A special disease is usually caused by the alteration of a series of functional related metabolites having a global influence on the metabolic network. Moreover, the metabolites in the same metabolic pathway are often associated with the same or similar disease. Based on these functional relationships between metabolites in the context of metabolic pathways, we here presented a pathway-based random walk method called PROFANCY for prioritization of candidate disease metabolites. Our strategy not only takes advantage of the global functional relationships between metabolites but also sufficiently exploits the functionally modular nature of metabolic networks. Our approach proved successful in prioritizing known metabolites for 71 diseases with an AUC value of 0.895. We also assessed the performance of PROFANCY on 16 disease classes and found that 4 classes achieved an AUC value over 0.95. To investigate the robustness of the PROFANCY, we repeated all the analyses in two metabolic networks and obtained similar results. Then we applied our approach to Alzheimer's disease (AD) and found that a top ranked candidate was potentially related to AD but had not been reported previously. Furthermore, our method was applicable to prioritize the metabolites from metabolomic profiles of prostate cancer. The PROFANCY could identify prostate cancer related-metabolites that are supported by literatures but not considered to be significantly differential by traditional differential analysis. We also developed a freely accessible web-based and R-based tool at  A major challenge in today's medicine and biology is to identify the key metabolites associated with complex diseases. Because metabolites are modulated by genetic and environmental perturbations; their alterations in the concentration can reflect disturbed metabolic functions and reveal novel physiological and pathophysiological information, which can not be obtained directly from the genomics, transcriptomics, and proteomics The main technology of metabolomics is using nuclear magnetic resonance (NMR) spectroscopy or liquid/gas chromatography-mass spectrometry (LC/GC-MS) to profile and quantify concentrations of hundreds of metabolites simultaneously The development and completeness of some high quality metabolic network databases have led to availability of computational method for prioritization of metabolites. The metabolites rarely function in isolation; rather, they carry out biological functions together through thousands of biochemical reactions which organize into intricate metabolic network http://bioinfo.hrbmu.edu.cn/PROFANCY.With these understandings, we developed a global computational method called PROFANCY  to prioritize candidate disease-related metabolites based on the assumption that metabolites associated to the same disease are functionally related in the context of metabolic pathways see . In our The known disease–metabolite associations were extracted from the Human Metabolome Database (HMDB) which collected detailed information of small molecule metabolites found in the human body, including their related disease phenotype information described in entries in OMIM For prioritizing disease metabolites in a global view, we reconstructed an undirected metabolic network in which nodes represented metabolites and two metabolites were connected if they were in the same reaction. To do this, we extracted the pathway structure information from two databases: KEGG The PROFANCY could prioritize candidate disease metabolites by fully exploiting the global functional similarity of metabolites and the functionally modules of metabolic network. To take advantage of global functional similarity between metabolites, we employed RWR method, introduced by Kohler, S et. al Some studies indicated that metabolites in the same modules (pathways), together exerting a special biological function, were prone to lead to a special or similar disease ability  .To access the performance of PROFANCY, we used leave-one-out cross-validation method on every disease metabolite. For each disease, each of the known metabolites was taken as one test case. For each test case, the remaining known disease metabolites were used as seed nodes. The held out metabolite and other metabolites in the network were considered as candidates. After the implementation of RWR method, each metabolite in the network was assigned a probability value. Then we could rank test metabolite with the other nodes in the network together. Therefore, for each test metabolite of every disease, we could obtain a rank list. Taking all rank lists of all disease metabolites together, we could calculate the ratio of the known disease metabolites which ranked in top n%.The receiver operator characteristic (ROC) curve could also be plotted and the area under this curve (AUC) could be calculated according to above results. The ROC curve plots the true-positive rate (TPR) versus the false-positive rate (FPR). For evaluating rankings of disease-metabolite predictions, here ROC curves could be interpreted as a plot of the frequency of the disease metabolites above the threshold versus the frequency of disease metabolites below the threshold, where the threshold is a specific position in the ranking In this section, we first assessed the performance of the PROFANCY method on 71 diseases which could be grouped into 16 classes. Then we assessed the robustness of the PROFANCY. After that, we investigated the contribution of functional pathway nodes in the prioritization process of PROFANCY. In the following two case studies, we predicted novel potential disease metabolites for Alzheimer's disease using PROFANCY. Furthermore, we applied our method in prioritizing the metabolites from metabolomic profiles of prostate cancer.To assess the performance of our method, we performed a validation with 338 known disease metabolites associated with 71 diseases obtained from the HMDB database see  [21]. FoWe found that our method have outstanding performance on some diseases. For example, all the known metabolites of maple syrup urine disease, lesch-nyhan syndrome and propionic academia were ranked in top 10%, respectively . MajoritAnother important issue of our method lies in the robustness of the PROFANCY. We investigated the robustness of our method from following aspects: (i) repeating all analyses in another metabolic network reconstructed from the EHMN database; (ii) randomizing the metabolic networks; (iii) perturbation of the candidate metabolites; (iv) setting different value of the restart probability At first, we reconstructed another metabolic network from the EHMN database see  and repeWe next assessed the robustness of PROFANCY after perturbation of metabolic network. After removing edges in the original metabolic network from a percent of 10% to 90%, we calculated the AUC value in these incomplete networks, respectively. We found that the PROFANCY had strong resistance against the incompleteness of network–the AUC value only had a slight decline (about 0.005 or 0.003) when deleting 10% edges of the KEGG or EHMN network ; Even whWe also investigated that whether our method still have stable performance under the perturbation of candidate metabolites. For each disease, we randomly selected 99 metabolites as candidates from original candidate metabolites  to sufficiently exploit functional modularity of metabolic network and thus to enhance prioritizing ability. To assess the contribution of FPN in the process of prioritization, we compared the performance of PROFANCY with FPN to that without these nodes. We deleted these nodes and then prioritized the candidate metabolites on the original metabolic network only. After we performed the validation using the same data as we did above, we found that in both metabolic networks, there were more known disease metabolites which ranked in top 5%, 10% and 50% by PROFANCY than that deleting the FPN . For exaFurthermore, the AUC value of PROFANCY for 71 diseases was higher than that without FPN in both networks . We furtThe FPN contributed not only to the above improvement but also to the robustness of PROFANCY. We found that the FPN might contribute to the strong resistance against incompleteness of network. The AUC value in had a larger decline in the incomplete networks without FPN than that with FPN. For example, when deleting 10% edges of the KEGG network with FPN, the AUC had only a slight decline of 0.005; but in the network without FPN, the decline would have a six-fold (0.036) amplification . This inHere we used the PROFANCY method to predict novel metabolic biomarkers for Alzheimer's disease (AD), which is considered to strongly associate with changes in systemic metabolite The PROFANCY ranked (S)-Methylmalonate semialdehyde in the first place in the KEGG network. Surprisingly, to our knowledge, there were no literatures which directly explored the role of (S)-Methylmalonate semialdehyde  We further investigated whether the top ranked metabolites generated by PROFANCY could be detected by the traditional differential analyses. To do this, we calculated the differential values of top 30 ranked metabolites by Wilcoxon rank-sum test between normal samples (benign adjacent prostates) and two kinds of cancer samples . We found that 5 metabolites were significantly differential in above 6 highly suspicious candidates  and overHowever, we also noticed that some top ranked metabolites were not considered to be significantly differential by traditional differential analyses. For example, glutamine, which ranked in 8th in both networks by PROFANCY, was not significantly differential between normal and localized cancer samples or between normal and metastatic cancer samples . To explIn this article, we presented a global method called PROFANCY to prioritize candidate disease-related metabolites based on the assumption that functionally related metabolites tend to associate with the same or similar diseases in the context of metabolic pathway. We first reconstructed a global metabolic network and added functional pathway nodes to fully exploit the modular information. Then we implemented the RWR method on this network. Finally, we could get the rank of the candidate metabolites. The PROFANCY had a good performance on prioritization on 71 diseases and achieved an AUC value up to 0.895. We also applied the PROFANCY on different disease classes and achieved an AUC value over 0.95 in 4 classes. To investigate the robustness of the PROFANCY, we repeated these analyses in another metabolic network reconstructed according to the EHMN database and obtained the similar results. The good performance and robustness were largely attributed to functional pathway nodes. The PROFANCY method also successfully predicted potential novel Alzheimer's disease-related metabolite and prioritized the metabolomics profiles of prostate cancer.The success of our method could be attributed to the combination of two aspects. Firstly, we took the advantage of the global functional relationships between metabolites. Diseases were usually the consequence of the breakdown of cellular process associated with some functionally related metabolites which were functionally interconnected through metabolic reactions generally grouping into metabolic network http://bioinfo.hrbmu.edu.cn/PROFANCY). It could be expected that PROFANCY would be a beneficial tool for prioritization and prediction of disease metabolites.We also noticed that there were some limitations of our PROFANCY method. At first, our method depended on the topology of the metabolic network, so the low-quality and incompleteness of reaction information of KEGG or EHMN database might limit its performance. Especially, there were no organ-specific reaction and pathway structure data available currently. Although the PROFANCY could perform well in the incomplete network, the performance could be further improved after more complete and specific reconstructions of metabolic network. Secondly, our result is limited to diseases with known metabolites from the HMDB database and the number of known metabolites might have influence on the performance. Integrating multiple metabolite data sources  and availability of well-annotated metabolic pathway may overcome this limitation. The PROFANCY could also be made more flexible not only by using customized seed nodes and candidates but also by fuzzy matching the metabolite names which were supported in our R based or web based tools  KEGG metabolic network and (B) EHMN metabolic network.(TIF)Click here for additional data file.Table S1The number of known disease metabolites of 71 diseases in top 10% rank.(DOC)Click here for additional data file.Table S2Proportion of known disease metablites in top % rank of all metabolites.(DOC)Click here for additional data file.Table S3The AUC value of PROFANCY when deleting edges of metabolic network.(DOC)Click here for additional data file.Table S4The AUC value of 16 disease classes by PROFANCY when randomly selecting candidate metabolites.(DOC)Click here for additional data file.Table S5Effect of  value.(DOC)Click here for additional data file.Table S6Deleted metabolites in the process of reconstructed metabolic network.(DOC)Click here for additional data file.


Isotope labeling experiments (ILEs) are increasingly used to investigate the functioning of metabolic systems. Some enzymes are subject to kinetic isotope effects (KIEs) which modulate reaction rates depending on the isotopic composition of their substrate(s). KIEs may therefore affect both the propagation of isotopes through metabolic networks and their operation, and ultimately jeopardize the biological value of ILEs. However, the actual impact of KIEs on metabolism has never been investigated at the system level.Escherichia coli in the context of 13C-ILEs, under different situations commonly encountered in laboratories. Results showed that the impact of KIEs strongly depends on the label input and on the variable considered but is significantly lower than expected intuitively from measurements on isolated enzymes. The global robustness of both the metabolic operation and isotopic patterns largely emerge from intrinsic properties of metabolic networks, such as the distribution of control across the network and bidirectional isotope exchange.First, we developed a framework which integrates KIEs into kinetic and isotopic models of metabolism, thereby accounting for their system-wide effects on metabolite concentrations, metabolic fluxes, and isotopic patterns. Then, we applied this framework to assess the impact of KIEs on the central carbon metabolism of 13C-ILEs. The proposed modeling framework is generic and can be used to investigate the impact of all the isotopic tracers  on different isotopic datasets and metabolic systems. By allowing the integration of isotopic and metabolomics data collected under stationary and/or non-stationary conditions, it may also assist interpretations of ILEs and facilitate the development of more accurate kinetic models with improved explicative and predictive capabilities.These results demonstrate the necessity of investigating the impact of KIEs at the level of the entire system, contradict previous hypotheses that KIEs would have a strong effect on isotopic distributions and on flux determination, and strengthen the biological value of The online version of this article (doi:10.1186/s12918-015-0213-8) contains supplementary material, which is available to authorized users. The bubstrate , ii) col methods –8, and ice (NMR) –12. Isotce (NMR)  and metace (NMR) , to assice (NMR) , to profce (NMR) , 17, andce (NMR) , 19.12CO2 over 13CO2 [i.e. metabolite concentrations and fluxes), and thus isotopic data themselves. However, the metabolic control may be distributed over different steps of a pathway, and in this case the change of rate constant of a particular reaction may not directly translate into a change of flux through the corresponding pathway. This systemic property of control distribution across the network was theoretically developed under the framework of metabolic control analysis [in vivo [The biological insights obtained from ILEs are valid provided isotopes do not modify the operation of the metabolic network investigated and no isotopic fractionation occurs in the network. However, many enzymes are subject to kinetic isotope effects (KIEs) that modify reaction rates depending on the isotopic composition of their substrate(s) . For inser 13CO2 . Therefoanalysis , 23 and [in vivo –27. Chan13C-ILEs [et al. [2H-ILEs to quantify the contribution of the pentose phosphate pathway to NADPH production in Escherichia coli. They corrected isotopic measurements for the strong isotopic fractionation related to 2H, assuming they have no impact on fluxes. Although highly informative, these studies were carried out at the level of a single metabolic node. Thus, they fail to account for the system-wide effect that these KIEs have over all metabolite concentrations, fluxes and isotopic distributions.The first attempt to assess the impact of KIEs on the distribution of isotopes in intracellular metabolites was published recently, in the context of 13C-ILEs . They co [et al.  carried E. coli, in the context of the most widely used 13C-ILEs. The impact of KIEs on metabolite concentrations, fluxes and isotopic distributions was quantified under a broad range of situations commonly encountered in laboratories .In this study, we first developed a modeling framework which combines isotopic and kinetic models, while taking the system-wide KIEs into account. This framework is based on the fluxomer concept , which rThe kinetic model published by  was usedvforw) and backward (vback) rates are equal to:the forward (The model thus contains 58 fluxes (32 irreversible and 13 reversible reactions) decomposed into 7376 fluxomers. This model describes the dynamics of 616 isotopomers (and 94 isotopologues) from 17 metabolites.Five reactions included in the model are catalyzed by enzymes for which KIEs were identified Table . Howeverrunsteady function of the rootSolve package (v1.6.5) of R . Absolute and relative error tolerances were set to 10−8 and 10−6, respectively. All the scripts used to construct the models, perform the simulations and generate the figures are distributed in supplementary information  were sampled over two orders of magnitude  from a log uniform distribution to ensure each order of magnitude to be sampled in similar proportions.A global sensitivity analysis was carried out to evaluate the robustness of our conclusions under a broad range of metabolic states. To this end, steady-states were simulated for 10,000 sets of random enzyme levels generated using the n carbon atoms is denoted by the coefficients , which take a value of 0 if the atom in the corresponding carbon position is 12C or a value of 1 if the atom is 13C. For instance, B0,1,1 represents the isotopomer of the metabolite B which is unlabeled in position 1 and labeled in positions 2 and 3. In the absence of KIEs, each isotopomer of a given metabolite reacts with a probability equal to its abundance relative to the total metabolite pool. Each isotopomer Aa,b,c is thus produced at the rate v1 weighted by Sa,b,c relative to the total S pool  but rather a local rate (i.e. the rate when considering the reaction isolated from the rest of the system). Bearing that in mind, we keep this terminology for sake of simplicity, but note the important distinction between these terms.It must be noted that the term "fluxomer" is somewhat misleading in the context of this study since it does not define a KIEs affect the rate constant of reactions depending on the isotopic composition of their substrate(s). Consequently, KIEs were included by weighting each fluxomer with a coefficient α which represents the KIE of a given enzyme with respect to its substrate(s) isotopomers. For instance, each coefficient Aa,b,c  is its unique substrate. The mass balance around Aa,b,c finally becomes:where B, two additional points must be taken into account. First, it is worth recalling that bidirectional isotope exchange that arise from reversibility significantly impacts the distribution of isotopes through the network [v3 in the model considered here. Second, in the case of reactions with more than one substrate, the impact of KIEs on reaction rate may depend on the isotopic composition of each substrate. Therefore, one fluxomer must be defined for each combination of substrates isotopomers. Reaction v3 was first decomposed into its forward (v3forw) and backward (v3back) components, each of them being then decomposed into fluxomers:To calculate the mass balances for the isotopomers of pool  network . ForwardBa,c,b is:and the mass balance around Using the same formalism, the mass balances around the isotopomers of C, D and E are:U where rows correspond to isotopomers and columns correspond to fluxomers. This matrix contains the stoichiometric coefficients of each substrate(s) and product(s) isotopomer(s) for each fluxomer frp (where p represents a particular (set of) substrate(s) isotopomer(s) consumed through the reaction r). A vector f is then defined that contains all the fluxomers  isotopomers), and a vector a that contains the coefficients αrp for each fluxomer frp. The isotopomer balances can be calculated by:The system of ordinary differential equations (ODEs) defined by Eqs. I is the vector of isotopomer concentrations and ∘ is the element-wise product operator, i.e. (f(t) ∘ a)x = fx(t). ax. The dynamics (and steady-states) of all the isotopomers can be simulated by solving this system of ODEs. Finally, fluxes and metabolite concentrations can be calculated by summing fluxomers and isotopomer concentrations, respectively. The numerical procedure and its implementation are summarized in Fig. where Escherichia coli grown on 13C-labeled glucose. The kinetic model published by [αrp coefficients listed in Table 13C-glucose, a mixture containing 80 % of 1-13C- and 20 % of U-13C-glucose, an equimolar mixture of 12C- and U-13C-glucose, 2,3,4,5,6-13C-glucose, 1,2-13C-glucose and 3,4-13C-glucose. These label inputs are representative of those commonly used in 13C-ILEs [We applied this framework to evaluate the impact of KIEs on the operation of the glycolytic and pentose phosphate pathways of the model bacterium ished by  was usedished by  Fig. 3)Escherich13C-ILEs –35.Fig. 13C-glucose. Since in this situation all the metabolites are fully labeled, impact of KIEs on reaction rates is also maximal. For instance, assuming that KIEs are cumulative at the level of a single reaction [For the metabolic state represented by the model, the relative changes of fluxes and metabolite concentrations caused by KIEs for each glucose input are shown in Fig. reaction , the reacirca 10 %) [13C-metabolic flux analysis (13C-MFA) [13C-MFA studies might be biased, and KIEs should be considered during flux estimation and sensitivity analysis when such high degree of precision can be reached.The predicted changes of metabolite concentrations are significantly lower than the precision commonly reached in metabolomics (ca 10 %) , 36, hen13C-MFA) , 6, 12. 13C-MFA) . Therefo13C-ILEs can be exploited quantitatively to infer information on the structure and the operation of metabolic systems. Since KIEs may impact isotopic data and ultimately jeopardize the validity of the biological interpretations, their impact must be assessed rigorously. This was performed for the various isotopic data that can be acquired with modern analytical platforms: isotopomer distributions [13C-glucose and 20 % of U-13C-glucose, and an equimolar mixture of 12C- and U-13C-glucose. The distributions of errors caused by KIEs are shown in Fig. Isotopic data collected in ibutions , 38, 39,ibutions , 40 and ibutions . The cor12C- and U-13C-glucose, and minimal for glucose at natural abundance. The predicted errors caused by KIEs are surprisingly low – below 0.001 – for virtually all metabolites and isotopic data. The only exception is pyruvate, with predicted errors up to 0.0045 for its isotopologues, 0.0047 for its isotopomers, and 0.0045 for its molecular enrichment. These errors originate exclusively from KIEs of pyruvate dehydrogenase (PDH). Here again, the system-level impact of KIEs on the isotopic distributions strongly differs from the impact that can be expected for isolated reactions. Moreover, impacts of individual KIEs do not add up at the system level, contrary to what was previously hypothesized [The sensitivity of isotopic data to KIEs strongly depends on the isotopic information considered and on the label input. As a general trend, the impact of KIEs is maximal for the equimolar mixture of thesized .13C-MFA. In the situations investigated here, the biases caused by KIEs on the distribution of isotopes into the glycolytic and pentose phosphate pathway metabolic intermediates are significantly lower than the precision and accuracy obtained by MS (or even MS/MS) [This example illustrates how the framework developed here can be used to evaluate the sensitivity of each isotopic data to KIEs. The less reliable measurements with respect to KIEs can be identified and discarded from the datasets exploited in quantitative approaches such as n MS/MS) , 42 and n MS/MS) , which ii.e. near the given metabolic state investigated. However, metabolic systems are highly non-linear and the impact of KIEs might strongly differ depending on the metabolic state considered [13C- glucose + 20 % U-13C-glucose as label input. Although it is clear that these sets are not representative of those expressed in vivo, they are expected to result in different metabolic states. This was confirmed by analyzing the distribution of some systemic steady-state variables, e.g. the glucose uptake flux varied between 0.02 and 1.6 mmol/gDW/s, and the carbon channeled into glycolysis varied between 0 and 98 % of the glucose uptake flux ), reactions downstream the irreversible step do not exert any flux control [i.e. without decoupling forward and backward reaction rates when constructing the equation system. It is important to mention that all the systemic properties that emerge from metabolic regulation (in particular the distributed control) are identical in both models since the rate laws remain unchanged. With the two models, the impact of KIEs on isotopologue abundances was simulated with and without isotope exchange  the operation of the central metabolic network of Escherichia coli and ii) the distribution of isotopes into metabolic intermediates, in the context of 13C-ILEs under metabolic steady state conditions. Simulations showed that the impact of KIEs is lower than expected from measurements obtained on isolated enzymes. Robustness of the metabolic operation – and thus also of the distribution of isotopes – to KIEs partly originates from the distribution of concentration and flux control over several steps of the network. Bidirectional isotope exchange due to reversibility is also a major determinant of the robustness of the isotopic patterns. This robustness was observed for virtually all the metabolic intermediates, for all the label inputs tested, and under a broad range of metabolic states. It is therefore unlikely that KIEs jeopardize the biological insights obtained in 13C-ILEs, at least for the metabolic network investigated here. The low impact of KIEs on central metabolic intermediates also confirms the interest of quantifying the labeling directly in these intermediates rather than in metabolic end products (such as proteinogenic amino acids). It is important to note that the impact of KIEs may be significant in other situations  and should be evaluated in the specific context of each study.As a case study, this framework was applied to assess the impact of KIEs on 13C- KIEs would have a strong effect on isotopic distributions [in vitro characterization of KIEs. Future knowledge can be readily integrated into the model developed here to obtain a more accurate picture of their impact on the system.These findings soften the suggestions of previous studies that ibutions  and stree.g.2H, 18O or 15N), or for other systemic variables. It may therefore facilitate accurate interpretation of isotopic data collected in ILEs and increase the reliability of the biological insights inferred from these data. We are also considering the application of this framework to better exploit the rich isotopic information collected in ILEs. In particular, it may allow a more accurate estimation of in vivo kinetic parameters of enzymes by integrating isotopic and metabolomic measurements obtained under metabolic and/or isotopic non-stationary states [in silico design of industrially competitive cell factories [The proposed modeling framework is generic and is applicable for other metabolic systems, for different isotopic tracers (y states . This isactories .The data sets supporting the results of this article are included within the article and its additional files.


Metabolic responses are essential for the adaptation of microorganisms to changing environmental conditions. The repertoire of flux responses that the metabolic network can display in different external conditions may be quantified applying flux variability analysis to genome-scale metabolic reconstructions.Escherichia coli metabolic reconstruction, in glucose minimal medium, with an additional constraint to account for the mechanism coordinating carbon and nitrogen utilization mediated by α-ketoglutarate. Flux variability can be decomposed into three components: internal, external and growth variability. Unexpectedly, growth variability is the only significant component of flux variability in the physiological ranges of glucose, oxygen and ammonia uptake rates. To obtain substantial increases in metabolic flexibility, E. coli must decrease growth rate to suboptimal values. This growth-flexibility trade-off gives a straightforward interpretation to recent work showing that most overall cell-to-cell flux variability in a population of E. coli can be attained sampling a small number of enzymes most likely to constrain cell growth. Importantly, it provides an explanation for the global reorganization occurring in metabolic networks during adaptations to environmental challenges. The calculations were repeated with a pathogenic strain and an old reconstruction of the commensal strain, having less than 50% of the reactions of the latest reconstruction, obtaining the same general conclusions.A procedure is developed to classify and quantify the sources of flux variability. We apply the procedure to the latest E. coli growing on glucose, growth variability is the only significant component of flux variability for all physiological conditions explored. Increasing flux variability requires reducing growth to suboptimal values. The growth-flexibility trade-off operates in physiological and evolutionary adaptations, and provides an explanation for the global reorganization occurring during adaptations to environmental challenges. The results obtained do not rely on the knowledge of kinetic and regulatory details of the system and are highly robust to incomplete or incorrect knowledge of the reaction network.In  Escherichia coli on glucose, reaching the optimal growth value calculated from a genome-scale in silico model [The survival of microorganisms in changing environments is based on the ability of metabolic networks to show adaptive responses. Adaptive potential depends on the variety of responses that the organism can display and is limited by constraints in network’s stoichiometry, rate laws and regulation . The greco model . On the co model .Bacillus subtilis, regulatory knockout mutants show improved biomass productivity, suggesting that the bacteria invest resources in anticipation of environmental conditions at the expense of optimal growth [E. coli are consistent with setting up a suboptimal growth to increase metabolic flexibility [E. coli evolution experiment, showing that the decay of unused catabolic functions makes an important contribution to growth rate increase during evolution [Trade-offs between metabolic pathways may restrict growth to suboptimal values. In l growth . Data frxibility . Productxibility . The travolution -9. Thesevolution .How the organism uses its metabolic capabilities to respond to environmental changes is still poorly understood. For instance, metabolic networks show extensive reorganization during adaptation to external perturbations, resulting in a rewiring of global network fluxes. In these global transitions, the expressions of hundreds or thousands of genes change by large factors -16. A maiJO1366[E. coli K-12 MG1655 metabolic reconstruction to date. The original model includes the stoichiometric constraints on the steady-state fluxes and the lower and upper bounds of fluxes under physiological conditions. Here, we introduce an additional constraint to account for the coordination of carbon and nitrogen utilization achieved with a regulatory mechanism, recently described in E. coli[E. coli may be explained by a small number of enzymes most likely to constrain cell growth [In the present work, we develop a procedure, combining flux variability analysis (FVA)  and fluxiJO1366, the latn E. coli. We chann E. coli. Our finl growth . In addil growth -16.in silico models represent the maximum metabolic capabilities of the organism [Genome-scale organism . They hai in the reference conditions, and internal reactions only. Δ quantifies how metabolic flexibility changes with respect to the reference conditions. For conditions more constrained than the reference ones, it always holds that 0 ≤ Δ < 1. If, in the more constrained conditions, the variability of only a small proportion of the reactions is decreased, the effect on the average would be very small, even when those rates were affected in a large extent. As a consequence, Δ values much smaller than one require that a large proportion of the reactions are significantly affected. For instance, Δ = 0.5 may represent that every reaction in the system looses 50% of its reference variability, that 50% of the reactions in the system loose all their variability or any intermediate situation. Therefore, Δ is particularly suited to quantify global changes in metabolic flexibility induced by different environmental conditions  includes the effects of internal and external variation, acting together. Subtracting Δint from Δint + ext, we obtain the additional variability obtained from external variation, Δext , the variability obtained, Δtot, results from the simultaneous action of the three sources: internal, external and growth variation. The contribution made by growth variation to flux variability, Δgro , is the difference between Δtot and Δint + ext , external (Δext), growth (Δgro) and total (Δtot) flux variability, fulfill: Δtot = Δint + Δext + Δgro. Note that the steady-state condition imposes that fixing only int and Δext may change but their sum (Δint + ext) and Δgro remain unaltered.Next we develop a procedure to determine the quantitative importance of each of the three sources of flux variability. We represent the rates of the internal, external and growth reactions by  Figure . Finally Figure . Internatot for the glucose minimal medium in aerobic conditions is, by definition, equal to 1. Imposing tot = 0.207, which is the maximum variability that can be achieved for the glucose minimal medium in anaerobic conditions. Thus, the absence of oxygen reduces the variability to approximately 20% of the reference value.The reference conditions used in this work to calculate Δ are those of the glucose minimal medium, described in Additional file Δ may be used to estimate the metabolic flexibility that an organism can display during physiological and evolutionary adaptations. For this purpose, we use the stoichiometry matrix representing the organism  and vgro is the maximum growth rate obtained fixing glucose uptake at lower values . These E. coli adapts to changes in glucose uptake staying as close as possible to the initial state, i.e. minimizing flux adjustment. This principle, called Minimization of Metabolic Adjustments , has bes  and SpoT (ppGpp synthetase and hydrolase), which in turn are responsible for any accumulation of ppGpp. Accumulation of ppGpp inversely correlates with nutrient richness or quality. It regulates rRNA synthesis and, as a consequence, growth rate. For instance, when fast growing cells are subject to amino acid starvation, inducing the stringent response [E. coli reorganizes its global gene expression when faced with starvation [E. coli regulates its growth rate is in agreement with our theoretical finding, suggesting that metabolic adaptations to environmental challenges require active mechanisms that reduce growth rate in order to increase the repertoire of responses. The fact that a global reorganization takes place during E. coli adaptation controlled by ppGpp is also consistent with growth variation being the source of flux variability, as was shown above  used in the present work. We tested the growth-flexibility trade-off in the iEco1344_EDL933 genome-scale reconstruction [E. coli O157:H7 EDL933 enterohemorrhagic strain. With this model of the pathogenic strain we arrive to the same general conclusions, namely, introducing the coordination of carbon and nitrogen utilization as an additional constraint, growth variability is the only significant component of flux variability in the physiological range of glucose, oxygen and ammonia uptakes , may be determined using Σ . Note that the calculation of Σ, for each new condition, requires solving 2 LP problems, which is much faster than the calculation of Δ. The analysis described in section Flux variability vs. uptake rates was performed using the alternative measure of flux variability, Σ, arriving to the same general conclusions . This is defined as the difference between the maximum and minimum values that the average flux can take, divided by the same quantity evaluated at the reference conditions: iJO1366 model [iJR904, [iJO1366, [iJR904 model and the results obtained are described in Additional file iAF1260[iJO1366[The measure of flux variability used quantifies the global behavior of the network, only changes in a large proportion of the rates producing significant effects. It is, therefore, likely that the general conclusions obtained with the 66 model  are robu[iJR904, ), includiJO1366, ), which e iAF1260. The res0[iJO1366, as expeE. coli growing in the conditions of glucose minimal medium, the growth-flexibility trade-off is the only significant source of metabolic flexibility. Internal and external variability are shown not to be significant components of variability of the internal fluxes. The question is why this is the case. For E. coli in the wild, external rates are affected by unpredictable environmental changes, external variation appearing to be unsuitable to modulate metabolic flexibility. On the other hand, it could be argued that external variation could be modulated by the same physiological mechanisms which are used to adjust uptake rates in response to external changes. However, as we saw, one of these fundamental mechanisms, coordinating carbon and nitrogen uptake [E. coli growing on glucose. Work is in progress to determine if the same principle operates in other environmental conditions and organisms.The results presented in this work show that, for n uptake , has preE. coli has to change its global flux variability. We show that the puzzling phenomenon of global reorganization occurring during adaptations to environmental challenges [iJO1366 genome-scale model [E. coli[A procedure is devised to classify and quantify the sources of flux variability. To our knowledge, this is the first method proposed for this purpose. The variability of the internal reactions may be decomposed into three components: internal, external and growth variability. Growth variability is the only significant component of flux variability in all physiological conditions studied. The increase in metabolic flexibility requires reducing growth to suboptimal values. This growth-flexibility trade-off is the only way that allenges -16,24,25le model  and the  [E. coli. Their vv) that maximizes growth rate (vgro) under mass balance, thermodynamical and flux capacity constraints. The LP problem can be formalized as follows [In FBA, LP is used to find a steady-state flux distribution , external rates (vext) and internal rates (vint). We call vint free (Δint), b) vext free and vint free (Δint + ext), and c) vgro, vext and vint all free (Δtot). Finally, Δext = Δint + ext − Δint and Δgro = Δtot − Δint + ext.where http://www.gnu.org/software/glpk) was used for solving all the LP problems included in this work.FBA, FVA and linear MoMA are formulations of linear programming (LP). The open source GNU Linear Programming Kit (GLPK) .Click here for fileGlucose minimal medium for iJO1366 in silico model.Click here for fileGrowth rate vs. glucose uptake.Click here for fileFlux variability vs. glucose uptake, in anaerobic conditions.Click here for fileFlux variability vs. growth rate, in anaerobic conditions.Click here for fileFlux adjustment vs. glucose uptake.Click here for fileSum of fluxes vs. glucose uptake.Click here for fileFVA in iEco1344_EDL933 model.Click here for fileVariability of the average flux vs. uptake rate.Click here for fileFVA in iJR904 model.Click here for file


Anatomical, physiological, and phylogenetic and analyses as well as computational modeling indicate that the establishment of a photorespiratory carbon pump (termed C2 photosynthesis) is a prerequisite for the evolution of C4. However, a mechanistic model explaining the tight connection between the evolution of C4 and C2 photosynthesis is currently lacking. Here we address this question through comparative transcriptomic and biochemical analyses of closely related C3, C3–C4, and C4 species, combined with Flux Balance Analysis constrained through a mechanistic model of carbon fixation. We show that C2 photosynthesis creates a misbalance in nitrogen metabolism between bundle sheath and mesophyll cells. Rebalancing nitrogen metabolism requires anaplerotic reactions that resemble at least parts of a basic C4 cycle. Our findings thus show how C2 photosynthesis represents a pre-adaptation for the C4 system, where the evolution of the C2 system establishes important C4 components as a side effect.CDOI:http://dx.doi.org/10.7554/eLife.02478.001 Environmental pressures sometimes cause different organisms to independently evolve the same traits. A dramatic example of this phenomenon, which is called convergent evolution, can be seen in the modes used by plants to convert carbon dioxide from the air into starch during photosynthesis.4 photosynthesis essentially represents a carbon dioxide concentration mechanism. It has evolved at least 62 times independently in 19 different families of flowering plants.Early plants existed in an environment with high levels of carbon dioxide in the air. Over time, carbon dioxide levels decreased, so plants evolved more efficient types of photosynthesis to cope. A very efficient type of photosynthesis, called C2 photosynthesis, is a stepping-stone to C4 photosynthesis. It is also known that the evolution of C4 photosynthesis required changes to the expression patterns of thousands of genes, but the exact mechanism that leads from C2 photosynthesis to C4 photosynthesis is not clear.Scientists have shown that a less advanced, low-efficiency version of photosynthetic carbon dioxide concentration, called CFlaveria, which belongs to the same family as sunflowers and asters. Under identical greenhouse conditions, plants that use three different photosynthetic pathways—C3 photosynthesis, C4 photosynthesis, or an intermediate between the two—were grown and their gene expression patterns were compared. Computer simulations were used to model the metabolism of plants that relied on C2 photosynthesis.To explore this in greater detail, Mallmann, Heckmann et al. studied plants from the genus 2 photosynthesis shifts the balance of nitrogen metabolism between two types of cell that are critical to photosynthesis. To rebalance the nitrogen, several genes are expressed to trigger an ammonia recycling mechanism. The same genes are turned on during C4 photosynthesis, and this recycling mechanism include parts of the C4 process.Based on the modeling, it appears that C4 photosynthesis evolved to prevent nitrogen imbalance. Over time, this mechanism was co-opted to become part of a more efficient form of photosynthesis, which may explain why so many different plants evolved from C2 to C4 photosynthesis.The findings of Mallmann, Heckmann et al. suggest that the initial steps in CDOI:http://dx.doi.org/10.7554/eLife.02478.002 The former reaction yields 3-phosphoglycerate (3-PGA), whereas the latter produces 2-phosphoglycolate (2-PG). 3-PGA is reduced to carbohydrates in the Calvin–Benson cycle and incorporated into biomass. However, 2-PG is toxic, which requires its removal by a metabolic repair pathway called photorespiration . In the p to 30% . Eight cp to 30% . The patp to 30% . Ammonia2 conditions, when the oxygenation activity of Rubisco is increased, the high rate of photorespiration becomes unfavorable for the plants , and the resulting four-carbon compound is transported to the bundle sheath cells and decarboxylated by NADP/NAD malic enzyme or phosphoenolpyruvate carboxykinase , two C4 (F. bidentis and F. trinervia), and five C3–C4 intermediate species . We were able to align approx. 50% of our reads to the Arabidopsis transcripts. This is lower as compared to a similar approach using 454 sequencing  to predict detailed flux distributions that follow biologically realistic optimality criteria , as well as for several C4 associated transporters, such as the pyruvate transporter BASS2, the H+/Na+ exchanger NHD, the PEP translocator CUE1 and the putative malate and aspartate transporters DIT1 and DIT2 (4 enzymes (like PEPC kinase or the PPDK regulatory protein) and enzymes with auxiliary functions of C4 enzymes (like pyrophosphatases or adenosinmonophosphatases) show a similar pattern  were measured by immunoblotting. The protein abundance correlates well with the transcript abundance .A gene encoding a mitochondrial NAD dependent malate dehydrogenase as well as several cytosolic and especially one mitochondrial Asp-AT were upregulated exclusively in the C brownii . Often, Flaveria species (http://dx.doi.org/10.5061/dryad.q827h)  .2 photosynthesis, is active in all analyzed C3–C4Flaveria species, as predicted by the computer simulations. Furthermore, it appears that even the most C3-like C3–C4 intermediate species analyzed within the present study, F. chloraefolia, exhibits low level C4 cycle activity. This activity is again in accordance with the in silico model, which predicts the C4 cycle to be a highly efficient ammonia recirculation pathway.Taken together, these data imply that the anaplerotic ammonia shuttle, required to maintain the nitrogen homeostasis in mesophyll and bundles sheath cells of plants performing C2 atmosphere, Rubisco can operate efficiently. But the current atmospheric CO2 concentration, combined with heat and drought, leads to an enhanced oxygenase activity and thereby the photosynthetic efficiency decreases  than the C3 species F. pringlei and F. cronquistii (4.1% and 7.7%)  . Thus ev3 plants immediately supported a shuttle that also involved decarboxylation and carboxylation reactions. C3 plants have considerable capacity for the decarboxylation of four-carbon organic acids in their bundle sheath cell  with additional light for 16 hr per day until 50 to 60 cm height and before the onset of flowering.Plants for experiment one were harvested in September, for experiment two in June, for experiment three in October and for experiment four in April. The plant material was immediately frozen in liquid nitrogen, stored at −80°C and used for the following analyses.2O. The RNA quality was tested with the Agilent 2100 bioanalyzer. 1 µg of total RNA was used for cDNA library generation, which was accomplished with the TruSeq RNA Sample Preparation Kit  via the Low-Throughput Protocol . Clusters were generated with the TruSeq SR Cluster Kit v2 according to the Reagent Preparation Guide with the Illumina cBot device. The single read sequencing was performed with the Illumina HiSeq2000.Total RNA was isolated from the second and fourth leaves according to  followed4 photosynthesis and refixation and recirculation of photorespiratory ammonia were identified among de novo assembled transcripts of F. robusta. De novo assembly was performed with either CLC Genomics Workbench  or the Velvet/Oases software package  was performed using BLAT  was used for plotting heat maps, hierarchical clustering and principal component analysis.The MEV software package  for 1 hr with 0.8 mA per cm2. Specific primary antibodies were raised against conserved Flaveria peptides . For the detection of specific proteins the nitrocellulose membranes were incubated with the primary antibodies and a Horseradish peroxidase-conjugated secondary antibody . An enhanced chemiluminescent Horseradish peroxide substrate was added and signals were recorded using a Fuji LAS-4000 mini CCD camera system. The signals were quantified with the Multi Gage analysis software . As loading control a gel was stained for 45 min with 0.25% Coomassie blue, 50% methanol, 7% acetic acid, and destained in 50% methanol, 7% acetic acid.Total proteins were isolated from plant material harvested together with the material for RNA isolation according to 2 and C4 cycle in the context of leaf metabolism, we conducted Flux Balance Analysis (FBA) based on a genome-scale metabolic reconstruction of C4 metabolism, C4GEM  cannot be captured by this constraint-based approach alone. To account for this issue, we coupled the FBA model with a mechanistic model of Cynthesis .C4GEM representing NADP-ME types was provided by the authors and FBA was conducted using this model:c is the vector of coefficients in the objective function, here the leaf biomass production. v is the vector of fluxes through the network reactions, S is the stoichiometric matrix of the metabolic network, and vmin and vmax represent constraints on the respective fluxes.subject to 3–C4 intermediate plants, S had to be modified. The plasmosdesmatal transport reactions in the original C4GEM model include malate, pyruvate, 3-phosphoglycerate, trioses, phosphates, sucrose, aspartate, alanine, phosphoenolpyruvate, CO2, and O2. Reactions were added to S in order to include transport of serine, glycine, glutamate, glutamine, asparagine, threonine, 2-oxoglutarate and water over the mesophyll/bundle sheath interface. Furthermore, the lack of photosystem II in the bundle sheath of certain C4 plants does not hold in our scenario , serine diffusion , and GDC reaction  can be obtained from the rate of Rubisco oxygenation in the mesophyll (Vom) and the fraction of photorespiratory CO2 in the bundle sheath derived from mesophyll oxygenations (ξ):To couple the genome-scale FBA model with the mechanistic model of carbon fixation, the following reactions were constrained using the values predicted by the mechanistic model: net CO3 state as given in ξ, which was set to a value of 0.98 .The mechanistic model was parameterized to the CIn the FBA part of the model, a minimization of total flux (MTF) analysis was conducted in order to narrow down the space of optimal solutions:vFBA is the flux distribution of the FBA optimization described above. w denotes a vector of weights, where plasmodesmatal flux received a higher weighting factor . This method implements a simple minimization of protein costs for a given optimal biomass production. The higher weights on plasmodesmatal fluxes account for the trade-off between CO2 containment in the bundle sheath and metabolite diffusion between the cells. Since this trade-off is difficult to quantify, we conducted a sensitivity analysis by varying the weight on plasmodesmatal transport reactions.subject to: In order to investigate the possible range that fluxes can take while yielding an optimal solution, flux variability analysis was conducted:vi:For each Maximize or MinimizeSubject to: sopt is the minimum for the weighted sum of absolute flux found in the MTF optimization.Where All simulations were conducted in the R environment for statistical computing  using thF. bidentis), SRP036881 , SRP036883 (F. brownii), SRP036884 (F. chloraefolia), SRP036885 (F. pringlei), SRP037526 (F. pubescens), SRP037527 (F. ramosissima), SRP037528 (F. robusta) and SRP037529 (F. trinervia).The read data have been submitted to the National Center for Biotechnology Information Short Read Archive under accession numbers SRP036880 ( review process). Similarly, the author response typically shows only responses to the major concerns raised by the reviewers.eLife posts the editorial decision letter and author response on a selection of the published articles . An edited version of the letter sent to the authors after peer review is shown, indicating the substantive concerns or comments; minor concerns are not usually shown. Reviewers have the opportunity to discuss the decision before the letter is sent  and 3 reviewers, one of whom, Chris Pires, has agreed to reveal his identity.Thank you for sending your work entitled “The role of photorespiration during the evolution of CThe Senior editor and the reviewers discussed their comments before we reached this decision, and the Senior editor has assembled the following comments to help you prepare a revised submission.4 evolution.This is a genuinely exciting and provocative study; if the results hold up, they are extremely important for the field, and represent a major advance in our understanding of C2 photosynthesis pump is an evolutionary precursor in the shift from C3 to C4 photosynthesis (which has happened multiple times). Across nine Flaveria species that includes C3, C4 and intermediate species taxa with intermediate C3 and C4 photosynthesis, transcriptome and protein data were collected and analyzed in a phylogenetic context. A global genome-wide metabolic model and flux balance analysis (FBA) was used to integrate models with transcript abundance. The coordinated changes in expression of all main photorespiratory enzymes strongly suggest an evolutionary scenario for the origin of C4 photosynthesis. Very little attention has been paid in the past to nitrogen effects of C2, yet the problem is obvious, and if the C4 cycle is the most direct way to rebalance N within the leaf tissue, then this route provides an immediate solution to a very important and poorly understood transition in the trajectory. It implies that C2 crosses a new threshold of C4 accessibility, and that C4 is all but an inevitable outcome. This also can partially explain the relative rarity of known C2 phenotypes – this may be a part of phenotypic space with a low 'persistence time' – an area that lineages rarely evolve into and very quickly evolve out of.The hypothesis tested is that the C2 system was done properly. I'd suggest getting an additional reviewer with expertise in metabolic modeling for that. The analysis done is fairly standard, but relies on several assumptions and choices that do not seem to be justified in the present version of the manuscript. In addition, robustness checks, particularly with respect to the uniqueness of the solutions, need to be obtained, analyzed, and subsequently interpreted.Key to your argument is whether or not the 're-tooling' of the C4GEM model to accommodate a CDetails:2 assimilation rate given a set of parameter values  as well as input values for partial pressure of CO2 and O2. The cited mechanistic model does not include the plasmodesmatal flux of glycine and serine or the decarboxylation of the GDC. Moreover, the CO2 uptake rate is assumed (not predicted by the model). These points need to be further elaborated on.1) How could the selected 11 fluxes be fixed from the mechanistic model? The cited mechanistic models  aim at p2) You state that you maximized biomass production rate. However, you do not comment on why fixed constraints on production of starch and fatty acids were removed; this should be supported by literature or clear reasons should be provided. The remaining model modifications seem plausible.3) The second objective applied is the minimization of the sum of absolute fluxes including transport processes . In doing so, higher weight was assigned to plasmodesmatal fluxes (expecting that they receive lower flux). However, as shown in the Methods section, the weight for the plasmodesmatal fluxes is seemingly arbitrarily chosen to be 1.1. What effect would the increase of this value to, say, 2 or 5 have on the drawn conclusions from this study? Either clear reasoning for selection of the value 1.1 should be provided  or additional tests should be carried out to explore the consequences of other  weights for these reactions.4) You state that this framework allows the prediction of detailed flux distributions that are biologically realistic. In the Methods section, you also indicate that the combination of several objectives was used to reduce the size of the space of optimal solutions. However, you do not provide a statement on whether or not the resulting distributions are indeed unique  The alternative solutions with a larger number of reactions are presented without providing how much they differ in terms of the total absolute values of flux from that of the preferred glutamate/2-oxoglutarate solution. The increase in the total absolute plasmodesmatal flux, evident in 6) The statement “In terms of biomass production rate, this shuttle represents another alternative optimal solution” in the Results section, is confusing and may be misleading. Is this an alternative solution for the same total absolute values of flux as the glutamate/2-oxoglutarate solution? If not, this sentence can be dropped since it was already indicated that alternatives were selected to “retain the same biomass output”.7) In the Results section, what do you mean by “In a restrictive scenario, all nitrogen containing compounds were excluded, except for glycine and serene”? What does that do to the reactions that use these metabolites? Are they also removed?8) The prediction of the model discussed in the Results section should be investigated with respect to the issues raised in points 3 – 5, above.4 photosynthesis in the genus Flaveria” for further consideration at eLife. Your revised article has been favorably evaluated by Detlef Weigel (Senior editor) and a member of the Board of Reviewing Editors. The manuscript has been improved but there are some remaining issues that need to be addressed before acceptance, as outlined below:Thank you for resubmitting your work entitled “The role of photorespiration during the evolution of CThe authors have carefully considered the suggestions provided about the earlier version of the manuscript and have: (1) offered detailed explanations of how the results of the mechanistic model were used to constrain the larger stoichiometric model as well as (2) conducted flux variability analysis for the different alternative scenarios to support the robustness of the predictions.2 in the bundle sheath derived from mesophyll oxygenations.The only remaining concern deals with the details on lower/upper boundary selection for the diffusion fluxes and their effects on the predictions. Additional clarifications  may further strengthen the predictions: The lower bounds on the diffusion of gylcine, serine, and NADPME reaction are fixed based on oxygenation rate and the fraction of photorespiratory CO2 in the bundle sheath derived from mesophyll oxygenations).1) Please, indicate the value for the latter parameter  To thoroughly examine the viability of the modeling strategy, it is also necessary to determine the variability of model predictions without specifying tight lower (and upper) boundaries , which may a priori fix the solution. What is the variability of the solutions with default lower/upper boundaries ) for the diffusion fluxes?This additional analysis can be readily conducted and included in the manuscript. 1) How could the selected 11 fluxes be fixed from the mechanistic model? The cited mechanistic models  aim at predicting CO2assimilation rate given a set of parameter values  as well as input values for partial pressure of CO2and O2. The cited mechanistic model does not include the plasmodesmatal flux of glycine and serine or the decarboxylation of the GDC. Moreover, the CO2uptake rate is assumed (not predicted by the model). These points need to be further elaborated on.2 uptake rate is predicted by the mechanistic model and can be readily used as a constraint in the flux-balance analysis.We apologize for not explaining these points in more detail. The mentioned fluxes are indeed not described explicitly, but are described by the model implicitly. We expanded the Method section to show how these were included. The net CO2) You state that you maximized biomass production rate. However, you do not comment on why fixed constraints on production of starch and fatty acids were removed; this should be supported by literature or clear reasons should be provided. The remaining model modifications seem plausible.2 assimilation rate, we removed the respective constraints from the model. This rationale is now described in more detail in the Methods section.The original C4GEM model does not contain starch and fatty acid production as part of the biomass function. Instead, the fluxes are fixed by constraints. Since we are not aware of data that explains how these fluxes scale with CO3) The second objective applied is the minimization of the sum of absolute fluxes including transport processes . In doing so, higher weight was assigned to plasmodesmatal fluxes (expecting that they receive lower flux). However, as shown in the Methods section, the weight for the plasmodesmatal fluxes is seemingly arbitrarily chosen to be 1.1. What effect would the increase of this value to, say, 2 or 5 have on the drawn conclusions from this study? Either clear reasoning for selection of the value 1.1 should be provided  or additional tests should be carried out to explore the consequences of other  weights for these reactions.2 containment suggests additional weight on plasmodesmatal fluxes, we have to admit that an exact value cannot be inferred from available data. To account for this issue, we conducted a sensitivity analysis against the weight on plasmodesmatal flux. The results presented in Although the trade-off between metabolite transport and CO4) You state that this framework allows the prediction of detailed flux distributions that are biologically realistic. In the Methods section, you also indicate that the combination of several objectives was used to reduce the size of the space of optimal solutions. However, you do not provide a statement on whether or not the resulting distributions are indeed unique . If the distribution for a fixed biomass production and a fixed sum of absolute flux values is not unique, the provided findings and interpretation are just one of many available alternatives! This point should be carefully examined ; this analysis must be coupled with the issues raised in point 3, above.Our rationale behind assuming a small solution space was the application of the two optimality criteria; but we agree with you entirely that this should be shown more rigorously. We thus implemented a flux variability analysis and added the results to the fluxes shown in 5) The alternative solutions with a larger number of reactions are presented without providing how much they differ in terms of the total absolute values of flux from that of the preferred glutamate/2-oxoglutarate solution. The increase in the total absolute plasmodesmatal flux, evident in, should be discussed with respect to biological implications.The sum of absolute flux over plasmodesmata was added to the legend of 6) The statement “In terms of biomass production rate, this shuttle represents another alternative optimal solution” in the Results section, is confusing and may be misleading. Is this an alternative solution for the same total absolute values of flux as the glutamate/2-oxoglutarate solution? If not, this sentence can be dropped since it was already indicated that alternatives were selected to “retain the same biomass output”.We agree with you that this point does not need further emphasis and removed the sentence.7) In the Results section, what do you mean by “In a restrictive scenario, all nitrogen containing compounds were excluded, except for glycine and serene”? What does that do to the reactions that use these metabolites? Are they also removed?We apologize for not stating that we exclusively excluded plasmodesmatal nitrogen compounds and changed the sentence to make this point clear to the reader.8) The prediction of the model discussed in the Results section should be investigated with respect to the issues raised in points 3 – 5, above.We now mention the alternative solution of the flux distribution shown in 1) Please, indicate the value for the latter parameter .2 in the bundle sheath derived from mesophyll oxygenation (0.98 – the derivation from transcriptome data is given in We indicate the fraction of photorespiratory CO2) To thoroughly examine the viability of the modeling strategy, it is also necessary to determine the variability of model predictions without specifying tight lower (and upper) boundaries , which may a priori fix the solution. What is the variability of the solutions with default lower/upper boundaries ) for the diffusion fluxes?2 photosynthesis in Flaveria in such a way that we can answer the question: Given our current understanding of C2 photosynthesis, what is the implementation of this pathway in the plant leaf that optimizes fitness-relevant criteria?The rationale behind our modeling approach was to incorporate current mechanistic knowledge about C2 photosynthesis (that includes diffusion of glycine and serine) through mechanistic equations and to yield lower bounds for the respective reactions in the stoichiometric model. We understand the reviewers’ question as an equivalent of asking:In our opinion, the most reasonable approach to answering this question was the description of the current conceptual model of C2 photosynthesis increases biomass yield, shouldn’t FBA be able to predict such a cycle without the need for further constraints?Why is it necessary to yield lower bounds for the fluxes of the photorespiratory pump from the mechanistic model? If C3-C4 photosynthesis, for constraining certain fluxes within the FBA model to integrate C2 photosynthesis by creating flux through this pathway. The mechanistic model explicitly accounts for concentrations of CO2 and O2 in the two cell types and predicts the rates of rubisco carboxylation and oxygenation that result from these concentrations. The fluxes mentioned by the reviewer: diffusion of glycine, serine and the GDC reaction belong to these fluxes that have to be constrained to ensure flux through the C2 cycle. When we remove these constraints the model will not predict C2 photosynthetic activity anymore.As stated in the Methods section of the manuscript Flux Balance Analysis is a powerful tool but it cannot model metabolite concentrations explicitly. Therefore fluxes related to concentration-dependent processes, like carbon concentration mechanisms, cannot be captured by this constraint-based approach. To account for this issue we used values, predicted by the mechanistic model of C2 photosynthetic cycle, but also the predicted fluxes to recirculate ammonia from bundle sheath to mesophyll cells, disappear when we remove constraints on the plasmodesmatal diffusion of glycine, serine, and CO2 and the GDC reaction. We added a sentence to the Methods section to clarify this point.We checked this and indeed fluxes through the C


The flux phenotype describes the entirety of biochemical conversions in a cell, which renders it a key characteristic of metabolic function. To quantify the functional relevance of individual biochemical reactions, functional centrality has been introduced based on cooperative game theory and structural modeling. It was shown to be capable to determine metabolic control properties utilizing only structural information. Here, we demonstrate the capability of functional centrality to predict changes in the flux phenotype.We use functional centrality to successfully predict changes of metabolic flux triggered by switches in the environment. The predictions via functional centrality improve upon predictions using control-effective fluxes, another measure aiming at capturing metabolic control using structural information.The predictions of flux changes via functional centrality corroborate the capability of the measure to gain a mechanistic understanding of metabolic control from the structure of metabolic networks. The metabolic state of a cellular system is characterized by the fluxes of the underlying biochemical reactions and the concentrations of the involved metabolites . In the functional centrality to predict changes in experimentally determined metabolic fluxes based solely on the structure of the metabolic network captured by its stoichiometric matrix.Alterations in the flux phenotype are triggered by internal or external shifts and imply rerouting of metabolic flux, for example from respiration towards fermentation in facultative aerobic bacteria , which iFunctional centrality combines cooperative game theory, in particular a modified version of the Shapley value for arbitrary restricted games , with flEscherichia coli.In our previous study we examined the relationship of functional relevance and transcriptional readout , wherebyE. coli resulting from a shift between aerobic and fermentative conditions and the corresponding changes of the two investigated measures. The flux data were obtained via stationary 13C labeling experiments and metabolic flux analysis by Fischer et al. [We examine the capability to predict flux changes using functional centralities as well as control-effective fluxes, which were found to be the two best-performing contending predictors of transcriptional change in a recent study of structural control of metabolism . To thisr et al. .E. coli’s central carbon metabolism provided by Schuetz et al. [In accordance with the definition of control-effective fluxes , we utilz et al. . For botz et al. .Table 1Aith (log-transformed) data point and the (log-transformed) predicted value, respectively; ith residual and The ability of control-effective fluxes and functional centrality to predict the observed flux changes (23 data points) is assessed by employing two statistical procedures. In the first, we fit a regression model. Inspection of the dataset indicates a non-linear relationship in the case of both measures. We utilize logarithmic transformation of the predictor’s and of the regressor’s values, respectively, to discount non-linearity and to render the distribution of the predicted quantity closer to normal. A linear regression model is fitted to the double-log-transformed data . The slope of the linear regression line then indicates the relative  change of flux resulting from a relative  change of the predictor. The goodness of fit is determined by the coefficient of determinationFunctional centrality, like control-effective fluxes, does not require any further information besides reaction stoichiometry, characterization of exchange fluxes and the choice of a metabolic function. Here we demonstrated that functional centrality enables prediction of changes in metabolic flux with improved accuracy, exceeding the results of control-effective fluxes. The functional centrality measure is based on the rich axiomatic framework of power indices in cooperative games, and is suitable for the analysis of structural control of metabolic networks, as supported by the analyzed data. Our results provide further indication that concepts from cooperative game theory can help in obtaining a better understanding of control in metabolic networks.z representing the objective to be optimized, Flux balance analysis is a structural modeling framework enabling prediction of steady-state metabolic flux . It reliFunctional centrality quantifies the contribution of individual reactions to a metabolic function, e.g., biomass production, by utilizing a formulation of the Shapley value for restricted cooperative games . The metv in a subnetwork formed by the reaction set S is determined by FBA. Let maximal chains. The calculation of functional centrality is as follows:The optimal value of the objective function i in maximal chain W is given byl(W) being the length of the maximal chain W and i with respect to the objective function v isLet efficienciesl in the EFM Control-effective fluxes are defined by advance) :6\documeE. coli originally published by Schuetz et al. [mglABC and ptsGHI is constrained from above arbitrarily by one. Isozymes in the model were deleted. We examine two environmental conditions: (i) aerobic respiration and (ii), fermentation (no oxygen and no nitrate import). The utilized objective functions are the fluxes through the reactions: (i) maint (ATP production) and (ii), biomass (biomass production).We utilize a model of central carbon metabolism of z et al. . Import