Biologically meaningful metabolic pathways are important references in the design of industrial bacterium. At present, constraint-based method is the only way to model and simulate a genome-scale metabolic network under steady-state criteria. Due to the inadequate assumption of the relationship in gene-enzyme-reaction as one-to-one unique association, computational difficulty or ignoring the yield from substrate to product, previous pathway finding approaches can’t be effectively applied to find out the high yield pathways that are mass balanced in stoichiometry. In addition, the shortest pathways may not be the pathways with high yield. At the same time, a pathway, which exists in stoichiometry, may not be feasible in thermodynamics. By using mixed integer programming strategy, we put forward an algorithm to identify all the smallest balanced pathways which convert the source compound to the target compound in large-scale metabolic networks. The resulting pathways by our method can finely satisfy the stoichiometric constraints and non-decomposability condition. Especially, the functions of high yield and thermodynamics feasibility have been considered in our approach. This tool is tailored to direct the metabolic engineering practice to enlarge the metabolic potentials of industrial strains by integrating the extensive metabolic network information built from systems biology dataset. E. coli1, S. aureus2, H. pylori3, M. barkeri4, S. cerevisiae5, B. subtilis6, and so on. The pseudo-steady state condition (PSSC) refers to the main assumption that the concentration of internal compounds keeps invariable over time. Thus, internal compounds satisfy dxc/dt = 0 where xc is the concentration of compound C7.Metabolic network, the pseudo-steady state condition (PSSC): Genome-scale metabolic network (directed graph) is used to model the metabolism of biological systems, such as microorganisms. A few of models have been published including Source and target, external and internal compounds, exchange reactions: For a genome-scale metabolic network, exchange reactions are transport reactions through which cells exchange materials with the environment. External compounds are the compounds in the extracellular environment, but they enter the cell through exchange reactions and then play a rule. Source and target are respectively the start and the end of the pathways we hope to find.8. Within a graph representation of a metabolic network, there may be multiple pathways. From the source compound to the target compound, there is a directed path with no cycles and in a particular determined metabolic pathway, and we refer to this directed path as metabolic path9. Of course and especially, when the pathway is branched, it may not be unique for this path. The metabolic pathway contains all the compounds and reactions involved in the pathway, all the internal compounds must be mass balanced in PSSC. Non-decomposability condition means that a pathway can’t be separated into two or more independent pathways.Pathway and path: A metabolic pathway (a subset of the whole metabolic network) is a set of reactions by which a living organism transforms a source compound into a target compound10.Smallest pathway in large-scale metabolic networks: For a metabolic network, many pathways may have no biological meaning and if we can find experimentally determined pathways, this may provide in-depth knowledge for biomedical or biotechnological applications. So methodologies on metabolic pathway will devote to discover biologically meaningful metabolic pathways in metabolic networks. There may be many pathways between a source and a target in a large-scale network, and it would be computationally impracticable to completely enumerate all these pathways. Thus, pathway finding methods should focus on finding a set of pathways which were defined by the stoichiometric constraints and could be able to span the complete solution space of pathways. The smallest pathway is defined as the pathway with least reactions which convert the source compound to the target compound. Although pathway research should not come down only to the smallest pathway, the smallest pathway is an important aspect of biological meaning12 provided a method to discover a set of genetically independent pathways and their work represented the first stoichiometric methodology for the computation of metabolic pathways. But their algorithm required big computational effort, so could deal with only metabolic networks of relatively small size. In addition, their approach was based on the assumption that the relationship in gene-enzyme-reaction was a one-to-one unique association. 2) Improved genetically independent pathways (IGIP): Mavrovouniotis15 developed the algorithm of Seressiotis and Bailey, and used it to deal with pathways which comprised multiple targets and sources. His approach can be applied to a moderate size of the metabolic network. 3) Elementary flux modes: Elementary flux modes (EFMs), i.e. non-decomposable pathways at PSSC, were named by Schuster and co-workers16. With the increase in the size of the metabolic network, the number of EFMs entails combinatorial fashion17. In order to overcome this combinatorial explosion, different strategies have been adopted20. 4) Extreme pathways: Extreme pathways (EPs), a refined set of EFMs, were proposed by Schilling et al.21. Apart from the non-decomposability condition and the PSSC defined above, the systemic independence condition must be satisfied by the set of EPs, i.e. no EP can be written as a non-trivial nonnegative linear combination of other EPs8. As for EFMs, when applied to large-scale networks, computing all the EPs will suffer a combinatorial explosion. But enumerating special EFMs or EPs, such as from a substrate to a product in a given large-scale metabolic network, is computationally feasible. 5) k-shortest EFMs and flux paths: Figueiredo and Planes have presented a method to find the shortest elementary flux modes in genome-scale metabolic networks with integer programming10. By examining carefully the paper and doing computational practice, we found that this method did not consider ATP maintenance and the yield from substrate to product, and at the same time it did not provide the actual flux distribution in the identified pathways.Pathway finding and approaches: As we mentioned above, pathway finding approaches aim to find a set of pathways that should satisfy the stoichiometric constraints, so they can be called stoichiometric approaches. 1) Genetically independent pathways (GIP): Seressiotis and Bailey10. We will show the difference and give a comparison in the result section of this paper. At the same time, although a pathway exists in stoichiometry, it may not always be feasible in thermodynamics. If we regard a pathway as an overall reaction and if we hope it is able to proceed spontaneously, it should satisfy the requirement of free energy change. Moreover, if there are several pathways which satisfy the condition, which one is more probable to occur in the cell?High yield and thermodynamics feasibility for a pathway: In the area of industrial biotechnology, improving bacterium is an important task and a high yield from substrate to product is the first target. For the construction of microorganism, we should utilize the pathway with high yield. The shortest EFMs may not be pathways with high yield and they are not equivalent to each other. But the two sets of pathways usually were regarded as equivalent, as stated in the literatureMotivation and our contribution: At present, the modeling and simulation method for the genome-scale metabolic network is constraint-based method which satisfies steady-state criteria. For the reason of inadequacy assumption , computational difficulty , or ignoring the yield (k-shortest EFMs and flux paths), previous pathway finding approaches as we stated above can’t effectively design optimal pathways to direct the metabolic engineering practice. In this work, by using MIP (Mixed Integer Programming) strategy we put forward an algorithm to identify the smallest balanced pathways (SBPs) which convert the source compound to the target compound in large-scale metabolic networks. Under PSSC, the resulting SBPs of our method can well satisfy the stoichiometric constraints and non-decomposability condition; Multiple pathways which meet the above-mentioned criteria can be found and provided as candidate design; In addition, high yield is a new function; Especially, thermodynamics feasibility has been considered in our approach. The smallest pathways founded by our method can provide good references in the pathway design for the industrial microorganism. Our model can be easily solved by existing optimization software.S, to describe genome-scale metabolic network and the elements in S are the coefficients of reactions22. Under steady-state criteria, the time derivatives of metabolite concentrations are zero7, i.e. those internal metabolites should satisfy mass balance, so the equations of mass balance for all the metabolites can be represented as followsS is the stoichiometric matrix, and αi and βi define the bounds through each reaction vi, R is the set of reactions.Usually, we can use a stoichiometric matrix, E. coli_iJO13661, there are more than 300 exchange reactions and we can choose any two as source and target.As for metabolic networks in genome-scale, the fluxes within a cell usually can be computed with flux balance analysis (FBA) that can give optimal growth phenotypes, though not unique. In mathematics, FBA is an equivalent to a large-scale linear programming (LP). In our algorithm, we confine source and target compounds to be external compounds, i.e. there are exchange reactions related to them. For example, for the genome-scale metabolic network of y of the same number of continuous variable v to indicate the absence or presence of a reaction vi.In order to find the smallest balanced pathways in large-scale metabolic networks, MIP strategy is used as the mathematic model. We introduce binary variable yi = 0 then vi = 0 and If yi = 1 then αi ≤ vi ≤ βi, we can express this idea as a constraint:If The source and target nodes should be external nodes, and there are exchange reactions connected to them. In order to give a connected pathway, two bounds are added.vt is to let vi of other reactions in the pathway not be beyond their constraints, and here constant1 and constant2 are positive values. Equation . The SBPs is smaller than the null space of the stoichiometric matrix.i = 0; In other case, certain reactions must be reversible, we can preset vmin = −1000, vmax = 1000. These could be achieved by setting the boundaries of the reactions. Then the solution of smallest balanced pathways is within the scope of the given conditions.For this model, we can easily preset the metabolic network to meet the requirement of the specific situations. For example, certain reactions must not be appearing, or some genes are to be disrupted, we just preset v24 here. With a statistic of the fluxes which are not zero in absolute value  or which yi is 1 (the two ways are consistent), we can determine those reactions which should appear, and further, we can obtain the smallest balanced pathways.For MIP, some existing software can be used to find its solution and we use Gurobi25. The approach of Bender’s cut is that iteration is used from an existing solution, at the same time in each iteration to exclude an existing solution by adding the following binary cutSometimes, there exist different states of integer variables but the objective value is the same, i.e. a MIP may have multi integer solutions. Up to date, as we know, there does not exist optimization tool which can give directly multi integer solutions for a MIP. Here we utilize a method proposed by Balas and Jeroslow, named Combinatorial Bender’s cutAll the multi integer solutions will be got by this way.chem of this chemical as the objective and we will get the theoretical ratio Vmax. Then we can use 95% of the value of highest yield Vmax as a constraint in our MIP model. Finally, we will get all SBPs with a high yield which is larger than 95% of the value of highest yield.SBPs have the least number of reactions but may not have the high yield of a chemical which the microorganism produces. High yield means a high amount of desired product and little or no by-product which might make the downstream complicated, costly, and polluted. In another word, high yield means cost-saving. Sometimes, high yield is our interesting aspect, so it is best to find SBPs with high yield. In order to estimate the reachable high yield of the chemical, we can use FBA with the exchange reaction rate vE. coli27. The thermodynamic data of E. coli model was calculated by Group Contribution Method28. There is a range of free energy change for every reaction and it is calculated by min/max delta G. The range of delta G could be used to decide the reversibility of a reaction.Although a pathway exists in stoichiometry, it may not always be feasible in thermodynamics. If we regard a pathway as an overall reaction and if we hope it is able to proceed spontaneously, it should satisfy the requirement that each reaction in the pathway must be thermodynamically feasible individually, i.e. the flux and the free energy change of this reaction must have opposite signs or the reaction is reversible. The data of free energy change for a microbe is not rich in literature and the first one is E. coli. By using our algorithm, we computed out the smallest balanced pathways from glucose  to succinic acid  in the genome-scale metabolic network of E. coli (its SBML model is iJO13661). In the process of computation, we restrict the input rate of glucose (vs = −100 mmol/g(Dw)h) and the output rate of succinic acid (vt ≥ 0.01 mmol/g(Dw)h). The given conditions are that we restrict the input and output of the cell to be only five compounds, i.e. glucose, succinic acid, CO2, H2O, and H. The reason for restricting only these five compounds is that succinic acid can be synthesized by them. There are 12 alternative solutions for this model, seeing Supplementary Material In this example, we hope to know how succinic acid is synthesized by glucose with One of these pathways, the first solution, was illustrated in Fig. From this pathway, we can know clearly the pathway to synthesize succinic acid and the balanced proportions among fluxes through every reaction in this pathway. We know also how these enzymes (or reactions) cooperate with each other to synthesize succinic acid. This means these reactions are equally important to fulfill the overall function of succinic acid production. The pathways including the reactions, genes, and fluxes should be regarded as ideal references to guide strain engineering activity. This will greatly reduce the scope of targets to enhance genes in order to accelerate the speed of producing succinic acid.E. coli27, seeing Supplementary Material With the data of free energy change of each reaction for E. coli is selected for the study. Threonine is an important chemical in industry, which can be produced by E. coli with glucose. We have computed all the threonine SBPs with highest yield in E. coli with glucose as substrate, and get 16 SBPs. All the SBPs have 50 step-reactions and the yield is 1.248:1 in a molar ratio which is near the theoretical yield. All the SBPs are in Supplementary Material In the above succinic acid case, the yield 171.43:100 has almost been the theoretical value. In order to show the difference of those with high yield and SBPs without high yield, threonine production with E. coli_iJO1366, illustrated in Supplementary Material In order to make a quantitative comparison with conventional methods, the method of k-shortest EFMs was selected as it is the nearest approach to ours. We use this algorithm to compute out all the shortest EFMs from glucose to succinate in the genome-scale metabolic network of E. coli can produce many other chemicals such as lactic acid, formic acid, fumaric acid and so on. In the model iJO1366, there are 324 exchange reactions. Only 25 reactions have low bounds which less than 0, while all the up bounds equal to 1000. We use glucose (start or source) as the input, at the same time use all these 324 reactions except for glucose as the output (target) respectively, and calculate the SBPs with maximum productivity for every chemical. For a given chemical, if E. coli can’t produce it, i.e. the maximum productivity for it is zero, the algorithm will not return its SBPs.In addition to succinic acid and threonine that we mentioned above, E. coli can produce and found that in many cases, the number of SBPs is less than 10 and that those cases which are larger than 100 only take a very small proportion, as shown in Fig. We have made a statistics for all the SBPs to a variety of chemicals which Up to date, modeling a genome-scale metabolic network in dynamics is still beyond the access of most laboratories, so the best way to make use of flooding metabolic network information to direct the metabolic engineering practice is the constraint-based approach which satisfies the pseudo-steady state condition (PSSC). A pathway that converts a given source compound to a given target compound should satisfy the stoichiometric constraints and non-decomposability condition. EFMs and EPs are two pathway finding approaches, but calculating the set of EPs or enumerating all the EFMs will suffer a combinatorial explosion when applied to large networks. Existed approaches of k-shortest EFMs and flux paths are not the methods of considering the yield from substrate to product which is highly biotechnologically relevant.In this work, by utilizing Mixed Integer Programming (MIP), we present an approach for pathway finding. Our algorithm has a number of good features: 1) It is a method of thorough stoichiometry. It can identify the balanced pathways in the genome-scale metabolic network. The balance here means that the mass of internal compounds is balanced, i.e. stoichiometric balance. The smallest means that the pathway identified has least reactions. 2) The pathways found by this approach are usually short enough, which simplify the metabolic engineering practice and also save the cellular energy consumption for synthesizing proteins for the reactions. It is well-known that protein synthesis is the most energy-intensive process. 3) Our algorithm can return all the alternative solutions, and this can provides more choices in industrial stain design. 4) High yield can be added as required condition, which is important for biotechnology purpose. 5) Thermodynamics data are integrated to allow the thermodynamics feasibility analysis.We recognized that although the short pathway has the advantages as mentioned above, the shortest pathway may not necessarily be biologically feasible and some biological pathways are not the shortest one in nature. Our algorithm is to break the evolutionary barrier and eventually help to create artificial cell factory. Furthermore, by just simply modifying our code, we can easily found all balanced pathway with the length of shortest plus 1, 2, …, and so on.The model of our approach comes down to a MIP and MIP is an essentially combinational problem. Computational complexity will be proportional to the scale of the problem. But for a large scale problem, existing solving software can solve it in not long time. Such as our case study with several thousand of variables, the computation time will take just several minutes by an HPC (high-performance computer) with 48 cores.In industrial stain design, high yield from the source substrate to the target product is the first important aspect. To implement this, biologically feasible and high yield pathways should be utilized. The smallest balanced pathway with high yield can provide an ideal reference to guide metabolic engineering practice. In particular, the balanced pathways tells many co-dancing reactions which are beyond the sight of normal biological knowledge. The metabolic bottleneck may not necessarily locate on the traditional biochemical pathway. The accessory reaction which is responsible to recycle the cofactors, intermediate or to supply the precursors is shown to be as important as the reactions in the known biochemical pathway. Meanwhile, the relative strength of the fluxes of different reactions also tells the metabolic engineer how to fine-tune the relative activities of different reactions. Integrating with the experimental determination of intracellular transcriptome, proteome and even metabolome, metabolic engineering should be able to identify the potential rate-limiting reactions which they need to put effort on.E. coli, the input rate of glucose is 100 mmol/g(Dw)h and the output rate of succinic acid is 171 mmol/g(Dw)h, so this pathway almost reaches the theoretical ratio of glucose/succinic acid in E. coli. If we fulfill the pathway in E. coli, it can make a good utilization of glucose in producing succinic acid. SBPs with high yield from glucose to a variety of chemicals, which E. coli can produce, have been calculated by our algorithm. Especially, we can make decisions on the thermodynamics feasibility by integrating the data of free energy change.In our first case study, producing succinic acid with Supplementary material aSupplementary material b/c/d


Recent developments in metabolic engineering have led to the successful biosynthesis of valuable products, such as the precursor of the antimalarial compound, artemisinin, and opioid precursor, thebaine. Synthesizing these traditionally plant-derived compounds in genetically modified yeast cells introduces the possibility of significantly reducing the total time and resources required for their production, and in turn, allows these valuable compounds to become cheaper and more readily available. Most biosynthesis pathways used in metabolic engineering applications have been discovered manually, requiring a tedious search of existing literature and metabolic databases. However, the recent rapid development of available metabolic information has enabled the development of automated approaches for identifying novel pathways. Computer-assisted pathfinding has the potential to save biochemists time in the initial discovery steps of metabolic engineering. In this paper, we review the parameters and heuristics used to guide the search in recent pathfinding algorithms. These parameters and heuristics capture information on the metabolic network structure, compound structures, reaction features, and organism-specificity of pathways. No one metabolic pathfinding algorithm or search parameter stands out as the best to use broadly for solving the pathfinding problem, as each method and parameter has its own strengths and shortcomings. As assisted pathfinding approaches continue to become more sophisticated, the development of better methods for visualizing pathway results and integrating these results into existing metabolic engineering practices is also important for encouraging wider use of these pathfinding methods. E. coli and S. cerevisiae, to separate the supply of these therapeutics from the plants they were sourced from. At the root of these successes is the identification of the requisite pathways and the systematic transfer of these pathways to a microbial host.Metabolic engineering is the scientific process of manipulating the metabolism of a microorganism to produce valuable compounds. Engineering microbial production involves the disruption of endogenous genes or adding genes from heterologous organisms to form pathways that tap into the natural metabolic network. There have been numerous successes of metabolic engineering, including the well publicized biosynthesis of artemisinic acid, a precursor to the antimalarial drug artemisinin , and theMetabolic pathfinding has clear applications to the first step in the design-build-test-learn cycle for developing biosynthetic pathways . We defiTraditionally, researchers have manually searched existing literature and databases to design pathways. However, the rapidly growing body of metabolic information makes it difficult to effectively survey and utilize all available resources. Computational approaches have been developed to enable researchers to take advantage of these growing resources. For example, pathways for production of 1,4-butanediol, a non-natural compound, were discovered with the assistance of a pathway-identification algorithm . ThousanAssisted metabolic pathfinding aims to solve two main challenges—the challenge of efficiently speeding up the pathway search process and the challenge of selectively finding biologically feasible, novel pathways. This paper focuses primarily on the approaches of pathfinding algorithms that address these two challenges. However, improvements in the search algorithms alone are not sufficient to solve these challenges, as the quality of the pathway results is also heavily dependent on the metabolic resources utilized by the search algorithm. Advancements in metabolic pathfinding rely on advancements in techniques for expanding the metabolic search space. For example, retrosynthesis-based approaches , 10 can E. coli. However, this approach is not yet able to computationally scale to very large metabolic networks [The metabolic pathfinding problem itself can be further divided into two different approaches: graph-based pathfinding and constraint-based pathfinding. This review will focus on graph-based pathfinding, which highlights the connections between compounds and reactions in the metabolic network. Graph-based approaches represent a metabolic pathway as a path that consists of an ordered series of intermediate compounds and reactions that transform some defined starting compound(s) to some defined target compound(s). Graph-based pathfinding utilizes a very well-studied data structure to represent the metabolic network, abstracting away more complicated interactions between compounds and enzymes in the cell. This abstraction enables graph-based methods to readily scale with larger metabolic networks spanning multiple organisms. However, since much of the underlying metabolic network is abstracted by the graph representation, there is a greater chance for graph-based approaches to return pathways without biological significance unless relevant parameters and heuristics are introduced to guide the search. Constraint-based methods  highlignetworks . Though networks , 21, we A metabolic network can be described as connections between compounds and the enzymes catalyzing reactions between compounds, which lends itself well to graph representation. There are many different ways a metabolic network can be represented as a graph Fig. b. One ofThis review covers the techniques supporting graph-based metabolic pathfinding algorithms and the heuristics that guide pathway discovery from networks, enzymatic reactions, and chemical structures to a specific host organism context Fig. b. We wilProperties of the metabolic network representation can be used to guide and constrain the search problem and rank the resulting pathways. The properties that have been used in the literature are the connectivity of the network and the length of pathways found. The individual compounds and reactions of a pathway can also be assigned weights based on biochemical and network-based properties.The graph-based representation of the network makes it intuitive to gravitate towards graph-based features and constraints, particularly graph connectivity Fig. a. Many aIn Faust et al. , differeIn MetaRoute , the weiThe connectivity of a graph is very simple to compute, and it is no surprise that it has been used by several metabolic pathfinding approaches. Despite its simplicity, connectivity can be used to effectively infer some biochemical information about the metabolic network. However, excluding features of the metabolic network based on connectivity alone may not reflect known biochemical properties. For example, excluding highly connected compounds to avoid currency compounds may also exclude compounds that play a significant role in pathways . Unlike other algorithms, M-path by Araki et al.  uses hubk-shortest paths [k-shortest paths) and used to organize pathway results. In order to distinguish pathfinding methods that actively include path length as a constraint or heuristic from methods that only use path length to rank pathway results, the latter cases were not marked as using path length in Table Pathfinding algorithms often optimize for pathways with the smallest number of enzymatic steps, as these pathways tend to require less manipulation in a metabolic engineering context Fig. b. Many pst paths , 42). RaMost network representations include both structures of compounds and reactions, along with parameters that give additional information on both these parts. The chemical structure of compounds in the metabolic network can be useful in inferring the existence of a biochemical reaction between compounds, as biochemical reactions tend to have products that structurally resemble one or more reactants. Structural information can be represented at different levels of detail, which introduces a trade-off between the accuracy of the similarity measure and the computational complexity of the overall metabolic pathfinding problem.k-shortest paths. The MetaRoute algorithm [At the finest level of detail, algorithms can track changes on atomic level Fig. c. Retainlgorithm  also uselgorithm  uses a hlgorithm , the patlgorithm , pathwaylgorithm , any realgorithm  to insurlgorithm  maximizelgorithm . Insteadlgorithm . Even soIf two compounds have similar chemical structures, there is a decent chance that these compounds can be connected by a common reaction. Several approaches have used different representations of chemical structure as a way of guiding, constraining, and ranking the search.Several approaches use chemical fingerprints and Tanimoto coefficients  to measuOther approaches rely on the graph representation of chemical compounds. Metabolic Tinker  uses a hUnlike chemical fingerprints, where a pre-determined set of chemical characteristics are used to compare two compounds, the graph comparison approach directly compares the chemical structure of two compounds against each other. The graph comparison approach tends to be more accurate in calculating structural similarity but is more computationally expensive . In GEM-Calculating compound similarity is not as computationally expensive as atom mapping and serves as a check that the reactions included in pathways are biochemically feasible. However, compound similarity falls short in the cases where two compounds share many common structural components but are not biochemically related.In addition to information about the compounds involved in the network, graph-based searches also include information on reactions. This information can be used to both constrain and expand the search to find novel pathways.Building off the idea of structural similarity, some algorithms introduced reaction rules, or more general transitions between compounds based on changes in chemical structure. Two enzymatic reactions may involve different reactants and products; however, if the same structural change occurs between reactants and products in these reactions , these reactions may both fall under the same reaction rule. Reaction rules allow new, potentially feasible pathways to be found by introducing reactions that may not yet have been added to metabolic databases. These rules can both be used to (1) create a metabolic network without directly requiring information on enzymatic reactions from metabolic databases and (2) help expand an existing metabolic network created based on a metabolic database.Reaction rules are based heavily on structural representations of compounds. In BNICE , 14, coml et al. , the molAnother common feature taken into account by pathfinding algorithms is thermodynamic feasibility of the reactions in pathways. Almost all algorithms that include thermodynamics use the component contribution method  for calcicTinker , missingIn BNICE , the \doo et al. , enzymesmentclasspt{minimathFinder  uses \doE. coli, compared to a graph-based search without stoichiometric constraints. Introducing stoichiometric constraints allows carbon flux paths to distinguish between oxic and anoxic conditions in E. coli, which was not possible in previous graph-based algorithms. However, this pathfinding method was only tested within the metabolic network of a single well-studied organism (E. coli) and, like constraint-based methods, is not easily scalable to large multi-organism networks.Graph-based pathfinding methods can incorporate reaction stoichiometry to limit the number of biologically irrelevant pathway results. The carbon flux paths algorithm proposed by Pey et al. , 43 intrEnzymes can have different reaction rates, depending on how efficient an enzyme is in converting the substrate to product. On the other hand, promiscuous enzymes can catalyze reactions which may not be found in existing databases and may be used to expand the metabolic pathfinding search. In Cho et al. , bindingMany algorithms give the user the ability to select an organism of interest. Arita et al.  mention Pathfinding is a critical and preliminary step in the development of novel biosynthetic pathways. Pathfinding is often done manually, though there are many existing tools that can enumerate putative pathways with minimal input from the user. After a pathway has been identified, much time and effort goes into building, testing, troubleshooting, and optimizing the biological system, and not the initial pathway discovery . This isThere has been a recent push to expand searches to non-native compounds using reaction rules, building on BNICE , 14, becAlthough the cumulative information that is available across all metabolic databases is extensive, manually searching, gathering, and compiling information from different databases is a challenging task. Each database often has its own representation and set of ID numbers for identifying components like compounds and reactions, in addition to its own organization schema, suited specifically for the intended purposes of the database. These differences make it challenging to determine the exact links and relationships between information in different databases. There have been a few recent efforts to integrate different metabolic databases and create a less redundant, more comprehensive, and more accessible resource for metabolic information (e.g., BKM-react , MetRXN As the pathfinding capabilities improve, so do the number of solutions that can potentially be generated, and with it the challenge of providing the user with tools to explore the solutions that can number in the thousands and identify pathways of interest. Because of this, there is an increasing amount of user interaction built into pathfinding webservers (see MRSD , BioSyntIn addition to visualizations, a well-developed interface could integrate suggestions for genes based on enzyme activity and evidence of heterologous gene expression so that the user can seamlessly transition from pathway discovery to the initial build phase. Databases, such as BRENDA , have exAlmost all pathfinding algorithms are limited to producing linear pathways with a few exceptions , 69. BraUltimately, the best pathfinding algorithm is the one that suits the user’s needs and is paired with an interface that facilitates pathway discovery. Pathfinding webservers can assist with the design of novel, feasible, and hopefully improved pathways, but as discussed, pathfinding needs to become more highly integrated with the entire process of metabolic engineering. This survey of the available features and future directions aims to increase adoption of existing pathfinding tools while advocating for advancements that will increase their utility.


Pseudomonas putida KT2440 and identified the discrepancies leading to inconsistent pathway calculation results. The mistakes in the models were corrected based on information from literature so that all the calculated synthesis and uptake pathways were the same. Subsequently we built a pathway-consensus model and then further updated it with the latest genome annotation information to obtain modelPpuQY1140 for P. putida KT2440, which includes 1140 genes, 1171 reactions and 1104 metabolites. We found that even small errors in a GSMN could have great impacts on the calculated optimal pathways and thus may lead to incorrect pathway design strategies. Careful investigation of the calculated pathways during the metabolic network reconstruction process is essential for building proper GSMNs for pathway design.Over 100 genome-scale metabolic networks (GSMNs) have been published in recent years and widely used for phenotype prediction and pathway design. However, GSMNs for a specific organism reconstructed by different research groups usually produce inconsistent simulation results, which makes it difficult to use the GSMNs for precise optimal pathway design. Therefore, it is necessary to compare and identify the discrepancies among networks and build a consensus metabolic network for an organism. Here we proposed a process for systematic comparison of metabolic networks at pathway level. We compared four published GSMNs of  GSMNsput flux . It is dSalmonella Typhimurium LT2 [To address this problem, efforts have been made to create a consensus metabolic network by merging GSMNs for the same organism. The first consensus metabolic network, Yeast 1, was created from available yeast networks iMM904 and iLl672 by using a jamboree approach [rium LT2  and Humarium LT2  which harium LT2 . A drawbrium LT2 .Pseudomonas putida KT2440 based on four previously published metabolic network models, iJN746 [One of the important applications of GSMNs is to design optimal pathways for the production of biochemicals. Using methods like flux-balance analysis (FBA) ,15, rese, iJN746 , iJP815 , iJN746 , PpuMBEL, iJN746  and iJP9, iJN746 . ActuallP. putida models were quite different. iJP815 and iJP962 were reconstructed by the same research group and had smaller differences in the growth yield (92.4 gDCW·molGlc-1vs 101.1 gDCW·molGlc-1) [P. putida KT2440 and further improved with updated genome annotation information to obtain model PpuQY1140 for P. putida KT2440. Compared with previous models, the simulation results from the new model are in better agreement with published experimental data.The original analysis results from the four olGlc-1) . By compolGlc-1) ,21. As tPseudomonas putida KT2440 models through a process summarized in P. putida KT2440.The pathway-consensus metabolic network reconstruction was bulit by taking the systematic comparison of published P. putida KT2440, iJN746, iJP815, PpuMBEL1071 and iJP962, have been reconstructed by three research groups. The optimal growth rate can be calculated by performing FBA with the biomass production reaction as objective function. The optimal ATP production rate can be calculated by using the ATP maintenance reaction as objective function [Four metabolic networks of function . The sim-1 compared to 0.46 h-1). More surprisingly, the obtained ATP production rate from PpuMBEL1071 was 999999 mmol·gDCW-1·h-1 which was actually the upper boundary of the reactions in that model. The ATP production rate remained constant at the value of the upper boundary even when we set glucose uptake rate to zero. This indicated that ATP was generated infinitely in PpuMBEL1071 without substrate consumption, which was obviously unreasonable for a biological network model. ATP plays an important role in cell metabolism as energy carrier. The generation and consumption of most metabolites are linked with energy metabolism, and thus mistakes in ATP production may also lead to incorrect calculation results for pathways to other metabolites. Therefore, we first analyzed the optimal ATP production pathways from the four models to identify the mistakes and correct them.It can be seen that there was nearly a two-fold difference between the highest and lowest growth rates H generation loops as shown in In view of the incorrect reaction loops caused by incorrect reaction equations, we further investigated if this kind of loops can be detected by using the method proposed by Gevorgyan et al  for checP. putida KT2440 [2 could be oxidized through the respiratory chain  for the production of 1 gram dry cell weight. j.After revising the models to obtain consistent ATP production rates, we further calculated the optimal growth rates of the four models  and then to PAPS (adenosine-5-phosphosulfate) [In above-mentioned example, the energy consumption for sulfate transport and metabolism was different in the four models . Two sulsulfate) . PAPS is+. The numbers of reactions corrected for all the three types of errors in the four models were shown in -1. The calculated sum of squared errors indicated that the results from iJP815 and iJP962 were close to those from the consensus network while iJN746 and PpuMBEL1071 had more errors in the model.As described in the ATP production pathway analysis section, incorrect reaction equation led to unlimited ATP production. Here by investigating the precursor synthesis pathways, we found more mistakes in reaction equations in all four models. For example in PpuMBEL1071 the reaction equation of R0749 was Folate + NADPH → Tetrahydrofolate + NADPP. putida KT2440 is well known for its ability to grow on many amino acids and organics acids as carbon source [P. putida [In all the above analysis glucose was used as the sole carbon source. Whereas n source ,32. Corr. putida ,31,33–36. putida . By comp2-dehydro-3-deoxy-phosphogluconate aldolase.However, there are still quantitative differences on the optimal growth rates calculated from different models. Actually we found that for 36 substrates the growth rate calculated with PpuMBEL1071 was higher than those obtained with other models. By investigating the pathways we revealed that the main reason was the incorrect reversibilty information of the reaction ED_edd  catalyzeThe two reactions were mistakenly set to be reversible and thus enabled the formation of D-Ribulose 5-phosphate by the opposite direction of Entner-Doudoroff (ED) pathway (G3P + Pyr → 6-Phospho-D-gluconate → D-ribulose 5-phosphate) which consumed less energy for some substrates rather than pentose phosphate (PP) pathway. We corrected this error and recalculated the growth rates in PpuMBEL1071 for further comparison. The process was repeated untill the growth rates from all 48 substrates were the same in all four models. The number of added and modified reactions during this process were also shown in Four updated models of iJN746, iJP815, PpuMBEL1071 and iJP962 with more reactions and genes were obtained –S6 FilesP. putida KT2440 in 2002 [P. putida KT2440 from NCBI and submitted it to the RAST annotation server [3-1→H+ + Pi + ADP + Oxaloacetate) was linked with an nonexist gene PP_5437 in the updated iJP962 model. From the annotation information we found the right gene should be PP_5347 annotated as pyruvate carboxyl transferase subunit A (EC 6.4.1.1). Altogether we added 155 genes and 74 reactions. The final pathway-consensus metabolic model PpuQY1140 contains 1140 genes, 1171 reactions and 1104 metabolites . The results shown in gnuK deletion strain which grew even faster than the wild type strain. This phenomenon might be caused by complex regulatory mechanisms and thus can not be explained by metabolic network analysis alone. Generally the simulation results from the consensus model are also better than those from other models, especially iJN746 and PpuMBEL1071. This is in agreement with the biomass precusor synthesis pathway simulation results as shown in P. putida KT2440 and its deficient mutants growing on glucose minimal medium, the growth rates of wild type P. putida KT2440 and two deficient mutants (gcd and glk) growing on toluene M9 minimal medium were also tested by del Castillo T et al [To test the accuracy of the updated model PpuQY1140, we compared the simulated growth rates from different models with the experimentally measured values reported by del Castillo T et al . They meP. putida KT2440, all synthesis pathways for biomass building blocks and substrate uptake pathways were made consensus. Comparative analysis of the models revealed that small errors in reaction equations and reaction reversibility could greatly affect the pathway calculation results, sometimes even led to infeasible pathways such as the unlimited NADH generation loops. Therefore the pathway examination step should be included in the metabolic network reconstruction process to make sure that the quality of network is high enough for reliable pathway design.We proposed a novel pathway-consensus process for identifying and solving the discrepancies between metabolic network reconstructions for the same organism by pathway level comparison. By applying this approach to four GSMNs of This pathway-consensus approach should be regarded as complementary to the network reconciliation approach proposed by Oberhardt et al . The netP. putida GSMNs in SBML format were obtained from supplementary materials of the publications [-1·h-1. The uptake rates of nitrogen source, oxygen, phosphate and sulfur were not constrained. Exchange reactions were added to PpuMBEL1071 because there were no reactions for the utilization of different substrates and nutritions in this model. The growth-associated and non-growth-associated energy maintenance (GAM) and (NGAM) [Four ications –19. The d (NGAM)  parameteFlux-balance analysis (FBA)  is a widThe P/O ration represents the number of ATP molecules (P) formed from per oxygen atom (O) . Here thThe four reactions were combined to get the overall reaction  by elimiS1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.S6 Table(XLSX)Click here for additional data file.S7 Table(XLSX)Click here for additional data file.S1 File(DOCX)Click here for additional data file.S2 File(DOCX)Click here for additional data file.S3 File(XML)Click here for additional data file.S4 File(XML)Click here for additional data file.S5 File(XML)Click here for additional data file.S6 File(XML)Click here for additional data file.S7 File(XLSX)Click here for additional data file.S8 File(XML)Click here for additional data file.


Oryza sativa japonica, no GSM with gene-protein-reaction association exist for Oryza sativa indica. Here, we report a GSM, OSI1136 of O.s. indica, which includes 3602 genes and 1136 metabolic reactions and transporters distributed across the cytosol, mitochondrion, peroxisome, and chloroplast compartments. Flux balance analysis of the model showed that for varying RuBisCO activity (Vc/Vo) (i) the activity of the chloroplastic malate valve increases to transport reducing equivalents out of the chloroplast under increased photorespiratory conditions and (ii) glyceraldehyde-3-phosphate dehydrogenase and phosphoglycerate kinase can act as source of cytosolic ATP under decreased photorespiration. Under increasing light conditions we observed metabolic flexibility, involving photorespiration, chloroplastic triose phosphate and the dicarboxylate transporters of the chloroplast and mitochondrion for redox and ATP exchanges across the intracellular compartments. Simulations under different enzymatic cost conditions revealed (i) participation of peroxisomal glutathione-ascorbate cycle in photorespiratory H2O2 metabolism (ii) different modes of the chloroplastic triose phosphate transporters and malate valve, and (iii) two possible modes of chloroplastic Glu–Gln transporter which were related with the activity of chloroplastic and cytosolic isoforms of glutamine synthetase. Altogether, our results provide new insights into plant metabolism.To combat decrease in rice productivity under different stresses, an understanding of rice metabolism is needed. Though there are different genome scale metabolic models (GSMs) of  Oryza sativa) is one of the major food crops cultivated worldwide and it provides nearly 20% of the caloric intake for humans. Several environmental conditions like drought, flood, nutrient availability etc. govern the rice yield. In order to understand the effect of these factors on rice production it is important to study rice cellular physiology which includes metabolism under various conditions. One of the approaches toward understanding rice metabolism is reconstruction and analysis of its genome scale metabolic model (GSM). GSMs represent a list of all reactions encoded in the genome of the target species and associated metabolites. GSMs of several plants have been reconstructed including Arabidopsis thaliana (japonica) was reported in 2013 which was used to study rice metabolism under varying light intensity   to stress conditions (Vc/Vo < 3). Also, plant leaves are constantly exposed to different intensities of sunlight. Such variations in light intensity may cause readjustments in plant metabolism. Previous studies have simulated the dependence of photosynthetic metabolism of prokaryotes, algae and plants on light energy  . We perft energy . These st energy . Furthermilation . The difmilation . Additiomilation .O.s. indica (OSI1136) which represents a photosynthetic leaf tissue, with 1136 reactions, 1330 metabolites and gene protein reaction (GPR) association for 3602 unique genes. The reconstructed model was simulated and analyzed under three conditions – (i) varying flux ratio of carboxylation to oxygenation of RuBisCO (Vc/Vo) from 1:1 to 5:1 (ii) varying light intensity (light scan) and (iii) different enzymatic costs by assigning random weights to the reactions in the model. Vc/Vo < 3 corresponds to increased rate of photorespiration which is representative of drought stress in plants  based ScrumPy metabolic modeling package . The biomass transporters were set to carry fixed flux  were left unconstrained, unless specified. A cell maintenance cost was assumed to 0.1 flux unit through a generic ATPase reaction , FVA was performed. FVA calculates the maximum and minimum allowable flux values of each of the reactions of the solution space, while satisfying the optimality of a given objective function. The optimal objective value of the primary objective function  was computed for synthesis of all the biomass components in experimentally defined proportions. For each reaction in the solution space, the reaction flux was maximized and minimized to get the allowable range of flux values.To find the allowable range of flux of each of the reactions under drought like and normal air conditions (v = vv) was varied, starting at the point at which solution was obtained till changes in reaction-fluxes remained linear. Thus, the photon flux was varied from 0.33 to 10.00 flux unit. The lower limit indicated the photon flux below which there existed no feasible solution for biomass synthesis under defined constraints. The upper limit indicated the photon flux beyond which the flux plot of the reactions remained uniform. An additional constraint was that the flux of cyclic photophosphorylation could not exceed that of non-cyclic.In addition to the above-mentioned constraints, the photon flux (Vc/Vo) of RuBisCO from 1:1 to 5:1. The RuBisCO catalyzed carboxylation and oxygenation reactions were combined into a single reaction according to the Vc/Vo investigated  was reported in 2013 (indica we started with its protein and we used the updated rice japonica model (CK1721) as a reference for gap filling. Recently, a rice japonica model (iOS2164) was reported . These unique reactions are mainly involved in secondary metabolism such as jasmonic acid synthesis pathway , phytoalexin synthesis pathway  fatty acid beta oxidation  etc. . Compared to iOS2164 the indica model has lesser number of reactions firstly, because the former has considered reactions associated with the thylakoid, vacuole and ER compartments. Secondly, instead of including all the steps of cyclic and non-cyclic photophosphorylation (as considered in iOS2164), in OSI1136, we represented them as single reactions which were obtained from elementary modes analysis . At the same time fluxes of cyclic and non-cyclic photophosphorylation showed that the total ATP and NADPH generated was maximum at Vc/Vo = 1 and minimum at Vc/Vo = 5 . Despite the changes in total ATP and NADPH, the ATP:NADPH ratio was found to be same from Vc/Vo = 2 to Vc/Vo = 5 . While the non-cyclic photophosphorylation was always active the cyclic photophosphorylation carried flux only at Vc/Vo = 1. The higher amount of ATP generated in the chloroplast at Vc/Vo = 1 was found to be partly used in photorespiratory ammonia fixation in the chloroplast  and the rest of it got utilized in the recycling of glycolate  which is formed from phosphoglycolate (Pgly) produced in the RuBisCO oxygenase catalyzed reaction. Accordingly, the flux of these reactions was maximum at Vc/Vo = 1 . Most of the other ATP consuming reactions in the chloroplast did not show variation in the flux except chl_Ru5Pk (EC 2.7.1.19) and chl_PGK (EC 2.7.2.3). The former is the source of ribulose bisphosphate (RuBP) in the chloroplast which participates in RuBisCO carboxylase/oxygenase reaction to generate 3-phosphoglycerate (3-PGA or PGA). PGA in turn gets phosphorylated to 1,3-bisphosphogycerate (BPGA) by phosphoglycerate kinase (PGK). Both RuBP generation (by chl_Ru5Pk) and phosphorylation of PGA to BPGA (by chl_PGK) were found to be maximum to sustain the C3 cycle and to synthesize the same amount of biomass under limited carbon conditions at Vc/Vo = 1 . The other major source of ATP (besides cyclic and non-cyclic photophosphorylation) is the mitochondrial ATP synthase (Complex_V) which also carried maximum flux at Vc/Vo = 1 . Thus, the ATP generated in the mitochondrion by Complex V and ATP released by the mitochondrial ATP transporter to cytosol was highest at Vc/Vo = 1. This was because, while chloroplastic ATP met increased PR demands, ATP demand for rest of cellular metabolism was met by mitochondrial ATP. In addition, we also calculated the quantum demand  from Vc/Vo = 1 to Vc/Vo = 5. As expected, the fall in the QD from Vc/Vo = 1 to Vc/Vo = 5 was similar to that observed for photon flux . The higher photon flux ultimately reflects the requirement to synthesize the same amount of biomass under limited carbon conditions where the efficiency of photosynthetic triose phosphate production reduces and where carbon recycling by photorespiration becomes primary.We calculated the photon flux needed to produce ATP and NADPH which ultimately are required for biomass synthesis in fixed proportion and cellular maintenance. There was a decrease in photon flux from Vc/Vo < 3) when the chloroplastic NADPH generation is high (as described in the previous section) the activities of Mal-OAA transporter and NADP–MDH were also high; and with decrease in photorespiration  the flux through the Mal–OAA and NADP–MDH decreased . The observation suggested that the malate valve is activated to transport excess reducing equivalents out of chloroplasts under drought stress and at higher rates of photorespiration. This observation was supported by a previous experiment on tobacco plants which reported reduced expression of NADP–MDH at decreased rate of photorespiration (Plant membranes are broadly impermeable to NAD(P) and NAD(P)H, so they possess specific transporters for the exchange of Mal and OAA which enable the indirect transport of reducing equivalents between different cellular compartments. NADPH dependent malate dehydrogenase (NADP–MDH) in the chloroplast converts OAA to Mal, facilitating the regeneration of the electron acceptor NADP in the chloroplasts. The enzyme (MDH) is known to play an important role in maintaining redox balance in plants under changing environmental conditions . The ‘mapiration .Vc/Vo.The glycolytic pathway in plant’s cytosol consists of alternative ways to metabolize GAP to PGA. One way occurs via the GAPDH (EC 1.2.1.12) and phosphoglycerate kinase  generating NADH and ATP; the second is a single step catalyzed by non-phosphorylating glyceraldehyde-3-phosphate dehydrogenase  and generating NADPH . The stuVc/Vo . However, GAPDH and PGK were inactive at Vc/Vo = 1 , active at Vc/Vo = 3  and the flux through these reactions increased from Vc/Vo = 2 to Vc/Vo = 5 . The export of GAP from the chloroplast increased at Vc/Vo = 3 which was used in GAPN and GAPDH. At the same time the flux through the mitochondrial Complex V decreased. Consequently, the ATP generation in the mitochondrion and its release decreased . Under this condition the need of ATP and NADH in the cytosol were fulfilled by the combined activity of GAPDH and PGK. On the other hand, the ATP generated in the mitochondrion by Complex V was maximum at Vc/Vo = 1 . Thus, the mitochondrion serves to play an important role in supplying the cytosolic ATP under drought stress as discussed earlier. Cytosolic GAPDH and malate valve are important for maintaining cellular redox homeostasis in plants  and normal air condition (Vc/Vo = 3). The minimum and maximum flux obtained from FVA  for chloroplastic Mal-OAA shuttle and malate dehydrogenase showed decrease in their activities at Vc/Vo = 3 compared to Vc/Vo = 1 which supported our results of FBA . Also, the flux range for GAPDH and PGK catalyzed reactions showed that at Vc/Vo = 1 both the reactions carried zero flux and were operative at Vc/Vo = 3. This also supported our FBA predictions as described in Figure 3. While some reactions like chl_61118RXN, chl_DXSRXN, HISTALDEHYD-RXN showed FBAval = FVAmin = FVAmax , other reactions like mit_AconDHatase, mit_AconHydr etc. always showed FBAval = FVAmin < FVAmax . Non-cyclic modes of TCA cycle can be operative if the demand for ATP is low or if alternative sources of ATP are available . Glycine oxidation and MalDH are sources of mitochondrion NADH. The flux through part of TCA cycle which operated to support biomass synthesis remained constant. As such any fluctuation in mitochondrion ATP production was associated with changes in MalDH and GDC activity. Although MalDH activity was minimum at Vc/Vo = 1, the flux of mitochondrion complex V was maximum . Thus, under such conditions photorespiratory glycine oxidation was important for ATP supply.The TCA cycle and the Calvin cycle form a part of the central metabolic pathways in plants. The flux analysis showed increase in the flux through the Calvin cycle under stress condition. For example, variations in the fluxes through some of the reactions associated with Calvin cycle are shown in oportion . Only a vailable . Flux anncreases . Here, tVc/Vo = 1 corresponds to increased photorespiration, accordingly our results showed increase in the ammonia generated in the mitochondrion via glycine decarboxylase (GDC) . The analysis of flux values through ammonia transporters showed that an equivalent amount of mitochondrial ammonia released into the cytosol got imported into the chloroplast where it was completely utilized in the GS/GOGAT pathway . It is well established that the photorespiratory ammonia generated in the mitochondrion is transported to plastids, which is then re-assimilated into glutamate by GS and GOGAT .nd GOGAT . AccordiVc/Vo = 1 both chloroplastic ATP and NADPH were maximum , the cellular ATP demand was fulfilled mainly through mitochondrial glycine oxidation. Concomitantly, ammonia generated by glycine oxidation was refixed by GS2. Refixation of ammonia, the glycerate kinase reaction (photorespiratory metabolism) and necessary recycling of RuBP utilized the excess chloroplastic ATP . The excess reductant was transported out to the cytosol by the malate valve; a part of this excess reductant was used in HPR1 to sustain PR and the rest was utilized to support other cellular processes. Thus, at Vc/Vo = 1 we observed coordinated metabolism wherein PR served as a sink for excess chloroplastic ATP and redox. At Vc/Vo = 3, ATP generation in the mitochondrion and its release to the cytosol decreased . Simultaneously, the export of GAP from the chloroplast increased which was used in GAPN and GAPDH. Under this condition the need of ATP and NADH in the cytosol were fulfilled by the combined activity of GAPDH and PGK. Such plasticity in plant metabolic network across different cell organelles is useful in maintaining cellular ATP and NAD(P)H homeostasis, further discussed below.The chloroplast is the site of cyclic and non-cyclic photophosphorylation for ATP and NADPH generation. However, depending on environmental conditions metabolic adjustments particularly in mitochondrial metabolism becomes important in maintaining cellular ATP and redox homeostasis . AlthougPhotosynthetic metabolism is light dependent. Studies have reported that varying light conditions affect gene expression and therefore enzyme activity . In-siliFigure 6A. This observation supports the view that photorespiratory metabolism may serve to dissipate excess light energy and mitigate photoinhibition . With further increase in light, the chloroplastic triose phosphate exchange reactions became active to fulfill the increasing reductant demand of HPR1 . GAP, formed through PGK and GAPDH catalyzed reactions of the Calvin cycle was exported to the cytosol. In the cytosol, GAP to PGA conversion took place and the PGA thus produced was recycled back to the chloroplast. Chloroplastic reductants and ATP were made available to the cytosol through this recycling between PGA and GAP. This reductant was exported to the peroxisome and made available for HPR1 through Mal-OAA shuttle and malate dehydrogenase catalyzed reactions of the cytosol and peroxisome compartments. Thus, photorespiratory metabolism facilitates export of ATP and reducing equivalents from the chloroplast. Increased light stress leads to generation of reactive oxygen species in photosynthetic systems and photorespiration alleviates this stress especially in the chloroplast . This is because the AOX component of the ETC decouples ATP generation from redox dissipation . Simultaneously, the fluxes of chloroplastic MalDH  and malate valve increased to supply reductant to the cytosol which was finally used in the HPR1 catalyzed reaction . The chloroplastic triose phosphate and Mal-OAA transporters are important shuttle systems for transporting reducing equivalents out of the chloroplast. In a study on NADP-MDH Arabidopsis mutants, the NADP-GAPDH was the only alternative that operated to supply reductants to the cytosol . Although at low and medium light we found that glycine oxidation was coupled to oxidative phosphorylation . On the other hand, reaction fluxes correlated with light intensity over the range 0.0–1.0 . Figure 7C shows the comparison of reactions that were found to be strongly correlated either with RuBisCO carboxylase/oxygenase or light intensity or both. Forty-seven reactions were found to be strongly correlated with both RuBisCO carboxylase/oxygenase activity and light intensity. This included the reactions of photorespiration in the chloroplast, mitochondrion and peroxisome and the reactions associated with Calvin cycle. A study showed that genes associated with Calvin cycle and photorespiration are co-expressed  were also found to be highly correlated with RuBisCO carboxylase/oxygenase activity and light intensity. Some of the reactions that showed high correlation only with RuBisCO carboxylase/oxygenase were found to be moderately correlated with light intensity . This was because the fluxes of these reactions namely mitochondrial complex V (mit_Complex_V), chloroplastic transporters for Mal-OAA , GAP (chl_GAP_tx), and PGA (chl_PGA_tx) showed significant variations with increase in light intensity Figure 6. Cytosolic glutaminase reaction (GLUTAMIN-RXN) and chloroplastic Glu-Gln transport (chl_Gln_Glt_tx) were found to be highly correlated with light intensity but not with Vc/Vo . With increase in light intensity, flux through cyclic photophosphorylation (chl_LightCyc), and thus ATP generated in the chloroplast increased. Cytosolic glutaminase reaction (GLUTAMIN-RXN) and glutamate-glutamine transporter (chl_Gln_Glt_tx) operated along with chloroplastic glutamine synthetase (GS2) and the ammonia transporter across the chloroplast to utilize the ATP.Reaction correlation with xpressed . Also, aVc/Vo) was fixed at 3:1 and Case 2 – RuBisCO carboxylase/oxygenase activity was not fixed in any ratio. Plants have acquired several adaptive mechanisms including flexibility in metabolic pathways to combat different environmental stress conditions  . Variation in the activity of the enzymes of malate valve is known to occur in plants under different conditions like high light, high CO2, cold stress etc . This activity of the malate valve which acts as an indirect export system for reducing equivalents serves to balance the ATP/NADPH ratio in the chloroplast (When or NADP) . Most ofor NADP) . The resress etc . Our resoroplast . Fifty-soroplast . The resVc/Vo fixed at 3:1) we found that different modes of chloroplastic Glu–Gln transporter operated. It operated maximum number of times  to import Glu into the chloroplast and export Gln out of the chloroplast . At other times  it operated in reverse direction, i.e., Glu was exported out of the chloroplast and Gln entered into the chloroplast  except once where it was found to be inactive. In, Mode A, most of the times low photon flux was required (≈ 0.33–0.33 flux units) and in Mode B the photon flux was in the range of 0.47–0.48 flux units . Concomitantly, the ATP:NADPH ratio was less for Mode A than for Mode B . These observations were related to changes in the cytosolic (GS1) and chloroplastic (GS2) glutamine synthetase activities. The relative amounts of these isoenzymes GS1 and GS2 . GS2 is the predominant isoform of GS in C3 species The increased activity of the malate valve under drought stress indicates its possible role in transporting reducing equivalents out of the chloroplast.(2)Vc/Vo increases .GAPDH and PGK can also act as source of cytosolic ATP when (3)For the light conditions investigated, we have presented a coherent mechanism of photorespiratory metabolism in conjunction with other reactions namely mitochondrion ETC, glycolysis, and intracellular transporters which function to maintain cellular ATP and NAD(P)H homeostasis.(4)Under different enzymatic cost conditions there exists variation in participation of peroxisomal glutathione-ascorbate cycle and different modes of the chloroplastic TPTs and the malate valve may become operative. Also, chloroplastic Glu–Gln transporter may show different modes of activity related with the functioning of GS1 and GS2, which may serve as alternative routes for stress adaptation in plants.AC and BH reconstructed the model. AC, BH, and RS carried out simulation and analysis. AC and BH wrote the manuscript. SK supervised the work.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The model was then used to probe the cells metabolic state and dynamics, performing a dynamic metabolic flux analysis (dMFA) study. Indeed, MDSCs maturation correlates with a high glycolytic flux contributing to up to 95% of the global ATP turnover rate, while most of the glucose-derived carbon enters the TCA cycle. Model simulations also reveal that pentose phosphate pathway and oxidative phosphorylation activities were kept at minimal levels to ensure NADPH production and anabolic precursors synthesis. Surprisingly, MDSCs immunosuppressive activity, i.e. L-arginine uptake, metabolism and endogenous synthesis, only consumes sparse quantities of energy-rich nucleotides (ATP and NADPH). Therefore, model simulations suggest that MDSCs exhibit a heterogeous metabolic profile similar to tumour cells. This behavior is probably an indirect immunosuppressive mechanism where MDSCs reduce the availability of carbon sources in the tumour periphery microenvironment, which could explain the dysfuntion and death of immune effector cells.Recent years have witnessed an increasing interest at understanding the role of myeloid-derived suppressor cells (MDSCs) in cancer-induced immunosuppression, with efforts to inhibit their maturation and/or their activity. We have thus modelled MDSCs central carbon metabolism and bioenergetics dynamic, calibrating the model using experimental data on  One of the mechanisms of immunotherapy specifically targets the inhibition of myeloid-derived suppressor cells (MDSCs) maturation and activity. Briefly, MDSCs are a heterogenous cell population of macrophages, dendritic cells, granulocytes, to name only the most abundant cell types2. These cells metabolize the semi-essential amino acid L-arginine through the enzymatic activities of arginase 1 and inducible nitric oxide synthase 3. Both the sparse availability of L-arginine and the accumulation of nitric oxide derivatives  trigger the suppression of specific anti-tumour immune response4. Despite the considerable progress achieved in the comprehension of MDSCs biology that has resulted in multiple therapeutic approaches proposed to overcome MDSCs-mediated tumor escape, the metabolic events supporting MDSCs immunosuppressive potential are still ambiguous and poorly investigated.The invasiveness of conventional anti-cancer therapies appeals to the establishment of novel therapeutic strategies. Specifically, the immunotherapy approach is gaining in interest as it showed promising results in the treatment of cancer of various types5. Likewise, LPS-activated M1 macrophages display enhanced glycolytic metabolism and reduced mitochondrial activity6. Therefore, we concentrated our efforts to study the central carbon metabolism and bioenergetics of MDSCs, investigating their specific requirements to acquire an immunosuppressive phenotype8. The analysis of intracelullar metabolites concentration suggested that MDSCs exhibit a glycolytic metabolism and a high TCA cycle activity providing the immunosuppressive mechanisms with energy-rich nucleotides and carbon intermediates.Previous work on the activation of dendritic cells with lipopolysaccharides  showed that cells undergo a PI3K/Akt-dependent metabolic transition from oxidative phosphorylation to aerobic glycolysis11. However, such approach, as well as other metabolic modelling approaches, have not been applied yet to study the immunosuppression phenomenon, to the best of our knowledge. We thus propose here to apply a modelling approach11 previously validated on Chinese Hamster Ovary (CHO) cells11, on the maturation process of bone marrow cells into MDSCs, and thus perform dMFA to unreaveal metabolic traits of MDSCs’ maturation process.Dynamic metabolic flux analysis (dMFA) have shown being useful, as a quite unique tool, to describe extracellular and intracellular nutrients and metabolites concentration as well as fluxes transient behavior in mammalian cells8. We are thus first presenting a descriptive model as well as evaluating its simulation capacity. Sensitive kinetic parameters and their confidence intervals were determined to identify the key kinetic parameters and biochemical reactions to be considered as potential targets for modulating MDSCs maturation and immunosuppressive activity. Then, a dMFA study was performed through model simulations for evaluating MDSCs metabolic performance.The dynamic metabolic model combines the central carbon metabolism (CCM) and cell energetics, redox states and metabolic regulation mechanisms, and includes MDSCs immunosuppressive machinery (ARG1 and iNOS enzymes) and L-arginine endogenous synthesis reactions. The model was calibrated on experimental data of extra- and intracellular metabolites generated in a previous work13.Model simulations confirmed the hypothesis that MDSCs maturation correlates with a high glycolytic flux sustaining ATP turnover and also supporting a high TCA cycle activity, with low but not suppressed pentose phosphate pathway and oxidative phosphorylation activities generating NADPH and anabolic precursors. Interestingly, MDSCs immunosuppressive machinery reveals not being energetically costly, while the overall nutritional profile and metabolic flux studies showed that MDSCs mimic tumour cells’ metabolic plasticity8 where experimental settings are well detailed.Experimental data used herein to verify the accuracy of the metabolic model were taken from our previous work2.Briefly, BM cells were extracted from 6- to 8- weeks old C57BL/6 mice . Animal experimentations were performed in accordance with the Canadian Council on Animal Care guidelines and the protocol was approved by the Université de Montréal’s ethical committee. Mice were kept under specific pathogen–free conditions prior to euthanasia by CO2 and 37 °C incubator. The maturation of BM-derived MDSCs was performed by culturing BM cells for 96 hours in the supplemented medium mentioned above in the presence of 40 ng/mL of GM-CSF (granulocyte macrophage - colony stimulating factor) and 40 ng/mL IL-6 (Interleukin-6) as shown by Marigo et al.14.BM cells were cultured in RPMI1640 medium  supplemented with 10% (v/v) irradiated fetal bovine serum , 1 mM Sodium Pyruvate (Sigma), 50 µM β-Mercaptoethanol (Sigma), 100 U/mL Penicillin, 150 U/mL Streptomycin (Cedarlane) in a 5% COIt should be noted that the term “BM-derived MDSCs” is used when referring to experimental and simulation results on BM cells derived into MDSCs. When referring to literature, the more general term MDSCs is used because it is the terminology normally accepted for these cells.et al.15.Every 24 hours, extracellular nutrients and metabolites in medium were measured using a dual-channel immobilized oxidase enzyme biochemistry analyzer  and metabolites were extracted using cold methanol and sonication on ice method modified from Kimball 4OAc at pH 7.0. Organic acids concentrations were assessed using the above-mentioned UPLC-MS/MS system with a Hypercarb column . Mobiles phases were 20 mM amoonium acetate at pH 7.5 and 10% (v/v) methanol in water.Nucleotides concentrations were measured using a 1290 UPLC system coupled to a 6460 triple quadruple mass spectrometer. A Symmetry C18 column  was employed for the separation. Mobile phases consisted of 10 mM ammonium acetate with 15 mM DMHA  at pH 7.0 and 50%/50% (v/v) acetonitrile, 20 mM NH17 and CHO cells18 where it showed satisfactory results simulating experimental data. The global procedure for model development is described as Supplementary material. Briefly, we have here developed a model integrating metabolic pathways known to be expressed in MDSCs, by applying a modelling approach thus previously validated with eukaryotic cells. Basically, the network of biochemical reactions was first built including central carbon metabolism as well as biochemical reactions known to be of major importance in MDSCs. Metabolic flux kinetics and regulation mechanisms were then described, based on literature on MDSCs when available, or on previous works on animal cells. The model was then describing known metabolic network in MDSCs as well as it was anchored specifically onto MDSCs by performing model structure calibration and parameters value identification thanks to experimental in vitro metabolomic data with these cells.The construction steps while building the structure of the metabolic model presented in this study is based on previous models describing the central carbon metabolism of plant3. Furthermore, the catabolic pathways related to the amino acids metabolism  were also considered since these are known to contribute as carbon source. Therefore, the model describes major inputs, such as major nutrients, and outputs, such as cell growth and the management of cell metabolites from the immunosuppressive phenomenon. This biosystem network is thus highly simplified but it considers the major set of interlinked biochemical reactions allowing to describe MDSCs behaviour.The model metabolic network Fig.  see nom represenFlux kinetics consider the effect of substrates as well as co-factors (i.e. energetic and redox nucleotides).19. Therefore, intra- and extracellular metabolites that are consumed or secreted were taken as being at the same concentration across the cell membrane; a reliable assumption we have demonstrated in past works dealing with similar models18.Except for the amino acids alanine, asparagine, aspartate, glutamine and glutamate, all other extracellular metabolite concentrations are considered higher that the affinity constants of associated cell membrane transportersThe reactions of the adenylate kinase and ATPase enzymes are used to balance the time evolution of AMP, ADP and ATP energetic shuttles, with the synthesis of AMP being described.+, NADH and NADP+, NADPH. NAD+ synthesis is thus described, from which NADP is synthesized.The model assumes non-constant energetic metabolites concentration: NAD+/NADPH and NAD+/NADH, respectively.Enzymatic activity of the NADPH oxidase and the mitochondrial proton leak phenomenon are employed to balance the time evolution of NADP9.The stoichiometry of the reaction describing cell division and growth was based on average cell composition for CHO cells, since this information for MDSCs was not availableMoreover, the modelling strategy is based on the following considerations/assumptions:20. The fluxes are modeled by multiplicative Michaelis-Menten type equations and a factor of non-competitive inhibition is added when metabolites show inhibitory effects. Nutrients and metabolites as well as cell initial concentration (i.e. at t = 0) are presented in Table The final  dynamic model includes 44 reactions Table  and mass11 (and from references therein), a first sensitivity analysis was performed on the resulting model, aiming to identify the most critical (i.e. sensitive) parameters. In brief , because of the large number of parameter values to be determined, an iterative procedure including manual trials on sub-groups of parameters and a model simulation global error minimization step, allowed identifying optimal model parameter values. Sensitivity analysis of model parameters on the model acuity to simulate experimental reality was performed as follow. Values of model parameters were changed by ±5 or 10%, once at a time, from their optimal value, and the normalized sum-squared differences were calculated as described below. A model sensitivity analysis on initial conditions has also been performed to evaluate the effect of measurement errors. Using the parameter values determined in a previous work on CHO cellsFinally, the 95% confidence intervals on the estimated model parameters were computed, using the Matlab functions “nlinfit.m”, “nlparci.m” and “nlpredci.m”. Following the parameter estimation step (“nlinfit.m”), the confidence intervals were computed for the estimated model parameters (“nlparci.m”). The 30 most sensitive parameters Table  have beeThe resulting metabolic model has then been used to simulate metabolites concentration with time, supported Fig.  or not  with exp11. Taking all of the above, the model structure was not reduced.The sensitivity analysis Fig.  procedur18. In complement, we also observed that the model is less sensitive to errors on initial conditions . These TDFs indirectly induce a similar metabolic behavior to tumor cells and this is further confirmed in this work from the dynamic metabolic flux analysis (dMFA) performed using our model.Dynamic metabolic flux analysis confirms MDSCs mimick tumour cells metabolic profile. Indeed, model simulation of experimental data confirm that BM-derived MDSCs exhibit a high glycolytic activity level as revealed by the continuous increase of the flux through pyruvate kinase Fig. . Moreove23. The high glycolysis-TCA cycle activity is probably associated to the acquisition of the immunosuppressive phenotype, and the maintenance of inflammatory environment at the tumour edge, by supporting enzyme and surface markers expression, cytokine/chemokine synthesis, etc. In addition, some of the TCA cycle intermediates have roles other than being a carbon source. For instance, the accumulation of fumarate and succinate stabilizes hypoxia induction factor 1α24 that was shown to be expressed in MDSCs to adapt to low oxygen tension in tumour25. Since BM-derived MDSCs exhibit a low growth rate during the 96 hours of the study, a longer culture period or the analysis of flux distribution in in vivo generated MDSCs is required to confirm if this behavior, i.e. high TCA cycle activity, is associated to proliferative purposes as previously reported in cancer cells22. Moreover, the analysis of the G6P branch point shows that only 20% of the glucose-derived carbon enters the pentose phosphate pathway, since the ratio of the flux through G6PDH to the one through HK was kept constant at 20%  only contributes sparsely to the replenishment of TCA cycle intermediates Fig. . However+ and superoxide (O2−), the latter being a precursor for the generation of immunosuppressive species ROS and RNOS28. A similar decreasing trend from 6 to 1% was simulated for the percentage of ATP consumed by the L-arginine metabolism  do not use considerable quantities of ATP and NADPH. In fact, the percentage of NADPH used by the L-arginine metabolism is decreasing from 5 to 1% Fig. . This deism Fig. . These fism Fig.  on the 1in silico platform thus allows prospecting MDSCs dynamic behaviour under stimulation or inhibition conditions, as well as it represents a complementary tool to existing tools for studying the immunosuppression phenomenon29. Cell metabolomic studies provide new and complementary insights enabling to better understand the immunosuppression phenomenon, and such dynamic model may be useful to the identification of novel biomarkers as well as to define therapeutic strategies to modulate this phenomenon. The validation of the predictive capacity of the model will, however, be possible with the accumulation of large experimental data sets, as well as further implementing the metabolic network. This first modelling work on MDSCs thus brings a basic framework for the study of the immunosuppression phenomenon, with the most sensitive parameters as keys of further model development.This work on model simulation of MDSCs maturation, used a wide set of experimental data for extra- and intracellular metabolites concentration to develop a descriptive and predictive dynamic metabolic model. The model then enabled performing a dMFA study, which results allowed highlighting the carbon distribution dynamics during MDSCs maturation and also in fully mature and active cells. Mainly, MDSCs revealed to be dependent on the glycolysis and the glucose-derived carbon to ensure high central carbon metabolism activity and sustained production of ATP. Pentose phosphate pathway and oxidative phosphorylation showed being active at the minimal level allowing to replenish the NADPH pool and anabolic precursors. This metabolic behaviour was not justified by specific requirements of MDSCs immunosuppression machinery neither at the carbon intermediate or energy level. However, this metabolic profile indirectly favors tumour invasiveness and shall be considered as a target for anti-cancer immunotherapy. In this work, the interpretation of carbon flux distribution simulated by the model leads to the identification of the specific metabolic signatures of mature MDSCs that are directly associated to the immunosuppression phenotype. This Supplementary information


Microbial communities are ubiquitously found in Nature and have direct implications for the environment, human health and biotechnology. The species composition and overall function of microbial communities are largely shaped by metabolic interactions such as competition for resources and cross-feeding. Although considerable scientific progress has been made towards mapping and modelling species-level metabolism, elucidating the metabolic exchanges between microorganisms and steering the community dynamics remain an enormous scientific challenge. In view of the complexity, computational models of microbial communities are essential to obtain systems-level understanding of ecosystem functioning. This review discusses the applications and limitations of constraint-based stoichiometric modelling tools, and in particular flux balance analysis (FBA). We explain this approach from first principles and identify the challenges one faces when extending it to communities, and discuss the approaches used in the field in view of these challenges. We distinguish between steady-state and dynamic FBA approaches extended to communities. We conclude that much progress has been made, but many of the challenges are still open. Thus, we do not discuss interactions between microorganisms that have no direct metabolic component, such as physical interactions or signalling processes . The approaches we describe are all constraint-based, stoichiometric, modelling methods for metabolic networks. The associated models are essentially mappings of genes to metabolic enzymes, the reactions of which form a  metabolic network where the edges and nodes represent  reactions and metabolites, respectively.Constraint-based modelling has been developed for sequenced microbes in monoculture, and many methods have been developed to reconstruct, query and predict the metabolic capacities of a species based on its genome sequence –24. The As we explain later in more detail, the results of FBA-type approaches mainly depend on (i) the quality of the reconstructed metabolic model, including the biomass composition of the associated microorganism and the assumed gene–protein reaction rules, (ii) the chosen objective function, (iii) the considered constraints for exchange and intracellular rates, and (iv) the considered nutrients that can be used for biomass and product formation. If FBA is extended to analyse metabolism on a community level, then additional layers of complexity are added to all four of these points.With respect to reconstructions, despite the progress that has been made in automating the reconstruction of metabolic models on the genome scale –34, modeOnce a genome-scale model has been reconstructed, it is essential for community modelling that it can be combined with other models in a meaningful way. The construction of community models is complicated by the fact that, in most cases, such models will have been created by different authors and research groups. Consider, for example, that all models should be encoded to be readable by the same simulation software; model components  must be unambiguously annotated such that they can be used to link models together and community models themselves should be reproducible and exchangeable. Fortunately, with regards to model interoperability, the constraint-based modelling community has recently adopted a standard model encoding format that allows for efficient model exchange . HoweverAnother difficulty is to define a community objective function in both biological and mathematical terms; typically, a combination of the objective functions of individual species is optimized but the exact formulation can differ ,17,36–3913C-labelling experiments Desulfoviates. In , pairwisates. In . Consideates. In ,38,100. ates. In .Under the constraint that two organisms have to be able to produce biomass at a rate greater than a certain threshold—which allows growth rates to differ—medium compositions that can induce interactions between two species were determined . With thThese examples show that a lot of valuable information can be gained without assuming equal growth rates, but there are two issues regarding this kind of approach. First, as discussed earlier, these results will describe only a snapshot of the community dynamics, because unequal growth rates will result in rapid changes of shared external metabolites and the biomass abundances of the species. This means that stable relative biomass abundances cannot be inferred when the species' growth rates differ. If this is desired to compare with experimentally determined data, then the equal growth rate constraint needs to be taken into account.iw. In other words, all resources will be invested in the least expensive biomass. Technically, this issue can be avoided by assuming equal growth rates [There is a second point to consider when an approach such as equation (3.5) is used, which occurs for communities whose members compete for shared metabolites. If the community species differ in their biomass composition, then a weighted sum of biomass-forming rates will lead to a solution where all available resources are invested in the growth of the organism with the highest biomass yield, i.e. there will be only one biomass formation reaction that carries an actual flux, and which one this is depends on the chosen weights th rates , by settth rates ,99, or bth rates .One might argue that this problem could be solved by interspecies feeding mechanisms. The reasoning behind this is that then resources cannot only be invested in one organism, but also in the other one because they depend on each other. While this will indeed lead to several metabolically active networks and an exchange of metabolites, still only the biomass-forming reaction of the organism with the highest biomass yield will carry a non-zero flux (if both organisms compete for the same resource and have different biomass yields for this substrate). The network of the other organism will only be used to provide the required metabolite, but resources will not be invested in growth. This is rather artificial as these fluxes require a catalyst—biomass. Coupling of excretion flux to growth rate is one way this problem has been tackled .Besides using explicit constraints on the growth rates, one can also overcome this issue by merging the species' biomass equations into one, so that all the required macromolecules are produced. Instead of maximizing 4.Escherichia coli [Steady-state cFBA based on balanced growth is well suited to make predictions about communities in fairly constant environments, such as chemostats, regarding their metabolic interactions and optimal relative biomass abundances. However, in batch cultures and many natural communities, organisms are exposed to dynamically changing conditions and can grow sequentially, something this framework cannot accommodate. For such an analysis, dFBA can be used—under simplifying conditions. dFBA was first used to describe the diauxic growth of hia coli  and has hia coli ,102–107.dFBA models are similar to FBA models, except that the constraints on the input fluxes are made dependent on extracellular concentrations through kinetic rate expressions. Usually Michaelis–Menten kinetics are used, which are sometimes extended with inhibitory terms ,4.1jK parameter is equated to the affinity of the transporter, equation (4.1) describes purely substrate-limited uptake, and thus assumes that the transport step is fully controlling the downstream metabolic pathway. From metabolic control analysis, we know that this is not necessary and in fact not very likely, as control over steady-state flux tends to be distributed [jK can be interpreted as the Monod constant for growth . In praall biomass components, so also proteins, are in steady state. As long as proteome reallocations are not explicitly modelled in genome-scale metabolic models—but they will be in the future—this complication is not an issue. The concept of dFBA is summarized in One important assumption in dFBA is that the time constants related to intracellular dynamics are much smaller than those that describe changes of external concentrations. This is the basis for the quasi-steady-state (QSS) approximation inherent in the approach. The assumption that metabolism is in QSS during the relatively slow medium transitions, invoked by the cell's own metabolic activities, is very reasonable and generally accepted in the field. However, for adaptations that require gene-regulatory processes that may act at comparable time scales to the environmental changes, this does not apply, and so cells need not to be in balanced growth, in the sense that Extending dFBA to communities is then relatively straightforward: one defines input fluxes for which kinetic expressions are required, and solves the set of differential equations, using FBA for each organism individually. However, here we also face a challenge in the interactions between the species, and different solutions that researchers have suggested.4.1.Rhodoferax ferrireducens and Geobacter sulfurreducens in an anoxic subsurface environment leading to predictions about the conditions under which one can outcompete the other [E. coli and Saccharomyces cerevisiae that—in this study—exclusively consume xylose and glucose, respectively, to engineer a co-culture system in which both sugars are consumed simultaneously [et al. [dFBA has been proven to be a very useful tool to analyse metabolism on a community level –107,110.he other . Later oaneously . Chiu et [et al.  combinedIn these studies, the important assumption is made that communities are spatially homogeneous. Often, however, natural occurring communities tend to be structured, which can give rise to interesting dynamics –114. ThiAs for any application of FBA, the choice of the objective function has certain implications. It has been debated for a long time on which level natural selection occurs: on the species or community level –97. WithD), even though, in the long run, providing D to another organism would provide a growth benefit later on. The models cannot predict the optimal strategy over a longer period of time, only at each time instance. If another organism is auxotrophic for this compound D and it is not provided in the medium, the growth dynamics of this organism cannot be described without explicitly setting the model up for this purpose. In contrast, in steady-state cFBA, this interaction would show up without explicitly enforcing it.One very interesting—and challenging—consequence of optimizing organisms individually is that one needs to hardwire the interactions between the organisms, as they cannot be predicted. The reason for this is that at each time instance FBA will predict the currently most optimal flux distribution for growth. It will not predict the suboptimal excretion of a metabolite  and where metabolic interactions are known. In these cases, modelling the community with dFBA provides flux distributions within and between species, and can provide insight into the strength of metabolic interactions that cannot be measured directly.5.In this paper, we illustrated and discussed how steady-state cFBA can be derived from classical FBA without any additional assumptions. We made a clear distinction between different types of fluxes—specific internal fluxes, exchange fluxes and fluxes towards biomass—as they have different units that are relevant in a community setting. We concluded that stable biomass abundances in communities can only be modelled if (i) the species' relative biomass abundances are explicitly considered and (ii) all organisms grow with the same growth; this ‘community growth rate’ can then serve as the objective function.cFBA allows optimal biomass abundances and the associated community growth rate at a steady state of balanced growth to be calculated. Furthermore, this approach can be used to infer essential interactions between species in a certain environment without making any assumption about how and whether species interact. However, the cases in which community members all grow at the same rate may be rather limited because that can only be achieved in fairly stable environments. In natural occurring communities, however, dynamically changing environmental conditions are prevalent which cannot be incorporated into cFBA. Here, dcFBA can be used. This approach is, however, limited in its predictive power of unknown interactions and usually requires that the entire system structure is defined beforehand. This is, in particular, true for mutual interactions based on suboptimal growth strategies, i.e. if the excretion of a by-product comes at a growth cost but would benefit an organism in the long run, as it would allow growth of another organism that conversely provides growth-promoting metabolites. While dcFBA is a very powerful tool to describe small synthetic well-characterized communities, its extension to larger communities is not straightforward, owing to the number of parameters required to model transport rate dynamics and the associated numerical instability. One way to keep the number of parameters in a reasonable range is to use explicit exchange kinetics only for metabolites that are essential for the community to grow optimally. This information could be revealed by performing FVA on the solution computed by steady-state cFBA. This combination of cFBA and dcFBA therefore seems promising.We still face many challenges in modelling metabolism in communities that go significantly beyond insufficient experimental data or reconstructed genomes. We require advances in how to define the objective function of communities, how to deal with dynamics and subsequent (sub)optimal dynamic strategies within the constraint-based modelling format, and how to incorporate the recent advances made in modelling monocultures –84. It s