E. coli growth rates under different media and gene essentiality, amongst other things. In order to improve predictions, additional constraints are coupled with optimization of the biomass function. Studies have suggested, however, that unicellular organisms - like multicellular organisms - do not grow at optimal rates. To further improve FBA predictions, particularly of internal cell fluxes, new techniques to explore the sub-optimal solution space need to be developed.Flux Balance Analysis (FBA) is a widely used tool to model metabolic behavior and cellular function. Applications of FBA span a breadth of research from synthetic engineering of biofuels to understanding evolutionary adaptations. FBA predicts metabolic reaction fluxes that optimize a given objective. This objective is generally defined for unicellular organisms by a theoretical reaction which simulates biomass production. FBA has been extremely successful at predicting in corsoFBA based on the optimization of protein cost at sub-optimal objective levels. Our method shows good agreement with experimental data of E. coli grown at different dilution rates. Maintaining the objective function close to its maximum value predicts metabolic states that closely resemble low dilution rates; while higher dilution rates can be mirrored by lowering the biomass production value. By using a modified version of Extreme Pathways, we are also able to quantify the energy production and overall protein cost for all possible pathways in the central carbon metabolism.We present an innovative FBA method called E. coli central carbon metabolism can be better predicted by exploring the sub-optimal FBA solution space. The corsoFBA method presented here is able to predict the behavior of PEP Carboxylase, the glyoxylate shunt and the Entner-Doudoroff pathway at different glucose levels, a behavior not predicted by the minimization of metabolic steps and FBA alone. This technique can be used to better predict internal cell fluxes under different conditions, and corsoFBA will be of great help for the study of cells from multicellular organisms using Flux Balance Analysis.Metabolic flux distributions at the optimal objective can be substantially different from the near-optimal distributions. Importantly, the behavior of The online version of this article (doi:10.1186/s12918-015-0153-3) contains supplementary material, which is available to authorized users. Genome-wide metabolic reconstructions provide a powerful platform for the analysis of metabolic pathways. Reconstructions for at least sixty-five different species spanning fifty-one different genera, including humans ,2, are aA vast array of computational methods for the analysis of Constraint Based Models is available, and the number continues to grow ,6. PerhaE. coli the uptake and release rates of certain metabolites [The FBA solution is not unique. There are several fluxes within the model that are not well defined, but can exist within certain bounds while the objective function is being optimized [ptimized . These fOrganisms might not be operating at maximum capacity [capacity -18. In tThe observed metabolic state is also not unique. That is, a single flux distribution cannot explain all the flux states observed in the experiments, and variation occurs within the bacterial population. Wintermute et al. [cloud theory for metabolic regulation, where bacteria are allowed to fluctuate within a near-optimal solution space. The study also demonstrates that the variability of fluxes within this region matches the observed variability within the data.e et al.  proposesThermodynamically infeasible loops can appear in the FBA output. These are sets of pathways termed “type III pathways” [athways” , which aathways” .This technique is most commonly applied to metabolic reconstructions of unicellular organisms with the optimization of a theoretical Biomass reaction. This reaction consumes resources such as amino acids, nucleotides and ATP at the rate the given organism would need in order to grow and multiply ,9. FBA aabolites -12, cellabolites ,11 and gabolites  with greabolites , mainly To better predict internal fluxes, some studies have relied on additional thermodynamic constraints . SeveralSignificant efforts have also been directed toward integrating omics data and FBA -38, but E. coli chooses its pathways based on the minimization of protein cost [More recent studies have relied on the theory that ein cost ,40 and nein cost . Severalein cost , minimizein cost ,42,43 anein cost -49. One ein cost .These methods have been very successful at improving predictions of growth rate, substrate usage and internal cell fluxes in unicellular organisms. Several studies have suggested, however, that unicellular organisms in reality grow at rates lower than those predicted by FBA alone -17. AlthE. coli can vary freely within a near-optimal space [Additionally, these one-step optimization methods with additional constraints return a single flux distribution, and they are unable to explore the near-optimal solution space. This limitation is significant given a recent study has suggested the flux distribution of al space . TherefocorsoFBA), which is suitable for sub-optimal objectives. Rather than imposing additional constraints when optimizing the objective function, we fix this objective at a predefined value. An estimated protein cost throughout the metabolism is then minimized in order to predict the internal cell fluxes. By varying the biomass production value, we are able to predict how changes in pathway usage depend on changes in other conditions, particularly glucose availability. Although this method is not well suited for predicting growth rates, we are able to predict metabolic flux distributions within a near-optimal solution space. Furthermore, by decomposing the model using an adapted version of the Extreme Pathway analysis, we are able to break down the energy production pathways and further understand the model behavior as glucose concentrations change. We validate our methods using E. coli as the model organism.To address this need, we propose a two-step optimization FBA method for predicting internal fluxes, termed COst Reduced Sub-Optimal FBA , the enzyme molecular weight (MW), and a thermodynamic penalty for reversible reactions. The cost term used in corsoFBA is defined as: Some of the methods most successful at predicting internal cell fluxes have been based on the theory that nstraint -49. FiveΔrG′o is the standard Gibbs free energy of the given reaction, R is the ideal gas constant and T is the temperature. The molecular weight term is included to represent the amount of resources needed in order to produce a sufficient amount of enzymes to maintain the associated reaction flux. The thermodynamic penalty, applied only to reversible reactions, represents the cost associated with the change in the concentration of metabolites required for the reaction to flow in the desired direction. That is, a reaction with positive ΔrG′o would require a large disparity in the concentration of the associated metabolites, so the cost term is multiplied by a positive number larger than one. On the other hand, if ΔrG′o is negative, and the reaction is therefore favorable, the cost term is multiplied by a positive number between zero and one, given that little or no metabolic adjustment is necessary. It is worth noting that this thermodynamic cost does not directly represent a change in enzyme concentration, but rather an increase or decrease in the overall cost associated with the reaction based on its standard Gibbs free energy. Furthermore, this term is applied separately to forward and backward directions of reversible reactions, favoring the direction with negative standard Gibbs free energy. A similar thermodynamic cost, used without molecular weight considerations, has been applied by Holzhütter [Where lzhütter , weighinα is chosen to be Finally, the parameter ΔrG′o) or zero , and only the thermodynamic cost would essentially be considered. In that case, reaction directionality would essentially be predetermined based solely on the standard Gibbs free energy, which could be problematic.This value is chosen in order to balance the contribution of molecular weight and thermodynamic penalty, yielding a prediction considering both costs  molecular weights alone, (2) thermodynamic penalties alone, (3) the previously mentioned combination of molecular weights and thermodynamic penalties and (4) uniform costs. The use of uniform costs gives a simple minimization of the overall flux through the enzyme associated reactions. This minimization strategy is a modified version of a widely regarded two-step optimization method called pFBA . pFBA haSimulations comparing these four costs have been performed for growth rates ranging from 50 to 100% of the predicted optima. Flux distributions were normalized by the flux of glucose to glucose-6-phosphate, and results for several central carbon metabolism reactions can be found in the supplemental information , and the highest correlation values for the higher dilution rates in the Yao et al. data .The same set of simulations was also compared to several data points from two Metabolic Flux Analysis (MFA) experiments: Ishii et al.  and Yao In order to visualize the trend of how different fluxes change in the sub-optimal space, simulations utilizing molecular weight costs, thermodynamic costs and a combination of both, normalized again by the flux of glucose to glucose-6-phosphate, were plotted alongside the experimental values from the two MFA experiments. Fluxes were plotted starting at 100% down to 75% of the predicted optima, and the results for several central carbon metabolism reactions are presented in Figure corsoFBA flux distributions show close agreement with MFA data for higher growth rates  to relieve enzymatic cost, and that considering these costs during FBA may increase internal flux predictions when comparing to the minimization of metabolic steps alone.Predicted fluxes using molecular weights only and a combined cost also found excellent agreement with the experimental values in the reactions PPC (PEP Carboxylase) and ICL (Isocitrate Lyase),62. Bothn et al. , that focorsoFBA approach can better predict fluxes through certain reactions, such as PPC and ICL. While previous studies have shown that the FBA solution space increases drastically when considering the objective function at near-optimal to optimal values [Simulation results also suggest that the optimization of the biomass function may yield fluxes that are fundamentally different from those at near-optimal conditions. At optimal growth, there is no predicted flux through the glyoxylate shunt, considerably lower fluxes through the TCA cycle and PPP, and a flux through the PPC reaction not present at near-optimal conditions. Although comparisons between experimental data and simulated flux distributions show that the highest correlation and lowest error are found at optimal growth, our simulations also indicate that the implementation of these costs yield comparable results in the sub-optimal space  pathway. Genes  E. coli , but the E. coli . Due to  E. coli ,62, whice et al. , where fE. coli iJR904 reconstruction were decomposed using the Fundamental Pathways analysis described in the Methods section. Details on how these reactions were calculated can be found in the supplemental information , according to ATP production by both mmol of glucose and protein cost. The most energy productive pathway is the full oxidation of glucose through the TCA cycle (OP2). The most cost efficient pathway was found to be the production of acetate through glycolysis (OP1). Although this pathway potentially produces less than half the amount of ATP as OP2, the total enzymatic cost per mmol of ATP is lower. Also in agreement with general knowledge, this analysis predicted the release of acetate to be more efficient than the release of both lactate and ethanol.In accordance with general OP2 to OP1 is observed as the objective function value decreases. This trend also supports the idea that overflow metabolism takes place in order to alleviate enzymatic cost. Under low glucose conditions, E. coli would need to extract from glucose the largest possible amount of energy in order to sustain growth. As more glucose becomes available, however, this bacteria can afford to consume more substrate and produce energy through cheaper pathways.In the simulations presented in previous sections, a gradual transition from NOP2 and NOP3 both produce more ATP per mmol of glucose than OP1 but less than OP2, while remaining less cost efficient than OP1 but slightly more so than OP2. NOP2 and NOP3 reduce the flux through upper glycolysis by partially re-routing the flux through the PPP, and they exhibit no flux through Phosphoglucose isomerase (pgi). A third Near Optimal Pathway, termed NOP1, skips the upper glycolysis through the ED pathway. This pathway is both less cost and energy effective than OP1.One interesting observation from this analysis is the existence of Near Optimal Pathways (NOP), which combine the previously described optimal pathways with the PPP or ED pathways. −1 (Figure ΔpfkA deficient E. coli strains reduce flux through Phosphofructokinase 1 by diverting fluxes through the PPP [NOP2 and NOP3 instead of OP1 or OP2 when the cost through upper glycolysis is increased.The use of these near optimal pathways could explain the inconsistent PPP fluxes reported by the MFA experiments considered here. A short recovery in the simulated PPP flux near a growth rate of 0.65 h 1 Figure  demonstr the PPP , hence uOP2 to OP1 as we move away from optimal growth. Although this is in fact the general trend we observe, anaplerotic needs also need to be considered. These needs are addressed most efficiently by reactions not in OP1 or OP2, such as PEP carboxylase and the glyoxylate shunt. Interestingly, the model also predicts the use of the ED pathway with anaplerotic purposes at high growth rates. While this pathway has been studied mostly for its catabolic activity in Z. mobilis and several Pseudomonas species, simulations here predict this pathway to be the cheapest way to get glucose shuttled to the TCA cycle for the production of building blocks, while giving up little efficiency in energy pathways through NOP1.This Fundamental Pathway analysis elucidates how we would expect the model to behave in terms of energy generation as we optimize the protein cost at sub-optimal states. Based on this analysis, in order to fulfill its catabolic needs, the model transitions from corsoFBA, a method for analyzing and predicting metabolic flux distributions at sub-optimal states based on protein and thermodynamic cost minimization. CorsoFBA demonstrates that the optimization of protein cost at near-optimal states can produce significantly different results from those at the optimal objective. Furthermore, although correlation and error calculations indicate better predictions at the optimal solution, protein-optimal results at sub-optimal objectives show better agreement with MFA experiments and gene expression profiles for anaplerotic reactions. These results suggest it is important to explore the sub-optimal FBA space in order to better predict internal cell fluxes. Although the method described here is not suited for predicting growth rates, it provides a platform for analyzing internal cell fluxes in the sub-optimal space.Here we present corsoFBA will be particularly useful given recent studies have suggested E. coli can exist freely within a near-optimal space [We believe al space . We alsoal space  and FBAwal space , would a


By mapping translated metagenomic reads to a microbial metabolic network, we show that ruminal ecosystems that are rather dissimilar in their taxonomy can be considerably more similar at the metabolic network level. Using a new network bi-partition approach for linking the microbial network to a bovine metabolic network, we observe that these ruminal metabolic networks exhibit properties consistent with distinct metabolic communities producing similar outputs from common inputs. For instance, the closer in network space that a microbial reaction is to a reaction found in the host, the lower will be the variability of its enzyme copy number across hosts. Similarly, these microbial enzymes that are nearby to host nodes are also higher in copy number than are more distant enzymes. Collectively, these results demonstrate a widely expected pattern that, to our knowledge, has not been explicitly demonstrated in microbial communities: namely that there can exist different community metabolic networks that have the same metabolic inputs and outputs but differ in their internal structure. Vertebrates play host to an enormous diversity of microbes, and while the numbers alone are impressive, exceeding our own cell count by at least an order of magnitude , it is tOur poor understanding of these organisms is largely due to the fact that they are quite difficult to work with: many or most will not grow in laboratories and they interact not only with the vertebrate host but also with each other in a variety of complex ways. Fortunately, applications of inexpensive DNA sequencing technologies  are transforming our understanding of the microbial world more rapidly than perhaps any technology since van Leeuwenhoek first looked through his microscope. To date, most surveys of microbiomes both in vertebrate hosts and in other environments have used taxonomic approaches, attempting to identify the different species that are present. The most effective technique for such assays has been using the 16S rDNA gene as a phylogenetic marker ,7,11–13.etal.  and to a catalog of enzymes, we show that some of the observed taxonomic dissimilarities are not necessarily mirrored at the metabolic level. Second, we hypothesized that, while the metabolic inputs and outputs of our samples would be similar (the inputs because of the common diet and the outputs because of the needs of the host species), there would be differences in the internal structure of metabolism between the samples. We tested this hypothesis in several ways, including asking if the variation in copy number for microbial enzymes that can interact with the host is smaller than the variation observed in other enzymes and by showing that the variation in enzyme abundance between the two animals is too large to be explained by sampling variation in the metagenomic sequences. Since the networks are also distinctly non-random in both their reaction and metabolite distributions, we argue that there are metabolically similar but not identical microbial assemblages that are capable of performing the same processes from the host's perspective, even if they appear distinct at the taxonomic level.n = 35; initial body weight = 333.77 ± 8.54 kg; age = 10.14 ± 0.12 mo). These animals were weighed, administered an anthelmintic  and randomly assigned to four pens  each equipped with two GrowSafe®  feed intake bunks  where the model fitted was,i = average actual daily feed intake for animal i, β0 = regression intercept, β1 = partial regression coefficient of actual daily feed intake on daily body weight gain for animal i, and β2 = partial regression coefficient of actual daily feed intake on metabolic mid-test body weight for animal i. The two steers chosen for the metagenomic experiment had similar body weight gains with different feed efficiencies . To obtain the microbial DNA for sequencing, we followed the procedure of Guan etal.  were constructed following the manufacturer's recommended protocol with reagents supplied in Illumina's DNA sample preparation kit. Genomic DNA was sheared using a BioRuptor  to generate fragments. The resulting 3′ and 5′ overhangs were removed by an end repair reaction using a 3′ to 5′ exonuclease activity and polymerase activity to blunt the fragment ends. A single adenosine was added to the 3′ ends of the blunt fragment followed by the ligation of Illumina adapters. The adapter-ligated fragments were then size selected using an agarose gel. Fragments of average length 436  or 477  bp were recovered from the gel slice by elution and ethanol precipitation. Each purified library was quantified with a Qubit assay and fragment size was confirmed by Agilent BioAnalyzer High Sensitivity DNA assay.Libraries were diluted and sequenced according to Illumina's standard sequencing protocol on a GenomeAnalyzer II. The two libraries  were each sequenced on two lanes of the instrument, resulting in 150 bp, paired-end sequences. The average insert size was 303 bp for animal 1 and 345 for animal 2. Raw sequence reads are available from NCBI's short read archive (Project accession number PRJNA291523).Paired-end reads were quality filtered by truncating each read after the first run of three bases with a phred quality score <15 . From thTo explore the taxonomic structure of these two animals’ ruminal metagenomes, we searched the filtered reads for fragments of 16S rDNA genes. We did so by comparing them to a reference database made up of two pieces: 16S rDNA genes from the Ribosomal Database collection of sequences  and 16S Database sequences were clustered into Operational Taxonomic Units (OTUs) by first computing all possible pairwise Needleman-Wunsch sequence alignments  using oubL, the likelihood obtained from fitting both animals to a common distribution, and 1L and 2L, those obtained when allowing distinct distributions for each animal. We then compared the value ΔlnL = (ln(1L) + ln(2L)) − ln(bL) from the real samples to the same value computed on 1000 datasets where the OTUs were randomly repartitioned between the two animals .As shown in Figure  animals . As the We obtained the complete catalog of microbial metabolic networks known to the MetaCyc project . This caWe next constructed two metabolic networks for our analysis, one for the bovine host and one for the microbes. In our framework, nodes in the metabolic network  to 174 (for 100N).For all networks, we defined edges in the metabolic networks to connect pairs of nodes that share a metabolite. Only annotated metabolites present in at least two taxa were considered for these purposes. Because a handful of metabolites, such as water and hydrogen ions, occur in an enormous number of reactions, it is necessary to remove these ‘currency metabolites’ from the metabolic networks. The alternative would be to have nearly every reaction connected to every other reaction. Unfortunately, there is no universal definition of a currency metabolite . InsteadWe defined three potential sets of metabolites exchanged between the microbes and the host animal, sets that we refer to as ‘interface metabolites’. The most minimal set (set VFA) consisted of (the anions of) three VFAs: acetate, propionate, and butyrate. VFAs are important nutrients for ruminants  but unfoOur second set (VFA + AA) expands the VFA set to include the 20 amino acids, which are also important ruminant nutrients. Finally for completeness, we created a greatly expanded interface metabolite set (VFA + AA + HUM). In addition to the metabolites of VFA + AA, this set incorporates a large number of metabolites known to be transferred into human cells from the extracellular matrix. To obtain this set, we started with the list of 404 exchangeable human metabolites from the human metabolic network of Duarte et al. . We matcGiven the interface metabolite list and these added reactions, we defined edges between the host and microbial metabolic networks as any case where a reaction in the host network and one in the microbe network shared an interface metabolite. The result was a single merged metabolic network for the host and microbes  longer than 45 amino acids. We then used these metagenomic ORFs as queries in searching an enzyme database (see next section).We queried 1000 reads whose translations produced strong hits to the MetaCyc protein database  against the nucleotide version of that database. The results were discouraging; only 30% of those reads produced any BLASTN  hit.Programs such as BLAST, because they are optimized to not miss distant matches, are very slow for searching metagenomic ORFs against protein databases. To speed our searches, we developed a tool based on the SeqAn library and OpenMP . For eacWe next assigned reads to metabolic network nodes if they had hits to annotated sequences for that node meeting the above criteria. Enzymes in the sequence database are often annotated as catalyzing more than one reaction. In such cases, if an ORF pair has hits to multiple database sequences, one of three scenarios can be observed. First, all of the database hits may map to the same set of reactions. Second, some of the database hits may only map to a subset of the reactions of other hits. Finally, different database hits may map to non-overlapping sets of reactions. In the first two cases, we compute the reactions catalyzed by an ORF pair as the union of the reactions catalyzed by each enzyme with hits to that ORF pair. In the last case, the read pair is discarded because we cannot be certain of the identity of the reactions in question. Cases where read pairs did not both map to the same enzymes were likewise omitted. Note that while this mapping approach is applicable to many metagenomic datasets, our analysis of differences between animals from similar environments precludes comparing these data to other samples from different species  or envir25, N50N and 100N with no mapped reads. No major omissions are apparent from these data.We sought to assess if there were highly connected enzymes from MetaCyc that might be expected to be in the rumen that were not identified with our read mapping approach. Supplemental Table S6 lists the 10 most connected reactions  from networks p) and the average number of reads mapped to those nodes with at least one mapped read (r). We then calculated Pearson's correlation coefficient between these two values and the layer's distance to the host network. To assess whether the observed trends were stronger than expected by chance we randomized the read assignments among the microbial nodes 1000 times and recalculated these two correlations. For p, we randomized read counts across all microbial nodes, occupied or not. For r (the average number of mapped reads), we only randomized the read numbers within the set of nodes with at least one mapped node.For each layer of the microbial network in Figure 2 ratio of abundances for the animals, we normalized all reads counts by the total number of reads mapped for each animal . We then pooled the mapped reads, randomly reassigned 1n of them to animal 1 and 2n of them to animal 2 and recomputed the number of nodes with every abundance difference .P < 0.001, ‘Materials and Methods’ section). We also normalized the read counts for each animal and compared the percentage of reads from the two that were mapped to the same OTU: only 44% of reads from the two animals mapped to the same OTUs.To define microbial OTUs, we computed those OTUs  from a database of known 16S rDNA sequences by all-against-all pairwise alignment and sequence clustering . Using t25N) to moderate . While these networks disregard the compartmentalization of the ruminal ecosystem into distinct cells, any compartmentalized metabolic network for this environment will be a subset of the community network.It is conceptually obvious that one could infer the gene contents of a metagenome from a reference database. As we were interested in metabolism, we chose the collection of metabolic network reconstructions in MetaCyc  as our dMore than 1.2 million read pairs from the two animals mapped uniquely to protein sequences from MetaCyc. Those protein sequences in turn catalyze one or several reactions each . Of the 6140 nodes in the microbial metabolic network, 2022 nodes had at least one mapped read pair and 1734 had read pairs mapped from both animals. A reaction from the electron transport chain interconverting ubiquinones and ubiquinols had the largest number of mapped reads: 16 443 reads from a single animal.r = 0.31, Spearman's ρ = 0.57, P < 10−10 in both cases). However, given that one strong predictor of a reaction having many sequences in the MetaCyc database is that the reaction is widely distributed phylogenetically, we argue that the magnitude of these correlations do not suggest database coverage is the primary signal being detected here. Similarly, the number of reads mapped to a node is correlated to that node's metabolic centrality (node degree), but this effect is rather weak . Central nodes also have a very slight tendency to be more variable between animals after accounting for the number of mapped reads for networks 50N and 100N , but no such effect was seen for 25N.We were concerned that the number of reads that mapped to a reaction might simply be a function of the number of known enzyme sequences for that reaction. For those nodes with at least one read mapped, there is a statistically significant correlation between the number of reads that mapped to a reaction and the number of known enzyme sequences for that reaction . Moreover, there are 2022 reactions with mapped sequence reads compared with 122 OTUs detected, meaning that the metabolic network in fact has more potential points of variation.The two animals are much more similar in their enzyme node profiles than in their OTUs: 74% of the reads between the two animals matched at the node level. A similar situation was observed when considering the between-animal correlation in OTU counts or in nodes with mapped reads: the OTU mapping was more variable between individuals than was the node mapping, especially when considering non-parametric correlation statistics Figure  versus Cinterface metabolites: three VFAs and the twenty amino acids . These interface metabolites allowed us to infer the layered networks of Figures We next sought to assess how the microbiome might interact metabolically with the bovine host by inferring a host metabolic network. To do so, we first used our previously described orthology inference tool  to map tWe used these merged networks to measure how closely a given microbial reaction interacts with the host's metabolism. A microbial reaction that involves one of the interface metabolites has distance 0 from the host (and vice versa for host reactions). If a reaction involves a metabolite that is also involved in one of the distance 0 reactions (but does not itself possess an interface metabolite), that reaction has distance 1, and so forth. Note that interface metabolites were considered whether or not they were also defined as currency metabolites (see above). All of our observations also hold for a larger set of interface metabolites including the VFAs, the amino acids and human extracellular metabolites . Supplemental Figure S2 illustrates how the network structure changes using this larger interface set.p) and the average number of reads that mapped to a node (r) for all three networks .This layered network structure has several features that suggest that it reflects an underlying biological reality. There is a strong correlation between the distance to the host network (layer number) and the proportion of nodes with at least one mapped read pair .Figure We can also make limited inferences regarding the set of metabolites that are present in the microbiome by assessing the proteins that are found there and the reactions that they catalyze. We first ranked the interface metabolites by the number of read pairs that mapped to each microbial reaction that involved such an interface metabolite. As can be seen in Figure P < 0.001 for all three networks). Moreover, the two animals were more similar in their metabolite profiles than would be expected by chance: for all reactions using each metabolite, we computed the net difference in normalized read count between animals. The sum of this statistic across all metabolites was much smaller than that found when the read counts were randomized between the two animals . Table The total set of metabolites inferred to be present in the microbiome (based on the enzymes present) is also non-random. The number of metabolites associated to nodes with mapped read pairs is smaller than would be expected if the same number of nodes were selected at random (Considering that much of ruminal nutrition is thought to be provided by VFAs , we nextWe have presented an example where two bovine ruminal microbiomes that appeared rather different at the taxonomic level were much more similar in their metabolisms. While we do not, on the basis of two animals, claim this observation is universally true, it is in keeping with the known complexity of microbial ecosystems, where it is both possible to create taxonomically distinct assemblages with similar metabolic properties and taxonomically similar ones with differing metabolic properties ,55. It aWhile previous work has compared taxonomy and gene complements ,17,21–24It would be very desirable to understand this difference in how feed is used for growth using predictive stoichiometric metabolic models ,57–58. UThe conclusion that these two steers are functionally similar in their metagenomic metabolic networks is hardly unexpected given the shared environment and diet. However, the fact that detectable differences are evident even under these rather controlled conditions, suggests another point: there is more than one way to build an ecosystem . This poThis last result has an interesting linkage to one of the more surprising discoveries of systems biology: the highly redundant structure of metabolic networks ,63. ThisUnfiltered metagenomic sequences are available from NCBI's short read archive under project accession number PRJNA291523.


Rapid advances in mass spectrometry have allowed for estimates of absolute concentrations across entire proteomes, permitting the interrogation of many important biological questions. Here, we focus on a quantitative aspect of human cancer cell metabolism that has been limited by a paucity of available data on the abundance of metabolic enzymes. We integrate data from recent measurements of absolute protein concentration to analyze the statistics of protein abundance across the human metabolic network. At a global level, we find that the enzymes in glycolysis comprise approximately half of the total amount of metabolic proteins and can constitute up to 10% of the entire proteome. We then use this analysis to investigate several outstanding problems in cancer metabolism, including the diversion of glycolytic flux for biosynthesis, the relative contribution of nitrogen assimilating pathways, and the origin of cellular redox potential. We find many consistencies with current models, identify several inconsistencies, and find generalities that extend beyond current understanding. Together our results demonstrate that a relatively simple analysis of the abundance of metabolic enzymes was able to reveal many insights into the organization of the human cancer cell metabolic network. Metabolism constitutes a fundamental component of cell physiology. It allows for the processing of nutrients through chemical reaction networks, resulting in the production of energy and biosynthetic components and regulation of signal transduction processes by affecting the levels of metabolites that control the activity of proteins. Its function is essential for human health and its aberrant status is a hallmark of many diseases,2. A quaOne major limitation in this systems level understanding stems from the lack of quantitative measurements of protein abundance. The absPrevious studies have carried out extensive analyses of the transcriptional abundance of metabolic genes. These sAdvances in mass spectrometry based proteomics have allowed for in depth identification and quantitation of mammalian proteomes from biological samples–17. Theshttp://wzw.tum.de/proteomics/nci60. We began by filtering out proteins in the CPC dataset that were detected in only one sample or tissue type. These sample proteins also contained a far lower average CPC than all other samples  indicating that they might not be relevant for making global predictions on metabolism. Each protein in this list was mapped to 86 known metabolic pathways using the Kyoto Encyclopedia of Genes and Genomes  mapping of genes to pathways. Any protein that was included in at least one pathway was included as part of the metabolic proteome. The average CPC values across all cell lines for each metabolic and non-metabolic protein were used to calculate the metabolic percentage. The pathway percentages were calculated in a similar manner, though, one protein could be involved in multiple pathways, and thus the sum of all percentages does not necessarily equal 100%. In order to calculate the various probability distribution functions of different protein classes, all of the CPC measurements across cell lines were inputted into PRISM (version 6.03), with a standardized analysis computing bin centers.To begin our analysis we considered the NCI-60 cell line panel which is a set of cell lines developed and maintained by the National Cancer Institute that has been used extensively for integrated molecular analyses and drug sensitivity profiling. The proFor each protein involved in the Glycolysis/Gluconeogenesis pathway from the KEGG database, the distribution was classified as the CPC values across all cell lines. The core glycolytic pathway was defined as the progressive steps through which glucose entering glycolysis is converted to lactate or can be diverted to multiple different biological pathways. In order to visualize the differences in protein counts throughout core glycolysis, a pathway was created in CytoScape (version 3.1.1) with the size of nodes corresponding to the average CPC of the respective proteins,21.In order to isolate metabolic pathways containing branching steps, we utilized the Recon 2.2 stoichiometry matrix to separate pathways where a single metabolite acted as a reactant to multiple different reactions—these were defined as our branches. Since sWe then separated the branches into 2 additional categories—one way leaning pathways where branching scores produced a score above. 8, and equally distributed pathways where the top 2 BD score was less than. 2 or the top 3 BD score was less than 0. Branches were filtered to make sure no reactions were repeated in each set. For both sets of branches, either the top 2 or top 3 involved enzymes—dependent of which type of score was used to differentiate them—were separated and mapped to their respective KEGG pathways. For each set, the number of enzymes falling into each pathway was summed and a Fischer’s Exact Test was performed to see if there were any pathways that differed significantly across the two branching sets. Ratios of counts were computed by dividing the number of involved One Sided enzymes by the number of Equally Distributed Enzymes for each of the KEGG pathways.th 2013) identifiers [We defined oxidoreductases as proteins that either had NADP+/NADPH or NAD+/NADH as the reactants or products. Both reactants and products were included so as to allow for proteins with reversible reactions. EC Numbers of appropriate reactions were extracted using the BRaunschweig ENzyme DAtabase  database and then mapped to their appropriate Uniprot (Release 2013_11) or Entrez  interface was used to obtain kinetic properties for all metabolic proteins. We excluded all values not referenced as a wild-type experiment  and further refined the list by excluding any outlier measurements. We then used a previously published list of available ΔG° values[10(CPC), log10(KM), ΔG° values for proteins for which we obtained all three of these variables  and producers  of NAD(P)H are subject of major research efforts as drug targets against cancer[We first attempted to analyze the relative usage of nitrogen, or which aminotransferases were most prevalent within a cell. Using the BRENDA database we isolated all aminotransferases that were detected within the dataset, and found that among the most abundant enzymes were GOT2, GLUD1, and IDH2 . Togetheize NADPH. A majorst cancer,33–36.M) and standard Gibbs Free Energies (ΔG°) of the reactions  and were therefore responsible for the overall lack of correlation between these three variables. This finding is in contrast to a previously held assumption that larger protein concentrations are required for reactions close to equilibrium[M and ΔG° for each reaction involving a given protein concentration appears uncorrelated. There were however a few exceptions to this general rule. First, the proteins in group 2  contained enzymes with either very large KM values or very low ΔG°. The extreme KM values indicate that these enzymes need a substantial buildup of substrates in order to result in an appreciable forward flux while reactions with very low ΔG° are highly irreversible reactions. Indeed, three enzymes with large KM values  directly drain glycolytic intermediates into biosynthetic pathways while three enzymes with very low ΔG°  utilize phosphoribosyl diphosphate (PRRP) derived from the pentose phosphate pathway for NAD(P)H and nucleotide synthesis. Also several enzymes in group 3  are involved in arginine, aspartate, glutamine metabolism, for which the metabolites have some of the highest intracellular concentrations and/or fluxes.Ultimately, we note that that the reaction rate or flux through a point in metabolism involves not only the enzyme concentration, but kinetic parameters and the thermodynamics of the chemical compounds involved in the reaction as well. These parameters include the Michaelis constant  derived from the label-free quantification (LFQ) output generated using the MaxQuant  software(XLSX)Click here for additional data file.S2 TableM values were retrieved from BRENDA and ΔG° from Henry et al.[Kry et al..(XLSX)Click here for additional data file.


Metabolic flux analysis (MFA) was used to constrain a flux balance metabolic model which included 671 biochemical and transport reactions within the central metabolism. This highly confident flux information was eventually used for comparative analysis of flux vs. transcript (metabolite). Metabolite profiling succeeded in identifying 79 intermediates within the central metabolism, some of which differed quantitatively between the two accessions and displayed a significant shift corresponding to flux. An RNA-Seq based transcriptome analysis revealed a large number of genes which were differentially transcribed in the two accessions, including some enzymes/proteins active in major metabolic pathways. With a few exceptions, differential activity in the major pathways  was not reflected in contrasting abundances of the relevant transcripts. The conclusion was that transcript abundance on its own cannot be used to infer metabolic activity/fluxes in central plant metabolism. This limitation needs to be borne in mind in evaluating transcriptome data and designing metabolic engineering experiments.An attempt has been made to define the extent to which metabolic flux in central plant metabolism is reflected by changes in the transcriptome and metabolome, based on an analysis of  Gaining an understanding of metabolism is a central goal of biology, as it defines the growth and development of an organism. In the ‘omics era, cell processes can be described at the level of the transcriptome, the proteome or the metabolome, or possibly combinations thereof. Although none of these approaches actually measure metabolic activity, the data obtained can be used to make indirect inferences. The direct determination of metabolic flux would be highly desirable, as it represents a highly informative aspect of the metabolic phenotype , an important temperate oilseed crop, and a close relative of the model plant Arabidopsis thaliana. Our data demonstrated a disconnect between transcript abundance and the corresponding metabolic flux. The seemingly low contribution of transcriptional regulation over metabolic flux control and the biological significance of this finding are discussed.The aim of the current study was to attempt to relate transcript abundance with metabolic flux on a genome-wide scale, with a view to assessing its relevance for understanding the central metabolism of a crop seed. The plant model employed was the developing embryo of oilseed rape (−2 s−1) and 60% relative humidity. Intact embryos were isolated 20 days post flowering and maintained for 10 days under 50 μmol quanta m−2 s−1 at 20°C in a liquid culture containing a source of organic carbon and nitrogen, as described by Schwender et al.  were grown under conditions of 18°C, a 16 h photoperiod  and total experimental time 5 h 40 min. To calculate the volumes of the different seed organs, the MRI-dataset was imported into the software AMIRA (Mercury Inc.) and image segmentation was conducted. The average signal in each of embryo organs was calculated as previously described  using an absolute quantification method , we designated a reaction “T”  if the flux magnitude is higher in accession 3170, “S” (starch responsive) if the flux magnitude is higher in 3231, and “N” if a flux is unchanged. For a difference to be judged as a change the numerical tolerance was 10−7 μmol/h. bna572+ is referenced to the Arabidopsis genome, i.e., reactions have associations with Arabidopsis gene identifiers (Gene-Protein-Reaction associations). As the B. napus transcriptome was annotated by sequence homology to Arabidopsis, differences in transcript abundance between the two accessions could be compared to differences in flux based on the common Arabidopsis reference.Experimental details and the analysis of data related to MFA and flux variability analysis are detailed in the accompanying paper by Hay et al. . In shorB. napus embryos was isolated using the Spectrum Plant Total RNA kit (Sigma) according to the manufacturer's protocol. The samples for transcriptome analysis were prepared using an Illumina kit following the manufacturer's instructions. Briefly, beads with Oligo(dT) were used to isolate poly(A) mRNA from the total RNA. Fragmentation buffer was added in order to convert mRNA into short fragments. Taking these short fragments as templates, random hexamer-priming was used to synthesize the first-strand cDNA. The second-strand cDNA was synthesized using buffer, dNTPs, RNaseH, and DNA polymerase I. Short fragments were purified with the QiaQuick PCR extraction kit and resolved with EB buffer for end repair and for addition of poly(A). Subsequently, the short fragments were connected with sequencing adapters. Following agarose gel electrophoresis, the suitable fragment fraction was selected for PCR amplification. Finally, the library was sequenced using Illumina HiSeq™ 2000 .The total RNA from the Brassica rapa and Brassica oleracea using the splice-aware aligner TopHat (v2.0.8b)  putative cDNA sequences by aligning RNA-seq reads to the genome references of diploid progenitors www.bioconductor.org) using default parameters were run for the normalization of the RNA-seq read count data. The negative binomial test implemented in DESeq was used to assess differential expression between the two genotypes. Variance stabilizing transformation  using the org.At.tair.db v2.9.0 package (www.bioconductor.org). A Fisher exact test, as implemented in topGO v2.12.0 (www.bioconductor.org), was employed to test for the significance of category enrichment  to a particular functional category, GO annotations were retrieved from TAIR (http://primer3.ut.ee) to generate an amplicon size of 150–200 bp, targeted mainly the 3′-UTR of the selected genes (three pairs of primers per gene). The specificity and amplification efficiency of each primer pair was checked by means of running standard curves with melting curves. Each assay comprised three biological replicates, each of which was repeated three times. Relative transcript abundances were estimated using the 2-ΔΔCt method . A 100 ng template of this cDNA provided the template for a qPCR based on the SYBR® Green PCR Master Mix . The necessary primers, designed with Primer3 software (RNASeq data derived from this study (accession SRP047515), including all project and biosample data were made publicly available under the following links:http://www.ncbi.nlm.nih.gov/bioproject/?term=PRJNA262144http://www.ncbi.nlm.nih.gov/biosample/?term=SRS709415http://www.ncbi.nlm.nih.gov/biosample/?term=SRS717382.http://mapman.gabipd.org) was used for the functional characterization of DTGs. The threshold for significance was set to 0.01 with a minimum log2 (fold change) of 2. Differentially expressed transcripts that exhibited similarity to annotated A. thaliana genes, but showed a different trend in expression level were sorted out for further analysis with MapMan software.The MapMan visualization tool  as the major class of storage lipid. The flux data consist of flux variability bounds, calculated using the extended bna572+ stoichiometric model  and flux-change-value are positive in accession 3170 vs. 3231 or vice versa. VANTED was used to create a simple hierarchical map of the bna572+ model , we selected two accessions: 3170 accumulated more lipid but slightly less dry matter in its mature seed than 3231  and genome wide transcript profiling (RNA-sequencing). As detailed in the Hay et al. , followed by organic acids and free amino acids  between the accessions were accompanied by obvious shifts in the corresponding intermediates. The outcome of the combined analysis is presented in Figure In order to compare metabolite profiles with net flux rates  to the two rapeseed accessions ; the dataset is listed in Supplementary Table Based on the definition of differential gene expression , the RNA-Seq data suggested that 2156 transcripts were more abundant in accession 3170 than in 3231 (up-regulated DTGs), while 1958 were less abundant (down-regulated DTGs) . Supplementary Table Arabidopsis associated gene identifiers. Arabidopsis related MapMan ontology is also shown  and starch (higher in 3231) content and in analogy to the flux responsiveness types “T”  and “S” , we designated significantly higher transcript levels as “T” and “S,” respectively. For further interpretation the genome of the closely related model plant species ls Table . For 847ls Table .Arabidopsis genes  while others were down-regulated  in high-oil accession.The presence of DTGs within the MAPMAN category “regulation” provided some leads to explain the contrasting metabolic phenotypes of the accessions Figure . There wArabidopsis genes map to 545 reactions. 860 of these genes where found in the B. napus transcript annotations. Supplementary Table In the bna572+ metabolic model, 966 The generic photon uptake flux in reaction #6  is found TAG responsive. Note that the embryo culture experiment of the two accessions took place in parallel under the same light conditions. However, this observation might be explainable considering the indication of up-regulation of photosynthetic genes in the high oil accession Table . This suThe metabolic network derived from the bna572+ model comprised 515 nodes, with some model reactions for metabolite uptake and secondary pathways having been excluded. This set of reactions is shown as Figure Overall, there is little evidence for a scenario where a positive fold change of one data domain (transcript) is leading to a corresponding fold change in the related data domain (flux). The inevitable conclusion was that transcript abundance on its own cannot be used to infer metabolic activity/fluxes.http://sourceforge.net/projects/vanted/), the ViewData-Addon can be readily installed, using the addon manager implemented in VANTED—this feature will enable the user to browse details of the data contained within each node. For example, it allows to easily explore multiple mappings by listing all of the Brassica transcript IDs that are related to one model reaction ID  were quite distinct Figure . The com2 fixation, to provide additional ATP/NADH and eventually to contribute to the light-dependent regulation of fatty acid synthesis  fatty acid synthesis pathway Figure . This fiB. napus has biological significance. Similar lack of correlation has been found for prokaryotic and eukaryotic microorganisms .In conclusion, this genome-wide study has revealed a remarkably low level of connectivity between transcript abundance and metabolic fluxes. With few exceptions , Hardy Rolletschek, Ljudmilla Borisjuk and Jörg Schwender designed the research. Ljudmilla Borisjuk analyzed data. H. Roll. (seed composition) and Jörg Schwender (13C-MFA) performed research, analyzed data, and wrote the paper. Jordan O. Hay analyzed data. Christina König performed research (qPCR), analyzed data and wrote the paper. Inga Hebbelmann performed research . Nicolas Heinzel performed research  and analyzed data. Matthias Klapperstück analyzed data  and wrote the paper. Eberhard Munz, Peter M. Jakob and Ljudmilla Borisjuk performed research (MRI) and analyzed data. Peter Denolf, Stefanie De Bodt, Henning Redestig and Evelyne Caestecker performed research  and analyzed data.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.


Mycobacterium tuberculosis after exposure to antibiotics using proteomics data and flux balance analysis (FBA). The use of FBA to study prokaryotic organisms is well-established and allows insights into the metabolic pathways chosen by the organisms under different environmental conditions. To apply FBA a specific objective function must be selected that represents the metabolic goal of the organism. FBA estimates the metabolism of the cell by linear programming constrained by the stoichiometry of the reactions in an in silico metabolic model of the organism. It is assumed that the metabolism of the organism works towards the specified objective function. A common objective is the maximization of biomass. However, this goal is not suitable for situations when the bacterium is exposed to antibiotics, as the goal of organisms in these cases is survival and not necessarily optimal growth. In this paper we propose a new approach for defining the FBA objective function in studies when the bacterium is under stress. The function is defined based on protein expression data. The proposed methodology is applied to the case when the bacterium is exposed to the drug mefloquine, but can be easily extended to other organisms, conditions or drugs. We compare our method with an alternative method that uses experimental data for adjusting flux constraints. We perform comparisons in terms of essential enzymes and agreement using enzyme abundances. Results indicate that using proteomics data to define FBA objective functions yields less essential reactions with zero flux and lower error rates in prediction accuracy. With flux variability analysis we observe that overall variability due to alternate optima is reduced with the incorporation of proteomics data. We believe that incorporating proteomics data in the objective function used in FBA may help obtain metabolic flux representations that better support experimentally observed features.We present a study of the metabolism of the  This is, for instance, the approach followed by the E-flux method  is the flux vector, and c is the vector of coefficients of the linear combination. The dimension N of both vectors is equal to the number of reactions (i.e. metabolic fluxes) in the model. In the case of biomass maximization, vector c is an all-zero vector except for a one (1.0) in the position corresponding to the biomass reaction:vbio is the corresponding flux for biomass in the model. In our method we propose to use the same linear combination of fluxes for the objective function, but instead of maximizing the biomass flux, we calculate the coefficients ck from proteomics data.In this section we describe our proposed objective function. We explain how proteomics data can be used to determine an objective function for FBA in cases where the organism is under drug-induced stress, and thus optimal growth should not be assumed as the metabolic goal of the cell. We propose to define the objective to be a linear combination of fluxes as in , 21. Howp containing the quantitative values of protein levels obtained with the proteomics experiment , the number K of identified proteins is only a subset of the whole proteome of the cell, a difficulty stemming from two facts; (1) the method performs identification by comparison of peptide fragments against a database, so that only previously identified proteins are accounted for and (2) not all proteins may be susceptible to the cleavage procedure.We first define a vector ment cf.  for one 6h control but not in sample day 1 mefloquine), we set the levels of all proteins absent from a sample to zero. It is also important to note that while the proteome experiment quantifies both enzymes and signaling proteins, vector p contains only the subset of proteins with enzymatic activity and that are present in the in silico model. Although this leaves a number of important regulatory proteins not accounted for, we propose to include regulatory information in a subsequent analysis.Moreover, since some proteins may not appear in a specific sample . For this reaction the catalytic proteins are combined in the following boolean expression:OR and AND respectively. The proteins in this expression are the two transferases Rv2612c (IGY178), Rv1822 (I6X2EA) and the synthase Rv0046c (I6X8D3), all involved in inositol synthesis , since the AND expression is calculated using the minimum of the two values in As is clear from the objective function We note that by using data from different time points it is possible to define different objective functions for different time points, something that it is not possible when either the more common objective biomass yield or any other time-independent objective function is used. In this work we assume that our proteomics data for the control group should not be significantly different even for different time points, thus we use an average value of these data to perform FBA for the control condition. Our proposed methodology focus on defining an objective function by using proteomics data. Therefore, our FBA constraints are unaltered and are the same as the ones used with the regular FBA procedure. This way, when we present results of comparisons between our method and the E-flux method, we are comparing two variants of the plain FBA procedure modified by the introduction of proteomics data: one method (E-flux) uses proteomics data to redefine flux constraints and a biomass objective function, while the method proposed here uses proteomics data to define the objective function and unconstrained internal fluxes (as in the regular FBA method).and are catalyzed by essential enzymes needed for growth as presented by [essential reactions .In this study we have performed comparisons of the proposed methodology with the alternative method E-flux . This meented by . Here weAs a validation step, we performed comparison of prediction error between our proposed method and the E-flux method for a control condition and treatment conditions in different time points. We perform FBA for both methods using randomly chosen subsets of our proteomics data and the remaining subset of proteins to evaluate the prediction of the model in terms of enzyme abundances. This cross-validation step was performed as follows: For one specific time point and experimental condition the set of proteomics data was randomly split in two groups using a 80/20 rule, i.e. 80% of the proteins were used to defined the objective function in our proposed method and to define normalized constraints for the E-flux method, while 20% of the proteins were used as a validation set to compare fluxes and enzyme abundances. This procedure was repeated 16 times with different random splits. The enzymes in the validation set were evaluated in the boolean expressions and the resulting values were used for comparison with the corresponding fluxes obtained with FBA. Normalized squared prediction error was used to evaluate prediction accuracy of the two methods. In doing so, we normalized the error by the number of reactions in the validation set, as without normalization different splits would result in a different number of reactions depending on the boolean expressions evaluated. The validation procedure was repeated and results obtained in different realizations are in agreement. In order to obtain some insight into the metabolic behavior for alternative optima, we perform a final step of flux variability analysis, again comparing both methods. Our results are presented and discussed in the next section.in silico genome-scale metabolic network of the Mycobacterium tuberculosis presented in [Using the reconstructed ented in , we perfented in . For eacessential reaction we mean a metabolic reaction catalyzed by enzymes considered essential for growth according to Sassetti et al. [First we compare the results of FBA for the biomass objective function and the objective function defined using quantitative proteomics data from the control condition only. We must check whether using a proteomics objective function instead of the more common biomass goal, still produces sound flux results. One possible way is to observe the number of reactions carrying zero flux that are considered essential, and where by an i et al. . In the i et al. , the numi et al. ). The rein silico model is the following:Mycobacterium tuberculosis. The names of metabolites in this stoichiometric equation follow the nomenclature of convenience used in the GSMN model and can be found in the additional data file 6 from [PE (L-1-phosphatidyl-ethanolamine), TAGbio (triacylglycerol), PIMs (phosphatidylinositol mannosides), LAM (lipoarabinomannan), MAPC , P-L-GLX (poly-L-glutamate-glutamine), CL (cardiolipin), LM (lipomannan), PI (phosphate).It is important to discuss further the need for a biomass constraint. In the GSMN, the biomass reaction is a convenience equation defined as a weighted linear combination of macromolecule precursors such as DNA, RNA, protein, other small molecules, essential cell wall components, etc. The biomass reaction used in our simulations with the GSMN-TB Since the biomass function above is an external convenience transport reaction in the model, when we modify the objective function from biomass to the one defined in terms of the proteomics data (which affect mainly intracellular reactions which are precursors of the components in the biomass equation), the consumption and production of biomass components will no longer be maximized, and the resulting optimal flux vector will be different from the one obtained when we assume biomass maximization. Moreover, since the proteomics objective function may produce a metabolic state with biomass flux zero even under the control, it is important to constrain the biomass equation to a minimum value so that conclusions are not off-target. In the above comparison we constrained biomass yield to the same value obtained with regular FBA when maximizing a biomass objective.It is important to note though, that our goal is not to use proteomics-defined objective functions as a replacement for biomass maximization, but rather for situations of drug stress. As a source of validation however, it is reasonable to expect that, by using control data to define the objective function, the metabolic functioning of the cell should be similar. That is why we performed comparisons for the control condition as well as for the treatment condition.t-test on the difference of the errors for the two methods and report in the last row the p-values for a significance level of 95% and 15 degrees of freedom. We observe that even for higher p-values, the error difference is consistently lower in the case of using the proposed methodology for all conditions. In After having compared essential reactions, we compared our proposed methodology with the E-flux method in terms of prediction error. To this end we performed several runs of FBA with a subset of the proteomics data and validated the results with the remaining subset, as explained in the previous section. Results for mean squared error of prediction are presented in In constraint-based optimization it may be possible that optimal solutions are not unique. Alternative optima represent situations where the metabolic system reaches the same optimal objective function value using a different set of reactions, which is possible due to redundancies inherent to the metabolic network. Therefore, we next use flux variability analysis (FVA)  with ourAlternative optima are responsible for the situation where different uses of the underlying network of metabolic reactions correspond to the same cellular function . By defiWe also observed, for each experimental condition, the flux variability in reactions catalyzed by essential enzymes according to the essentiality criterion in . It is iThe FVA simulations reveal that, besides reducing the number of reactions that show large variability, using the proteomics objective function also reduces the magnitudes of these variabilities when compared to using the biomass function. The obtained results indicate that there are clear advantages to use objective functions defined by experimental proteomics data, mainly in situations of cellular stress (e.g. antibiotics exposure), where biomass maximization may not be the best assumed objective. We believe that more research in this direction is required to further evaluate this new and promising approach to FBA.The metabolic model comprises 856 reactions for which an optimal flux is obtained with FBA. When we modify the objective function from biomass to one defined by proteomics data, out of 856 reactions, a small number (10%) of the reactions in the control condition present significant change in their optimal flux value (i.e. 76 reactions). It is important to note that by using an objective function defined in terms of proteomics data, as mentioned above, implicitly assumes that metabolic fluxes are mainly regulated by enzyme concentrations, disregarding the fact that their activity may also be regulated by metabolite concentrations or other signalling proteins. Nonetheless, it is a useful option whenever none of these extra data is used.katG—Rv1908c (P9WIE5), for peroxidase-catalase activity, in the control condition. All reaction names and formulae are available in [The intracellular fluxes that most greatly varied from one objective function to the other are part of metabolic pathways related to carbon source (glucose) degradation and energy production, as can be seen in the plot for the region with lower indices . Other two reactions with fluxes that varied significantly are R134, R363, due to the presence of high levels of protein lable in  in the akatG observed in proteomics may not translate into high enzymatic activity due to the presence of inhibitor molecules or other regulator proteins that are not being accounted for in the simple FBA optimization.Many proteins present both enzymatic as well as signal transduction roles in the cell, but in FBA only the enzymes are taken into account. It is therefore possible, that some proteins having high levels in the proteome for roles other than enzymatic activity, will produce spurious results in FBA. One important factor that may cause difficulties when using proteomics data to define the objective function is that enzyme activity is not simply a function of enzyme levels, but is also regulated by metabolite concentrations and other regulation mechanisms. This is actually a fact that can help with the understanding of metabolic regulation. If a proteomics-defined objective function is not close to the one obtained when biomass is maximized, it is possible that the main differences are largely due to lack of information on metabolite concentrations and enzyme regulation. As an example, the high levels of The incorporation of transcription factors  and reguin silico metabolic model itself (GSMN-TB) is not complete and many blanks are left in those parts of the metabolic network that are either not known, not implemented in the model, are presently not associated with specific enzymes or even have annotation inconsistencies. These factors, together with the lack of signalling information, may account for the major differences observed when proteomics is used to define an objective function.Lastly, two other facts may also cause interference in the FBA results. First, the limited number of proteins that a proteomics experiment can identify compared to the complete proteome of a cell. Further, the After having compared the metabolic flux results in the control condition, we now turn to compare the changes in metabolic configuration using only objective functions defined in terms of proteomics data for both control and drug conditions. We observe the resulting fold-change differences in metabolic fluxes between the two conditions. We limit the comparison to fluxes presenting fold-change larger than 2 or smaller than 0.5. We discuss the significance of the obtained fluxes by comparison with biological knowledge on the behavior of the bacterium when exposed to mefloquine, as presented in .The fold-change in flux is presented for each time point in Rv0904c (I6WZQ9), Rv3411c (I6X784) and Rv3515c (I6YCB1) show large fold-change values. None of these three genes are present in our proteomics data. However, the pathways in which these enzymes participate are correctly identified by FBA. For example, large metabolic fold-change is observed in reactions R156, R163 and R495, all pertaining to pathways for lipid biosynthesis, like the FAS1, where Rv0904c is the gene encoding the catalyzing enzyme. We note that these are predicted by FBA only on day 2 and day 4, but not on the 6 hours time point. Gene Rv3411c, encoding an enzyme participating in the pathway for nucleotide (purine) biosynthesis, although not available in proteomics, catalyzes a reaction in a pathway that is correctly predicted by FBA (in time point 6 hrs) to have larger fluxes upon mefloquine exposure. A similar conclusion can be drawn for the protein encoded by the gene Rv3515c. These results indicate that FBA can correctly predict reactions in pathways that have been shown to be more active upon mefloquine exposure.According to Table II in , upon exFBA results also show a large increase in biotin synthesis , which is a precursor molecule in the FAS1 system  of lipidRv2249c (I6X3P8) and Rv3302c (I6Y352) are not in the proteomics data, so that the flux is driven indirectly by the expression of other enzymes in the model.By using a proteomics-defined objective function for FBA allowed us to obtain a metabolic flux configuration on a per-time point basis, something that is not possible with maximization of biomass or any other function that is not time-dependent. We have observed this advantage with the biotin reactions discussed above. As another example, we observe that reaction R003, in the pathway for glycerol metabolism, presents flux changes over time. In the 6 hour sample this flux has fold-change 0.2, changing to 0.5 in day 2 and back to 0.2 in day 4. It is interesting to note that the genes coding for the enzymes that catalyze this reaction, Rv1127c (O06579), which is not in the proteomics data, however flux through it increases over 100 fold from time point 6hr to time point day 2.Another reaction with dynamic behavior is observed for reaction R069 in pyruvate metabolism. The enzyme catalyzing this reaction is encoded by R080), threonine biosynthesis , biotin biosynthesis , peptidoglycan  biosynthesis .In terms of metabolic pathways, pathways that consistently present large fold-change are degradation of branched-chain amino acids such as valine and isoleucine, of which several reactions are present in the top reactions in all three time points. In the case of studying metabolism to identify metabolic pathways used for survival one should observe the later time points, when bacteria are closer to death. In these time points, large fold-change are observed in pathways for propanoate metabolism . The proposed approach allows the derivation of a specific objective function for each treatment condition. Then, an optimal steady-state metabolic phenotype can be obtained by performing FBA for each specific time point.cn+1. This weighting could be used, for example, to limit the biomass contribution if biomass maximization is not expected to be the main metabolic goal of the cell under a specific experimental condition. Biomass yield can also be constrained directly using minimum and/or maximum reaction constraints in the linear program.The proposition of using proteomics in the definition of objective functions for FBA can be combined with other strategies. For instance, the proposed objective function can be complemented with a biomass term weighted by a suitable coefficient In this article we evaluated the possibility of using proteomics data to determine an experimental condition-dependent objective function for flux balance analysis. Three main advantages of using proteomics data to define the objective function for FBA are the following:Comparisons were performed in terms of number of reactions and enzymes essential for growth Click here for additional data file.S1 File(ZIP)Click here for additional data file.S1 Table(CSV)Click here for additional data file.S2 Table(CSV)Click here for additional data file.S3 Table(CSV)Click here for additional data file.