle. Though we cannot claim on the basis of this evidence that this will always be the case in all feasible metabolic states, nevertheless the fact that there are situations where it can occur undermines the use of AQ as an indicator of the degree of photorespiration (e.g., Skillman, Our AQ values for an expanding leaf are comparable to those measured experimentally, as is the magnitude of the difference between using NHHowever, in spite of the differences we have highlighted between the central carbon metabolism of the leaf when it is exporting phloem sap as compared to growing, the most striking finding is how little most of the fluxes in central carbon metabolism change in order to redirect the output. The flux patterns predicted by FBA for growing microorganisms do not appear to be highly sensitive to the precise biomass composition used as the output constraint. This is likely to be a significant component of the robustness in flux patterns that we see here, though it is possible that the compartmentation, especially of the chloroplast metabolism, further insulates the central metabolism from its eventual outputs. In terms of exploring the properties of plant metabolism models with FBA, this is an advantage to the modeler in that, since it is experimentally difficult to measure accurately the inputs and outputs of specific plant tissues, the relative insensitivity of the fluxes to this data compared with the sensitivity to light intensity gives some confidence that it is feasible to discern some general trends in the metabolic responses. It must be admitted nevertheless that the model results may over-state the degree of robustness, since all the solutions are obtained with the same optimization criterion which therefore selects particular regions of feasible metabolic space. Since the regulation of plant metabolism will have evolved to balance multiple optimization objectives, and may never perfectly satisfy any of them, then real plant cells may well show greater variability in their actual responses. Even so, we believe that modeling has a role to play in formulating detailed and coherent hypotheses about how plant metabolism could potentially behave, for comparison with experimental evidence (c.f. Williams et al., The work was designed and conceived by David A. Fell, Mark G. Poolman, and Sudip Kundu. Mark G. Poolman developed ScrumPy and the Python modules used for the analyses reported here. All authors participated in developing and curating the rice metabolic model and running the analyses. The manuscript was drafted by David A. Fell and Mark G. Poolman and checked and approved by all authors.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


However, studies refining these approaches by performing a meta-analysis of massive experimental metabolic flux measurements, which are closely linked to cellular phenotypes, are limited. In the present study, experimentally identified metabolic flux data from 96 published reports were systematically reviewed. Several strong associations among metabolic flux phenotypes were observed. These phenotype-phenotype associations at the flux level were quantified and integrated into a Saccharomyces cerevisiae genome-scale model as extra physiological constraints. By sampling the shrunken solution space of the model, the metabolic flux fluctuation level, which is an intrinsic trait of metabolic reactions determined by the network, was estimated and utilized to explore its relationship to gene expression noise. Although no correlation was observed in all enzyme-coding genes, a relationship between metabolic flux fluctuation and expression noise of genes associated with enzyme-dosage sensitive reactions was detected, suggesting that the metabolic network plays a role in shaping gene expression noise. Such correlation was mainly attributed to the genes corresponding to non-essential reactions, rather than essential ones. This was at least partially, due to regulations underlying the flux phenotype-phenotype associations. Altogether, this study proposes a new approach in shrinking the solution space of a genome-scale model, of which sampling provides new insights into gene expression noise.Sampling the solution space of genome-scale models is generally conducted to determine the feasible region for metabolic flux distribution. Because the region for actual metabolic states resides only in a small fraction of the entire space, it is necessary to shrink the solution space to improve the predictive power of a model. A common strategy is to constrain models by integrating extra datasets such as high-throughput datasets and C These models have been widely used in molecular evolution studies [constraint-based model (CBM). Therefore, shrinking the predicted solution space is necessary to improve the predictive ability of a CBM.As a powerful tool for biological interpretation and discovery, over 100 genome-scale metabolic networks for more than 35 organisms have been reconstructed  is the most extensively employed in biased methods. By optimizing an objective function, FBA attempts to capture the region where real flux distributions are most likely to reside [Diverse constraint-based reconstruction and analysis (COBRA) methods have been developed to probe the solution space . These cibutions . On the o reside . FBA is o reside ,18, proto reside , and meto reside . In parto reside . Recentlo reside  systemato reside , 23. TheS. cerevisiae has been rapidly accumulating in the past decades. It has laid a solid foundation on flux phenotype correlation analysis; however, this kind of data has not been extensively utilized. In the present study, a meta-analysis of experimental flux data from publications has been performed to shrink the solution space of the yeast CBM.Extensive experimental evidences suggest that cellular phenotypes could be synergistically regulated by global biological regulatory factors under certain rules –27. CompS. cerevisiae model to explore the influence of the metabolic network on gene expression noise. Gene expression noise is defined as the stochastic fluctuation of a gene’s expression at the protein level between isogenic cells under identical environment [A refined model benefits biological discoveries. In the present study, we applied the refined solution space of a ironment . It is vironment . Previouironment , 32, genironment , gene exironment , 33, traironment –36, chroironment ,37, and ironment –40. A reironment . HoweverS. cerevisiae CBM to refine its solution space. Using the refined model, we examined whether the metabolic network influences expression noise of enzyme-coding genes.In the present study, we first determined the correlations among several metabolic flux phenotypes through a systematic review of experimentally measured metabolic flux data. The correlations were quantified and imposed into a Materials and Methods; S1 Dataset). Because sugar uptake rate plays a central role in shaping the global metabolic system under a carbon-limited condition [S. cerevisiae can be mainly in any of two metabolic states, respiration and fermentation. In the former state, glucose is completely oxidized into CO2 through the mitochondrial respiration pathway, whereas in the latter, glucose is predominantly fermented into ethanol. Because of the existence of two metabolic patterns, it is necessary to identify the metabolic state that the S. cerevisiae is in prior to exploring flux-flux phenotype correlations.All the metabolic flux data we collected were measured under the conditions that the yeast strains were cultivated aerobically with glucose as the only carbon source  is an indicator of metabolic states, RQ values against glucose uptake rates ·h), the et al. [Because the maet al. . Therefo2 uptake rate, ethanol production rate, and glycerol secretion rate against glucose uptake rate were plotted, respectively. Results showed that when glucose uptake rate was <4 mmol/ (g (DW)·h), the O2 uptake rates positively correlated with glucose uptake rates ). On the other hand, when the glucose uptake rate was >4 mmol/ (g (DW)·h), the O2 uptake rate negatively correlated with the glucose uptake rate). Unlike the O2uptake rate, ethanol production rates were always positively correlated with glucose uptake rates, independent of the metabolic state of yeast ). Glycerol secretion rates were correlated with glucose uptake rates ). Based on these findings, the correlation between the three flux phenotypes  and glucose uptake rate was quantified (Table A in S3 File).Next, O2 uptake rate, ethanol production rate, and glycerol secretion rate, FBA was employed to predict the upper and lower bounds of growth rate . Fig 3shows that almost all the experimentally identified growth rates were within the predicted space, indicating that our strategy was suitable for the refinement of flux bounds. In addition, when the glucose uptake rate was <4 mmol/(g(DW)·h), the experimental data fitted well with the predicted upper bound (R2 = 0.83), indicating the dominant role of the respiration pathway in supplying energy for growth. When the glucose uptake rate was >4mmol/ (g(DW)·h), the data points dispersed in the space. This finding suggested that once the nutrients in the environment are sufficient to support a high glucose uptake rate, S. cerevisiae would be relaxed from evolutionary pressures for survival. Under this condition, “biomass growth” is just one of the several goals that a cell strives to achieve [With the refined bounds for O achieve , and groS. cerevisiae [average metabolic flux (AF) level of each metabolic reaction was estimated and compared to the corresponding gene expression level. Table 1showed that AF moderately correlated with mRNA level and protein abundance, which was consistent the findings of a previous study [Several studies have revealed a close relationship between metabolic flux and gene expression for various pathways in revisiae , 44, 45,revisiae . In the us study . Contrarus study , our anaet al. conducted a systematical research on gene expression noise of S. cerevisiae. They proposed DM (which is short for distance to median) value as a measure of gene-specific noise . The noise is able to propagate and cause fluctuations in growth through corresponding metabolic reactions [Materials and Methods), and was compared with corresponding DM value. Results showed no significant correlation between FF and DM in all enzyme-coding genes (data not shown). A possible reason is that for many reactions, the flux levels are not controlled by enzyme concentrations, but by ubiquitous allosteric regulatory mechanisms [dosage sensitive reactions (DSRs). According to Newman et al., protein abundance levels are measured in both rich (YEPD) and minimal media (SD) [2(SD/YEPD)| > 1,were considered as DSR genes. Finally, a total of 41 genes were obtained and subjected to correlation analysis. In the DSR genes, FF moderately correlated with DM ). To ensure the robustness of this result, three different cutoffs (log2(SD/YEPD)>0.5,0.7,1.0 respectively) were used to retrieve DSR genes for correlation calculations. The correlations between FF and DM were always positive. The more stringent the cutoff, the stronger the correlation. These findings ascertained that for DSR genes, the level of gene expression noise was subject to the tolerance of the metabolic network to flux fluctuations.Gene expression noise describes the cell-to-cell differences in protein level while maintaining homeostasis. In 2006, Newman eactions . To knowchanisms . Thus, wdia (SD) . BetweenFig 4(B)). However, we did not observe a significant correlation in the genes that corresponded to essential reactions ).Gene expression noise undergoes selection pressures when it is beneficial or detrimental to the survival of an organism –32. HoweFig 5). A simulation test was also performed to ensure the robustness of this result , which showed that the simulated difference values between two groups were normally distributed around 0, with a standard deviation σ = 0.26. The observed difference value was at least four standard deviations away from the simulated mean difference. Therefore, the observation that FF values of non-essential reactions were higher than those of essential ones occurred by chance was highly unlikely .The DM and FF values between the essential and non-essential reaction groups were also compared. While no obvious differences were observed in the average DM values between the two groups, the FF values of non-essential reactions were generally higher than those of essential reactions .To avoid the possibility that all the results obtained in this section were sampling artifacts of a specific part or the entire solution space, FF values were re-calculated by sampling another part of the shrunken space where the glucose uptake rate fluctuates within 20-22mmol/(g (DW)·h). These FF values were also used in the correlation analysis, and the results were the same as those obtained earlier ). However, for genes related to essential reactions, newly calculated FF values strongly correlated with the DM values ). These findings indicated that the global regulations underlying the phenotype-phenotype correlations mitigated the correlation between FF and DM in genes corresponding to essential reactions.In the previous section, we revealed the difference between “non-essential reaction”-associated and “essential reaction”-associated genes in FF and DM coupling. The difference was speculated to be related to the flux phenotype-phenotype correlations that were quantified and imposed into the yeast model as additional constraints. To test this hypothesis, the FF values of DSR genes were re-calculated by sampling the yeast model’s solution space without the constraints. Removal of the constraints did not remarkably affect the strong correlation with the “non-essential reaction”-related genes . Fig 8showed that the majority of FCS values range within 0–0.1 (746/885), indicating the broad effect of the regulatory mechanism underlying the constraints. However, we did not observed a significant correlation between flux constraint strength and gene expression noise . This implied that the regulatory strength does not play a key role in shaping gene expression noise.In previous section, we have revealed that metabolic network has influence on gene expression noise. To know whether the influence is related to the extra constraint strength, we used FCS to estimate the level of flux constraints posed on each reaction . The retrieved metabolic data met following criteria:A comprehensive search of English-language published reports was performed using three search engines . Several publisher archives, including “Applied and Environmental Microbiology”, “Yeast”, “Enzyme and Microbial Technology”, “Applied Microbiology Biotechnology”, and “Microbial Cell Factories”, were also thoroughly surveyed. The search terms included "h−1”; The units of measurement for other metabolic flux data is (or could be converted to)“mmol/ (g (DW)·h)”;The unit of measurement for growth rate is “The yeast strains used in experiments did not undergo any artificial genetic manipulation at the molecular level such as gene deletion or overexpression;All the wild-type yeast strains were cultivated aerobically in a steady state; andGlucose was the only carbon source for yeast, and carbon was the only nutrient limitation of the culture.S1 Dataset), which includes glucose uptake rates, O2 uptake rates, CO2 production rates, respiratory quotient (RQ) values, ethanol production rates, and glycerol secretion rates.After selection according to these criteria, we aggregated and normalized the data to generate a metabolic flux dataset  to minimize experimental noise.2 uptake rate, ethanol production rate, and glycerol secretion rate, respectively.We examined the relationship between the glucose uptake phenotype and three metabolic flux phenotypes, namely,O2 uptake rate and ethanol production rate linearly well correlate with glucose uptake rate , we learned linear models for them. To ensure robustness and avoid publication bias in the linear model, a procedure analogous to leave-one-out cross-validation was performed [m elementary datasets are available for analysis, then m LOE datasets will be obtained). Linear regression analysis was conducted using the data from each LOE dataset, and m slope values and corresponding R2 values were obtained. The results showed that the m slope values were almost equal to each other, with R2>0.8, indicating the robustness of our modeling strategy.Because Oerformed : The datα  was defined. While fixing the α value, two β values, namely, βl and βu, were set through visual inspection to define a space covering > 90% of the following experimental identified points:vglu represents glucose uptake rate; and lb (ub) represents lower (upper) bound for ethanol (or O2) exchange rate.By performing linear regression analysis, the slope value α value as follows:lbgly (ubgly)represents the lower (upper) bound of the glycerol secretion rate.Glycerol secretion rate did not correlate well with glucose uptake rate. Therefore, its bounds were defined, somewhat arbitrarily, by modifying the α and β values are listed in Table A in S3 File. The newly refined glucose uptake-dependent bounds for O2 consumption rate, ethanol production, rate, and glycerol secretion rate are as follows:All aforementioned S. cerevisiae genome-scale metabolic network model iMM904 was used because of its high predictive power among available yeast models [voxy, veth and vgly values were uniformly sampled within the bounds defined by ;v is a vector containing metabolic flux vi of N reactions; and lbi (ubi) represents the lower (upper) bound for vi. When lboxy <0.016 mmol/ (g (DW)·h) at a certain glucose uptake rate, we set lboxy to 0.016 mmol/ (g (DW)·h) [t models , 53. To t models . At eachfined by , 2), an, anS. cevmax (vmin) the yeast was able to achieve under a glucose uptake rate. The vmax (vmin) under glucose uptake rates ranging from 0 to 24 (step size = 0.1) were all computed.After repeating this process 10,000 times, the biggest  value in the 10,000 simulated growth rate values was regarded as the maximum (minimum) growth rate Fig 3), the predicted vmax (vmin) was divided into several segments according to glucose uptake rates, for each of which linear regressions of the data were performed separately .The resulting equations were used as upper (lower) bound for the growth rate (All the equations are listed in Table B in S3 File). For simplicity, the bounds were presented as follows:Because the upper (lower) bound for growth rate was likely to be a combination of several linear functions (S. cerevisiae's solution space. The sampling was restricted to the part of solution space where glucose uptake rate fluctuates within 18-20mmol/ (g (DW)·h) for two considerations: (1) Fluctuations of catabolically active enzymes could lead to growth fluctuations [voxy, veth and vgly were set according to (The average flux level (AF), flux fluctuation (FF), and flux constraint strength (FCS) of each metabolic reaction were estimated by sampling tuations ; and 2)tuations . The upptuations rding to , respectAFi is defined as average flux level of the i-threaction; and FFi is the flux fluctuation of the i-th reaction. vi,max represents the maximum (minimum) flux value among the sampled flux values of the i-th metabolic reaction.The sampled flux values of each metabolic reaction were extracted from the 500,000 flux distributions. Given a reaction, the top and bottom 5% simulated flux values were discarded. The remaining sampled flux values were used to calculate AF and FF as follows:vi,max,ori  represents the i-th maximum (minimum) flux value, which was generated from the original solution space. Reactions and metabolites participating in the intracellular loops were not included in the analysis [one gene-one reaction relationship. Bi-directional reactions were also not involved in AF and FF calculation.To estimate the constraint strength posed on each reaction, we also sampled yeast model's solution space 500,000 times before imposing the extra constraints. After removing the top (bottom) 5% flux values of each reaction, FCS was defined as follows:analysis . To exclvori of yeast model iMM904 without any extra constraints. We iteratively set reaction flux vi in the yeast model to 0 and employed FBA again to predict the growth rate vgro,i. When vgro,i = 0, this i-th reaction was defined as an “essential reaction.” When vgro,i = vori, this i-th reaction was defined as a “non-essential reaction.”Setting “biomass growth” as the objective function to be optimized, FBA was conducted to predict the growth rate FF values of the 41 DSR genes were shuffled and randomly divided into two groups, one consisting of 20 values and the remaining values were binned into another one. Difference in average FF values was calculated by subtracting the average FF value in one group by that of another. This process was repeated 100,000 times.MATLAB, which was interfaced with the COBRA toolbox and ‘glpk’ solver. All correlations described in this report are Spearman’s rank correlations.All simulations and statistical analyses were performed in S1 Dataset(XLSX)Click here for additional data file.S1 File(PDF)Click here for additional data file.S2 File(PDF)Click here for additional data file.S3 File.Correlations between metabolic flux and gene expression noise .Relationship between metabolic flux constraint (FSC) and gene expression noise (DM) .The newly defined bounds (Table A).Regression analysis of growth rate versus glucose uptake rate in each segments. .Regression analysis of growth rate against glucose uptake rate in each segment (PDF)Click here for additional data file.