Retrosynthesis, a concept originally proposed for synthetic chemistry, iteratively applies reversed chemical transformations  starting from a target product to reach precursors that are endogenous to the chassis. So far, a wider adoption of retrosynthesis into the manufacturing pipeline has been hindered by the complexity of enumerating all feasible biosynthetic pathways for a given compound.Synthetic biology is used to develop cell factories for production of chemicals by constructively importing heterologous pathways into industrial microorganisms. In this work we present a retrosynthetic approach to the production of therapeutics with the goal of developing an In our method, we efficiently address the complexity problem by coding substrates, products and reactions into molecular signatures. Metabolic maps are represented using hypergraphs and the complexity is controlled by varying the specificity of the molecular signature. Furthermore, our method enables candidate pathways to be ranked to determine which ones are best to engineer. The proposed ranking function can integrate data from different sources such as host compatibility for inserted genes, the estimation of steady-state fluxes from the genome-wide reconstruction of the organism's metabolism, or the estimation of metabolite toxicity from experimental assays. We use several machine-learning tools in order to estimate enzyme activity and reaction efficiency at each step of the identified pathways. Examples of production in bacteria and yeast for two antibiotics and for one antitumor agent, as well as for several essential metabolites are outlined.We present here a unified framework that integrates diverse techniques involved in the design of heterologous biosynthetic pathways through a retrosynthetic approach in the reaction signature space. Our engineering methodology enables the flexible design of industrial microorganisms for the efficient on-demand production of chemical compounds with therapeutic applications. RecombiIn recent years, many successful examples of bioproduction of chemicals with therapeutic interest through metabolic engineering have been reported. Among others, plant secondary metabolites that are of medicinal value, such as the terpenoids artemisinic acid  and paclIn an attempt to rationalize the biosynthetic design process, metabolic engineering models the metabolic network of the cell as a whole ,17. A sude novo biosynthetic pathways are extended beyond what is present in metabolic databases like KEGG [In silico methods for de novo pathway prediction and optimization are mainly based on two approaches: homologies of chemical structure transformation patterns [Through metabolic modeling, the repertoire of biochemical transformations in ike KEGG  and Metaike KEGG . In silipatterns -29, and patterns ,31. Retrpatterns  perform patterns , where mpatterns . BEM entpatterns  are reprpatterns ,36. In tpatterns  is an alpatterns .de novo pathway design and the use of experimental information, we present here a tool based on the coding of compounds and reactions through molecular signatures [h. A metabolic reaction signature is given by the difference between the signatures of products and substrates [de novo reactions and consequently de novo pathways can be controlled.A retrosynthetic search in the metabolic hypergraph might lead to a combinatorial explosion. For instance, using only 50 reaction rules, 100,000 reaction routes were predicted for the production of isobutanol , far morgnatures . The molbstrates . As furtOnce metabolic models for the heterologous biosynthesis of target compounds have been determined, individual performances for the predicted pathways need to be characterized in order to prioritize the engineering of the most promising routes into the chassis organism. Several computational frameworks have proposed different factors that might influence the performance of an engineered strain. PathMiner introduced a path cost associated with the number of heterologous enzymes measured through a chemical distance . BNICE ah of the maximum diameter of the molecular graph, whereas signatures at lower height h provide a way to search for and enumerate similar chemical compounds. Likewise, reaction signatures, which are biochemical reactions coded into the molecular signature representation (Equation 7 in Methods), are used in order to search for and enumerate similar reactions. We define the extended metabolic reaction space (EMRS) as the set of all possible reactions that can be generated from signatures contained in the metabolic network. Therefore, the EMRS consists of both reactions in the metabolic network and additional putative reactions, which are assumed to be promiscuously catalyzed by enzymes present in the organism. Given a finite height h, novel reactions are discovered through this method by performing a search in the metabolite signature space of combinations of stoichiometric coefficients of metabolites having the same signature as either the substrates or the products. Figure E. coli . Molecular signatures, which are a representation of the molecular graph, can be used in order to code reactions . This pri Figure  and of tS Figure .h = 0. In this space, compounds are represented by their elemental formula. Similarly, the combination of the substrates and products in the reaction are represented by their total molecular formula. Thus, any combination of compounds satisfying the elemental formula is considered a putative set of reactants. In order to compute the EMRS of height h = 0, we need to solve Diophantine equations in the signature space of height h = 0 that generally lead to a set of solutions too large to be of use. In the case of h = 1, the number of newly created reactions is still significantly large . This number, nevertheless, becomes tractable once we consider heights higher than h = 2, which corresponds to a 17.72% increase in the number of reactions with respect to nominal reactions, as it is shown in Table An illustrative example is the metabolite signature space of height h of molecular resolution (Equation 8 in Methods). Those putative reactions generated by our molecular signature-based algorithm need to be validated and ranked. Figure The EMRS introduces putative novel reactions that share the same signature as their parent nominal reactions at the chosen height i Sprocessing the reaction r* in the pathway:We introduce the following function to quantify the cost of inserting an exogenous enzyme sequence promis(iS) is the predicted enzyme promiscuity for the sequence iS, perf is the estimated catalytic performance of the given sequence i Sfor reaction r*, and het(iS) is the gene compatibility of the sequence iS. pω, e ωare parameters used in order to weight the contribution of each term to the cost function. All three terms are normalized before entering the expression so that each score is always given by a value in the same range between 0 and 1. Therefore, the cost function r* as a side reaction. In the same fashion, enzyme performance contributes negatively since reactions with higher performance are considered less expensive in terms of the cost of insertion. Once all terms are defined for each reaction r* in the EMRS, this strategy enables the determination of those gene sequences S* that minimize the insertion cost:where p in the chassis organism, may be obtained either from experimental databases [c, with a cost function defined as follows:Furthermore, several additional adverse effects may be hindering the successful expression and performance of inserted enzymes, while the toxicity of intermediate metabolites might impede cell survival and growth. These effects need to be taken into account in order to rank the pathways. For instance, an estimate of toxicity values  for the intermediates atabases  or from atabases . In addiW considers the following effects: cv(ρ), nominal yield of compound c in pathway ρ; p), the inverse of the IC50 value. Parameters  need to be adjusted in function of the desired weight given to the costs of pathway insertion and metabolite toxicity. In our method, these parameters were optimized so that pathways that are fully annotated in the reference database, for instance KEGG, are ranked first with respect to predicted pathways (see details in Methods).where W) at the optimal pathway:The minimum of this cost function W in Equation 3.provides a trade-off between the simultaneous goals of obtaining the maximum nominal yield while keeping the overall process efficient and side effects attenuated. In the following sections, we present our approach in order to quantify each term in the pathway cost function r*, we must rely on the prediction of enzymes as putative candidates to process other substrates (multispecificity) or to catalyze a promiscuous reaction other than their native ones [Our method provides for each reaction in the EMRS a ranked list of candidate sequences, as given by the score in Equation 1, along with their predicted catalytic efficiencies. When there is no sequence information in databases about enzymes catalyzing the desired reaction ive ones . FurtherPutative reactions need to be validated for their directionality or thermodynamic feasibility. We performed this validation assuming that the metabolites' concentration are spatially invariant and that temperature and pressure are constant. Under these assumptions, standard Gibbs free energies of reactions can be estimated using a group contribution approach ,50. OnlyAs part of our methodology for biosynthetic pathway design, candidate enzyme sequences catalyzing feasible reactions in the EMRS have to be identified from the set of known enzymes. Namely, our procedure for extending the metabolic network relied on the underlying assumption that reactions with the same signature are likely to be processed by similar enzyme sequences , which iThe next step consists of searching for candidate enzymes to process a given reaction in the EMRS. In case that no known enzyme sequences were available for the reaction, candidate enzymes were determined by a signature-based enzyme-reaction predictor by following the procedure known as the tensor product . We assuTherefore, reactions generated by the enumeration algorithm in the EMRS were first clustered into groups of similar reactions by a distance metrics, which was defined as the Tanimoto similarity of reaction signatures . The tenM K, and inhibition constant iK). As shown in Figure r*, iS) for the list of candidate enzymes entered into our decision flowchart in order to score the sequences in Equation 1.In addition, performance of exogenous enzymes needs to be evaluated. We have developed a decision tree learning method to estimate enzyme activity  using kiAnother aspect to be addressed when considering the overall enzyme cost defined in Equation 1, is the effect of inserting heterologous genes, since the diversity of base-pair content is organism-specific. By minimizing this difference, expression levels can be maximized . In ordeFurthermore, the successful expression of a heterologous gene depends on several additional sequence-independent factors, such as an adequate selection of promoters, RBS, and codons . In someQ2 = 0.68. For any given reaction in the EMRS, toxicity was given by the sum of the predicted toxicity for each product, allowing us to identify pathways involving highly toxic metabolites in order to rank them with lower score.Exogenous enzymes inserted in the chassis might catalyze reactions synthesizing new products in the organism. As a side effect, however, intermediate metabolites involved in the exogenous pathways as well as any other side product of the new reactions may induce undesired toxic responses in the cell. Therefore, it is necessary to consider toxicity effects of the compounds. For this purpose, we have developed a structure-activity relationship model based on a library of 150 tested compounds covering a wide range of toxicity levels . The modE. coli such as penicillin, it is necessary to introduce genes that code for β-lactam resistance in the organism in order to make bacteria immune to that antibiotic. Therefore, if resistance to some product is going to be inserted into the strain, the attenuation effects in toxicity for that family of compounds has to be updated into the model.Special consideration when predicting compound toxicity should be given to those cases when genes encoding for resistance to the compound are going to be engineered as part of the biosynthetic gene cluster. For instance, when producing an antibiotic in The insertion of new reactions into the chassis organism can perturb its metabolic network and therefore the equilibrium of the steady-state fluxes might be altered . By usinρ(c) that produces a compound c, we have shown in the previous sections how to estimate the individual contributions to the cost function (Equation 3). By using the cost function, thus, biosynthetic pathways ρ(c) can be ranked. However, in order to rank all viable biosynthetic pathways ρ(c) for a compound c of interest, the problem of pathway enumeration needs to be addressed. For this purpose, modeling of the metabolic network in the EMRS was done by using directed hypergraphs, where reactions are represented by hyperedges that connect sets of vertices (the substrates) to disjoint sets of vertices (the products) [h of the molecular signatures. Higher values of h imply that the number of pathways between two metabolites is approximately the same as the number of possible pathways in metabolic networks of annotated databases such as KEGG [h values generate more novel reactions and therefore more possible pathways are formed between those two metabolites. This result is illustrated for the case of pathway enumeration between chorismate and tyrosine in E. coli for different heights h using a reaction representation at the level of the 3rd digit in the EC number classification , new reactions are unlikely to be generated and therefore the number of pathways becomes the same as the number of pathways available in KEGG (the reference metabolic database); whereas as the height h decreases, the number of new reactions and, thus, the number of pathways starts growing while getting closer to those results that were obtained in BNICE by using BEM matrices [Given a biosynthetic pathway roducts) . Directe as KEGG  or MetaC as KEGG , while ln Figure . In genematrices .ρ*(c) in Equation 4 that produces the target compound c is equivalent to finding the shortest hyperpath in a weighted hypergraph. This problem is known to be an NP-hard problem [ρ(c) and computing their associated costs W in Equation 3.In a general setting, the problem of finding the optimal pathway  problem , althoug problem . In the E. coli. These strains were rendered unable to synthesize those essential compounds by inactivation of the enzymes that natively produce them. We assumed that native pathways, which have been selectively conserved under evolutionary pressure, are efficient ways to produce the compounds while keeping cell growth. The validation, thus, consisted of checking if the pathways that were ranked at the top of the list correspond to native pathways. In order to find all possible ways to synthesize the amino acids, we ran the retrosynthetic search in these auxotrophic strains. The output results of the search, which are given in Table A validation test for the ranking score was carried out by testing its ability to identify native biosynthetic pathways for several essential metabolites  in auxotrophic strains of p-value <0.05) to native genes of E. coli. These results are significant since the sequences under test were not part of the training set used for building the gene compatibility predictor. In summary, this test showed that the proposed ranking function can potentially identify heterologous biosynthetic pathways to insert in an organism to produce a desired compound while selecting the ones that are close to native pathways in the chassis.An additional validation test was performed in order to evaluate the accuracy of the gene compatibility predictor. The result of this test, summarized in Table E. coli EMRS of height h = 6. Furthermore, the distribution of the number of alternative biosynthetic pathways in the compound set follows a power law, as it is shown in Figure As shown in previous sections, the procedure of pathway selection by retrosynthesis is a complex task that implies the adoption of several design decisions, some of them on a case-by-case basis. In order to help on the decision-making process, we have developed an online tool: the RetroPath webserver that guides the designer through the retrosynthesis process. The design starts by choosing the target compound, which can be given as an SDF molecular file. Additionally, the user decides the level of molecular resolution to use in the molecular signature representation. For instance, we have analyzed the set of molecular structures in DrugBank  as initiβ-lactams antibiotics in E. coli , and of one antitumor drug (taxol) in yeast.In order to illustrate the design process, we next present three examples of heterologous pathway design using the RetroPath webserver, the production of two Penicillium chrysogenum. A recent study has opened up the possibility of producing penicillin G in an organism that is used as a producer of pharmaceuticals; the yeast Hansenula polymorpha [β-lactam antibiotic, cephalosporin, which is produced in the fungus Acremonium chrysogenum and synthetised from isopenicillin N, the penultimate precursor for penicillin production [The industrial production of penicillin G occurs via fermentation using the filamentous fungus lymorpha . Interesoduction .β-lactam antibiotics, in particular penicillin and cephalosporin -L-cysteinyl-D-valine synthetase (EC 6.3.2.26) and isopenicillin N synthetase (EC 1.21.3.1). These pathways are the same as those that were implemented in the aforementioned studies in yeast and fungi to produce the isopenicillin N. In the cephalosporin biosynthesis pathway the isopenicillin N is converted into penicillin N, itself transformed into deacetoxycephalosporin. The retrosynthetic maps of height h = 4 for heterologous production of penicillin N and deacetoxicephalosporin in E. coli are shown in Figure E. coli while fluxes were estimated from a reconstructed metabolic model of E. coli, as described in the Methods section. The optimal pathway involves five exogenous enzymatic steps, while the alternative pathways involves up to seven steps. In Table E. coli.Using the retrosynthetic method that we have developed, retrosynthetic graphs were generated for  Figures . The choetase EC .3.2.26 aTaxus brevifolia. Today, taxol derives largely by semisynthesis from the advanced taxoid 10-deacetylbaccatin III obtained from the European yew tree Taxus baccata [Saccharomyces cerevisiae) which was computed for a signature height h = 4,  is an anticancer drug first isolated from the Pacific yew tree  baccata . Current baccata . The ret, Figure , goes frα-ol: The isopentenyl, native to yeast, undergoes 3 reaction steps to form the taxadien-5α-ol. Those are catalyzed by the geranylgeranyl-diphosphate (GGPP) synthase (EC 2.5.1.29) that forms the GGPP (C00353) [α hydrolase (EC 1.14.99.37) that forms the taxadien-5α-ol [E. coli [1. From isopentenyl (IPP) to taxadien-5(C00353) , by the (C00353)  and finaen-5α-ol . The fir[E. coli  and, furα-ol to taxol: From the taxa-4(20),11(12)-dien-5α-ol two pathways are possible, producing either taxa-4(20),11(12)-dien-5α,13α-diol by the taxane 13α hydrolase (EC 1.14.13.77) or the taxa-4(20),11(12)-dien-5α-yl acetate by the taxadien-5α-O-acetyl transferase [β hydroxylase (EC 1.14.13.76) is producing the taxa-4(20),11(12)-dien5α,10β-diol 5 acetate [Saccharomyces cerevisiae [α-O-benzoyltransferase (EC 2.3.1.166), and the Baccatin III catalyzed by taxane 2α-O-benzoyltransferase [2. From the taxadien-5-nsferase . Taxane  acetate . This parevisiae . The nexnsferase  to finaltox λ= 0) and therefore the optimal weighting terms in Equation 3 were taken accordingly (see details in Methods). The two alternative routes are given by the way the precursor 10-deacetyl-2-debenzoylbaccatin is produced. The optimal pathway involves 8 exogenous enzymes, while the alternative one involves 9 enzymes.Table We presented in this work an automated protocol to assist synthetic biologists and metabolic engineers in the design and insertion of efficient heterologous biosynthetic metabolic pathways in chassis organisms. Our method is based on the retrosynthesis algorithm, an idea borrowed from the allied field of synthetic chemistry. In order to perform this analysis in metabolic networks, we used the molecular signature descriptor, a 2D representation of molecular graphs that provides a characterization of compounds and reactions in the network. Molecular signatures provide a homogeneous way to represent through hypergraphs the set of chemical species and transformations present in cell's metabolism. The representation in the molecular signature space is also an efficient way to measure chemical similarity between compounds and reactions. We use this framework to develop an algorithm to generate putative novel reactions between compounds in the network, leading to the extended metabolic reaction space (EMRS). The algorithm consists of searching for all combinations of compounds with the same signature as known metabolic reactions.h of the molecular signature. As h increases, the number of possible pathways converges to the annotated pathways in metabolic databases. Lowering h, in turn, leads progressively to a combinatorial explosion with multiple alternative pathways containing putative reactions, as the ones obtained in the bond-electron and atom tracking models of the metabolic graph.In order to explore new biosynthetic pathways for compounds, we implemented a retrosynthetic algorithm in the EMRS to build the map of all reachable compounds from the chassis organism through biochemical transformations. The complexity of the retrosynthetic search, a problem that has been limiting so far the adoption of the retrosynthetic approach into the manufacturing pipeline, has been efficiently addressed in our method through the atomic height E. coli in the list of compounds of medicinal interest in DrugBank follows a power law, being in some cases in the order of thousands. Therefore, it is necessary to implement an efficient ranking function as the one presented here in order to select the best heterologous pathways to insert in the chassis organism. For instance, we applied the retrosynthetic algorithm in order to search for heterologous biosynthetic pathways for two compounds in DrugBank: penicillin N and taxol. In both cases, several alternative pathways for bioproduction were found. The identified pathways contained both known biochemical transformations previously reported as well as other alternative pathways. In order to select the best combinations to engineer, pathways were ranked according to several cost factors such as number of inserted enzymes, gene compatibility, toxicity, and nominal fluxes. The individual contribution of these factors to the ranking function was optimally adjusted so that native pathways were ranked first with respect to predicted pathways. Our multi-criteria approach can be easily tuned depending on the data available for organisms, as it was illustrated by the optimal adjustment of the weighting parameters for different combinations of factors. The ability of the ranking function to identify native pathways was tested and validated in the case of biosynthetic pathways of several essential metabolites  in auxotrophic strains of E. coli. In this test, native enzymes were correctly ranked by means of our methodology at the top of the enumerated biosynthetic pathways.The retrosynthetic map contains both annotated and putative reactions catalyzed by identified exogenous enzymes, providing several alternative pathways leading to the target compound. We associated a cost of insertion to each pathway based on several criteria such as gene insertion cost, expression levels, enzyme efficiency and nominal fluxes. Furthermore, an algorithm similar to the shortest pathway search has been implemented in order to rank all possible pathways. We showed that the distribution of alternative biosynthetic pathways for Even though our methodology searches for enzymes providing the best performance for the overall process, we might be interested in some cases in increasing the efficiency levels for some of the promiscuous reactions involved in the pathway due to their poor performance, a rate-limiting factor in the production of the target compound. In that case, it would be necessary to introduce mutations in order to re-engineer enzyme variants with detectable levels of the desired catalytic activity. Using protein molecular signatures and kernel methods, we already proposed a methodology to search for promiscuity hot-spot residues in the enzyme sequence and outlined a method to find variants with enhanced promiscuity levels , which mG =  be a molecular graph, where vertices V correspond to atoms, and edges E to bonds. An atomic signature is a canonical representation of the subgraph of G surrounding a particular atom x ∈ V . This subgraph includes all atoms and bonds up to a predefined distance from the given atom, the signature height h.Let G =  is a molecular graph, where vertices V correspond to atoms, and edges E to bonds, then the molecular signature of G is given by:The molecular signature is a vector whose components are represented in the space defined by a basis formed by atomic signatures. Initially developed for chemicals , the sighσ(x) is the atomic signature of G rooted at atom i xof height h.where r : s1S1 + ... + nSn s→ p1P1 + ... + mPm p, where i sand j pare the stoichiometric coefficients of substrates i Sand products jP. The signature of reaction R of height h is defined by the vector:We assume that enzymatic reactions take the general form: R is formed by the set of reactions r in the network, which are defined as ordered pairs of substrates s ∈ C and products p ∈ C belonging to the metabolite space C:In a metabolic network, the reaction space hσ(R) of height h is given by mapping of the set of metabolic reactions r ∈ R into signature reactions hσ(r) according to Equation 7. Extended metabolic reaction space (EMRS). The extended metabolic reaction space generated by signatures of height h, hσ -1(R), corresponds to the inverse mapping from the signature space into the reaction space. Since the projection of R into the signature space hσ (R) involves some degeneracy, the regeneration of the metabolic map creates new putative reactions consisting of combinations of substrates and products that verify the reaction signatures in addition to the nominal ones:The signature reaction space h by using the Tanimoto similarity coefficient:We define a measure of chemical similarity in the signature space between reaction signatures of height where operations are applied into the vector space determined by the net difference of the signatures of products and substrates (Equation 7).h is increased up to the maximum diameter of the graph or canonical signature, the similarity measure extends further up to the rest of the molecular structure. By definition, two reactions r and r* that share the same signature up to some height h possess identical signatures up to that molecular resolution h:This similarity measure focus on the reaction centers that define the chemical transformation rather than on the full atomic structure. As the height ρ ∈ ρ(c) for a target compound c ∈ C is defined as a collection of reactions {r1, r2, ..., nr} in the EMRS that connects metabolites in the chassis organism to the product c through biochemical transformations.An exogenous biosynthetic pathway Reaction thermodynamic feasibility was computed through the estimation of Gibbs energy of the reaction by using a group contribution approach [approach ,50. Thisapproach  in orderi nis the stoichiometric coefficient of each species, and Δi Gtheir estimated Gibbs energy.where Enzyme promiscuity was estimated by a support vector machine that was trained from the string or k-mer spectra [kσ(S) in KEGG [ spectra  of enzym in KEGG  as inputS, as in [Enzyme promiscuity in the training set was defined by comparing the chemical similarity of reactions catalyzed by the enzyme sequence S, as in :(13)Reaction clustering of the reaction signature space was performed by a hierarchical agglomerative algorithm using as distance metrics the chemical dissimilarity between reactions d:iC, i = 1...n clusters was determined by the maximum average silhouette [The optimal partition of the reaction signature space into lhouette .Enzyme-metabolite interaction prediction was computed within a given signature reaction space cluster by using a kernel approach known as tensor product [ product . For eackK is the sequence string kernel defined in Equation 12 and hk is given by the reaction similarity matrix computed by using the reaction chemical similarity s defined in Equation 14. Enzyme performance was estimated through a decision tree algorithm implemented for each reaction cluster, as in [cat kand M Kprovided by the BRENDA database [where r, as in . Performdatabase . Input fE. coli and yeast). The training set consisted of a balanced positive set, formed by the list of sequences in the chassis strains, and a negative set formed by sequences selected randomly from the list of organisms other than the chassis. In the model of E. coli, we found that the average score for positive hits had a z-score = 6.12  for a positive set of 24,894 sequences in E. coli strains among the total set of 681,518 sequences. We used this predictor in order to rank the annotated genes for a given enzyme class, where a p-value was associated to each predicted gene by computing the probability of ranking that gene in the given percentile if it were picked at random from the list of genes.Sequence descriptors were computed from the EMBOSS package of sequence analysis . PhylogeCompound toxicity in the chassis organism E. coli was estimated through a partial least squares structure-activity relationship model implemented from an in-house database for E. coli of 150 compounds with experimentally determined IC50 . Input descriptors of the model are given by the following molecular descriptors: molecular weight; solubility; average bond length; partition coefficient; molecular surface; and molecular signatures of the compounds.Nominal fluxes v were predicted by using a reconstructed metabolic model of E. coli [c ∈ C and a putative exogenous biosynthetic pathway ρ, an augmented model of the metabolic phenotype of the engineered strain was built from the reference model. The nominal flux of the desired compound cv(ρ) in the augmented model was obtained through linear programming optimization of the stoichiometric mass balance subject to the following constraints: E. coli  and yeas E. coli  in the C E. coli . For a gS is the stoichiometric matrix, Z is the objective function of maximizing the biomass formation (growth) rate, f (cv(ρ), Z) is a definite positive function that monotonically increases with both cv(ρ) and Z, and α, β are the model flux constraints [f (cv(ρ), Z) = cv(ρ) · Z, although in general other objectives might be possible as well (see for instance in [where straints . The chotance in ).λflux, λpath, λtox) in the cost function given by Equation 3 are adjusted by optimization. The chosen criteria is that pathways that are fully annotated in KEGG should be ranked first with respect to other pathways based solely on predictions. Our approach is similar to the one proposed in [ρ ∈ ρ (c) producing a given compound c, we define its ranking accuracy as:Weighting parameters  in KEGG that are ranked at the same or higher score than ρ, TN nare the number of pathways of ρ(c) not in KEGG which are ranked below ρ, and |ρ(c)| are the total number of pathways producing c.where ρ yextended to the list of enumerated pathways in the EMRS:The objective is to maximize the overall aggregate sum of λpath, λtox, λflux) are not independent since a simultaneous increase of the same magnitude in the three parameters would leave the ranking unchanged. Therefore, in order to solve the problem, we need to fix at least the value of one of the parameters, for instance taking λpath = 1.0 and p ω= e ω= 1. We give three possible solutions depending whether both toxicity and fluxes estimates are available or only one of them , the optimal value for the toxicity parameter was For the ranking optimization problem, parameters . Figure S1 plots pathway ranking accuracy for different values of parameter λtox without considering fluxes (λflux = 0); optimal value is obtained for λflux without considering toxicity (λtox = 0); optimal value is obtained for λtox, λflux); optimal values are (Click here for file


The growing prevalence of metabolic diseases, such as obesity and diabetes, are putting a high strain on global healthcare systems as well as increasing the demand for efficient treatment strategies. More than 360 million people worldwide are suffering from type 2 diabetes (T2D) and, with the current trends, the projection is that 10% of the global adult population will be affected by 2030. In light of the systemic properties of metabolic diseases as well as the interconnected nature of metabolism, it is necessary to begin taking a holistic approach to study these diseases. Human genome-scale metabolic models (GEMs) are topological and mathematical representations of cell metabolism and have proven to be valuable tools in the area of systems biology. Successful applications of GEMs include the process of gaining further biological and mechanistic understanding of diseases, finding potential biomarkers, and identifying new drug targets. This review will focus on the modeling of human metabolism in the field of obesity and diabetes, showing its vast range of applications of clinical importance as well as point out future challenges. Metabolism, the set of chemical reactions taking place in a cell, plays an important part in maintaining cell functionality by responding to various perturbations, sustaining the production of essential molecules and cell components, breaking down compounds for energy production and catabolizing xenobiotics. The drivers behind these typically thousands of reactions are enzymes, whose concentrations are controlled by several levels of regulation, affected both by the cell type and its surrounding environment. Due to the central role of metabolism it is not surprising that its dysfunction is associated with several complex diseases, of which prominent examples are obesity and diabetes. The severity of this is further emphasized by the fact that more than 360 million people are suffering from type 2 diabetes (T2D) and that in 2011 this disease contributed to more than 3.5 million deaths in middle-income countries  that are Haemophilus influenza metabolism , all other values are set to zero. Under the constraint-based modeling framework, it is assumed that the concentrations of all metabolites are constant, meaning that the sum of fluxes of the reactions where the metabolite is consumed has to be equal to the sum of fluxes of the reactions where the metabolite is produced. Mathematically, this can be written as Sv = 0, where v is a vector of fluxes for each reaction. This system is underdetermined, i.e., there are many possible flux vectors that solve the system. However, the solution space can be shrunk by applying constraints on v, based on current physiochemical and biological knowledge. A common approach is to use linear programming to find a flux vector that optimizes an objective function , given the constraints on v and the condition Sv = 0. This approach is called flux balance analysis, FBA  are also useful resources for new reconstructions, in particular when considering cell-type specific networks. Manual reconstruction is very laborious and because of this much interest has been put into algorithmic approaches for automated or semi-automated GEM reconstruction  intake on adipose tissue gene expression among subjects with metabolic syndrome, Morine et al.  converteThe previously mentioned studies used GEMs to analyze transcriptome data, however, other high-throughput data can also be contextualized with the aid of metabolic networks. Deo et al.  analyzedThe examples in the previous section reflect how the topology of GEMs can be used to interpret high-throughput data in a metabolic context. Besides this, GEMs have also been applied as models for simulation of metabolic fluxes in the study of diabetes and obesity. An important application in this context is to use clinical data of exchange fluxes to predict intracellular metabolic fluxes.Sv = 0, resulting in a set of flux vectors, or candidate metabolic network states, which enabled the authors to investigate capable and most probable fluxes through selected reactions. Their analysis showed that network stoichiometry, as opposed to active enzyme levels, could explain the reduced flux through mitochondrial pyruvate dehydrogenase in diabetes.One of the first studies using GEMs in the context of diabetes was that of Thiele et al. . The autWhen modeling human metabolism it is of course important to consider cell-type specific metabolism. Becker and Palsson  developeBordbar et al.  used RecSv = 0 and the constraints on v) were calculated using a random sampling algorithm (Bordel et al., Mardinoglu et al.  extendedHuman GEMs have proven to be very valuable in studies of metabolic disorders, such as obesity and diabetes. Through compilation of years of community research the human GEMs encompass state of the art genome-wide metabolic knowledge. As such, they provide a biologically meaningful context for the interpretation of various high-throughput datasets. As shown in many of the studies discussed in this review, topology-based analysis can successfully identify results that are not evident from traditional analyses. An example of this is the study by Deo et al.  where acOne of the strengths of GEMs is their ability to generate new hypotheses and predictions, as shown in many of the previously mentioned studies. As for any modeling approach, validation of the results is of course essential. In particular, since GEMs are represented on a genome-wide scale they integrate well with omics data. This means that predictions made by the GEMs, such as reporter metabolites as candidate biomarkers, can be validated on transcript, protein as well as metabolite levels. In general, the previously mentioned studies tend to support their modeling results with evidence in the literature. A high correlation with experimental data is of course confirming GEMs as a relevant modeling approach. However, to strengthen the actual novel predictions the ambition should be to validate and confirm these through subsequent experiments, e.g., as in Frezza et al. . With thSeveral challenges still remain in the area of human metabolic modeling. One is to improve constraint-based modeling techniques for human metabolism, in particular the issue of formulating valid metabolic objective functions that reflect healthy and disease phenotypes in a manner that leads to correct biological conclusions. Further on, the predictive power will always be limited by the content of the used GEM. Thus, advances in the reconstruction procedure, both of generic and specific GEMs, will be important in order to sustain the production of up-to-date networks. Since the pathology of obesity and diabetes is highly dependent of the interplay between liver, adipose and muscle tissue, the next step in metabolic modeling should be to focus on model integration, both in terms of capturing interactions of cell types within each tissue, as well as between tissues. First steps include the multi-tissue model (Bordbar et al., 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.


Saccharomyces cerevisiae during its metabolic cycle, as well as in response to three fundamentally different biological perturbations, namely gene knockout, nutrient shock and nutrient change. While the kinetic constraints applied at the level of individual reactions were found to be poor descriptors of the mRNA-metabolite relationship, their use in the context of the network enabled us to correlate changes in the expression of enzyme-coding genes to the alterations in metabolite levels. Our results highlight the key contribution of metabolic network connectivity in mediating cellular control over metabolite levels, and have implications towards bridging the gap between genotype and metabolic phenotype.One of the primary mechanisms through which a cell exerts control over its metabolic state is by modulating expression levels of its enzyme-coding genes. However, the changes at the level of enzyme expression allow only indirect control over metabolite levels, for two main reasons. First, at the level of individual reactions, metabolite levels are non-linearly dependent on enzyme abundances as per the reaction kinetics mechanisms. Secondly, specific metabolite pools are tightly interlinked with the rest of the metabolic network through their production and consumption reactions. While the role of reaction kinetics in metabolite concentration control is well studied at the level of individual reactions, the contribution of network connectivity has remained relatively unclear. Here we report a modeling framework that integrates both reaction kinetics and network connectivity constraints for describing the interplay between metabolite concentrations and mRNA levels. We used this framework to investigate correlations between the gene expression and the metabolite concentration changes in  Regulation of metabolic activity in response to environmental and genetic perturbations is fundamental to the growth and maintenance of all cells. A primary regulatory process used by cells to control the activity of their metabolic network is the alteration in the expression of enzyme-coding genes. How these alterations regulate metabolite concentrations is an important question in the quest towards unraveling the genotype-phenotype relationship. The link between the expression levels of enzymes and metabolite concentrations is governed by the kinetics of individual reactions, which in turn are interlinked with each other due to the complex connectivity structure of metabolic networks. Although the enzyme-metabolite relationship is relatively well studied at the level of individual reactions, our understanding of the regulation of metabolite levels in complex networks has remained incomplete. In this study, we show that the constraints imposed by the network connectivity are key determinants of the relationship between gene expression and metabolite concentration changes. Our results provide mechanistic insight into the function of complex metabolic networks and have implications for health and biotechnological applications. Cellular metabolic networks provide basic biochemical building blocks and a thermodynamically favorable environment for growth and maintenance. Due to this crucial role of metabolism, cells have evolved various mechanisms to regulate metabolic reactions in response to genetic and environmental changes. Metabolic reactions can be regulated either by modulating the availability of the corresponding enzymes, e.g. through altered transcription and/or translation, or, by modulating the enzyme activities through post-translational modifications or through binding of small molecules. Our knowledge of the landscape of transcriptional, translational and post-translational regulation of metabolism is expanding with the increasing availability of datasets that provide genome-wide views of the abundance and interactions between mRNAs, proteins and metabolites Saccharomyces cerevisiae. We postulate that two primary mechanisms will largely determine the association between the changes in mRNA and metabolite levels: reaction kinetics  kinetics for all reactions. In essence, MM kinetics describes the flux or reaction rate V as a function of three parameters: i) concentration of the substrate, S; ii) maximum capacity of the enzyme pool, Vmax; and iii) a parameter reflecting the enzyme's kinetic properties, MK  according to the CoCCoA equations, which are developed in the subsequent sub-sections. To assess the proportion of variance in metabolite changes that can be attributed to transcriptional regulation, we compared the calculated CoCCoA scores with the experimentally measured metabolite concentration changes. The overall workflow used is depicted in By analogy to flux coupling analysis ties, KM . The cenThe first step in our analysis is to calculate a representative transcriptional fold-change for each reaction. As the yeast metabolic network consists of several reactions that are each governed by multiple proteins, we classified all reactions into three types: i) reactions catalyzed by a single enzyme, ii) reactions catalyzed by two or more isoenzymes, and iii) reactions catalyzed by enzyme complexes. We then applied the following rules to calculate the representative fold-changes for all reactions: in the case of isoenzymes, we averaged the fold changes of the related transcripts, while in the case of complexes, we picked the transcript with the lowest fold change . We usedWe used four published experimental datasets for evaluating the proposed CoCCoA models. These case studies included three pairwise comparisons – one genetic S. cerevisiaeA genome-scale metabolic reconstruction of th degree, 1st degree, 2nd degree, and so on  of any given metabolite. 1st degree CoCCoA additionally considers the production of the metabolite by using mass balance constraints. 2nd degree CoCCoA further expands the degree of network connectivity accounted for in the model by including the producing reactions of the precursors of the metabolite in question. Alternatively, the 2nd and higher degree models can also be expanded on both the consumption and production sides of the metabolite as described in the following sub-sections  remain unchanged in the experiment, by using MM kinetics one obtains (We consider metabolite concentration changes relative to a reference condition that can be arbitrarily chosen from the conditions pertaining to the experiment under investigation. Assuming that the enzyme properties (represented by  obtains :(1)* denotes the reference condition. The relative nature of this formulation allows circumventing the problem of the lack of availability of Min vivo K values. Furthermore, by assuming that &th degree coupling0, meaning that the metabolite S is not considered to be directly coupled to any other metabolite and is connected only to the enzyme that uses it as a substrate (Where ubstrate .(2)in vivo concentrations for several metabolites, especially from central carbon metabolism, are close to the corresponding MK values V are close to half of the maxV. Although the assumption of maxV≪V is not strictly applicable in this flux regime, numerical simulations showed modest errors (around 20%) due to this approximation  (The second major assumption is that the fold-change in mRNA level can be used as a proxy for the fold-change in enzyme abundance and ultimately for the fold-change in  0.0001) . We note 0.0001) . As mRNAth degree CoCCoA model is equivalent to the analysis of the transcript/protein-metabolite relationship reported by Sauer and co-workers r = 0.81, P = 0.048). In the other two pairwise comparison case studies, the 0th degree model failed to correlate with the experimentally observed metabolite changes  is eliminated in the 1st degree coupling equation and is replaced by two new terms, prod/Tprod*)ln(T and *)ln term can be approximated by the geometric mean of the transcript ratios of all the consumption (or production) reactions ln term equates to assuming that the preceding metabolite's concentration does not change between the two conditions; an alternative to omitting this term is explored below, in the 2nd degree CoCCoA model, in which the ln(R/R*) term is estimated by use of the 1st degree CoCCoA model. The effect of omitting the *)ln, and a reasonably good correlation  for the genetic perturbation case study  with the 1st degree CoCCoA relationship for the corresponding precursor metabolite , we obtained the 2nd degree coupling relationship. This 2nd degree model accounts for the gene expression changes corresponding to the precursor's production reactions  of several enzymes in the network, or if the metabolite concentrations are considerably above the corresponding MK values (saturated enzymes). Furthermore, the CoCCoA model needs to exclude reactions for which the flux directionality is ambiguous, and it assumes that the flux directions do not change for the rest of the reactions. Post-translational regulatory mechanisms, which can affect the kinetic parameters, are also not included in the current CoCCoA formulation, as sufficient data are not available to enable their modeling. The latter is perhaps the most restrictive limitation of our model. Post-translational regulation is known to play a crucial role in the yeast central metabolism, wherein several enzymes are controlled by allosteric binding of small molecules CoCCoA is not applicable in the case of perturbations that are likely to drastically affect the kinetic properties  showed positive correlations , adjusting the transcript ratios in each simulation by a randomly sampled correction factor to account for the expected difference between the mRNA and protein fold changes. The sampling space for the correction factors was estimated based on the variance in the slopes of linear regression lines between mRNA and protein abundance fold changes across different datasets  in a large fraction of these simulations   .st and higher degree CoCCoA). Thus, inclusion of gene expression changes associated with the both upstream and downstream reactions was critical for explaining metabolite concentration changes. For all three pairwise comparison case studies, CoCCoA models explained more than 60% of the variation in metabolite changes based on gene expression. For the metabolic cycle case study, CoCCoA could explain variation in about 33% of the measured metabolites, with correlation coefficients as strong as 0.90.The correlation between metabolites concentrations and transcript fold changes becomes evident only when including network connectivity constraints lnln(R/R term in the right-hand side of the 1st degree CoCCoA equation) (P = 0.0006). In these cases, the post-translational regulation may be counteracting the transcriptional change. Post-translational regulation of an enzyme can change its MK value and can thereby directly affect CoCCoA scores. Consider, for example, 1st degree CoCCoA score. When changes in MK values are included in the 1st degree CoCCoA formula, the score becomes: MK ratios in this new score will partially cancel out or even override the transcript ratios. When assuming constant MK values, the discrepancy between the transcript and MK ratios in some cases might be sufficiently large to result in CoCCoA scores with opposite sign. On the other hand, the inconsistency between the directions of transcriptional and post-translational regulation  implies non-optimal regulation and is unlikely to be a general mechanism used by the cell. However, non-optimal regulation is a possibility for certain enzymes, with two plausible biological explanations: i) the highly non-linear scenario of regulation  can mean that the cell needs to make some locally non-optimal choices in order to achieve a global optimality in regulating the overall metabolism ; ii) the observed behavior is both locally and globally non-optimal in case of certain perturbations. The second scenario would imply that the perturbations in question are unknown or new to the cells in the evolutionary sense.Intriguingly, several of the observed negative correlations were found to be not only significant but also quite strong, with  as 0.86 . These nquation) . This obin vivo measurements of fluxes, metabolite concentrations, protein abundances and functional post-translational modifications. Nevertheless, we note that our model revealed significant correlations in several cases, including perturbations of very different nature. We also note that, in the case of metabolic cycle dataset, significantly more positive correlations were observed than negative . Together, the statistical and mechanistic considerations suggest that the CoCCoA model captures considerable mechanistic essence of the complex processes governing metabolite levels.In addition to the unaccounted post-transcriptional regulation, the simplifying assumptions of constant flux directions and flux split ratios may also be contributing to the observed negative correlations. A wrongly considered flux direction for a reaction would mean that the corresponding fold change in the expression level would be treated in the opposite direction. Similarly, moderate changes in the flux split ratio can also cause a sign reversal in the CoCCoA score if one of the fluxes is significantly lower than the other(s). The interaction between the various missing/simplifying factors in our model can further amplify the difference between the CoCCoA scores and actual concentration changes. How these interactions lead to the reversal of correlation while retaining statistical significance is yet unclear. Further investigation into the mechanisms underlying these intriguing negative correlations would require network-wide Overall, our model-guided analysis highlighted the role of metabolic network connectivity in modulating metabolite concentration changes and revealed much stronger correlations between gene expression and metabolite levels than previously appreciated. The proposed model can be extended to include translational and post-translational regulation as the data becomes available. From this perspective, we see CoCCoA as a framework with a strong mechanistic yet parameter-free basis, rather than a general relationship. We anticipate that, due to its parameter-free nature, the CoCCoA framework will be widely applicable for modeling metabolite level changes in large metabolic networks.S. cerevisiae were used. The first study, Fendt et al.GCR2, a transcription factor responsible for activation of glycolytic genes et al.et al.Four different experimental studies reporting gene expression and metabolite concentration measurements for the yeast Saccharomyces cerevisiae metabolic network by Forster et al.glpk solver (http://www.gnu.org/software/glpk/) accessed through a C library.A genome-scale reconstruction of www.bioconductor.org). Probe intensities were corrected for background by using robust multi-array average method (RMA) limma package Preprocessing of the Affymetrix CEL files was carried out with the statistical software environment R/Bioconductor  using the function cor.test. Metabolite changes were used as dependent variables and CoCCoA scores as independent. P-values for the null hypothesis of no correlation (regression slope = 0) were estimated by using the same function. In addition, we performed a permutation test by shuffling gene labels before calculating CoCCoA scores. The originally paired data was randomly permuted without replacement 1000 times. For each permutation, a correlation coefficient was calculated and the P-value was estimated as a fraction of squared correlation coefficients that were larger than in the case of the original paired data. The results were similar to those estimated with the cor.test function.Pearson correlation coefficients between loghttp://www.patil.embl.de/supplementaryFigure S1Correlations between experimentally measured metabolite concentration changes and CoCCoA scores based on gene expression fold changes. A) Facet columns correspond to three different pairwise comparison datasets used in our work; rows represent different CoCCoA models. B) Heatmap of Pearson correlation coefficients assessing the applicability of CoCCoA models to the metabolic cycle study. In the present figure, the significance thresholds for the transcript and metabolite fold changes are relaxed in comparison to the data shown in (PNG)Click here for additional data file.Figure S2A. Error (Z-axis) as a function of V/Vmax and V*/Vmax*. The error function is shown in supplementary B. Error estimates around the points where V/Vmax = V*/Vmax*, representing a situation in which the enzyme saturation levels remain unchanged in the perturbed condition. C. 2-D projection of the plot in A, where the errors are represented with different colors.Estimates of error in predicting metabolite concentration changes with MM kinetics when assuming V≪Vmax (see main text for the motivation behind the use of this assumption). (PNG)Click here for additional data file.Figure S3Correlation between protein abundance changes and the corresponding mRNA abundance changes is stronger for metabolic proteins. A, D, G, J, M, P) Correlation including all proteins measured in different datasets. B, E, H, K, N, Q) Correlations including only metabolic proteins Click here for additional data file.Figure S4Coefficients of determination for the correlations between experimentally measured metabolite concentration changes and CoCCoA scores corresponding to different degrees. The significance of correlations was assessed against correlations obtained with random permutations of gene labels.(PNG)Click here for additional data file.Figure S5et al. case study.Example CoCCoA score calculations. Shown is the case of fumarate in the Fendt (PNG)Click here for additional data file.Table S1Summary of the growth conditions from the three pairwise comparison case studies used in our analysis.(DOCX)Click here for additional data file.Table S2Physiological data from the pairwise comparison case study 1.(DOCX)Click here for additional data file.Table S3Physiological data from the pairwise comparison case study 2.(DOCX)Click here for additional data file.Table S4Physiological data from the pairwise comparison case study 3.(DOCX)Click here for additional data file.Table S5Reaction directions used for the case studies 1 and 2.(DOCX)Click here for additional data file.Text S1Supporting text.(DOCX)Click here for additional data file.


Motivation: Although constraint-based flux analysis of knockout strains has facilitated the production of desirable metabolites in microbes, current screening methods have placed a limitation on the number knockouts that can be simultaneously analyzed.Results: Here, we propose a novel screening method named FastPros. In this method, the potential of a given reaction knockout for production of a specific metabolite is evaluated by shadow pricing of the constraint in the flux balance analysis, which generates a screening score to obtain candidate knockout sets. To evaluate the performance of FastPros, we screened knockout sets to produce each metabolite in the entire Escherichia coli metabolic network. We found that 75% of these metabolites could be produced under biomass maximization conditions by adding up to 25 reaction knockouts. Furthermore, we demonstrated that using FastPros in tandem with another screening method, OptKnock, could further improve target metabolite productivity.Availability and implementation: Source code is freely available at http://www-shimizu.ist.osaka-u.ac.jp/shimizu_lab/FastPros/, implemented in MATLAB and COBRA toolbox.Contact:chikara.furusawa@riken.jp or shimizu@ist.osaka-u.ac.jpSupplementary information:Supplementary data are available at Bioinformatics online. Metabolic engineering of microbes has been successfully used for the production of a variety of useful compounds in microbes . Flux baIn silico screening of genetic modifications is a widely used application of FBA for metabolic engineering, and to date several such algorithms have been proposed  are selected. In the second iteration, in addition to the reaction knockouts selected in the first iteration, the effects of additional single reaction knockouts are screened. This approach has a drawback, however, of incompletely searching the knockout combinations. For example, when target production yields under biomass maximization are used as a score for screening, iterative screening fails to identify the combinations of two knockouts that show higher production yields only when they are disrupted simultaneously. To overcome this drawback, several systematic screening methods have been developed, such as OptGene , which uses biomass production maximization to identify sets of metabolic reactions whose simultaneous knockouts result in the production of a target metabolite. In this algorithm, we adopted a novel score for iterative knockout screening based on the change in biomass production flux caused by a slight increase in the target production flux, In the present study, we developed a new iterative screening algorithm, E.coli K-12 MG1655 named iAF1260  and MATLAB on a Windows machine with Intel Xeon 2.66 GHz processors. For all simulations, glucose was used as the sole carbon source, and its uptake rate was set to 10 mmol/gDW/h. The oxygen uptake rate was set to 5 mmol/gDW/h, which corresponds to a microaerobic condition, i.e. the oxygen uptake is insufficient to oxidize all NADH produced in glycolysis and the tricarboxylic acid cycle in the electron transfer system. This relatively low oxygen uptake rate was chosen, as higher production yields of target metabolites can be obtained under these conditions, in comparison with the higher oxygen uptake rate when carbon is mainly used to generate biomass and COConsider the case in which the production flux of a target metabolite is zero under biomass flux maximization. In this case, the increase in the target production flux from zero flux brings about a decrease in the biomass production flux. In contrast, if the target is produced under biomass production maximization, it corresponds to the case that an increase in the target production flux increases the biomass production flux. The change in biomass production flux caused by the increase in target production flux is a useful measure to represent the potential of the target production. In this study, we defined the potential of the target production, M and R are the set of metabolites and reactions, respectively. jv is the metabolic flux of reaction j. growthv, glc_uptakev, o2_uptakev and atp_mainv are the biomass production rate, the glucose uptake rate, the oxygen uptake rate and non–growth-associated ATP maintenance requirement, respectively. i,jS is the stoichiometric coefficient of metabolite i in reaction j. Rirrev and Rrev are the set of irreversible and reversible reactions in the metabolic model, respectively, and Rrev involves the exchange reactions of available nutrients for a cell, based on a previous article .where Supplementary Figure S1. Starting from a reduced metabolic model of E.coli with N possible single knockouts, the P × N knockout sets), and among these knockout sets that increased The screening procedure is schematically illustrated in P = 0.5N, P = N and P = 1.5N. We found that the number of screened metabolites in the case of P = 0.5N was significantly smaller than the case of P = N (∼18% metabolites screened in P = N were failed to be identified), whereas the number of screened metabolites was the same for P = N and P = 1.5N. The average calculation times for performing the knockout screening of one metabolite by single Xeon CPU (2.66 GHz) were 2.6, 6.2 and 11.4 h for P = 0.5N, P = N and P = 1.5N, respectively. Based on these analyses, we determined P = N is appropriate for FastPros screening using the reduced metabolic network of E.coli in this study.The number of parent knockout sets, P, was determined heuristically. We performed FastPros screening to obtain metabolites whose production is predicted by adding up to 25 reaction knockouts using E.coli metabolic model and the screened reaction knockout sets that result in the production of each metabolite when the biomass production is maximized. For each target metabolite, iterative screening of the reaction knockouts for increasing the production was performed as described earlier in the text. From this screening, positive or zero Supplementary Table S1 (available at http://www-shimizu.ist.osaka-u.ac.jp/shimizu_lab/FastPros/).To investigate the performance of FastPros, we selected 625 metabolites in the Supplementary Table S1). It should be stressed that the computational time of comprehensive screening generally increases exponentially with the number of knockouts, and that the maximum number of knockouts is accordingly limited. In contrast, FastPros enables the screening of a larger number of knockouts for target production with low computational cost and has an accuracy that is comparable with that of comprehensive screening methods. In fact, our method demonstrated that a significant number of metabolites exist whose production requires >10 reaction knockouts, an outcome that would be difficult to identify by comprehensive screenings.The accuracy of the iterative screening by FastPros was evaluated by comparing the screening results to those obtained by the comprehensive screening method OptKnock. Owing to the computational cost, the maximum number of reaction knockouts was set to 3 for OptKnock screening. Comprehensive screening by OptKnock showed that 152 of 625 metabolites are produced when maximizing the biomass production flux by adding three or fewer reaction knockouts. Of the 152 metabolites screened by OptKnock, 136 metabolites were also identified under a maximum of 3 knockouts using our iterative screening based on Supplementary Table S1. Among the 247 metabolites screened by OptGene, 244 were also screened by FastPros, whereas all 55 metabolites screened by GDLS were screened by FastPros. As shown in Supplementary Figure S2, although OptGene and GDLS successfully identified knockout sets when using a small number of reaction knockouts, they failed when relatively large numbers of simultaneous knockouts were necessary for the metabolite productions. This result is because the target production flux, which was used as the fitness score, needs to be increased in iterative knockout screenings. The target production flux can be used for the fitness score only when the target metabolites are already produced by the wild-type network or after a small number of simultaneous knockouts. Otherwise, searching the huge number of possible knockout sets without target production makes finding a set of knockouts with non-zero target production extremely difficult. For example, in OptGene, the initial population of knockout sets is usually determined randomly. If there is no set of knockouts that result in the target production in the initial population, selecting knockout sets with higher target production is effectively impossible. In contrast, in FastPros, the use of Furthermore, we compared the screening performance of FastPros with OptGene and GDLS, which are widely-used iterative knockout screening methods. In the OptGene and GDLS screenings, we adopted the same parameter sets used in the original reports . We found that for 106 (28%) of the target metabolites, production yields increased by >5% of the theoretical maximum yield (TMY) in comparison with the cases in which FastPros only was used. For example, the production yields of succinate and sedoheptulose 7-phosphate were predicted by FastPros only to be 22 and 55% of the TMY, respectively, but were 74 and 79% of TMY when using FastPros-based OptKnock screening , indicating the proposed approach can be an alternative to the other knockout screening methods. Therefore, we proposed an alternative algorithm for knockout screening for high-target production using both FastPros and OptKnock. As mentioned earlier in the text, iterative screening using creening A and B. creening C. These E.coli. Therefore, the design of appropriate metabolic networks for GPP production is valuable for engineering applications. We performed FastPros screening for GPP production and identified 88 sets of reaction knockouts that resulted in the production of GPP when biomass production was maximized. These knockout sets contained 25 unique reactions that were selected for the OptKnock screening (Supplementary Table S3). Knockouts of seven reactions resulted in the highest yield of GPP, 0.34 g/g-glucose (53.3% of TMY). Supplementary Material).Geranyl diphosphate (GPP) can be biologically converted into geraniol, which is an aromatic material commonly used in perfume. GPP is also an intermediate in a terpenoid biosynthesis pathway . Accordingly, reaction knockouts that increase the biosynthesis flux toward GPP can increase the production of terpenoids in l-Phenylalanine (l-Phe) is an aromatic amino acid with many applications in the food and pharmaceutical industries, such as aspartame. Because chemical synthesis of l-Phe generates racemic mixtures of d- and l-Phe, the production of pure l-Phe in bioprocesses is important. E.coli contains a natural l-Phe biosynthetic pathway that has been used in commercial production. We performed FastPros screening and identified 57 knockout sets for the production of l-Phe, including 44 unique reactions. Of these, 30 reactions contributing higher production yields were selected for OptKnock screening (Supplementary Table S4). A production yield of 0.27 g/g-glucose (58.0% of TMY) was estimated for the knockout of 10 reactions. l-Phe production network. One mole of l-Phe is synthesized from 2 mol of phosphoenolpyruvate (PEP) in glycolysis and 1 mol of erythrose 4-phosphate (E4P) in the pentose phosphate pathway. Accordingly, reactions that convert PEP or other metabolites in upper glycolysis into pyruvate were knocked out, enhancing the carbon flow from PEP and E4P to l-Phe .The results of FastPros screening demonstrated that metabolites often share the same reaction knockouts for their production. Here, we analyzed the similarity of knockout candidate sets among the target metabolites, with the aim of identifying a common knockout set for the production of a specific class of metabolites. The identification of such common knockout sets enables the design of a common parent strain, from which production strains for various target metabolites can be generated by adding a variety of additional reaction knockouts to the parent strain.Supplementary Table S5). For example, Cluster 1 in l-Phe, etc.), and knockouts of PPC, pyruvate carboxylase, MGS and phosphoglycerate dehydrogenase were shared by the metabolites in this cluster. Cluster 3 consisted of 29 target metabolites, most of which were sugars or sugar phosphates, the production of which shared knockouts of PPC, pyruvate kinase, phosphoglycerate dehydrogenase and glucose 6-phosphate dehydrogenase. The detailed mechanisms to produce the metabolites in Clusters 1, 2 and 3 are discussed in the Supplementary Material.Supplementary Fig. S2). We expect that the use of FastPros will greatly accelerate computer-aided metabolic design for industrial bioproductions.We have developed a novel algorithm, FastPros, to screen sets of reaction knockouts that produce target metabolites. We used a screening score, in silico methods for metabolic engineering, for example, for the production of non-native metabolites. Although in this study we considered only the screening of reaction knockouts from a wild-type metabolic network, FastPros screening would be applicable, for example, after the addition of heterologous reaction pathways to produce desired non-native targets (The FastPros screening method we have proposed can be used in collaboration with other  targets . This sttktA and tktB gene sets), which avoids cases where only a part of the reactions encoded by the same gene sets is disrupted in silico. By considering the relationship between metabolic reactions and genes encoding corresponding enzymes, we can develop strategies for gene manipulation using in silico screening by FastPros.Although FastPros is based on reaction knockouts, we also considered gene deletions. As mentioned in in silico predictions can be eliminated by experimental evolution. Several studies have demonstrated that when a microorganism strain is cultured for an extended period to select individuals with optimized growth under a given condition, the realized flux profile gradually approaches the calculated optimal flux profile (in silico screening and experimental evolution that achieves an optimal flux profile experimentally is a potentially practical application for obtaining valuable strains for bioproduction.The algorithm of FastPros is based on the assumption of biomass production maximization, that is, that metabolic fluxes are organized to achieve an optimal profile for cellular growth. Of course, this assumption is not always the case experimentally. If a strain after the predicted reaction knockouts cannot be obtained due to no or slow growth, screening should be performed again with consideration of lethal or growth-defect knockouts. The integration of data on synthetic lethality (E.coli. E.coli whose production was enhanced under biomass production maximization only when multiple reactions were simultaneously knocked out. We expect that our algorithm and the concept of In conclusion, we have developed a novel computational algorithm, FastPros, that accelerates microbial strain improvement and have demonstrated the applicability of FastPros to cell-wide metabolite productions in


Rhodobacter sphaeroides is one of the best studied purple non-sulfur photosynthetic bacteria and serves as an excellent model for the study of photosynthesis and the metabolic capabilities of this and related facultative organisms. The ability of R. sphaeroides to produce hydrogen (H2), polyhydroxybutyrate (PHB) or other hydrocarbons, as well as its ability to utilize atmospheric carbon dioxide (CO2) as a carbon source under defined conditions, make it an excellent candidate for use in a wide variety of biotechnological applications. A genome-level understanding of its metabolic capabilities should help realize this biotechnological potential.R. sphaeroides strain 2.4.1, designated iRsp1095, consisting of 1,095 genes, 796 metabolites and 1158 reactions, including R. sphaeroides-specific biomass reactions developed in this study. Constraint-based analysis showed that iRsp1095 agreed well with experimental observations when modeling growth under respiratory and phototrophic conditions. Genes essential for phototrophic growth were predicted by single gene deletion analysis. During pathway-level analyses of R. sphaeroides metabolism, an alternative route for CO2 assimilation was identified. Evaluation of photoheterotrophic H2 production using iRsp1095 indicated that maximal yield would be obtained from growing cells, with this predicted maximum ~50% higher than that observed experimentally from wild type cells. Competing pathways that might prevent the achievement of this theoretical maximum were identified to guide future genetic studies.Here we present a genome-scale metabolic network model for R. sphaeroides and closely related organisms.iRsp1095 provides a robust framework for future metabolic engineering efforts to optimize the solar- and nutrient-powered production of biofuels and other valuable products by  This facultative bacterium is capable of either aerobic or anaerobic respiration, depending on the availability of oxygen (O2) or alternative electron acceptors. When O2 is absent or limiting, light energy can be harnessed by a photosynthetic electron transport chain that has features similar to those used by plants and other oxygen-evolving phototrophs [R. sphaeroides is capable of autotrophic or heterotrophic growth using either carbon dioxide (CO2) or organic carbon sources [Photosynthetic organisms perform many functions of significance to the planet and society. Plants and photosynthetic microbes are responsible for harvesting solar energy, evolving oxygen and sequestering atmospheric carbon dioxide . In addiil fuels . The abitotrophs . During  sources ,5. Thus,R. sphaeroides has also received significant attention due to its biotechnological potential, with its ability to produce large amounts of carotenoids or isoprenoids as a source of biocommodities, H2 as a potential biofuel, or polyhydroxybutyrate (PHB) as raw material for biodegradable plastics [R. sphaeroides makes it a potential organism for use in the synthesis of chemicals or polymers that can serve as raw materials in the production of biofuels, or as a means of sequestering atmospheric or industrially-produced CO2 [R. sphaeroides that are based on genomic information, which can be informed and integrated with laboratory analysis of wild type and mutant strains [plastics . Further strains ,7.Synechocystis sp. PCC 6803 [R. sphaeroides metabolic networks that use flux balance analysis (FBA) [Over the last decade the field of constraint-based metabolic modeling has witnessed significant progress, which has led to major advances in the modeling, understanding and engineering of different biological systems -11. As aPCC 6803 -14. ModePCC 6803  and smalis (FBA)  and enseis (FBA)  have alsR. sphaeroides strain 2.4.1 consisting of 796 metabolites, 858 transformation reactions and 300 transport reactions. The reconstruction includes 1,095 genes, covering about 25% of the recognized R. sphaeroides open reading frames. To facilitate improved predictions, the biomass composition of R. sphaeroides was determined under a variety of growth conditions and used in generating biomass objective functions suitable for developing predictive models. FBA [2 fixation and the electron transport chain. Overall, iRsp1095 shows good qualitative and quantitative agreement with experimental observations. Thus, iRsp1095 provides concepts and a basis for extensive future studies of this bacterium, other related bacteria and photosynthetic organisms in general.Here we present iRsp1095, a manually curated genome-scale metabolic reconstruction for els. FBA -20, fluxels. FBA  and alteels. FBA ,23 were R. sphaeroides metabolic network was constructed by extracting genomic and metabolic information from KEGG [R. sphaeroides model was further analyzed for stoichiometrically balanced cycles (SBCs) - internal network loops that carry flux in a closed system  with no net production or consumption of metabolites [The initial rom KEGG , and comrom KEGG  analysisrom KEGG   that houses the photosynthetic apparatus [R. sphaeroides, we experimentally determined the major macromolecular constituents of aerobically and photosynthetically grown cells . Based on these experimentally determined macromolecular components  have gene-protein-reaction (GPR) assignments, with 203 of these having associated experimental data, while 95 (8.2%) of the reactions without GPR assignments correspond to place holder reactions for which a putative gene could not be assigned. The remaining 14 reactions correspond to known spontaneous or diffusion reactions  as the electron donor was also simulated.We used FBA and other constraint-based approaches to interrogate the properties of the iRsp1095, with simulations conducted for aerobic respiration, dark anaerobic respiration in the presence of the electron acceptor dimethyl sulfoxide (DMSO) and photoheterotrophic growth (anaerobic growth in the presence of light and an electron-rich carbon source) using Sistrom's minimal media (SIS)  containi2 while supplied with SIS minimal media. The model was capable of predicting growth in the dark in the presence of O2 or DMSO as known electron acceptors, under photoautotrophic conditions using CO2 as the sole carbon source and either H2 or H2S as electron donor, and photoheterotropically with a variety of organic carbon sources  have previously been reported [As a first step in assessing the performance and breadth of iRsp1095, we used FBA to test for the ability of the model to predict the production of biomass and Hes Table . In addireported ,42,43 . Under these conditions, iRsp1095 predicts that a core set of 293 reactions (25% of the network) are essential for growth . These observed differences could be the result of several factors, including stress and feedback inhibition, which cannot be captured in stoichiometric models. Furthermore, many laboratory strains are not necessarily evolved for maximization of growth and thus do not meet the FBA predicted growth rate prior to adaptive evolution experiments [R. sphaeroides strain 2.4.1 is not as far from optimal growth under the conditions we analyzed.To assess iRsp1095 quantitatively, we used FBA and alternate optima analysis to sample the feasible solution space and make predictions about specific growth rate and the rate of production of key metabolic products during photoheterotrophic growth on a variety of carbon and nitrogen sources , as well as during aerobic growth on succinate and ammonia. We compared the predicted fluxes to experimentally determined growth rate and production rates for these key metabolites during e Figure , with aneriments . Nevertheriments ,46, sugg2, PHB and CO2 presented in Figure 2, PHB and CO2 generally ranged from within 4% to 200% of the experimentally measured fluxes  can be affected . However, for all carbon sources tested the theoretical H2 production maxima were reached under suboptimal growth conditions with biomass fluxes around 0.055-0.060 h-1. For comparison to experimental production rates, a reference chemostat yielded a H2 flux that was about two thirds of the theoretical maximum of 11.5 mmol/g DW h  as shown in Figure 2 producing capacity is proportional to substrate reducing power, irrespective of the carbon source. The intercept of this relationship, where no electrons are available to support H2 production, shows the reducing power that supports growth alone. The derived slope, which equals 1, indicates that maximizing H2 production can theoretically be achieved by directing all electrons in excess of that required for growth to H2 production. This is a significant finding since there are multiple competing pathways that can dissipate substrate reducing power, so this result suggests that H2 production can be increased from experimental values to theoretical maxima if these other pathways are silenced.In Figure ceptance . We foun2 production potential than resting cells, since, in all cases studied, metabolism with no flux in the biomass reaction yielded the lowest maxima of H2 flux. Therefore, the breakdown of substrates in biomass synthesis pathways seems necessary to provide maximal reducing power for H2 production. The relationship of theoretical maxima at the no-growth condition to the reducing power of the substrates was similar to those with growing cells  is still capable of photoautotrophic growth, when using less reduced electron donors than H2  [2 assimilation pathways can support growth under these conditions. Pyruvate carboxylase has previously been shown not be one of these alternative routes [2 sequestration under these conditions. The first enzyme in this pathway, crotonyl-CoA carboxylase/reductase, catalyzes the reductive carboxylation of crotonyl-CoA to ethylmalonyl-CoA [2 fixation in R. sphaeroides, and the only one currently incorporated in the model that is capable of supporting photoautotrophic growth in the absence of RubisCO.As expected, during photoautotrophic growth iRsp1095 predicts there is a high flux through ribulose-1,5-bisphosphate carboxylase/oxygenase (RubisCO) and the Calvin cycle, as it represents a major pathway for COmilation ,51. Howee routes . iRsp109onyl-CoA ,53 and i2 being produced as the rate of ammonia uptake used in simulation (1 mmol/g DW h) results in nitrogen limiting conditions, allowing excess succinate supplied to the model to be converted to H2. iRsp1095 does not predict flux through RubisCO to be essential for photoheterotrophic growth; however, it is known that RubisCO is essential for photoheterotrophic growth of wild-type R. sphaeroides on carbon sources like succinate and malate, where there is reductive assimilation of CO2 [2; (ii) the sulfite reductase reaction resulting in the production of H2S; (iii) PHB synthesis; or (iv) the use of the ethylmalonyl pathway  and NADH dehydrogenase, with both enzymes predicted as being essential during growth on succinate and ammonia. The essentiality of the Fbc complex might be expected as it serves as the only means of providing reduced cytochromes required for the photosynthetic light reaction ,54. In c2 and trace amounts of urea. iRsp1095 also predicts that cyctochrome c oxidase (Cox) activity is sufficient and required for optimal aerobic respiratory growth. In the absence of Cox activity, quinol oxidase (Qox), which is capable of ubiquinol oxidation to ubiquinone coupled to direct O2 reduction, is predicted to support aerobic respiratory growth, but the predicted growth rate in this mutant is only 60% of the predicted optimum. A similar reduced growth rate is also predicted in the absence of the Fbc complex, as this also results in flux being directed through Qox in order to oxidize ubiquinol  as alternative routes for dissipating excess reducing power. While the role of some of these processes have been experimentally verified [R. sphaeroides on RubisCO for photoheterotrophic growth, a phenotype not corroborated by iRsp1095, suggests that these alternative routes for dissipating excess reducing power could either represent silent functional states or are insufficiently active to support growth in the absence of the Calvin cycle.Previous research has shown the potential of constraint-based analysis for understanding metabolic networks . Given tds or H2 . Furtheroduction ,7,17, iR2 production potential of R. sphaeroides with iRsp1095 showed that continuous culture performance reached two-thirds of the predicted maximum H2 production . Hence, these reactions provide predictions on the pool of electrons that can be diverted from biomass synthesis to H2 production.Our evaluation of Hn Figure . To harnR. sphaeroides possesses two cytochrome oxidases (Cox): aa3-type cytochrome c oxidase and cbb3-type cytochrome c oxidase, which carry out the same reaction but have different oxygen affinities. R. sphaeroides also possesses two quinol oxidases (Qox) - QoxBA and QxtAB - that provide a less energetically efficient means for recycling reduced electron carriers [Rhodobacter capsulatus [R. capsulatus, R. sphaeriodes is predicted to contain two isozymes of the NADH dehydrogenase complex, with genes encoding both enzymes being expressed during photoheterotrophic growth [R. sphaeroides is required to compare with the predictions of iRsp1095.FBA has also enabled us to model the flow of electrons through the aerobic respiratory chain. carriers . While icarriers , which icarriers ). Furthepsulatus ,57. Furtc growth . ExperimR. sphaeroides reinforces the challenge of making accurate predictions about condition-dependent metabolic fluxes as not all feasible functional states are relevant to wild type cells. Thus, to obtain improved predictions of the flux distributions through the network of wild-type R. sphaeroides, additional constraints on iRsp1095 will be required.Finally our simulations predict that several alternative optimal solutions are often possible under any given condition, reinforcing the need to analyze the space of alternate optima -23. The R. sphaeroides possesses multiple pathways that could be exploited as electron sinks during photoheterotrophic growth, though experimental results suggest many of these are silent in wild type cells. Other results predict that additional gains in H2 production are possible as the production capacity of wild type cells is only about two-thirds of the theoretical maximum, with pathways and reactions that could increase production predicted using iRsp1095. An alternative route for CO2 fixation, the ethylmalonyl pathway, was predicted using iRsp1095. This prediction could potentially resolve the question of how R. sphaeroides assimilates CO2 in the absence of RubisCO. iRsp1095 also predicts the reversibility of the NADH dehydrogenase complex and its essentiality during photoheterotrophic growth on succinate, where it plays a key role in oxidation of ubiquinol. Further experimental work is needed to confirm these predictions and improve our understanding of the metabolic network of this and possibly other related bacteria. Finally, quantitative predictions made using iRsp1095 showed good agreement with experimental observations, verifying the utility of the model and highlighting the potential for its use in quantitative analysis of R. sphaeroides metabolism.iRsp1095 represents the first comprehensive genome-scale metabolic reconstruction for a facultative photosynthetic bacterium. This genome-scale reconstruction has enabled us to examine the metabolic capabilities of this purple non-sulfur bacterium. Our modeling results predict that m × n, was generated from the reconstruction with the rows (m) representing the metabolites, the columns (n) representing the reactions and the entries in the matrix representing the stoichiometric coefficients for metabolites involved in each reaction. Flux balance analysis (FBA) [in silico growth by solving the linear programming problem:A stoichiometric matrix, Sis (FBA)  was usedBiomass is the flux through biomass objective function (BOF); v is the vector of steady state reaction fluxes; and vmin and vmax are the minimum and maximum allowable fluxes. The values in vmin and vmax were set to -1000 and 1000 mmol/g DW h for reversible reactions, 0 and 1000 mmol/g DW h for forward only reactions, and -1000 and 0 mmol/g DW h for backward only reactions, respectively. During simulation all exchange reactions were assigned as being forward only , except the exchange reactions for media components required by the cell for growth, which were set to measured values for limiting substrates - carbon and nitrogen sources, or allowed to be freely exchanged with the extracellular space, i.e., -1000 ≤ v ≤ 1000. In addition, the non-growth associated ATP maintenance limit was set to 8.39 mmol/gDW h [where vol/gDW h .Flux variability analysis (FVA) was carried out as described in  by firstwhere Z is the optimal flux through the BOF predetermined using FBA.Alternate optima analysis was conducted as described in , using ai, wi ∈ {0, 1}, NZ is a set of indices that keeps track of non-zero fluxes of interest for each iteration j. During each iteration through j, at least one of these fluxes of interest vi with a non-zero value must be set to zero and thus yi for the corresponding flux is set to 1 (Equation 6). When yi takes the value 1, wi is forced to 0 (Equation 8), forcing the upper and lower bounds of vi to zero (Equation 9). Equation 7 ensures that previously identified optima are not revisited by forcing at least one non-zero flux to have a zero value for the next iteration. Fluxes of interest used in our alternate optima analysis were restricted to those observed to be involved in redox balancing or for which we had experimental measurements for comparison  had non-zero fluxes.where yDeletion analysis was initially carried out at the reaction level by sequentially setting the flux of each reaction to zero, then using FBA to compute the optimal growth rate. Reactions which led to the production of no biomass were considered essential. At the gene level, the fluxes of all reactions associated with a particular gene were set to zero and FBA used to compute the optimal growth rate. Genes encoding proteins whose reactions were required for the formation of biomass, and for which there existed no isozymes in the model, were considered essential.For analysis of potential carbon, nitrogen, phosphorus and sulfur sources utilized in iRsp1095, simulations were conducted using SIS as the baseline media, which contains succinate, ammonium, phosphate, and sulfate as the only the sources of carbon, nitrogen, phosphorus, and sulfur, respectively. To test a different source, the original metabolite was removed and replaced with the metabolite to be tested. When needed, temporary sink reactions  were addR. sphaeroides 2.4.1 was cultured in 20 mL chemostats at ~30°C, either continuously illuminated by an incandescent light source for photosynthetic growth , or continuously aerated (4 mL/min from a compressed air cylinder) in dark conditions for aerobic growth. The turbidity of photosynthetic cells was monitored using a Klett-Summerson photoelectric colorimeter , while that of aerobic cultures was measured spectrophotometrically at 600 nm wavelength with a UV-1601 Spectrophotometer . Reactors were started in batch mode [To obtain steady state growth data for FBA, wild type tch mode  containiCultures were centrifuged  to obtain cell pellets for biomass analysis. Cell pellets pooled from several chemostats were resuspended in 1X SIS medium, mixed, and distributed into different subsamples for measuring individual biomass components. The major cellular components measured were protein, DNA, RNA, cell wall, lipids, bacteriochlorophyll, carotenoids, glycogen and PHB.R. sphaeroides [Total cellular protein was quantified via the Lowry assay ,60, whilaeroides .E. coli [The PHB content of cells was determined by GC-MS  ,65. CellE. coli . FinallyE. coli .biomass represents the overall measurement of COD in cells, CODPHB and CODglycogen represent COD of PHB and glycogen obtained from experimental measurements and theoretical COD/weight ratios (1.67 mgCOD/mgPHB and 1.18 mgCOD/mg glycogen), and θ is the COD/weight ratio for the cell mass according to the biomass reactions established in this study (θ is 1.62 for photosynthetic and 1.56 for aerobic cultures).The biomass reaction of the metabolic model was formulated using major biomass components as detailed in Additional File 2 uptake, an important parameter in the FBA of aerobic growth, was indirectly measured by COD, which was previously used for analysis of electron fate in photosynthetic cultures of R. sphaeroides [2 utilization by the cells due to the mass balance of electrons [Substrate uptake rates of all cultures and gas composition of the headspace in phototrophic chemostats were measured using previously described protocols  see Add. No gas aeroides . Brieflylectrons .The authors declare that they have no competing interests.R. sphaeroides continuous cultures and obtained analytical data. SI and LSY participated in the determination of the R. sphaeroides biomass composition. JLR provided code samples for metabolic modeling. TJD and DRN conceived of project and coordinated research. SI wrote paper with critical reading and revisions by LSY, JRL, DRN and TJD. All authors read and approved the final manuscript.SI and LSY participated in the reconstruction, curation and assessment of iRsp1095. US, ASG and LSY set up Supplemental materials and methods Additional File 1 contains details of the model reconstruction and refinement process, as well as details of GC/MS and supernatant analysis.Click here for fileiRsp1095 Metabolic Reconstruction Additional File 2 contains 12 tables. Table S1 list all the reactions in iRsp1095 including official reaction names, reaction stoichiometry, GPR assignments, directionality assignments and localization information. Table S2 contains information about metabolites in the model. Table S3 contains thermodynamic calculations used in the determined reaction directionality. Table S4 lists reactions constrained to eliminate SBCs. Table S5 lists the genes present in the model. Table S6 summarizes simulated growth phenotypes with various carbon sources. Table S7 lists all the references used in curation of iRsp1095. Table S8 lists reactions added to the model based on metaSHARK analysis. Table S9 details the compositions of SIS minimal media. Table S10 lists essential genes identified by FBA analysis. Table S11 list the gap filling reactions added to iRsp1095. Table S12 contains as description of the confidence scores assigned to the reactions in iRsp1095.Click here for fileBiomass calculations This contains calculations of the coefficients of the biomass precursors based on determined contribution to biomass and genomic information for aerobic and photosynthetic growth.Click here for fileiRsp1095 in SBML SBML format of iRsp1095 for distribution and use in other modeling environments.Click here for fileSensitivity analysis Additional File 5 contains additional sensitivity analysis conducted to assess the effects of light, biomass composition and P/O ratio on growth and metabolite production rates.Click here for file