One ultimate goal of metabolic network modeling is the rational redesign of biochemical networks to optimize the production of certain compounds by cellular systems. Although several constraint-based optimization techniques have been developed for this purpose, methods for systematic enumeration of intervention strategies in genome-scale metabolic networks are still lacking. In principle, Minimal Cut Sets  provide an exhaustive enumeration approach. However, their disadvantage is the combinatorial explosion in larger networks and the requirement to compute first the elementary modes (EMs) which itself is impractical in genome-scale networks.E.coli with combinations of up to 5 reactions. We also applied the new algorithm exemplarily to compute strain designs for growth-coupled synthesis of different products  by E.coli. We found numerous new engineering strategies partially requiring less knockouts and guaranteeing higher product yields  than reported previously. The strength of the presented approach is that smallest intervention strategies can be quickly calculated and screened with neither network size nor the number of required interventions posing major challenges.We present MCSEnumerator, a new method for effective enumeration of the smallest MCSs (with fewest interventions) in genome-scale metabolic network models. For this we combine two approaches, namely (i) the mapping of MCSs to EMs in a dual network, and (ii) a modified algorithm by which shortest EMs can be effectively determined in large networks. In this way, we can identify the smallest MCSs by calculating the shortest EMs in the dual network. Realistic application examples demonstrate that our algorithm is able to list thousands of the most efficient intervention strategies in genome-scale networks for various intervention problems. For instance, for the first time we could enumerate all synthetic lethals in  E.coli demonstrate that our algorithm is able to list thousands of the most efficient intervention strategies in genome-scale networks for various intervention problems.Mathematical modeling has become an essential tool for investigating metabolic networks. One ultimate goal of metabolic network modeling is the rational redesign of biochemical networks to optimize the production of certain compounds by cellular systems. Accordingly, several optimization techniques have been proposed for this purpose. However, for large-scale networks, an effective method for systematic enumeration of the most efficient intervention strategies is still lacking. Herein we present MCSEnumerator, a new mathematical approach by which thousands of the smallest intervention strategies (with fewest targets) can be readily computed in large-scale metabolic models. Our approach is built upon an extended concept of Minimal Cut Sets, the latter being minimal (irreducible) combinations of reaction (or gene) deletions that will lead to the fulfilment of a given intervention goal. The strength of the presented approach is that smallest intervention strategies can be quickly calculated with neither network size nor the number of required interventions posing major challenges. Realistic application examples with  PLOS Computational Biology Methods article.This is a Stoichiometric and constraint-based modeling techniques such as flux balance analysis or elementary modes analysis have become standard tools for the mathematical and computational investigation of metabolic networks m internal metabolites and n reactions can be formalized by an m×n stoichiometric matrix N. A common assumption of constraint-based methods is that the network is in steady state  resulting in a system of homogeneous linear equationsr is the vector of (net) reaction fluxes or reaction rates. In addition, the non-negativity constraints on fluxes through irreversible reactions must be fulfilled:Irrev comprises the indices of the irreversible reactions). The two constraints (1) and (2) form a convex polyhedral cone (the flux cone) in the n-dimensional space of the rate vectors r. Flux Balance Analysis  and (2) and in addition a non-decomposability property. The latter demands that an elementary mode e is irreducible , hence, there is no vector r≠0 obeying (1) and (2) andr) and P(e) represent the support of r and e, respectively, i.e., they contain the indices of the vector elements being non-zero: P(t) = {i | it≠0}. Elementary modes (EMs) represent stoichiometrically balanced metabolic pathways or cycles and several important properties of a metabolic network can be analyzed by its unique set of EMs Metabolic networks consisting of sis FBA;  searchesOne ultimate goal of metabolic network modeling is the targeted manipulation of the network behavior. A typical application is metabolic engineering where one is interested in the optimization of the production of a certain compound by a given host organism. A number of constraint-based optimization techniques have been proposed for this purpose minimal hitting sets of the set of (target) EMs that generate these behaviors The method of Minimal Cut Sets (MCSs) directly addresses the enumeration of metabolic intervention strategies Another approach to compute MCSs, which exploits the inherent dual relationship between EMs and MCSs, was recently presented by Ballerstein et al. constrained minimal cut sets (cMCSs) was introduced by Hädicke and Klamt However, there are two potential problems related to MCSs. First, when the reactions contained in an MCS are removed, we are sure that the targeted network functions are disabled but other (desired) functions might be blocked as well. For instance, it can occur that an MCS which disables low-yield pathways synthesizing a desired product also blocks growth of the organism making this MCS impractical. To prevent such side effects, the concept of The second and more serious problem of (c)MCSs is that their full enumeration in large/genome-scale networks becomes prohibitive. The algorithms requiring as inputs the target (and possibly desired) EMs are usually not applicable: despite large progress in algorithmic design On the other hand, for the purpose of applying MCSs in real networks, those with the smallest number of elements are usually the most relevant. Thus, it is worthwhile to consider computing only the (c)MCSs with low cardinality. The effective enumeration of the smallest cut sets is therefore the key goal of the present work.n is the number of possible cuts and k the size of cut set candidates). Therefore, it is not normally possible to find genome-scale MCSs in reasonable time with more than 4 knockouts using this scheme.Usually, the unwanted/desired functionalities to be disabled/kept in a metabolic network can be described by sets of linear equalities and inequalities over the fluxes. For the purpose of computing MCSs, we could therefore use an exhaustive FBA-based scheme by testing all single, double, triple and higher knockout sets whether they are suitable cut sets or not. The formulation of FBA problems would circumvent the problem to enumerate the EMs first. However, as discussed above, this approach becomes problematic if larger knockout sets are required to solve an intervention problem, as it must test a large number of candidate sets with increasing MCS size . As shown by the authors, this approach can readily be applied to genome-scale networks to find the first hundred or even thousand shortest EMs involving the fewest number of reactions.Whereas the direct calculation of smallest MCSs in large-scale networks cannot be properly addressed yet by current methods, a method for computing the smallest (or shortest) EMs in genome-scale networks was recently presented by de Figueiredo et al. k-smallest MCSs from a given network structure. We show that this can be achieved in two steps. First, the original network and the actual intervention goal are converted to its dual representation using the approach of Ballerstein et al. The goal of the present work is to realize a similar approach for computing the k-shortest EMs and introduce several modifications improving the performance of this algorithm. In particular, we will make use of certain features of MILP solvers provided for effective enumeration of solutions of a MILP problem.The paper is organized as follows: we will first briefly review the approach of de Figueiredo et al. for computing constrained MCSs can be computed within this framework. Finally, to demonstrate the power of our new approach we will exemplify its use by computing relevant intervention strategies (of different complexities) in iAF1260, a genome-scale metabolic model for E.coliE.coli up to size 5 which was not possible before. Moreover, we show that the algorithm facilitates the calculation of thousands of the minimal intervention strategies that lead to growth-coupled synthesis of certain compounds by E. coli.Thereafter we will describe how the network constraints (including inhomogeneous constraints) and the intervention goal have to be translated into their dual description in which we can then enumerate the shortest EMs to obtain the smallest MCSs in the primal network. We shall also explain how For the sake of simplicity, throughout the manuscript we will deal with reaction cut (or knockout) sets, which must in practice be translated to gene knockout sets to construct the corresponding mutants. This transformation can be easily achieved if the corresponding gene-enzyme-reaction associations are available. The latter could also directly be included in the problem formulations given below to compute gene (instead of reaction) cut sets.indicator variables, a feature provided by advanced MILP solvers . An indicator is a binary variable that can be thought of as controlling the activity of one or more constraints. Indicators can be part of the objective function and constraints controlled by indicators may in turn influence other indicator variables as well. An important application of these variables that we use here is to indicate whether another variable is equal or greater than zero. More precisely, we use an indicator variable iz to indicate whether a real and non-negative variable ix is greater than zero:c = 1 as threshold for a variable to be greater than zero because the solutions (the EMs) to the MILPs set up here are scalable by arbitrary factors due to the unboundedness of the ix. In principle, a different positive value could be chosen for c but setting c = 1 can be expected to not cause any particular numerical problems.Both elementary modes and minimal cut sets can be represented as sets of reactions (sets of active reactions in case of EMs and sets of deleted reactions in case of MCSs). Since we are mainly interested in the composition and size  of EMs and MCSs it is important to represent them efficiently in the MILP problem to be formulated. Here we will make use of iz will turn the linear problems discussed so far into a MILP problem with discrete and continuous variables. In contrast to Figueiredo et al. The functionality of indicator variables is often implemented by a “big M” formulation with integer variables cf. , but as N contain only irreversible reactions. This is no limitation since reversible reactions can be decomposed into two irreversible ones, one in forward and one in backward direction. Using (6) we now define indicator variables for the reaction rates ir:c = 1). For all reaction pairs , s,t ∈ {1,…, n} that were derived from the same formerly reversible reaction we demand that only one of both (directions) can be active to avoid spurious cycles:r = 0, we demand in addition that an EM must contain at least one active reaction:r and z so that all constraints are fulfilled and the value of the objective function is minimized. The vectors r and z contain the shortest EM in vector and set representation, respectively. Note that this MILP does not yet contain constraints enforcing the elementarity of the solution. However, due to the non-decomposability property of EMs all solutions minimizing (10) must be EMs and, moreover, they are the shortest EMs as they involve a minimal number of reactions.We now rephrase the MILP problem presented in k-shortest EMs as implemented by de Figueiredo et al. iz (see below). The pseudo-code for enumerating the k shortest EMs thus reads:The actual enumeration of the ALGO1: k-shortest EMs via de Figueiredo et al. [23]ems = {};k = 0;WHILE k < MaxNumEMk++;   newem = solveMILP; /* calculate one optimal solution   (k-shortest EM) of the MILP */ems = ems ⋃ {newem};   add_exclusion_constraint(newem);   ENDWHILEsolveMILP calls. An exclusion constraint takes the following form . We can therefore fix the size control constraint to s  so that only EMs of exactly this size are calculated. As long as solutions of size s are enumerated, exclusion constraints for the solutions would only be required to prevent the same solution from being found again because supersets of these solutions are already excluded by the size control constraint. This opens up the possibility to use the MILP without adding exclusion constraints at all while generating the solutions of a fixed size s by using the warm start feature of advanced MILP solvers. With this feature, the preprocessing will not be reiterated when computing the EMs of size s and the search tree generated during the previous search for a solution can be reused for finding the next solution. This improves the efficiency of the whole procedure and by continuing with the same search tree it is also made sure that the same solution is not returned twice. In CPLEX, this feature is provided by a function populate allowing the enumeration of all possible solutions to a MILP problem. Also, when searching for EMs of a fixed size only, the problem does not require an optimization over the sum of the iz any more (since the latter is fixed as a constraint) and becomes thus merely a search for a feasible solution which is potentially easier to solve.We restate that the exclusion constraints (11) are needed to prevent supersets of known EMs from being erroneously identified as EMs. If all EMs up to size s have been, enumerated exclusion constraints for the found EMs must be added as usual before continuing with s+1 (to avoid that supersets of EMs of size s will be found in subsequent iterations). However, the advantage of this approach remains because exclusion constraints need not be added when processing all EMs with cardinality s. We summarize the basic scheme as follows:Importantly, when all EMs of size ALGO2: k-shortest EMs via fixed sizenewem = solveMILP; /* calculate first optimal solution of theMILP (the shortest EM) */             s = objective_value(newem); /* s: current lower boundary of EMsize */              ems = {newem};i */remove_objective_function; /* remove the minimization over the zWHILE s< = maxEMsizesetConstraint(EMsize = s); /* fixed size of EM */ newems = populateMILP; /* enumerate all feasible EMs with size s */                ems = ems ∪ newems; add_exclusion_constraints(newems); s++; ENDWHILEpopulateMILP call can usually be halted  and continued so that the solutions found so far can be accessed before the search is finished. This means that even if for a given set size more solutions than can be practically calculated exist it is still possible to use this scheme to get at least a partial result.The search that is conducted during a r to be disabled by the MCSs) by a suitable inequality constraintt is a (n×1) vector. Usually, t corresponds to a single row with zeros except a single 1 for a target reaction (rate) whose operation is to be blocked . Setting in addition b to 1 we would target all flux vectors in which the rate of the target reaction is non-zero .We present now the key methodological development of this work showing that the basic algorithm for enumerating shortest EMs introduced in the previous section can also be used to compute smallest MCSs. The procedure is based on the duality properties of EMs and MCSs presented by Ballerstein et al. T (of size t×r) together with t inhomogeneous inequality constraints defining the target flux polyhedron (which may be bounded becoming then a polytope). It must be made sure that the zero flux vector is not contained in the target flux polyhedron as it can not be blocked by reaction knockouts. A nice feature of (14) is that we may directly include inhomogeneous constraints to characterize target flux vectors .Constraint (13) specifying the target flux vectors can be generalized to:I is the (n×n) identity matrix). These constraints ensure that the system becomes infeasible as the zero flux vector implied by (15) contradicts (14). Note that (15) can be seen as the maximal  cut set knocking out every reaction in the network. In fact, the MCSs correspond to minimal subsets of the homogeneous equations in (15) which ensure (induce) inconsistency of the inequality system posed by constraints (1), (2), (14) and (15). Minimal subsets of constraints that induce inconsistency of an inequality system are also known as irreducible inconsistent subsets  and to the standard network constraints (1) and (2), Ballerstein et al. augmented the system by equality constraints setting all reaction rates to zerots IISs; . GeneralNdual is the “dual stoichiometric matrix” and rdual the dual “rate” vector):n-|Irrev| zero rows at the position of reversible reactions  must sometimes be split to properly describe the target flux polyhedron). As described above, the MCSs in the primal correspond to particular EMs of the dual system (16) which have minimal support in the v variables. The dual variables iv, i∈{1 … n} are thus of particular importance as their values indicate which reactions participate in an MCS. Concretely, if iv≠0 then reaction i is part of the MCS (irrespective of the sign of iv), if iv = 0 then it is not. Therefore, similar as we did for reversible reactions when computing shortest EMs, both positive and negative values of iv must be checked with indicators and in order to facilitate this each iv is split into two variables, ivp and ivn, both with the lower bound 0. Furthermore, since h≥0 and because the MILP can directly operate on inequalities, we can rewrite (16) to:i refer to the part of the irreversible reactions and subscript r to the part of the reversible reactions of the primal system). As mentioned above, for the ivp and ivn we introduce the associated indicators izp and izn, and ) the constraintsivp and ivn cannot be active simultaneously. The constant c in (17) can again be set to any positive value ; this will not change the set of minimal non-zero combinations of ivp and ivn fulfilling (17) which are relevant for the optimization problem formulated below , (2), (14), (15) into its dual which can be written as follows  must be adapted accordingly to  sums here over izp+izn as in the objective function (19).After dualization, we can now compute the smallest MCSs of the primal system by applying algorithm ALGO2 in the dual system. As constraints we need to consider (17) (replacing (1) and (2) from the primal system) as well as (18) and as objective function we exchange (10) withz-vector of the solutions found in the dual; z is obtained by collapsing izp and izn: iz = izp+izn.The MCSs of the primal network are eventually obtained by taking the constrained MCSs can be computed by this approach. As it turns out, this is straightforward: one first enumerates the smallest MCSs blocking the undesired flux vectors as described above. We can assume that the desired flux vectors (of which at least one has to be kept) is formulated by appropriate inequalities - similar as for the targeted undesired flux vectors in (14):In the previous subsection we dealt with enumeration of smallest MCSs, however, we have not yet clarified how sted see  section.CellNetAnalyzer package, a MATLAB toolbox for biological network analysis http://www.mpi-magdeburg.mpg.de/projects/cna/etcdownloads.html.The MCSEnumerator method has been integrated as a new functionality in the We analyze basic properties of the runtime behavior of our algorithm by means of three realistic benchmark problems with different complexities. All computations were performed with the CPLEX 12.4 MILP solver. When using multiple threads deterministic parallel mode was used to get repeatable behaviour. The search tree that CPLEX dynamically constructs took up less than 3 GB of RAM for all the systems used here.E. coli for growth under different substrates . The MCSs determined in this way will thus correspond to the synthetic (reaction) lethals for E. coli (whose compositions depend strongly on the provided substrate). Before using the different MCS calculation routines the metabolic network is compressed by combining correlated reactions (operating with a fixed ratio under steady state conditions) to single cumulated reactions In order to compare our MILP-based MCS enumeration scheme to other approaches the same benchmark problems as in The number of calculated MCSs and computation times are shown in smallest MCSs, we can use it here even for enumerating all of them. The EMs in the dual network  where computed with both MILP formulations for shortest EM calculation: ALGO1  than ALGO1 based on the scheme used by de Figueiredo et al. Although the MILP algorithm developed herein was actually developed to compute the The main advantage of our new approach can be seen in the case where only the MCSs up to size 4 have to be calculated  and the ATP maintenance requirement was set to the standard value of mmol/(gDW⋅h). Analogous to Suthers et al. minμ≥0.01⋅maxμ = 0.0093 −1h. With these inhomogeneous conditions, the MCSs will thus correspond to synthetic reaction lethals as also computed by Suthers et al. To demonstrate this, we use the We also tested the homogeneous version of the above intervention problem, that is, we calculated the MCSs blocking growth without the additional constraints for ATP maintenance (E. coli produce a biofuel (ethanol) from glucose. The intervention goal is thus to disable flux vectors with a low ethanol yield in E. coli (undesired behavior) while retaining the capability for both maintenance and growth of the bacterium under anaerobic conditions . This forms a constrained MCS problem. All cMCSs that fulfill the stated requirements will lead to obligatory coupling between growth and ethanol formation.The following third example relates to a typical problem of finding rational intervention strategies for metabolic engineering purposes. We here focus on a biotechnologically relevant application, namely to let E. coli metabolism but this time with the oxygen uptake removed to establish anaerobic conditions on the network. As before, glucose is the only available carbon source. To study the effect of different capacities for substrate uptake, we considered two possible limits for the glucose uptake rate: mmol/(gDW⋅h) and mmol/(gDW⋅h). The latter value has been measured under anaerobic conditions where E. coli tends to exhibit higher substrate uptake rates mmol/(gDW⋅h).We used again the iAF1260 genome-scale network model of minμ≥0.001 −1h was demanded.With these values in mind, we formulated the following intervention goal: the task is to identify cMCSs that guarantee a minimal ethanol yield of Eth/GlcY(r) denotes the ethanol yield of the reaction rate vector r). The set of desired behaviors from which we want to keep at least some flux vectors is given by:With these inhomogeneous constraints we can now specify the target flux polyhedron containing all undesired network behaviors to be eliminated by the cMCSs:−1h  based on our approach requires to first compute the MCSs blocking the undesired behavior and to keep afterwards only those MCSs that admit the desired behavior. This test is done for each found MCS by solving a separate linear program (LP) which verifies whether the remaining network supports the desired behavior. To reduce the search space, blocked reactions for the network under desired ethanol production conditions were determined and removed in a preprocessing step using flux variability analysis izp and izn indicator variables to zero.We then computed the cMCSs. As described in the After network compression, the  network could be reduced to 562 metabolites and 958 (lumped) reaction subsets of which 845 can be knocked out.Note also that the disruption of glucose uptake or ATP maintenance are valid MCSs deleting all undesired behaviors but they violate for trivial reasons the desired functionality (growth not possible) and can thus not be contained in any valid cMCSs. Such reactions being essential for the desired flux space could also be identified at an early stage and then be excluded from the search space.As can be seen in We then analyzed the cMCSs in more detail. A first observation in The situation is different in the case of increasing E. coli) would actually cut two reactions at the same time for which the model predicts that E. coli can not grow anymore. Thus, only four of the eight cMCSs remain valid on gene basis. However, as already explained earlier, those effects can be taken into account based on gene-enzyme-reaction associations.The cMCSs for scenario 1  is a surprising fact on its own. Previous work on computing intervention strategies for ethanol overproduction in a smaller (core) network of E.coli were presented in any growth rate of the mutant.We mention here that two other intervention strategies with three knockouts for production of ethanol by −1h) and that in order to have a growth rate larger than 0.1−1 h it is necessary to use cut sets with a least 6 knockouts. If higher growth rates and/or smaller cut sets are required the minimal product yield would have to be lowered.Having exhaustively enumerated the cMCSs up to a given size enables one to analyze essential features and performance measures of all found intervention strategies by which eventually the optimal knockout strategy can be selected. Other performance measures of designed mutant strains can be studied as well. One such proposed measure is substrate-specific productivity (SSP) which is the product of the growth-rate and the product yield populate procedure to suppress these redundant solutions. Whether the integrated approach can be reformulated in a manner that facilitates a more efficient calculation of its cMCSs solutions is a potential topic for further investigation.As a technical note, it is not absolutely mandatory to have all MCSs  enumerated before running the LP checks for testing the “survival” of some desired flux vectors: these checks could be (independently) performed as soon as an MCSs has been found by the MILP solver. In fact, it is in principle possible to integrate the LP into the MILP so that the cMCSs are computed directly which offers the advantage that far fewer exclusion constraints need to be integrated while the enumeration proceeds. In practice, however, this approach showed a markedly inferior performance for the system studied here. One reason is that the LP adds further degrees of freedom to the solution space and leads to redundant solutions for the cMCSs which requires a more intricate control of the E.coli. To the best of our knowledge, this exceeds by far other attempts to enumerate such metabolic engineering strategies in large-scale networks.To summarize the results of this sub-problem, our algorithm enabled the enumeration of all reaction knock-out sets up to size 7 that lead to coupled ethanol and biomass synthesis in If more computational capacity is available, one might try to find even larger cMCSs. However, the best knockout strategy to be implemented is likely to be contained among the up to 8819 smallest cMCSs found as the number of required interventions will be one (though not the only) key criterion when deciding for a concrete strain design.E.coli has been presented by Feist et al. E.coli model the iAF1260 reconstruction −1h was chosen and an ATP maintenance of 8.39 mmol/(gDW⋅h) required. Both glucose and oxygen uptake were limited to 20 mmol/(gDW⋅h). Given this setup it was possible to calculate strain designs for many substrate/product pairs but for some of them strains with only low productivity or even no strains with growth-coupled product synthesis were found.One large-scale study to evaluate the growth-coupled production potential in Here we wanted to test the potential of our method for some of the intervention problems. We focused on the aerobic production of either fumarate or serine from glucose which both have a potential for high yield as calculated by FBA. However, growth-coupled strains for the production of fumarate only achieved 20%  respectively 23%  of the theoretical maximum while for serine no growth-coupled strains could be identified in To demonstrate the power of our method in dealing with large-scale systems, we increased the search space drastically compared to mmol/(gDW⋅h) . As for the ethanol study, all these values are independent of the assumption of optimal growth. Likewise, in the case of serine production, the MCSs up to size 6 were calculated (taking 3.1 h) from which 140 cMCSs  could be extracted. These would result in strains with with a guaranteed serine yield between 0.71 and 0.91  corresponding to minimal production rates between 36.6% and 47.0% of the theoretical maximum (38.71 mmol/(gDW⋅h)). Hence, our results show that significantly larger fumarate production rates can be achieved with 7 knockouts than computed by OptGene. In case of serine where no suitable knockout strategy could be identified in For fumarate production, the MCSs up to size 7 were calculated (taking 13.6 h) from which 30 cMCSs  could be extracted. Applying those cMCSs would result in production strains exhibiting – at maximal substrate uptake rates – a guaranteed  fumarate yield between 0.71 and 0.89 corresponding to minimal production rates between 40.9% and 51.3% of the theoretical maximum of 34.68 In this work we presented MCSEnumerator, a new algorithmic approach to enumerate the smallest (c)MCSs up to a given size in genome-scale networks. This approach is based on a MILP problem calculating the shortest EMs in the dual representation of the metabolic network eventually yielding the smallest cMCSs. The whole procedure can be summarized by five steps:Build the metabolic network as usual by specifying the stoichiometric matrix and the irreversibility constraints . OptionaDefine the space of undesired (target) flux vectors and  the space of desired flux vectors by means of the linear inequalities (14) and (21), respectively. The (c)MCSs to be computed will ensure that no target flux vector can operate whereas the operation of at least one desired flux vector will be feasible.z) for the v variable and pose the MILP optimization problem for computing the shortest EM in the dual system (19).Build the dual system which is immediately given by (17). Introduce indicator (or binary) variables (k-shortest solutions (EMs) of the MILP problem from step 3 by using ALGO2.Enumerate the Translate the EMs found in the dual to MCSs in the primal. If desired behaviors were specified in step 2, run one LP for each MCSs to check whether it is a constrained MCS, i.e., whether some desired flux distributions remain feasible after cutting the reactions contained in the MCS.With these five steps, MCSEnumerator provides a generic approach for enumerating smallest intervention strategies; one just has to plugin the corresponding matrices in Apart from the combination of dualization and shortest EM calculation in step 3, another key development made herein is the improvement of the required sub-routine for computing shortest EMs (ALGO2) which is now based on a more efficient enumeration of feasible EMs with fixed size and which consequently makes use of available enumeration features of modern MILP solvers. Appropriate integration of such functionalities could also be useful to effectively solve other enumeration problems in the field.all (c)MCSs with our approach is slower compared to other approaches requiring EMs to be calculated in a first step, it has the advantage that the smallest (c)MCSs, which are often the most interesting ones, can be found first and that no EMs need to be calculated beforehand. This property renders (c)MCSs calculation feasible in genome-scale networks. Also, the number of elements in an MCS has no major impact on the performance as it would have in brute-force enumerations  and as it has been observed also for several directed search algorithms.Despite the fact that calculation of all MCSs. However, the shown application examples demonstrated that our approach is capable to compute hundreds of thousands of smallest MCSs and several thousand smallest constrained MCSs in genome-scale networks  calculate the smallest (c)MCSs with neither network size nor the number of elements in the (c)MCSs posing major challenges. With these results and due to the fact that the approach of (c)MCSs allows the setup of complex intervention problems in a flexible and convenient way, we expect that a large number of metabolic network studies can benefit from our conceived framework.An interesting aspect for future work will be to investigate how far ALGO2  can be generalized to enumerate also other elementary sets arising in different contexts of computational biology (e.g., for calculating minimal intervention sets in signaling or regulatory networks


Saccharomyces cerevisiae to efficiently ferment pentose sugars such as D-xylose and L-arabinose into biofuels such as ethanol through heterologous expression of the fungal D-xylose and L-arabinose pathways. However, one of the major bottlenecks in these fungal pathways is that the cofactors are not balanced, which contributes to inefficient utilization of pentose sugars. We utilized a genome-scale model of S. cerevisiae to predict the maximal achievable growth rate for cofactor balanced and imbalanced D-xylose and L-arabinose utilization pathways. Dynamic flux balance analysis (DFBA) was used to simulate batch fermentation of glucose, D-xylose, and L-arabinose. The dynamic models and experimental results are in good agreement for the wild type and for the engineered D-xylose utilization pathway. Cofactor balancing the engineered D-xylose and L-arabinose utilization pathways simulated an increase in ethanol batch production of 24.7% while simultaneously reducing the predicted substrate utilization time by 70%. Furthermore, the effects of cofactor balancing the engineered pentose utilization pathways were evaluated throughout the genome-scale metabolic network. This work not only provides new insights to the global network effects of cofactor balancing but also provides useful guidelines for engineering a recombinant yeast strain with cofactor balanced engineered pathways that efficiently co-utilizes pentose and hexose sugars for biofuels production. Experimental switching of cofactor usage in enzymes has been demonstrated, but is a time-consuming effort. Therefore, systems biology models that can predict the likely outcome of such strain engineering efforts are highly useful for motivating which efforts are likely to be worth the significant time investment.Biofuels derived from lignocellulosic biomass offer promising alternative renewable energy sources for transportation fuels. Significant effort has been made to engineer  Lactococcus lactis was used to enhance production of diacetyl, a flavoring compound found in dairy products Pseudomonas putida was used to improve the production of poly-3-hydroxyalkanoates (PHA), which are biodegradable polyesters synthesized to replace petrochemical based plastics Reconstruction and simulation of genome-scale metabolic networks provides a powerful approach to guide metabolic engineering efforts Increases in fuel prices coupled with concerns about global warming and energy security, have rekindled interest in producing ethanol and other biofuels from lignocellulosic raw materials such as agriculture and forestry waste S. cerevisiae is often chosen for ethanol production because of its high inhibitor tolerance and its ability to grow at low pH to avoid bacterial contamination S. cerevisiae has the substantial drawback that it cannot fully utilize the substrates available from breakdown of plant biomass. That is, wild type S. cerevisiae can metabolize the hexose sugars, but not the pentose sugars. To overcome this problem, D-xylose and L-arabinose utilization pathways have been incorporated into the host microorganism. For example, S. cerevisiae was engineered to utilize D-xylose using both fungal and bacterial D-xylose utilization pathways Pichia stipitisThe yeast S. cerevisiae was engineered to utilize L-arabinose using the fungal reduction/oxidation-based and bacterial isomerization-based pathways. In the bacterial pathway, enzymes L-arabinose isomerase (AI), L-ribulokinase (RK), and L-ribulose-5-P 4-epimerase (R5PE) are responsible for conversion from L-arabinose to L-ribulose, L-ribulose-5-P, and finally D-xylulose-5-P, respectively S. cerevisiaeSimilarly, S. cerevisiae strains containing the fungal pentose utilization pathways +. Similarly, the cofactor specificity for L-arabinitol and L-xylulose reductase are NADH and NADPH, respectively. Thus, the operation of these pathways results in a cofactor imbalance that places a demand on the rest of the network to rebalance these cofactor pools. In order to eliminate this cofactor imbalance within the engineered pathways, protein engineering techniques are used to change the cofactor specificity of XDH and LAD to NADP+. This change will have the effect of making the pathways redox neutral, meaning that they will not cause an imbalance in cofactor utilization that would then need to be compensated for elsewhere in the network. Aerobically NADP+ dependent malic enzymes were used to increase the cystolic or mitochondrial level of NADPH in S. cerevisiaePrevious studies have shown that accumulation of xylitol is ultimately responsible for inefficient production of ethanol in engineered We used a genome-scale constraint-based metabolic model to study for the first time the effects on the global network that result from cofactor balancing associated with the engineered fungal D-xylose and L-arabinose utilization pathways. It was found that cofactor balancing increased predicted pentose sugar utilization efficiency while retaining the flexibility and flux correlation structure of the wild type strain. In addition, the genome-scale model predicts quantitatively an increase in ethanol production of 24.7% that would result from cofactor balancing the introduced pentose utilization pathways – providing strong motivation for the initiation of a laborious and time-consuming enzyme engineering project to change cofactor specificity. Thus, this study provides an example of prospective design of a labor-intensive synthetic biology project using the tools of systems biology.S. cerevisiae iMM904 S. cerevisiae ; 2) engineered cofactor imbalanced ; and 3) engineered cofactor balanced . Dynamic flux balance analysis (DFBA) calculations were done on the engineered cofactor imbalanced model and engineered cofactor balanced model. Flux variability analysis and sampling of the flux space were done on all the three models.For our simulations, we modified the most recently published genome-scale metabolic model: revisiae . The resS. cerevisiae strains have shown significant amount of L-arabinitol accumulation DFBA simulation of batch fermentations for the engineered cofactor imbalanced model was carried out using 20 g/L of glucose in the presence of minimum oxygen for the maximization of biomass production. Apart from glucose, D-xylose and L-arabinose were mixed in 50 g/L and 30 g/L, respectively. The initial concentration and uptake rates for glucose and D-xylose were taken from reported data in literature +. The difference in cofactor specificity leads to additional demands on the metabolic network to maintain intracellular redox balance. Extracellular L-Arabinitol accumulation in the simulations resulted in inefficient utilization of D-xylose/L-arabinose and decreased ethanol yield. This cofactor imbalance issue can be addressed by two different protein engineering strategies. One of them is to change the cofactor specificity of LAD and XDH from NAD+ dependent to NADP+ dependent, whereas the other strategy involves the change of cofactor specificity of XR and LXR from NADPH dependent to NADH dependent. We simulated both strategies and found that the results were equivalent. Thus, only the strategy of switching the cofactor specificity of LAD and XDH from NAD+ dependent to NADP+ to make the pathways redox neutral will be shown here (Pichia stipitis XDH (psXDH) has been successfully changed experimentally through protein engineering for efficient fermentation of D-xylose to ethanol using recombinant S. cerevisiaeDFBA simulates extracellular L-arabinitol accumulation due to the difference in cofactor specificity between XR with NADPH and XDH with NADown here . CofactoS. cerevisiae. We simulated the batch processes with both the cofactor imbalanced and cofactor balanced pentose utilization pathways. Here we constrained our model to utilize L-arabinose immediately after D-xylose. The genome-scale model predicted that the strain with the engineered cofactor balanced pathway would have significantly higher ethanol production (46 g/L ethanol) than the strain with the cofactor imbalanced pathway (36.9 g/L of ethanol). The engineered cofactor balanced strain showed significant increase in biomass of 8.03 g/L compared to the cofactor imbalanced strain of 6.27 g/L of biomass. This represents a 24.7% increase in ethanol production from the same amount of substrate, which provides strong motivation for experimental efforts to modify the cofactor specificity – typically a long and laborious process. Interestingly, extracellular L-arabinitol accumulation is not predicted when the engineered cofactor balanced pathway is introduced, leading to the immediate utilization of L-arabinose after complete consumption of D-xylose. Furthermore, the L-arabinose consumption rate is faster than is found with the cofactor imbalanced pathways. Also of critical importance to overall performance, the total time required to consume the mixed sugars glucose, D-xylose, and L-arabinose is predicted to be just 94 hours for the strain with the cofactor balanced pathways compared to 312 hours for the strain with the cofactor imbalanced pathways. Thus by cofactor balancing the metabolic network has improved ethanol production from 36.9 g/L to 46 g/L and simultaneously reduces the utilization time from 312 hours to 94 hours. The cofactor balanced pathway thus has the potential to improve the engineered S. cerevisiae strain for ethanol production.Simulation of ethanol fermentation from mixed sugars was performed with 20 g/L glucose, 50 g/L D-xylose, and 30 g/L L-arabinose as carbon sources. The variation of glucose, D-xylose, L-arabinose, ethanol, and cell biomass concentrations as a function of time are shown in S. cerevisiae metabolic model has been extensively validated S. cerevisiae strain −1. Experimental batch fermentation under the same condition as with the wild type strain of S. cerevisiae consumed 20 and 30.4 g/L of glucose and D-xylose, respectively and produced 16.8 g/L of ethanol S. cerevisiaein silico as a function of extracellular glucose concentration Of key importance in using the model to guide an experimental program is to ascertain whether the predictions made from the model are generally reliable. The genome-scale + generated during the conversion of D-xylose to xylitol can be utilized by NAD+ specific XDH. Recently, the batch fermentations were done on a recombinant S. cerevisiae strain containing the XR-XDH pathway from P. stipitis with engineered NADH-specific XR (YPS270R) NADS. cerevisiae genome-scale metabolic network. At optimal growth, a range of variability exists in each flux in the network in terms of the range of flux values it can achieve at steady-state. First, the maximum value of the biomass objective function was calculated and then the maximum value of biomass was used as a constraint when calculating the feasible range of reaction fluxes by subsequent maximization and minimization of each reaction flux. We have applied this technique, known as Flux Variability Analysis (FVA) ECI -SpanECB. A difference flux span or span change (SC) was calculated between engineered cofactor imbalanced and engineered cofactor balanced models reactions, and are grouped into four categories, SC > 0.5, 0.01 < SC < 0.5, 0.0 < SC < 0.01 and SC = 0 with 4%, 42%, 19% and 35% of total reactions respectively, in the entire metabolic network  between any two fluxes (vi and vj) in the network was evaluated using uniform random sampling of the steady-state flux space. The glucose, oxygen, D-xylose, and L-arabinose consumption rates were kept same for the wild type, engineered cofactor imbalanced and cofactor balanced models. The optimal growth rates for wild type, engineered cofactor imbalanced model and engineered cofactor balanced model are 0.14, 0.15, 0.19 hr−1 respectively. The correlation pattern obtained from sampling provided an efficient way to distinguish the effects of changes to the metabolic network. Here, the metabolic network has been changed by adding new pathways and changing the cofactor specificity for selected reactions. Pairwise correlation coefficients were calculated between all fluxes  fully coupled: the activity of one reaction fixes the activity for other reaction and vice versa, ii) directionally coupled: the activity of one reaction implies the activity of the other but not necessarily the reverse. iii) partially coupled: the activity of one reaction implies the activity of the other and vice versa, iv) uncoupled: the activity of one reaction does not implies the activity for other reaction and vice versa. These reactions can have any flux ratio and can operate independently.The functionally related coupled reaction sets are identified using flux coupling analysis max  =  max(ν1/ν2) & Rmin  =  min(ν1/ν2) were calculated . The different cofactor specificity, NAD+ for LAD and XDH, NADPH for XR and LXR, in engineered D-xylose and L-arabinose utilization pathways has contributed to intercellular redox imbalance, which results in reduced pentose sugar consumption rates and ethanol productivity – which the model predicts as a consequence of the demands placed on the metabolic network to re-balance these co-factors. To address the cofactor imbalance issue, the cofactor specificity was changed computationally from NAD+ to NADP+ for two enzymes in the D-xylose and L-arabinose utilization pathway including LAD and XDH. The GEM predicts that engineering cofactor balanced pathways will greatly enhance utilization of pentose sugars and increase ethanol production. To validate the model predictions, the computational data were compared with reported experimental data. The experimental ethanol production is 25.3 g/L with 66.1 g/L sugar consumption, while our DFBA calculations have shown 33 g/L of ethanol with 70 g/L of sugar consumption, indicating a very good agreement between model predictions and experimental data.To build a GEM of Based on this revised GEM, flux variability analysis was carried out to further investigate the variation of reaction fluxes in the entire metabolic network. The increase in flexibility of the reaction fluxes resulted in increases in the flux range of the engineered cofactor imbalanced model. Cofactor balancing the engineered pathways restored network flexibility to a state that was very similar to that of the wild type strain. Furthermore, uniform random sampling was carried out to calculate the probability distribution for fluxes through all reactions. Variations in correlation patterns among the reactions were observed with the addition of the engineered cofactor imbalanced and engineered cofactor balanced pathways. The added D-xylose and L-arabinose pathways have increased the correlation among the reactions of the entire metabolic network. Furthermore, pairwise correlation coefficients were calculated for fluxes through all reactions of wild type, engineered cofactor imbalanced, and engineered cofactor balanced models. The wild type network correlation pattern was lost when D-xylose and L-arabinose pathways were added to the cell. Thus, by adding new pathways we have seen an increase in solution space as evident from flux variability analysis. Sampling of allowed flux space has shown an increase in correlations among the reactions. The reactions are interdependent with each other with increase of correlations as evident from the pairwise correlation map. Thus, increased correlation patterns in the engineered cofactor imbalanced model are responsible for the increase in rigidity of the reaction network compared to the wild type network. The addition of new pathways to the cell affected the solution space of the network and also the reaction correlation patterns. The range of possible metabolic network states of the model was much more similar to the wildtype when cofactor balancing was performed on the engineered pathways, suggesting that native regulation in the cell would be much more likely to respond well to the additional carbon flux from the pentoses. Taken together, cofactor balancing increased pentose sugar utilization efficiency while retaining the flexibility and flux correlation structure of the wild type strain. Moreover, model guided cofactor balancing has emerged to help the metabolic engineering of microorganisms to fuels production.S. cerevisiae to investigate the global effect of cofactor imbalance in engineered pentose sugar utilization pathways. The insights gained from the computational studies will enable the strain design for improved ethanol production in a rational and systematic way. This approach of cellular design promises solutions to some of today's most difficult problems in metabolic engineering of microbes and opens up an alternative perspective to analyze biological systems. Our future goals include the experimental implementation of the strain design proposed herein and the continued development of strategies for model guided biofuel production.We used a modified genome-scale metabolic model of All studies described below were done using the Constraint-Based Reconstruction and Analysis (COBRA) Matlab Toolbox S. cerevisiae iMM904 max and vmin are the vectors containing the maximum and minimum capabilities of the fluxes.We used the publicly available genome-scale metabolic network S. cerevisiae on glucose, D-xylose and L-arabinose using the COBRA toolbox Dynamic flux balance analysis was used to simulate the batch growth of S_ex and VP_ex are the exchange fluxes for the substrate and the product, respectively. During each small time step, Δt, we assume that uptake and secretion rates and μ are constant. The concentration of each external metabolite was computed at each time step, including for glucose, D-xylose, and L-arabinose. The glucose and D-xylose uptake rates were taken from batch experiments X(t), S(t), P(t) are the biomass, substrate and product concentrations, respectively, at a given time point. VS. cerevisiae. The range of fluxes is useful for understanding the redundancies in the system. First, the maximum value of the objective function was calculated and this value was used to calculate the feasible range of reaction fluxes by subsequent maximization and minimization of each reaction flux Flux variability analysis was used to calculate the minimum and maximum allowable flux values for each reaction of the genome-scale metabolic network of biomass is the value of the biomass objective function. If n is the number of fluxes then the 2n LP problems are to be solved for flux variability analysis. The above method was applied to determine the maximum and minimum flux values for all the reactions in the model while satisfying FBA mass balance conditions and all other constraints on the system ij) between any two fluxes (vi and vj) in the network was evaluated using random sampling of the steady-state flux space Flux distributions in the genome-scale model corresponding to maximal cell growth were computed using FBA. Uniform random sampling was done to characterize the space of all flux distributions max (max v1/v2) and Rmin (min v1/v2) respectively between two fluxes v1 and v2. We have applied the previously developed Flux coupling finder for finding coupled reactions sets in constraint-based genome-scale metabolic models 1 and v2.The flux ratios for every pair of fluxes are used to determine different types of coupling shared between the two fluxes vmin = 0 and Rmax > 0, then reactions are directionally coupled(a) If Rmax - Rmin) > 0, then reactions are partially coupled.(b) If (Rmax - Rmin)  =  0, then reactions are fully coupled.(c) If  0.01 <SpanECI -SpanECB < 0.5 and (c) 0.0 <SpanECI -SpanECB < 0.01. The span change or difference of flux span between engineered cofactor imbalanced (ECI) and engineered cofactor balanced (ECB) models is given by, SC = SpanECI -SpanECB.The minimum and maximum allowable flux values obtained for reactions with different values of span change (SC), (a) Span(DOCX)Click here for additional data file.Table S2max (max v1/v2) and Rmin (min v1/v2) various types of coupling were identified for wild type, engineered cofactor imbalanced (ECI) and engineered cofactor balanced (ECB) models.Based on the flux ratio limits R(DOCX)Click here for additional data file.


Zymomonas mobilis ZM4 is a Gram-negative bacterium that can efficiently produce ethanol from various carbon substrates, including glucose, fructose, and sucrose, via the Entner-Doudoroff pathway. However, systems metabolic engineering is required to further enhance its metabolic performance for industrial application. As an important step towards this goal, the genome-scale metabolic model of Z. mobilis is required to systematically analyze in silico the metabolic characteristics of this bacterium under a wide range of genotypic and environmental conditions.Z. mobilis ZM4, ZmoMBEL601, was reconstructed based on its annotated genes, literature, physiological and biochemical databases. The metabolic model comprises 579 metabolites and 601 metabolic reactions , built upon extensive search of existing knowledge. Physiological features of Z. mobilis were then examined using constraints-based flux analysis in detail as follows. First, the physiological changes of Z. mobilis as it shifts from anaerobic to aerobic environments (i.e. aerobic shift) were investigated. Then the intensities of flux-sum, which is the cluster of either all ingoing or outgoing fluxes through a metabolite, and the maximum in silico yields of ethanol for Z. mobilis and Escherichia coli were compared and analyzed. Furthermore, the substrate utilization range of Z. mobilis was expanded to include pentose sugar metabolism by introducing metabolic pathways to allow Z. mobilis to utilize pentose sugars. Finally, double gene knock-out simulations were performed to design a strategy for efficiently producing succinic acid as another example of application of the genome-scale metabolic model of Z. mobilis.The genome-scale metabolic model of Z. mobilis under various conditions as validated by experiments and literature information. This reconstructed metabolic model will allow better understanding of Z. mobilis metabolism and consequently designing metabolic engineering strategies for various biotechnological applications.The genome-scale metabolic model reconstructed in this study was able to successfully represent the metabolic characteristics of  The impact of biotechnology on industry and society is dramatically gaining momentum, particularly in the field of agriculture-food, medicine and chemical production. For the chemical industry, which aims to producing value-added chemicals and fuels in a sustainable way, efforts have been put into strain improvement of microorganisms, utilizing many newly emerging state-of-art techniques, for the overproduction of chemicals of interest -6. Yet, In silico genome-scale metabolic modeling and simulation have proven to be useful in the field of systems metabolic engineering. This approach has successfully contributed to the design of strategies for engineering microorganisms for the production of amino acids, including L-valine .,39.Z. moe Figure . DespiteZ. mobilis was found to have a unique feature compared to other organisms, which allows for tolerance to higher alcohol levels. Because short-chain alcohols  directly interacts with the lipid bilayer and increases its fluidity, the cell tries to maintain its membrane fluidity by changing the composition of the lipid layer; increasing the amount of long-chain fatty acids to create a rigid cell wall and synthesizing hopanoids, a pentacyclic lipid compounds, which can adjust the cell membrane permeability. This abundance of hopanoids and vaccenic acid (C18:1) in Z. mobilis was proposed to explain the evolutionary adaptation of Z. mobilis to survive in the presence of high ethanol level [Z. mobilis are composed of three groups of compounds: phospholipids, hopanoids, and nonpolar lipids [Z. mobilis were included in the same manner based on existing reports.The equation for biomass formation, which requires precursors from a set of biosynthetic reactions, was constructed to describe the cell growth  under aerobic condition. Because of this enzyme, the pool of NADH, which is used for ethanol production, is decreased, resulting in a decrease in capacity for producing ethanol under aerobic condition [eductase . Thus, tondition .Z. mobilis were modeled at several different values of the constraints  applied to the NADH oxidase activity during the simulation under aerobic condition  is that glucose is metabolized to glucose-6-phosphate via glucokinase, and fructose is metabolized to glucose-6-phosphate via fructokinase and phosphoglucose isomerase. The strongest intensity value for the flux-sum was obtained from growth on sucrose because of its disaccharide chemical structure of glucose and fructose, resulting in having the effects of two carbon sources at the same time.Metabolites, including some cofactors, amino acids, and others involved in central carbon metabolic pathways, were selected and categorized into a few groups to display the characteristic of each pathway. Flux-sum intensity of all the aforementioned metabolites, except for F6P in Z. mobilis and E. coli can be explained through the differences in the structure of their metabolic network. The metabolic network of Z. mobilis is small and even if some of the branch points are to be deleted, such as Pfk (phosphofructokinase) in glycolytic pathway, SucA (2-oxoglutarate dehydrogenase), and Mdh  in TCA cycle, there is little chance for the carbon flux to be distributed through other metabolic pathways . This outcome was similar to the reported experimental result of Seo et al. [Z. mobilis. Next, the pyruvate decarboxylase reaction was introduced into the E. coli metabolic model to verify its role for ethanol production in E. coli. With the addition of the pyruvate decarboxylase reaction, the maximum in silico yield in the E. coli metabolic model improved to 2 mol from 1.85 mol ethanol/mol glucose. To further investigate the exact impact of pyruvate decarboxylase, other reactions of the E. coli metabolism, which can be utilized in the production of ethanol, but not found in Z. mobilis, were removed to determine its role in the production of ethanol. If the removal of the reactions resulted in a decrease in ethanol production, then the pyruvate decarboxylase reaction was concluded to not be the sole factor for the improved yield in E. coli. The significant differences of reactions between Z. mobilis and E. coli are that E. coli has only the phosphofructokinase reaction in glycolytic pathway, the 2-oxoglutarate dehydrogenase reaction and the malate dehydrogenase reaction in TCA cycle. Therefore, these reactions, which do not exist in Z. mobilis, were removed from the E. coli metabolic model. Despite the removal of all these reactions, the maximal in silico ethanol yields remained at 2 mol ethanol/mol glucose through alternative available metabolic pathways. Furthermore, the elimination of other reactions, such as glutamate dehydrogenase, ethanolamine ammonia-lyase, and acetaldehyde dehydrogenase, did not affect the maximum in silico yield of ethanol in E. coli metabolic model. Through these simulation results, it can be concluded that pyruvate decarboxylase is the main factor that allows Z. mobilis to have a greater capacity for ethanol production than E. coli. The presence of the other reactions were not seen to have direct correlation with the ethanol production capacity in E. coli.Maximum  ethanol ,60. To eo et al.  that theZ. mobilis, were examined in their role in producing ethanol in E. coli using the wild type E. coli metabolic model, which lacks pyruvate decarboxylase. The reaction corresponding to the enzyme of transaldolase was removed, and resulted in the declined ethanol production yield, 1.78 mol ethanol/mol glucose. Because pentose phosphate pathway generates NADPH, the deletion of transaldolase reaction resulted in the decreased supply of reducing power. Therefore, it implies that the pentose phosphate pathway has an important role for producing ethanol in the E. coli wild type strain. It should be noted that EcoMBEL979 and iAF1260 produced the same results for this study.The reaction above not found in Z. mobilis cannot utilize pentose sugars due to incomplete metabolic pathways of pentose [Z. mobilis. However, Zhang et al. [Z. mobilis for utilizing xylose as a carbon source. De Graaf et al. [Z. mobilis CP4 produces ethanol with xylose as a carbon source by introducing the same enzymes. Deanda et al. [Z. mobilis to utilize arabinose as a carbon source. According to these results, new pathways  were introduced in the metabolic model ZmoMBEL601  in ZmoMBEL601 . Simulations of double gene knockout, however, resulted in the combination of pyruvate decarboxylase and D-lactate dehydrogenase as the best targets for succinic acid overproduction  for regulating the flux more realistically. The calculation of the maximum in silico yields of ethanol was done using the metabolic model of Z. mobilis (ZmoMBEL601) and E. coli (EcoMBEL979 and iAF1260). As the pyruvate dehydrogenase reaction in E. coli has low activity under anaerobic conditions [E. coli metabolic models. Uptake rate of glucose is fixed to 10 mmol/gDCW/h, and reaction for oxygen uptaking was deleted to describe anaerobic condition in both genome-scale metabolic models. The NGAME (i.e. non-growth associated maintenance energy) values for both genome-scale metabolic models were eliminated. Ethanol production rate are normalized to the glucose uptake rate.Constraints-based flux analysis is a method for studying metabolic networks with the assumption of a pseudo-steady state and constraints are imposed by mass balance of the metabolites ,71. Thisnditions , the pyri is formulated as Sij is the stoichiometric coefficient of a metabolite i in the jth reaction and vj is the flux of the jth reaction. The Sij • vj means the absolute values of consumption or generation rate of metabolite i in the jth reaction. The flux-sum of metabolite i is calculated by dividing the Sij • vj by one half. The flux-sum intensities of metabolites from central metabolism in Z. mobilis were analyzed to investigate the turnover rate of each metabolite using the ZmoMBEL601 model and compared to the flux-sum intensity of each metabolite in E. coli using the EcoMBEL974 model. The analysis of flux-sum intensity between both organisms was carried out with the three kinds of carbon sources including glucose, fructose, and sucrose.The flux-sum is defined as the half of the summation of all consumption and generation rate around a particular metabolite under pseudo steady-states ,51. To uZ. mobilis ZM4 strain stock (with 70% glycerol) at -70°C was inoculated into a sealed tube containing 10 mL of ZM medium. ZM medium contains per liter: 50 g glucose, 2 g KH2PO4, 1 g (NH4)2SO4, 1 g MgSO4·7H2O, 10 g yeast extract. After incubating at 30°C for 12 hrs, the culture was transferred to a 500 mL sealed flask containing 100 mL ZM medium for subculture. Fermentation was carried out at 30°C in a 6.6 L bioreactor  containing 2 L of ZM medium. The pH was controlled at 5.5 with 5 M NaOH. Anaerobic condition was achieved by 50 rpm agitation speed and flushing the bioreactor with oxygen-free CO2 gas . In case of aerobic culture, the dissolved oxygen concentration was maintained above 40% of air saturation by supplying air at 1 vvm (air volume/working volume/minute) and by automatically controlling the agitation speed up to 1,000 rpm.Frozen 2SO4.The cell growth was monitored by measuring the absorbance at 600 nm using an Ultrospec 3000 spectrophotometer . Metabolites were analyzed by high-performance liquid chromatography , equipped with an Aminex HPX-87H column , UV/VIS  and a refractive index  detectors. The column was eluted isocratically at 50°C at a flow rate of 0.5 mL/min with 0.01 N HZ. mobilis ZM4 and various Z. mobilis strains  but also from other species for this purpose, because it was not possible to describe all the formulation mechanism with only the data from Z. mobilis ZM4. The data was properly manipulated and the biomass composition and reaction of Z. mobilis ZM4 strain was determined  coverage of reconstructed metabolic modelsClick here for fileZymomonas mobilis ZM4Biomass composition of Click here for fileZymomonas mobilis for the utilization of xylose and arabinose and (B) single gene knockout mutants based on the engineered strain for glucose, xylose, and arabinose as a carbon sourceTrade-off curves of (A) engineered strain of .Click here for fileDouble gene knockout targets for succinic acid production identified by constraints-based flux analysisClick here for fileZymomonas mobilis ZM4Batch culture profile of Click here for file


Microorganisms rarely live isolated in their natural environments but rather function in consolidated and socializing communities. Despite the growing availability of high-throughput sequencing and metagenomic data, we still know very little about the metabolic contributions of individual microbial players within an ecological niche and the extent and directionality of interactions among them. This calls for development of efficient modeling frameworks to shed light on less understood aspects of metabolism in microbial communities. Here, we introduce OptCom, a comprehensive flux balance analysis framework for microbial communities, which relies on a multi-level and multi-objective optimization formulation to properly describe trade-offs between individual vs. community level fitness criteria. In contrast to earlier approaches that rely on a single objective function, here, we consider species-level fitness criteria for the inner problems while relying on community-level objective maximization for the outer problem. OptCom is general enough to capture any type of interactions  and is capable of accommodating any number of microbial species (or guilds) involved. We applied OptCom to quantify the syntrophic association in a well-characterized two-species microbial system, assess the level of sub-optimal growth in phototrophic microbial mats, and elucidate the extent and direction of inter-species metabolite and electron transfer in a model microbial community. We also used OptCom to examine addition of a new member to an existing community. Our study demonstrates the importance of trade-offs between species- and community-level fitness driving forces and lays the foundation for metabolic-driven analysis of various types of interactions in multi-species microbial systems using genome-scale metabolic models. Microorganisms rarely live isolated in their natural environments but rather function in consolidated and socializing communities. Despite the growing availability of experimental data, we still know very little about the metabolic contributions of individual species within an ecological niche and the extent and directionality of interactions among them. This calls for development of efficient modeling frameworks to shed light on less understood aspects of metabolism in microbial communities. Here, we introduce OptCom, a comprehensive mathematical framework for metabolic modeling and analysis of microbial communities, which relies on a multi-level/objective optimization formulation to properly describe trade-offs between individual vs. community level fitness criteria. OptCom is general enough to capture any type of interactions  and is capable of accommodating any number of microbial species involved. We first demonstrate the capability of OptCom to quantify known metabolic interactions in a well-characterized microbial community. We next apply it to more complex communities to assess the optimality levels of growth for each microorganism, elucidate the extent and direction of inter-species metabolite transfers and examine addition of a new member to an existing community. Our study lays the foundation for metabolic-driven analysis of various types of interactions in multi-species microbial systems. Solitary species are rarely found in natural environments as most microorganisms tend to function in concert in integrative and interactive units, . Natural microbial ecosystems drive global biogeochemical cycling of energy and carbon Clostridium butyricum and Methanosarcina mazeiet alet alet alE. coli mutants using a graph-theoretic approach and analyzed them by extending dynamic flux balance analysis model of Varma and Palsson E. coli mutants on various carbon sources in a batch culture E. coli mutants. Each pair was modeled using an extended form of the minimization of metabolic adjustment (MOMA) hypothesis Recent advances in the use of high-throughput sequencing and whole-community analysis techniques such as meta-genomics and meta-transcriptomics promise to revolutionize the availability of genomic information et alRhodoferax ferrireducens and Geobacter sulfurreducens in an anoxic subsurface environment. The same procedure was also employed in a study that characterized the metabolic interactions in a co-culture of Clostridium acetobutylicum and Clostridium cellulolyticumet alAll these studies aimed primarily at modeling communities where one or both species benefit from the association while none is negatively affected. The first study to characterize a negative interaction between two microorganisms using genome-scale metabolic models was published by Zhuang et alet alDespite these efforts, all existing methods for the flux balance analysis of microbial communities are based on optimization problems with a single objective function , which cannot always capture the multi-level nature of decision-making in microbial communities. For example, the flux balance analysis model described in in vivo observations in terms of the levels of optimality of growth for each participant of the community. We first analyze a simple and well-determined microbial community involving a syntrophic association between D. vulgaris and M. maripaludisHere, we introduce OptCom, a comprehensive flux balance analysis framework for microbial communities, which relies on a multi-level optimization description. In contrast to earlier approaches that rely on a single objective function, OptCom's multi-level/objective structure enables properly assessing trade-offs between individual vs. community level fitness criteria. This modeling framework is general enough to capture any type of interactions  for any number of species (or guilds) involved. In addition, OptCom is able to explain OptCom postulates a separate biomass maximization problem for each species as inner problems. The inner problems capture species-level fitness driving forces exemplified through the maximization of individual species' biomass production. If preferable, alternate objective function . The optimality level for each one of the microorganisms is quantified using a variation of OptCom which we refer to as descriptive. Descriptive OptCom incorporates all available experimental data for the entire community  as constraints in the outer problem and all data related to individual species as constraints in the respective inner problems while allowing the biomass flux of individual species to fall below (or rise above) the maxima , are negatively affected , or combination of both. Mutualism, synergism and commensalism are examples of positive interactions, whereas parasitism and competition are examples of negative interactions. A pictorial representation of how these interactions can be captured within OptCom by appropriately restricting inter-organism metabolic flows is provided in OptCom can capture various types of interactions among members of a microbial community. Symbiotic interactions between two (or more) populations can be such that one or more species benefit from the association  were taken from D. vulgaris and M. maripaludis was predicted to be 2.28 based on our simulations. This is consistent with in vivo observation that D. vulgaris dominates in the co-culture by a ratio of at least 2∶1 First, we examined whether our model is capable of predicting the relative abundance of species  in the community by maximizing the community biomass as the outer problem objective function. Each microorganism was allowed to maximize its own biomass yield in the inner problems. Consistent with Stoylar 2 evolution rate, however, is lower in all time intervals (except for 62–76 hr) than the measured values. Between 62 hr and 76 hr the experimental data show that the CO2 evolution rate is close to zero, which may indicate that all CO2 produced by D. vulgaris is consumed by M. maripaludisWe next explore how well OptCom performs in predicting various metabolic activities across different stages of syntrophic growth. To this end, we applied OptCom for each time interval and compared the model predictions for acetate, methane and carbon dioxide evolution rates as well as total biomass production rates with experimental measurements Hydrogen and formate are primary shuttle compounds for interspecies electron transfer. There are two enzymes in D. vulgaris that are involved in production of hydrogen and formate namely pyruvate oxidoreductase and pyruvate-fomrate lyase D. vulgaris is constrained to be at most 13.7 µmol/hr , OptCom predictions show that in a co-culture consisting of D. vulgaris and a mutant of M. maripaludis the growth rate of both D. vulgaris and M. maripaludis is reduced by 26%. The simulation results also show that no fomrate is produced by D. vulgaris in this case, which was expected, as it cannot be consumed by the M. maripaludis mutant. Despite no formate production by D. vulgaris, OptCom reveals that the flux through pyruvate formate lyase is higher compared to the community having the wild-type strains. Further investigation of the in silico flux distributions shows that the entire amount of formate produced by the pyruvate formate lyase reaction is directed towards CO2 production. This in turn results in an increased consumption of CO2 by the M. maripaludis mutant and consequently a lower accumulation of CO2 in the extracellular environment compared to the community with the wild-type strains. The predictions by OptCom for the community with mutant of M. maripaludis are in agreement with experimental results by Stolyar et alD. vulgaris and the M. maripaludis mutant MM709 lacking the two annotated formate dehydrogenase enzymes. It was observed that this co-culture is able to grow, confirming that hydrogen alone can support the syntrophic growth of both species. Nevertheless, the growth rate, biomass yield and lactate uptake rates were lower compared to the syntrophic growth between the wild-type strains D. vulgaris in Stolyar's experiment is replaced with a mutant lacking pyruvate-formate lyase, so as all electron equivalent is produced in the form of hydrogen, then the co-culture should be able to restore growth to that of wild-type species community as hydrogen alone can carry all required electron equivalents.When hydrogen production by Synechococcus spp (SYN), filamentous anoxygenic phototrophs (FAP) related to Chloroflexus and Roseiflexus spp and sulfate-reducing bacteria (SRB) as well as other prokaryotes supported by the products of the photosynthetic bacteria 2 and producing storage products such as polyglucose as well as O2 as a by-product of photosynthesis. High levels of O2 relative to CO2 stimulate the production of glycolate. Glycolate is then used as a carbon and energy source by other community members such as photoheterotrophic FAP. At night, the mat becomes anoxic and cyanobacteria start to ferment the stored polyglucose into small organic acids such as acetate, propionate and H2. FAP can incorporate fermentation products photoheterotrophically while SRB oxidizes the fermentation products under anaerobic condition and produces sulfide Here we examine the applicability of OptCom for modeling a more complex microbial community containing three interacting guilds, the phototrophic microbial mats of Octopus and Mushroom Springs of Yellowstone National Park  et alSynechococcus spp were chosen to represent the mat's primary carbon and nitrogen fixers. FAP from the family Chloroflexaceae, were selected to represent metabolically versatile photoheterotrophs that capture light energy as phosphodiester bonds but require external reducing equivalents and carbon sources other than CO2. A SRB guild representative whose metabolic behavior was based on several well-studied sulfate-reducing bacteria was also included in the community model description This microbial community has been previously modeled and analyzed by Taffs 2 competes with CO2 for the rubisco active site, leading to production of glycolate (O2+ribulose−5−P+ATP→glycolate+triose phophate+ADP) instead of additional reduced carbon (CO2+ribulose−5−P+ATP→2 triose phophate+ADP) 2/CO2) was measured for the Octopus and Mushroom Spring microbial mats and reported to vary approximately between 0.03 and 0.07 2/CO2 flux ratio = 0.07) to 20.26 (O2/CO2 flux ratio = 0.03), which are significantly higher than the experimentally determined values of 1.5 to 3.5. This suggests that the reason for the discrepancy in prediction may be that the SYN guild does not maximize its biomass. Therefore, we decided to test this hypothesis by using the descriptive mode of the OptCom procedure  is of significant ecological importance. The ratio of cyanobacterial (SYN) to FAP biovolumes in a Mushroom Spring mat was determined experimentally to be 1.6∶1 dure see  and estanges see . OptCom tios see . On the tios see .2/CO2 flux ratios  to supply other guilds and increase the overall community biomass imposes extra energy demands on the SYN guild. In contrast, for low O2/CO2 flux ratios the maximum community biomass when SYN grows sub-optimally is lower compared with when it grows optimally  and optimize a community-level fitness criterion . We investigated the effect of sub-optimal growth of the SYN guild on the total community biomass production across different values of SYN/FAP biomass and Otios see . As illuet al2/CO2 flux ratio and environmental conditions.Notably, two different cases were considered by Taffs et alClostridium cellulolyticum, Desulfovibrio vulgaris Hildenborough, and Geobacter sulfurreducens. Cellobiose was provided as the sole carbon and energy source for C. cellulolyticum whereas the growth of D. vulgaris and G. sulfurreducens were dependent on the fermentation by-products produced by C. cellulolyticum. D. vulgaris and G. sulfurreducens were supplemented with sulfate and fumarate, respectively, as electron-acceptors to avoid electron acceptor competition C. cellulolyticum was the dominant member in the co-culture and confirmed the presence of D. vulgaris and G. sulfurreducens. It was, however, not possible to quantify experimentally the flow of shared metabolites among the community members as their concentrations were below the detection limits. Therefore, the authors proposed an approximate model of the carbon and electron flow based on some measurements of the three species community at steady-state, pure culture chemostat experiments and data from the literature In a recent study, Miller C. cellulolyticum  and G. sulfurreducens were reconstructed by Salimi et alet alD. vulgaris containing 86 reactions was introduced by Stolyar et al D. vulgaris consists of 145 reactions and is capable of supporting growth on acetate as well as ethanol. This model is available in the supplementary material  in G. sulfurreducens may have a dual function, i.e., they can act both mutually (with exchange of another compound such as succinate) or independently , similarly to those in E. coli FBA simulations showed that the metabolic model for G. sulfurreducens 2 accumulation in the extracellular environment deviated significantly from the experimental observations by Miller et al 2 in the extracellular environment which agree well with 2.7 and 3.3 moles/gDW.hr of acetate and CO2, respectively, observed in the supernatant of the bioreactor (per mole of cellobiose) by Miller et al While the relative molar abundance of each species was measured experimentally by Miller et al C. cellulolyticum can be completely utilized by D. vulgaris to reduce sulfate to hydrogen sulfide. A rough estimate for the ratio of hydrogen to ethanol, which serve as electron donors for D. vulgaris, is given in by Miller et al2/Ethanol = 20) based on the pure culture data under similar conditions. The simulations with OptCom using genome-scale metabolic models of the community members, however, indicate a much higher contribution of ethanol in inter-species electron transfer (H2/Ethanol = 2.34). We performed a flux variability analysis to see if this ratio can change under the examined condition, while maintaining the maximum community biomass, but no changes in this ratio were possible. This suggests that under the observed experimental condition, a H2/Ethanol ratio of 2.34 is needed to support the maximum growth for each species as well as for the community as a whole. While acetate serves as the only carbon substrate for both G. sulfurreducens and D. vulgaris, it was not possible to determine experimentally if D. vulgaris directly uses the available acetate in the medium released by C. cellulolyticum or it derives acetate from ethanol. OptCom results support the latter scenario  which could be utilized by other trophic anaerobic bacteria M. barkeri is strongly dependent on the value of growth-associated maintenance (GAM), which was found to be a function of the proton translocation efficiency of the Ech hydrogenase reaction − that result in a growth yield consistent with in vivo observations was computed by Feist et alM. barkeri in the tetra-culture community across different GAM values associated with 0.2–2 protons translocated/2e−. This analysis showed that M. barkeri is capable of consuming the entire 2.48 moles of acetate produced by C. cellulolyticum and D. vulgari. Depending on the GAM value and the proton translocation efficiency, M. barkeri was predicted to constitute 2.5 to 10.4% of the total community biomass  with the other three members growing at rates similar to the ones obtained for the tri-culture. C. cellulolyticum still dominates the co-culture as before with biomass fractions ranging from 69.6 to 75.7% (depending on M. barkeri's biomass flux). The methane evolution rate by M. barkeri was predicted by OptCom to range from 2.36 to 2.45 moles/gDM.hr. It is important to note that previous studies have reported that the internal carbon and electron flow of M. barkeri could be altered by D. vulgaris in a co-culture grown on an organic substrate such as acetate, D. vulgaris strives to keep the partial pressure of hydrogen low enough to shift the catabolic redox system of methanogen so that more H2 is produced by M. barkeri (compared to pure cultures) and more acetate is oxidized to CO2 instead of methane D. vulgaris to take up all hydrogen produced by M. barkeri (in addition to that produced by C. cellulolyticum), no such shift in methanogenesis was observed for the tetra-culture according to the OptCom predictions. A possible reason might be that enough hydrogen (as well as ethanol) is already available to D. vulgaris from C. cellulolyticum, obviating the need to alter methanogenesis in order to gain the reducing equivalents. This hypothesis is supported by the experimental observation that if excess H2 is added to the co-culture of M. barkeri and D. vulgaris, it is completely consumed by D. vulgaris and the acetate catabolism by M. barkeri is no longer affected The biomass flux of 2 produced by C. cellulolyticum and G. sulfurreducens is available in the medium, OptCom predicts that it remains completely unused in the tetra-culture. This was expected as growth of M. barkeri on CO2 relies on presence of hydrogen, which we assumed that it was consumed completely by D. valgaris. In order to examine if M. barkeri is indeed capable of utilizing the available CO2 as a carbon source (in addition to acetate), we temporarily allowed M. barkeri to take up the hydrogen produced by C. cellulolyticum. For this case, OptCom revealed that if the entire hydrogen produced by C. cellulolyticum is available to M. barkeri, it can support growth on CO2 only for proton translocation efficiencies of less than one/2e−. Notably, for proton translocation efficiencies of more than one, even though no CO2 is assimilated by M. barkeri, OptCom shows that the availability of hydrogen will lead to an increase in the methane production by about 26–28%.Even though 3.22 moles/gDW.hr of COHere, we introduced OptCom, a comprehensive computational framework for the flux balance analysis of microbial communities using genome-scale metabolic models. We demonstrated that OptCom can be used for assessing the optimality level of growth for different members in a microbial community  and subsequently making predictions regarding metabolic trafficking  given the identified optimality levels. Unlike earlier FBA-based modeling approaches that rely on a single objective function to describe the entire community et alClostridium butyricum and Methanosarcina mazei to relieve the inhibition of fermentation products and increase production of 1,3-propanediol (PDO) by Clostridium butyricum. Mixed cultures have been also established for overproduction of polyhydroxyalkanoates (PHA) Clostridium thermocellum, which is used for ethanol production, has been found to be capable of utilizing hexoses, but not pentose sugars generated from breakdown of cellulose and hemicellulose C. thermocellum with other thermophilic anaerobic bacteria capable of utilizing hexoses as well as pentose to produce ethanol  has been previously examined in vivoet alet alAn important goal of studying natural and synthetic microbial communities is their targeted manipulation towards important biotechnological goals . This has motivated researchers to construct simple synthetic microbial ecosystems, which are amenable to genetic and engineering interventions, for biotechnology- and bioenergy-related applications. As an example, Bizukojc Table S1D. vulgaris and details of the model corrections.Updated model of (XLSX)Click here for additional data file.Text S1D. vulgaris.Optimization formulation and solution procedure for OptCom and details of the update procedure for the metabolic model of (PDF)Click here for additional data file.