The identification of such "epistatic" essential relationships between network components is critical for the understanding and eventual manipulation of robust systems-level phenotypes.Biological robustness results from redundant pathways that achieve an essential objective, e.g. the production of biomass. As a consequence, the biological roles of many genes can only be revealed through multiple knockouts that identify a in silico genome-scale model of E. coli. A large majority of these "essential sets" contain 5 or more reactions, and thus represent complex epistatic relationships between components of the E. coli metabolic network.We introduce and apply a network-based approach for genome-scale metabolic knockout design. We apply this method to uncover over 11,000 minimal knockouts for biomass production in an E. coli metabolic network. Unlike previous approaches, our method yields results regarding high-order epistatic relationships and is applicable at the genome-scale.The complex minimal biomass knockouts discovered with our approach illuminate robust essential systems-level roles for reactions in the  Determination of the systems level role of biological components has been classically approached through the study and characterization of knockout phenotypes. However, the robustness of biological systems obscures the role of most individual components, which are redundant and seemingly "dispensible". The role of such robust modules can only be revealed through multiple knockout of complex ial sets ,2.in vivo or in silico phenotype. A recent study by Deutscher et al. employs in silico multiple knockout analysis to reveal novel essential roles for reactions in the yeast metabolic network [This property of complex biological systems is particularly true for small-molecule metabolism, which is governed by an intricate and highly robust network of biochemical reactions that leaves most single knockouts without a discernible  network . These rin silico network models can help suggest "epistatic" candidate gene combinations for genomic association studies linking genotype to phenotype (e.g. human disease). Derivation of such interactions from a functional network model is one important way systems biology could impact applied genomics.Interest in epistasis between biological network components is motivated by practical considerations. Firstly, the emergence of microbial resistance motivates the search for new antibiotics. Systems biology can inform this search through "rational" identification of multivalent pharmaceutical targets via a functional analysis of biological network robustness. Secondly, higher order interactions detected in in silico analysis of essentiality and epistasis in metabolism employ flux balance analysis (FBA), a linear programming (LP) based approach that optimizes biomass production subject to a given combination of capacity constraints on reactions [in silico mutants. This approach, though applicable to analysis of low-order (≤ 4) knockout combinations, is untenable for higher-order mutant combinations [14 linear programs to exhaustively test all possible quintuple-knockout combinations.Current approaches to eactions . Applyininations . For exaR for an objective reaction j is a minimal set of reactions that intersects all j-containing EM [j-containing EM [A more "elegant" approach for probing essentiality in metabolic networks is the minimal cut set (MCS) algorithm of Klamt and Gilles . This alining EM . As a reining EM . The maipathway fragments, which arise as the extreme pathways of a submatrix of the stoichiometry matrix formed by taking a subset of its rows. Alternatively stated, pathway fragments are flux configurations that place only a subset of species in the system at steady state. Pathway fragments naturally emerge in the intermediate steps of the tableau algorithm for elementary mode computation [j can be constructed by enumerating minimal hitting sets for j-containing pathway fragments. Though the resulting cut sets are not guaranteed to be minimal, they can be reduced to minimality via a second LP based step. As we show, this method offers a practical and high-yield approach for MCS computation and the study of epistasis in genome-scale metabolic networks.In this paper, we demonstrate a scalable approach for uncovering high-order epistatic relationships between components of large metabolic networks. Our method is based on the analysis of putation , and areE. coli, iJR904 [E. coli metabolism and illuminate essential systems level roles of reactions in highly redundant and robust E. coli subnetworks.We demonstrate the applicability of this approach to a genome scale metabolic model of , iJR904 . We use n - dimensional vectors with real and positive components, and ℝm × n is the set of all m × n matrices with real entries. Given m, n ∈ ℕ, we use the notation M = {1, ..., m} and N = {1, ..., n}. For a set C, we use |C| to denote its cardinality. If A ∈ ℝm × n and U ⊆ M, then AU denotes the submatrix of A containing the rows with indices in the set U. Therefore, if x ∈ ℝn, i ∈ N, and U ⊂ N, then xi and xU ∈ ℝU| |denote its ith component and the vector formed by taking components with indices in set U, respectively. The inequality x ≥ 0 is interpreted componentwise, i.e., xi ≥ 0, i = 1, ..., n. Each vector x ∈ ℝn induces a ray, r = {αx| α > 0}. We denote the set of nonzero indices of a ray r ⊂ ℝn as NZ(r) ⊂ N. The notation r1 + r2, where r1, r2 are rays, refers to the usual (Minkowski) set sum.ℝ is the set of real numbers, C is a cut set for an objective reaction j in metabolic network S if and only if vj > 0 is feasible in the wild type (i.e. ∃v ∈ K|vj > 0) andA cut set for an objective metabolic function is a set of reactions whose knockout abolishes that function . Formallwherefeasible flux cone of S.is the C ⊂ N a cut set for an objective reaction set J ⊂ N if the wild type is able to sustain flux through every reaction in J and Equation 1 is satisfied for at least one j ∈ J. For example if J corresponds to the set of biomass component sinks in the network, a cut set for J will be a reaction set C whose knockout disables the producibility [at least one biomass component.More generally, we call cibility  of at leC is minimal if no proper subset of C is a cut set. Minimal cut sets (MCS) represent "elementary failure modes" of metabolic networks [k-essential"  for a metabolic objective (e.g. biomass production) if it belongs in a MCS of size k for that function.A cut set networks . MCS alsj. To test whether a reaction set C is a cutset for k, one employs an LP to determine the feasibility of vj > 0 subject to vC = 0, v ∈ K. MCS can also be identified as "minimal hitting sets" of elementary modes [hitting set of a collection of sets U, is a set H ⊂ U that intersects every set in H ⊂ N as a hitting set for a collection of vectors E ⊂ ℝn if H intersects the nonzero components of r for every r ∈ E. H is a minimal hitting set for E if none of its subsets are hitting sets.Brute force LP approaches (e.g. FBA) can be applied to find MCS by exhaustively testing a collection of reaction knockouts to determine which of these "cuts" the objective reaction ry modes . In combj is a minimal hitting set of the collection of all elementary modes that employ j [j-containing elementary modes, then one will constrain the flux through reaction j to 0 in all feasible fluxes. These results directly extend to extreme pathways, which are equivalent to the elementary modes of an irreversible metabolic network [j is a minimal hitting set of all the j-containing extreme pathways. We choose the extreme pathway convention in this paper because it tends to be a more compact representation of the pathway structure of metabolism [The results of Klamt and Gilles show that an MCS for an objective reaction employ j ,10. This network . Namely,tabolism .k ≤ 2), though high performance computing and restriction of the search to a subset of model reactions can extend this limit to k ≤ 4 [Both the brute-force LP approach and the MCS algorithm of Klamt and Gilles have deep limitations in discovering genome-scale MCS. The size of most genome-scale metabolic networks (> 500 – 1000 reactions) renders brute-force LP approaches practical only for finding low cardinality MCS , called extreme pathways [E(K) associated with stoichiometry matrix S is an iterative procedure that computes the extreme rays E(Ki) for a series of polyhedral cones Ki ⊂ ℝn, i ∈ {0, ..., m} given by:The feasible flux cone pathways . The staK0 = E(K0) consists of rays induced by the Euclidean basis vectors ej ∈ ℝn. At each iteration i ∈ {1, ..., m}, the generators E(Ki) are computed from the analysis of rays in E(Ki - 1) in three steps.The algorithm is seeded with the initial cone Ei-1 is tested to determine whether it belongs to the hyperplane Siv = 0. Rays in E(Ki - 1) that belong to this hyperplane are added to the collection E(Ki). In the second step of iteration i, the algorithm considers each ray pair in E(Ki - 1) that lies on opposite sides of the hyperplane Siv = 0. The intersection of the set sum of each ray pair with Siv = 0 induces a new ray that lies within the cone Ki. Each such ray is added to the collection E(Ki).In the first step, each ray in i involves removal of non-extreme rays from E(Ki). This is implemented by comparing the sparsity patterns of each ray pair in E(Ki) and removing any ray r for which there exists an r' such that NZ(r') ⊂ NZ(r). Following iteration m, the tableau algorithm terminates, having computed the extreme rays of polyhedral cone K = Km. However, given the computational complexity of the third step in each iteration, the tableau algorithm fails to terminate (i.e. reach iteration m) for most genome-scale metabolic networks.The third and final step of each iteration i of the tableau algorithm produces a collection of rays E(Ki) ⊂ ℝn, which we refer to as pathway fragments. Each pathway fragment in E(Ki) obeys the quasi steady state assumption for the subset Mi ⊆ M of species in the system Sv, v ≥ 0. Though a collection of pathway fragments contains incomplete information about metabolic network dynamics, we will show that it offers much insight into its failure modes. We exploit this property in our network-based genome-scale knockout design approach. Each pathway fragment collection E(Ki) contains the extreme rays of the cone Ki in Equation 3.Each iteration C for the j-containing rays in E(Ki) is an MCS for reaction j in the "relaxed" system v ≥ 0. This means that C is a minimal. set of reactions satisfying the relation:Applying Klamt and Gilles' criterion to Equation 3, a minimal hitting set Kigenerated by a pathway fragment collection E(Ki) is an overapproximation of the final feasible ux cone K  not all cut sets are guaranteed to be found and 2) cut sets that are found are not guaranteed to be minimal. To fully reduce cut sets generated by MinHit to minimality, we apply an LP based post-processing step Reduce (Table Reduce in more detail in the Methods section.Our "relaxed" cut set criterion is able to generate genuine cut sets for the ce Table  to 1) chset of objectives J (e.g. the set of biomass sinks). In this case a cut set obtained for one reaction j1 ∈ J may be a subset of a cut set obtained for a second reaction j2 ∈ J. Both may be MCS for their respective objectives, however one (or both) may be non-minimal with respect to the objective set J. For example, if J corresponds to the set of biomass sinks in the network, an MCS for L-isoleucine production may be built by adding reactions to an L-threonine MCS. Such non-MCS may be immediately pruned through a pair-wise comparison of cut sets generated by MinHit for the various individual sinks in J, and removal of sets for which there exists a subset.There may be additional sources of non-minimality when one pursues MCS for a As may be intuitively expected, the quality of cut sets obtained with our approach directly depends on the "quality" of pathway fragments. At each iteration, the tableau algorithm "learns" more about network constraints imposed by the steady state requirement for each individual species. As a result, later iterations of the tableau algorithm yield more informative pathway fragments. In other words, pathway fragments gathered from an early iteration of the algorithm are "naive" and will yield fewer cut sets that are farther from being minimal. Conversely, "mature" pathway fragments gathered from a later iteration will yield larger numbers of cut sets that are closer to being minimal.i reached by the tableau algorithm is the "local greedy" optimization strategy described by Bell and Palsson [A simple approach that we apply to maximize the iteration  Palsson . This stE. coli IJR904 genome-scale metabolic network model. In rich media, all extracellular nutrients are made available, resulting in many redundant pathways for biomass biosynthesis. This redundancy makes biomass production very difficult to suppress via single or double knockouts.To test our approach, we examined failure modes for rich media biomass production in the E. coli network. As shown in Figure Our network based analysis approach found 11,706 MCS for biomass production in rich media. These MCS target 36 of 49 biomass components and employ 355 of the 1324 possible non-sink reactions in the E. coli iJR904 groups reactions into 30 "subsystems" [E. coli metabolic network. Superimposition of the MCS on the subsystem reaction classification yields 58 unique "subsystem signatures", which are shown in Figure E. coli metabolic network.The original model annotation of systems" . The MCSin silico metabolic knockout analysis approaches: brute-force LP and random knockout. For brute-force LP, we tested all single and double knockouts. In our random knockout approach, we sampled 250,000 random reaction sets of cardinality 10. For each such set, we determined whether its knockout cut the production of biomass and reduced it to minimality with respect to biomass production (via Reduce).To demonstrate the utility of NetKO, we benchmarked it against two standard NetKO was able to yield a larger number of MCS that targeted more reactions in the network than either brute force or random knockout approaches. Table k < 10-essential for biomass production for rich media E. coli. Though we employ different cardinality limits for the network based (k ≤ 10) and brute force (k ≤ 2) approaches in this benchmark, we note that these results reflect a similar order of magnitude of LP operations , resulting in higher return for a similar expenditure of computational resources. In comparison to the random approach, which also tests reaction sets of cardinality 10, we note that NetKO employs two orders of magnitude fewer linear programs than a random knockout approach  while yielding many more high-order interactions.Comparing the results Table  we foundNetKO results show that in many ways the two approaches are complementary . Because of these differences, one can use "brute force LP" results to determine general network properties regarding the rate of interaction between genes for a given degree of epistasis k [NetKO. Conversely, unlike brute force LP, one can use NetKO to uncover very high-order epistatic relationships for robust network functions.Comparison of brute KO and ry Table . For exaE. coli metabolic network  to reduce these random high-cardinality cut sets to minimality. In contrast, cut sets generated through pathway fragment analysis in NetKO are much closer to minimality, requiring much fewer LP's in the Reduce computational step.Our random KO results demonstrate quite strikingly how difficult it is to find high order MCS in the rk Table . Though E. coli iJR904, L-threonine production is invulnerable to all single or double knockouts. However, NetKO discovers 10655 MCS that target the production of this amino acid: all but 10 of these L-threonine targeting MCS employ more than 5 reactions, and 9725 involve 8 or more reactions.In E. coli, which is depicted in Figure E. coli to the functioning of a highly parallelized biosynthetic subnetwork. Epistasis between components of this subnetwork only become apparent through the analysis of high-order knockouts. The L-threonine subnetwork shown in Figure Interestingly, these 10655 genome-scale MCS arise exclusively from a 41 reaction subnetwork of The simplest of the 10655 L-threonine targeting MCS discovered using our approach consist of reactions immediately upstream of L-threonine in this subnetwork. As shown in Figure any subset of these MCS will allow L-threonine production to be maintained in this silico strain. For example, knockout of L-threonine transport and threonine-aldolase will allow L-threonine to be produced from L-aspartate via the pathway shown in the bottom left of Figure in silico can employ any one of these parallel pathways for L-threonine biosynthesis.The most intuitive of these MCS consists of the three L-threonine transporters  in combination with threonine synthetase (THRS) and threonine aldolase (THRAr). Variants of this MCS replace THRS with aspartate-semialdehyde dehydrogenase (ASAD), homoserine kinase (HSK), homoserine kinase (HSK), or aspartate kinase (ASPK). A second set of variants replaces the three L-threonine transporters with the L-threonine nutrient flux. 5 MCS apply an interesting variation upon this theme by replacing the sodium dependent THRabc transporter with either the sodium nutrient flux or inhibition of the three sodium proton antiporters . Because of their minimality, the knockout of A large number of MCS discovered using our approach target L-threonine biosynthesis by disabling pathways upstream of acetaldehyde. As shown in Figure NetKO to unravel the link between network components and systems-level functions. We further note that unlike manual pathway annotations, this subnetwork is derived purely through the analysis of flux dynamics in the genome-scale metabolic model. As a result, it serves as a rigorous and objective distillation of E. coli iJR904's behavior with respect to a particular function, i.e. L-threonine production.The L-threonine subnetwork described in this section demonstrates a biologically intuitive pathway-like structure. The ease with this network can be understood testifies to the ability of E. coli, there are numerous genome-scale metabolic reconstructions of pathogenic microbes in which such an approach could be used to reveal drug targets. Such organisms include S. aureus, H. pylori, and B. anthracis [MCS for essential metabolic objectives (e.g. biomass) represent potential targets for drug development. Though the model employed in this study represents a non-pathogenic strain of nthracis -19. Furtnthracis .NetKO could provide a powerful approach to apply "a posteriori" biological knowledge to study the role of epistasis in disease. Namely, one could employ NetKO to generate hypothesis in the form of MCS on a given pathway model and test such hypotheses against genotype-phenotype data.MCS correspond to subsets of genes whose perturbation or knockout is predicted to effect a network-level phenotype. Such a gene subset provides a reasonable "epistatic" candidate hypothesis for a genetic association study that explore links between genotype and phenotype, e.g. for human disease. Current approaches to whole genome association studies employ a unsupervised approach that test all possible loci for association with a phenotype. Given the high dimensionality of genotypic (e.g. SNP) data, these studies are limited by computational resources and statistical power to searching for binary gene-gene interactions. A "systems-based candidate-gene" approach based on K onto these reaction subsets [MCS discovered using our approach cluster into subnetworks that link individual reactions to their systems-level roles. In contrast to the daunting complexity of the entire metabolic network, these subnetworks have an intuitive pathway structure that can be understood by simple inspection. The close dual relationship between the failure and function of of metabolism has been previously outlined by Klamt . This du subsets .et al. refer to this generalized concept of essentiality as "k-robustness" in their investigations of multiple knockouts in yeast metabolism [k identified by our approach is conceptually equivalent to Deutscher et al.'s "essential set". High cardinality MCS represents an instance of a higher-order genetic or biochemical interaction between several reactions, enzymes, and genes that is mediated by the metabolic network. Similar to the results of Deutscher et al., we find that application of this generalized notion of essentiality significantly increases the number of E. coli reactions that can be thought of as participating in "essential processes" (as defined by biomass production).Many of our MCS reveal essential roles for reactions whose function is normally obscured by metabolic network redundancy. Deutscher tabolism . Each coet al. show that such an approach may be better equipped to capture functional features such as condition-dependence when compared to traditional structured vocabulary-based annotation schemes like Gene Ontology [NetKO provides a powerful tool for this kind of annotation by helping uncover functional links that are normally buried by redundant pathways.The use of a genome-scale model to find essential links between genes and systems-level processes exemplifies a novel "network-based" approach to functional gene annotation. Shlomi Ontology . NetKO pin vivo experiment and in silico analysis.Our approach can be applied in an iterative model building protocol that combines NetKO is the simple validation of model completeness and accuracy on the genome-scale. A more profound application is to unravel the systems-level roles of individual reactions, in particular those participating in robust and redundant network functions.One specific application of in vivo model validation experiments. The first corresponds to the knockout of that MCS and the subsequent lethality prediction. If the in vivo knockout fails to be lethal, then this suggests that either there is additional redundancy in the pathway structure of the network or the specific biomass target of that MCS is non-essential for growth [in vivo lethal, an interesting set of experiments can be performed that test the contributions of individual reactions to the function disabled by a given MCS. To do so, one would design knockouts that disable all but one of the reactions in that MCS. Such a perturbation would "pinch" the network, allowing only extreme pathways that utilize the remaining reaction in that MCS. As a result, the flux through that reaction would be predicted to become a simple linear multiple of the growth rate .Fundamentally, each MCS can be understood to suggest several important r growth . Once anFor example, the cysteine transporter (CYSabc), taurine transporter (TAURabc), biotin synthase (BTS2), and the sulfate transporter (SULabc) form an MCS for biomass by targeting L-cysteine production. Knockout of CYSabc, TAURabc, and BTS2 would be predicted by this network model to force all fluxes destined for L-cysteine production through the sulfate transporter (SULabc). According to the model, the rate of uptake of sulfate in this triple knockout will be in direct proportion to the flux through the L-cysteine sink, which corresponds to the growth-mediated dilution of L-cysteine and its consumption by protein synthesis. Such a discrete "pinching" experiment would determine whether the sulfate transporter is sufficient to sustain L-cysteine production. Extension of such an experimental paradigm to analyze further subsets of complex MCS at intermediate levels of inhibition could be used to quantitatively identify the "marginal" contributions of individual reactions/pathways to systems-level functions.NetKO discovers valid genome-scale MCS using only partial information regarding metabolic network dynamics. However, because it only employs partial information, it is not guaranteed to find all MCS for a given objective. For example, despite detecting many high-order interactions, our approach fails to detect nearly half of the cardinality k ≤ 2 MCS. Furthermore, the biomass targeting MCS that we find utilize only 355 of the potential 1324 reactions in the model. Though this may suggest that the remaining reactions in the network participate only in highly redundant (i.e. k > 10-robust) network functions, it is also likely that our approach fails to find a significant number of k ≤ 10 MCS.As mentioned earlier in the paper, the yield of our method depends directly on the "quality" of pathway fragments generated from the application of the tableau algorithm to the stoichiometric matrix. Specifically, the number of reactions belonging to a biomass-targeting MCS identified by our approach corresponds to the number of reactions that share a pathway fragment with a biomass sink. Improving the reaction "span" of these biomass-containing pathway fragments would increase the number of reactions employed by biomass-targeting MCS as well as the total yield of MCS.One approach for improving the yield of MCS would be to achieve additional incremental improvement in the progress of the tableau algorithm. Each iteration of the tableau algorithm processes the steady state requirements of another metabolite in the network, and thus "learns" more about the constraints imposed by network structure. By applying more raw computational power in the form of memory and processor speed, one could achieve several more iterations that would link more reactions to the collection of biomass-containing pathway fragments. In addition, one could apply high performance computing employing a parallel out-of-core approach to achieve additional progress . Though A more finessed approach for improving MCS yield may be to use an alternative metabolite "traversal" strategy for the tableau algorithm. In our implementation, we use a "local greedy optimization" strategy that chooses the "cheapest" next metabolite using a generic evaluation of each metabolite's "cost" . Though maximal number of reaction deletions that allow biomass production to be sustained, the computation of MCS corresponds to finding a minimal number of reaction deletions that cause biomass production to be abolished.Our approach is not the first attempt at "rational" genome-scale knockout design. Maranas and colleagues have previously applied mixed integer linear programming (MILP) to design mutants that improve byproduct yield or identify "minimal reaction sets" that are capable of sustaining a given biomass optimum ,25. Thesa priori unclear that a MILP-based MCS algorithm would be able to generate as many MCS as our network based approach.Though a precedent does not exist, MCS discovery could potentially be formulated as a MILP. Such a MILP would employ as its objective the minimization of the number of deleted reactions that abolish biomass production. Once an MCS is found as the solution of the MILP, additional MCS could be discovered through the execution of successive MILPs that incorporate additional constraints to prevent the rediscovery of previous optima. Such an approach is promising, however requires further investigation to address at least two major concerns: Firstly, MILPs are NP-complete, and thus scale poorly with the dimension of the search space, i.e. the number of reactions. Secondly, repeated addition of constraints to discover alternative optima may increase the "stiffness" of successive MILPs as further MCS are sought. As a result, it is in vivo knockout experiments in E. coli. These experiments could be used for iterative model building and functional annotation of genes. Future applications of our network based knockout design approach includes analysis of the metabolic networks of pathogenic organisms and generation of epistatic candidate models for genome-wide association studies.We have introduced and applied a network-based method for genome-scale knockout design. Our approach identifies high-order essential epistatic interactions that are normally obscured by metabolic network redundancy. These interactions cluster along interesting and physiologically important subnetworks that allow systems-level roles of individual reactions to be precisely and intuitively captured. Our method provides a plethora of predictions that can readily translate into informative E(Ki) at the first iteration i that this limit is met. In our implementation, we also apply heuristic "local greedy" optimization strategy that dynamically rearranges the rows of S at the end of each iteration with the goal of minimizing computation at the next iteration [i, we rearrange rows i + 1, ..., m of S to minimize the number of ray pairs in E(Ki) that lie on opposite sides of hyperplane Si+1v = 0.We implement the tableau algorithm according to previously described implementations ,15, addik or less of a collection E of rays (i.e. pathway fragments) using MinHit . The resulting collection can be easily shown to form a minimal hitting set collection for the rays 1...q in collection E that have already been processed. Upon iterating through the entire collection E, the output E.We compute the it Table , which iMinHit are a cardinality limitation k and a subset of indices of interest R to which minimal hitting sets can be restricted. The cardinality limitation is implemented by discarding all sets with cardinality greater than k at each iteration. The subset limitation is implemented by only considering elements in R at each augmentation step.Additional arguments to Reduce  of dimension 761 × 2085.We use the computational framework developed in this paper to compute MCS for biomass production in the le model , which hS represent the inflow, outflow, and interconversion of small-molecule chemical species in an E. coli cell grown in a rich nutrient media. Each species "sink" reaction represents its growth mediated dilution and macromolecular consumption. Of the 761 species, 49 correspond to "biomass components" that are considered to be essential substrates for survival and growth in the original Reed et al specification [at least one of the sinks corresponding to an essential biomass component.Reactions in fication . In thisNetKO , this procedure determines the feasibility of fluxes in J through the execution of a single linear program.All algorithms were written and executed within the MATLAB programming environment on a Pentium 2.0 GhZ PC with 2 GB of RAM. We used the semidefinite programming package SeDuMi for MATLAB to implement the linear flux feasibility analysis used in approach . In thisMI formulated the theory, implemented the algorithm, designed the study, conducted the analysis, and drafted the manuscript. CB helped to formulate the theory and draft the manuscript. All authors read and approved the final manuscript.NetKO algorithm for E. coli biomass production in rich media.Supplementary Data. The data provided lists the reaction labels corresponding to each minimal cut set discovered by the Click here for file


Constraint-based modeling of reconstructed genome-scale metabolic networks has been successfully applied on several microorganisms. In constraint-based modeling, in order to characterize all allowable phenotypes, network-based pathways, such as extreme pathways and elementary flux modes, are defined. However, as the scale of metabolic network rises, the number of extreme pathways and elementary flux modes increases exponentially. Uniform random sampling solves this problem to some extent to study the contents of the available phenotypes. After uniform random sampling, correlated reaction sets can be identified by the dependencies between reactions derived from sample phenotypes. In this paper, we study the relationship between extreme pathways and correlated reaction sets.E. coli core, red blood cell and Saccharomyces cerevisiae metabolic networks respectively. All extreme pathways are enumerated for the former two metabolic networks. As for Saccharomyces cerevisiae metabolic network, because of the large scale, we get a set of extreme pathways by sampling the whole extreme pathway space. In most cases, an extreme pathway covers a correlated reaction set in an 'all or none' manner, which means either all reactions in a correlated reaction set or none is used by some extreme pathway. In rare cases, besides the 'all or none' manner, a correlated reaction set may be fully covered by combination of a few extreme pathways with related function, which may bring redundancy and flexibility to improve the survivability of a cell. In a word, extreme pathways show strong complementary relationship on usage of reactions in the same correlated reaction set.Correlated reaction sets are identified for Both extreme pathways and correlated reaction sets are derived from the topology information of metabolic networks. The strong relationship between correlated reaction sets and extreme pathways suggests a possible mechanism: as a controllable unit, an extreme pathway is regulated by its corresponding correlated reaction sets, and a correlated reaction set is further regulated by the organism's regulatory network. A framenetworks -4. As renetworks , COBRA hS. With the homeostatic-steady-state hypothesis and fluxes boundaries, all allowable steady-state flux distributions are limited in a space which can be represented asThe COBRA framework represents a metabolic network as a stoichiometric matrix Sm × n is the stoichiometric matrix for a network consisting of m metabolites and n fluxes and vn × 1 is a vector of the flux levels through each reaction in the system [where e system .extreme pathways (ExPa),  [extreme pathways (ExPa):Given the reversibility of reactions, an internal reversible reaction can be decoupled into two separate reactions for the forward and reverse directions separately. It means all fluxes should take a non-negative value and the solution space is now a convex polyhedral cone in high-dimensional space ,7. This  ..., k) ,9. EveryExtreme pathways (ExPa) have the following properties which make them biologically meaningful [aningful ,11:1. The ExPa set of a given network is unique.2. Each ExPa uses least reactions to be a functional unit.3. The ExPa set is systemically independent which means an ExPa can't be decomposed into a non-negative combination of the remaining ExPas.elementary flux modes (EM) [elementary flux modes (EM) treats internal reversible reactions differently from that for ExPas. Actually, ExPa set is a systemically independent subset of elementary flux modes (EM) and each EM can be represented by a non-negative combination of ExPas. The relationship and difference between ExPa and EM have been studied and articulated in literatures [A similar network-based pathway definition as ExPa is des (EM) -14. The eratures ,15.ExPas and EMs lead to a systems view of network properties  and theycorrelated reaction sets (CoSet). Correlated reaction sets (CoSet) are unbiased, condition-dependent definitions of modules in metabolic networks in which all the reactions have to be co-utilized in precise stoichiometric ratios [correlated reaction sets (CoSet) go up or down together in fixed ratios. We may think about whether CoSets provide clues about regulated procedures of a metabolic network.A rapid and scalable method to quantitatively characterize all allowable phenotypes of genome-scale networks is uniform random sampling . It studc ratios . It meanEscherichia coli core metabolic network, human red blood cell metabolic network and Saccharomyces cerevisiae metabolic network as examples to start our research.Both ExPas and CoSets are determined by the topology of a metabolic network. Although lots of analyses were done on them separately -25, few E. coli core model published on the web site of UCSD's systems biology research group. It is "a condensed version of the genome-scale E. coli reconstruction and contains central metabolism reactions" [We use the actions" . Detailsactions" . The netThe computation of the extreme pathways for E. coli core model results in 7784 ExPas, in which 7748 are type I or II ExPas and 36 are type III ExPas . The type I and II ExPas will be focused on herein and the reason for neglecting type III ExPas will be explained in Methods section. Twenty CoSets are identified on this network based on pairwise correlation coefficients between all reaction fluxes and listed in table Cj, we check how many type I and II ExPas use k reactions in Cj, where k ranges from zero to the size of Cj. The result is shown in table E. coli core model covers in each CoSet in an 'all or none' manner. We also calculate, for each ExPa pi, the ratio of reactions in any CoSet which is fully covered by pi to all reactions in pi. The distribution of the ratios is shown in Figure E. coli core model covers at least one CoSet. The coverage rates are higher than 40% which implies that ExPas are under well control of CoSets.For each CoSet red blood cell (RBC) metabolic network has been well reconstructed and simulated [Human imulated -31. The imulated .There are 55 ExPas calculated from the stoichiometric matrix of RBC model, among which 39 are type I or II ExPas and the others are type III ExPas. We focus on type I and II ExPas only. Type I and II ExPas are described in additional file The relationship between ExPas and CoSets is shown in table Embden-Meyerhof-Parnas pathway (EMP), while all other internal reactions in CoSet 1 are in pathway Pentose Phosphate Pathway (PPP). As for CoSet 3, 'R5PI' belongs to pathway PPP and all other reactions are in EMP. Since EMP provides the metabolite 'G6P' to PPP and inversely, PPP offers the metabolite 'GA3P' to EMP, the two pathways should cooperate with each other to fulfill the functions of the metabolic network. In order to work normally, the metabolic network may either utilize an ExPa using all the reactions in CoSet 1 (CoSet 3) or combine two (or more) ExPas together to fully cover CoSet1 (CoSet 3). By splitting some CoSet on different ExPas, it may bring redundancy and flexibility which are important properties for a cell to survive in various environments.The reasons for the complementary relationship on usage of reactions in CoSet 1 and CoSet 3 are as follows. 'PGI' belongs to one of 'historical' metabolic pathways named Both 'Ex_NADP' and 'Ex_NADPH' belong to CoSet 1, indicating the need of RBC cell to balance the NADPH/NADP ratio. According to "historically" partition of metabolic pathways, when pathway PPP is up-regulated, the quantity of NADP increases. When metabolic pathway EMP is up-regulated, the quantity of NADPH comes up. From the point of view of ExPa, 'Ex_NADP', 'Ex_NADPH' are used together in opposite direction by ExPas. It means that the fluxes through these reactions increase or decrease together. As a result, the quantity of NADP increases when that of NADPH decreases and vice versa. Situation is similar for reactions 'Ex_NAD' and 'Ex_NADH' in CoSet 5.E. coli core metabolic network, nearly 1/3 ExPas of RBC model has a CoSets coverage rate higher than 20%. There are 7 ExPas whose CoSets coverage rate is 0. All these 7 ExPas utilize relatively few reactions , among which, ExPas 10 and 11 utilize the regulated reaction 'IMPase', ExPas 12 and 13 are type II ExPas which serve to dissipate excess ATP, and ExPas 14, 15, 16 which participate in nucleotide metabolism may be regulated by the quantity of inosine and adenosine. In short, ExPas are in control of the regulatory structure of the metabolic network and our study suggests that the regulatory command usually spread from the regulated reactions to CoSets and finally to the related ExPas.Figure S. cerevisiae, iND750, has been reconstructed and validated in 2004 [S. cerevisiae. Model iND750 accounts for 646 metabolites, 1149 internal reactions as well as 116 exchange fluxes excluding the objective reaction. Since the scale of iND750 is too large, enumerating all the ExPas of the model is computational intractable. Thus we samples a subset of ExPas to represent the whole ExPas (See Methods Section). The sampling procedure has executed 1000 times with 250–300 internal reactions being randomly removed out every time and finally resulted a sample set of 56496 unique ExPas. The lengths of sample ExPas range from 20 to 80  and malate (MAL) across the epicyte in opposite directions. Reaction 'AKGt2r' transports AKG and hydrogen ion (H) across the epicyte in the same directions. And 'MALt2r' transports MAL and H across the epicyte in the same directions as well. If the quantity of AKG rises, the fluxes through 'AKGMAL' will grow up taking AKG and H out of the cell and bringing MAL into the cell. As a result, the quantity of H rises causing an increase on the flux of 'MALt2r'. Vice versa. These three reactions work together to balance the AKG/MAL ratio inside the cell and thus form a CoSet. Among the sample ExPas, we find that some of them utilize 'AKGMAL' and 'AKGt2r' while others use 'MALt2r' only. But, there are also some ExPas utilizing 'AKGt2r' while we don't find any sample ExPas that use the other two reactions in the CoSet. However, according to the above analysis, there should be some complemental ExPas utilizing reactions in the CoSet other than 'AKGt2r'. Otherwise, the cell will die due to the insupportable internal environment. Since the whole ExPa set is extremely large, the available ExPa sample set can only give a glance at the tremendous ExPa set and will certainly lose some information.CoSets and the relationship between ExPas and CoSets are completely listed in additional files S. cerevisia metabolic network is much larger. However, complementary relationship on usage of reactions in a CoSet is repeated as that in E. coli core metabolic network and RBC metabolic network.The scale of in-silicon representations of three metabolic networks. These models are different in species and scale. However, the experiment on each model leads to similar results that ExPas show strong complementary relationship on the usage of reactions in the same CoSet. It implies that this kind of relationship may exist in most of organisms. Since both CoSets and ExPas are generated from the topology information of metabolic networks, this phenomenon may reflect some inherent properties resulting from the topology constraints composed on the networks.In this study, we investigated the relationship between CoSets and ExPas on the Moreover, our study not only reveals the interesting relationship between CoSets and ExPas but also provides a new sight of how the metabolic network works and how it is adjusted. The strong relationship between CoSets and ExPas provides clues about regulated procedure of a metabolic network, thus suggests a possible mechanism of how a metabolic network transferring its phenotype from one steady state to another. As functional units, ExPas are in control of the regulatory structure of the metabolic network, and the regulatory command usually spreads from regulated reactions to CoSets and finally to the related ExPas. As fluxes through each ExPa change according to the regulatory orders from its corresponding CoSets, the flux distribution of the whole metabolic network transfers towards a new steady state. By interrogating the relationship between CoSets and ExPas, we can tell which ExPas are possible to be up (down) regulated caused by an increasing (decreasing) flux in a given CoSet. This result may help predict the function of regulatory factors acting on metabolism. However, in order to answer the question which ExPas are really regulated, more information should be considered, such as regulatory structure of the metabolic networks as well as kinetic and thermodynamic constraints, which will be our future work.ExPas are computed by an open source tool, 'expa', developed by Steven L. Bell and Bernhard O. Palsson . The exce-8while identifying CoSets of each metabolic network assuring that reactions in the same CoSets have strong correlation with each other. The procedure of CoSets identification has been carried out 20 times for each model and the results are quite stable.The CoSets of each metabolic model is generated by COBRA toolbox, an integrated toolbox of functions which are useful for analysis and simulation of organism's metabolic behavior . For eacS. cerevisiae's iND750 model, and enumerate all the ExPas of the sub network. Then, the dimensions of deleted reactions are inserted back with zeros to these ExPas. As proved in Theorem 1, the ExPa set derived from sampling is a subset of the whole ExPa set of iND750. One thousand ExPa sets of different sub networks of iND750 model have been generated and merged together without redundancy. The union of all these ExPas constitute the sample set of ExPas used in the analysis on Saccharomyces cerevisiae metabolic network.We randomly delete a few reactions in Theorem 1. Suppose G is a metabolic network and ℙ is the ExPa set of G, then for any sub network G', its ExPa set ℙ' is a subset of ℙ.Proof. We assume that the available steady state flux distribution (v) of G lies in the convex cone G' is generated from G by deleting reactions vk, vk+1, ..., vn, then the steady state flux distribution of G' lies in the convex cone Without loss of generality, we assume ai | ai ∈ j = k, ..., n}. Obviously, Assuming that ai ∈ ∀j = k, ..., n, then ∀pi ∈ ℙ", j = k, ..., n, where pi is the ith ExPa in ℙ and jth component of pi.Since pi | pi ∈ ℙ and j = k, ..., n}. Thus, Assuming that ℙ' = {G' is unique, ℙ' is the ExPa set of G', and Because The abbreviations used in this study are listed in table The authors declare that they have no competing interests.YX designed the system, implemented programs, carried out the analysis, and participated in manuscript preparation. YPC supervised the project and suggested ways of improving the study, and participated in writing the manuscript. MC helped implement programs. WW participated in discussion of the research. FW designed and directed the research, and drafted the manuscript. All authors read and approved the final manuscript.Maps of Reactions and ExPas of RBC metabolic network. This is a PDF file with a table and a figure. The table describes all the internal reactions in RBC metabolic network and the figure shows all the type I and II ExPas of this model.Click here for fileAll the CoSets of S. cerevisiae metabolic network. This is an Excel® file of all the 135 CoSets of S. cerevisiae metabolic network.Click here for fileRelationship between ExPas and CoSets for S. cerevisiae model (full version). This is an Excel® file of relationship between ExPas and all the 135. CoSets for S. cerevisiae model.Click here for fileThe reaction abbreviation list of E. coli core metabolic network. This is an Excel® file of reaction abbreviations and reaction names of E. coli core metabolic network.Click here for fileThe reaction abbreviation list of S. cerevisiae metabolic network. This is an Excel® file of reaction abbreviations and reaction names of S. cerevisiae metabolic network.Click here for file


Vanilla planifolia. Currently vanillin is mostly produced via chemical synthesis. A de novo synthetic pathway for heterologous vanillin production from glucose has recently been implemented in baker's yeast, Saccharamyces cerevisiae. In this study we aimed at engineering this vanillin cell factory towards improved productivity and thereby at developing an attractive alternative to chemical synthesis.Vanillin is one of the most widely used flavouring agents, originally obtained from cured seed pods of the vanilla orchid Arabidopsis thaliana in the vanillin producing S. cerevisiae strain served to decrease product toxicity. An in silico metabolic engineering strategy of this vanillin glucoside producing strain was designed using a set of stoichiometric modelling tools applied to the yeast genome-scale metabolic network. Two targets (PDC1 and GDH1) were selected for experimental verification resulting in four engineered strains. Three of the mutants showed up to 1.5 fold higher vanillin β-D-glucoside yield in batch mode, while continuous culture of the Δpdc1 mutant showed a 2-fold productivity improvement. This mutant presented a 5-fold improvement in free vanillin production compared to the previous work on de novo vanillin biosynthesis in baker's yeast.Expression of a glycosyltransferase from In vivo verification of the targets, selected based on their predicted metabolic adjustment, successfully led to overproducing strains. Overall, we propose and demonstrate a framework for in silico design and target selection for improving microbial cell factories.Use of constraints corresponding to different physiological states was found to greatly influence the target predictions given minimization of metabolic adjustment (MOMA) as biological objective function.  Vanilla planifolia. The remaining demand for vanillin is fulfilled by chemical synthesis from lignin or fossil hydrocarbons, in particular guaiacol [Hansen et al (2009), who demonstrated de novo vanillin biosynthesis from glucose in baker's and fission yeasts as a major step towards developing an environmental friendly and economically sustainable process [de novo pathway is 3-dehydroshikimate (3-DHS), an intermediate of the shikimate pathway for aromatic amino acids biosynthesis. To convert 3-dehrydroshikimate into vanillin, four genes encoding the required four enzymatic activities were obtained from different organisms, Podospora pausiceta, Nocardia sp., Escherichia coli and Homo sapiens . This problem was formulated by Burgard et al. (2003) as a bi-level optimization algorithm termed OptKnock [The aim of this study was to design and construct an improved S. OptKnock . OptKnocOptKnock . OptimizOptKnock .et al. (2002), where it is advocated that the cellular objective for a mutant strain is to minimize its metabolic distance from the wild type flux distribution [S. cerevisiae genome-scale stoichiometric model iFF708 [The most widely used approach for calculating flux distribution is flux balance analysis (FBA), where a given flux (or a linear combination of chosen fluxes) is used as the objective function . For micribution . In MOMAribution . Within l iFF708  was usedl iFF708 . MOMA [2l iFF708  was usedS. cerevisiae, growth defect is significant with concentrations as low as 0.5 g/l [Vanilla planifolia [et al. (2002) in Schizosaccharmyces pombe [Van/molglc to 0.35 mmolVan/molglc. On a mass basis, the maximum achievable yield of 486 mgvan/gglc changes to a relatively modest 293 mgVan/gglc. Nevertheless, given the toxicity and low solubility of vanillin, reaching high titers is not a favourable option. In case of Vanillin β-D-glucoside (or VG), extracellular concentration up to 25 g/l has been shown not to affect growth and is thereby more suitable for commercial production.Vanillin is toxic to many living organisms. In case of anifolia ,26. ThisS. pombe, heterologous expression of a gene encoding a plant family 1 glycosyltransferase from Arabidopsis thaliana (UGT72E2) resulted in 80% conversion of vanillin to vanillin β-D-glucoside [UGT72E2 was expressed in the vanillin producing S. cerevisiae strain VAN286, obtained from Hansen et al. [In lucoside . Within n et al. . The resS. cerevisiae has the ability to grow in the absence of oxygen, producing ethanol as a major by-product. In the presence of oxygen, respiration occurs but if the glucose concentration and/or uptake rate surpasses a critical threshold value, the metabolism becomes a combination of respiration and alcoholic fermentation [Existence of a large number of alternative flux routes (pathways) in genome-scale metabolic models requires the use of experimental constraints in order to obtain physiologically meaningful flux distributions. This is even more so in the case of MOMA, where predictions of mutant flux distributions will be highly dependent on the solution provided for the wild type (or reference) flux distribution . Thus, tentation ,28.S. cerevisiae are characterized by different nutrient uptake rates, different metabolite production rates and different biomass yields. Consequently, it is important to decide which metabolic state/s should be used to constrain the metabolic model in order to obtain reliable target predictions for genetic manipulation towards improved productivity. In addition, it is to be expected that different constraints (corresponding to different metabolic states) may lead to different suggestions for the metabolic engineering targets. To address this issue, we used three different scenarios for obtaining the reference flux distribution for MOMA simulations. Reference 1 represented exclusive respiratory metabolism, characterized by no ethanol formation and low glucose uptake rate. Reference 2 was simulated for respiro-fermentative metabolism, characterized by high glucose uptake rates, alcoholic fermentation and active respiration. Since both flux distributions were obtained by using FBA for maximizing biomass production, no accumulation of VG or related compounds was predicted. A third FBA simulation was performed to obtain the flux distribution for VG0 (Reference 3). The model was constrained using data obtained in this study from chemostat cultivations at a dilution rate of 0.1 h-1. Highly fermentative metabolism was observed at this dilution rate indicating limited respiratory capacity of the strain. Together, the three different reference flux distributions span all relevant life styles of S. cerevisiae, and may therefore be used to identify potential targets for genetic manipulations by using OptGene simulation framework. As steady state approaches cannot predict changes in substrate uptake rates, and hence productivity for mutants, Patil et al. (2005) suggested the use of Biomass Product Coupled Yield (BPCY) for design objective. BPCY is defined as multiplication of product yield and biomass flux [Different metabolic states of ass flux .et al., 2002 [in vivo than large adjustments. This was taken into account by introducing a new metric for ranking in silico predicted mutants, viz., the Reward-Risk-Ratio (R3), defined as the ratio between BPCY (reward) and metabolic adjustment (risk). The most interesting targets obtained following ranking of each prediction according to the R3 score are presented in Figure Simulations were performed using OptGene  for predl., 2002 ) was use3 ranking are very different, demonstrating that the best targets in one physiological scenario are not necessarily the best targets in another. The results of the prediction analysis imply that VG production is favoured at those physiological conditions which lead to respiro-fermentative metabolism as compared to physiological conditions resulting exclusively in respiratory metabolism. The outcome of minimal metabolic adjustment is to divert the ethanol flux towards formation of VG rather than diverting the flux from biomass constituents. Indeed, several of the candidates suggested in Figure Depending on the reference flux distribution used in MOMA, different targets were suggested for knockout. Some of the targets, for example GDH1, were identified in more than one physiological growth condition. However, their positions following the Rin vivo implementation were selected by giving strong emphasis to the R3 score of different targets under different simulation conditions, in combination with a manual evaluation of the suitability of the putative gene targets based on available data in the literature. The literature and database search included the possible existence of iso-enzymes, experimentally observed single gene deletion phenotypes and the assessment of the importance of regulatory links to other processes [PDC1 (Pyruvate decarboxylase) and GDH1 (Glutamate dehydrogenase), were selected as the candidates for strain construction and characterization. The Gdh1 catalyzed reaction was predicted as a prime target for knockout when using respiratory or respiro-fermentative metabolism, and in both cases, relatively large metabolic adjustment was predicted. GDH1 encodes an NADPH-dependent glutamate dehydrogenase involved in ammonium metabolism through glutamate biosynthesis, which is reported to provide 85% of the cellular nitrogen sources [S. cerevisiae and in particular, deletion of GDH1 was previously used as a metabolic engineering strategy for improving ethanol and sesquiterpenes production [The targets for rocesses . Based o sources . Ammoniuoduction ,8,31. ThS. cerevisiae metabolism and the branch point between respiratory and fermentative metabolism. Pyruvate decarboxylases (PDCs) have a crucial significance for fermentation, since this decarboxylation reaction converts pyruvate to acetaldehyde, an intermediate towards ethanol formation [S. cerevisiae genome harbours three PDC structural genes , one regulatory gene (PDC2) and two other genes with potential contribution towards PDC activity (PDC3 and 4) [pdc1Δ, pdc5Δ & pdc6Δ) creates a mutant that is unable to grow on glucose as sole carbon source [in silico analysis, PDC was found as a target to increase the formation of VG considering both respiratory and respiro-fermentative reference flux distributions for MOMA, but not when VG0 data was used to constrain the network. Furthermore, complete absence of pyruvate decarboxylase activity under a highly fermentative mode was predicted to result in zero growth, as lack of PDC activity would require a very large metabolic adjustment. This observation, in combination with the experimental data available in the literature for the mutant without PDC activity [GDH1  ,33. Compn source . By in sactivity , raise a gene PDC and two activity .gdh1Δ and pdc1Δ, were constructed in the VG0 background resulting in VG1 and VG2, respectively. To test whether simultaneous deletion of PDC1 and GDH1 would have a positive synergistic effect on VG accumulation, a mutant with both deletions was obtained (VG3). The strains were initially characterized in batch cultures in 2L well-controlled bioreactors, using minimal medium and an initial glucose concentration of 20 g/l (Table pdc1Δ) showed an overall increased fitness compared to the reference strain as documented by a 43% higher maximum specific growth rate  α doubling time-1) in comparison to VG0. Likewise the yield of biomass on glucose  is 40% higher than observed for VG0. On the other hand, the mutant VG1 (gdh1Δ) showed reduced strain fitness, illustrated by poor μmax and reduced YS X. These adverse effects on VG1 fitness were partially relieved by deletion of PDC1, as documented by slightly improved μmax and YS X values for the strain VG3 (pdc1Δgdh1Δ). The decreased fitness of the strains in which GDH1 was deleted, is due to a reduced nitrogen assimilation rate [GDH1, the GS-GOGAT system  [GDH2 [GDH1 in silico mutants  ,37 and t1) [GDH2 , are ress Figure  and 2C. pdc1Δgdh1Δ ↑GDH2) showed a significantly improved cellular fitness compared to VG3 with μmax and YS X values similar to those observed for VG2 and better than those obtained with VG0. At these experimental conditions (batch cultivation), none of the introduced mutations seem to affect ethanol production to any significant extent except that the strains harbouring the GDH1 deletion tend to show a slight increase in the substrate specific yield of ethanol.The resulting strain VG4  and protocatechuic aldehyde (PAL) accounted for more than 50% of the total products formed. Vanillin, other intermediates and by-products such as vanillic acid and vanillyl alcohol were found in very low amounts and were not taken into account for further analysis. The strain VG1 showed the lowest total yield of compounds related to the vanillin biosynthetic pathway Figure , which mThe extent to which VG production is affected by the presence or absence of alcoholic fermentation is still unknown. Above a critical threshold for glucose uptake rate, co-existence of respiration and fermentation takes place and the biomass yield is significantly lower due to carbon channelling towards ethanol, known as the Crabtree effect . This ph-1and 20 g/l feed glucose concentration. VG2 showed increased fitness as demonstrated by a higher biomass yield (YS X) accompanied by slightly increased ethanol and a slightly decreased glycerol yields, as compared to VG0  were selected for further characterization in glucose-limited chemostat cultures at a dilution rate of 0.1 h and VG4 S) of 3.9 ± 0.2 mmolglcggw-1.h-1, whereas VG2 has an uptake rate of 3.5 ± 0.2 mmolglcggw-1.h-1. The lower glucose uptake decreases the overflow metabolism in the strain, leading to decreased rates of ethanol, glycerol and acetate formation. At the same time, VG2 exhibits a higher conversion of PAC into the products of the later steps in the vanillin pathway , a two-fold increase compared to that of VG0, which produced 250 mg/l (15 mgVG/gglc)  implies that the critical dilution rate (indicative of respiratory capacity) of the strains is very low. By gradually decreasing the dilution rate in a glucose-limited chemostat, we verified that the critical dilution rate for both VG2 and VG0 was below 0.015. Such a low respiratory capacity could be the result of combined effects of product/by-products toxicity and due to the background of the strain. Employing this experimental setup made it possible to lower the ethanol production rate to 0.130 mmol) Figure . These r2 production rates, were added as constraints to the metabolic model. The bounds for the deleted genes were set to zero, as in the case of GDH1 deletion in VG4. However the choice of constraints for the PDC1 deletion is not straightforward, as deleting PDC1 does not mean that pyruvate decarboxylase activity will be zero. To circumvent this issue, and to account for different glucose uptake rates of the mutants, the upper bound for PDC flux was identified in each condition. Subsequently, the phenotypes were simulated with upper bound for PDC constrained to 80% of the previously found upper bound.In an attempt to better understand the metabolic flux changes at the whole network level and, therefore, the basis for the observed improved VG production, the flux phenotypes of VG0, VG2 and VG4 were simulated by using FBA . The expa, i.e. with no change between the VG0 reference strain and the tested mutants. The chemostat experiments were carried out at the same dilution rate for all the strains, and as a consequence, the simulation of reactions directly coupled to biomass biosynthesis all fall within this category. Examples include reactions from lipid, nucleotide and amino acid metabolism.The flux distributions obtained with FBA are guaranteed to be optimal, but not necessarily unique due to the existence of a large number of alternative routes. This renders the transformation of the experimentally determined levels of the products obtained into intracellular fluxes, a difficult task. Nevertheless, stoichiometric simulations provide an estimate of the possible range of flux values for every reaction in the network. Fluxes which are unique will have the same maximum and minimum possible values. The flux ranges of all reactions of VG2 and VG4 were calculated and compared with those of VG0, resulting in different categories as illustrated in Figure b and c contain the majority of the reactions (~70%) for the VG2 and VG4 strains, yet the distribution among the two categories is not alike for the two mutant strains. In the case of VG2, 226 reactions exhibit a larger range than observed for the reference strain (category b) and a similar number of reactions exhibit a smaller range than observed in the VG0 (category c). For the VG4 strain, most of the reactions fall in category b, as expected due to its higher glucose uptake rate. The VG2 strain exhibits a decreased glucose uptake rate and the same biomass formation rate as compared with VG0. Nevertheless, several reactions from the central carbon metabolism show an increased flux range (category b). These reactions mainly belong to the tricarboxylic acid (TCA) cycle, the pentose phosphate pathway and gluconeogenesis, reflecting that this strain has decreased overflow metabolism and ethanol production. A more active respiration in this strain is further confirmed by the in silico predicted increased oxygen uptake rate. Even though this reaction is found in category c (with decreased flux range), its lower bound is higher in VG2 than in VG0.The categories d, where the mutant flux upper bound is higher than the reference flux upper bound, and category e where the mutant flux lower bound is lower than the reference flux lower bound. Together, categories d and e comprise the reactions with the clearest differences between the mutants and the reference. These include reactions related to product formation (e.g. biosynthesis of S-adenosylmethionine - the methyl-group donor in the vanillin pathway) and glucose uptake , as well as reactions from the ammonia metabolism.The remaining reactions present flux variability ranges with partial or no overlap between the reference strain and the mutants. These reactions were grouped in category Despite the increased VG production, the VG2 strain exhibits a decreased flux through the aromatic amino acid biosynthesis pathway from which the vanillin precursor is derived. Likewise, this strain shows a reduced total flux through the VG pathway. The same trend was found for the VG4 strain, implying that the metabolic network is being adjusted for increased PAL and VG production at the expense of a reduction of the total carbon flow into aromatic amino acids until the VG biosynthesis branch. In actual fact, the reaction after which the production is increased is the conversion from PAC to PAL. This reaction uses NADPH and ATP, two of the most highly connected metabolites and cofactors that are competed for by growth requirement.minimization of metabolite turnover . This LPP formulation guarantees to find the minimum turnover of a given metabolite that ensures the observed phenotype. The direction of optimization, i.e. minimization, not only avoids the unbound cyclic fluxes around the metabolite under question, but also confers with the biological hypothesis of minimal resource allocation by the cell in terms of enzyme expression. Minimum metabolite turnover denotes how much flux needs to pass through a given metabolite, although the distribution of this flux among possible reactions may not be unique in all cases. Nevertheless, the turnover calculated in this way provides a lower bound on the flux through a metabolite that can be used in complementation with flux variability analysis.To systematically explore the usage of cofactors and other metabolites in the engineered strains, the turnover of these metabolites can be calculated by summing all the fluxes which are producing (or consuming) them . As the Besides NADPH and ATP, the minimum turnover of some other relevant metabolites was also calculated Figure . The minin silico predicted increase in the product yield was above 2-fold  allowed us to conclude that they display increased cofactor availability for VG production. Further increase of cofactor availability would be of great interest in attempting to decrease the accumulation of intermediates  and to favour their conversion into VG. Subsequently, identification and overexpression of an eventual rate limiting enzyme from the vanillin biosynthetic pathway may serve to enhance conversion of pathway intermediates into the final product, VG. Furthermore, all the strains, including the reference, were found to have poor respiratory capacity and thereby high ethanol yield. Improving respiratory capacity of the selected overproducers will be an essential feature for future work. In fact, low dilution rate continuous cultivation (concurrent with better respiration) of an overproducer strain resulted in notably high titer of vanillin β-D-glucoside - 500 mg/l, 5-fold higher than the 45 mg/l reported by Hansen and co-workers [The in silico target prediction that accounts for the available physiological information; ii) systematic ranking of the targets based on the predicted metabolic adjustments; iii) in vivo verification through genetic engineering and fermentation; and iv) reaction/metabolite centric analysis of the experimental results. Our results demonstrate the applicability of in silico modelling tools for overproduction of a product from a multistep heterologous pathway in a eukaryotic system.In summary, the framework presented in this study comprises of i) Saccharomyces cerevisiae stoichiometric model [ftp://ftp.gnu.org/gnu/glpk/, while MOMA simulations were performed using quadratic programming library OOQP [Five new reactions were introduced in the ic model  to conveary OOQP .S. cerevisiae was performed by using OptGene with Biomass-Product Coupled Yield (BPCY) as design objective function [Strategy design to improve VG production in function .i denote metabolite turnover of metabolite i and its mathematical definition is given by ik Srepresents the stoichiometric coefficient of metabolite i in reaction k and k vis the flux of reaction k. By calculating the sum of all absolute flux values through (in and out) a given metabolite eliminates further concern about reactions reversibility. Furthermore, given the steady state assumption, the metabolite turnover will be half of the calculated sum.Metabolite turnover or flux-sum is the sum of all incoming or outgoing fluxes around a particular metabolite under pseudo-steady state conditions ,46. Let minimum of metabolite turnover was calculated, given predetermined exchange fluxes (including growth), using a linear programming formulation as follows:Due to existence of alternative optimal FBA solutions within genome-scale models, Saccharomyces cerevisiae VAN286 obtained by Hansen et al. was used as the background strain in this work. In order to produce vanillin, this strain must be transformed with a plasmid containing the gene EntD from Escherichia coli, coding for a PPTase. This enzyme is indispensable for post-translational activation by phosphopantetheinylation of ACAR in S. cerevisiae [EntD prior to cultivation in order to produce VG.The strain revisiae . All theArabidopsis thaliana coding for a UDPG-glucosyltransferase was obtained by replacing the URA3 marker by the HIS3 marker in plasmid pJH665 with the restriction enzyme XmaI. Restriction enzymes and buffers from New England Biolabs were used and the conditions for restriction followed manufacture instructions. The HIS3 gene was PCR amplified using the primers His3_Fw and His3_Rev . The plasmid ARB021 was verified by restriction analysis and sequencing of the PCR amplified HIS3 marker with the primers MarkSeq_Fw and MarkSeq_Rev from Additional file SphI and transformed into the yeast TPI1 promoter locus of VAN286, thus creating the strain VG0, producing VG from glucose. High efficiency yeast transformation method was used to construct the yeast strains [The integrative plasmid pARB021 containing the gene UGT72E2 from  strains .PDC1 and GDH1 gene deletions, as well as GDH2 overexpression were achieved by gene targeting through homologous recombination of bipartite PCR fragments, using URA3 gene from Kluyveromyces lactis as a marker [a marker . The mara marker .PDC1 and GDH1 gene (approximately 500 bp each) are listed in Additional file K. lactis URA3 flanked by direct repeats from the plasmid pWJ1042 [GDH1 in the strain VG0. Strain VG2 was obtained by deleting the gene PDC1 also in the strain VG0. Strain VG3 was obtained by deleting gene GDH1 in the strain VG2. The deletions were verified by analytical PCR using the primers PDC1_Ver_FW and PDC1_Ver_REV for PDC1 deletion, and GDH1_Ver_FW and GDH1_Ver_REV for GDH1 deletion  used for homologous recombination was obtained from VG3 genomic DNA with the primers GDH2(UP)_Fw and GDH2(UP)_Rev  with 20 g/l glucose as sole carbon source was used for cell cultivation [4)2SO4, 3.0 g/l KH2PO4, 0.5 g/l Mg2SO4, 2.0 ml/l trace metal solution, 1.0 ml/l vitamins solution, 0.05 ml/l antifoam 204 (Sigma-Aldrich A-8311) and 80 mg/l L-methionine. Trace metal solution contained 3 g/L FeSO4.7H2O, 4.5 g/L ZnSO4.7H2O, 4.5 g/L CaCl2.6H2O, 0.84 g/L MnCl2.2H2O, 0.3 g/L CoCl2.6H2O, 0.3 g/L CuSO4.5H2O, 0.4 g/L NaMoO4.2H2O, 1 g/L H3BO3, 0.1 g/L KI and 15 g/L Na2EDTA.2H2O. Vitamins solution included 50 mg/l d-biotin, 200 mg/l para-amino benzoic acid, 1.0 g/l nicotinic acid, 1.0 g/l Ca-pantothenate, 1.0 g/l pyridoxine HCL, 1.0 g/l thiamine HCl and 25 mg/l m-inositol.A defined minimal medium as described by Verduyn tivation . The med®-Plus Sartorius AG, Geottingen, Germany) and added after autoclavation.The pH was adjusted to 5 by addition of 2N NaOH prior to autoclavation, the glucose was autoclaved separately and methionine and vitamins solutions were sterile filtered (0.2 μm pore-size Ministartvolume air per volume of broth per minute).Batch cultivations were executed in well-controlled, aerobic, 2.2 B Braun Biotech Biostat B fermentation systems with a working volume of 2 L . Proper mixing conditions were ensured by two disk-turbine impellers rotating at 800 RPM and 4 baffles. The pH was automatically controlled at 5 by addition of 2N NaOH. The temperature was kept constant at 30°C. The air flow rate was 1 vvm . Minimal medium as described above was used to grow the precultures with 20 g/l glucose. The bioreactors were inoculated to an initial OD600 nm ranging from 0.5 to 0.7.Prior to inoculation, 100 ml precultures were cultivated in 500 ml baffled shake-flasks at 30°C until OD-1. The volume was kept constant at 1.5 l by controlling the level of broth inside the vessel. Steady state conditions were assumed after at least 5 residence times and CO2 and biomass concentrations were constant.Aerobic, carbon limited continuous cultivations were carried out in 2.2 B Braun Biotech Biostat B fermentation systems (as described above for batch cultivations) with a constant working volume of 1.5 L. The temperature was kept at 30°C, the pH was maintained at 5 by addition of 2N NaOH, the stirring speed was 600 RPM and the air flow was 1 vvm. Minimal medium with 20 g/l glucose was used to feed the bioreactors at a constant dilution rate of 0.1 hFor both cultivation modes (batch and continuous), off-gas passed through a condenser to minimize evaporation loss during the fermentation and filter sterilized before carbon dioxide and oxygen were quantified in a Brüel & Kjær 1308 acoustic gas analyser .600 nm) and dry cell weight. OD600 nm was measured throughout all the fermentation in a Shimadzu UV mini 1240 spectrophotometer . The samples were diluted with distilled water in order to obtain measurements in the linear range of 0 to 0.6 OD600 nm. Dry cell weight was determined by filtering a known volume of fermentation broth with pre-dried 0.45 μm pore-size nitrocellulose filters , which were subsequently washed with a 3× sample volume 0.9% NaCl saline solution. The filters were then dried for 20 minutes at 150 W in a microwave oven and kept in a desiccator while cooling for at least 2 h. The filters where finally weighted using an analytical balance.Samples were maintained at 4°C post sampling and the biomass concentration was monitored by optical density at 600 nm  and an UVD340U absorbance detector (Dionex) set at 210 nm.The fermentation samples were immediately filtered using a 0.45 μm pore-size syringe-filter  and stored at -20°C until further analysis. Glucose, ethanol, glycerol, pyruvate, succinate and acetate were determined by high performance liquid chromatography (HPLC) analysis using an Aminex HPX-87H ion-exclusion column . The column temperature was kept at 60°C and the elution was performed using 5 mM HExtracellular vanillin, vanillin β-D-glucoside (VG), protocatechuic acid (PAC), protocatechuic aldehyde (PAL) and vanillic acid were quantified by high performance liquid chromatography (HPLC) using Agilent 1100 series equipment with a Luna C18 column (Phenomenex). A gradient of methanol (+ 1% tetra-fluoroacetic acid) and water (+ 1% tetra-fluoroacetic acid) at a flow rate of 0.3 ml/min was used as mobile phase. The column was kept at 300 bar and 30°C. Metabolite detection was performed using a UV diode-array detector set at 280 and 310 nm.The authors declare that they have no competing interests.KRP conceived the study. ARB, KRP and UM designed the study. ARB and CM performed the experiments. ARB analyzed the data and drafted the manuscript. ARB, KRP, UM, JH and BLM contributed to the analysis of the results and manuscript writing. KRP, UM, JH and BLM supervised and co-ordinated the overall study. All authors read and approved the final manuscript.Table S1: List of primers used in this study.Click here for file