Gammaproteobacteria species.It is generally accepted that gene duplication followed by functional divergence is one of the main sources of metabolic diversity. In this regard, there is an increasing interest in the development of methods that allow the systematic identification of these evolutionary events in metabolism. Here, we used a method not based on biomolecular sequence analysis to compare and identify common and variable routes in the metabolism of 40 The metabolic maps deposited in the KEGG database were transformed into linear Enzymatic Step Sequences (ESS) by using the breadth-first search algorithm. These ESS represent subsequent enzymes linked to each other, where their catalytic activities are encoded in the Enzyme Commission numbers. The ESS were compared in an all-against-all (pairwise comparisons) approach by using a dynamic programming algorithm, leaving only a set of significant pairs.patchwork model in the evolution of metabolism in Gammaproteobacteria.From these comparisons, we identified a set of functionally conserved enzymatic steps in different metabolic maps, in which cell wall components and fatty acid and lysine biosynthesis were included. In addition, we found that pathways associated with biosynthesis share a higher proportion of similar ESS than degradation pathways and secondary metabolism pathways. Also, maps associated with the metabolism of similar compounds contain a high proportion of similar ESS, such as those maps from nucleotide metabolism pathways, in particular the inosine monophosphate pathway. Furthermore, diverse ESS associated with the low part of the glycolysis pathway were identified as functionally similar to multiple metabolic pathways. In summary, our comparisons may help to identify similar reactions in different metabolic pathways and could reinforce the The online version of this article (doi:10.1186/s12864-015-2113-0) contains supplementary material, which is available to authorized users. The study of the evolution of metabolism is central to understanding the adaptive processes of cellular life, the emergence of high levels of organization (multicellularity), and the diversity and complexity of the living world , 2. At pMetabolism can be considered one of the most ancient biological networks, where the nodes represent substrates and/or enzymes and the edges represent the relationships among them. From this perspective, the study of metabolic networks has focused on describing topological properties and has showed the existence of a structured network architecture –7. AnothGammaproteobacteria division. Gammaproteobacteria are excellent models to consider because they contain a large diversity of species [Escherichia coliK-12, for which a large number of molecular and functional mechanisms have been elucidated. In addition, Gammaproteobacteria include organisms widely distributed throughout diverse environments, such as the endocommensal bacterium Ruthia magnifica [Baumannia sp. and Buchnera sp., photoautotrophs such as Halorhodospira halophile [Yersinia spp. and Vibrio spp., among others [In this work, we ask whether there are groups of similar reactions in different or in the same metabolic pathways, which might suggest a transfer of enzymatic activities, and whether these groups can be used to define common and variable metabolic pathways in 40 organisms belonging to the  species , such asagnifica , obligatalophile , and mamg others , 18.patchwork model in the evolution of metabolism in Gammaproteobacteria.To this end, we implemented a general strategy that considers the transformation of the metabolic maps deposited in the KEGG database into linear Enzymatic Step Sequences (ESS) and their posterior comparison with a dynamic programming sequence alignment algorithm. From these comparisons, we show that maps associated with the metabolism of similar compounds also contain a high proportion of similar ESS. In addition, we evaluate the possible contribution of two ancient pathways, glycolysis and IMP, to the metabolic pathways growth. Finally, we consider that our comparisons may provide clues reinforcing the Gammaproteobacteria division, a collection of ESS was generated from their corresponding metabolic maps. In this regard, an ESS was defined as a linear collection of consecutive enzymatic reactions from a given substrate to a given product, in a similar way as a previously proposed definition of metabolic pathways [r2 = 0.78, p = 1.7x10-14) than small genomes   dataset. From this filtering, 7970 different nrESS were considered for posterior analyses. The nrESS length histogram was similar to that for the complete set of ESS, with a mean length of 5.4 and a mode equal to 4 Fig. . In thisIn a second step, the nrESS were compared by using the dynamic programming Needleman and Wunsh (NW) algorithm in an all-against-all strategy. The alignment generated by this algorithm was evaluated by using an entropy based normalized function that yields values in the interval from 0 to 1. Hence, values close to 0 mean less entropy and more homogeneous columns in the alignment, reflecting more similar nrESS. Conversely, values close to 1 reflect dissimilar nrESS.From these comparisons, we found that the distribution of the scores resembled an extreme value Gumbel distribution  and, in conjunction, they were present in more than 75 % of the species analyzed. Based on this definition, the set included 1484 sequences from 74 different metabolic maps, with 69 % of the total alignments corresponding to alignments between the same metabolic maps (1805 of 2633), whereas 31 % corresponded to alignments between different metabolic maps  moderately functionally conserved maps, with percentages between 30 % and 69 %; 3) barely functionally conserved, i.e., those maps with percentages between 1 % and 29 %; finally, 4) variable maps, i.e., with 0 % EC classified as functional conserved. From these data, less than one-third of the analyzed maps (24 of 86) were classified as highly or moderately functionally conserved, while more than two-thirds were considered as barely functionally conserved or variable. All these data showed that more than half of the metabolic maps analyzed did not exhibit common nrESS in Gammaproteobacteria and, by consequence, may be considered variable, suggesting a high variability in the metabolism of this bacterial division.To assess the nrESS similarity of each metabolic map as an indicator of functional conservation, we used the alignments that occurred within them , metabolism of some amino acids , components of the cell wall , metabolism of some cofactors , and novobiocin biosynthesis (00401). These functional similarity also correlate with the fact that amino acid metabolism pathways for valine, leucine, isoleucine, and lysine have been identified as pathways with diverse duplicated genes in the three cellular domains of life [In detail, maps classified as highly  of life , 23.functionally conserved. In this category were included the pathways for metabolism of purines (00230) and pyrimidines (00240), glycolysis/gluconeogenesis (00010), the citrate cycle (00020), metabolism of glycerophospholipids (00564), terpenoids backbone (00900), and some cofactors, like riboflavin (00740), nicotinamide (00760), folate (00790), and thiamine (00730). It is interesting that the central part of glycolysis (00010), the Embden-Meyerhof pathway, is partially conserved among Gammaproteobacteria  and fructose biphosphate aldolase (EC4.1.2.13) are considered variable. A similar result was observed with the glycolysis input, where the mechanisms by which the hexoses enter the pathway are variable. In addition, the enzymatic steps to transform pyruvate to lactate and the ethanolic fermentation from acetate are also variable. In a similar way, gluconeogenesis from oxaloacetate is partially functionally conserved in Gammaproteobacteria, where the enzymes allowing the input from the oxaloacetate  and the enzyme that dephosphorylates fructose 1,6-bisphosphate to fructose 6-phosphate  are considered variable. These results are congruent with those from a previous study, where it was concluded that glycolysis is a plastic pathway and that the lower part of the glycolysis pathway is the more conserved section among the three cellular domains [The second group includes those maps defined as moderately ria Fig. , whereasidines 000, glycolfunctionally conserved reactions that converge the synthesis of mono-, di-, and triphosphate ribonucleotides and deoxyribonucleotides. In the case of purine metabolism . Congruently, the classical synthesis of ATP (module M00049) and GTP (module M00050) from IMP is also functionally conserved, although there are many variable enzymatic steps that catalyze the production of nucleosides and nitrogenous bases. Finally, the pathways for degradation of purines via xanthine and allantoate utilization are variable in Gammaproteobacteria. Therefore, in purine metabolism we observed a general functional conservation of synthetic pathways and a general non-functional conservation of degradation pathways. These results, in conjunction with recent data suggesting that nucleotide metabolism is highly conserved across all the organisms [Another example is the case of purine 00230) and pyrimidine (00240) metabolism. In general, both metabolic maps show 0 and pyrrganisms , reinforrganisms , 27.Fig.functionally conserved, such as the pathway for glycerophospholipid metabolism (00564). We found that the biosynthetic pathways to CDP-diacylglycerol and then to phosphatidyl glycerol, phosphatidyl serine, and phosphatidyl ethanolamine are conserved, while the biosynthetic pathway to phosphatidyl choline and the degradation pathways are variable. A similar result arises for the biosynthesis of cofactors like thiamine-diphosphate (map 00730), riboflavin (map 00740), NAD+ and NADP+ (map 00760), and tetrahydrofolate (map 00790). In conjunction, it is possible to deduce a functional conservation pattern for Gammaproteobacteria, where some metabolic maps contain a biosynthesis-related core of similar enzymatic steps, and some variable steps that include the degradation of various compounds. These variable or dispensable steps may represent possible alternative pathways in different organisms and/or in different ecological niches, as has been previously suggested [A similar conservation pattern is observed in other metabolic maps classified as moderately uggested , 28.functionally conserved includes important processes, such as amino acid metabolism, fatty acid degradation (beta-oxidation), and glycerolipid metabolism. In this context, we identified many variable reactions in the map that describes alanine, aspartate, and glutamate metabolism (map 00250), suggesting the existence of alternative pathways to produce these compounds. In this regard, there are three possible enzymes that catalyze the conversion of L-glutamate to L-glutamine: one of them by a ligation reaction  and two by reversible hydrolysis  amidohydrolase, EC3.5.1.38). In particular, the L-glutamine (L-asparagine) amidohydrolase also catalyzes the deamination of asparagine to aspartate. This finding suggests more flexible networks for the production of amino acids and reinforces the notion of various alternative enzymes for the production of amino acids [Gammaproteobacteria; nevertheless, there are some alternative enzymes that may work as alternative paths for the synthesis of methionine. Interestingly, some of these alternative enzymes were identified as functionally conserved in this work, suggesting not only the absence of a conserved canonical route but also important alternative enzymatic steps.The group of metabolic maps classified as barely no acids . A similvariable maps include a high diversity of metabolisms types. Some of them contain few or fragmented enzymatic steps present in at least one Gammaproteobacteria species, suggesting the absence of those metabolic maps in this clade. However, other maps contain many enzymes present in Gammaproteobacteria; such as those for seleno compound metabolism, galactose metabolism, pentose phosphate and pentose metabolism, and glucuronate metabolism, among others. In general, the maps classified in this category represent pathways for degradation of uncommon compounds (xenobiotics) or for alternative carbon sources (carbohydrate metabolism). Altogether, these observations in addition to supporting the previously proposed idea concerning the reduced conservation of degradation related pathways; reinforce the notion of differential enzyme recruitment across the clade. Also, our results support the proposed preponderance of central carbon and anabolic pathways in the evolution of metabolism [Finally, the tabolism , 27, 29.core of similar enzymatic steps in Gammaproteobacteria. This core includes primarily reactions of the central carbon metabolism (low part of glycolysis and tricarboxylic acid cycle), and the biosynthetic pathways for nucleotides, cofactors and some amino acids. In addition this core is complemented with a set of variable pathways that primarily includes degradation pathways for carbohydrates, amino acids and xenobiotics that may be essential to the particular life style of each organism.In summary, all these data allow the identification of a Gammaproteobacteria is available as KEGG weblinks in Additional file The complete set of functional conservation of metabolic maps in In this section, we asked whether the similarities between nrESS might help to identify those metabolic maps that convert similar compounds and uncover explicitly the functional relations between metabolic maps. In this regard, we explored the general similarities between metabolic maps identified by nrESS comparisons. To do so, the total number of shared alignments between each pair of metabolic maps was calculated, considering only those alignments with scores of ≤0.3. The counts of the shared alignments were normalized to the total number of alignments for each map and used as similarity vectors in a hierarchical clustering analysis with the Spearman rank correlation as similarity measure Fig. . Considefunctionally conserved pathways can be used to identify the possible recruitment patterns in the metabolism of Gammaproteobacteria. In this context, the corresponding nrESS of the lower part of the glycolysis pathway and the IMP pathway for de novo synthesis of purines were used to scan the complete nrESS dataset. Both pathways are considered ancient [+ or NADP+ as acceptor), 2.7.1 , and 4.2.1 (carbon-oxygen hydrolyases) are within the top 10 in nrESS database abundance. This result shows a broad similarity of the lower part of the glycolysis pathway with many other metabolic processes and suggests similar catalytic processes are used to transform some compounds in different metabolic maps. In turn, this observation suggests an outstanding proportion of enzyme recruitment events from glycolysis to other metabolic pathways and may reflect the utilization of similar products generated for similar reactions in different metabolic maps. On the other hand, the major number of hits for the IMP pathway corresponds to alignments within the same map, suggesting that this pathway has increased its size by duplication and recruitment of its own enzymes. Although both metabolic pathways may be considered ancient and were classified as functional conserved in this study, the patterns of functional similarities are different and may reflect the constraints of enzyme recruitment and the ubiquity of some types of compounds.Based on the previous sections, we ask if  ancient , 30. We In this work we used a simple workflow for the comparative study of metabolism through the alignment of linear sequences of ESS. The metabolic maps stored in KEGG were transformed into linear ESS by using an exhaustive and well-defined graph search algorithm. Then, the ESS were compared to identify the commonalities and differences between them. This approach allows the identification of similarities at the Enzymatic Step Sequences (ESS) level in a set of metabolic pathways. In this regard, the use of the functional information of the enzyme activity rather than the (protein and DNA) sequence information suggest that metabolism comprises a complex and dynamic network that may have different proteins to achieve the same or similar function.Diverse methods for the alignment of biological networks have been suggested, such as protein-protein interaction networks (for some examples see references –33) and In this work we used the alignment of linear enzymatic step sequences, similar to the previously described approaches , 40, whecore of metabolic pathways associated with central carbohydrate metabolism, lipid, cell wall, and cofactors, and biosynthetic pathways. In contrast, variable maps are those associated with degradation pathways, except the glucose-related pathways and the TCA cycle. In addition, amino acid metabolism is an example of a pathway with multiple routes to yield similar compounds from different routes, characterized for alternative pathways.Based on these comparisons, we detected a E. coli bacterial strains, where a small proportion of universal protein families [Gammaproteobacteria metabolism.In addition, two scenarios can be suggested to exemplify the growth of the metabolism. The first one, associated to the glycolysis, where a significant proportion of functional similarities from this pathway were observed in other metabolic pathways; suggesting the utilization of similar substrates/products processed by similar reactions in different metabolic maps. The second scenario is associated to the high number of hits for the IMP pathway associated to alignments within the same map, suggesting that this pathway possibly has increased its size by duplication and recruitment of its own enzymes and arising the possibility of major biochemical coupling restrictions for the recruitment of the enzymes in the IMP pathway. Therefore, the different patterns of ESS similarities of two ancient pathways suggest that the recruitment of catalytic activities in the metabolism is restricted by the metabolic context, being not a random phenomenon. Albeit our data suggest functional and, probably, evolutionary conservation of diverse catalytic steps, additional information must be considered to have a better approximation of metabolism evolution, such as gene transfer and gene loss, among other processes. For this reason, we do not exclude the possibility of diverse genetic phenomena, such as the continuum interchange of genetic material that diminishing the border between bacterial species, as it has been recently described in families  and a lafamilies  have beefamilies , capturiGammaproteobacteria, the method can be extended to any organism or clade for which there is metabolic information. Finally, we understand that the approach described here does not consider the effect of promiscuous enzymes, defined as those enzymes with more than two different E.C. numbers. However, previous analysis have described that around 10 % of the total enzymatic repertoire in bacterial and archaeal organisms corresponds to promiscuous enzymes [Therefore, the method described here is able to identify alternative enzymes involved in similar metabolic processes, and although the conclusions can be restricted to the metabolism covered by  enzymes , 44, sugGammaproteobacteria species. These organisms were selected from the 275 Gammaproteobacteria genomes included in the KEGG database as of June 2011 [Gammaproteobacteria species. These organisms are representative of the division as it is shown in Additional file In this study we included the small-molecule metabolism of 40 different une 2011 . We chosune 2011 , with a Gammaproteobacteria in June 2011 from the KEGG database. Based on these metabolic maps, the ESS were constructed by using the BFS algorithm. In brief, a directed graphical representation of each metabolic map was created in which the nodes represented enzymes and the edges represented a shared substrate/product between two enzymes. This representation takes into account the reversibility of the reactions. In a posterior step, a group of BFS trees was generated for each metabolic map from a set of initialization nodes, used as roots. An initialization node was defined by two criteria: a node which substrate is not catalyzed by another enzyme in the metabolic map, and a node which substrate comes from another metabolic map and with two or fewer neighbors in the graph. These criteria represent the metabolic input for each pathway; the first criterion considers the substrates not created in the same pathway, and the second one considers the connections with other pathways. Each initialization node was used as a root for the construction of a BFS tree. Finally, each tree was used as a guide for the construction of the ESS. Thus, a BFS tree creates as many ESS as the number of branches it has. The graph representation of the metabolic maps and the BFS trees were generated using the Networkx Python module [We downloaded the KGML files (version 0.71) that describe the metabolic maps (pathways) of 40 n module  Fig. 6)GammaprotIn a posterior stage, ESS were organized in a relational database. In this database, each EC number contained in a sequence was related to its corresponding protein(s), species, metabolic map. This database has a high degree of redundancy, because an ESS may be the same in different species. Thus, a nrESS dataset was constructed by filtering identical ESS and leaving only one representative. Each ESS in the nrESS dataset is linked to the original ESS. All analyses were conducted using the nrESS dataset and referring to the original data when necessary. The ESS and nrESS data are provided as supplementary material  algorithm as described in reference . This alTo determine the statistical significance of the nrESS alignments, we compared the alignment scores of the real database against the scores from10 different random databases. These random sequences were constructed by shuffling the EC number content of the entire database, maintaining the nrESS length and EC composition of the original sequences. Each random database was submitted to the same all-versus-all alignment approach used for the real data, and the distribution of alignment scores considered the mean ± SD. The threshold considered statistically significant corresponded to a score of ≤0.3, i.e., that point with higher dispersion of the real data relative to the mean random databases scores and where the loss of nrESS due to extreme dissimilarity was less than 1 %, i.e. this threshold includes the 99 % of the nrESS.functionally conserved enzymatic steps in Gammaproteobacteria for each metabolic map. Two nrESS were considered conserved if their alignment scores were below or equal to 0.3 and if, in conjunction, they were present in more than 75 % of the organisms. This criterion was employed because we assumed that a pair of conserved ESS would be shared by at least all of the species with genomes greater than 2000 ORFs, i.e., 30 of the 40 Gammaproteobacteria organisms. From the ESS that fulfilled this criterion, we selected those that corresponded to the same metabolic map. This subset of sequences was named the Metabolic Map Functional Conserved Dataset (MMFCD). To identify the conserved ESS, the aligned identical EC numbers from each alignment were mapped in the corresponding position in KEGG metabolic maps.We used the information provided by the nrESS pairwise alignments to identify the http://www.tm4.org/mev.html). The similarity between maps was calculated with the Spearman’s rank correlation, and elements were clustered with the average method. A cutoff of 0.46 of the total length of the dendogram was used to classify the metabolic maps into groups and is displayed with the E.T.E. 2 Python toolkit [In order to identify the functional similarities among metabolic maps, we selected a subset of nrESS pairwise alignments with score values of ≤0.3. These alignments were used to construct a similarity matrix where each cell corresponded to the count of the alignments shared by each pair of metabolic maps. The rows representing the metabolic maps were normalized by the total alignments in each row. The matrix was used as input to a hierarchical clustering analysis with the program MeV4 ( toolkit .


Methane-utilizing bacteria (methanotrophs) are capable of growth on methane and are attractive systems for bio-catalysis. However, the application of natural methanotrophic strains to large-scale production of value-added chemicals/biofuels requires a number of physiological and genetic alterations. An accurate metabolic model coupled with flux balance analysis can provide a solid interpretative framework for experimental data analyses and integration.Methylomicrobium buryatense strain 5G(B1) was constructed and used for evaluating metabolic engineering strategies for biofuels and chemical production with a methanotrophic bacterium as the catalytic platform. The initial metabolic reconstruction was based on whole-genome predictions. Each metabolic step was manually verified, gapfilled, and modified in accordance with genome-wide expression data. The final model incorporates a total of 841 reactions (in 167 metabolic pathways). Of these, up to 400 reactions were recruited to produce 118 intracellular metabolites. The flux balance simulations suggest that only the transfer of electrons from methanol oxidation to methane oxidation steps can support measured growth and methane/oxygen consumption parameters, while the scenario employing NADH as a possible source of electrons for particulate methane monooxygenase cannot. Direct coupling between methane oxidation and methanol oxidation accounts for most of the membrane-associated methane monooxygenase activity. However the best fit to experimental results is achieved only after assuming that the efficiency of direct coupling depends on growth conditions and additional NADH input . The additional input is proposed to cover loss of electrons through inefficiency and to sustain methane oxidation at perturbations or support uphill electron transfer. Finally, the model was used for testing the carbon conversion efficiency of different pathways for C1-utilization, including different variants of the ribulose monophosphate pathway and the serine cycle.A stoichiometric flux balance model of M. buryatense strains.We demonstrate that the metabolic model can provide an effective tool for predicting metabolic parameters for different nutrients and genetic perturbations, and as such, should be valuable for metabolic engineering of the central metabolism of The online version of this article (doi:10.1186/s12934-015-0377-3) contains supplementary material, which is available to authorized users. Methane, as a pipeline-based, cheap source of carbon is becoming an attractive feedstock for biosynthesis –4. TakinMethane is a natural element of the global carbon cycle , 9. The 1-metabolism are relatively well established, only a few mathematical descriptions of methane or methanol utilization have been developed . B. Bredox ion Fig. b, c.+/NADH = 8.32 (with 92 % efficiency) . Br. Br2:CH4direct coupling as the most optimal solution for methane oxidation . In that case, the loss of electrons would be refilled by Complex I/III. To evaluate this hypothesis, we tested two scenarios in which a part of the NADH produced from formaldehyde oxidation was used to replenish (reenergize) methane oxidation. The outcomes of the scenario 1 (1 mol of NADH supports oxidation of 10 mol of methane) correlate best with all experimental data obtained for unlimited growth on methane , while the growth rate and CCE were too low  with 1/3 NADH input, while electrons from methanol oxidation enter the respiration chain ; and (2) 1/2 of NADH input, while electrons from methanol oxidation enter the respiration chain . Predictions from scenario 1 show some correlation with biomass growth, while scenario 2 shows good correlation with oxygen-consumption at unlimited conditions.direct coupling and uphill electron transfer is the amount of NADH needed to drive methane oxidation; the exact organization of the oxidation machinery still requires additional experimental validation. In addition, it is possible that some other part of the metabolic network is not correctly reconstructed. However, the triple constraints of growth rate, CCE, and O2;CH4 ratio and the body of evidence supporting the components of the metabolic network make it unlikely that an error in the metabolic network could be sufficiently large to support the redox arm results.Based on our in silico simulation data and experimental parameters, we propose that methane oxidation should be considered as a dynamic process that depends on electron transfer from a methanol oxidation step to methane oxidation. The exact nature of the transfer remains to be established. It should be kept in mind that for all in silico experiments the only fundamental difference between low-efficiency 1-biocatalysis awaits additional experimental data. However, a direct coupling with an input from respiration was assumed to be the most likely mode for methane oxidation, since it correlates best with the experimental results. That mode has been used to test the contribution of different assimilatory pathways.Confirmation of this part of CM. buryatense 5G(B1) for the direct coupling metabolic mode. The flux distribution between the EMP and EDD pathways was set at 3 to 1 as previously reported for a related strain  step . The incorporation of phosphoketolase is predicated to significantly improve the carbon conversion efficiencies of glucose-utilizing microbes, as well as methanol-consuming, engineered microbes , after which the silylated monosaccharides were identified by GC–MS (Agilent GC 7890A—Agilent MS 597C inert XL HSD) with the following analysis parameters: HP5 MS column , 1 µl injected, inlet at 280 °C, running at constant He flow of 1 mL/min. The oven ramp program  was developed for optimal resolution of the anomeric silylated monosaccharide derivatives and can be summarized as follows: 80 °C for 2 min; 5 °C/min to 175 °C, hold for 1 min; 70 °C/min to 130 °C; 70 °C/min to 190 °C; 70 °C/min to 165 °C, hold for 1 min; 3 °C/min to 174 °C, hold for 2 min; 5 °C/min to 230 °C, hold for 3 min. Integration and calibration calculations were carried out by Agilent Chemstation for GC-FID (B.04.01).Each parameter shown in Table id assay . For EPSSterols and squalene were quantified in extractable lipids; in brief, chloroform:methanol (2:1 v/v) was used for lipid extraction from 100 mg of freeze-dried harvested cells using an accelerated solvent extractor (ThermoScientific), after which the lipids were analyzed by GC directly without derivatization. Identification was carried out by GC–MS (as above) with the following parameters: inlet at 350 °C, running at constant He flow of 1 mL/min. The oven ramp program  was developed for optimal resolution of hydrocarbons, sterols and hopanoids; 100 °C for 1 min; 10 °C/min to 270 °C, hold for 7 min; 20 °C/min to 325 °C. Integration and calibration calculations were carried out by Agilent Chemstation for GC-FID after data was normalized for the addition of cholestane as an internal standard.The scaffolds and annotations for 5GB1 were obtained from JGI’s IMG and converted into PathwayTools Pathologic input . This instop solution [g at 4 °C for 10 min. Total RNA samples from two biological replicates of exponentially grown batch cultures and two biological replicates of bioreactor cultures were prepared and sequenced as previously described [bwa version 0.7.8-r455 under default options [SAMTools version 0.1.19-44428 cd and assigned to ORFs using HTSeq version 0.5.4p3 in the intersection-nonempty mode and the final abundances were examined as DeSeq 2 normalized counts and reads per kilobase of transcript per million reads mapped (RPKM) [Samples of RNA were extracted from exponentially grown batch cultures (at OD = 0.6–0.7), grown as described above, and from cells grown in bioreactors . The cesolution , the celescribed . The raw options . The alid (RPKM) –65.3 (1 g/L) was replaced with 0.3 g/L of urea or 0.53 g/L of ammonium chloride; MgSO4 (0.2 g/L) was replaced with 0.2 g/L of sodium sulfide nonahydrate and 0.16 g/L of magnesium chloride. For low pH medium the carbonate buffer was omitted and phosphate solution  was used as a buffer.To test different sources of nitrogen and/or sulfur sources, the following modifications of the growth medium  were mad


The computational analysis of phototrophic growth using constraint-based optimization requires to go beyond current time-invariant implementations of flux-balance analysis (FBA). Phototrophic organisms, such as cyanobacteria, rely on harvesting the sun’s energy for the conversion of atmospheric CO2 into organic carbon, hence their metabolism follows a strongly diurnal lifestyle. We describe the growth of cyanobacteria in a periodic environment using a new method called conditional FBA. Our approach enables us to incorporate the temporal organization and conditional dependencies into a constraint-based description of phototrophic metabolism. Specifically, we take into account that cellular processes require resources that are themselves products of metabolism. Phototrophic growth can therefore be formulated as a time-dependent linear optimization problem, such that optimal growth requires a differential allocation of resources during different times of the day. Conditional FBA then allows us to simulate phototrophic growth of an average cell in an environment with varying light intensity, resulting in dynamic time-courses for all involved reaction fluxes, as well as changes in biomass composition over a diurnal cycle. Our results are in good agreement with several known facts about the temporal organization of phototrophic growth and have implications for further analysis of resource allocation problems in phototrophic metabolism. Constraint-based modeling of cellular metabolism, most notably flux-balance analysis (FBA), has become a versatile tool to study the functioning and optimality of large-scale metabolic networks1The assumption of a time-invariant metabolism, however, does not always hold. Almost all organisms are known to exhibit temporal variations in their metabolism, for example in response to environmental conditions, such as nutrient availability or diurnal rhythms, or imposed by different cellular requirements during cellular growth and division.In particular phototrophic organisms, whose metabolism is based on harvesting the sun’s energy, typically exhibit a diurnal lifestyle. Phototrophic metabolism involves at least two distinct phases: a light phase that includes synthesis of cellular precursors as well as storage compounds, and a subsequent dark phase where storage compounds are mobilized to ensure survival in the absence of light. Typically, the transition between these two states is not abrupt and phototrophic metabolism is characterized by continuous temporal change.et al.et al.et al.2 fixation requires energy and redox equivalents in the form of ATP and NADPH, derived from the photosynthetic light reactions. Light harvesting makes use of pigments that are products of metabolism. Clearly, such autocatalytic cycles give rise to multiple interdependencies within cellular metabolism. The temporal order in which the cellular building blocks are synthesized itself influences the metabolic capacity at subsequent timepoints. It can be assumed, therefore, that the cellular machinery has evolved a suitable regulatory structure to ensure an appropriate, if not optimal, temporal allocation of its resources. We note that the assumption of such optimally adapted allocation of cellular resources is commonly employed in conventional FBA. Furthermore, the fact that cellular growth and resource allocation, at least to a certain extent, can be understood based on the assumption of optimal resource allocation, has been demonstrated experimentally19Synechocystis sp. PCC 6803 over a full diurnal cycle. Our ultimate aim is to understand the principles of temporal resource allocation for phototrophic growth in a periodic environment.As yet, such temporal transitions are difficult to describe using conventional FBA. While there have been a number of recent metabolic reconstructions for phototrophic organisms, including reconstructions for cyanobacteria3456891011131415Our approach is based on the fact that cellular growth is inherently autocatalytic. We implement the corresponding constraint-based optimization problem by constraining each flux by the amount or activity of the compound that facilitates the respective flux. In particular, we assume that the flux through any metabolic reaction is constrained by the amount of the respective enzyme, the total synthesis rate of enzymes is constrained by the amount of ribosomes, and light harvesting is constrained by the amount of pigments. Importantly, each of these compounds is a product of metabolism itself. To simulate time-dependent metabolism, time is subdivided into discrete intervals, such that fluxes at different time intervals are distinct entities. Intracellular compounds are allowed to accumulate and the difference between synthesis and consumption rates over time corresponds to an increase or decrease of the respective amounts. The total amount of accumulated compounds can itself be subject to minimization to reflect cellular size constraints. The network can adopt any flux distribution that is consistent with the specified constraints. A flux distribution is obtained by maximizing a given objective function. Suitable objective functions are the accumulated concentration of a target compound over the entire simulation period, or, in our case, maximal growth of the compound amount vector over a full diurnal period.X, Y, and Z. We assume that the compound X can be taken up with a rate ν1 and its conversion into the final product Z is catalyzed by the enzyme Y. Hence the respective conversion flux ν3 is bounded by the availability of Y. The enzyme Y is itself synthesized from X, the respective reaction ν2 is again catalyzed by Y. Synthesis of Z can then be cast as an optimization problem, such that the compound X is balanced whereas the compounds Y and Z are allowed to accumulate. The corresponding global optimization problem can be described by a set of linear constraints, given in M(tend) is a multiple of the initial compound amounts M(tstart),Our approach is illustrated in T = tend − tstart denotes the time interval, typically a full diurnal period. The optimization objective is to maximize the factor α. Importantly, we do not aim to pre-assign the detailed composition of the compound amount vector M. Rather, the cellular composition emerges as a result of the optimization problem. Only for compounds without immediate catalytic activity, the optimization problem must be supplemented with additional constraints on minimal compound quotas to ensure their production within the simulation period. In the example shown in Z is 0.5. The quota is enforced only at a single timepoint (simulation start) and the relative amount may change during the simulation.where Y is synthesized. At a time t ≈ 6.2 h, the system undergoes a metabolic switch. At this point, the system starts to synthesize the target compound Z which is subsequently accumulated linearly during the remaining simulation period. In the following, we employ this approach to simulate cyanobacterial growth in a periodic environment. Definitions and computational implementations are detailed in the section “Methods”. Time courses of compound synthesis are reported in absolute amounts, unless otherwise noted, not in concentrations relative to total biomass. We note that, at this point, we neglect potential influences of cell division and only consider diurnal cellular growth. The computational results can therefore be interpreted to represent an average cell in a growing culture under diurnal illumination.The results of the time-dependent optimization problem are shown in Synechocystis sp. PCC 6803, based on an available genome-scale reconstruction of the organism2 uptake, carbon fixation by the Calvin-Benson (CB) cycle, accumulation of glycogen as a storage compound, uptake of inorganic ions, the synthesis of precursors for cellular growth, as well as a TCA cycle and respiration to account for storage-based metabolism in the absence of light. The model, depicted in 2 and reduction of plastoquinone (QH2). Transport of the electron down the electron transport chain (ETC) results in an accumulation of protons in the thylakoid lumen and generation of NADPH via photosystem I (PSI) and the FNR complex. Cyclic electron transfer is encoded as a distinct process mediated by PSI. We note that the molecular details of cyclic electron transport are as yet not fully understood. ATP is regenerated by the ATPase complex. The ETC also incorporates the enzyme complex NDH and cytochrome C oxidase to allow for respiratory activity in the absence of light.To study phototrophic growth over a full diurnal cycle, we implement a simplified metabolic network model of the cyanobacterium 2 and bicarbonate In the cytosol, inorganic carbon is taken up and incorporated into organic compounds. With respect to carbon uptake, no distinction is made between COGrowth of the system is constrained by multiple interdependencies. The respective constraints are incorporated as inequalities of the formMj(t) denotes the amount of the cellular component j that constrains flux νi(t) through the reaction i at time t. The factors kcati,j denote catalytic efficiencies. The key constraints incorporated within the model are: (i) light harvesting in photosystem I (PSI) and II (PSII) is constrained by the amount of available pigments; (ii) the total enzyme synthesis rate is constrained by the amount of available ribosomes; (iii) each metabolic reaction is associated with a dedicated enzyme, whose amount limits the flux through the respective reaction. In addition, the model incorporates several constraints on relative compound quotas. In particular, cellular components that do not fulfill an immediate catalytic role, such as cell wall, inorganic ions, soluble metabolites, and lipids must be present in minimal quotas relative to cellular biomass, where biomass is a weighted sum of all cellular components. The quotas ensure that compounds without catalytic activity are synthesized. For simplicity, a subset of metabolites in central metabolism is assumed to be mass-balanced, i.e., these metabolic intermediates are not required to accumulate prior to cell division. We note that this approximation is also employed in conventional FBA, where dilution of internal metabolites is commonly neglected despite the synthesis of biomass (cell growth). The approximation can be straightforwardly eliminated, such that all cellular compounds are part of the compound amount vector M, at the expense of additional computational effort. Here, the approximation is motivated by the fact that the metabolic burden due to dilution of internal metabolites is small compared to the turnover of metabolic flux for the synthesis of main cellular components.where A full list of dependencies is provided in Synechocystis sp. PCC 6803 shown in α in Equation T = 24 h, corresponding to maximal overall growth of an average cell. To this end, the day is subdivided into two distinct phases, a light phase of TL = 12 h and a subsequent dark phase of TD = 12 h. During the light phase, light utilization is only limited by the amount of pigments. Time is discretized into n = 48 uniform intervals. See section “Methods” for the choice and impact of different discretization intervals.Using the model of M at dawn is itself part of the optimization problem. That is, the relative quotas of enzymes, ribosomes, pigments and glycogen are not constrained and emerge as a result of the optimization. Minimal relative quotas are set for the compounds cell wall, lipids, RNA, inorganic ions, and soluble metabolites, as described above. The compound DNA must fulfill a minimal quota only at the beginning and, implicitly, at the end of the simulation period. Solving the constrained optimization problem over a full diurnal cycle, we obtain the time-evolution of each flux within the system, such that the solution ensures an optimal resource allocation for cellular growth. That is, at each time point the local fluxes are organized such that the factor α in Equation T = 24 h. We note that the solution is not necessarily unique and flux variability analysis is performed at each time point. To this end, the maximal factor α is fixed and all fluxes and compound amounts are subsequently minimized and maximized in each time step, corresponding to two optimization runs per compound and flux per time step. The resulting flux variability is indicated in all subsequent figures. Overall growth and relative biomass composition over the full diurnal cycle is shown in The simulation results recover several known features of cyanobacterial growth. As expected, most compounds, as well as total biomass, exhibit exponential growth during the light period. Carbon fixation and flux through the CB cycle is exponentially increasing during the day. Also other synthesis fluxes, such as for cell wall and RNA exhibit exponential increase during the day. The storage compound glycogen is synthesized during late afternoon  are confined to brief periods, most notably the production of the enzymes responsible for the synthesis of ribosomes, DNA, glycogen usage, and import of inorganic ions. Intermittent behaviour is also observed for several reactions fluxes, most notably At dusk, the system undergoes a pronounced metabolic shift. Night metabolism is dominated by utilization of glycogen that is metabolized via the TCA cycle. The respiratory reactions provide ATP to meet the requirements for maintenance metabolism. A small number of other synthesis reactions remain active in the absence of light, such as the production of DNA, ribosomes, lipids, as well as uptake of inorganic ions. We note, however, that the total night synthesis of lipids makes up less than 2% of the total lipid production over the full simulation period. The time courses for all cellular compounds and synthesis fluxes are provided in the As yet, light availability was considered to be a binary variable and light absorption was only limited by the amount of available pigments. However, in most natural environments the intensity of sunlight follows an approximately bell-shaped curve and light harvesting is a function of both, light availability and the amount of pigments. Extending the optimization problem considered above, we therefore implement a bell-shaped light intensity. Simulations were carried out as described above, such that light absorption is proportional to the amount of pigment multiplied with the time-dependent light intensity. Small differences are also observed in the overall biomass composition over the full simulation period, shown in i,j, while being reasonable first approximations, are not precise estimates of the actual values. We therefore study the robustness of our results with respect to these values. Specifically, we evaluate the respective change in maximal growth yield, corresponding to the factor α, in response to a change in the catalytic efficiencies kcati,j of each catalyzing compound. The catalytic efficiencies are perturbed individually for each compound, with a fold change 10−3 to 10+3 from the reference value, and the effect on the factor α (growth), as well as on the compound composition vector M, is recorded. In addition, we record if a given synthesis reaction is active in the absence of light. Results are shown in i,j, corresponding to a catalytic compound with higher catalytic activity, results in an increase of the factor α, hence higher growth yield over one diurnal period. The effect is most pronounced for compounds that make a significant contribution to the compound composition vector M, such as photosystem II and ribosomes. Similar, an increase in any of the kcati,j results in a reduction of the amount of the respective compound in the compound composition vector M. With respect to the results shown in i,j therefore correspond to a global change in the respective enzyme properties.While the overall simulation results are in good agreement with several known features of diurnal phototrophic metabolism, it must be expected that the precise forms of the time courses also depend on parameter values and model assumptions. In particular the catalytic efficiencies kcati,j. Given our model definitions, i,j results again in an increasing amount of Differing from the behaviour of most other compounds, we observe a sudden discontinuous decrease of Synechocystis sp. PCC 6803 exhibits a highly reduced metabolism during the night, and no growth is observed. Nonetheless synthesis of few cellular compounds may proceed also during the night phase. We therefore investigate the possibility of synthesis reactions in the absence of light in the dependence of the catalytic efficiencies kcati,j. For each catalyst the value of kcati,j was varied around its estimated reference value (fold change 10−3 to 10+3) and the activity of synthesis reactions was recorded. The results are shown in i,j. The catalytic efficiencies kcati,j that exert most influence on the night activities of synthesis reactions are those of ribosomes, those of ribosome synthesizing compounds, as well as those of amino acid synthesizing compounds. We note that the dependency of night activity upon the kcati,j is not necessarily confined to one-sided intervals. That is, for some compounds, night activity occurs for increase as well as decrease of kcati,j. The latter finding indicates that compound synthesis during night is indeed the outcome of a global resource allocation problem and dependent on several factors, such as catalytic efficiencies, costs for storage and energy generation and competition between common building blocks, such as amino acids.A related question concerns the activity of cellular metabolism during the night. Metabolism in the absence of light is dominated by the (enforced) requirement for ATP for cellular maintenance. Nonetheless, as shown in Synechocystis sp. PCC 6803 over a full diurnal cycle. Based upon existing computational concepts2122A computational analysis of phototrophic growth using constraint-based optimization requires to go beyond current time-invariant implementations of FBA. In particular, to describe the growth of cyanobacteria in a periodic environment necessitates new approaches that enable us to incorporate the temporal organization and conditional dependencies into a constraint-based description of metabolism. In this work, we have employed such an approach to describe the metabolic activity of the cyanobacteria Our approach results in a time-course for all involved reaction fluxes, as well as changes in biomass composition over a diurnal cycle. The results are in reasonable agreement with several known properties for the temporal organization of phototrophic metabolism. We observe exponential growth during light period and only minor metabolic activity during night. Glycogen is accumulated before darkness, as also observed experimentally for some cyanobacteria27Synechocystis sp. PCC 6803 exhibits only reduced metabolic activity at night, synthesis of individual compounds as well as transport may still be active, as also indicated by global transcription data that exhibit few genes that peak at night, including genes related to transportin vivo.Nonetheless, our simulation framework already allows us to formulate several hypotheses with respect to the optimality of metabolism under diurnal light availability. For example, to what extent a compound is synthesized in the absence of light strongly depends not only on its own catalyst but also the catalytic efficiency of other pathways. This finding reflects the fact that synthesis at night makes use of common storage compounds, hence strong coupling between all pathways must be expected. While it is known that in-silico testing of knockout mutants and the identification of essential genes under diurnal light availability. As yet, we consider the approach presented here primarily as a proof-of-concept for the application of FBA on diurnal cyanobacterial metabolism. Necessary improvements include a more refined distinction between balanced cellular compounds and those which are allowed to accumulate, corresponding concepts were developed recently in more detailSimilar to conventional FBA, our computational framework can be extended into a multitude of further applications, such as Of high relevance from a biological perspective is to incorporate further conditional dependencies into the computational description of phototrophic metabolism. While in this study, most key interdependencies of phototrophic growth have been considered, the list is far from complete. For example, high light intensities are known to have adverse consequences including oxidative stress and reducing the lifetimes of key proteins. We therefore expect that trade-offs between capacity and potential damage in changing light are among the important factors that further shape cyanobacterial metabolism.Taken together, we envision our framework to be able to contribute novel insights to the expected evolutionary trade-offs in metabolic resource allocation. In this respect, we consider the present analysis a pilot study that demonstrates the feasibility of diurnal simulations of metabolism using constraint-based approaches. We expect that aspects of our method must be expanded upon before the solution of the computational resource allocation reflects actual resource allocation of phototrophic growth. Nonetheless, our simulation results already give rise to several testable features of temporal resource allocation that can be verified or refuted in future experiments. We expect that this and similar methods will become instrumental to analyze, and eventually understand, the principles that shape metabolic resource allocation in complex environments.Synechocystis sp. PCC 6803. The model incorporates the main metabolic processes required to describe phototrophic growth in a diurnal environment. The cell harvests energy from incoming light using the photosynthetic apparatus (reactions 2. The Cytb6f complex transfers the electrons to plastocyanin (PC). At PSI electrons are transferred to ferredoxin and further to NADPH via the ferredoxin-NADP+ reductase , energy (ATP), redox (NADPH) equivalents, and inorganic compounds. The compound C3 is generated by the Calvin-Benson cycle. The cycle is split into the RubisCo reaction which fixes carbon dioxide and uses ribulose-1,5-bisphosphate (C5) as a precursor to generate two molecules of C3. The remaining part of the cycle is represented by an overall reaction which regenerates C5 from C3  period of 12 h is sufficient to catalyze its own flux distribution (self-consistency). To this end, we obtain estimated reference flux distributions for day and night conditions, denoted as j is given byFor many cellular compounds, precise estimates of their catalytic activities are not available. We therefore approximated the respective kcatwith the estimationj and i,j accordingly . A complete list of dependencies is provided in where Synechococcus elongatus PCC 7942et al.Synechocystis sp. PCC 6803 genes. We note that the lumped protein sets corresponding to lumped overall reactions are not disjoint. The reference amount of enzymes for the synthesis of the The reference compound amounts To represent overall cellular maintenance a Maintenance reaction is introduced that consists of two parts. First, there is a basal growth-independent minimal activity of the Maintenance reaction proportional to biomass. This proportion was chosen such that the Glycogen quota reported in a previous time-invariant FBAFor the cellular components nr reactions and nm compounds. In contrast to conventional implementations, only a subset Similar to conventional FBA, our approach makes use of a stoichiometric matrix nt flux distributions nt time intervals tk according to flux distribution vk complying with the Euler scheme. The flux capacities in time interval  are linearly dependent on the compound amounts Mk at time point tk.The method starts with the initial amounts Additionally the method takes into account linear constraints on the compound amounts. The problem corresponds to a global optimization problem and is implemented as linear program (LP) as follows:tk according to the flux in time frame k, constraint (7) limits the capacities according to pre-assigned values and allows integration of environmental changes (when appropriate). The constraint (8) encodes the set of ncap capacity constraints with matrices of inverse kcats k. While the kcati,j are assumed to be time-independent, the matrix i,j for the compound wT is the transposed vector) and the number of quota constraints k. Constraint (10) encodes the set of nmain maintenance constraints with k the the quota constraint matrices tk. Constraint (11) reflects the fact that compound amounts must not be negative. Constraint (12) enforces the synthesis of the compound vector (cyclic growth), with α denoting the fold change. Constraint (13) limits the starting amount of biomass. Biomass is defined as a weighted sum of all components in Mk. The variables in the LP problem are M0, vk, and Mk for all k from 1 to nt.Constraint (5) enforces the mass balance for metabolites in steady state, constraint (6) updates the compound amounts at time point α. Our objective is the maximal biomass fold change α. The maximal value was estimated using bisection . The algorithm computes the maximal α, for which the LP has a solution.The formulation allows for a global optimization for any given α, each flux value and each component level is minimized and maximized within each time interval. The difference between minimum and maximum is denoted as flux and compound level variability, respectively. We note that estimation of variability is computationally demanding and requires two optimization runs per flux/compound and per time interval. For the implementation nt = 48 intervals were chosen, results for different choices of nt are shown in nt. A run with a time-discretization of nt = 96 is provided in the The solution is not necessarily unique. Variabilities of flux and compound levels are estimated as follows: Using the pre-determined  value of TM as a linear optimization problem. The optimizations were performed with Gurobi 12.2 on a 3.2 GHz computer (Intel® Xeon® Processor E5-1650) with 6 GB RAM. Simulations were tested with different solvers (Gurobi and CPLEX 12.6) with identical outcomes. The model size grows linearly with the number of compounds, the number of reactions, the number of additional constraints nc and quadratically with the number of time steps nt. For the presented model the runtime of one LP increased by a factor 10.000 with nt increasing from 48 to 512 (about 10 min on the specified computer). The size of this problem would be equivalent to an LP for a model with 550 reactions, 550 compounds and nt = 48.The method was implemented in MATLABHow to cite this article: Rügen, M. et al. Elucidating temporal resource allocation and diurnal dynamics in phototrophic metabolism using conditional FBA. Sci. Rep.5, 15247; doi: 10.1038/srep15247 (2015).


Metabolite levels together with their corresponding metabolic fluxes are integrative outcomes of biochemical transformations and regulatory processes and they can be used to characterize the response of biological systems to genetic and/or environmental changes. However, while changes in transcript or to some extent protein levels can usually be traced back to one or several responsible genes, changes in fluxes and particularly changes in metabolite levels do not follow such rationale and are often the outcome of complex interactions of several components. The increasing quality and coverage of metabolomics technologies have fostered the development of computational approaches for integrating metabolic read-outs with large-scale models to predict the physiological state of a system. Constraint-based approaches, relying on the stoichiometry of the considered reactions, provide a modeling framework amenable to analyses of large-scale systems and to the integration of high-throughput data. Here we review the existing approaches that integrate metabolomics data in variants of constrained-based approaches to refine model reconstructions, to constrain flux predictions in metabolic models, and to relate network structural properties to metabolite levels. Finally, we discuss the challenges and perspectives in the developments of constraint-based modeling approaches driven by metabolomics data. The metabolome comprises the complete set of metabolites, the non-genetically encoded substrates, intermediates, and products of metabolic pathways, associated to a cell  fresh weight (FW). While relative changes in metabolite levels provide sufficient information for many applications, there is an increasing focus on the determination of absolute metabolite levels. For a comprehensive review about the spectrum of metabolomics approaches we refer to Dettmer et al.  with the corresponding parameters  constant Km). Therefore, the solution of the resulting system of ordinary differential equations, dX/dt = N · v, with X representing the concentration of metabolites, N representing the stoichiometric matrix, v the vector of metabolic fluxes , and p standing for the various parameters, yields the concentration-time trajectories of the metabolites. These approaches have successfully been applied to study small and moderate-sized metabolic networks  and moderate probability reactions (CM). High-probability reactions are those that are part of human-curated tissue-specific pathways. A reaction is considered to be a member of the group of moderate probability reactions only if it was necessary for the inclusion of a liver metabolite that appeared in the metabolomics data or if it was supported by at least two of the used data sources.The Model Building Algorithm (MBA) makes use of metabolites that were detected in a given organ or tissue  from a generic model of Arabidopsis thaliana   which becomes time-demanding for very large networks.The algorithm was developed to study the metabolism of the bacterium Yizhak et al.  presenteE. coli for which proteomics, metabolomics, and flux measurements were available.The approach was validated via two comparative analyses: First, the predictive performance of the method was compared to that of Minimization of Metabolic Adjustment (MOMA) a method commonly used to identify a feasible flux distribution of a perturbed system which is closest to the wild-type flux distribution  measurements of metabolite levels can be directly integrated to obtain more accurate flux predictions. Two general DFBA formulations were introduced—static and dynamic  metabolic networks and for quantifying their robustness with only a limited knowledge of kinetic parameters  in Hordeum vulgare) by integrating static organ-specific models with a whole-plant dynamic model. However, the static variant of DFBA is restricted to integrate only metabolite levels of import and export reactions from the analyzed system while in the dynamic variant also internal metabolite levels can be included as well as kinetic expressions. To this end, DOA variants of DFBA can predict flux and metabolite levels even beyond the measured time points.In contrast, Grafahrend-Belau et al.  used theNevertheless, due to the computationally intense formulation in terms of orthogonal collocation on finite elements, requiring a large number of variables, the application of DFBA-based is currently restricted to relatively small metabolic networks. The underlying mathematical problem of DFBA results in a combinatorial explosion in the number of unknown variables as the network size increases.G, given by:Metabolite concentrations in metabolic networks are intrinsically tied to the thermodynamic potential of Gibbs Energy ΔG0 is the standard Gibbs Energy, R is the universal gas constant, T the temperature, and P and S are the product and the substrate concentrations of the reaction, respectively. A negative Gibbs Energy indicates that the respective reaction proceeds in the forward reaction, whereas a positive Gibbs Energy indicates that the reaction is proceeding backwards. Several approaches make use of these information to either integrate metabolite levels or estimates of concentration ranges, or to infer these information form the models predictions  ,   in a continuous non-aqueous fractionation density gradient prior to detection  activation of reactions in response to external and internal cues  is unknown. In addition, the lack of biochemical data can result in uncertainties in assigning correct (condition-specific) directionality to a reaction which can have a significant impact on the network's performance  Burgard et al., e.g., FBA, is solved in the first step. A second objective (e.g., minimization of the sum of fluxes Holzhütter, Optimization problems, such as those typically encountered in constraint-based modeling, can result in non-unique flux distributions for a unique optimum value of the assumed objective. Therefore, to understand the quality and robustness of predictions, the alternative optima need to be investigated. In general, for constraint-based modeling approaches, two ways can be applied to deal with alternative optima (Mahadevan and Schilling, With the ever-increasing quality of data from high-throughput technologies, these data can be readily employed to obtain more accurate metabolic network reconstructions. One promising future direction is to consider more refined methods to analyze condition-specific thermodynamic properties which may have a large effect on the resulting predictions.In addition, plants experience a natural day-night cycle which implications are rarely investigated in the context of large-scale modeling (Cheung et al., Addressing these perspectives necessitates the development of additional refined approaches which can bridge the gap between statistical approaches applied in data analysis and the mechanistic large-scale view taken in the constraint-based modeling framework. Furthermore, in the future a transition from the usage of absolute metabolite levels, favored and necessary in kinetic modeling, to the easier to obtain relative levels usually reported in metabolomics studies in plants and animals has to be considered in research efforts.Finally, constraint-based modeling approaches are currently hampered by the validation of the predicted flux distributions. Fluxes can only be estimated by using various isotope labeling approaches (Schuetz et al., 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.


Escherichia coli with allosteric interactions obtained from relevant databases. This model is used to integrate multi-omics datasets and analyze the coordinated changes in enzyme, metabolite, and flux levels between multiple experimental conditions. We observe cases where allosteric interactions have a major contribution to the metabolic flux changes. Inspired by these results, we develop a constraint-based method (arFBA) for simulation of metabolic flux distributions that accounts for allosteric interactions. This method can be used for systematic prediction of potential allosteric regulation under the given experimental conditions based on experimental data. We show that arFBA allows predicting coordinated flux changes that would not be predicted without considering allosteric regulation. The results reveal the importance of key regulatory metabolites, such as fructose-1,6-bisphosphate, in controlling the metabolic flux. Accounting for allosteric interactions in metabolic reconstructions reveals a hidden topology in metabolic networks, improving our understanding of cellular metabolism and fostering the development of novel simulation methods that account for this type of regulation.Modeling cellular metabolism is fundamental for many biotechnological applications, including drug discovery and rational cell factory design. Central carbon metabolism (CCM) is particularly important as it provides the energy and precursors for other biological processes. However, the complex regulation of CCM pathways has still not been fully unraveled and recent studies have shown that CCM is mostly regulated at post-transcriptional levels. In order to better understand the role of allosteric regulation in controlling the metabolic phenotype, we expand the reconstruction of CCM in  This metabolite was recently identified as a key flux-signaling metabolite in the glycolytic flux-sensing mechanism of E. coli  and 24 single knockout mutants growing at the reference dilution rate (0.2 h−1). Herein, we will refer to the wild-type strain growing at 0.2 h−1 as the reference condition, and the remaining as the perturbed conditions .In order to understand how the coordination between hierarchical and metabolic regulation drives the metabolic flux, we used the reconstructed model to integrate and analyze a multi-regulation analysis introduced by ter Kuile and Westerhoff (hρ) and metabolic (mρ) control coefficients during flux change between two experimental conditions (hρ + mρ = 1). We applied the generalization proposed in Chubukov et al.  present an estimated hierarchical control coefficient above 0.5. Hence, only these reactions are likely to be predominantly regulated at the transcriptional level.The data were analyzed using the concept of sterhoff  to decomv et al.  to simulv et al. . This geFBA positively correlates with its two activators, citrate and pep. Some correlation is also observed between ATP levels and two of its inhibition targets, GND and PFK.Given the lack of evident hierarchical control for most enzymes, one can try to analyze the allosteric control exerted by single effectors in a similar fashion see . The resS. cerevisiae , due to the sparsity of the data , this study was restricted to all reaction-condition pairs with sufficient data to perform a meaningful analysis see . This rePFK, PPC, and PYK) are depicted in Figure PFK and PYK, which are catalyzed by multiple isozymes and regulated by multiple effectors. The logarithmic change of flux and all measured intervening molecules for the selected reaction-condition pairs is presented . Regarding the change in substrate levels, it can be observed that, in most cases, it is also opposite to the direction of the flux change.The regulation mechanisms of the three reactions involved  and its main substrate (pep). This increase can be explained by the increased concentration of its allosteric activator (fdp). There are cases where the different allosteric regulators have a cooperative effect in flux control  and cases where there is a competing effect . One can observe that flux change is not always controlled by the same combination of effectors. For instance, at high dilution rates (0.4–0.5 h−1) the flux of PFK increases with the decrease of its inhibitors (ATP and pep), despite the decrease of its activator (ADP). However, at an even higher dilution rate (0.7 h−1), the flux increase coincides with higher levels of the activator, whereas the two inhibitors change in opposite directions.The effect of allosteric control is evident in some scenarios. For instance, in the ΔThe interpretation of the results is hampered by the lack of protein and metabolite measurements for many experimental conditions. One cannot exclude the possibility that some flux changes are also driven by changes in unmeasured isozymes, cofactors, or reaction products.2.3omics datasets with all the data required to perform a quantitative analysis of allosteric regulation, we developed a constraint-based approach for model-based predictions. This method is based on the assumption that, if a reaction is activated  by a compound present in a pathway, then its flux change should be positively  correlated with the flux change in that pathway  if metabolite i activates  reaction j, and 0 otherwise (note that the stoichiometric matrix S is not changed). The ijw parameters are arbitrary weights that represent the strength of the interaction between effector i and reaction j. If all ijw are close to zero, then the method defaults to a simple pFBA simulation. The minimization of the extra terms in the objective function affects the respective fluxes when regulation is active. For an activation, the subtraction forces the flux and turnover ratios to be the same. For an inhibition, the term forces that a change in the turnover is compensated by an opposite change in the flux. A detailed justification for these terms is given in the Supplementary Material. The full implementation of the method is slightly more complex due to the presence of reversible reactions and reactions without flux in the reference condition  distance between the predicted and measured flux distributions. The original ensemble is split into two groups containing the models with prediction accuracy above and below the median. We then perform enrichment analysis by comparing the distributions of each parameter between the two ensembles. For a particular experimental condition, if a parameter ijw has systematically higher values in the ensemble with higher predictive accuracy, then the assumption of allosteric control between effector i and reaction j results in improved flux predictions for that condition.In general, it is not possible to know the strength of the allosteric interactions beforehand. Therefore, we implemented an ensemble modeling approach in order to find the most plausible models Figure . The appters see . The simters see . The acct-test values for all parameters across all experimental conditions. Although there are not clearly defined clusters in the clustered heatmap, some general patterns can be observed. About one-quarter of the interactions are positively enriched for most experimental conditions, representing probable cases of active allosteric control for those conditions. On the other hand, almost half of the parameters are negatively enriched for a majority of conditions. These represent allosteric constraints that, in most cases, hamper the predictive ability of the models. Finally, there is a subset of allosteric interactions which are neither positively nor negatively enriched. Accounting for these interactions has very little effect in the prediction of flux distributions for the given experimental conditions.Figure PPC and PYK by fdp; and inhibition of the glyoxylate shunt by multiple effectors. Interestingly, several parameters that are positively enriched for a subset of conditions are also negatively enriched for some of the remaining conditions. Hence, although the respective interactions improve the flux predictions in some conditions, in other conditions they make predictions worse.The most frequent positively enriched interactions include inhibition of the oxidative phase of the pentose-phosphate pathway (PPP) by reducing agents NADH and NADPH; mutual inhibition between PPP and upper glycolysis; feedforward activation of in silico approach, we analyzed the enrichment results for the potential cases of allosteric control previously detected by data-driven analysis , activation of PPC by fdp in the ΔppsA mutant , and activation of PYK by fdp in the Δgnd mutant  and the ΔgalM mutant .In order to test the predictive ability of our s Figure B. Some oa posteriori calibration of the weighting factors (see It should be noted that we are using our simulation method (arFBA) in the reverse direction, i.e., a model ensemble is compared with experimental data to find which parameters (weighting factors) result in improved predictions. Although, in theory, one could use the method in the forward direction, i.e., to perform simulations with improved flux predictions, this would require finding a “universal” parameter configuration that fits all conditions. The previous results show that such universal configuration cannot be found due to the condition-specific nature of allosteric regulation. Nonetheless, we tested the accuracy of arFBA by measuring the distance between simulated and experimental flux distributions. Figure tors see . It can 3E. coli. For this, we extended a constraint-based metabolic model of E. coli with allosteric regulation. The application of such a model is twofold. First, it can be used as an integrative scaffold for multi-omics dataset analysis, revealing the coordination between enzyme, metabolite, and flux levels. Second, it can be used for in silico-based predictions that account for allosteric regulation in the simulation of the metabolic phenotype. For that purpose, we implemented an FBA variant, named arFBA, that accounts for allosteric interactions in the determination of the flux distribution.In this work, we analyzed the role of allosteric regulation for flux control in the central carbon metabolism of omics dataset for E. coli  to determine the transient profile of glycolytic intermediates in dynamic cultures switching between glycolysis and gluconeogenesis. A kinetic ensemble model for glycolysis was used to test 126 putative interactions. The results not only confirmed previously known interactions but also predicted new interactions that had not been previously reported. Although the model used in this study differs from ours, the results regarding interactions common to both models are consistent. In particular, both studies revealed the importance of PFK as an active regulation target for controlling the glycolytic flux, and the role of fdp as key regulator of PPC and PYK to control pep consumption.An ensemble modeling approach was also employed by Link et al.  for systE. coli . It has been shown that PTMs, such as acetylation, have important regulatory functions in omics datasets will be necessary for a deeper understanding of metabolic regulation. Herein, we used a previously published dataset for chemostat cultures. However, steady-state data may be insufficient to analyze regulatory responses. It has been observed that fast metabolic responses precede the slower transcriptional response during metabolic adaptation . Hierarchical and allosteric regulation analysis using a multi-omics dataset revealed that there is no predominant mechanism of regulation across all experimental conditions. Nonetheless, situations of predominant allosteric control could be identified for some reactions at particular conditions. Our new method for model-based prediction of allosteric control was able to capture at least a few of these situations. However, the assessment of the predictive ability of this method is hampered by the lack of more comprehensive data.In this work, we focused on the role of allosteric regulation in central carbon metabolism. The reconstruction of an allosteric model revealed that allosteric information is inconsistent among different data sources even for these highly studied pathways. The allosteric interactions added a new layer to the network topology, changing the overall network connectivity and revealing metabolic hubs that would otherwise be ignored . In these cases, we used the most frequently reported effect.The original model of the core metabolism of 5.25.2.1iJ) can be generically described in terms of the concentrations of the respective enzyme(s) (iE) and all the intervening metabolites :kcat is the turnover rate of the enzyme, and f (M) represents a non-linear function of the metabolite concentrations. Regulation analysis introduced by ter Kuile and Westerhoff (The metabolic flux of a reaction (sterhoff  decomposf (M) is generally unknown, one can estimate hρ (and consequently mρ) by measuring the enzyme and flux levels across different conditions. Chubukov et al. (iE) and log(iJ) across all experimental conditions using a robust linear regression method (Theil–Sen estimator).Since v et al.  generalif (M) component, using a power-law approximation:S, P, A, I represent, respectively, the set of substrates, products, activators and inhibitors of reaction i, and ijγ is the apparent kinetic order of effector j in reaction i, as defined in Biochemical-Systems Theory  for each effector as:We further generalized this concept to the study of allosteric regulation, by decoupling the effect of allosteric regulators in the reaction flux from the non-linear ry Voit, . This alijγ ≤ 1). Hence, the allosteric control coefficient is bound by the slope of the linear regression.With the exception of effectors exhibiting cooperative binding, we can assume that the kinetic orders are close to or below unity  regulated reactions were experimentally measured. Due to gaps in the proteomics dataset, we restricted the analysis to enzymes with available data for at least 10 (out of 29) experimental conditions.5.2.2Allosteric effects were analyzed for each perturbation individually by comparing the logarithmic change of enzyme, flux, and metabolite levels between all 28 perturbed conditions and the reference condition. Due to the sparsity of the data , this analysis was restricted to all reaction-condition combinations where the following criteria were satisfied: (1) at least one associated enzyme was measured; (2) all main substrates (excluding cofactors) were measured; (3) at least one effector was measured. Furthermore, we excluded flux changes that were not significant .E)/Δlog(J) < 0.5) or substrate abundance (Δlog(S)/Δlog(J) < 0.5), and is at least partly related with changes in one allosteric activator (Δlog(A)/Δlog(J) > 0.25) or inhibitor (−Δlog(I)/Δlog(J) > 0.25). For reversible reactions, the effect of flux changes arising from changes in the thermodynamic driving force cannot be excluded. Therefore, for these reactions we only considered reactions where the products were experimentally measured (excluding cofactors) and the flux change cannot be fully explained by the change in product abundance (−Δlog(P)/Δlog(J) < 0.5).Evidence of allosteric control was detected by selecting conditions where the flux change is not fully explained by changes in enzyme concentration (Δlog(5.2.34 models was built by sampling the weighting factors (ijw parameters) from a log-normal distribution. Each model is constrained with the experimentally measured glucose and oxygen uptake rates, and the growth rate, which is given by the dilution rate.For each experimental condition, an ensemble of 105.2.44 arFBA models was built as described above; the accuracy of each model was determined by the L1-norm distance between the experimental and simulated flux distributions; the calibrated weighting factors were calculated as the average of the 10% most accurate models.Condition-specific weighting factors were calibrated for each experimental condition as follows: an ensemble of 10The 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.http://journal.frontiersin.org/article/10.3389/fbioe.2015.00154The Supplementary Material for this article can be found online at Click here for additional data file.


Escherichia coli (E. coli) and Salmonella spp. are thought to have evolved over 100 million years from a common ancestor, and now cause disease in specific niches within humans. Here we have used a genome scale metabolic model representing the pangenome of E. coli which contains all metabolic reactions encoded by genes from 16 E. coli genomes, and have simulated environmental conditions found in the human bloodstream, urinary tract, and macrophage to determine essential metabolic genes needed for growth in each location. We compared the predicted essential genes for three E. coli strains and one Salmonella strain that cause disease in each host environment, and determined that essential gene retention could be accurately predicted using this approach. This project demonstrated that simulating human body environments such as the bloodstream can successfully lead to accurate computational predictions of essential/important genes.Microorganisms have evolved to occupy certain environmental niches, and the metabolic genes essential for growth in these locations are retained in the genomes. Many microorganisms inhabit niches located in the human body, sometimes causing disease, and may retain genes essential for growth in locations such as the bloodstream and urinary tract, or growth during intracellular invasion of the hosts’ macrophage cells. Strains of  E. coli, to multi-cellular eukaryotic organisms. By constructing genome-scale metabolic models (GEMs), the nature of an organism can be explored through computational analysis of its genome content. The E. coli K-12 strain MG1655 has had extensive computational metabolic networks generated for it so far, and its existing models are quite advanced that contain >2,000 reactions, >1,000 genes, and >1,000 metabolites [Computational modeling has been widely used as an efficient approach in microbiology, which introduces mathematical components including variables, parameters, and equations in network constructions to reflect the behavior of organisms. Numerous types of networks have been constructed including signaling, regulatory, and metabolic pathways for organisms ranging from microorganisms, such as abolites ,8, and lE. coli metabolic networks have been constructed for commensal, enterohemorrhagic, and extra intestinal pathogenic strains [E. coli metabolic models, a Salmonella Typhimurium LT2 metabolic model was used to examine metabolic reactions and the corresponding essential genes that are necessary for cell viability during the infection process under simulated conditions inside the host [S. typhimurium LT2 during human infection [Currently, numerous  strains ,4. Unlikthe host . The evonfection .E. coli pangenome which contains the union of all genes that encode metabolic reactions from 16 genomes of E. coli, 2) using flux balance analysis to systematically test growth predictions in three simulated host environments of all single gene mutants, and 3) comparing the essential/important gene predictions (i.e. those that promote growth and would likely have been retained over time) with sequenced enterobacterial genomes to determine if these genes were retained or lost in modern day strains.To systematically explore genes predicted as essential and important for cell growth in a given environment, we used an approach that focused on three main components: 1) generating a metabolic network and corresponding metabolic model representing the metabolic capabilities of the E. coli, that cause human disease in locations other than the intestinal tract. Extraintestinal E. coli infections may result in serious illness and even death, and globally 130–175 million cases of urinary tract infections are caused by Extraintestinal E. coli [E. coli causing bloodstream infections, which cause more than 40,000 deaths from septicemia each year worldwide [In this work, we have developed new methods using constraint-based optimization and metabolic model construction to identify genes important for growth/survival in environments simulating three locations within the human body and have compared the predictions with actual evolutionary outcomes of sequenced genomes of enterobacterial pathogens, such as extraintestinal  E. coli . The uriorldwide . TherefoComputational modeling allows us to conduct experiments of disease-causing bacteria where actual testing in humans is not an option. These are the three main objectives that were investigated: i) Can different locations in the human body be modeled using constraint-based linear programming? ii) Are there different predictions of essential/important genes for growth in simulated conditions representing three human body locations? iii) Do these gene predictions correlate with the genome content of modern-day enterobacterial pathogens that actually cause disease in each of the three locations? Overall, this study illustrated that mathematical constraints can be used with metabolic models to simulate the nutrient conditions the pathogen encounters during the infection process, and the genes predicted using FBA with the metabolic model simulating conditions during infection correlate with transcriptional gene-expression data obtained for conditions representing host-pathogen interactions. The central hypothesis is that the essential and important genes for bacterial growth in certain environments should be mostly remained over time in the genome of strains that cause disease in the corresponding human body locations, whereas the loss of those essential and important genes should not cause dire consequence for strains that invade different human locations.For the three simulated conditions, analytical data were used to add constraints that dictate metabolite availabilities respectively under three simulated conditions, the human macrophage cell , the bloFor the three simulated niches examined in human body, there were 15 available metabolites used as constraints shared in common for all three host niches, whereas 51 metabolites varied depending on the environment, indicating that differences in human body locations lead to different metabolite compositions available to the microrganisms .When FBA analysis for single reaction deletions and their corresponding genes was conducted in the three simulated environments, the results varied in the total number of predicted essential and important reactions and associated genes for each condition . FollowiE. coli UTI89, E. coli 53638, and Salmonella LT2) were used for essential and important gene comparison, and the genome of E. coli O157:H7 was used as a control because of the pathogen’s capability to cause disease in the human intestine. E. coli UTI89 is able to infect the urinary tract or the bloodstream in human body, causing disease outside the intestinal track. Both E. coli 53638 and Salmonella LT2 can cause disease by invasion of a host cell . In contrast, the pathogenic E. coli O157:H7 that causes disease in the intestinal tract would most likely have lost the most number of essential and important genes predicted for each of the three host niches. The host niche condition was not simulated for the control in this project. As shown in The central hypothesis is that the pathogens that actually cause disease in a given host location should have lost the fewest number of essential and important genes predicted for that conditions simulated in silico metabolic modeling and prediction of genes required for growth and survival in three human body locations. Based on the numerous differences of metabolites present in three different human body niches, this study illustrates that multiple environmental niches in a human can be simulated to study microbial metabolism by using constraint-based linear programming and computational model. Simulation of these three conditions led to different predictions of essential and important genes/reactions, which match the real evolutionary outcomes when compared to the control genome of the intestinal pathogen enterohemorrhagic E. coli O157:H7 strain EDL933, a strain that causes disease in the intestine and was predicted to have lost the most of the essential or important genes in the three other host niches. In the case of intracellular invasion, although the strain isolated from a urinary tract infection has the fewest essential/important genes lost, the two genomes of strains that actually cause disease through this route had very similar low numbers of lost essential/important genes. In the case of the simulations for the human bloodstream and urinary tract, E. coli UTI89 is the strain that actually causes disease in these locations, and had the least amount of necessary/important genes lost, which agreed with the evolutionary outcome. This project demonstrated that human body environments such as the bloodstream can successfully lead to accurate predictions of essential/important genes using optimization and constraint-based metabolic techniques. The discrepancies from the predictions for the urinary tract may indicate that more information is required for additional constraints to more accurately simulate this environment, or that the E. coli strains that have been characterized as causing disease in only one niche in the human body may also be capable of causing disease in numerous locations in the human body. Overall, this project was a success and lays a foundation towards future work to model metabolism of pathogenic microbes in different locations inside a human host. Since the actual infection study of these organisms in human is not a possibility, computer modeling of related disease processes becomes an emerging approach and field that is likely to grow immensely. By addressing these research ideas revealed by this project using optimization and constraint-based linear programming, the field of microbial system biology can be furthered to efficiently examine genome evolution.This study investigated E. coli pangenome (iEco1712_pan) used in this work was previously reconstructed based on the gene to protein to reaction (GPR) information of 16 E. coli genomes obtained from the ASAP database [E. coli, of which 16 are completely finished and were used in the construction of the metabolic model of E. coli pangenome (iEco1712_pan) [E. coli pangenome (iEco1712_pan) reconstruction used in this work are available as supplemental information along with the sbml file for the iEco1712_pan GEM [The metabolic model representing the nome iEco712_pan udatabase . There cs-related fluxes in a metabolic network [E. coli pangenome metabolic network is described as a stoichiometric matrix  with rows (iЄI) representing the metabolites and columns (jЄJ) indicating reactions that correspond to genes (gЄG). In a steady-state, the mass balance equation can be described as below, with v being the flux vector. Additional constraints are showed as lower and upper limits for the values of fluxes through reactions in a network.Flux balance analysis (FBA) has been commonly applied for mathematical analysis of GEMs, which can predict reaction network . By cons network . FBA wasE. coli pangenome GEM contains 1,726 metabolites (I) and 2,324 reactions (J) that associate with 1,712 genes (G). Three different niches located in the human body  were simulated to set constraints for FBA in this study, with possible metabolite compositions being identified through literature review that determined analytical compositions of nutrients present in each bodily location. The simulated condition for macrophage contains 32 metabolites, the bloodstream environment contains 19 metabolites, while there are 14 metabolites that belong to the urinary tract niche Click here for additional data file.S2 DataThis file contains three tables, the first contains all predicted essential reactions during simulation of human macrophage, the second contains all human bloodstream predicted essential reactions, and the third contains predicted essential reactions during simulation of the human urinary tract.(XLSX)Click here for additional data file.