E. coli and S. cerevisiae to test the method benchmarking the capability of these industrial microbes for overproduction of acetate and glycerol under aerobic conditions and succinate and ethanol under anaerobic conditions. The results illustrate that OptEnvelope is capable to find multiple strong coupled envelopes located in the desired solution space because of its novel target point oriented strategy of envelope search. The results indicate that E. coli is more appropriate to produce acetate and succinate while S. cerevisiae is a better host for glycerol production. Gene deletions for some of the proposed reaction knockouts have been previously reported to increase the production of these metabolites in experiments. Both organisms are suitable for ethanol production, however, more knockouts for the adaptation of E. coli are required. OptEnvelope is available at https://github.com/lv-csbg/optEnvelope.Finding the best knockout strategy for coupling biomass growth and production of a target metabolite using a mathematic model of metabolism is a challenge in biotechnology. In this research, a three-step method named OptEnvelope is presented based on finding minimal set of active reactions for a target point in the feasible solution space (envelope) using a mixed-integer linear programming formula. The method initially finds the reduced desirable solution space envelope in the product versus biomass plot by removing all inactive reactions. Then, with reinsertion of the deleted reactions, OptEnvelope attempts to reduce the number of knockouts so that the desirable production envelope is preserved. Additionally, OptEnvelope searches for envelopes with higher minimum production rates or fewer knockouts by evaluating different target points within the desired solution space. It is possible to limit the maximal number of knockouts. The method was implemented on metabolic models of  The organism strains used in biotechnology define the opportunities and limitations of biotechnological production, therefore, their selection and modification are important ways to improve the production features  and sustSeveral methods have been published for the prediction of necessary reaction deletions and/or insertions for growth-coupled strain design. The developers choose different platforms to implement methods mostly in Matlab  required to keep the metabolism active in the target point are determined and the other reactions (non-MAR reactions) are removed. The non-MAR reaction deletions lead to a new growth-coupled production envelope. While the strategy of the other methods is to find the best knockouts, OptEnvelope finds MAR for a target point and then, by removing non-MAR reactions, a new production, MAR variability determined envelope is obtained. Then, maximizing reinsertion of the removed nonMAR reactions, it is attempted to reduce the required number of knockouts attempting to keep the previously achieved MAR- determined production envelope. The word “envelope” was used in the name of this method because of its different approach compared to the previous coupling methods: OptEnvelope finds the engineered strain production envelope before finding the required knockouts.OptEnvelope searches to find various envelopes by implementing the method for target points around the original target point selected by the user. OptEnvelope can find multiple envelopes in one run by changing the target point in the desired space, thus possibly discovering various valuable envelopes. The user can compare and select the best strain designs characterized by envelopes based on several factors like fewer knockouts, higher minimum and maximum production rates, etc. to choose the optimum envelope for coupling. The strategy of defining a target point combined with the low CPU time of OptEnvelope makes it easy to switch the target point to inside feasible space and find other favourable envelopes. OptEnvelope is also a good tool for fast benchmarking of different organisms for production of particular metabolites due to its fast operation. The appropriateness of an organism to produce a particular metabolite is determined by the shape of the envelope and the number of necessary deletions.E. coli and S. cerevisiae, respectively. The models were used in the irreversible form (each reversible reaction was separated into two separate forward and backward reactions) to simplify the solution. The growth on glucose minimal media was simulated by considering the upper bounds of 10 mmol/gDCW/h for glucose uptake rate and 1000 mmol/gDCW/h for NH4, H2O, SO4, O2, H+, phosphate, and inorganic ion consumption reactions under aerobic conditions. The same glucose uptake rate used for the two models makes it possible to compare the capabilities of structures of the metabolic network. Oxygen uptake was bound to zero in iJR904 for the anaerobic growth simulation of E. coli. For S. cerevisiae, cytochrome c oxidase was removed from iMM904 to implement anaerobic conditions as very small amounts of oxygen are essential for biomass [In this study, the genome-scale metabolic models iJR904  and iMM9 biomass . The upt biomass  and Gurohttps://github.com/lv-csbg/optEnvelope) includes three steps: 1) selecting a target point (most desirable operation point) in the feasible region of a wild-type product-biomass envelope by the user, 2) determining the minimal active reactions (MAR) at the selected point and removing the other reactions to find a desired envelope for coupling, and 3) reinsertion of the non-MAR reactions removed at step 2 to find minimal knockouts required to support the desired envelope.OptEnvelope  was applied according to the LP problem presented in The maximum and minimum growth rates on the glucose minimal medium were initially calculated considering biomass reaction as the objective function. Then, the space between the minimum and maximum growth values was divided into 100 points including the endpoints. The objective function was changed to the exchange reaction of the desired product and the minimum and maximum production rates at each point of the growth rate were calculated. Production rate versus growth rate was plotted and the feasible region was specified. A typical envelope of product excretion rate versus growth rate for a wild-type strain and growth-coupled strains is presented in The plots in j); the variable zj is a binary variable that can only take the values of zero and one; and vj,max is the upper bound of reaction j. j according to For finding MAR of each target point, it has to be mentioned that the reactions can be categorized by flux variability range into four groups at each feasible point in j = 0. So, to avoid the simultaneous use of forward and backward directions in reversible reactions, j,f and zj,b are binary variables for forward and backward fluxes of reversible reaction j, respectively. Thus, if one direction of the reaction has a non-zero flux, As the metabolic model is in the irreversible form, the metabolic model might activate the forward and backward fluxes of reversible reactions at the same time and make cycles to unrealistically increase the number of genes with zAfter solving the MILP problem, all fluxes were bound to zero except reactions belonging to the set of MAR, and then, the production envelope was drawn. This envelope is determined by the flux variability of MAR at the target point. The coupling is strong if the minimum secretion rate of the desired product in lack of growth as shown in After finding the optimal envelope and MAR, sequential reinsertion of the deleted reactions was done to find minimal reaction knockouts needed to support the minimum secretion rate of the desired product if the coupling is strong. In fact, the minimum secretion rate was preserved in the reinsertion step to be sure that the coupling is strong and the lack of secretion of the desired product is infeasible.In case of unsatisfactory features of found envelopes setting the target point from envelope boundary to the internal area of the solution space can be useful, because it may result in an envelope with similar maximum production rate as for the primary target point but better other parameters (higher minimum production rate and/or fewer knockouts). So, evaluation of the envelopes for internal target points located in the desired space and comparison with the primary envelope obtained for the original target point located on the upper edge is necessary. Therefore, in this research, after finding the primary envelope for the primary target point, the line space between the production rate of the primary target point and the MP point as shown in For all target points, the envelope and its important parameters  are determined and considered selecting the best envelope. If the minimum production rate for an envelope is lower than that for the primary envelope or the number of knockouts for an envelope is more than that for the primary envelope, the envelope is not favourable and the envelope is not considered as an alternative. For the selection of the best envelope, various criteria can be considered. Higher values of maximum and minimum production rates at zero growth rate as well as higher production rates at the MP point of the envelope are desirable. For the similar production rates at MP point, higher growth rate is better to achieve higher productivity. Furthermore, the required number of knockouts to obtain the envelope is an important criterion for the decision. After running the code, all the data are presented in a table on the MATLAB’s command and the user can select the most appropriate envelope depending on the specificity of the biotechnological task.After finding the envelope and reinserting the reactions, the number of knockouts is determined by OptEnvelope. If necessary, it is possible to reduce the number of knockouts, however, that may result in an envelope with lower production rate. Hence, the effect of the reduction of the number of knockouts is required to be studied. For this purpose, a procedure for using the dual problem for the inner LP problem similar to the method used by Tepper et al.  is impleFor each envelope found in the previous section, it is easily possible to study the effect of the reduction of the number of knockouts. MAR of that envelope is added to the list of reactions that are not allowed to be knocked out and the number of allowed knockouts is determined. If it is equal to or more than the value found by the reinsertion step of OptEnvelope, the same envelope is found. Otherwise, if the number of allowed knockouts is set to be less than the determined value by the third step of OptEnvelope, an expansion of the envelope is observed after reducing the number of knockouts. An example in the results (subsection 3.2.) is presented to illustrate the effect of knockout reduction on an envelope. The pipeline of OptEnvelope is presented in S. cerevisiae and E. coli was investigated using OptEnvelope. The primary envelopes of two hosts obtained by the primary target points were compared in this research for simplicity.OptEnvelope can be implemented simply and quickly for various hosts, and thus can easily evaluate the impact of host change. Similar to the process of selecting the best envelope for a model, various criteria including higher values of maximum and minimum production rates, more production rate at the MP point of the envelope, and fewer necessary knockouts can be considered for the selection of the better host. The coupling of the production of acetate, glycerol, ethanol, and succinate in E. coli metabolic model at 3% of the maximal growth rate was selected. MAR and the primary envelope for the primary target point were calculated. Then, OptEnvelope selected target points inside the space using the MP point of the primary envelope, and after finding MARs for these target points, the corresponding envelopes were calculated. The characteristics of envelopes including the number of knockouts, name of reactions, and the rates for all envelopes found by OptEnvelope on E. coli for acetate production under aerobic condition are presented in According to the explanations in the previous section, a primary target point on the upper edge of the wild-type envelope of the The envelopes indicate that diverse results are presented for the middle points and it must be mentioned that some of the envelopes are found multiple times. The minimum number of knockouts is three , that correspond to the 8th envelope with a maximum growth rate of 0.146 1/h at an acetate production rate of 17.4 mmol/gDCW/h and minimum and maximum production rates of 7.6 and 25.6 mmol/gDCW/h, respectively. While this envelope represents the minimum number of knockouts, its production rate at MP point is less than the in other envelopes and even less than in the primary envelope. The 2nd envelope with six knockouts is also recommended having maximum growth rate of 0.143 1/h at a production rate of 22.7 mmol/gDCW/h and minimum and maximum production rates of 9.5 and 27.1 mmol/gDCW/h, respectively. The minimum production rate is increased 2.1 times compared to the primary envelope while a slight reduction in the maximum production is observed. The production rate at the MP point is a little more than that for the primary envelope which is valuable. So, all criteria for this envelope are better compared to the primary envelope and this demonstrates the usefulness of switching the target point into the solution space. It is interesting that knockout of ATP synthase is only suggested for envelopes with 3 and 6 knockouts. For the other envelopes with more knockouts, the removal of this important reaction is not needed. Thus, the various strategies proposed by OptEnvelope give the user freedom to decide not only the number of reactions but also the pathway of reactions to be knocked out.The highest minimum production rate and the production rate at MP point are 19.0 and 24.7 mmol/gDCW/h, respectively, which belongs to the 10th envelope with nine knockouts. Its maximum production rate is reduced to 25.2 mmol/gDCW/h which is about an 8 percent reduction compared to the primary envelope. This envelope has the minimum value of maximum growth rate (0.022 1/h) and this low growth rate might have a negative effect on the productivity of the knockout strain and needs to be evaluated by the user. So, if the higher number of knockouts and low growth rate are not acceptable, this envelope can be selected as the candidate envelope for stain design.To implement the limitation of the number of knockouts, after selecting an envelope  for E. coli and S. cerevisiae, respectively. Furthermore, the envelope of S. cerevisiae after reinserting the reactions (step three of OptEnvelope) is worse than its optimal envelope  including 7 reaction knockouts are almost the same. So OptEnvelope predicts that S. cerevisiae is a better host for glycerol production.S. cerevisiae is a well-known producer of glycerol and its better results illustrate that its metabolism has evolved to be a good glycerol producer. The experimental results show that S. cerevisiae uses glycerol as a sink for excess NADH and glycerol production increases with increased cytosolic NADH concentrations. Hence, the deletion of NADH2_u6cm (NADH dehydrogenase) suggested by OptEnvelope is logical. The experimental reports confirm that achieving high glycerol production yield by S. cerevisiae is possible. By deleting tpi1 and adh1 genes and overexpressing gpd1 and ald3, Cordier et al. [tpi1Δ nde1Δ nde2Δ gut2Δ S. cerevisiae strain.r et al.  achievedr et al.  achievedE. coli and previous reports confirm that E. coli is not a natural producer of glycerol and its fermentation has been achieved in E. coli using added pathways from other organisms [S. cerevisiae with deletions of the tpiA, mgsA, and edd genes [The experimental data also agree with the prediction of OptEnvelope for rganisms . A glycedd genes .E. coli is a better succinate producer than S. cerevisiae. The maximum theoretical yield of succinate for E.coli under anaerobic growth is 1.12 g/g which is higher than this value for S. cerevisiae (0.84 g/g) as presented in E. coli is excellent with a minimum succinate production yield of 0.93 g/g and a maximal growth yield of 0.01 g/g at a succinate yield of 1.1 g/g. This envelope can be obtained with nine knockouts while for achieving the envelope of S. cerevisiae, at least 46 knockouts are required. The succinate yields presented in two review papers [E. coli is an ideal host, and the yields for S. cerevisiae are much lower. It is also mentioned that achieving the succinate yield suggested by OptEnvelope of 1.1 g/g glucose is possible using E. coli [ldhA, pta, citF, and ptsGH supporting reactions LDH_D, PTAr, CITL, and GLCpts proposed by OptEnvelope for succinate overproduction by E. coli.Unlike with glycerol, w papers ,26 confi E. coli . The exp E. coli –27 also S. cerevisiae and E. coli can be promising ethanol producers  at a maximal anaerobic growth yield of 0.115 g/g according to S. cerevisiae strains can achieve ethanol yields above 90% of the maximum theoretical. For example, with some production processes in the Brazilian fuel production industry, the yield of 0.469 g ethanol per g glucose is reported [S. cerevisiae seems to be the better ethanol producer.While for three earlier cases, one of the two hosts was clearly superior, both microbes present acceptable results for ethanol production that indicate roducers . Both mireported . In addiE. coli and the ethanol yield at maximal anaerobic growth is improved from 0.12 to 0.466 g/g  with eight reaction knockouts. These results demonstrate that more knockouts are required to have an ethanol producer of E. coli compared to S. cerevisiae. The experimental data confirm that achieving high values of ethanol yield is possible even for E. coli with multiple gene knockouts. For example, by deleting eight genes from E. coli MG1655, Trinh et al. [Δzwf Δndh ΔsfcA ΔmaeB ΔldhA ΔfrdA ΔpoxB Δpta), which could produce ethanol with a yield of 0.36 g/g glucose in anaerobic conditions. Furthermore, by adding pdc and adhB genes from Zymomonas mobilis to the TCS083 strain, the yield improved to 0.49 g/g. Woodruff et al. [E. coli strain LW06 which can reach up to 80% of the theoretical yield on glucose.OptEnvelope is highly effective in the overproduction of h et al.  producedf et al.  also devWhile the previous methods of coupling attempt to directly find the best knockouts, OptEnvelope first uses a MILP formula to find minimal active reaction (MAR) at a biotechnologically attractive target point in the solution space of wild type strain. The strategy of initially finding the envelope and then finding knockouts makes OptEnvelope able to suggest a strong coupling if it exists.Considering that sometimes the envelopes located inside the area are more desirable because of some of their features, OptEnvelope tries to find all desired envelopes based on moving the target point towards the middle of the feasible space. As OptEnvelope is simple and fast to run, different target points can be easily evaluated and exploited. Then, the user can compare the envelopes based on various criteria  and select the best envelope for strain design. The user can decide about the number of knockouts and whether moving to the upper edges or staying inside the feasible solution is better depending on the number of knockouts. Furthermore, the diversity of envelopes located in the desired space with various sets of knockouts proposed by OptEnvelope enables the user to consider different priorities during the selection of the final envelope.It is also possible to determine the number of allowed knockouts as an input of OptEnvelope. After selecting the best envelope, if the number of knockouts is not acceptable, it can easily be reduced to a favourable value by the user and the effect of the reduction of the number of knockouts on the shape of the envelope is presented by OptEnvelope (section 3.2.). The existence of acceptable envelope with smaller knockouts depends on the features of the model. Increasing the number of middle points can increase the chance of finding good alternative envelopes at the cost of increasing the computation time.The size of the envelope and the number of deletions depend on the peculiarities of the metabolism of the producer organism. OptEnvelope is a fast tool for finding the most appropriate organism for a particular product having better productivity at maximal growth and a smaller number of deletions as a criterion.OptEnvelope ranked correctly the appropriateness of the analysed hosts indicating the natural adaptation of microbes for a specific product. A host is not appropriate for a product if the optimal envelope is not strong coupled or if the number of knockouts is too high for implementation. In such cases changing the host can be considered instead of shifting to a worse envelope of existing host with a lower number of knockouts. A good production envelope that is achievable with a small number of knockouts is an important indication that the metabolism of a microbe has naturally evolved to synthesize a product of interest.OptEnvelope can serve also for the assessment of sustainability features of an organism for production of a metabolite of interest due to easy switch between the models of organisms and the possibility to implement sustainability objective function  as a criS1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.


Standard multivariate analysis methods were then applied, and were complemented by univariate statistical methods to identify differentially expressed primary metabolites and related metabolic pathways. The results showed carbohydrate and lipid metabolism to be the most relevant in all the calli assayed, with most discriminant metabolites being fructose, glucose and to a lesser extent choline. The glycolytic rate was higher in embryogenic calli, which shows, overall, a higher rate of sugar catabolism and a different profile of phospholipids with a choline/ethanolamine analysis. In general, our results show that a distinct primary metabolome between embryogenic and non-embryogenic calli occurs and that intracellular levels of fructose and sucrose and the glucose to sucrose ratio seem to be good candidates as biochemical biomarkers of embryogenic competence.Tamarillo is a solanaceous tree that has been extensively studied in terms of in vitro clonal propagation, namely somatic embryogenesis. In this work, a protocol of indirect somatic embryogenesis was applied to obtain embryogenic and non-embryogenic callus from leaf segments. Nuclear magnetic resonance spectroscopy was used to analyze the primary metabolome of these distinct  Solanum betaceum Cav. (=Cyphomandra betacea (Cav.) Sendt.), is a small solanaceous tree or shrub endogenous to South America [Tamarillo,  America . Because America . Tamaril America . The agr America . Further America ,5. There America ,7. callus tissue before somatic embryo conversion, or direct if the presence of callus is minimal or absent [SE is a complex process in which a somatic cell or tissue, under certain stimuli and without fecundation, originates a structure similar to a zygotic embryo . This str absent . Althougr absent ,14.callus formation after 12 to 14 weeks [callus tissue obtained can be maintained and multiplied in the same type of culture medium or converted into somatic embryos by stopping external auxin signaling and lowering sucrose concentration. In this protocol, it is also possible to distinguish two types of callus tissue according to their embryogenic competence: embryogenic callus (EC), which develops somatic embryos, and non-embryogenic callus (NEC) that is unable to evolve into somatic embryos and that becomes necrotic if picloram supplementation is cut [callus lines begin to show genetic abnormalities and lower rates of somatic embryo conversion after being maintained in a culture for periods of more than 2 years [In tamarillo, when the initial explants are leaf segments cultured in a high-sucrose culture medium supplemented with the synthetic auxin picloram, an indirect SE process occurs with 14 weeks . The caln is cut . Further 2 years ,16. The  2 years ,18. Solanum lycopersicum [Coffea sp. [Zea mays [Daucus carota, to assess the optimal harvest time and maximize bioactive compound accumulation in the final product [Metabolite or metabolome-wide approaches have also been employed in plant model species to study several phenomena from the metabolic changes that occur in pollen germination  to long-persicum  as well ffea sp.  and Zea Zea mays . These tZea mays ,24. Some product . In gene product .calli obtained from an indirect SE protocol to identify the main metabolites present in each distinct phenotype, in order to evaluate the most important metabolites and metabolic pathways for embryogenic competence. This approach was combined with a standard chemometric analysis to derive models of metabolite relevance as well as a one-to-one differential analysis of different phenotypes using a long-term callus (LTC) as a reference state to help identify possible markers of embryogenic competence. The results are aimed at differentiating the two types of phenotypes in terms of the main metabolic pathways expressed and help to putatively identify possible biomarkers of SE in general or, more specifically, embryogenic competence.The objective of this study was the NMR-based metabolic fingerprinting of embryogenic and non-embryogenic The induction protocol previously described led to the development of callus tissue on the original leaf explant. After approximately 12 weeks, several callus could be seed and morphologically distinguishable as embryogenic or non-embryogenic and were sub-cultivated as described in the Materials and Methods section. Additionally, a callus line that had been previously induced as embryogenic (EC), but lost that competence through subcultures, was used as long-term callus LTC, A. To cont-test (p < 0.05) was found between either the mass increment or the number of somatic embryos of embryogenic calli, EC2 presented slightly higher values of both .Although no statistical significance using an unpaired Protein quantification was carried out on all the calli used in this work A. LTC shMetabolome compositions of different cell lines were assessed with 1H-NMR spectroscopy. Qualitative spectral differences were apparent upon visual inspection A,B. AlthIn the region from 0.6 to 4.5 ppm A, severaIn the low field region  account for 91.7% of the accumulated variance A, with acallus line forms a cluster, supporting the PCA analysis previously presented  were commonly over-expressed and two (chlorogenic acid and tyrosine) were under-expressed. On the contrary, NEC cells presented a distinctly different common metabolic profile when compared with LTC with five metabolites  being over-expressed in all calli and lactate being under-expressed. Additionally, each individual cell line displayed characteristic distinct metabolic differences. The fold changes of each metabolite were used for construction, as described in the Materials and Methods section.After the multivariate analysis, a complementary investigation of differential expressed metabolites in the p) are presented in The full list of metabolites in each group along with the respective value of log2(F) and −log10, with studies also employing embryogenic and non-embryogenic callus to determine the molecular mechanisms underlying the emergence of both phenotypes and understand the SE process as a whole [The protocol used in this work can be defined as an indirect two-step process, in which dedifferentiated errupted . The emesegments , with pramarillo . Similar a whole ,28. Furt a whole .calli lines have been previously described in tamarillo [Picea abies), in which the conversion of somatic embryos from embryogenic callus is considered by the authors as one of the most important factors for the large-scale implementation of SE protocols [calli show a greater similarity in the mass ratios but a higher disparity in total protein content. These observations are in accordance with previous studies of these types of calli that have shown EC and NEC callus to be morphologically distinct [calli as a highly hydrated tissue. Furthermore, previous studies have shown some differences at the proteomic level on similar callus lines [callus-secreted proteins [The EC derived from this work shows a similar  embryogenic competence but varies in terms of both total protein content and fresh-to-dry mass ratios, revealing some heterogeneity in the first analysis. However, differences in the somatic embryo conversion of several amarillo , as wellrotocols . The NECdistinct  and presus lines  and quanproteins .callus obtained in SE studies. Free amino acids, for example, have been found in cultures of Coffea arabica L. [Dactylis glomerata [Cuminum cyminum [calli choline and formate have been described in Saccharum sp. suspensions of calli derived with SE protocols in an NMR-based approach [Coffea arabica [The main metabolites identified in this work are consistent with those described in the literature for abica L. . Other slomerata  and stim cyminum . Acetateapproach . Chlorog arabica .calli used in this study were induced and maintained in a Murashige and Skoog medium supplemented with sucrose and picloram. Consequently, glucose and fructose found in calli can be inferred to have derived from sucrose. However, the culture medium contains only the basic inorganic salts needed for plant growth and some organic compounds: myo-inositol, nicotinic acid, pyridoxine and thiamine. Furthermore, the calli underwent two or three cycles of in vitro multiplication to achieve enough mass for the subsequent tests (chemometrics and conversion assays). Therefore, the metabolites detected were synthetized by the calli in anabolic pathways that start in intermediates derived from the catabolic activity. Lactate is an end-product of glycolysis [The ycolysis ; formateycolysis . Acetateycolysis .Amino acid synthesis in plants is highly complex and is connected with several metabolic pathways, notably carbohydrate metabolism and namely the tricarboxylic acid (TCA) cycle, where 2-oxoglutarate is an important metabolite that can originate the non-aromatic proteinogenic amino acids ,41. Othecalli, namely the amino acids that can be derived from the main carbohydrate metabolism, particularly the TCA cycle. Additionally, nicotinic acid as a nucleotide precursor has been extremely well reviewed [Additionally, the identified aromatic amino acids  and chlorogenate are products of the phenylpropanoid pathway ,49 that reviewed ,52.callus tissue; however, the overall pathways are similar in many plant families. For example, the Shikimate (phenylpropanoid) pathway is common to several plant families [In general, the described metabolic reactions have not been specifically identified in the tamarillo plant or families  and, altcalli samples along the first two PCs with fructose, glucose, sucrose and choline being the greatest contributors to the overall variance. The medium sugar concentration has long been recognized as an important factor in increasing SE efficiency in several species, namely in Cucumis sativus [calli [Cichorium sp. and Picea asperata [Following spectral processing and the metabolite identification and construction of the proper multiplet-based data matrices, multivariate statistical methods were applied to the resulting data, namely a principal component analysis (PCA) followed by a Projection to Latent Structures Discriminant Analysis (PLS-DA). Similar methodology workflows have been described and are often employed to address the type of data that results from a metabolic screening based on NMR spectroscopy ,55. PCA  sativus  and tama sativus ,26, with sativus ,60. Mores [calli . Altogetasperata ,62, and asperata , which ccalli from similar groups; however, the relative distance between the groups does not follow an immediate pattern (EC or NEC clusters close to each other), hitting the high heterogeneity of the cell populations in the study. Previous studies in other species such as Olea europaea and Arabidopsis thaliana have shown a great diversity of the callus response in terms of in vitro protocols [The dendrogram presented was obtained with a hierarchical clustering analysis, a type of classification procedure where a specific distance metric with an associated classification scheme is applied to the data, leading to the classification of the instances based on shared similarity . Such merotocols ,65. The calli studied, with lipid metabolism, represented in some models by choline, also being relevant . The amino acid proline, over-expressed in some EC and NEC, has been linked to SE as a stimulant agent [calli with the same embryogenic phenotype. In fact, some studies have already highlighted different stress response mechanisms in EC and NEC in Vitis vinifera [The next step of the analysis used a supervised method, namely a Projection to Latent Structures Discriminant Analysis (PLS-DA), a technique that is amply used in chemometric studies . PLS-DA nt agent  and indint agent . Interesvinifera  as well vinifera . Furthervinifera .calli separation, a volcano plot analysis was used to address differentially expressed metabolites in the embryogenic and non-embryogenic calli using LTC as a common reference. This type of univariate analysis can be considered complementary to the multivariate analysis used [calli when compared to the non-embryogenic groups, supporting the global statistical analysis that shows NEC callus as having a greater intrinsic heterogeneity. Sucrose and its immediate hydrolysis products appear in several analyses as either over-expressed or under-expressed, whereas choline and chlorogenate are more uniformly over-expressed in LTC. In general, these results appear to support the hypothesis that the carbohydrate is one of the main determinant factors to the embryogenic phenotype, as found in this work and previously described [calli.After the analysis of the general data structure and the main metabolites involved in sis used  and is fsis used , combinisis used ,75. The escribed ,77, whilS. lycopersicum, and studied in the context of several physiological phenomena [calli and assumed that at least a significant fraction of glucose and fructose are products of sucrose hydrolysis. In fact, the higher ratios of both glucose and fructose to sucrose found in all the calli may support this hypothesis by suggesting a high activity of hydrolysis. Previous studies using stable isotope labelling on tomato suspensions have shown no gluconeogenesis [calli when compared to EC , which, assuming the high hydrolysis and low biosynthesis rate hypothesis, might indicate an overall lower metabolic activity of NEC in terms of carbohydrate metabolism. In fact, previous proteomic-based studies in similar calli have shown different levels of the expression of several glycolytic and TCA enzymes, with some key enzymes (enolase and fumarate hydratase 1) being over-expressed in EC callus [callus to elucidate, for example, what is the relation between glycolytic and oxidative catabolism.Sucrose is the main sugar transported in plants and, as such, its homeostasis processes have been extensively studied. In cellular uptake, the involved protein transporters are largely, but not exclusively, sucrose/H+ symporters ,79. In ahenomena ,82. Of togenesis , which fC callus . This obC callus ,84: EC1 callus line and not very useful as a discriminant metabolite, although it could be employed to indicate different stress levels within the same phenotype. Alanine, although not as connected with stress response phenotypes as proline, is an important amino acid in several physiological responses and may be related to the overall energetic availability of the cell [calli and lower values in LTC and non-embryogenic callus (with the exception of NEC2), which might indicate some importance in embryogenic competence and an implicit regulation mechanism of the concentration of this metabolite. Tyrosine presents a distinct profile from all other amino acids found, with the lowest levels in EC calli. This pattern can be interpreted as a result of the higher rate of protein synthesis in these calli or possibly in terms of the underlying pathway of synthesis. Furthermore, as previously described, the aromatic amino acids are synthetized in the Shikimate pathway, an important anabolic route of the synthesis of several classes of secondary metabolites and regulatory factors [calli and in LTC (in this case with chlorogenic acid) represents an end-product of the Shikimate pathway: either by not being incorporated into proteins or by the lack of metabolic branching originating other compounds. GABA is a non-proteinogenic amino acid that has been recently related to several phenomena such as SE, by influencing several important pathways, namely the auxin-related regulation routes [calli studied, GABA does not appear to be closely linked to embryogenic competence in general but to specific non-embryogenic phenotypes.In terms of the amino acid analysis, proline shows a greater variance between groups of phenotypes than all other metabolites individually analyzed. As previously stated, this amino acid has been closely linked to the stress response. Therefore, it could be linked to individual stress mechanisms of each the cell . This methe cell . In gene factors . Therefon routes ,89. In tcalli lines. As previously discussed, both molecules are key metabolites in the biosynthesis of the main phospholipids found in eukaryotes, namely phosphatidylcholine and phosphatidylethanolamine, with ethanolamine being a precursor to choline [callus is achieved: although there are still statistically significant differences between EC1 and EC2, the embryogenic callus shows a higher value of this ratio. Taking the assumptions previously described, this result might indicate higher concentrations of phosphatidylcholine. As previously described, both metabolites originate in serine, which can be synthesized from the glycolytic intermediate 3-phosphoglycerate [calli and, consequently, in embryogenic competence.Finally, choline and ethanolamine and their ratios provide indirect information about the phospholipid profile of the  choline . Therefolycerate , again rcalli metabolome to obtain insight into the principal metabolic mechanisms that drive somatic embryogenesis. The results of our study describe the response of various metabolic pathways during the SE, with the major contributions of carbohydrate metabolism, as was previously observed for other species [The development of complementary omics  in the past two decades led to an increased understanding of the flow of information encoded by the genome, and provided insight into molecular processes in living organisms. At the top of the omics pyramid, the study of the metabolome reflects the information expressed and modulated by other omics. As the closest reflection of the phenotype, metabolomics is a rich source of biomarkers but also provides information on biological roles of metabolites as well as their interaction with the other omics. As such, it is an integral part of basic and applied studies of plant development and function . Unlike  species . Despitecalli tissue used in this work were obtained from leaves of previously established shoot cultures of tamarillo seedlings (red variety) germinated in vitro. After germination, plantlets were cloned through the culture of apices or nodal segments on a Murashige and Skoog (MS) medium [−2s−1 (white cool fluorescent lamps).The ) medium  suppleme2, randomly punctured on the abaxial side (3 to 4 punctures per segment) and placed on Petri dishes (9 cm in diameter and 15.9 mm in height) with 35 mL of the MS medium supplemented with 26 mM of sucrose, 20 µM of picloram and 2.5 g/L of PhytagelTM  as a gelling agent. The explants were kept in the dark at 24 ± 1 °C for 12 to 14 weeks until callus development was apparent. At this point, callus samples from apparently embryogenic (EC1 and EC2) and non-embryogenic  phenotypes were selected and subcultured in the same medium for multiplication. Each subculture lasted 1 month and samples for a metabolic analysis were retrieved after 2 to 3 subcultures. Additionally, a long-term callus (LTC) previously established from the same clones and continuous subcultures (more than 3 years) that had shown a loss of embryogenic competence were also used.The apical leaves from shoots were used for SE induction as previously described ,16 with calli lines, a mass of about 250 mg was transferred to Petri dishes with the MS medium supplemented with 11.6 mM of sucrose and 2.5 g/L of PhytagelTM as a gelling agent and kept in the dark at 24 ± 1 °C for 5 weeks. The final mass was weighed and the number of somatic embryos per mass was registered. The mass increment of the callus during the conversion period was registered as a percentage of the initial mass /initial mass × 100). Conversion assays were carried out in triplicate.To confirm the embryogenic competence of the All culture media used in this work were adjusted to pH 5.7 (using either HCl or KOH) before adding the gelling agent and autoclaved at 121 °C for 20 min.calli samples were collected and immediately ground in liquid nitrogen before extraction in a methanol–water solution with pH 7.0 (2 mL/g FW). Similar solvent systems have been previously described in the literature and have been shown to be effective in these cell lines [g, 10 min, 4 °C), the supernatants were evaporated at 65 °C (approximately 24 h), and the metabolites were resuspended in a phosphate-buffered (0.2 M) D2O solution before an NMR analysis.The ll lines . Furtherll lines . After cg, 10 min, 4 °C) and the supernatant was used for quantification with a Bio-Rad Protein Assay based on Bradford’s reaction [callus (75 mg) was immediately weighed and dried for 72 h to determine the dry to weight ratios. These determinations were also made in triplicate.For soluble protein quantification, samples were ground in liquid nitrogen and extracted (2 mL/FW) in a 0.1 M sodium phosphate buffer, pH = 7.0. The extract was centrifuged . Variables (metabolites) were submitted to Pareto scaling prior to the multivariate analysis. A principal component analysis (PCA) evaluated the initial data structure and was used to identify outliers and evaluate possible clustering. A hierarchical clustering dendrogram (HCA) was also constructed with the Ward clustering algorithm using Euclidean distance. Next, a supervised method, a Projection to Latent Structures Discriminant Analysis (PLS-DA), was applied to identify differentially expressed metabolites. Metabolites with a PLS-DA VIP > 1 were considered relevant to group separation. PLS-DA models validated by 5-fold cross-validation and the R2Y and Q2 were used to assess the fitting validity and predictive abilities of the models. Metabolite assignment was based on reference spectra available in public databases such as HMBD. Differentially expressed metabolites were further analyzed with volcano plots using LTC as a reference state.The aqueous cell extracts were thawed, homogenized using a vortex and centrifuged . 1H NMR spectra of the extracts were acquired on a 500 MHz Brucker Advance III HD Spectrometer (11.7 T) equipped with a 5 mm double-resonance broadband probe, using the following acquisition parameters: 298 K, a 5.7 kHz spectral width, a 0.1 s mixing time, 2 dummy scans, a total relaxation time of 7 s, a 90 °C pulse angle, a 2.85 s acquisition time and 64 scans. Spectra were processed by multiplying FIDs with the exponential apodization function (line broadening of 0.3 Hz) prior to Fourier transformation. Additionally, spectra were manually phased in TopSpin 4.0.8 . Further spectral processing and bucketing were performed on the online platform NMRProcFlow . Chemicat-test was used with a p-value of 0.01, FDR-corrected, and a fold change threshold of 2) with LTC as the reference state was applied to all samples. To help visualize the results, fold changes of the significant metabolites were calculated for each sample (the non-significant fold changes were set to 0) and a heatmap based on mean aggregation was built in MATLAB®. Furthermore, all the identified metabolites were analyzed with standard one-way statistical methods, namely an analysis of variance (ANOVA) followed by a Tukey test (p < 0.05). These results were presented using a heatmap based on the normalized data using Euclidean distance as the metric and Ward’s clustering method.After the multivariate analysis, a differential univariate analysis with volcano plots (p < 0.05). If this test was passed, the analysis of variance (ANOVA) followed by a mean comparison with the Tukey test (p < 0.05) was used. If the homogeneity of variances was not met, a Kruskal–Wallis non-parametric ANOVA followed by Dunn’s multiple comparison test was used. These results were analyzed and plotted in GraphPad® Prism v 8 for Windows.Finally, ratios of some metabolites  were also studied. These ratios were analyzed with standard one-way statistical methods. In general, the homogeneity of variances was tested with the Brown–Forsythe test  vary in terms of the proteome and metabolome. The data also suggest that the simple determination of specific metabolites  can be used to infer the embryogenic competence of calli, particularly in terms of specific metabolic fluxes of glycolysis and TCA, to achieve a higher degree of information about glycolic and oxidative catabolism as well as the connection with the anabolic pathways necessary to achieve the metabolites found in this and other studies.Future studies should aim to further characterize this


We found that phosphoenolpyruvate carboxylase (PEPC) played a crucial role in the accumulation of the internal CO2 pool when the CO2 uptake rate was limited during stomatal closure. Based on the model simulation, PEPC mechanistically enhanced drought tolerance in cassava by providing sufficient CO2 for carbon fixation by RuBisCO, resulting in high production of sucrose in cassava leaves. The metabolic reprogramming decreased leaf biomass production, which may lead to maintaining intracellular water balance by reducing the overall leaf area. This study indicates the association of metabolic and physiological responses to enhance tolerance, growth, and production of cassava in drought conditions.Cassava is a staple crop that acclimatizes well to dry weather and limited water availability. The drought response mechanism of quick stomatal closure observed in cassava has no explicit link to the metabolism connecting its physiological response and yield. Here, a genome-scale metabolic model of cassava photosynthetic leaves (leaf-MeCBM) was constructed to study on the metabolic response to drought and stomatal closure. As demonstrated by leaf-MeCBM, leaf metabolism reinforced the physiological response by increasing the internal CO The impact is more pronounced under exacerbating climate changes during the past decades. The circumstance necessitates new strategic development of drought-tolerant crops, for which an understanding of plant responses to stress at the metabolic level is essential to address the challenges of limited water availability for crop production and food insecurity .Manihot esculenta Crantz) has been recognized as an ideal crop to combat food insufficiency in the future, especially under the threat of climate change. Cassava starchy roots provide competitively high calories per cultivation area over other staple crops. Cassava roots contain up to 70-90 percent of starch on a dry matter basis. The main cultivation areas of cassava are in tropical and subtropical regions, though it can be grown in broad climatic conditions. Cassava is one of only a few crop plants that tolerate drought well. It can survive and produce reasonable yield even in marginal environments where other crops fail  in cassava suggests its potential role in enhancing respiratory CO2 capture when intracellular gas exchange was limited by stomatal closure during water stress (2 availability around RuBisCO enzyme and hence lower oxygenase reaction (photorespiration) under stress conditions  allows the prediction of steady-state reaction fluxes in metabolism by applying mass balance constraints. FBA calculates optimal fluxes for biomass production, predicting the growth and production rates of biotechnologically important compounds under conditions of interest  related to 10 pathways, including photosynthetic light-dependent reactions, Calvin-Benson cycle, photorespiration, respiration, pentose phosphate, nitrogen assimilation, starch and sucrose metabolism, amino acid metabolism, primary cell wall metabolism, and fatty acid synthesis. The leaf-MeCBM was first verified by simulations to represent cassava leaf growth under normal conditions. The leaf-MeCBM was subsequently used to investigate metabolic responses to drought by restraining the rate of CO2 exchange to the environment . The resulting high fluxes through PEPC and RuBisCO reactions set the initial hypothesis of the study to investigate the involvement of PEPC in metabolic adaptation under drought conditions. Through in silico perturbation of PEPC activity, flux distribution analysis was performed to study the association of enzymatic reactions in metabolism and the physiological response to stress. The model prediction was finally validated based on the related expression of enzymatic genes and the collective evidence in cassava literature. Comprehension gained in this study would bridge the gap on how metabolic and physiological responses act in concert to boost tolerance to drought conditions.Here, computational analysis was performed to study the response of cassava leaf metabolism under drought conditions. The study also investigated the involvement of PEPC in supporting the robustness of leaf carbon metabolism against drought stress. In this work, central carbon metabolism related to cassava leaf growth was reconstructed mainly based on a genome-based metabolic network of cassava , availab22.1Arabidopsis  identity percentage ≥ 60, and (3) coverage percentage ≥ 80). Reactions related to drought-responsive pathways , from the published metabolic models of Arabidopsis (https://www.genome.jp/kegg/) and Plant Metabolic Network (https://plantcyc.org), databases.The leaf-MeCBM model was constructed primarily based on the reported metabolic network of cassava photosynthetic tissues (ph-MeReCon), which contains nine biochemical pathways , pentose phosphate pathway (PPP), photorespiration, starch and sucrose metabolism, and anabolic pathways of amino acids, fatty acids, fibers, and nucleic acids). Additiobidopsis , and ricbidopsis , and verbidopsis  and ricebidopsis , were albidopsis   was constrained to the experimentally measured values. For the scenario-based simulation of drought conditions, flux through the PEPC reaction was increased by ten times the normal condition. The resulting simulations were expressed both in terms of flux quantity and relative flux ratios.The leaf-MeCBM was used to simulate carbon metabolism inside cassava leaves according to data of cv. Kasetsart 50 (KU50) grown in greenhouse conditions (in-house unpublished data). The uptake rate of carbon  to Vc : Vo = 5  using the same set of model constraints. The patterns of flux fold changes in central metabolism and photorespiration-related pathways were examined for concordance with the predicted metabolic responses of plant leaves to different levels of photorespiration  and curated by information from published metabolic models of Arabidopsis leaves  and photosynthates . It was constructed based on a genome-based metabolic pathway of primary carbon metabolism in cassava leaves . The corresponding photon uptake rate was estimated based on the light use efficiency (LUE) of cassava under well-watered conditions (c/Vo=3) as observed in a typical ambient condition  through amino acid biosynthesis (GS/GOGAT cycle) was also found in the leaf-MeCBM , instead of CO2 . The process generally occurs in the leaf mesophyll at a high O2 to CO2, typically during stomatal closure in response to stress. Here, we simulated the level of photorespiration by decreasing the carboxylation to oxygenation ratio of RuBisCO (Vc/Vo), from a low (Vc/Vo = 5) to high (Vc/Vo= 1) degree of photorespiration; the ratio is approximately equal to 3  relative to normal conditions (Vc/Vo=3) (c/Vo<< 3), fluxes of the photorespiration-related reactions  were more active, corresponding to the increased fluxes in the nitrogen assimilation pathway  and down-regulation of oxidative phosphorylation and TCA cycle. The highly active photorespiration pathway led to the higher ammonia produced and assimilated through GS/GOGAT cycle. The higher glycine decarboxylase (GDC) reaction flux, a part of photorespiration, supplied the reducing equivalent molecules  for the mitochondrial electron transport chain , leading to metabolic adjustment within the mitochondria to level down the activity of TCA cycle . The simulated flux patterns were consistent with studies on leaf metabolism in rice . The flux was about six times higher at 50% reduction of CO2 uptake  of RuBisCO under drought stress by recycling the respiratory CO2 to the fixation reaction. The possible pathway was highlighted based on the observed upregulation of carbonic anhydrase protein (CA) reaction increased its flux and the amount of intracellular CO2, suggesting higher activity of PEPC in the decarboxylation pathway , an enzynditions . In this3.2.22 pool in response to PEPC perturbation were investigated. We found that the increased CO2 pool was contributed mainly by the phosphoenolpyruvate carboxykinase (PEPCK) reaction and oxidative pentose phosphate pathway (OPPP) (enolpyruvate (PEP) and released CO2. Our simulation found that the elevated PEPC activity increased CO2 generation through the PEPCK, accounting for an approximate 1.88% increase in the CO2 pool relative to normal conditions (2 pool was the higher cytosolic oxidative pentose phosphate pathway (OPPP) activity. The flux through OPPP was increased from 9.17 to 9.23 mmol/gDW/day in response to the increased PEPC activity ) and the lower catabolic pathway activity as indicated by the reduced CO2 flux from biomass biosynthesis and the tricarboxylic acid (TCA) cycle under PEPC perturbation H) balance, which crucially influenced the metabolic status by modulating the interrelationship between catabolic and anabolic processes in leaf metabolism. Our simulation showed that metabolic processes in chloroplast were more energy intensive under increasing PEPC activity, attenuating the energy allocated to the cytosol as a result Figure 32 level. These changes affected the catabolic and anabolic relationship in cellular metabolism. Since the elevated PEPC reaction activated CO2 reassimilation by RuBisCO and flooded carbon fluxes through nitrogen assimilation, amino acid biosynthesis, and sucrose metabolism, the imbalance in energy demand and supply led to metabolic reprogramming toward improving the efficiency of energy usage during the response to the perturbation. It implied that the change in carbon balance mediated by the elevated PEPC activity impacted the metabolic state, especially in energy and redox balance, which has consequences for plant growth and development under drought-stress conditions.Overall, the rebalancing of metabolic energy costs was associated with carbon metabolism. In response to the increased PEPC activity, the metabolism was globally adjusted towards maintaining redox and energy homeostasis at a high CO3.2.4via nitrate reductase (NR) (via glutamine synthetase (GS) and glutamate synthase (GOGAT)  metabolism through nitrogen-related pathways. We found that the higher fluxes through the photorespiration pathway in mitochondria required higher amounts of the tetrahydrofolate derivatives as cofactors . Simulations showed the redirection of carbon fluxes towards sucrose biosynthesis rather than biomass production. At PEPC conditions, biomass biosynthesis pathways, namely amino acids, lipids, and carbohydrates, had relatively low fluxes compared to normal conditions, resulting in reduced biomass production rates of up to 79 percent , while limiting biomass production for leaf growth.The increasing CO3.3In silico perturbation of PEPC activity demonstrated the metabolic responsive mechanism in leaves that possibly rescued cassava from the stress of water limitation. An increase in PEPC activity led to a rise in the CO2 concentration in mesophyll via PEPCK and OPPP; the accumulated CO2 was then re-assimilated by RuBisCO. The altered carbon flux resulted in metabolic reprogramming in energy metabolism, nitrogen assimilation, sugar metabolism, and biomass biosynthesis. The overall response caused a reduction in leaf growth as more carbon flux was allocated to sink tissues. The simulated mechanism was consolidated by meta-transcriptome data   and 6-phosphogluconate dehydrogenase (6PGD)  corresponded to the predicted contribution in providing additional CO2 and the associated process of metabolic re-adjustment in the oxidative pentose phosphate pathway  and PEPCK (Manes.08G138300 and Manes.09G128000) genes were increasingly expressed in the last three hours after treatment (HAT), with PEPCK expression still high after 24 hours ; 42 assimilation in the photosynthesis of C4 and CAM (Crassulacean Acid Metabolism) plants. It catalyzes PEP and HCO3- to form the C4 metabolite oxaloacetate (OAA), which is later decarboxylated to release CO2 for RuBisCO. The mechanism was proposed to enhance the acclimation of plants to relatively hot and dry environmental conditions  during CO2 fixation by RuBisCO. In photosynthetic tissues of typical C3 plants, the fundamental function of PEPC is to replenish tricarboxylic acid cycle intermediates that are withdrawn for a variety of biosynthetic pathways and nitrogen assimilation  and maintains membrane potential during stomatal opening , and then produced a three-carbon acid . The primary metabolism of cassava leaves was assumed to take place primarily in mesophyll cells across four sub-cellular compartments: cytosol, chloroplast, mitochondria, and peroxisome. The C4-photosynthesis pathway in cassava was modelled according to the presence of the related genes in cassava genome and the cassava literature. It was composed of PEPC in cytosol, NADP-ME in the chloroplast, NAD-ME in the mitochondria, and PEPCK in the cytosol. The leaf-MeCBM showed that PEPC pathway was upregulating and involved in maintaining the steady state of photosynthetic carbon fixation under simulated drought condition (2 enrichment (FACE) condition, though stomatal conductance was observed reducing. These plants showed lower specific leaf area, but higher final harvest root yield with respect to the atmospheric CO2 condition , the chloroplast-located PEPC isoform was reported to play a crucial role in nitrogen metabolism as found the alteration in ammonium assimilation and amino acid synthesis  in both control and drought conditions. PEPC was proposed to alleviate oxidative damage and be more related to high endogenous saccharide decomposition that enhanced drought tolerance in rice plants  and nitrogen metabolism and balance proved critical for drought stress tolerance. This work also captured the metabolic mechanism behind energy and redox homeostasis. The overall metabolic reprogramming resulted in high sucrose production but a low biomass production rate. This work provides a holistic view of the leaf metabolic and physiological responses of cassava to drought stress. The insights gained could be leveraged to develop tolerant cultivars. Ultimately, this model could also be extended to explore the source-sink relationship and guide metabolic engineering toward enhancing yield and abiotic stress tolerance in cassava and other crops.In summary, the The original contributions presented in the study are included in the article/TS conceived and designed the experiment. TS and SK supervised the project. NP developed the model structure, performed all computational analysis, and prepared the figures. TS and NP analyzed and discussed the results. SK discussed the results. NP and TS drafted the manuscript. All authors contributed to the article and approved the submitted version.


Arabidopsis thaliana core metabolism. The findings pinpoint practical aspects that need to be considered when applying local approaches for flux estimation in large-scale plant metabolic networks.Quantification of reaction fluxes of metabolic networks can help us understand how the integration of different metabolic pathways determine cellular functions. Yet, intracellular fluxes cannot be measured directly but are estimated with metabolic flux analysis (MFA) that relies on the patterns of isotope labeling of metabolites in the network. For metabolic systems, typical for plants, where all potentially labeled atoms effectively have only one source atom pool, only isotopically nonstationary MFA can provide information about intracellular fluxes. There are several global approaches that implement MFA for an entire metabolic network and estimate, at once, a steady-state flux distribution for all reactions with identifiable fluxes in the network. In contrast, local approaches deal with estimation of fluxes for a subset of reactions, with smaller data demand for flux estimation. Here we present a systematic comparative review and benchmarking of the existing local approaches for isotopically nonstationary MFA. The comparison is conducted with respect to the required data and underlying computational problems solved on a synthetic network example. Furthermore, we benchmark the performance of these approaches in estimating fluxes for a subset of reactions using data obtained from the simulation of nitrogen fluxes in the  They afIntracellular reaction fluxes cannot be measured directly and, instead, are estimated by applying computational methods that integrate data from labeling experiments into a metabolic model. Stoichiometric models provide a mathematical description of biochemical reactions; together with assumed optimality principles and physiological constraints  ), such m13C-MFA, from Escherichia coli metabolism  carbon source the isotopically stationary state can be informative for flux estimation. This is the case since at the isotopically stationary state, for this labeling set-up, not all C atoms of all metabolites will be fully labelled, and classical approaches from MFA can be employed for flux estimation. For labeling experiments with plants grown autotrophically, CO E. coli . The secThe integration of labeling patterns into metabolic models in INST-MFA can be performed on a global level, using all reactions in a given metabolic model and imposing constraints on exchange fluxes. This global INST-MFA approach leads to a computationally difficult problem for which widely applied toolboxes exist (e.g. INCA ) alongsihttps://github.com/MetaSys-LISBP/IsoSim). This existing test case was further modified to determine the effect of the number of simulated measurements and different simulated measurement errors. In the second scenario, these local INST-MFA approaches were tested on the nitrogen flux through the metabolic network model AraCore of A. thaliana central metabolism  , non-statabolism . The rev213C or 15N labeling experiments, the transition map of all carbon or nitrogen atoms must be provided alongside with the subnetwork.All three local approaches for INST-MFA require as input the structural information of the sub-network containing the reaction whose fluxes are to be estimated. This structural information consists of the reactions in the network along with the involved metabolites and their stoichiometry. In addition, NSMFRA and ScalaFlux also require the mappings of atom transitions for the considered reactions. For instance, for The input for all approaches also includes the experimental data of the isotopomer distribution for the metabolites involved in the sub-network. In experiments which use mass spectrometry to identify mass isotopomer distributions (MIDs) of the considered metabolites, usually the relative abundance of isotopomers with the same mass, called cumomers, is measured . The claThe output of KFP is limited to estimate the total flux through one metabolite, instead of individual reactions. Both KFP and NSMFRA require data on absolute metabolite concentration data only in the case when absolute fluxes are of interest; in absence of such data, these approaches can still estimate relative fluxes, i.e. the fractional turnover of metabolites. We note that NSMFRA is the only of the three compared approaches that uses simulated labeling data based on Hill kinetics for metabolites without measured isotopomers. However, the applicability of NSMFRA is limited to specific metabolites in the metabolic network, where pathways converge. The approach estimates the relative local fluxes at these nodes. In contrast, ScalaFlux is designed to estimate fluxes for any reaction or a subnetwork for which sufficient labeling data are available. The principle of KFP can also be adapted to many more network motifs than the simple one, shown in All three approaches then solve the ODEs describing the change of the MID fractions with the reaction fluxes as parameters, optimized to fit the measurements or specified analytic functions (see below for details). In the case of ScalaFlux/IsoSim, the ODEs to solve are constructed from the network structure in an automated fashion. In contrast, for KFP and NSMFRA, setting up the ODEs must be performed manually, since no automated implementation is available. In the following, we provide a brief overview of the mathematical formulation and computational details of the three existing INST-MFA approaches.3KFP relies on a system of ODEs for the unlabeled fraction of two metabolites, or which one is a product of a single reaction that uses a labeled substrate; in addition, some amount of recycling from other, unlabeled molecules is allowed; on , allowing us to apply them on the example network included in the IsoSim implementation.ScalaFlux is the only of the compared local INST-MFA approaches that is available in a ready-to-use implementation. The implementation is available in the form of IsoSim , a softw5To compare the three approaches, we applied them with simulated data from two distinct networks: (1) the synthetic example network from ScalaFlux/IsoSim and (2) nitrogen fluxes in the AraCore model network with atom mappings obtained from i = 10(i-1)log10(16)/160-1, 1 ≤ i ≤ 161, from a 15-minute-long simulation of the network. More specifically, the second time point was ~1 second after the start of the simulation and the second to last timepoint was ~16 seconds before the end of the simulation. The nitrogen labeling of the AraCore model network was sampled equidistantly at 81 time points for a 320-minute-long simulation. For the performance analysis, four subsets of these samples, containing 6, 11, 21 and 81 measurements, were used for each network.The simulation data for the synthetic example was sampled at 161 time points, specified by t6m+0A in H, with two atoms. The input fitting was tested for all one-atom metabolites except Sout (since Sout was set to be fully labeled from the start). IsoSim fits the input labeling data for each metabolite to a logistic and a double logistic function, each multiple times with randomized starting values. The fit with the smallest distance to measurements is then chosen as the input function to the system of ODEs used for the flux estimation. In the case of the synthetic network and simulated flux distributions, in all but one case, a logistic function . After careful evaluation of the source code, we decided to change the method of sensitivity analysis to be used with the data. IsoSim conducts a sensitivity analysis by repeating the second step of its process with randomized noise added to the measured  data, based on the standard deviation of the actual measurements (or expected standard deviation for the simulation). In doing so, however, the fitting of the input labeling data is not repeated. Since the fitting of input data is the first step in the process, with major impact on the resulting estimation, we decided to conduct our sensitivity analysis by repeating the whole process with noisy data. In addition, the default number of repetitions in IsoSim was rather low (fixed to 4), and we increased it to 100. This modified approach also allowed us to conduct comparative analyses with the other compared approaches. While these modifications increase the computation time, the steps are easy to parallelize.Here, we aimed to estimate the flux of individual reactions, the most fine-grained local setting, since it also enabled us to compare the performance between approaches. First, we tested the approaches on simulated data from the synthetic network provided with the IsoSim implementation  could be employed, if applicable. The consequence of these findings is that IsoSim is applicable for reliable estimate of fluxes of reactions that involve metabolites with a difference of their label enrichment that is bigger than the standard deviation of the enrichment measurements.One factor to be considered in interpreting these findings is the very small difference in the labeling of reactant and product in the reactions whose fluxes are estimated. This difference reaches a maximum of around 0.01, well within the expected standard deviation of the measurements Figure 8The test of KFP on the reactions from AraCore failed, the confidence intervals are small, but the true values are not contained in these intervals Figure 9-1*h-1. The comparative analysis estimates are based on our implementation of the core principles of NSMFRA using the input fitting method of IsoSim. NSMFRA might perform better with their original implementation, which, however, is not publically available.For NSMFRA, our implementation showed poor results for the pair of reactions chosen . For both reactions the confidence interval is rather big and still the true flux values are not covered , which is expected to improve the quality of the estimate.Even if good local estimates are only possible for a small range of reactions in a large network, the inclusion of those local flux estimates as constraints in flux balance analysis (FBA) problems can lead to more pronounced reductions in the solution space of FBA problems due to the imposed reaction couplings.https://github.com/sebahu/Local_INST-MFA.Publicly available datasets were analyzed in this study. This data can be found here: Conceptualization, ZN. Implementation, SH. Formal Analysis, SH. Writing – Original Draft, SH, ZN. Writing – Review and Editing, SH and ZN. All authors contributed to the article and approved the submitted version.


Complex feedback regulation patterns shape the cellular metabolic response to external or internal perturbations. We propose here a framework consisting of a sampling-based metabolic control analysis of kinetic models to investigate the modes of regulatory interplay in metabolic functions. NADPH homeostasis, for instance in a context of oxidative stress, is an example of metabolic function that involves multiple feedback regulations which raises the issue of their concerted action. Our computational framework allows us to characterize both respective and combined effects of regulations, distinguishing between synergistic versus complementary modes of regulatory crosstalk. Synergistic regulation of G6PD enzymes and PGI enzymes is mediated by congruent effects between concentration sensitivities and reaction elasticities. Complementary regulation of pentose phosphate pathway and lower glycolysis relates to metabolic state-dependent range of regulation efficiency. These cooperative effects are shown to significantly improve metabolic flux response to support NADPH homeostasis, providing a rationale for the complex feedback regulation pattern at work. Metabolic control analysis (MCA) provides a rigorous theoretical framework to study the sensitivity of metabolic networks with respect to biochemical and environmental variations ,2. MCA hThe role of complex feedback regulatory scheme in shaping the network response to environmental changes is recognized in many contexts ranging from nutrient utilization, end-products homeostasis, or stress response ,14,15. TTo address systemic properties of regulation patterns, our kinetic modeling framework extrapolates metabolic control analysis beyond a reference state, by combining mathematical analysis of control equations and sampling analysis of kinetic space. The idea is to represent the statistical distribution of control coefficients on low-dimensional subspaces defined and constrained by control equations. We first depict a global picture of the control pattern related to NADPH homeostasis driven by oxPPP in the absence of regulation, which reveals some trends which are in contradiction with experimental evidences. Combined mathematical and sampling analysis of control pattern further reveals how the presence of feedback regulation promotes PPP flux rerouting and NADPH homeostasis, involving also synergistic and complementary modes of cooperation. NADPH-dependent inhibition of G6PD and 6PG-dependent inhibition of PGI exhibits synergistic cooperation due to congruent concentration control of 6PG and G6P metabolites. Such a regulatory scheme must be supplemented with feedback inhibition of lower glycolysis to extend the efficiency range of NADPH homeostasis beyond a reference flux state.N defines the stochiometric matrix, To investigate metabolic control properties associated with feedback regulations, we consider the following kinetic modeling framework restricted to the main pathways involved in PPP-driven maintenance of NADPH homeostasis A. The co satisfy:NvGiven Equations  and 3),,3), we do oxPPP) B. MathemThe general form of the function k parameter subsets To provide a preliminary statistical picture of control patterns associated with NADPH homeostasis, a distribution of control coefficients can be obtained from random sampling of kinetic parameters in the absence of feedback regulations . This saux modes A. The saux modes  to a two+ binding to G6PD provides a primary source of oxPPP flux increase in response to NADPH depletion where Parameter sampling confirms expected trends in the control pattern with many sign-definite coefficients B,C. NADPe stress ,27,31. TFrom the matrix expression relating control and elasticity coefficients, one can derive a control equation for NADPH homeostasis as function of a set of regulatory parameters. Keeping in mind that oxPPP flux control and NADPH concentration control are related by Equation ), we canEquation ) dependsEquation ) to dissumptions .+ as a cofactor of G6PD enzyme, which provides a maximum flux control of In the absence of regulation, an increased consumption of NADPH enhances the PPP flux control due to the concomitant increase in NADPEquation  and FiguEquation A. The reEquation  and FiguEquation B. The reEquation  and FiguEquation C. In shaquations  and  F. FinallEquation  (Figure Equation G. To sumEquation H.2O2, a major source of ROS, directly interacts with and inhibits several glycolytic enzymes, notably GAPD and PFKFB3, through S-gluthationylation modifications. We therefore apply now metabolic control analysis to a context where the increase in GR-dependent oxidation of NADPH into NADP+ is mediated by an increased production of H2O2, shifting the nature of parametric perturbation from grk to oxk for which control coefficients are computed. The model incorporates now the H2O2-dependent oxidative inhibitions of GAPD and PFK1. In this scenario, control manifold equations can be derived (see After identifying a synergistic mode of allosteric regulation which is only efficient when glycolytic flux out competes oxPPP flux (ppp>Jpgi ,33. In tived see  to obtai2O2 promotes significant NADPH homeostasis, but only for negative enough level of To analyze the control properties associated with this expression, random sampling of kinetic space is performed again to plot the statistical distribution of Equation . The sam compare A–D. EnhaEquation F.To summarize, the upregulation of G6PD enzyme mediated by  to Jpgi G. BecausThe present study proposes a methodological framework to investigate the mode of regulatory crosstalks in the functional response of metabolic networks. The context-dependent control of metabolic fluxes involves complex regulation patterns as exemplified in the regulation of carbon flux rerouting into oxidative branch of the PPP to meet cellular demand in NADPH ,22. A nuSynergistic allostery usually refers to allosteric binding to separate sites of a same enzyme thereby increasing enzymatic activity in a cooperative manner ,37. The  in 6PGD ,40 compa in 6PGD . Rapid p in 6PGD  could alControl coefficients computed for a reference metabolic state can already identify a set of rate-limiting enzymes that are likely to be conjointly regulated supporting the requirement of distributed control ,43. In t


Fibrobacter succinogenes is a cellulolytic bacterium that plays an essential role in the degradation of plant fibers in the rumen ecosystem. It converts cellulose polymers into intracellular glycogen and the fermentation metabolites succinate, acetate, and formate. We developed dynamic models of F. succinogenes S85 metabolism on glucose, cellobiose, and cellulose on the basis of a network reconstruction done with the automatic reconstruction of metabolic model workspace. The reconstruction was based on genome annotation, five template-based orthology methods, gap filling, and manual curation. The metabolic network of F. succinogenes S85 comprises 1,565 reactions with 77% linked to 1,317 genes, 1,586 unique metabolites, and 931 pathways. The network was reduced using the NetRed algorithm and analyzed for the computation of elementary flux modes. A yield analysis was further performed to select a minimal set of macroscopic reactions for each substrate. The accuracy of the models was acceptable in simulating F. succinogenes carbohydrate metabolism with an average coefficient of variation of the root mean squared error of 19%. The resulting models are useful resources for investigating the metabolic capabilities of F. succinogenes S85, including the dynamics of metabolite production. Such an approach is a key step toward the integration of omics microbial information into predictive models of rumen metabolism.F. succinogenes S85 is a cellulose-degrading and succinate-producing bacterium. Such functions are central for the rumen ecosystem and are of special interest for several industrial applications. This work illustrates how information of the genome of F. succinogenes can be translated to develop predictive dynamic models of rumen fermentation processes. We expect this approach can be applied to other rumen microbes for producing a model of rumen microbiome that can be used for studying microbial manipulation strategies aimed at enhancing feed utilization and mitigating enteric emissions. Fibrobacter succinogenes has been particularly studied  and eukaryotes (protozoa and fungi) which concur to the degradation and fermentation of the feed components, and particularly complex fibrous substrates that cannot be digested by the host. Rumen bacteria, fungi, and protozoa participate in the degradation of the plant cell wall lignocellulose , produci studied . F. succer diets  and is per diets . It has  animals .F. succinogenes S85 has been isolated from a bovine rumen a long time ago  encoding carbohydrate-active enzymes (CAZymes) . A GEM is a mathematical representation of a metabolic network that allows the study of genotype-phenotype relationships  . The genCAZymes) , F. succn system . This spacterium . This stacterium , but theacterium . F. succentified . In addiy sector . Firstlyy sector . Deciphey sector . Secondlmolecule , ,24. Homolecule . An effiionships  and faciionships . For a gionships -30. Hoionships . Kineticionships  for a reionships . The objF. succinogenes strain S85 (ATCC 19169) was grown in triplicates in a chemically defined medium  according to the manufacturer’s recommendations. Cellobiose consumption was estimated by quantification of the remaining reducing sugars in the culture medium using Miller’s method .F. succinogenes S85 was performed using the freely available workspace AuReMe (automatic reconstruction of metabolic models) (ad hoc packages to reconstruct and handle GEMs. It uses (i) the outputs of the Pathway Tools software (Python library for handling metadata of metabolism [F. succinogenes S85 metabolic network.The metabolic reconstruction of  models) . AuReMe software , 40 to psoftware , 42 to psoftware  to perfotabolism ) to ensuF. succinogenes S85 were downloaded, respectively, from https://www.ncbi.nlm.nih.gov/nuccore/CP001792.1 and https://www.ncbi.nlm.nih.gov/nuccore/CP002158.1. Each F. succinogenes S85 genome contains 3.84 Mbp with, respectively, 3,160 and 3,174 genes identified.The two complete annotated genomes of Escherichia coli K-12 MG1655 .The biomass reaction of 2 MG1655  was adapF. succinogenes growth (Table S2). The final products’ (targets’) list was prepared according to our knowledge on the metabolism of this bacterium metabolism and network reconstruction needs (Table S2).The list of seeds  was prepared based on the minimal medium composition needed for Bacteroides thetaiotaomicron iAH991  and theal tools , 50) forThe draft network was manually curated to find potential errors and filling gaps based on the phenotype and experimental data reported in the literature. FBA was used to reconstruct and validate models for maximizing the biomass reaction flux.basic local alignment search tool [F. succinogenes S85 translated genomes. The identified proteins with identity >76% with coverage throughout the sequence were associated with their corresponding reactions in the GEM. We set a high identity percentage to avoid biological inconsistencies by linking a gene to a reaction without experimental validation. Reactions with no gene associated or with gene coding protein of lower similarity were retained in the model only when present in the E. coli K-12 MG1655 model  using the reaction Enzyme Commission (EC) number. The corresponding protein sequences were aligned using BLAST (rch tool ) to the 55 model .The dynamics of metabolism can be described by the following generic differential equation resulting from applying a mass balance S contains the stoichiometric matrices for intracellular  . Hence, terature , which aterature , which aDifferently from other methods, NetRed performs the reduction of the stoichiometric matrix of the full network through matrix algebra based on given flux vectors and a list of protected metabolites . This meThe reduction of the GEM followed several steps: (i) calculation of fluxes by FBA, (ii) carbon balancing, (iii) compacted lumped biomass reaction, (iv) re-calculation of fluxes by FBA, and (v) network reduction.To keep the flexibility of the full network, the flux distribution of the GEM was calculated by FBA considering different objective functions that maximize the production of specific metabolites . Furthermore, several input fluxes were considered for the three substrates: glucose, cellobiose, and cellulose. Details about the values are described in the section Network reduction.The results were analyzed in terms of yields for which all the obtained fluxes were divided by the uptake flux of glucose, cellobiose, or cellulose. Yield analysis allowed to verify the carbon balance of the network as well.Further reduction of the network was achieved by computing a compact lumped biomass reaction, which was based on the pathways identified as essential for biomass production. This approach is like the construction of a core metabolism. In our case, however, we have only used this core for biomass allowing for other pathways to contribute as well to the production of metabolites needed for biomass. Finally, the obtained fluxes from the network with compacted biomass formulation and correct carbon balance have been introduced to NetRed to compute the final reduced network which was used to compute EFMs.in vitro experimental data detailed in the sections Culture conditions and sample preparation and Quantification of substrate consumption and metabolite production, where F. succinogenes was grown on three different substrates . During culture on these substrates, growth , production of metabolites , ammonia and carbohydrate consumption were monitored at six time points. The dynamic concentration of the metabolites were used in the model calibration routine using the maximum likelihood approach implemented in the MATLAB toolbox IDEAS . The estimation of the parameters of Monod kinetics is known to be hampered by practical identifiability problems. That is, the parameters cannot be estimated uniquely from noisy and limited data , illustrating that the two genome sequences are not complete.The two published genomes of the eactions  and 1,11F. succinogenes S85 first model obtained from Pathway Tools . The gaps in the model were first filled automatically by mapping and transforming KEGG/BiGG identifiers to MetaCyc IDs using the MetaNetX package. Ninety-nine reactions were added by Meneco  and 85 targets (molecules known to be produced by the bacterium) for y Meneco , and ally Meneco . Twenty-In our reconstruction process, the aim was to obtain a functional high-quality network, which produces biomass yield. For this purpose, we first focused on reaching topologically all the targets according to the qualitative network-expansion criteria. Forty-one reactions were expertly added to the gap-filled model network. These reactions belong to four distinct databases: MetaCyc , KEGG 6, BiGG 6, and RHEAfterward, we manually unblocked all the pathways referring to FBA analysis, which were in direct and indirect relationships with each component of the biomass reaction. We therefore focused on curating the network and the pathways involved in carbon and nitrogen metabolism as well as some essential cofactor biosynthesis. In particular, we checked the different pathways of glycolysis, the glycogen cycle (see below), and the short-chain fatty acids biosynthesis. This required adding 490 manually curated reactions in the pathways of the biomass compounds.F. succinogenes S85 model reactions are linked to 1,317 genes, leading to 77% of reactions associated with a gene  metabolic pathways are complete at more than 75% of the reactions present in the KEGG and MetaCyc databases. 76% of those active pathways have at least one reaction with flux according to the FBA analysis, and 150 pathways are 100% active in flow . All the essential reactions are present in the active pathways.F. succinogenes during all growth phases  (EC 2.7.7.27), glycogen synthase (glgA FSU_RS16140 FISUC_RS15965) (EC 2.4.1.21), and glycogen-branching enzyme (glgB FISUC_RS15575 FSU_RS01770) (EC 2.4.1.18) (pgm FSU_0773) that was linked to the reaction EC 5.4.2.2 by manual curation .As an example to illustrate the use of the reconstructed network, we analyzed the glycogen biosynthesis and degradation pathways, because glycogen has been shown to be simultaneously synthesized and degraded in h phases . Intrace.4.1.18) . All themalP FSU_RS06195) and EC 2.4.1.25  identified by annotation (glgX) and EC 3.2.1.20 alpha-glucosidase . The maltotetraose formation reaction present in E. coli model was added to our model, and no gene was linked because of no significant BLAST similarity with the F. succinogenes genome .The known glycogen degradation pathway on MetaCyc 23.0 was detected with the presence of the reactions EC 2.4.1.1  biomass and succinate and (ii) biomass and acetate. To enlarge the possible flux distribution, different input fluxes of glucose, cellobiose, and cellulose ranging between 0 and 1,000 mmol/gn were composed of six and five molecules of glucose, respectively. Additionally, a new hypothetical reaction reaction  was addeC. FBA was performed again to compute the flux vector and the reduction was done with NetRed. The protected metabolites corresponded to biomass, acetate, succinate, formate, glycogen, glucose, cellulose, cellobiose, protons, ammonium, and fructose-6P. The reduced network contained 146 reactions and 78 metabolites whose size was still large for the computation of EFM.This new reaction allowed to balance carbon and produce biomass with a mass of 25.394 g/molC following the formula C3.69H6.76O2.66N0.25S0.010 previously reported for the biomass composition of F. succinogenes S85 . This approach is similar to the computing of lumped biomass employed by Lugar et al. . Detailsenes S85 .i, PPi, and ADP were not needed as sources, so their fluxes were also assumed to be zero. A reduction of the extracellular cofactors was made accepting small changes in yield analysis from FBA. Cofactors such as NADPH, NADP, NAD, and NADH were not needed as sources, whereas ADP and NADH were not needed as sinks.The new network comprising the lumped biomass reaction and the carbon balance was used to calculate flux vectors subject to several constraints. All the reactions used for the construction of the lumped biomass reaction that did not correspond to essential reaction were blocked to zero flux. Furthermore, we verified that cofactors such as FAD (Flavin adenine dinucleotide), P2; proton (cytosolic and extracellular); ATP; salts; glycogen; PPi; and the three carbon sources glucose, cellobiose, and cellulose. The reduced network  is appropriate for the computation of EFM.Flux vectors for the three substrates and the protected metabolites mentioned before were used in NetRed to obtain a reduced network of 63 reactions with 36 intracellular metabolites and 16 extracellular metabolites. The biomass reaction of the reduced network accounts for a term called “salts” gathering all the metabolites that do not participate in any other reactions, but that are, nevertheless, necessary to produce biomass. The extracellular metabolites were biomass; acetate; succinate; formate; ammonium; coenzyme A  or a positive sign (n). These EFMs are used to select a minimal set of macroscopic reactions for the DMM as discussed below.where the coefficients https://doi.org/10.5281/zenodo.7228115.F. succinogenes on glucose, cellobiose, and cellulose, respectively. The mathematical modeling of the rumen ecosystem is a useful endeavor to provide tools for improving rumen function. Current kinetic rumen models do not consider genomic information , 73, 74.F. succinogenes S85 was performed using the AuReMe platform, selected for its full traceability reconstruction .The obtained GEM of Ruminococcus flavefaciens previously reconstructed  and limit the calculation of computationally expensive analysis  .Our model contains 2.5 times more genes than the model of the rumen cellulolytic bacterium structed  by Modelstructed  and gapsstructed , as wellandidate . GEMs arg., EFM) . Hence, g., EFM) . For ourg., EFM)  was instF. succinogenes is known to synthesize glycogen during all its growth phases (Yield analysis was used in the flux vectors to verify the carbon balance of the network. The obtained yields showed that carbon balance was not respected, and the difference was coming from the glycogen pathways. Some of the glycogen pathway reactions were identified from the databases as generic reactions. h phases . We focuh phases . A 2-D rh phases . The EFMF. succinogenes. It should be noted that the resulting macroscopic reactions included in the models correspond to the active sets of EFMs specific to the experimental here studied while the subsets of all EFMs at the vertices of the polygon enclosing the yield spaces shown in The resulting model structures are similar in degree of complexity with respect to the rumen fermentation model developed by Muñoz-Tamayo et al. , where cF. succinogenes. However, F. succinogenes and appears to be submitted to a futile cycle that results from simultaneous utilization and storage (The model performances were acceptable to capture the dynamics of fermentation by  storage , 96. As  storage . However storage  and Schu storage  to accou storage , this ap