Genome-scale metabolic models (GEMs) are increasingly applied to investigate the physiology not only of simple prokaryotes, but also eukaryotes, such as plants, characterized with compartmentalized cells of multiple types. While genome-scale models aim at including the entirety of known metabolic reactions, mounting evidence has indicated that only a subset of these reactions is active in a given context, including: developmental stage, cell type, or environment. As a result, several methods have been proposed to reconstruct context-specific models from existing genome-scale models by integrating various types of high-throughput data. Here we present a mathematical framework that puts all existing methods under one umbrella and provides the means to better understand their functioning, highlight similarities and differences, and to help users in selecting a most suitable method for an application. Arabidopsis thaliana  have become a useful tool to investigate metabolism. They present numerous applications, from basic research on metabolic functioning and cell physiology  improve flux predictions through further constraining of the solution space  as well as modern developments . However, gene expression is also at the top of the hierarchical chain of events that govern metabolic fluxes, which may explain the relatively low correlation values between these two quantities, as reported in previous works . More specifically, the inconsistency score is given by the dot product of the flux distribution and the reaction penalty, defined as the vector difference of the associated expression values from the threshold. The reaction associated expression level is obtained following the standard GPR rules , which is more computationally challenging than the LP formulation of GIMME.GIMWhen a given RMF operates in different contexts, the operability constraint may lead to more accurate context-specific model reconstructions and flux distributions. This issue has been evaluated in a recent review : First, it forces each reaction to be active and evaluates the similarity, and then repeats the process in a similar way by forcing each reaction to be inactive. The final outcome is computed by comparing the two obtained similarities. A reaction is termed active if its inclusion results in higher similarity to data, and it is termed as inactive, if its inclusion decreases this similarity. In the case that both similarities are equal, iMAT categorizes the reaction as undetermined.INIT was optimized to integrate evidences from the Human Protein Atlas, although expression data are integrated when proteomic evidences are missing. In this case, INIT does not group reactions in categories in contrast to iMAT. Instead, it adopts experimental data to weight the binary variable of the corresponding reaction, whereby the weight is a function of experimental data  or a set of arbitrary numbers that quantify the color code of the entries of the Human Protein Atlas. In addition, INIT imposes a positive net production of metabolites for which there is experimental support for that context or tissue. Hence, when a metabolite is experimentally determined to be present, its net production is forced to comply with a given lower bound. As a result, INIT allows the integration of metabolomics data in a qualitative way. This method has been applied to generate a human metabolic reaction database  of being active in a certain context. Once these sets are defined, the MBA-like methods prune the GEM by eliminating non-core reactions that are unnecessary to ensure consistency in the core set, i.e., no blocked reaction is allowed in the final model. Thereby, all reactions must carry non-zero flux in at least one feasible solution. As a result, checking model consistency is a crucial part of these methods and also the main difference in comparison to the other methods. FVA have been used to pinpoint blocked reactions, but it is computationally expensive since it requires solving two optimization problems per reaction , if evidence comes from well-curated biochemical knowledge in that particular context, and a set with moderate likelihood (MC) if evidence comes from context-specific high-throughput data. The algorithm performs the pruning iteratively and randomly by selecting a non-core (CN) reaction to be eliminated, and checking consistency at each step: if HC and a user-defined fraction of MC remain unblocked, MBA removes the reaction out of the model along with MC and CN corresponding blocked reactions. This routine is repeated until no reaction is left in CN. The topology of the final model clearly depends on the order in which non-core reactions are eliminated. Therefore, to remove artifacts due to the order, the algorithm is repeated a number of times  and repeats the LP over the remaining set of reactions. If no reaction is found to be active, FVA is applied to each reaction to determine whether it is blocked. The process is repeated until all reactions have been classified either as blocked or unblocked.MBA divides the core set in two subcores: a set with high likelihood to be present in the context-specific model  production of key metabolites is not impaired and (2) the relation between the number of blocked core and non-core reactions matches a predefined ratio. To check model consistency, mCADRE maintains the procedure proposed in MBA, although adapted to use FastFVA , as missing information on one data set can be complemented by another. Moreover, imposing the whole core set inclusion can be highly advantageous, as reactions with overwhelming evidence would always be included in the context-specific model. Moreover, like the iMAT-like family, MBA-like methods are independent of a RMF and, hence, appropriate to be employed if no RMF is known to operate in a given context. Nevertheless, we would like to emphasize that MBA-like methods provide only a context-specific model reconstruction, in contrast to the iMAT-like methods which generate both a context-specific reconstruction and a flux distribution.MBA-like methods follow two ways to define the core set of reactions: MBA takes into account well-curated biochemical knowledge and a variety of experimental data . While this approach to define the core set of reactions may be more accurate, it is also time-consuming due its manual nature. On the other hand, the definition of the core set in mCADRE allows for full automation, since it relies only on determining a threshold to expression-based evidence.L1-norm to prune non-core reactions renders the pruning step more efficient due to the possibility to remove a once more than one reaction. These modifications make FastCORE the fastest algorithm in this family of methods, as it is able to extract a context-specific model in a computational time two to three orders of magnitude smaller than that expended by mCADRE and MBA . The good time-related performance of FastCORE is due to two main innovations: First, the maximization of the cardinality represents a softer objective than the maximization of the total sum of flux values (used in MBA), since fluxes are only required to be above a small positive value. Consequently, solving this optimization problem usually results in more active reactions per iteration than the MBA counterpart. Second, the computation of the Here we presented a classification of the existing approaches for extracting context-specific metabolic models. We classified the methods into three families according to their mathematical formulation. Furthermore, we also proposed a mathematical generalization for each family, which summarizes the fundamental principles shared by its members.Altogether, the classification and generalization constitutes a mathematical framework that aims to fulfill three main purposes: First, it provides a better understanding of the rationale behind methods, allowing an easy inspection of its main characteristics as well as highlighting the advantages and shortcomings. Second, such structured knowledge may facilitate the envisioning of novel approaches to extract context-specific models. Third, it may help users in choosing a best suited method for their particular problem, since the classification outlines the differences in the data and knowledge requirements as input to the particular methods.3E may depend on the interest to integrate metabolomics data along with transcripts profiles, the computational platform of the current implementations, or the difference in computing time. For instance, the choice is between the COBRA toolbox in Matlab, for GIMME, or its version in Python, for GIM3E (“The OpenCOBRA Project,” 3E.The flow-chart on Figure Without the information about the operability of a particular RMF in a given context, the iMAT-like family may provide the method of choice. To select between iMAT and INIT one could take into account the flexibility on integrating different types of experimental data, since iMAT was developed to integrate transcript profiles, whereas INIT can integrate semi-quantitative proteomic data, transcript profiles and metabolic evidences. In addition, one could consider the possibility of the method to discriminate between multiple optima with same similarity score, together with the computational cost for performing this task.In contrast, if only a context-specific model extraction is required, one may opt for any of the presented method. However, the methods in the MBA-like family have some advantageous properties, namely, the integration of a variety of experimental data sources and the inclusion of reactions for which there is strong experimental evidence in the context-specific reconstruction. One may then choose based on the core set definition of each method as well as on the total computational time required. The MBA-like family proposes two ways to define the core: the MBA semi-automated procedure, whereby reactions are included in the core set if there is sufficient positive evidence across different databases, and the mCADRE automated procedure, whereby reactions are included if the expression value of the respective transcript is larger than a given threshold. Thus, if an appropriate number of databases contain experiments about the context of interest and the computation time is not a primary limitation, the MBA core definition may be a suitable alternative. As previously commented, this procedure can cross-validate the confidence on a reaction to belong to a certain context, due to the simultaneous usage of several databases. Subsequently, one can readily employ MBA to extract the context-specific model, or can opt for FastCORE, which can perform the extraction, using the previously defined core, in a more efficient way. On the other hand, mCADRE could be preferentially applied when an automated core definition is preferred. Moreover, the mCADRE relaxation of whole core inclusion can improve accuracy when a core reaction diminishes the overall coherence with respect to the data, through the inclusion of non-core reactions with negative evidences to ensure consistency. Finally, one can also apply FastCORE to a core set defined in an automated way to benefit of its rapid computation. However, neglecting the characteristic core relaxation and ranking of non-core reactions of mCADRE.Development of new approaches for extraction of context-specific metabolic models can further expand on the advantages of the existing methods, while facilitating efficient computation accounting for the shortcomings. This will allow rapid devising of context-specific models and their interconnection in larger multilevel models, typical for complex eukaryotes, to allow for more realistic simulation scenarios.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.


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


Pichia pastoris has been recognized as an effective host for recombinant protein production. In this work, we combine metabolomics and instationary 13C metabolic flux analysis (INST 13C-MFA) using GC-MS and LC-MS/MS to evaluate the potential impact of the production of a Rhizopus oryzae lipase (Rol) on P. pastoris central carbon metabolism. Higher oxygen uptake and CO2 production rates and slightly reduced biomass yield suggest an increased energy demand for the producing strain. This observation is further confirmed by 13C-based metabolic flux analysis. In particular, the flux through the methanol oxidation pathway and the TCA cycle was increased in the Rol-producing strain compared to the reference strain. Next to changes in the flux distribution, significant variations in intracellular metabolite concentrations were observed. Most notably, the pools of trehalose, which is related to cellular stress response, and xylose, which is linked to methanol assimilation, were significantly increased in the recombinant strain. Pichia pastoris has become one of the most commonly used expression systems for recombinant protein production during recent years ..25]. TheWithin a dataset, expected dynamics are observed: The enrichment dynamics of the intermediates of the lower part of the network (TCA cycle) and the storage carbohydrate trehalose were slower compared to glycolysis and PPP metabolites. The glycolytic intermediates reached isotopic steady states after about 10–15 minutes, which is high compared to the turnover time (data not shown) but a commonly observed delay ,36,37. TBased on the labeling enrichment dynamics and measured metabolite concentrations, metabolic fluxes were estimated .The metabolic network used contained more detail (fluxes and metabolites) than used in our previous study. Nevertheless, comparing the results for the same reactions, the results of the previous study could be reproduced . These d13C flux estimations . In fact, calculation of NADPH biosynthetic demand for both strains was 0.85 ± 0.03 and 0.97 ± 0.07 mmol/gDCW/h for expressing and control strain cells. These values were lower than the total generated NADPH in both cases . However, for both strains no statistically significant difference was observed between the generated NADPH and the demanded for biosynthesis. This could reflect the observation that some Crabtree negative yeast appear to have alternative mechanisms involved in the re-oxidation of the NADPH produced in the PPP, e.g. by mitochondrial external alternative dehydrogenases that use NADPH [No significant differences have been observed in the amount of Glc6P entering the oxidative branch of the PPP: 77% and 69% of the Glc6P, in the control and Rol-expressing strains, respectively. However, the Rol-producing strain showed a slightly reduced biomass yield. Since the PPP is the main pathway for cytosolic NADPH formation, the flux through the oxidative branch of the PPP is generally directly correlated to the biosynthetic demand for NADPH . The prese NADPH . Alterna2 . This trend can be seen in the enrichment of F6P and DHAP, which is higher (resp. less diluted from unlabelled carbon entering from methanol) in the producing strain. The increased methanol direct oxidation has also been observed using steady-state measurements [13C-NMR based MFA approach [The Rol-producing strain shows a tendency for a higher fraction of the assimilated methanol being directly oxidized to COurements . The oriapproach .The flux through the trehalose cycle seems to be altered by Rol production. As it can be seen from In particular, the following distinct traits between the Rol-producing and the reference strain could be identified:TPS2, encoding for trehalose phosphatase, as one of the genes being induced in an IRE- and HAC1-independent manner by ER stress with a likely function in alleviating ER stress in yeast.13C-NMR based MFA approach [The TCA cycle shows a trend towards higher flux for the producing strain. The flux through this part of the network cannot be discriminated statistically, but the trend is in agreement with the increased NADH production (increased oxygen uptake) in the Rol producer, as also observed in our previous study, where such differences were assessed as statistically significant using the approach .13C approach provides additional insights regarding bidirectional reactions. Notably, the high exchange fluxes for oxaloacetate, malate, and Asp, which indicate amino acid pool buffering and the activity of Malate/Aspartate shuttle [As previously reported , the INS shuttle , are sigThe impact of Rol production on the methanol assimilation pathway results in altered behavior of the exchange fluxes in PPP. For instance, the exchange flux of the aldolase reaction was significantly increased in the Rol-producing strain, whereas the exchange flux between DHAP and GA3P was reduced . As statHigher trehalose could confer increased protection under stress conditions derived from the UPR . In thisP. pastoris X-33 (Invitrogen) derived strains were used in this study. Namely, a control strain harboring pGAPAα (Invitrogen) as mock plasmid [Rhizopus oryzae (Rol)- secreting strain, X-33/pPICZAα-ROL [AOX1 genomic locus.Two recombinant  plasmid  and a RhCZAα-ROL , a straiD = 0.09 h−1. The aeration rate was set to 1 vvm, controlled by a mass flow controller . The pO2 was always maintained above 40% ensuring fully aerobic conditions. The O2 and CO2 concentrations in the bioreactor off-gas were measured on-line using a combined paramagnetic/infrared analyzer . The reported values are based on steady-state off-gas measurements before the switch to 13C substrate (13CO2 has different absorption characteristics). Pressure, pH, stirring speed and temperature were controlled at 1.2 bars, pH 5 (titration with 20% v/v NH3), 490 rpm and 25 °C, respectively.Duplicate chemostat cultivations were performed in a 2-L bioreactor  with a working volume of 1 L, using the Sartorious Biostat B+ controller. Culture media, growth conditions were the same as described in our previous study . BrieflyAfter a minimum of five residence times of continuous cultivation, the feed was switched to the labeled medium. The composition of the labeling feed was the same as described by Jordà and co-workers  and the Samples for intracellular metabolite and amino acid concentration measurements were taken one hour before the switch to the labeled feed using a dedicated rapid-sampling setup . Quenchi13C-based metabolic flux analyses was the same used in our preceding baseline study [13C model includes balances for all intracellular metabolites as well as the extracellular substrate. Protein turnover for biomass and product protein was not considered. Nevertheless, large amino acid pools  were added to the model with bidirectional fluxes (synthesis and degradation). Distinct biomass compositions were considered for each strain, based on measurements obtained under analogous growth conditions [The metabolic network used in this study for ne study   minus the number of parameters (34). As a result of the fitting gPROMS provides the determined parameters together with the standard deviations and 95% confidence intervals  of calculated fluxes and mass isotopomers compared to the measured extracellular fluxes and mass isotopomer distributions, weighted by the corresponding experimental variance. The metabolic network model contains 37 metabolite concentrations, required for the dynamic solution, of which a total of 27 were measured  were performed as described earlier ,46. The nditions . In all nditions ,27,50, uThe consistency of the measured intracellular metabolite concentrations for the both strains was verified with a method that is based on the second law of thermodynamics . All thet-distribution with a confidence interval of 0.85.The feasible ranges of the quantified intracellular metabolites were calculated using the respective experimental mean and standard deviation. The lower and upper limits were defined according to a Student’s P. pastoris, as well as pointing at some adaptive physiologic mechanisms to cope with the metabolic burden caused by foreign protein expression. Remarkably, a clear impact of Rol secretion on trehalose levels was observed, also suggesting an increased flux through the corresponding ATP futile cycle. Increased trehalose levels may contribute to avoid death under UPR stress.Combined metabolomic and fluxomic analyses has shed light on the impact of heterologous protein secretion on central carbon metabolism of 13C-MFA methodology yielded coherent results with previous METAFoR-based MFA studies, confirming the impact of Rol overexpression on specific parts of methanol metabolism and TCA cycle, as well as energetic demands. In fact, recent studies suggest that increased ROL copy number could result in increased metabolic burden and stress levels leading to a stronger reduction in biomass and product yields [P. pastoris. Furthermore, the INST-13C-MFA allowed calculating fluxes in a more detailed network—including exchange fluxes in reversible reactions and connected pathways like the trehalose metabolism. Conversely, the use of a larger metabolic network including an increased number of reversible reactions and, therefore, of degrees of freedom, leads to higher uncertainty in the calculated fluxes. Nonetheless, the consistency between independent studies clearly points out that such metabolic flux differences do exist and are not due to experimental variation.Importantly, the INST-t yields . These s13C-MFA methodologies and quantitative metabolomics illustrates how multi-level omic studies can bring new insights on key modules of cell metabolism in relation to recombinant protein production, which should provide a comprehensive basis for future metabolic engineering of P. pastoris for improved recombinant protein production.Overall, the combination of two distinct