Understanding how microbes assemble into communities is a fundamental open issue in biology, relevant to human health, metabolic engineering, and environmental sustainability. A possible mechanism for interactions of microbes is through cross-feeding, i.e., the exchange of small molecules. These metabolic exchanges may allow different microbes to specialize in distinct tasks and evolve division of labor. To systematically explore the space of possible strategies for division of labor, we applied advanced optimization algorithms to computational models of cellular metabolism. Specifically, we searched for communities able to survive under constraints (such as a limited number of reactions) that would not be sustainable by individual species. We found that predicted consortia partition metabolic pathways in ways that would be difficult to identify manually, possibly providing a competitive advantage over individual organisms. In addition to helping understand diversity in natural microbial communities, our approach could assist in the design of synthetic consortia. in silico genome-scale models. In particular, we used mixed-integer linear programming to identify trade-off solutions in communities of Escherichia coli strains. The strategies that we found revealed a large space of opportunities in nuanced and nonintuitive metabolic division of labor, including, for example, splitting the tricarboxylic acid (TCA) cycle into two separate halves. The systematic computation of possible solutions in division of labor for 1-, 2-, and 3-strain consortia resulted in a rich and complex landscape. This landscape displayed a nonlinear boundary, indicating that the loss of an intracellular reaction was not necessarily compensated for by a single imported metabolite. Different regions in this landscape were associated with specific solutions and patterns of exchanged metabolites. Our approach also predicts the existence of regions in this landscape where independent bacteria are viable but are outcompeted by cross-feeding pairs, providing a possible incentive for the rise of division of labor.Microbes face a trade-off between being metabolically independent and relying on neighboring organisms for the supply of some essential metabolites. This balance of conflicting strategies affects microbial community structure and dynamics, with important implications for microbiome research and synthetic ecology. A “gedanken” (thought) experiment to investigate this trade-off would involve monitoring the rise of mutual dependence as the number of metabolic reactions allowed in an organism is increasingly constrained. The expectation is that below a certain number of reactions, no individual organism would be able to grow in isolation and cross-feeding partnerships and division of labor would emerge. We implemented this idealized experiment using IMPORTANCE Understanding how microbes assemble into communities is a fundamental open issue in biology, relevant to human health, metabolic engineering, and environmental sustainability. A possible mechanism for interactions of microbes is through cross-feeding, i.e., the exchange of small molecules. These metabolic exchanges may allow different microbes to specialize in distinct tasks and evolve division of labor. To systematically explore the space of possible strategies for division of labor, we applied advanced optimization algorithms to computational models of cellular metabolism. Specifically, we searched for communities able to survive under constraints (such as a limited number of reactions) that would not be sustainable by individual species. We found that predicted consortia partition metabolic pathways in ways that would be difficult to identify manually, possibly providing a competitive advantage over individual organisms. In addition to helping understand diversity in natural microbial communities, our approach could assist in the design of synthetic consortia. Escherichia coli that evolved on minimal glucose medium have been observed to give rise to a specialized subpopulation of cells that use the acetate secreted as a by-product of glucose fermentation  of artificial microbial consortia specifically designed to display obligate mutualism. Current approaches to building synthetic communities of interacting microbes have so far mainly relied on intuition about simple genetic perturbations that would cause organisms to engage in obligate cross-feeding. In these interactions, one strain is unable to synthesize an essential metabolite  that is supplied via overproduction or leakage by another strain –43. This–in vivo, computational models can provide a preliminary assessment of the landscape of possible strategies and of how these strategies depend on different constraints on metabolic network complexity. Constraint-based models of metabolic networks, such as flux balance analysis (FBA)  may enais (FBA) –58, can ) –27–49–, 59–63, division of labor in metabolic networks” (DOLMN). In particular, using DOLMN, we explore the space of feasible single-strain or multistrain metabolic networks by systematically limiting the number of intracellular and transport reactions in each metabolic model. After introducing the mathematical and integer linear programming formulation of DOLMN, we illustrate its capabilities through an analysis of division of labor based on core carbon metabolism in E. coli  We expect each strain’s subnetwork to represent a well-connected, fully functional metabolism, so as to be capable of producing that strain’s biomass . (iii) Upon simulation of cocultures of multiple coexisting strains, we require that all such strains must have equal growth rates, so that they would be able to stably coexist in a chemostat  into subnetworks representing individual organisms  , which is formulated as a combinatorial optimization problem. Inputs of DOLMN consist of the global network ; the number of target strains (K); and constraints on the number of intracellular (TIN) and transport (TTR) reactions allowed in each strain. Key outputs of DOLMN consist of a binary reaction vector (t) whose elements indicate whether a given reaction is present in a given strain and a continuous flux vector (x) for all reaction rates. Note that there is no specific requirement for two or more strains to end up using different reactions from the global network. A specific solution could entail multiple strains having exactly the same reactions and yet not interacting with each other. We expect division of labor to arise only upon making the TIN or TTR value too small for any individual strain to be able to survive without receiving specific molecular components from a metabolically distinct partner . Our problem is NP  complete. It can be solved exactly for core metabolic network models , but it requires heuristics and long computational times for genome-scale models . Despite the use of the heuristic speed-up methods, we still obtain a single optimal solution for each value of TTR, TIN, and K.DOLMN, described in detail in Materials and Methods, involves the use of E. coli core carbon metabolism (E. coli core network) for a given limit on the number of allowed reactions .As a first test and illustrative example of DOLMN, we investigated how tabolism  on minimhemostat , 64, 65.x  into 2-oxoglutarate and generating NADPH. Meanwhile, strain x generates oxaloacetate, NADH, and ATP through the transformation of 2-oxoglutarate in the second part of the TCA cycle.An interesting outcome of this analysis, obtained for subnetworks containing no more than 11 transport reactions and 26 intracellular reactions, was the discovery of a metabolic strategy in which each of two strains performs half of the tricarboxylic acid (TCA) cycle . Both stx , orange x . The excess 2-oxoglutarate is utilized by strain y for biomass as well as for the production of pyruvate. Pyruvate, in turn, is converted to biomass, and its excess is utilized by strain x.Neither of the strains, in this case, was able to perform all needed metabolic functions without the inflow of specific metabolites produced by the partner. In particular, exchange of 2-oxoglutarate and pyruvate was necessary for survival of this 2-strain consortium . Strain This example illustrates how, even for a relatively small network, DOLMN can provide putative division of labor strategies that could not be easily designed manually. DOLMN could be similarly applied to other core metabolic models  such as E. coli metabolism , individual strains reach a limit beyond which they cannot sustain growth, whereas consortia of two and three strains are still viable. In the example analyzed in To display how growth rates vary as a function of 10.1128/mSystems.00263-18.1FIG S1TTR,TIN) landscapes of 3-strain subnetworks. The gray region depicts the infeasible region in which strain subnetworks cannot grow because there are not enough transport reactions to take up and secrete metabolites. Strain subnetworks were required to maintain a biomass flux of at least 0.1 h−1. Each data point represents a single simulation. (a) Growth landscape of 3-strain subnetworks. (b and c) Growth landscape of the differences in growth rates between 3- and 1-strain subnetworks (b) and the differences in growth rates between 3- and 2-strain subnetworks (c), where the constraints under which 3-strain subnetworks grew faster than 1-strain (b) or 2-strain (c) subnetworks are indicated. Only constraints under which 1- and 3-strain subnetworks (b) or 2- and 3-strain subnetworks (c) can both grow are included. (d) Metabolic distance landscape of 3-strain subnetworks, averaged over the distances between strains A and B, A and C, and B and C. Strains that are more metabolically differentiated (have fewer reactions in common) are represented by a greater distance. (e and f) The growth rates of 3-strain communities compared to 1-strain (e) and 2-strain (f) communities. Gray circles represent constraints where 1-strain (e) or 2-strain (f) communities grew faster than 3-strain communities, and the colored circles represent constraints where 3-strain communities grew faster than 1-strain (e) or 2-strain (f) communities. (g) The number of metabolites exchanged between strains in 3-strain subnetwork simulations. Download FIG S1, TIF file, 1.8 MB. as a function of the number of strains (K). (b) Number of intracellular reactions in common between 2 strains (orange) and 3 strains (purple) at their minimum TIN. (c) Transport reactions kept when the number of transport reactions allowed was 9. Download FIG S2, TIF file, 1.9 MB.(a) Minimum number of intracellular reactions needed for growth  and minimizing TTR (metabolic exchange). This nonlinearity implies that removing the same number of transport reactions at different points along the frontier of the feasible region can be compensated for by adding different numbers of intracellular reactions. For example, decreasing TTR by 2 at large TTR values can be compensated for by adding a single intracellular reaction (increasing TIN by 1), while removing the same number of transport reactions at small TTR would require a much larger compensation with intracellular reactions . Irrespective of the number of strains in the community, it appears that the E. coli strain subnetworks require at least 9 transport reactions in order to support growth, corresponding to the main elemental sources and other irreducible biomass requirements; this strict bound is illustrated with a gray, shaded region in the  landscape  landscape can be obtained by plotting the metabolic distance  between the subnetworks of the strains  and 11 (b). The number of exchanged metabolites increases as the Jaccard distance increases for 2-strain (c) and 3-strain (d) communities. (e) Phi coefficient of Jaccard distance or (f) point-biserial correlation of Euclidean distance and metabolite exchange profiles of 2-strain subnetwork simulations are indicated. Positive values indicate that a metabolite is exchanged when pathways are metabolically differentiated, and negative values indicate that a metabolite is not exchanged when pathways are metabolically differentiated. Download FIG S3, TIF file, 2.9 MB.(a and b) Jaccard distance between 2-strain subnetwork reaction binary vectors (a) and the Euclidean distance between 2-strain subnetwork fluxes (b) as a function of Copyright © 2019 Thommes et al.2019Thommes et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the TIN because they distribute metabolic reactions and exchange metabolites , all strains (for 1-strain and 2-strain simulations) use the same metabolic strategy for core energetic requirements. In particular, they display similar uses of the TCA cycle , the 2-strain subnetworks move away from each other, indicating that they diversify into different metabolic strategies. Note that the specific path that is followed by these networks as TIN decreases is also a function of TTR  . Clusters in the principal-component space would indicate common metabolic strategies, hardly detectable through visual inspection of the network themselves; paths between these clusters would additionally portray how the strain subnetworks move through this metabolic space as constraints become more stringent. We observed three clusters, indicating three major metabolic strategies . The larCA cycle  and of oCA cycle . These me medium , 58, 67.n of TTR .10.1128/mSystems.00263-18.4FIG S4x  and strain y  in 2-strain subnetworks at the indicated TTR. The color of the marker indicates if the point represents a large TIN (red) or small TIN (purple). Download FIG S4, TIF file, 1.7 MB.Principal-component analysis. Each subplot shows the PCA plot for strain Copyright © 2019 Thommes et al.2019Thommes et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the TTR,TIN) landscape . A striking outcome of this metabolic distance analysis was the fact that, for a broad range of TTR values , the 2-strain subnetworks had a large difference in their TCA cycle  landscapes of metabolic differentiation by pathway. Data represent the Jaccard distance between the reaction binary vectors (t) of each pathway in 2-strain subnetwork simulations. Strains that are more metabolically differentiated (have fewer reactions in common) have a greater distance. Download FIG S5, TIF file, 2.9 MB.Jaccard  Euclidean landscapes of metabolic differentiation by pathway. Euclidean distance between flux vectors (x) of each pathway in 2-strain subnetwork simulations. Strains that are more metabolically differentiated have a greater distance. Download FIG S6, TIF file, 2.9 MB. landscape to track how constraints affect the metabolites being exchanged (l-glutamate below the TIN boundary for 1-strain communities). Notably, succinate is shown to be exchanged predominantly at the TIN boundary of 2-strain communities  landscape where 1-strain communities are infeasible. As shown above, what makes these consortia viable  is the possibility of metabolite exchange between the 2-strain communities.Consortia of obligate symbiotic partners are predicted to emerge in regions of the  landscape. In the specific setup used for the in silico experiments, among a total of 143 extracellular metabolites, only 37 (25.9%) metabolites were exchanged in at least one simulation of 2-strain communities. Most (78.4%) of these exchanged metabolites were exchanged in at least 10% of all coculture simulations  landscape], making the use of existing algorithms challenging. We thus applied the Spearman correlation to exchange reaction fluxes , as an indicator of fundamental metabolic trade-offs (X can provide A only if Y provides B), or as a broad suggestion of the existence of unavoidable couplings in the interactions present in a microbial community. Similar analyses of coupling between fluxes, e.g., through linear optimization –71, elem–n fluxes  in order and TIN , we also and TIN , obtaini and TIN  to the o strains .10.1128/mSystems.00263-18.9FIG S9FIG S9, TIF file, 2.4 MB.(a) Pearson correlation and (b) Bayesian flux covariance of exchanged metabolites in 2-strain communities, clustered as described for Copyright © 2019 Thommes et al.2019Thommes et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the l-arginine, l-histidine, l-threonine, and uridine, which are all correlated with each other, whereas the second set includes acetate, l-alanine, l-isoleucine, l-leucine, l-tryptophan, l-proline, ornithine, and l-serine. Interestingly, these anticorrelated block sets do not seem to map trivially to different precursor pathways , suggesting that other metabolic trade-offs may determine these patterns. One can also observe a second block structure dominated by amino acids that are all correlated, containing d-alanine, l-lysine, l-asparagine, l-phenylalanine, l-tyrosine, pyruvate, and—to a lesser extent—fumarate, 2-oxoglutarate, putrescine, and l-valine.Two major patterns emerged from this analysis. First, by looking at the hierarchically clustered correlation matrix, one can immediately recognize several block structures. The largest block structure seems dominated by amino acid exchange. In particular, two sets of (mostly) amino acids seem to be highly correlated within each set but to be highly anticorrelated across the sets. The first set includes TTR,TIN) landscape where succinate is exchanged matches very closely with the region in which the 2-strain communities show very distinct forms of use of the TCA cycle , indicating reciprocal exchange. These two metabolites are intermediates of the TCA cycle and are involved in sequential steps, suggesting that this anticorrelation corresponds to the metabolic division of labor strategy characterized by splitting of the TCA cycle . This isCA cycle  and e anCA cycle e and f.in silico experiments on the full E. coli network, across 1-, 2-, and 3-strain communities, under conditions of multiple constraints on the number of transport and intracellular reactions. For each organism’s model, we take into account large numbers of variables . Efficient algorithms therefore represent a key step toward exploring possible strategies for division of labor in synthetic microbial communities and toward understanding how metabolic specialization may arise in natural microbial consortia.Although this study was purely computational, the data provide a new conceptual framework and new predictions, including specific testable modifications, and enable us to perform analyses that are currently beyond current experimental capabilities. The phenotypic space that we explore involves 5,000 The spontaneous emergence of division of labor in natural microbial systems is still a poorly understood process. One possible mechanism for this type of interdependence is the Black Queen hypothesis, on the basis of which division of labor could arise in complex microbial communities through the loss, instead of the gain, of functions that can be performed by “leaky” partners , 47. OurOur results may be relevant for microbial ecology of natural communities, as well as for the study of synthetic microbial consortia. Ongoing efforts in synthetic ecology are mostly focused on engineering metabolic dependencies by making one strain unable to produce a terminal biomass precursor  which is then provided by another strain. Although this strategy has yielded new insight into how microbes interact within communities, it may not reflect the possible complexity of natural metabolic interactions. Our approach has the capacity to uncover a much broader set of potential opportunities for obligate cross-feeding, including the exchange of metabolites that are part of core metabolic processes, or “deep symbiosis” between organisms.E. coli under anaerobic conditions . Consequently, there is evidence that some of the strategies representing the division of labor identified by our approach are similar to the pathway configurations of existing consortia.Interestingly, the TCA cycle splitting that we observed in the model predictions occurred at the metabolites 2-oxoglutarate and oxaloacetate, both of which are used to create various amino acids. 2-Oxoglutarate is used to produce the amino acids glutamate, glutamine, proline, and arginine, whereas the amino acids aspartate, asparagine, methionine, threonine, isoleucine, and lysine can be produced from oxaloacetate. The biological significance of a split TCA cycle is also manifested in the patterns of secretion and uptake reported in the literature. In particular, both 2-oxoglutarate and pyruvate (the two exchanged metabolites) have known transporters in E. coli , 86. TheE. coli –89, indibacteria  and in “regatum” , a photoOur predictions were initially produced under the assumption that the different perturbations applied by our method correspond to genetic modifications. However, they could equally be interpreted as being a consequence of instances of gene downregulation instead of gene loss . In othe90–E. coli may prove challenging due to the multiplicity of gene deletions that would have to be simultaneously performed, although conceptually driven complex redesign of metabolic networks has been successfully implemented experimentally before  and laborious generation of modified strains, it is important that instances of division of labor similar to what we predicted may be found from further scrutiny of known symbiotic relationships , 101 andS denote the stoichiometric matrix of dimensions m × n, where m is the number of metabolites and n is the number of metabolic fluxes. Metabolic fluxes are defined as vector x, where xlb and xub are the lower and upper bounds, respectively, of the metabolic fluxes. These bounds are implied by empirical evidence of irreversibility or by nutrient availability in the growth medium. The cellular objective is expressed as a vector of weight coefficients for each reaction , denoted by c, and the optimal objective value is a scalar value corresponding to Zopt. The FBA problem is formulated as follows:0 is the vector of all zeroes and the prime indicates transposition.To mathematically formulate FBA, let S, which expresses the stoichiometric coefficients of all metabolic reactions in the community irrespective of the organism they belong to, as previously described  from the environment is encoded in the extracellular reactions, and intracellular reactions encode each organism’s metabolism. Organisms use transport reactions to move metabolites between their intracellular compartment, which is unique to each organism in the community, and the extracellular environment, which is shared by all organisms in the community.In order to perform FBA capturing all reactions spanning an entire microbial community, we introduce a “universal stoichiometric matrix,” also denoted by escribed . Specifi10.1128/mSystems.00263-18.10FIG S10S. Block Se represents the set of extracellular reactions used to take up nutrients from or secrete nutrients into the environment. Blocks St1 and St2 represent the set of transport reactions between extracellular and intracellular metabolites. Block Si represents the set of intracellular reactions among intracellular metabolites. (b) The structure of the stoichiometric matrix for the whole-community t. Download FIG S10, TIF file, 0.8 MB.The structure of the stoichiometric matrices. (a) Structure of universal stoichiometric matrix Copyright © 2019 Thommes et al.2019Thommes et al.Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the S to construct putative stoichiometric matrices for each species in the community. In particular, we construct a community stoichiometric matrix Sc, whose structure is shown in Se, St1, St2, and Si in Sc are consistent with those in S. Organisms in the community share the same nutrients and extracellular reactions. Because there are K organisms in the community, we replicate the block  that includes transport reactions and intracellular reactions K times and diagonally arrange them in Sc. Similar compositions of stoichiometric matrices had used in previous work on community-level flux balance modeling . Notice that Sc has 1 block column for extracellular reactions (Ne columns) and K block columns (of dimension Nt + Ni), one for each organism, including all transport and intracellular reactions.After the intracellular metabolites are obtained via the transport reactions, intracellular reactions take place inside each organism. This construction leads to the community stoichiometric matrix t = , where j = 1,…, Nc is a binary variable, indicating whether the j-th reaction is included in the corresponding organism  denotes a diagonal matrix whose main diagonal consists of the elements of vector x, R is a regularization matrix, and tmin and tmax are appropriately defined constant vectors. Specifically, by appropriately defining R, tmin, and tmax, we can impose constraints on the number of internal and transport reactions for each organism.The problem of identifying K organisms. The upper bounds on the number of active transport reactions and intracellular reactions in each organism are TTR and TIN, respectively. We let k = 1,…, K. We also let kTR and kIN denote the index sets of the transport reactions and intracellular reactions for each organism k, respectively. For example, suppose for organism k the transport reactions have indices 4 and 6 and the internal reactions have indices 2, 5, and 9. Then, kTR = {4,6} and Nc} for the community. The MILP (as shown in problem 2) takes the following form:x*,t* denote an optimal solution of the MILP problem above.Suppose there are E. coli core models can be done relatively quickly (on the order of minutes or hours). On the other hand, solving the problem for a community model of two iJR904 E. coli models is very time-consuming. We employ certain methods to speed up finding an optimal solution. One method leverages the fact that instances with similar values for TTR and TIN have similar sets of active reactions. Specifically, as we decrease the values of TTR and TIN, we use the sets of active reactions corresponding to larger TTR and TIN values to generate feasible solutions that are offered as putative solutions to the MILP solver. This tends to drastically decrease solution times. A complementary approach uses a decomposition idea. In particular, for solving problems involving a community of K organisms, we can use solutions for K − 1 organisms and append solutions for the additional organism. This generates feasible solutions, and it is possible to search for an effective feasible solution by varying the way the K-organism community is decomposed into a (K − 1)-organism community and an additional organism.We note that solving such a large-scale MILP problem, which involves hundreds or thousands of integer variables, is computationally expensive. Our experiments suggest that solving problem 3 for a community of two t* of the first-stage problem (problem 3) and where the biomass fluxes are also set to the optimal values obtained by the first-stage problem (problem 3). Specifically, we use the following equations:In order to reduce levels of redundant fluxes in transport and intracellular reactions, a second optimization problem is introduced where the integer variables are fixed to the optimal solution 1 norm of the flux vector (excluding exchange reactions) to induce sparsity and can be rewritten as a linear programming problem.This problem minimizes the ℓTTR, DOLMN outputs a structure, C (“model”), for each strain. This structure C contains fields to indicate the constraint on the number of intracellular reactions, TIN (“model.sparse_con”); the reaction names in the global network (“model.rxns”); the growth rates at each TIN (“model.biomass”); the reaction flux values at each TIN (“model.flux”); and the reaction binary integer values at each TIN (“model.int”). For each value of TIN, TTR, and K, only a single simulation was performed.For each constraint on the number of transport reactions, E. coli model. The scripts dolmn1a_parse_iJR904.m and dolmn1b_parse_core.m apply the function algorithm2models to all of the DOLMN outputs for the full and core iJR904 E. coli models, respectively. The function algorithm2models parses C into individual metabolic models, calculates the exchange flux of each individual strain (instead of the community exchange flux), and identifies exchanged metabolites. The scripts dolmn2a_summary_iJR904.m and dolmn2b_summary_core.m restructure the data for plotting, calculate the Jaccard distance and exchange flux correlations, and perform standard PCA (MATLAB function pca). Interpolations for the constraint landscapes are performed in dolmn2a_summaryInterp_iJR904.m and dolmn2b_summaryInterp_core.m. The only exception is the flux coupling analysis, which is performed separately. All main text figures were plotted using dolmn3_figures_main.m, and all supplementary figures were plotted using dolmn4_figures_supp.m.The analysis of the DOLMN output is performed in several MATLAB scripts. All analyses are split between the core and full iJR904 https://github.com/segrelab/dolmn). Analysis was performed with MATLAB 2017b. MILP problems were solved by the use of Gurobi 7.0 , functions, and scripts can be found in the GitHub repository  is the portion of the stoichiometric matrix for extracellular metabolites and transport reactions  is typically represented by exchange reactions. However, in community flux balance analysis, organisms share exchange reactions . In ordeions see .pdist2 was used to calculate Jaccard and Euclidean distances with the “jaccard” and “euclidean” metrics, respectively.Two metrics were used to measure metabolic differentiation based on intracellular reactions. Jaccard distance measures differences in reaction content and quantifies diversification at the level of network topology. In contrast, Euclidean distance evaluates differences in the magnitude and direction of reaction fluxes and therefore illustrates how the network topology is being utilized differently between strains. Both Jaccard and Euclidean distance metrics were used because, at the extreme, strains could have kept the same reactions (could have a zero Jaccard distance) but could have used the reactions differently (could have a nonzero Euclidean distance), as shown in identifyExchangedMets to determine which metabolites, if any, are exchanged between strains.Metabolites are exchanged if one strain secretes the metabolite (has a positive exchange flux) and the other takes it up (has a negative exchange flux). Metabolites that were part of the medium  were not considered to be exchanged even if one strain secreted the metabolite and the other took it up. We created the MATLAB function pca. The biomass flux was excluded from the intracellular reactions and was instead used to normalize the intracellular flux values.Principal-component analysis (PCA) was performed on the intracellular flux values of 1- and 2-strains using the built-in MATLAB function corr was used to calculate the Spearman and Pearson correlations of exchange reaction fluxes, normalized by biomass flux, providing information on how metabolites are exchanged together. The Spearman correlation of exchange reaction fluxes was hierarchically clustered by the inner squared Euclidean distance (Ward’s method) using the MATLAB functions linkage and dendrogram.The MATLAB function bfba, which evaluates reaction fluxes as distributions instead of a single value. We sampled FBA solutions with 200 samples of 5 independent Markov chain Monte Carlo methods for a total of 1,000 flux vector samples, which represent all possible flux configurations compatible under the given constraints of the use of minimal glucose medium. We used thinning and accepted only every 1,000th flux sample to reduce the correlation of successive Markov chain Monte Carlo samples. Solutions were obtained with Gurobi .All data generated and analyzed in this study and the corresponding codes are available in the GitHub repository (


Genome-scale metabolic network reconstructions are low level chemical representations of biological organisms. These models allow the system-level investigation of metabolic phenotypes using a variety of computational approaches. The link between a metabolic network model and an organisms’ higher-level behaviour is usually found using a constraint-based analysis approach, such as FBA . However, the process of model reconstruction rarely proceeds without error. Often, considerable parts of a model cannot carry flux under any condition. This is termed model inconsistency and is caused by faulty topology and/or stoichiometry of the underlying reconstructed network. While there exist several automated gap-filling tools that may solve some of the inconsistencies, much of the work still needs to be carried out manually. The common “linear list” format of writing biochemical reactions makes it difficult to intuit what is at the root of the inconsistent behaviour. Unfortunately, we have frequently observed that model builders do not correct their models past the abilities of automated tools, leaving many widely used models significantly inconsistent.ModelExplorer, which main purpose is to fill this gap by providing an intuitive and visual framework that allows the user to explore and correct inconsistencies in genome-scale metabolic models. The software will automatically visualize metabolic networks as graphs with distinct separation and delineation of cellular compartments. ModelExplorer highlights reactions and species that are unable to carry flux (blocked), with several different consistency checking modes available. Our software also allows the automatic identification of neighbours and production pathways of any species or reaction. Additionally, the user may focus on any chosen inconsistent part of the model on its own. This facilitates a rapid and visual identification of reactions and species responsible for model inconsistencies. Finally, ModelExplorer lets the user freely edit, add or delete model elements, allowing straight-forward correction of discovered issues.We have developed the software Overall, ModelExplorer is currently the fastest real-time metabolic network visualization program available. It implements several consistency checking algorithms, which in combination with its set of tracking tools, gives an efficient and systematic model-correction process.The online version of this article (10.1186/s12859-019-2615-x) contains supplementary material, which is available to authorized users. Genome-scale metabolic reconstructions have become a standard approach for the computational investigation of living organisms’ phenotypes , bridginIn order to predict the growth rate of an organism from a genome-scale metabolic reconstruction, one usually applies a constraint-based modeling method such as Flux Balance Analysis (FBA). The FBA approach is based on a steady-state approximation of cellular growth. In FBA, an empirically acquired biomass function is optimized while the metabolic reconstructed network is subject to constraints on nutrient uptake reactions. Additional information may be included in the model either to further constrain it, as exemplified by the MOMENT method , or to eThe draft of a high-quality genome-scale metabolic reconstruction is often created with automated tools, such as the SEED , or the E. coli model they were addressing could not be fixed using their algorithms, while for S. cerevisiae this number was 58%. This is a significant issue that must be fully acknowledged and appreciated. Existing tools are quite simply not enough. The problem is further complicated by the fact that model building and gap-filling tools may use the same metabolic reaction repositories, rendering gap-filling useless.The first-line tools in identifying and fixing the cause or causes for model inconsistencies are automatic gap-filling algorithms. These can either address all blocked reactions at once  or firstWhen automatic tools fail, it is currently necessary to manually identify the cause, or often multiple causes, for the deficits. This is a tedious process, complicated by the linear list format of metabolic models. While it is quite straightforward to identify lists of blocked reactions, using e.g. existing functions in the COBRA toolbox  or in COThe main purpose of ModelExplorer is to aid the user in correcting inconsistencies that cannot be addressed with automatic algorithms. The software provides a visual interface and multiple analysis modes to facilitate the identification of blocked reactions and in searching for and correcting the source of their inactivity. Based on our hands-on experience with manual curation of more than 10 genome-scale metabolic models, we have found that when significant parts of the metabolic network are shown to be inconsistent , the inconsistency can often be corrected by adding or modifying one, or very few (thus key) reactions in the network. Similarly, we identified the need for a visual workflow for model curation in order to speed up the process of fixing the large number of reactions that are not automatically corrected by current software. With ModelExplorer, the user can get an intuitive overview over every blocked part of the model, allowing the user to identify and fix key reactions which need to be corrected without leaving the software, as well as quickly identifying related, broken parts of the metabolic network.ModelExplorer has been developed as a stand-alone graphical application under Linux Additional file ModelExplorer allows the visualization of a metabolic reconstructed networks as bipartite graphs: Metabolites and reactions are represented by nodes, and links (shown as arrows) only connect metabolites to reactions and vice versa. The arrows may be unidirectional or bidirectional, depending on the encoded reaction reversibility in the metabolic reconstruction. Metabolites and reactions are automatically grouped by their compartment, as specified in the reconstruction. The compartment grouping is visualized and may be highlighted.The network layout is calculated using a force-directed algorithm, as we found this to give the most aesthetically pleasing results. In the Network View  blocked if it is unable to carry a (FBA) steady state flux. A metabolite is shown as blocked if all reactions that can generate it are blocked. In order to reduce the time it takes to perform consistency checking in FBA mode, we have developed a radically improved version of the FastCC algorithm , which wThe FBA mode is useful to identify which parts of a model may be removed without affecting the results of any FBA simulation. Restoring the consistency of these reactions may improve the model’s resilience against knock-outs. Using this mode we consistency-checked 13 models from the OpenCOBRA model repository used by Ebrahim et al.   blocked if it will block the biomass (growth) reaction when added to the list of its reactants. A reaction is then determined to be blocked if any of its reactants are blocked. The dynamic mode is useful in the process of assessing the fidelity of a draft reconstruction, since it allows us to identify which existing metabolites may potentially be part of the biomass reaction without blocking it. It is the only mode that will show valid results when the user has not yet added a biomass function or any export reactions to the model, as the dynamic mode can solely rely on imports. This mode also adds a higher level of realism compared to the FBA mode, since it shows if the reconstructed network can support a constant concentration of a metabolite during exponential growth. Unfortunately, this topic is usually overlooked as exponential growth cannot be directly addressed using the steady state approximation of FBA. The Dynamic mode is the fastest to compute among the three modes, and it always needs only one round of optimization. The details of the algorithm will be published elsewhere .If the user wants to know whether a specific reactions is blocked, ModelExplorer makes it is possible to directly look up reactions and metabolites by their name through the search function and highlights them on the network view Fig.  panel a.When blocked reactions and metabolites are identified, the user is presented with four tracking tools for determining the source of error (accessed through the “Neighbour view” menu).The first option, called “None,” does not highlight anything except the node itself. However, in this mode one may edit existing species, reactions and compartments by clicking on them. By using the Text Panel, it is possible to change their properties.The second option, called “Ego-centric,” highlights the selected node’s direct neighbours and can be used for brute force exploration of blocked nodes. For instance, it makes it easy to distinguish reactants from products, as well as to asses which reactions produce and consume a metabolite.The third option, called “Node ancestry,” is more intricate. Here, ModelExplorer will highlight the smallest subset of the network necessary to synthesize a species or activate a reaction in question, given that a non-cyclic solution exists. One such path is highlighted by ModelExplorer in Fig. separately from the rest of the network. This is done through the View menu. The layout algorithm is then run only on the blocked module, and the module is plotted on its own. This makes it much easier to visually identify the source of the inconsistency, as crowding in the visual display of the network is very much reduced. Model editing and tracking can be done on the module in the same way as on the whole model, with all changes being applied to the model itself.The fourth option is called “Blocked Module” and highlights unconnected modules, as described by Ponce-de-Leon et al. . Each moen masse node purging functions. These tools may be useful if, for instance, a reconstructed network has boundary (or extracellular) metabolites instead of import reactions. In that case, ModelExplorer can purge such species, allowing reactions consuming these metabolites to become import reactions.ModelExplorer allows the user to interactively edit, add and delete any species, reaction or compartment in the model. It can even be used to build models from scratch by hand. Editing can be performed on any object with the “None” tracking tool option activated, by right-clicking the object and then altering its properties in the Text Panel. Adding and deleting objects is done through the “Add” and “Purge” menus. In addition to deleting objects one by one, ModelExplorer provides the user with several We have observed many publicly available reconstructed networks to consist of multiple disconnected graphs, where all graphs, except the one containing the biomass, obviously are useless from a modelling perspective. If it would be of interest to remove these, ModelExplorer includes a function to purge disconnected clusters. This function can also be useful after a purge of boundary or extracellular metabolites that may leave behind rudimentary, disconnected reactions. The user also has the choice to only purge species and reactions which are unconnected to any other species or reaction, since we have observed some models to contain unused metabolites in the hundreds.To our knowledge, there are at least five other packages that address the issue of visualization of metabolic networks: MetDraw , Escher MetDraw is also based on Graphviz. However, it does not provide an interactive network view since it will only output still images. Escher and MetExploreViz, are interactive web-applications centered around pathway visualization. These tools draw networks disentangled into pathways, for which human input is necessary since the way one divides a network into pathways is strictly subjective. This approach means that side-metabolites appear plotted multiple times, which could complicate deciphering inconsistencies and tracking ancestry, if such options were to be implemented.Cytoscape and Gephi on the other hand, are generalist network visualization tools. Cytoscape can use the cy3sbml plugin to import, layout and view SBML files, while Gephi accepts only standard graph formats such as “dot”, requiring a prior conversion from SBML into one of these formats. Both of the tools can make layouts similar to that of ModelExplorer, but lack any other functionality, as mentioned above.This highlights a principal difference between comparable existing software and ModelExplorer: Escher, MetExploreViz, Cytoscape and Gephi are mainly designed for network visualization of finished models, whereas ModelExplorer is designed for consistency checking and correction of metabolic models at any stage of construction and refinement. This, however, does not mean that ModelExplorer is inferior at visualization. It is in fact the opposite in terms of speed. Visualization speed can be measured in terms of the frame rate, which is the number of times the image could change per second. A low frame rate slows down the navigation around the network and can be very annoying to the user. In order to conduct a reasonable a side-by-side comparison of these very different visualization tools , we tested the frame rates when visualizing the iTO977 model using a DELL laptop with an Intel Core i5-5300U CPU ∙modelEpxlorerLibs and extraLibs - Folders with libraries (COIN-OR Clp and Graphviz)∙install.sh - a Linux installation script∙arial.ttf - Font file∙test.xml - Test model (iTO977)∙ModelExplorer_User_Manual.pdf - User manual that contains information about software installation procedures, usage and licence.∙LICENSE.txt - A license notice. ∙Additional file 2ModelExplorer - Windows binary file (ModelExplorer v1.0 executable)∙∙ A set of library files - (COIN-OR Clp and Graphviz)arial.ttf - Font file∙test.xml - Test model (iTO977)∙ModelExplorer_User_Manual.pdf - User manual that contains information about software installation procedures, usage and licence.∙LICENSE.txt - A license notice. (ZIP 4801 kb)∙


Biology is turning from an analytical into a synthetic discipline. This is especially apparent in the field of metabolic engineering, where the concept of synthetic metabolism has been recently developed. Compared to classical metabolic engineering efforts, synthetic metabolism aims at creating novel metabolic networks in a rational fashion from bottom-up. However, while the theoretical design of synthetic metabolic networks has made tremendous progress, the actual realization of such synthetic pathways is still lacking behind. This is mostly because of our limitations in enzyme discovery and engineering to provide the parts required to build synthetic metabolism. Here I discuss the current challenges and limitations in synthetic metabolic engineering and elucidate how modern day enzymology can help to build a synthetic metabolism of the future. One of the most important and disruptive events in the history of chemistry was its transformation from a purely analytical-descriptive into a synthetic-constructive discipline, which took place more than one hundred years ago –2. UnderEscherichia coli cell [A fundamental feature of living systems is metabolism, which can be defined as the dynamic chemistry that allows life to organize itself in three and four dimensions . The incoli cell –8, as weoli cell . This diIn the past, many efforts centered on manipulating the metabolism of cells to obtain a target molecule. Most of these approaches were based on the concept of metabolic engineering . AccordiClassical metabolic engineering efforts, however, are limited in a way that they are still bound to existing pathways and reactions, which limit the accessibility of certain compounds, as well as the efficiency with which those compounds can be produced. In an ideal world, the way a target molecule is produced should not be dictated by the serendipity and constraints of evolution, but be accessible through rational design. However, this requires a fundamental understanding of those principles that are necessary for designing, realizing and operating multi-reaction sequences and metabolic networks de novo.Recently, the concept of “synthetic metabolism” was developed that aims at overcoming the limitations provided by natural metabolism through the realization of completely novel metabolic networks –12. The 2 into organic acids were developed recently [2-fixation cycles should be able to convert more carbon dioxide with less energy in a given time and hence succeed natural photosynthesis in volumetric capacity and energetic efficiency. One of these designs, the so-called CETCH cycle  from a total of nine different organisms from all three domains of life [As an example, several novel level 3 and level 4 pathways for the conversion of COrecently –14. ThesCH cycle , a synth of life . Compare of life .In a similar fashion, multiple level 3 and level 4 routes for the transformation of the one-carbon compound formate into cellular building blocks were designed that should theoretically outcompete natural formate assimilation pathways –19. SomeYet, while an increasing number of theoretical designs are proposed, the successful experimental realization of many of these designs in the lab is still falling short. This is especially true for pathways of design levels 4 and 5 that feature novel reactions, for which the corresponding enzymes are unknown . The realization of these pathways is severely restricted by our limited ability to discover and/or engineer new-to-nature enzymes. Notable exceptions are the formolase pathway and CETCH cycle that required each the establishment of three novel enzymatic reactions for their successful realization. However, other level 4 pathway designs require the establishment of more than ten so-far unknown enzyme reactions, emphasizing the challenge to realize truly synthetic metabolic networks .From above examples it becomes evident that for building completely novel pathways and/or complex reaction cascades, resources are required that provide synthetic biologists with the information to find individual enzymes for a given synthetic metabolic network. More than 116 million proteins were deposited into protein sequence databases, such as UniProtKB . More thWhile existing databases might provide a good resource to find the parts to reconstruct level 3 pathways, this task becomes more challenging in respect to level 4 and level 5 designs that require new-to-nature reactions. How can these new enzyme reactions be identified or established? One option is the de novo-design of enzymes assisted by computational methods, which have been developed over the last couple of years. When combined with experimental evolution and elaborate screening methods, these efforts have allowed to establish completely novel enzyme reactions from scratch –34.However, even though considerable progress has been made in creating enzymes with the help of computational methods , it is a2, but are still found very often misannotated as their CO2 fixing homologs RubisCO, with which they share a common evolutionary history [These efforts in exploiting the promiscuity of enzymes to create novel catalysts might profit from new computational methods that succeeded in creating active sites of remarkable promiscuous activities in the scaffold of existing enzymes . Such co history .A solution to overcome the problem of misannotation might come from novel computational tools that were developed recently to analyze the diversity of enzyme (super)families in respect to new functions –55. WhilAnother problem is that even in databases that list the experimentally confirmed activity of enzymes, an important aspect is very often not well documented: substrate (and reaction) promiscuity. Yet, this information is essential to identify suitable candidate templates to engineer or evolve a new activity within the backbone of a given enzyme. For example, although the BRENDA database is probably one of the best resources to learn about the detailed catalytic properties of enzymes, it only provides in selected cases detailed information on the activity of a given enzyme with different substrate analogs. Besides providing the necessary information to identify interesting enzyme candidates for level 4 and level 5 pathway construction, more systematic data on enzyme promiscuity would also allow a more holistic view onto the catalytic (and evolutionary) potential of a complete enzyme superfamily .Note that the information on substrate and/or reaction promiscuity is not only important to establish novel enzyme reactions, it is also of very practical information in the actual construction and optimization of synthetic metabolic networks. One problem in realizing metabolic networks from scratch with enzymes that did not evolve in the same physiological context is that the individual enzymes in such mix-and-match networks are prone to feature side reactivities with substrates or products of other enzymes in the synthetic network, most likely because they lack a common evolutionary history that selects for stringent substrate specificity . These uAgain, the CETCH cycle provides a good example, why information on the promiscuity of enzymes is so important for metabolic retrosynthetic efforts. In the first versions of the synthetic pathway, a promiscuous methylmalyl-CoA lyase caused the accumulation of malyl-CoA from an undesired side reaction of the enzyme with acetyl-CoA, which stalled the cycle. To overcome the problem of unwanted malyl-CoA accumulation, a malyl-CoA thioesterase  had to bYet, it needs to be mentioned that even if complex synthetic metabolic networks can be realized in vitro, this does not mean that these metabolic networks can be easily transplanted into living cells. The introduction of new reactions and metabolites into a host cell is expected to create interactions with the native metabolic and regulatory network of the host. Again, promiscuity poses a major challenge. Even though the metabolites and reactions might be completely non-native to the cell, these intermediates might be still drained due to unwanted side reactions or create unwanted metabolic and regulatory effects that the negatively affect or even prohibit operation of the synthetic metabolic network inside the host. This problem is exacerbated by the fact that for a well-studied organism like E. coli, the function of a large number of enzymes remains still unknown and there are likely to be hundreds if not thousands of unknown reactions and metabolites, often described as catalytic or metabolic “dark matter” ,60. ThusIn summary, synthetic biology can develop its full potential, if it becomes able to harness the diversity of the millions of different enzyme variants and homologs that naturally exist. While such information is collected and made available by many enzymology and biochemistry laboratories worldwide in a community effort, it is not provided in an optimal way so that it can be used for the synthetic metabolism community. How could this apparent gap be bridged?First, it will be necessary to collect enzymatic data in a more standardized fashion. As a matter of fact, standardization has been an important driver in the development of synthetic biology. This is probably best demonstrated by the BioBrick System  and the Second it will be important not only to investigate a given enzyme in respect to its native reaction, but also study its  side reactivities more systematically. For every new enzyme characterized, it would be helpful if the enzymologist tested at least a small set of substrate and/or cofactor analogs. Even though a detailed kinetic data would not necessary be required, the fact that a certain side reactivity exists in the scaffold of a given enzyme would already be a highly useful and relevant information for the synthetic biologist. On the one hand, this information could be used to identify a target enzyme for further engineering to develop the side reactivity as main activity –39. On tThird and lastly, there cannot enough enzymes be described. The discovery of new enzymes as well as the characterization of homologs of known enzymes needs to be continued and eventually even intensified. Only these efforts will allow to build an exhaustive library of enzyme parts for level 3, level 4 and level 5 metabolic engineering. At the same time the methods of (re-)engineering and the de-novo design of enzymes need to be further developed. This will allow to further develop and improve catalytic activities in enzymes and create new enzyme reactions that cannot be found naturally. Altogether, these activities will expand the limits of natural metabolism and pave the way for synthetic metabolic networks. Enzymology is far from being an old-fashioned business, its most fruitful era might just have begun.


However, the precise metabolic target of PPi inhibition in vivo remained elusive. Here, CE-TOF MS analyses of major metabolites characteristic of gluconeogenesis from seed lipids showed that the Glc6P;Fru6P level significantly increased and that Glc1P level was consistently somewhat higher in fugu5 compared to wild type. In contrast, the UDP-Glc level decreased significantly in the mutants. Importantly, specific removal of PPi in fugu5, and thus in AVP1pro:IPP1 transgenic lines, restored the Glc1P and the Glc6P;Fru6P levels, increased the UDP-Glc level ~2.0-fold, and subsequently increased sucrose synthesis. Given the reversible nature of the Glc1P/UDP-Glc reaction, our results indicate that UGP-Glc pyrophosphorylase is the major target when excess PPi exerts inhibitory effects in vivo. To validate our findings, we analyzed metabolite responses using a mathematical theory called structural sensitivity analysis (SSA), in which the responses of concentrations in reaction systems to perturbations in enzyme activity are determined from the structure of the network alone. A comparison of our experimental data with the results of pure structural theory predicted the existence of unknown reactions as the necessary condition for the above metabolic profiles, and confirmed the above results. Our data support the notion that H+-PPase plays a pivotal role in cytosolic PPi homeostasis in plant cells. We propose that the combination of metabolomics and SSA is powerful when seeking to identify and predict metabolic targets in living cells.Pyrophosphate (PPi) is produced by anabolic reactions and serves as an energy donor in the cytosol of plant cells; however, its accumulation to toxic levels disrupts several common biosynthetic pathways and is lethal. Before acquiring photosynthetic capacity, young seedlings must endure a short but critical heterotrophic period, during which they are nourished solely by sugar produced from seed reserves by the anabolic process of gluconeogenesis. Previously, we reported that excess PPi in H Later, Kornberg described the first PPi-producing biological reaction2 and proposed that pyrophosphorylases acted in the direction of PPi production favoring the formation of biochemical compounds3. Further, it was suggested that inorganic pyrophosphatase (PPase)-mediated PPi hydrolysis rendered the above reactions practically irreversible4, a hypothesis that is now widely accepted. PPi hydrolysis has a ∆G′° of −33.4 kJ/mol and can therefore drive reactions that are otherwise energetically unfavorable, including many biosynthetic steps5. Almost 200 different reactions produce PPi9. The loss of PPase activity arrested growth in bacteria10 and yeast11 and triggered developmental blockage at an early larval stage in worms12, supporting a vital role for PPi homeostasis in living cells. In the model plant Arabidopsis thaliana , we previously reported that vacuolar proton pyrophosphatase (H+-PPase) is essential for maintaining adequate PPi levels13, and that cytosolic PPa isozymes that exhibit non-overlapping subcellular localization patterns14, particularly PPa1, act cooperatively with H+-PPase to prevent an increase in PPi concentrations to toxic levels15. The PPi concentration in the cytosol of plant cells was 0.2–0.3 mM16. Moreover, the constitutive expression of vacuolar proton pyrophosphatase (H+-PPase) increases plant growth under a variety of abiotic stresses, rendering the encoding gene of critical importance to crop breeders18. However, the actual target of excess PPi in vivo and the physiological roles of PPases remain enigmatic in all living organisms, and little is known about the master regulator of cytosolic PPi homeostasis in plants5.Inorganic pyrophosphate (PPi) was discovered in the 1919 and characterized vacuolar H+-PPase loss-of-function fugu5 mutants of Arabidopsis; these are viable but exhibit defects in cotyledon development and hypocotyl elongation13. The postgerminative growth defects recover when sucrose (Suc) is supplied or when PPi is removed by the yeast cytosolic PPase IPP1 in the AVP1pro:IPP1 lines13. This indicated that H+-PPase played a major role in the hydrolysis of inhibitory PPi21. The PPi level was ~2.5-fold higher, and the Suc level 50% lower, in fugu5 etiolated seedlings compared to those of wild-type (WT)13. Thus, excess PPi likely inhibits gluconeogenesis from seed storage lipids , but the precise metabolic target remained unclear13. Thus, we examined how excess PPi inhibited gluconeogenesis in vivo.Against this background, we isolatedfugu5 alleles compared to WT , malate synthase (MS), and phopshoenolpyruvate carboxykinase (PEPCK), respectively 29 to analyze the effect of the fugu5 mutation on metabolic dynamics. The qualitative responses of the steady state metabolite concentrations and fluxes induced by perturbations in enzyme levels can be determined from the network structure alone; it is unnecessary to assume reaction rate functions or parameter values. When applied to the metabolic pathway responsible for Suc production from Fru1,6P2  was required to explain the empirical results (please see the Methods for details). Figure Figure 6P2 Fig. , SSA  acts to control PPi levels, but the cytosolic PPi level of transgenic plants with very low levels of this enzyme are barely affected, suggesting that other mechanisms are involved30. H+-PPase has been proposed as a potential key player in PPi metabolism. However, no H+-PPase mutants were available, and any possible role for the enzyme thus remained unresolved22. The widespread belief that proton pumping is the major role of H+-PPase is partially supported by the increased tolerance to abiotic stress of many crops engineered to overexpress the enzyme to date17, but any possible contribution made by PPi hydrolysis has been overlooked18. Characterization of fugu5 mutants revealed the pivotal role played by H+-PPase in PPi homeostasis and suggested that gluconeogenesis might be compromised by excess PPi13. Here, we used a comparative metabolomics approach to confirm that gluconeogenesis is, indeed, affected and provide robust evidence that UGPase is a major target of excess PPi in vivo.PPi is universally produced in large amounts by a variety of vital biosynthetic reactions32, and is thought to be regulated by substrate availability alone at the enzyme level31. UGPase has been purified from a wide variety of organisms, including yeast, plants, animals, the slime mold Dictyostelium discoidium, and several bacterial species33. Although UGPase has been suggested to be classified structurally into both prokaryotic and eukaryotic groups, they have almost identical catalytic properties34. The Arabidopsis genome contains three genes encoding UGPase: AtUGP1, AtUGP2, and AtUGP336. We have previously demonstrated that recombinant AtUGP3 catalyzed the formation of UDP-Glc from Glc1P and UTP36. Moreover, we examined the effect of PPi on the UGPase activity of recombinant UGP3 and found that the addition of various PPi concentrations (0–10 mM) strongly inhibited the UGPase activity of the recombinant UGP336, as has been reported for other UGPases, via product inhibition . Thus, the enhanced stress tolerance of crops constitutively expressing H+-PPase is, in part, attributable to increased photosynthetic efficiency, and UGPase is a novel useful target in efforts to genetically engineer crops with increased yields18.UGPase is an important enzyme for the metabolism of UDP-Glc, a key precursor in the synthesis of Suc, cellulose, and callosefugu5 mutants and the AVP1pro:IPP1#8-3 and AVP1pro:IPP1#17-3 strains have been previously described13. Seeds of the icl-2, mls-2, and pck1-2 strains were the kind gift of Professor Ian Graham (the University of York) and have been described previously26. The seeds were sterilized and sown in plates containing Murashige and Skoog Plant Salt Mixture , 0.1% (w/v) 2-(N-morpholino) ethanesulfonic acid (MES) (pH = 5.8 as adjusted with KOH), and 0.2% (w/v) gellun gum37. The seeds were left in the dark for 3 days at 4 °C, exposed to light (50 µmol m−2 s−1) to facilitate germination at 22 °C for 6 h, and then maintained at 22 °C in the dark for 66 h. Three sets of experiments were conducted in parallel for each genotype. The first set featured the WT, fugu5-1, fugu5-2, and fugu5-3 strains. The second set included the WT, fugu5-1, AVP1pro: IPP1#8-3, AVP1pro: IPP1#17-3, icl-2, mls-2, and pck1-2 strains. Three-day-old etiolated seedlings were immediately frozen in liquid nitrogen after sampling and stored at −80 °C prior to CE-TOF MS analysis.Arabidopsis Col-0 was the WT strain, and all the mutants and transgenics were in the Col-0 background. The g for 3 min at 4 °C. Next, 500 µL chloroform and 200 µL water were added. The mixture was vortexed for 3 min and centrifuged at 20,400 g for 3 min at 4 °C. Methanol in the mixture was evaporated in a centrifugal concentrator for 30 min at 45 °C. The resulting upper layer (100–200 µL water associated fraction) was centrifugally filtered through a Millipore 5-kDa-cutoff filter (Merck Millipore) at 9,100 g for 120 min. The filtrate was evaporated to dryness in a centrifugal concentrator for 120 min. The residue was dissolved in 20 µL water and other internal standards  added before CE-TOF MS analyses. All compounds and solvents were purchased from Sigma-Aldrich  and Wako Pure Chemical Industries , respectively.About 50-mg quantities of frozen seedlings were homogenized using a Zirconia bead in a Safe-seal micro tube  with the aid of a Mixer Mill (Retsch). Then, 500 µL methanol containing internal standards  was added, followed by repeat homogenization and centrifugation at 20,400 +, m/z = 65.0597) and reserpine ion   or the FA dimer ion  and reserpine ion   afforded the lock masses allowing precise mass measurements. Mass data were acquired at 1.5 cycles/s over the 50–1,000 m/z range. Further experimental information has been presented elsewhere39. The raw CE-TOF MS data were converted, and the peaks were automatically identified, aligned, and annotated, using our in-house software (“Masterhands”)40. Suc levels in 3-day-old etiolated seedlings were measured as described previously13. The two-tailed Student’s t-test was used for statistical evaluations. Principle component analysis (PCA) was performed as described previously41.CE-TOF MS experiments were performed using an Agilent G7100A CE Instrument (Agilent Technologies), an Agilent G6224A TOF LC/MS, an Agilent G1311C 1260 Infinity Quat Pump VL, a G1603A Agilent CE-MS adapter, an Agilent G1607-60002 CE ESI Sprayer II (Agilent Technologies), and G1601BA Agilent ChemStation Ver. B.04.03 software. Separations were performed with the aid of a capillary filled with fused silica  filled with 1 M formic acid (FA) or 20 mM ammonium formate (pH 10.0) as the electrolyte for cation or anion analyses, respectively. The capillary temperature was maintained at 20 °C. Fifteen nanoliters of sample solution was injected under 50 mbar for 15 s. The sample tray was held at <10 °C. Prior to each run, the capillary was flushed with the electrolyte for 5 min. The voltage used for separation was 30 kV. Methanol/water  containing 0.5 µM reserpine served as the sheath liquid, delivered at 10 µL/min. ESI-TOF MS was conducted in the positive-ion mode for cation analyses and in the negative-ion mode for anion analyses, and the capillary voltage was set to 4 kV. The flow rate of hot (300 °C) dry nitrogen was 10 psig. The fragmentor, skimmer, and Oct1 RF Vpp values were set to 105, 65, and 750 V, respectively, for cation analysis and to 100, 60, and 750 V, respectively, for anion analysis. Automatic recalibration of each spectrum was performed using the masses of reference standards. The methanol dimer ion  and reactions by i . In general, the state of a chemical reaction system is specified by the concentrations xm (t), which obey the following differential equationsStructural sensitivity analysis is a mathematical method to determine responses of steady state concentrations and fluxes in chemical reaction networks to the perturbation of each of reaction rate parameters from structure of networks alonev is called a stoichiometric matrix. Wi is called a flux, which depends on metabolite concentrations and also on a reaction rate parameter ki, which corresponds to amount/activity of enzyme mediating the reaction. We do not assume specific forms for the flux functions, but assume that each Wi is an increasing function of its substrate concentration:Here, the matrix xm is a substrate of reaction i,rim.Below, we abbreviate and emphasize nonzero jth reaction corresponds to changing the reaction coefficient as v.In this framework, enzyme knockdown of the 29, the metabolite concentration change A is given asA reflects structure of reaction network. We determine qualitative response of each chemical and flux from distribution of nonzero entries in the matrix A only. This implies that our theory depends only on the structure of reaction network.As shown inF1,6P → F6P + PPiF6P + PPi → F1,6PF6P → G6PG6P → F6PG6P → G1PG1P → G6PG1P → PPi + UDPGPPi + UDPG → G1PUDPG + F6P → S6PS6P → UDPG + F6PS6P → SucSuc → S6Pϕ (degradation)PPi → ϕ (outflow)Suc → ϕ → F1,6P (inflow)The metabolite pathway for Suc production in plant Fig.  consistsv is given byThe stoichiometry matrix A is computed asA, the signs of the entries of S are determined asrim. The disruption of H+-PPase corresponds to the perturbation S.The matrix Supplementary InformationSupplementary Table 1Supplementary Table 2Supplementary Table 3


The computer-aided design of metabolic intervention strategies has become a key component of an integrated metabolic engineering approach and a broad range of methods and algorithms has been developed for this task. Many of these algorithms enforce coupling of growth with product synthesis and may return thousands of possible intervention strategies from which the most suitable strategy must then be selectedE.coli for the growth-coupled synthesis of l-methionine and of the heterologous product 1,4-butanediol.This work focuses on how to evaluate and rank, in a meaningful way, a given pool of computed metabolic engineering strategies for growth-coupled product synthesis. Apart from straightforward criteria, such as a preferably small number of necessary interventions, a reasonable growth rate and a high product yield, we present several new criteria useful to pick the most suitable intervention strategy. Among others, we investigate the robustness of the intervention strategies by searching for metabolites that may disrupt growth coupling when accumulated or secreted and by checking whether the interventions interrupt pathways at their origin (preferable) or at downstream steps. We also assess thermodynamic properties of the pathway(s) favored by the intervention strategy. Furthermore, strategies that have a significant overlap with alternative solutions are ranked higher because they provide flexibility in implementation. We also introduce the notion of equivalence classes for grouping intervention strategies with identical solution spaces. Our ranking procedure involves in total ten criteria and we demonstrate its applicability by assessing knockout-based intervention strategies computed in a genome-scale model of http://www2.mpi-magdeburg.mpg.de/projects/cna/etcdownloads.html.The MATLAB scripts that were used to characterize and rank the example intervention strategies are available at Bioinformatics online. Bio-based production processes with renewable feedstocks hold a great potential for the sustainable provision of chemicals. Metabolic engineering aims for establishing and improving bioprocesses by redesigning and optimizing the metabolism of microorganisms through genetic and regulatory interventions . There aApart from their descriptive role, genome-scale models also support the identification of metabolic intervention strategies. In general, these strategies consist of gene or reaction deletions, insertions or up- and downregulations and, in case of high-volume chemicals, often aim for establishing a stoichiometric coupling of cell growth with the formation of the target product . With grE.coli for the growth-coupled production of the amino acid l-methionine and of the heterologous product 1,4-butanediol. In these case studies, the respective pools of ISs were computed as minimal cut sets but the presented criteria and ranking scheme could as well be applied to outputs of other algorithms.While several approaches have been developed for selecting endogenous and heterologous product synthesis pathways for metabolic engineering  has been computed by an appropriate strain design algorithm based on a constraint-based stoichiometric model of the metabolism of the respective wild-type production organism. In constraint-based metabolic models it is assumed that the intracellular metabolites are in steady state leading to the metabolite balancing equation:ir ≥ 0 must be fulfilled for irreversible reactions. Further linear (in)equalities can be added for including other known  constraints. The resulting solution space of steady-state flux distributions can be analyzed with a variety of methods (ilb and iub. to 0 if reaction i is knocked-out). Dependent on the chosen method, ISs often contain reaction or gene knockouts, which narrow down the solution space, but they may also comprise flux up- and downregulations or the insertion of heterologous metabolic reactions and pathways. The properties listed below evaluate a given IS with respect to its required experimental effort, performance and robustness.#int)Property 1: Number of required interventions Property 2: Maximum growth rate (The maximum growth rate is a measure of a mutant’s viability. In most strain design methods the lower limit for the maximum growth rate (or biomass yield) is defined as a constraint for computing the ISs to guarantee acceptable growth rates. The importance of the maximum growth rate depends on the chosen process type and process parameters. Higher growth rates of the mutant can be a driver for good volumetric productivity, especially in one-step batch fermentation with growth-coupled product synthesis. Combined with the minimum product yield, the maximum growth rate can be used to make statements about the productivity, either through a process simulation , the product synthesis rate or product yield at maximum growth rate is of major importance since this is considered as the operating point of the mutant after adaptive evolution . This criterion thus quantifies the strength of the coupling. Again the minimum product yield can be computed by linear-fractional programming as explained above.2O)Property 5: Requirement of anaerobic conditions Property CitT is such an example  that would lead to a disruption of the coupled growth and product synthesis if the cell was able to secrete or, at least temporarily, to accumulate them. The importance of this approach arises from the fact that there is a large number of promiscuous transporters with varying specificity. The citrate transporter In order to decrease the number of necessary interventions and because usually only few metabolites are excreted under a given condition, the set of potential product sinks can initially be reduced to the main fermentation products . SearchiTo test whether the excretion of a given metabolite could potentially disrupt growth coupling, the model is temporarily extended by an export reaction for this metabolite and with FBA it is verified whether the desired growth coupling is then still existent with desired specifications, e.g. with minimum product yield or production rate. This is done, one by one, for all metabolites that do not yet have an exchange reaction. The total number of metabolites that remove the growth coupling with the actual target product gives a measure for the robustness of the IS. An example is illustrated in Mutants that hold less alternative products tend to have a growth coupling that is more robust, for example, because the coupling mechanisms, such as cofactor regeneration, occur at the end of the product synthesis pathway. Our approach also allows one to exclude ISs with by-products that are likely to occur or have already been observed in previous experiments. Sometimes only the combined secretion of multiple alternative products leads to a disruption of growth coupling, however, we do not consider those combinations herein because they are less likely and their detection requires higher computational effort. Furthermore, if the likelihood of secretion can somehow be quantified, the approach could also be extended by associating individual penalty scores for each metabolite. For example, metabolites that are phosphorylated or bound to Coenzyme A are less likely to be secreted.A useful extension for the described approach is the identification of the nature of the respective coupling strategy. For this purpose, artificial reactions that recover co-factors such as ATP/ADP, NADH/NAD or NADPH/NADP ‘for free’ from the respective unphosphorylated (ADP)/phosphorylated (ADP) or oxidized (NAD(P))/reduced (NAD(P)H) form. If growth coupling is, for example, disrupted by the integration of an NADH oxidizing reaction, this would indicate that the underlying coupling mechanism relies on the balance of reduction equivalents.Equivalence classes of intervention strategiesequivalence) classes where all ISs of one class have identical solution spaces. To identify equivalence classes, a flux variability analysis is performed for each IS. All ISs with identical flux ranges belong to the same class. It is reasonable to consider only one representative strategy for each class to avoid ranking of redundant solutions, however, it remains to be specified what the best strategy of each class is. This is related to Property 7.In practice, different ISs can lead to identical solution spaces. The reason is the nature of the steady-state assumption. For example, a linear pathway can be interrupted through a cut of any of the sequential reactions. An example is given in #accessMet)Property 7: Number of accessible metabolites (accessible metabolites as a criterion to assess the risk of accumulation (and possible secretion) of metabolites in a given strain design. We suggest to identify the (best) representative for each IS class as the IS with lowest number of accessible metabolites. Accessible metabolites are all those metabolites that can, in principle, be synthesized by the reactions of a metabolic network. Note that this also includes metabolites for which, e.g. due to certain proposed interventions, no further metabolization pathways or sinks (excretion reaction) exist in a redesigned network. In Regarding linear pathways, an interruption at an intermediate step or at an endpoint of the pathway Property 8: Thermodynamics: Optimal max-min driving force Property 9: Overlap with other intervention strategies Property 10: Feasibility in reduced models  terms, to mark certain reactions to have only limited capacity. These reactions should then not be essential in a designed strain.EColiCore2, a model of E.coli’s central metabolism derived from the genome-scale model iJO1366  are still fulfilled. If this is not the case, the IS is classified as reliant on secondary pathways and will thus receive a lower score in the ranking procedure.In our examples we used  iJO1366 . It compIn particular, Scoring and rankingk with the most favorable value is scored with The ten criteria described above characterize the different ISs and can be used to compare them with each other; first on the basis of each single criterion. To obtain a comprehensive quantitative measure In the case of a preferably low value Criteria with a preferably low value are the number of necessary interventions, the number of metabolites that disrupt the growth-product coupling and the number of accessible metabolites. The score for the aeration requirement The total score The weights l-methionine and 1,4-butanediol produced via a homologous and a heterologous pathway respectively. We used the E.coli genome-scale model iJO1366 . All MCSs of one equivalence class lead to an identical solution space of steady-state flux vectors when applying the interventions in the model. To identify equivalence classes, we performed for each IS a flux variability analysis and grouped all MCSs with identical flux ranges in one class. We then selected one (the best) representative of each class which has the minimum number of accessible metabolites. If there are, within one class, several MCSs with a minimum number of accessible species, then, from these MCSs, the one with the highestoverall score is selected as the representative.After preselection, the MCS class representatives underwent the scoring and ranking procedure as described in Section 2. We used the weighting coefficients l-Methionine biosynthesis in bacterial hosts , pharmaceutics and nutrition . Despiteal hosts . A pathwiJO1366 model with the l-methionine proton antiporter YjeH , l-serine deaminase (SERD_L) and tryptophanase (TRPAS2) by which amino acid degradation pathways are blocked. While all MCSs contain the essential knockouts described above, specific interventions in the MCS now enforce different routes through the amino acid pathways with certain flux ratios. For the flux rerouting, different combinations of reaction knockouts are possible bearing different advantages and disadvantages. MCS 28 and 74 are less robust, as there are many more intermediates (e.g. up to 218 for MCS 28) which, if secreted, can abrogate growth coupling.We further analyzed the computed MCSs to understand the coupling mechanisms. In all MCSs the coupling was established through a combined deletion of the triose-phosphate isomerase reaction and one of the two final glycolysis steps catalyzed by phosphoglycerate mutase or enolase. As a result, sugar degradation has to take place along the Entner–Doudoroff pathway (ED) which forces the carbon flux to split into pyruvate and glyceraldehyde-3-phosphate (G3P) from where the metabolic pathway to PEP and pyruvate is blocked. The flux through pyruvate can join the TCA cycle to generate reduction equivalents mainly used for ATP synthesis via respiration. G3P cannot enter the TCA cycle directly and can only be drained via the pathways to serine and aspartate which are then further metabolized to methionine, consuming NADPH produced in the ED pathway . In addiAs described in Section 2 section (property 6), it was also tested, whether coupling is still existent when ATP is available at no cost, or electron sources or sinks are added that reduce or oxidize NAD(P)/H. We found that an artificial supply with ATP leads to the disruption of the growth coupling, suggesting that ATP synthesis (and therefore growth) is coupled to methionine synthesis. An external supply with electrons would also abolish coupling because the electron surplus can be used to increase ATP synthesis via respiration. Contrary, giving the mutants the option to drain electrons does not affect the coupling.tpiA and eno or pgm represent serious interventions in the core metabolism of the cell. While the knockout of tpi has been proven to be feasible in E.coli  and the glucokinase (glk) reaction because there would be not enough PEP available to use the PTS system . These strategies rely on the reversed malate oxidase reaction (MOX), which is thermodynamically infeasible under the considered physiological conditions. Furthermore, in all strategies, the essential knockouts of the genes n E.coli , the addE.coli  cycle involving five heterologous enzymes. The strain design was supported by the computation of knockout strategies based on the OptKnock algorithm which suggested the repression of the main fermentation pathways and of the oxidative operation of the TCA cycle to couple growth with product synthesis through the intracellular redox balance. Later studies sought to further enhance the production performance of these strain designs through enzyme engineering  by iJO1366 model (as well as in the EColiCore2 model) and computed the minimal cut sets that establish strong growth coupling for BDO production with this pathway. We identified 274 MCS strategies with 6 to 12 reaction knockouts each, that could be grouped in 107 equivalence classes. We picked one representative per MCS class and ranked them as described before.We integrated the pathway from 2-oxoglutarate to BDO, presented by In THD2pp) and then other (for each MCS specific) knockouts to establish full coupling. In all these strains, ATP synthesis is possible through glycolysis with the essential fermentation products formate, BDO and acetate. While acetate is a by-product of the BDO pathway, the ratio of formate and BDO is predetermined by the redox-state. Depending on the respective MCS, succinate and ethanol may occur as side products, ethanol as a product from a cycle in the glycine metabolism. The MCSs from the three remaining equivalence classes work under aerobic conditions and rely on the interruption of the TCA cycle through which BDO becomes an essential by-product of respiration. The intervention strategy pursued by adhE), pyruvate formate lyase (pfl), lactate dehydrogenase (ldh) and the malate dehydrogenase (mdh) and has thus a large overlap with the computed MCSs. In addition, the aerobic respiration control protein (arcA) was knocked-out by Yim et al. but not considered herein as it is a regulator protein and no metabolic enzyme. As predicted, acetate excretion was observed for these strains. Differences between the strategy of Yim et al. and the computed MCSs probably arise because (i) Yim et al. used a microaerobic process by which a knockout of the pyruvate formate lyase is allowed (this mutant cannot grow under strict anaerobic conditions) such that CO2 and acetate are the only essential by-products, and because (ii) the chosen knockouts of Yim et al. do actually not yet guarantee a BDO production in the iJO1366 model, even with simulated microaerobic conditions with an upper limit for oxygen uptake of 2 mmol/gDW/h.FBA and the thermodynamic OptMDF analysis predict the thermodynamic feasibility of all computed knockout strategies. In total, 104 out of 107 equivalence classes relied on anaerobic conditions all of which suggested the disruption of the tricarboxylic acid cycle , the ethanol and lactate pathways, the knockout of the NAD(P) transhydrogenase (ACALD), glucose 6-phosphate dehydrogenase (G6PDH2r), D-lactate dehydrogenase (LDH_D), malate dehydrogenase (MDH), phosphopentomutase 2 (PPM2) and the NAD(P) transhydrogenase (THD2pp). On the gene level this MCS can be established through the knockout of mhpF, ldhA, pntB, zwf, mdh, adhE and deoB. The list of all computed MCSs is provided in the The identified best MCS candidate (blue) consists of the reaction knockouts of the acetaldehyde dehydrogenase  it may be outperformed in a subset of other criteria (e.g. in the robustness of the strain designs).Many constraint-based strain optimization methods can generate a pool of intervention strategies from which one candidate has to be selected for strain development. In this work we introduced methods for the characterization and ranking of such a pool of IS candidates with a focus on growth-coupled strain designs. We presented a catalogue of ten partially new criteria for assessing and ranking individual IS candidates, broadly extending earlier approaches such as OptPipe (Depending on the specific needs, our ranking procedure could be easily adapted (e.g. by replacing our weighted score approach with the rank product method used by As an important tool for characterizing and ranking strain designs, we also introduced the notion of equivalence classes of ISs by which ISs with identical solution spaces can be grouped. This simplifies the analysis as well as the ranking of the strategies since then only one representative for each class needs to be taken into account. Once the optimal strategy has been identified, possible alternative solutions in its equivalence class can be investigated.The strength of our approach lies in its straightforward and generic applicability as it is independent from product, substrate, host organism and the computational method used to generate the IS candidates. The investigation of most criteria requires only an LP solver and the stoichiometric models of the wild type and the mutant. For the thermodynamic analysis, a relatively simple mixed-integer linear optimization problem must be solved (bty1065_Supplementary_FileClick here for additional data file.