Currently, computational techniques used to gap-fill a reaction network compute the minimum set of reactions using Mixed-Integer Linear Programming (MILP). Depending on the number of candidate reactions used to complete the model, MILP can be computationally demanding.Flux Balance Analysis (FBA) is a genome-scale computational technique for modeling the steady-state fluxes of an organism’s reaction network. When the organism’s reaction network needs to be completed to obtain growth using FBA, without relying on the genome, the completion process is called E. coli and yeast models with, in some cases, a three orders of magnitude execution speedup compared with MILP. We have implemented FastGapFilling in MetaFlux as part of Pathway Tools (version 17.5), which is freely available to academic users, and for a fee to commercial users. Download from: biocyc.org/download.shtml.We present a computational technique, called FastGapFilling, that efficiently completes a reaction network by using only Linear Programming, not MILP. FastGapFilling creates a linear program with all candidate reactions, an objective function based on their weighted fluxes, and a variable weight on the biomass reaction: no integer variable is used. A binary search is performed by modifying the weight applied to the flux of the biomass reaction, and solving each corresponding linear program, to try reducing the number of candidate reactions to add to the network to generate a working model. We show that this method has proved effective on a series of incomplete The computational technique presented is very efficient allowing interactive completion of reaction networks of FBA models. Computational techniques based on MILP cannot offer such fast and interactive completion. Gap-filling is a computational technique to complete a reaction network based on FBA without referring to the genome. Indeed, a complete knowledge of the functionality of the genome provides a complete reaction network and no gap-filling would be needed. Essentially, given a set of candidate reactions, gap-filling suggests to add some of these reactions to the model so that the FBA model grows, but without guaranteeing that the enzymes for the added reactions exist in the organism. This computational approach to complete a network is viable if it is unknown how to complete the reaction network based on the genome.Flux Balance Analysis (FBA) is a method for analyzing genome-scale steady-state models of metabolic networks ,2. ConstTo the best of our knowledge, all the current approaches to gap-fill -8 use MiC. neoformans. GapFind/GapFill uses MILP to find metabolites that cannot be produced and gap-fill the network of reactions of the model to produce them.For another example,  reports Although MILP can find a minimum number of reactions, those reactions are still only plausible suggestions to complete a reaction network. The reactions still need to be analyzed to confirm their validity for the organism. This analysis can be done by searching the scientific literature for references to pathways based on the suggested reactions to add. FastGapFilling also needs such an analysis, but it also provides several sets of reactions from which a broader analysis can be done.Moreover, these MILP computational techniques focus on finding the smallest set of candidate reactions to complete a model, but that set is not necessarily the most appropriate solution. For example, if only one reaction is needed to produce an essential compound, it might be the case that there is a solution with two reactions that better correspond to the taxonomy of the organism. Knowing the existence of this other non minimum solution might help discover the right missing reactions, which is a solution that might be given by FastGapFilling.In this paper we present a computational technique using linear programming (LP), avoiding MILP, for reaction gap-filling. Solving a linear program with thousands and even tens of thousands of variables is typically about 1 second. Therefore, LP is a much faster computational technique, compared to MILP, that can give almost immediate feedback on what is needed to complete a reaction network. The gap-filling solutions found by FastGapFilling can be the same or different from those with the MILP approach, as the applications presented in Section “Results” demonstrate. In fact, several sets of candidate reactions are suggested by FastGapFilling, all offering positive growth condition, which may add more insight to complete a reaction network.The next section presents the FastGapFilling algorithm based on LP.try-sets and numerical value parameters, called weights, provided by the user. A try-set is a set of candidates to fill the incomplete model. For example, the try-set of reactions is a set, typically large, of candidate reactions for completing the reaction network. A try-set of nutrients would be a set of candidate compounds that could be transported into the organism to enable growth. Each type of candidates  has its own weight. For each candidate added to the model, its corresponding weight is added to a global objective function and MILP maximizes that objective. Therefore, a positive weight indicates a desire to include as many candidates as possible in the model, and a negative weight indicates a desire to include a minimum number. A typical scenario is assigning a large positive weight for the biomass metabolites and assigning relatively smaller negative weights to all other try-sets. Such a scenario includes as many as possible candidate biomass metabolites by adding a minimum number of reactions, secretions, and nutrients. In MILP, the inclusion/exclusion of each candidate is controlled by an integer variable taking only one of two values, 0 (do not include) or 1 (include). Thousands of such binary variables can exist because — besides the nutrients, secretions, and biomass metabolites — thousands of candidate reactions are typical.To the best of our knowledge, all computational techniques published to date for gap-filling a reaction network are based on MILP, including the one used by MetaFlux . MetaFluLP and MILP differ in one main respect: all variables in LP can take only fractional values, whereas some variables in MILP must have integer values (for example the binary variables). This difference alone makes MILP computationally more demanding. Indeed, a typical MILP solver must iteratively apply a series of LP problems to find the right integer values to satisfy all constraints. This process can be demanding when thousands or even hundred of thousands of LP cases need solving. In contrast, our technique typically requires solving only a few LP problems.The FastGapFilling algorithm is presented in Figure M are included with the actual reactions N of the model to complete.1. When creating the LP formulation, all candidate reactions 2. All biomass metabolites are combined as one biomass reaction as if the FBA model were solved. However, the objective function to maximize is the flux of the biomass reaction, multiplied by a weight, minus the sum of the fluxes of candidate reactions multiplied by the weights provided by the user (See Section “Results” for a discussion about these weights).3. A binary search is performed based on the weight of the biomass reaction: the weight of the biomass flux is changed using a binary search between 0 and the number of candidate reactions. Each time the biomass reaction has a non-zero flux, the set of candidate reactions that are active is kept as one possible solution.The algorithm does not try to gap-fill nutrients or secretions, because the model is assumed to have the correct growth environment specified before attempting to complete the reaction networks. Accordingly, our description of the algorithm does not discuss the growth environment.M is a database of reactions such as MetaCyc, which includes approximately 12,000 reactions.The FastGapFilling algorithm accurately represents the model, because the entire biomass reaction is used as if solving the FBA model. The algorithm’s primary use is finding a small set of candidate reactions for adding to the model to produce greater biomass. In particular, if the biomass is zero , the algorithm tries to obtain growth by activating candidate reactions. That particular case implements reaction gap-filling. Typically, The generic reactions of MetaCyc are instantiated. That is, reactions that operate on classes of compounds are transformed to one or several reactions, where the classes are replaced by specific compounds that exist in the model. Any reversible reaction is transformed into two reactions, one for each direction, a standard practice in constructing FBA models. This transformation simplifies the mathematical modeling as the flux values of all reactions become non-negative.The algorithm’s output is a list of reactions sets. An implementation may output only the smallest set that would suggest the reactions for model completion. But other implementations may present all sets found and let the user select the most biologically appropriate set. The algorithm does not necessarily find the smallest possible set of candidate reactions to complete the given model. It does try to reduce the size of that set, but it does not compute the absolute minimum set of candidate reactions to complete the model. In other words, FastGapFilling uses an heuristic searching for the smallest set of candidate reactions to complete a model, but it may not find the smallest set.δ in the objective function. At each iteration of the search, that weight is adjusted either to help the solver increase the biomass flux fb or to reduce the number of candidate reactions added. The number of iterations done is bounded by ⌈log2|M|⌉.The search for a small set of candidate reactions to add to the model is based on one weight cr given as input to the algorithm are typically based on the kind  or taxonomic range  of the reactions. The cost of a reaction is proportional to its probability of occurring in a model. For example, a reaction that is not known to occur in the taxonomic range of the model  should have a higher cost than a reaction known to occur in the taxonomic range of the model. Examples of costs are presented in Section “Results”.The costs N and M” in the algorithm assumes that sets of nutrients and secretions are given. Actually, the implementation guides the details of this generation, as it may include many other parameters, such as lower and upper bounds on the flux of some reactions, constraints to avoid ineffective high fluxes, and so on. Essentially, the generated LP must be solvable, must satisfy the steady-state constraints, and must restrict the fluxes to non-negative values for all reactions of N and M, including the biomass reaction.The mathematical formulation of the LP problem of this algorithm follows the standard approach of solving an FBA model, except for the objective function described below and specified in Figure δ is a calculated weight by the binary search, fb is the flux of the biomass reaction, and the summation of the terms crfr is done over all candidate reactions of M. This function tends to increase the flux of the biomass, as a maximization is applied and the δfb is the only positive term in it. This function also tends to decrease the number of candidate reactions that have a non-zero flux  because the term fr and cost cr are non-negative values). Indeed, this is the objective of the algorithm: increasing the flux of the biomass while decreasing the number of candidate reactions to add to do so. The essential point is to find the right value for δ such that fb is non-zero . This is the objective of the binary search done by modifying δ such that growth is maintained and the number of active candidate reactions is reduced. Note that the initial value of δ is |M| . This value enables many candidate reactions to be active simultaneously at the beginning of the binary search.The main novelty of the LP formulation is the objective function that changes at each iteration of the binary search. The objective function to maximize is Note that, in general, this algorithm actually suggests adding candidate reactions to the model to increase the biomass. It could also be used for engineering more efficient metabolic pathways, although this aspect is not covered in this paper.The main shortcoming of the algorithm is that it does not find a solution when no set of candidate reactions can be found to produce the entire set of biomass metabolites. In such cases, we recommend reducing the number of metabolites in the biomass reaction.E. coli and yeast models.The following section demonstrates the application of FastGapFilling on an E. coli models and to one incomplete yeast model. We started with a working E. coli model for which no added reaction are needed to obtain growth and then removed from 1 to 14 reactions in order to prohibit growth. A similar procedure was done to create the incomplete yeast model. See the following subsections for more details on the creation of these incomplete models.We have applied the FastGapFilling algorithm to four incomplete E. coli model is based on the EcoCyc database (version 17.5). The model has 1,763 enzymatic reactions, including the instantiated generic enzymatic reactions. The biomass reaction has 69 metabolites. The growth media is composed of glucose, oxygen, ammonium, phosphate, diphosphate, sulfate, and iron. The secretions are carbon-dioxide, acetate, and water. An upper bound of 16 mmol/g/h was constraining the intake of glucose.The original For each incomplete model, we also ran MetaFlux  in develcosts if their values are negative and gains if their values are positive. Costs are applied to reactions, and a gain, to the biomass metabolites. The gain is not user specified when using FastGapFilling, because the weight to the biomass reaction is controlled by the algorithm, but only for MILP. The following costs and gain were used for all cases presented in this paper. In the MILP development mode, weights are user specified to control the candidate reactions to include in the model. They are called 1. A cost of 1 for one candidate spontaneous  reaction2. A cost of 5 for one candidate reaction inside the taxonomic range of the organism3. A cost of 10 for one candidate reaction of unknown taxonomic range4. A cost of 15 for one candidate reaction outside the taxonomic range of the organism5. A gain of 500 for one candidate biomass metaboliteThe relative values of these weights (costs and gain), as opposed to their absolute values, are important. For example, the cost of a spontaneous reaction is smaller than the cost of an enzymatic reaction, because a reaction that does not require an enzyme can occur in any organism. Similarly, the cost of a reaction that is outside the taxonomic range of the organism is set higher than the cost of a reaction in the taxonomic range of the organism because we prefer reactions in the taxonomic range of the organism selected. The candidate reactions are all coming from the MetaCyc database, and their taxonomic ranges are based on the curated pathways of that database.Notice that the gain of one biomass metabolite is high compared to the cost of any reactions. For example, the ratio between the gain and the cost of a reaction in the taxonomic range of the organism is 100. This means that up to 100 such reactions could be added to the model if one more biomass metabolite can be produced. The intention is to produce a maximum number of biomass metabolites even if a large, but still bounded, number of candidate reactions is needed to produce them. As shown in the following subsections, this general result was obtained for all cases presented because a few reactions produced all metabolites.Table E. coli model, we removed the following reaction from the original E. coli model: To create the first incomplete branched-chainaminotransferleu-rxn, which can be used as an unambiguous keyword to search for more information about that reaction at BioCyc.org.Note: in this subsection and the following subsections, the MetaCyc reaction unique identifier is shown between parentheses. In the reaction just shown, that identifier is That reaction, going right to left, is the last step in the biosynthesis pathway of the amino acid L-leucine and, going left to right, the first step in the L-leucine degradation pathway. No other reaction in the model produces L-leucine. Because L-leucine is part of the biomass reaction of the model, we expect that adding this reaction will be suggested when gap-filling is done. Indeed, the MetaFlux gap-filling MILP solution suggested adding the same reaction, in the right to left direction. MetaFlux could give the relevant direction as part of the solution because all reversible candidate reactions are split into two reactions, one for each direction. MetaFlux did not suggest adding the reaction in the opposite direction because the reaction was not essential for growth given the nutrients. SCIP required 125 seconds to obtain this optimal MILP solution.When the FastGapFilling algorithm was run on the same incomplete model, adding the same reaction, in the same direction, was suggested. Four iterations  were needed before that solution was found; the first three iterations found solutions with three reactions. The total solver running time of these four iterations was 6 seconds.This first simple example shows that FastGapFilling can find the exact same solution as the MILP technique in much less time.E. coli model is derived by removing, additionally to the reaction removed in the first incomplete E. coli model, three reactions that produce the compound tetrahydrofolate, which is part of the biomass. These additional reactions are: The second incomplete Notice that the reaction of the previous incomplete model and these three reactions are in different metabolic pathways.The MILP development mode of MetaFlux suggested adding three of the reactions that were removed: the first two reactions above, and the reaction removed in the first incomplete model. That is, the third removed reaction above was not suggested. The SCIP solver required 7,794 seconds or about 2:10 hours to find this optimal solution.We ran the FastGapFilling algorithm on the same incomplete model. The smallest set of suggestd reactions included the same three reactions. Other solutions proposed included four reactions. FastGapFilling performed 12 LP solving iterations, with a solver total execution time of 16 seconds.This second example shows that FastGapFilling can find the same solution as the MILP technique in substantially less time — in this case, well over 2 orders of magnitude faster.E. coli model tricarboxylic acid cycle (TCA cycle) pathway: For this third example, we selected four reactions to remove from the original E. coli: The MILP solution suggested adding two reactions, both in the taxonomic range of Although, these two reactions were not among the four reactions removed, the second reaction does produce the compound 2-oxoglutarate, one of the compounds produced by one of the reactions removed. Notice that the development mode of MetaFlux produces only one of the possible optimal solutions. Other different minimal cost solutions may provide the same value, but MetaFlux outputs only one of them. In this example, an optimal solution might include two of the four reactions removed, but we cannot confirm it. SCIP required 9,729 seconds or about 2:42 hours to find this solution.However, FastGapFilling found a solution of three reactions after 12 iterations lasting 13 seconds, the first two reactions being the same as the MILP solution plus the following reaction: The third reaction appears to be redundant because its flux, as given by FastGapFilling, is 0.00056, whereas the fluxes of the other two reactions are the same at 0.110394. The flux of the third reaction is much lower than those of the first two reactions.Indeed, the low-flux reactions suggested by FastGapFilling might simply be a way to increase the biomass and might not be reactions essential for growth. In general, this possibility can be verified by only adding the suggested reactions with relatively high fluxes and solving the resulting network. If the biomass can be generated, the low-flux reactions would be nonessential.E. coli model with 14 reactions removed. These reactions were selected because they produced at least one of the following metabolites: L-lysine, L-leucine, L-isoleucine, and L-histidine. All these metabolites participate in the biomass reaction. Essentially, this is an example where many biosynthesis pathways have been disturbed. The following reactions were removed. The fourth incomplete model is the original branched-chainaminotransferileu-rxn, diaminopimdecarb-rxn, and histaldehyd-rxn. These three reactions are among the 14 reactions that were removed.The SCIP solver could not find an optimal solution to the MILP problem after running for 24 hours. However, FastGapFilling produced the following solution, after 12 iterations that took 14 seconds by the SCIP solver, by suggesting three reactions: This example shows that FastGapFilling can be very useful in practice: no optimal or near optimal solution could be found after 24 hours using the MILP approach, whereas FastGapFilling quickly found a gap-filling solution.E. coli model, the original yeast model can grow. The original yeast model is based on the YeastCyc database (version 17.5). The model includes 1,454 enzymatic reactions, including the instantiated generic enzymatic reactions. The biomass reaction is composed of 41 metabolites. The growth media is composed of glucose, oxygen, ammonium, phosphate, sulfate, and iron. The secretions are carbon-dioxide, carbon-monoxide, formate, hydrogen-peroxide, glycolaldehyde, and water. An upper bound of 12 mmol/g/h was constraining the intake of glucose.As a last example of applying the FastGapFilling algorithm, we used a yeast model. As with the To generate an incomplete model, four reactions responsible for the biosynthesis of five lipids  were removed. These five lipids are part of the biomass. The reactions removed are: The first reaction (GPPSYN-RXN) appears in three different pathways , whereas each of the other reactions occurs separately in three other pathways.The optimal MILP solution for gap-filling this incomplete yeast model, required 21,027 seconds or about 5:50 hours, and suggested adding the four reactions above. This set is the least number of reactions expected because MetaCyc (version 17.5) includes no other reactions to produce these lipids.FastGapFilling found the same solution, after 12 iterations lasting 14 seconds using the SCIP solver — a much faster execution time when compared to MILP. The binary search of FastGapFilling also found other solution sets with up to 34 candidate reactions, but the smallest set included the exact four reactions that were removed.FastGapFilling is an efficient technique to gap-fill reaction networks allowing interactive completion of reaction networks of FBA models, whereas MILP fails to offer such an efficiency.The FastGapFilling algorithm increases the biomass flux by minimizing a weighted minimum sum of fluxes from new reactions, whereas the gap-filling approach using MILP is based on adding a minimum number of new reactions to obtain a non-zero biomass flux.Using concrete examples, we show that the FastGapFilling algorithm is efficient for performing reaction gapfilling requiring much less computation time than MILP-based approaches. This result is not surprising because MILP may have to solve hundreds or even thousands of LP problems, whereas the FastGapFilling approach requires solving only a few LP problems.The author declares that he has no competing interests.


Kluyveromyces marxianus, in glucose and xylose media using RNA-seq. The data were explored in a number of innovative ways using a variety of networks types, pathway maps, enrichment statistics, reporter metabolites and a flux simulation model, revealing different aspects of the genome-scale response in an integrative systems biology manner. The importance of the subcellular localisation in the transcriptomic response is emphasised here, revealing new insights. As was previously reported by others using a rich medium, we show that peroxisomal fatty acid catabolism was dramatically up-regulated in a defined xylose mineral medium without fatty acids, along with mechanisms to activate fatty acids and transfer products of β-oxidation to the mitochondria. Notably, we observed a strong up-regulation of the 2-methylcitrate pathway, supporting capacity for odd-chain fatty acid catabolism. Next we asked which pathways would respond to the additional requirement for NADPH for xylose utilisation, and rationalised the unexpected results using simulations with Flux Balance Analysis. On a fundamental level, we investigated the contribution of the hierarchical and metabolic regulation levels to the regulation of metabolic fluxes. Metabolic regulation analysis suggested that genetic level regulation plays a major role in regulating metabolic fluxes in adaptation to xylose, even for the high capacity reactions, which is unexpected. In addition, isozyme switching may play an important role in re-routing of metabolic fluxes in subcellular compartments in K. marxianus.We investigated the transcriptomic response of a new strain of the yeast  Kluyveromyces marxianus is emerging as a host for metabolic engineering and recombinant protein production, having a number of advantages over Saccharomyces cerevisiae. These characteristics include thermotolerance and the ability to utilise a wide variety of sugars, including the pentose xylose, that are abundant in lignocellulosic biomass. Moreover, it is probably the fastest growing eukaryote on Earth [K. marxianus strains, in terms of their proneness to fermentation and ability to utilize various substrates, suggesting genetic diversity within the species [Agave americana. To enable metabolic engineering of K. marxianus and other yeasts, it is important to understand genetic responses to environmental factors and different substrates. Such an understanding requires both advanced high-throughput omics methods as well as various integrative computational methods. Thus far, only two studies of genome-scale transcript levels in K. marxianus have been published. Work on strain DMKU 3–1042 suggested that the yeast up-regulated β-oxidation in the absence of glucose repression in a complex xylose medium due to the use of lipids as additional carbon source in the absence of glucose, implying possible utilization of the small amounts of lipids present in the rich medium [The yeast on Earth . Previou species . Our strNext-generation sequencing (NGS) has become a popular method not only for sequencing genomes but also for various other experiments ,6. RNA-sAnalysis of metabolic pathways could be a sensible additional approach as it gives a sense of directionality to the response, and the scientist often associates a certain endpoint metabolite with a pathway, providing a means to simplify the understanding of the dataset. Painted renderings could be made of individual pathways, but often the number of pathways excludes a concise representation, and the integrated nature of metabolism is lost. Further, in metabolic pathways the interactions (reactions) consist of hypergraphs containing more than one substrate or product, complicating the rendering. Cellular overviews, as is available with software such as Pathway Tools, summarises metabolism into a single image . HoweverAn approach that is complementary to the pathway-based understanding of metabolism is that of the study of metabolite levels. Metabolomics, which entails the characterisation and quantification of small compounds in the cell, is still technologically demanding and labour intensive, however . A nK. lactis [13C-Metabolic Flux Analysis, estimation of fluxes at different physiological states can be very informative. Metabolic Regulation Analysis (MRA) combines differential expression levels with differential flux estimates to reveal for each flux the contribution of the metabolic and hierarchical levels of regulation [Models of biochemical pathways have much potential to reveal new insights that are not obvious from the exploration of datasets. The understanding of complex biochemical datasets using computational models is called systems biology. Some flux modelling approaches such as Flux Balance Analysis (FBA) simulations could be done even at the genome scale ,16, as w. lactis . A long-gulation .K. marxianus UFS-2791 to glucose and xylose in a chemically defined medium under aerobic conditions, including a number of different systemic analyses. Although a major potential future application of K. marxianus may be ethanol production from lignocellulosic biomass, which is an anaerobic or oxygen limited process where both glucose and xylose may be present, we chose to perform aerobic cultivations with glucose or xylose separately to remove any confounding effects. The strain also utilizes these sugars sequentially. The high cultivation temperature of 35°C was also chosen as this strain was determined to have a growth optimum close to 35°C. Our samples were also taken during mid-exponential phase to eliminate the effect of any possible ethanol stress that may occur later during the fermentation. To address the need for effective integrative exploration of omics data, including RNA-seq, and to combine these data with modelling and simulation, we developed the Reactomica software. We combined gene set enrichment of Gene Ontology (GO), reporter metabolites, metabolic pathway maps with a strong focus on subcellular compartmentalisation, and two new approaches of representation, namely pathway-to-pathway networks and reporter metabolite-enzyme networks.Here we report on a detailed RNA-seq transcriptomics study to explore the response of + dependent xylitol dehydrogenase is present and that the co-factor independent isomerase reaction is absent, as in K. marxianus [The aims were to first effectively explore the key features of the differential response to xylose in a defined medium under aerobic conditions and determine whether the peroxisomal lipid catabolic response previously observed  was limiarxianus . Under aK. marxianus UFS-Y-2791 was sequenced on the Illumina HiSeq platform to 100-fold coverage at the Onderstepoort Biotechnology Platform, Pretoria, South Africa. Assembly was performed de novo using Abyss. Open reading frames were found by Augustus. Putative protein sequences were annotated using one of two methods. For annotation of enzymes (778 genes), creation of a pathway genome database (PGDB) and all subsequent analysis involving metabolic pathways, protein sequences were annotated against the Kegg-Kaas server with default settings on the server, resulting in a list of EC number annotations. Output was subsequently parsed and converted to input for the PathoLogic algorithm of Pathway Tools. For gene set enrichment using Gene Ontology (GO), sequences were additionally annotated against the UniProtKB database on a high-performance computing cluster, using BLASTP. An E-value cut-off of 1E-10 was used for gene set enrichment as was done by others [S. cerevisiae, 17.4% from K. lactis, 3.2% and 2.8% from two strains of K. marxianus, and the rest from other species. The draft genome, predicted open reading frames, predicted protein sequences and functional annotations are made available in the Supplementary materials : glucose or xylose, 5; (NH4)2SO4, 2.5; MgSO4·7H2O, 0.5; CaCl2·H2O, 0.03; NaCl, 0.1; citric acid, 0.25 and KH2PO4, 10. Filter-sterilised vitamins were added to the autoclaved medium at the following concentrations (mg l-1): biotin, 0.025; calcium pantothenate, 0.5; nicotinic acid, 0.5; p-aminobenzoic acid, 0.1; pyridoxine HCl, 0.5; thiamine HCl, 0.5 and myo-inositol, 12.5. Trace elements were added according to du Preez and van der Walt [600 of 0.8 was reached.All chemicals and fermentation media used in cultivations were obtained from Sigma Aldrich, Seelze, Germany. der Walt . The pH 690 of 0.8 by centrifugation at 1 000 × g at 4°C for 5 min. RNA extraction was carried out according to the RNeasy yeast RNA kit (Qiagen) protocol, including a DNAase step. Ribosomal RNA was removed by the Ribo-Zero rRNA Removal Kit (Illumina) and remaining RNA was sequenced at the Onderstepoort Biotechnology platform in Pretoria, South Africa. Paired-end reads were generated using Illumina HiSeq Next Generation Sequencing. For each of duplicate samples, 3.75 million trimmed paired-end reads were mapped to the UFS-Y2791 genome. Processing of sequencing data was carried out in Galaxy. Reads were trimmed using Trimmomatic [Cells from duplicate cultivations were harvested in mid-exponential phase at an ODmmomatic  and mappmmomatic  was usedmmomatic . Genes wFor gene set enrichment and all other network constructions and renderings, programs were developed as part of a new software suite for integrative systems biology that we call Reactomica, implemented in the Wolfram Mathematica language. Gene set enrichment scores for GO terms and pathways were calculated similar to that described by Ideker  as folloFor pathway gene set analysis, MetaCyc pathways were used from the BioCyc pathway genome database constructed for this strain using Pathway Tools, which is based on the MetaCyc database. Reporter metabolite enrichment scores were calculated in the same manner as described above and according to Patil and Nielsen . For rep2(fold change) colouring scheme, in the case of more than one enzyme that could perform the same function, the largest fold change in expression was used for the colour rendering. Additional gene-reaction linkages were made from a UniProt BLASTP annotation. Subsequent compartmentalisation made use of the GO ‘cellular_component’ ontology terms. For purpose, a mapping was built into Reactomica that maps GO ‘cellular_component’ ontology terms to subscellular compartments.To explore the metabolic response, metabolic pathway maps were created from MetaCyc pathways and RNA-seq data were mapped using various colouring schemes with Reactomica, harnessing automated hypergraph map layout and manual override. The initial linkage between genes and reactions were made by the Pathway Tools algorithm PathoLogic, with genomic annotations from the Kegg-Kaas annotation server. For the LogPathways were clustered by the number of metabolites in common to generate a scoring matrix. The number of metabolites in common was normalised by the smaller of the two metabolite sets of a pathway and a threshold was selected for including a mapping that resulted in optimal rendering. Orphaned pathways were clustered together.Molecules were clustered by the simple similarity criterion of string matching of SMILES strings of each compound in the PGDB using the edit distance. Only the closest match was included as a mapping. The method is similar to that done by Barupal et al. .The metabolic network was converted from a hypergraph into a graph in which only the interactions between differentially expressed enzyme genes and enriched reported metabolites were retained.K. marxianus UFS-Y2791. Some additional reactions were defined such as the combined electron transport and oxidative phosphorylation reaction. The biomass reaction was adapted from Fischer et al. [The aim was to approximate the fluxes on glucose and xylose, sufficient for approximation of MRA values. FBA was used which included optimisation of biomass formation, and measured specific sugar consumption rate and specific ethanol, acetate and were included to constrain the flux solution. The model was constructed in Reactomica using reactions from MetaCyc for which representative genes were found in the genome annotation of r et al. . The flur et al. . FBA useThe metabolic regulation of a flux can be separated into a metabolic component ρm and a hierarchical component ρh. The two levels of regulation are combined in the relation below .J is the flux though that enzyme, modelled by the rate equation v, and affected by changes in the concentration of metabolite X. The hierarchical component ρh models the effect of changes in maximal activity of the enzyme, which is usually linearly dependent on the enzyme concentration e and described by:The metabolic component ρm models the contribution to regulation that changes in metabolite concentrations make and is described byρh, ρm could also be calculated. Though maximal activity is affected not only by the protein concentration and post-translational modifications, it is reasonable and practical to use changes in transcript levels obtained from RNA-seq instead of maximal activities or protein levels for an estimated MRA. For MRA, gene expression changes were considered significant if at least one gene  was considered significant from q-values. Transcript fold changes were calculated from total transcript abundances for all genes mapping to a reaction, in case of isozymes resulting from paralogs or multi-functional proteins. In this manner, the method is robust to potential errors in annotation of paralogs since central metabolic genes are known to have on average higher transcript abundance in comparison with the vast majority of other genes. The fold changes of individual minor isozymes with very low expression levels also cannot dominate the analysis.The hierarchical component could thus be experimentally determined by measuring a difference in maximal enzyme activity. By using 600 values, with ethanol, glycerol and acetate as fermentation products. In xylose medium, fermentation products were absent, with an apparently purely respiratory metabolism. The maximum specific growth rate in glucose medium was approximately 0.8 h-1, while the maximum specific growth rate in xylose medium was approximately 0.35 h-1. All graphs and other renderings were generated using a new software suite for bioinformatics and integrated systems biology, termed Reactomica, which was developed in-house. Interactive datasets are provided in Computable Document Format (.CDF) as supplementary materials and are viewable using the free Wolfram CDF player, which can be downloaded from the Wolfram website [In glucose medium, respiro-fermentative growth was observed, even though fully aerobic conditions were ensured by the small working volume in a large flask, vigorous shaking, and sampling at low OD website , or by uWe compared results from reference , which rThirteen genes were uncorrelated with the reference data (constitutive in UFS-2791)  and are thus specific to either the strain or the rich medium. Most of these are uncharacterised proteins.S. cerevisiae [Finally, two genes were anti-correlated with the reference data (down-regulated in UFS-2791). These are the ammonia transport outward protein 3 (ATO3) and dihydroxyacetone kinase 1 (DAK1). The exact functions of ATO1, ATO2 and ATO3 are not currently known, apart from their possible involvement in mitochondrial retrograde signalling and ammonia production during starvation. It seems that ATO3 requires rich medium containing amino acids to be up-regulated, as was also observed in revisiae . In summA total of 1 611 GO terms were included in the UniProt annotations of all proteins in the genome see . To obtaK. marxianus since it does not possess a xylose isomerase.In the ‘molecular_function’ ontology, only three terms are regarded as significant. ‘Oxidoreductase activity’, ‘kinase activity’ and ‘peptidase activity’ . ‘OxidorThe ‘biological_process’ ontology is rich in providing a framework for exploring the regulation of cellular processes in response to different carbon sources. The ‘carbohydrate transport’ gene set was the most significantly altered, with 21 out of 65 transporter genes up-regulated and 7 down-regulated . The ‘trHGT1 homologs of K. lactis, were up-regulated as high as 1242-fold , only peroxiredoxin-5  and catalase T  were moderately differentially regulated, resulting in an enrichment score of 1.19, which was insignificant against the background enrichment.K. marxianus UFS-Y2791 also does not possess typical secreted xylanases, proteases, peptidases or lipases, which would allow a microorganism to thrive on plant matter or even attack a live plant. Instead, the strain possesses the inulinase gene INU1 which hydrolyses the fructan inulin or the disaccharide sucrose. The INU1 gene was dramatically up-regulated 91-fold and abundantly expressed in xylose medium.The data indicated several interesting aspects regarding sugar utilisation, including up-regulation of pathways for utilisation of galactose, xylose and arabinose (see S5). Several enzymes with β-glucosidase activity were found in the annotation see , whereasThe pheromone signalling system involved in sexual reproduction, as well as several other genes involved in the conjugation process as well as in invasive growth, were also up-regulated  or down-regulated .Most metabolic pathways for amino acid synthesis were down-regulated, as was expected at the lower growth rate; μTo capture the global metabolic response to growth on xylose in a single view, an innovative pathway-to-pathway network was constructed by clustering pathways together by their common metabolites . The widGUT2 gene 4.4-fold up-regulated. Note that the up-regulated glycerol-3-phosphate shuttle functions independently from down-regulated glycerol production.Fatty acid oxidation, peroxisomal ethanol degradation and mixed acid fermentation, which cluster together, were mostly up-regulated. Close by in the network is glycolysis, which was down-regulated. A moderately increased capacity in the glycerol-3-phosphate shuttle was evident here, with the mitochondrial glycerol-3-phosphate dehydrogenase (a) a marked change in capacity for their utilisation or production between conditions, (b) to have required a significant degree of regulation by their neighbouring enzymes to establish homeostasis in the different environment, or (c) to have a different concentration predicted between conditions where it may be a candidate as a signalling molecule. The top eight reporter metabolites of highest enrichment were 3-phosphoglycerate, acetaldehyde, NADH, glyceraldehyde-3-phosphate, β-alanine, NAD+, glycerate and ethanol, in this order . It was interesting to note that the enrichment score of ATP was among the lowest against the background and considered insignificant. Also, glutathione and its reduced form, which are known to be involved in redox metabolism, were not significantly enriched, suggesting no severe oxidative stress. Oxidative stress in K. marxianus is seemingly more important under oxygen limiting conditions, as imposed by static and high-temperature conditions [Reporter metabolite enrichment was performed to reveal those metabolites around which significant differential expression of enzymes took place. These compounds could be interpreted as those from which there was is order . NADH, NTo determine whether the reporter metabolites represented any distinct molecular structural groups, a molecular network of the reporter metabolites was reconstructed using a simple molecular structure similarity matching protocol. This approach could identify some co-regulated groups of structurally related molecules that were not evident from pathways-based analyses. Groupings of CoA-conjugates, long-chain and short-chain fatty acids are representative of increased catabolic activity of β-oxidation and activation steps. Up-regulated sugar clusters corresponded to those found in reporter metabolite-enzyme networks, but were represented in a clearer fashion. Noteworthy is that effectors of trehalose containing sugars and sugar lipids were down-regulated. The three-carbon molecules in central carbon metabolism, which are close together in the network including 3-phosphoglycerate, 2-phosphoglycerate, glyceraldehyde-3-phosphate and glyceraldehyde, were strongly enriched and their effectors down-regulated. This mapping is useful as a concise representation of potentially all metabolites in a cell, grouped by their structures. The method would especially be useful for visualising metabolomics datasets of which the link to reactions and pathways is not yet clear. A better separation of clusters is obtained in mapping larger metabolites as found in secondary metabolism.Combining both the reporter metabolites and the enzymes by which they are regulated into an enzyme-reporter metabolite network, effectively reveals the hotspots of metabolic regulation as well as the key players in regulation. Including all interactions with enriched compounds  was not feasible for a detailed investigation (1352 interactions). Instead, we extracted the interactions containing nodes with enrichment scores above 3.0 .+/NADH, oxygen and the aldehyde dehydrogenase have a strong involvement. A second subnetwork involves sugar metabolism and glycosylation. A third revolves around one-carbon metabolism. The subnetwork of NAD+ (enrichment score = 4.2) was extracted . The enzymes directly affecting NADPH are explored in IDP1  was only moderately up-regulated (2.2-fold). A more significantly up-regulated enzyme, mitochondrial quinone oxidoreductase  reduces 1,4-benzoquinone, as was shown by cloning this gene from K. marxianus in E. coli [YPR127W, a putative pyridoxal reductase that functions to degrade vitamin B6 and involved with multidrug resistance and not central metabolism [GND1 (6-phosphogluconate dehydrogenase) and SOL1 (6-phosphogluconolactonase) were, however, constitutively expressed. Another enzyme, SPS19 , was strongly up-regulated at 269-fold. It functions to reduce double bonds to facilitate β-oxidation of unsaturated fatty acids in the peroxisome [Since  E. coli . It is ntabolism . In the roxisome , anotherTo explore the metabolic response of the central carbon metabolism, metabolic pathway maps were created from MetaCyc pathways and RNA-seq data were mapped using various colouring schemes. Figs XYL1 was drastically up-regulated on xylose (48.8-fold) with very high gene expression levels on xylose. Xylitol dehydrogenase was absent from the annotation. However, is has been demonstrated that sorbitol dehydrogenase SOR1 can act as a xylitol dehydrogenase in S. cerevisiae [SOR1 by 208-fold supports this function. Xylulokinase XKS1 was also 11.3-fold up-regulated. Transaldolase TAL1 of the non-oxidative pentose phosphate pathway (PPP) and ribose-5-phosphate isomerase RKI1 were moderately up-regulated (4.8 and 2.6-fold). We did, however, not observe up-regulation of any enzymes in the oxidative branch to support additional NAPDH production for xylose utilisation, or to combat oxidative stress by charging of the glutathione system. We found a remarkably clear down-regulation of glycolytic genes on xylose with a moderate fold change. The gluconeogenesis-associated gene fructose-1,6-bisphosphatase FBP1 was also sharply up-regulated by 27-fold, which was also observed in a microarray experiment of a xylose utilising recombinant S. cerevisiae strain [An interesting differential expression pattern is evident in revisiae . Signifie strain . β-OxidaFurther, there was also a strong apparent down-regulatory effect on alcohol dehydrogenases and aldehyde dehydrogenases, and both the citrate synthase of the TCA cycle and the isocitrate lyase of the glyoxylate cycle were seemingly dramatically up-regulated. The latter two observations in this analysis, however, are misguided by the lack of compartmentalisation of the response. It should be noted that many metabolic reactions could be catalysed by more than one enzyme, where for some reactions like those catalysed by alcohol dehydrogenase (ADH), there are at least five gene products that could potentially catalyse the same reaction. +-specific acetaldehyde dehydrogenase (ALD) and glycerol production were down-regulated. Further, a number of reactions usually associated with the TCA cycle were also present in the cytosol and were constitutively expressed. More than one type of ADH with opposite regulatory direction is present in the cytosol. In the peroxisomal compartment  and ADHs were still isozyme switching reactions. Both ALD4 (up-regulated 83-fold) and ALD5 (down-regulated 167-fold) were strongly differentially expressed. Several ADH genes were found in K. marxianus. Two of these were annotated as ADH3 and ADH4, both mitochondrial, whereas five  were taken to be cytoplasmic. As previously reported [S. cerevisiae and K. lactis [S. cerevisiae and K. lactis where glucose stimulated ADH1 expression. Transcriptional rewiring of ADH isozymes is thus present in K. marxianus compared to its relatives.Subsequently, the GO ‘cellular_component’ terms from the UniProt_SwissProt_fungi were used to render compartmentalised maps reconstructed from MetaCyc pathways. ment see , β-oxidaoxisomes , is cleareported , ADH2 wa. lactis . Convers. lactis , which dICL1) was down-regulated. Upon further investigation, the isozyme present in the mitochondrion, which was mapped to the TCA cycle by the PathoLogic algorithm using Kegg-Kaas annotations, was in fact ICL2, the 2-methylisocitrate lyase, perhaps confusingly termed ICL2. Although ICL1 and ICL2 share a high sequence similarity, the latter does not use isocitrate as a substrate and does not produce glyoxylate but uses 2-methylisocitrate instead to produce succinate and pyruvate [ICL2 is part of the propionyl-coezyme A pathway, otherwise known as the 2-methylcitrate pathway [CIT3 (YNR001C), the mitochondrial enzyme that condenses oxaloacetate with propionyl coenzyme A to form 2-methylcitrate. Indeed, the citrate synthase that was up-regulated (CIT1 gene (YPR001W) that is both cytosolic and mitochondrial and associated with the TCA cycle, but instead the mitochondrial CIT3. Further inspection of the full GO ontology enrichment set revealed that all three key genes in the 2-methylcitrate pathway were significantly up-regulated. The strength of the response in the 2-methylcitrate pathway is given in CIT3, PDH1 and ICL2 were up-regulated 294, 32 and 28-fold, respectively, and GLY1). Another gene was also annotated as GLY1 and down-regulated. Thus, there is no conclusive evidence that threonine catabolism was up-regulated. The up-regulation of the 2-methylcitrate pathway is, therefore, more likely for the catabolism of short-chain fatty acids and not threonine.In the mitochondrial map, the NADPH specific isocitrate dehydrogenase gene was up-regulated, whereas citrate synthase of the TCA cycle and isocitrate lyase were seemingly up-regulated. Surprisingly, the glyoxysome map revealed that the glyoxylate cycle specific isocitrate lyase  scheme). Although transcript levels do not generally correspond well to protein levels and hence to fluxes according to reports using model organisms [Differential metabolic flux analysis can be combined with differential gene expression data in the framework of MRA. From Figs rganisms , the oveAlthough there is not always a linear correlation between transcript level, protein concentrations and maximal activities of an enzyme, we assume differential transcript expression to provide a sufficient approximation to hierarchical regulation, as was done by others . Fig 17 Modelling of bioprocesses has been attempted for a long time, in many different forms. It was realised in the second half of the twentieth century that several confounding factors had to be eliminated in the study of metabolism and its gene regulation, arguably with the growth rate as the most important confounding factor, since the expression level of many genes are correlated with the growth rate. Chemostat cultivation is a useful tool, since the growth rate can be easily controlled. However, for the vast majority of industrial applications, chemostats are unrealistic as industrial applications typically involve batch cultivation, or fed-batch cultivation to avoid catabolite repression, improve volumetric productivity and allow sufficient aeration by controlling the growth rate. Moreover, systems biology has become increasingly data-driven with the availability of high-throughput methods to measure large numbers of intracellular metabolites (metabolomics), proteins (proteomics) and especially RNAs (RNA-seq and microarray) from a single experiment. It is proposed here that much more could be learned in terms of genetic regulation in microorganisms by testing a variety of different cultivation conditions, especially substrates, in small batch experiments as compared to the same amount of work in a more sophisticated, labour intensive chemostat setup, or at least, complementary information. We showed that in a simple and cost-effective batch setup, a large amount of rich RNA-seq data could be generated and fruitfully explored. This small working volume also makes expensive isotope labelling studies feasible. In batch experiments, however, special care needs to be taken in terms of the timing of sampling, as, for instance, fermentation products would accumulate over time and a transcriptome sample late in the fermentation may be more reflective of chemical stress than of the metabolic mode. This may especially be a confounding factor when comparing the effects of the concentration of substrate. Our experimental design alleviated this effect and allowed us to focus on the effects of alternative substrates only.Previously, exploration of omics datasets mostly focused on only the lists of the most significantly up-regulated or down-regulated genes separately, or on one or two more advanced types of analyses such as GO enrichment, and occasionally on the extraction of active networks. Here we presented one of the first examples that explore high-quality RNA-seq data from various perspectives, using different types of enrichments and networks, and rationalisation of the response with FBA and MRA as theoretical frameworks. Furthermore, combining information from databases such as GO and MetaCyc in the same problem and with subcellular compartmentalisation revealed several important features that would have been missed using either on its own.A. americana [A. americana sample.The vastness of the xylose response under aerobic conditions indicates a different, opportunistic lifestyle that this yeast apparently adapts to when cultivated on xylose, which may be reminiscent of its natural environment where a variety of plant-derived substrates may be utilised. Down-regulation of many biosynthetic pathways is concordant with a lower growth rate, although there is a notable absence of growth rate specific gene sets in the enrichment statistics. Although many mitochondrial genes were differentially expressed, these are not the major enzymes in energy production in mitochondria. Oxidative stress also seems minimal in the aerobic xylose medium. Instead, a strong response is seen in the up-regulation of alternative sugar utilisation machinery, including inulinase, sugar transporters and catabolic routes for alternative sugars. Inulin is a fructan stored in large amounts in some plants, including mericana . Our strK. marxianus lacks enzymes such as secreted proteases, lipases and carbohydrate hydrolases. This yeast may thus be dependent on other fungi in the environment for these functions, or its natural habitat may be some commensal niche where these monomers are supplied by the plant. The transcriptional regulatory basis for this response is likely to be glucose repression by transcription factors such as MIG1 binding to carbon source response elements, as was suggested to be the case for the inulinase gene KmINU1 [e KmINU1 , 41.It is interesting to find that the majority of genes for a complete organelle like the peroxisome, which is dedicated to lipid oxidation, was dramatically up-regulated in the xylose medium, yet without apparent function in the experimental setting. Thus, glucose de-repression is likely sufficient to activate most of the response to enable lipid catabolism, and stimulation by lipids may play a smaller role. The mitochondrial 2-methylcitrate pathway for the degradation of three-carbon molecules was also strongly up-regulated, suggesting that a variety of odd-chain fatty acids originating from peroxisomes may be oxidised.FBA simulations predicted no significant up-regulation of the oxidative PPP flux, but a more intense up-regulation of the non-oxidative PPP flux and a down-regulation of glycolysis, which were consistent with RNA-seq data. Since biomass formation, the major sink for NADPH, is down-regulated in xylose medium, and another NADPH sink, xylose reductase, is up-regulated, it thus makes sense that the major source flux of NADPH (oxidative PPP) may be similar in both conditions . Normalising fluxes to the uptake rate of a carbon source or to the biomass formation rate could thus be misleading when interpreting expression data. FBA simulations here thus shed light on what could be expected in terms of gene regulation.S. cerevisiae classified these high-capacity reactions as well as the non-oxidative PPP reactions as pseudo-equilibrium or near-equilibrium reactions, suggesting that they can be sufficiently described by simple equations making use of thermodynamics and empirical studies at various dilution rates [K. marxianus showed that the transcript levels in lower glycolysis were substantially lower on xylose, and MRA showed a dominating hierarchical (genetic) level regulation. Flux through transaldolase was also dominated by hierarchical regulation. The contribution of hierarchical and metabolic level regulation of a reaction would differ between substrates utilised, and may also differ between species.MRA was used to separate metabolic regulation into hierarchical and metabolic levels. Reactions in lower glycolysis are known to a have high flux capacity due to high enzyme concentrations, and our transcript data also indicated this feature on glucose. Chemostat studies of on rates ; hence bReporter metabolite networking suggested that NAD(H), acetaldehyde, ethanol, glyceraldehyde-3-phosphate, 3-phosphoglycerate and hydrogen peroxide formed a strongly interconnected redox active system, with aldehyde dehydrogenases and alcohol dehydrogenases being the main players. This system may work across membranes, since acetaldehyde, ethanol and hydrogen peroxide can cross membranes, shuttles connect NAD(H) across compartments, and glyceraldehyde-3-phosphate and 3-phosphoglycerate are closely connected to NADH. At this stage it is not possible to resolve the fluxes and MRA through the acetaldehyde-dependent pyruvate dehydrogenase bypass. It was, however, evident that dramatic changes occurred in the transcript levels of the alcohol dehydrogenases and aldehyde dehydrogenases, including compartment-specific isozyme switching. As also suggested by Lertwattanasakul et al. [K. marxianus seemingly lacks the secreted enzymes required for depolymerisation of biopolymers, the species is probably dependent on other species for supply of monomers such as sugars, amino acids and free fatty acids, whereas inulinase is a specialist feature enabling this species to utilise this plant storage oligosaccharide. It would be interesting to see whether xylose may have a stimulatory role as suggested recently for Saccharomyces cerevisiae [We believe to have captured in a unique manner, and from a number of perspectives, a complex transcriptional pattern telling an interesting story about how the cell ‘explores its options’ when the nutrient availability changes under aerobic conditions. Strong up-regulation of transporters and pathways for utilisation of alternative carbohydrates was evident. In addition, the more opportunistic lifestyle was supported by invasive growth, and sexual reproduction was activated as a long-term survival strategy. The strong peroxisomal fatty acid catabolic response accompanied by the mitochondrial 2-methylcitrate pathway is likely explained by glucose de-repression, similar to that seen for carbohydrate utilisation. As revisiae  and throMRA was demonstrated here as an informative method to dissect the regulation of fluxes into the metabolic and hierarchical levels. It is evident that the genetic level plays a dominating role in the regulation of fluxes in central carbon metabolism, not only in the early enabling steps of utilisation of xylose as the carbon source, but also in the high capacity reactions of lower glycolysis. In kinetic modelling of metabolism, emphasis should thus be placed on genetic regulation, which is currently very challenging. Multiple omics would need to be combined to predict such regulatory networks and build realistic models. However, in order to resolve fluxes originating from pyruvate, isotopic tracer studies would be required, which currently is under investigation. In addition, the isozyme switching observed with alcohol dehydrogenase, aldehyde dehydrogenase and acetate-CoA ligase calls for a detailed investigation into the compartmentalisation and kinetics of these enzymes, and detailed bottom-up kinetic modelling to understand the role of this interesting behaviour.S1 Draft Genome(FA)Click here for additional data file.S1 Network(PDF)Click here for additional data file.S2 Network(CDF)Click here for additional data file.S3 Network(CDF)Click here for additional data file.S4 Network(CDF)Click here for additional data file.S5 Network(CDF)Click here for additional data file.S1 ORF(GFF)Click here for additional data file.S1 Pathway(PPTX)Click here for additional data file.S2 Pathway(PDF)Click here for additional data file.S3 Pathway(PPTX)Click here for additional data file.S1 Proteins(AA)Click here for additional data file.S1 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.S1 Text(PDF)Click here for additional data file.


Syntrophobacter fumaroxidans and the methanogenic archaeon Methanospirillum hungatei. The models were used to verify proposed mechanisms of ATP production within each species. We then identified additional constraints and the cellular objective function required to match experimental observations. The thermodynamic S. fumaroxidans model could not explain why S. fumaroxidans does not produce H2 in monoculture, indicating that current methods might not adequately estimate the thermodynamics, or that other cellular processes  play a role. We also developed a thermodynamic coculture model of the association between the organisms. The coculture model correctly predicted the exchange of both H2 and formate between the two species and suggested conditions under which H2 and formate produced by S. fumaroxidans would be fully consumed by M. hungatei.Microorganisms in nature do not exist in isolation but rather interact with other species in their environment. Some microbes interact via syntrophic associations, in which the metabolic by-products of one species serve as nutrients for another. These associations sustain a variety of natural communities, including those involved in methanogenesis. In anaerobic syntrophic communities, energy is transferred from one species to another, either through direct contact and exchange of electrons, or through small molecule diffusion. Thermodynamics plays an important role in governing these interactions, as the oxidation reactions carried out by the first community member are only possible because degradation products are consumed by the second community member. This work presents the development and analysis of genome-scale network reconstructions of the bacterium  Syntrophobacter fumaroxidans and the methanogenic archaeon Methanospirillum hungatei. These models were used to analyze energy conservation mechanisms within each species, as well as small molecule exchange between the two organisms in coculture. The coculture model correctly predicted the exchange of both H2 and formate between the two species and suggested conditions under which these molecules would be fully metabolized within the community.Natural and engineered microbial communities can contain up to hundreds of interacting microbes. These interactions may be positive, negative, or neutral, as well as obligate or facultative. Syntrophy is an obligate, positive interaction, in which one species lives off the metabolic by-products of another. Syntrophic associations play an important role in sustaining a variety of natural communities, including those involved in the breakdown and conversion of short-chain fatty acids  to methane. In many syntrophic communities, electrons are transferred from one species to the other through small molecule diffusion. In this work, we expand the study of a two-member syntrophic, methanogenic community through the development and analysis of computational models for both species: the bacterium  Microorganisms in nature engage in a variety of interactions with other species in their environment. Syntrophy is one such type of inter-species interaction in which one species lives off the metabolic by-products of another –3. SynthIn anaerobic syntrophic communities, electrons are transferred from one partner to the other through direct contact or small molecule diffusion . Traditi2 exchange between the sulfate-reducing bacterium Desulfovibrio vulgaris and the methanogenic archaeon Methanococcus maripaludis [One of the earliest microbial community models used flux balance analysis  to inveipaludis . In thisipaludis –19, as wipaludis –24. Thesipaludis –24 have ipaludis ,26 insteipaludis  extends ipaludis –24 to spSyntrophobacter fumaroxidans and the methanogenic archaeon Methanospirillum hungatei. In association with M. hungatei, S. fumaroxidans converts propionate to acetate, CO2, and H2 [2 and H2 can be interconverted to formate [2 and formate serving as the electron carriers between the two species. H2 and formate production are only observed during syntrophic growth. Using a thermodynamic, constraint-based model, we set out to test the proposed hypothesis that this behavior is governed by thermodynamics [Genome-scale models can also be used to study the relationship between thermodynamics and metabolism, by ensuring that network predictions are consistent with thermodynamic principles –34. In t, and H2 –37. CO2  formate –40, withdynamics ,6,8,9.S. fumaroxidans does not produce H2 in monoculture.We developed genome-scale metabolic reconstructions of both microorganisms, and verified proposed mechanisms of ATP production within each individual species. Additional constraints and a cellular objective function were identified to predict the proper flux through experimentally characterized carbon and electron transport pathways during monoculture and syntrophic  growth. Our analysis revealed that thermodynamic constraints alone are insufficient to explain why We also extended TMFA to model the syntrophic association between the two microorganisms. The association is modeled as a continuous coculture system with constraint-based models for each microbe and a mass balance around the reactor. Similar to cFBA , the cocS. fumaroxidans (iSfu648) and M. hungatei (iMhu428) were tested and parameterized using experimental data from growth on single substrates in monoculture and coculture. The iSfu648 and iMhu428 models were used to verify proposed mechanisms of energy conservation within each species. A coculture model was then developed to identify conditions where H2 and formate, produced by S. fumaroxidans, is fully metabolized by M. hungatei.Metabolic reconstructions of iMhu428 reconstruction of M. hungatei was built from the iMB745 reconstruction of M. acetivorans [iMB745 using the RAVEN Toolbox [M. hungatei orthologs were found for only 428 of the 745 genes in iMB745. To avoid extensive gapfilling, reactions from the iMB745 were copied into the M. hungatei reconstruction, with modifications to reflect key metabolic features of M. hungatei  had to be allowed to vary within a 99% confidence interval of its estimated standard transformed Gibbs free energy of reaction  and a Na+/H+ antiporter (NAT3_1) were selected to give an ATP yield matching the experimental estimates: two Na+ ions exported by MTSPCMMT_CM5HBCMT, and a one Na+ per H+ transported by NAT3_1. However, different stoichiometries for these reactions are also thermodynamically possible  and non-growth-associated (NGAM) ATP maintenance requirements for M. hungatei, as described in iMhu428 model, the NGAM was estimated to be 0.6 mmol ATP/gDW/day, GAM was estimated to be 47 mmol ATP/gDW, SURCO2 was estimated to be 75.7 mmol/gDW/day, and SURformate was estimated to be 955 mmol/gDW/day.Experimental measurements of growth rates, yields, and maintenance costs were also used to identify substrate uptake rates (SUR) for COiSfu648 reconstruction of S. fumaroxidans was built from the KEGG database using the RAVEN Toolbox [The  Toolbox . The res Toolbox ,48–51, wS. fumaroxidans: four in monoculture and one in coculture with M. hungatei  [FRD) consumes reducing equivalents (menaquinol) [RNF), the ferredoxin-oxidizing hydrogenase (frH2ase), the cytosolic hydrogenase (cytH2ase) and formate hydrogen lyase (FHL). The reduction of fumarate to succinate also generates the proton motive force (PMF) responsible for driving the RNF reaction and producing ATP.The oxidation of one fumarate to COredoxin) ,52, whilaquinol) . Electro2. Two additional moles of fumarate get reduced to succinate [During monoculture growth on fumarate plus propionate , one moluccinate ,48:prop2 produces one NADH and one pair of reduced ferredoxin, while the reduction of fumarate to succinate by FRD consumes menaquinol. Electrons are transferred from NADH and reduced ferredoxin to menaquinone through the combined action of the confurcating hydrogenase (cH2ase) and cytH2ase. Oxidation of propionate to succinate produces one ATP, while FRD generates the PMF necessary for additional ATP production.The oxidation of fumarate to acetate and CO2 via the methylmalonyl-CoA pathway [During coculture growth on propionate , propion pathway ,52:SDH), producing menaquinone. cytH2ase then transfers electrons from menaquinol to two protons, generating H2. The oxidation of fumarate to acetate and CO2 produces one NADH and one pair of reduced ferredoxin, and cH2ase couples NADH and ferredoxin re-oxidation with H2 production. Unlike in the monoculture growth modes, the H2 is not consumed intracellularly and must diffuse outside the cell. It has been proposed that the net production of H2 by S. fumaroxidans is only thermodynamically favorable at the low H2 concentrations maintained by methanogens, thereby explaining why S. fumaroxidans only produces H2 during coculture growth.ATP is generated during the oxidation of propionate to succinate, and this ATP establishes the PMF necessary to drive the endergonic oxidation of succinate to fumarate ,48,51S. owth ([2  yieldingcytFDH) substitutes for the activity of cytH2ase. In a second mechanism (cFDH) substitutes for cH2ase. Here, cFDH couples NADH and ferredoxin re-oxidation with the conversion of CO2 (from propionate oxidation) to formate.In one mechanism , activitechanism , the conS. fumaroxidans energy metabolism suggest that the carbon and electron transfer pathways shown in S. fumaroxidans, either by substrate-level phosphorylation or through establishment of a proton gradient used by ATP synthase [Experimental evidence and conceptual models of synthase . To testiSfu648 model correctly predicted the flux distributions shown in S. fumaroxidans has adapted to maximize its energy yield.When flux was restricted to a reduced network containing all the reactions shown in S. fumaroxidans have shown that H2 is not produced during growth in monoculture [2 production is only thermodynamically favorable at low partial pressures [2 production by consuming H2 and keeping its partial pressure low [2 production was observed in monoculture, H2 production ceased at a partial pressure of approximately 10 Pa [Experimental studies of oculture ,52,53, aressures ,8,9. In sure low ,8,9. Ind2 production under monoculture conditions, simulations reveal that H2 production remains thermodynamically feasible. For example, during monoculture growth on fumarate, the iSfu648 model predicts that H2 can be produced via the following mechanism:However, when maximizing H2 molecules produced by the ferredoxin-oxidizing hydrogenase are exported outside the cell, instead of serving as substrates for the cytosolic hydrogenase. As a result, no PMF is generated by fumarate reductase, and the net ATP yield is zero. Thus, while H2 production remains thermodynamically possible, H2 production is only associated with sub-optimal mechanisms of ATP generation. This suggests that thermodynamic considerations alone may not explain the absence of H2 production during monoculture growth, but that the observed flux distribution may instead be driven by demands for energy generation.In this scenario, H2 production was not predicted for monoculture conditions when ATP production was maximized, H2 production was initially predicted when growth was instead maximized. To eliminate monoculture H2 production in the TMFA model, we first sought to constrain ratios of metabolite concentrations with an approach similar to that used to correct TMFA growth predictions [2 production mechanisms, H2 production during monoculture growth could not be completely eliminated. If thermodynamics prevents H2 production in monoculture, then the current thermodynamic model may contain too much uncertainty in its Gibbs free energy estimates . Experimental measurements of growth rates, yields, and maintenance costs were used to identify the SURs, GAM, and NGAM parameters for S. fumaroxidans. These parameters were estimated using data from monoculture growth on fumarate alone and coculture growth on propionate alone . This discrepancy could be caused by differences in uptake rates or maintenance costs in the fumarate plus propionate condition compared to the conditions with propionate alone or fumarate alone.Using these parameter values, the redicted . Not suriSfu648 model predicted a wide range of product secretion rates. When the enzyme cost  was minimized at the maximum growth  and two pairs of electrons (used to reduce two fumarate). While this coupling arises naturally on the reduced network, the full metabolic network enables alternative coupling mechanisms (not shown) that permit other fumarate to propionate ratios. Since propionate oxidation generates carbon precursors and ATP for biomass, maximizing biomass production results in the model under-predicting the fumarate to propionate uptake ratio. Increasing the ratio of fumarate to propionate uptake (to 3:1) decreases the predicted propionate SUR and growth rate , the pTMFA-predicted intracellular flux distribution during monoculture growth on fumarate and propionate substantially deviated from that shown in S. fumaroxidans converts propionate to acetate, H2, and CO2 or formate [M. hungatei consumes acetate, CO2, H2, and formate and produces CH4 [M. hungatei can also optionally interconvert excess CO2 and H2 to formate via a formate dehydrogenase [During growth in coculture,  formate ,52, whiluces CH4 . M. hungrogenase .M. hungatei and S. fumaroxidans have been grown in both batch and continuous (chemostat) systems. During batch growth, H2 pressure rose during the lag phase and became constant during exponential growth [2 partial pressure [M. hungatei to S. fumaroxidans at constant H2 pressure  have not been reported. Instead, an overall reaction for the coculture ofM. hungatei to four S. fumaroxidans. Since initial conditions for batch experiments were not reported, a continuous culture model was constructed and first evaluated using a 3:4 relative biomass ratio (M. hungatei: S. fumaroxidans).Cocultures of l growth . Continupressure . Howeveriscussed , which cM. hungatei were produced by S. fumaroxidans.The continuous coculture model included constraint-based models for each microbe and mass balances around the reactor . As the reactor dilution rate increased, the predicted species yields of H2 and CO2/formate (S. fumaroxidans) and CH4 (M. hungatei) decreased slightly , M. hungatei did not fully utilize all of the H2 and CO2/formate produced by S. fumaroxidans, even at high dilution rates , M. hungatei growing at faster rates than S. fumaroxidans , or a combination of the two.Species’ uptake rates, secretion rates, and relative biomass ratio affects overall bioreactor yields, and these bioreactor yields were subsequently investigated . At a 3:on rates . The netly 1.6:1 . These sS. fumaroxidans passes electrons to M. hungatei via formate, as well as H2 [2  and formate , which must be maintained in order for methanogenesis to occur. All of these predictions were insensitive to both the dilution rate and biomass ratio (M. hungatei: S. fumaroxidans).Finally, steady-state metabolite concentrations in the coculture were predicted using thermodynamic variability analysis ,34 S1 T. SimilariMhu428 and iSfu648 thermodynamic models were successfully used to verify proposed carbon and ATP production pathways in M. hungatei and S. fumaroxidans; however, some more efficient pathways (based on ATP or biomass yields) were found in some cases. The computational results highlighted topics that necessitate further discussion relating to (1) the stoichiometry of transport reactions, (2) the thermodynamics of H2 production, and (3) the carbon and electron shuttles between species in coculture.The iMhu428 model content comes from the iMB745 reconstruction of M. acetivorans and still needs to be verified. Changes to model content could affect the conclusions drawn about M. hungatei behavior. Despite containing a complete methanogenesis pathway, the iMhu428 model was unable to identify the H+/Na+ transport stoichiometry of the energy-converting (Eha- or Ehb-type) hydrogenase , which is thought to pump H+/Na+ while reducing ferredoxin [HDR, 1.8.98.1) can also reduce ferredoxin, and the iMhu428 model predicted HDR to be the only ferredoxin-reducing reaction required for methanogenesis. This observation is consistent with the observation that the expression of Eha/Ehb is considerably lower than that of HDR [The majority of the t of HDR .MTSPCMMT_CM5HBCMT, E.C. 2.1.1.86) could drive transport of up to 4 Na+ ions under standard conditions, instead of the 2 Na+ ions used in the iMhu428 reconstruction. Furthermore, some studies suggest the archaeal A1A0 ATP synthase is coupled to Na+ instead of H+ translocation [iMhu428 model was modified to reflect this coupling, the model predicted the Na+/H+ antiporter was no longer active, as Na+ ions from MTSPCMMT_CM5HBCMT were directly used for ATP synthesis. Thus, while the modeled methanogenesis pathway is consistent with available data, it is not the only possibility.Additionally, different stoichiometries for other ion transport reactions important to methanogenesis remain thermodynamically possible. For example, the group contribution method predicted that tetrahydromethanopterin S-methyltransferase  of ferredoxin, resulting in no ΔrG'0 estimates for these reactions. Fortunately, new quantum chemical approaches for estimating the thermodynamics of metabolism [fG'0 estimates.Analysis of the tabolism  may poteG'0 of groups directly when modeling thermodynamics [E. coli made the model computationally difficult to solve. In this work, using either the ΔG'0 of molecules or groups to model thermodynamics proved computationally difficult (results not shown). Instead, only using ΔrG'0 as the basis for thermodynamic calculations enabled uncertainties in free energy estimates to be handled without any computational difficulties. However, using ΔrG'0 as a basis for thermodynamic calculations leads to larger uncertainties in ΔrG'0 and greater network flexibility, as it does not account for thermodynamic interconnectivity between reactions with shared metabolites. As a result, the model-predicted feasible ΔrG'0 range through a linear combination of reactions considerably exceeds the group-contribution predicted ΔrG'0 range of the overall reaction. In the future, thermodynamic interconnectivity should be captured using the ΔG'0 of molecules or groups, and optimization techniques are needed to improve the runtime performance of the resulting thermodynamic models.This work also raises important questions about the appropriate mathematical basis for representing thermodynamic constraints. Previous studies used the Δdynamics , and fourG'0 as a basis for thermodynamic calculations is insufficient to explain why the iSfu648 model could still produce H2 under monoculture growth conditions. As described in fG'0 was used as a basis for thermodynamic calculations when attempting to find additional constraints which would prevent H2 production. The failure to find such constraints indicates either that thermodynamics does not explain the absence of H2 production in monoculture, or that current thermodynamic models cannot capture this phenomenon. If it is the latter, more accurate group contribution methods with smaller error estimates may eventually be able to explain the role of thermodynamics in syntrophic associations.However, the use of Δ2 in electron transfer in the community, and led us to hypothesize that total H2 consumption by the community indicates that M. hungatei cells are more abundant and/or faster growing than the S. fumaroxidans cells. The coculture model correctly predicted that both H2 and formate could shuttle electrons between members of this community. Formate may be preferred over H2 for electron transfer for thermodynamic reasons, as the ΔrG'0 of 2 and H2, S. fumaxoridans could sustain propionate oxidation at higher extracellular concentrations of formate than of H2. Formate exchange could also be preferred due to differences in kinetics, diffusion, and/or volatility. These scenarios could stabilize the syntrophic association by enabling faster shuttling of electrons to M. hungatei.The thermodynamic coculture model of the syntrophic association between these species confirmed the role of formate and HiSfu648 model to predict the observed behavior of S. fumaroxidans. Additional constraints on reaction directions and flux ratios were required before iSfu648 could be combined with iMhu428 model to simulate the coculture. In addition, the iSfu648 model relied on data from gene expression and 13C NMR experiments, suggesting that constraint-based approaches will complement traditional top down (‘omics’) approaches [This work highlights some important obstacles to successful modeling of microbial consortia. In order for computational models of microbial communities to make meaningful predictions, individual species models must be integrated into a community model in a biologically relevant manner. Such integration will require an understanding of the objectives and constraints governing the behavior of each community member, and this work demonstrates that identifying the proper constraints and objectives requires extensive experimental characterization of the community. For example, neither maximization of growth rate nor maximization of ATP yield were sufficient for the proaches  by enablproaches .iMhu428 reconstruction of M. hungatei was built from the iMB745 reconstruction of M. acetivorans [iMB745 M. acetivorans reconstruction were copied into the M. hungatei reconstruction, with modifications to reflect key metabolic features of M. hungatei , and 639 metabolites. Of the 428 genes, 351 were added based on sequence homology, and 77 were added manually. The reconstruction is available in The final iSfu648 reconstruction of S. fumaroxidans was built from KEGG [iSfu648 reconstruction contains 874 reactions, 648 genes (associated with 770 reactions), and 893 metabolites. The reconstruction is available in The rom KEGG   and its flux (v) have opposite signs. Estimates   is a conn method  via the n method . TMFA wan method , with adpFBA  is a conFor the coculture simulations, a community model of growth in a continuous stirred-tank reactor was developed that accounts for the biomass concentrations of each species. The model minimizes the species-weighted total flux through the metabolic networks subject to TMFA constraints for each species and mass balances around the entire reactor. Details on the specific implementation used in this work can be found in The uptake fluxes for carbon and other nutrients used in the simulations are given in S1 Table in S1 DatasetThis file contains Supporting Tables S1 to S7 as described in the text.(XLS)Click here for additional data file.S2 Dataset(XLS)Click here for additional data file.S3 Dataset(XML)Click here for additional data file.S4 Dataset(XLS)Click here for additional data file.S5 Dataset(XML)Click here for additional data file.S6 Dataset(XLS)Click here for additional data file.S7 Dataset(XML)Click here for additional data file.S1 File(ZIP)Click here for additional data file.S2 File(ZIP)Click here for additional data file.S1 TextThis file contains Supporting Methods, Results, and Figs to complement the main text.(PDF)Click here for additional data file.