In this regard, the exploitation of microorganisms as microbial cell factories able to convert non-edible but renewable carbon sources into biofuels and commodity chemicals appears as an attractive solution. However, there is still a long way to go to make this solution economically viable and to introduce the use of microorganisms as one of the motor of the forthcoming bio-based economy. In this review, we address a scientific issue that must be challenged in order to improve the value of microbial organisms as cell factories. This issue is related to the capability of microbial systems to optimize carbon conservation during their metabolic processes. This initiative, which can be addressed nowadays using the advances in Synthetic Biology, should lead to an increase in products yield per carbon assimilated which is a key performance indice in biotechnological processes, as well as to indirectly contribute to a reduction of CO2 emission.The global warming conjugated with our reliance to petrol derived processes and products have raised strong concern about the future of our planet, asking urgently to find sustainable substitute solutions to decrease this reliance and annihilate this climate change mainly due to excess of CO While Nature has been orchestrated with a natural carbon cycle, the industrial revolution that begun in the early 19th century resulted in a rise of CO2 emission that slowly but definitively exceeded the natural geochemical carbon cycle. According to the Keeling curve, which reports the daily carbon dioxide measurements at Mauna Loa observatory, the CO2 emission has dramatically increased over the last 50 years, mostly due to deforestation and burning of fossil fuels (https://scripps.ucsd.edu/programs/keelingcurve/). These issues are now becoming critical for the human being, which urged the scientific community to find solutions to decrease our reliance on fossil fuels that should eventually change our life style. Biofuels and more generally biorefinery have emerged as promising solution whose purpose is to exploit microorganisms as cell factories to convert non-edible but renewable carbon sources such as lignocellulosic sugars into bioethanol as alternative energy  as well as other natural metabolic pathways that perform carbon fixation including reductive TCA cycle, 3-hydroxypropionate cycle, 3-hydroxypropionate/4-hydroxybutyrate cycle, and dicarboxylate/4-hydroxybutyrate cycle are not considered in this mini-review, since they have been extensively reviewed in previous excellent papers , among which emission of carbon dioxide  but will require a SBP-aldolase to condense DHAP and E4P into SBP, and a sedoheptulose phosphatase (Sbp) to recycle back S7P. Such cycle can potentially exist since Sbp is essential in the Calvin-Benson cycle, and has been identified in yeast as being implicated in ribogenesis  is a fundamental metabolic pathway in most living systems that decomposes sugars into pyruvate and recovers energy of this breakdown into ATP and reducing equivalents NADH. To fuel the cell with some essential anabolic precursors, pyruvate has to be decarboxylated into acetyl-CoA. This decarboxylation step releases carbon dioxide in the environment, resulting in 33% loss of carbon yield. This wasted COin vitro and in vivo functioning of NOG  and the experiment was carried out under anaerobic condition to avoid further oxidation of acetate in the TCA cycle. Under this condition, 2.2 moles of acetate per mole of xylose were produced by the engineered E. coli equipped with the NOG pathway. In theory, the maximal yield that can be obtained by this conversion process should be 2.5. This yield termed the thermodynamic feasibility “YE” can be calculated as the ratio between the degree of reduction of the substrate γs to that of the product γp. YE is independent of the stoichiometry of the pathway and provides yield limits of the thermochemical process whatsoever the followed pathway or the catalyst used  is 2.5 since γp of acetate = 6, whereas the stoichiometric yield “Yst” is 1,66. Therefore, the efficiency of the NOG pathway which can be calculated as the ratio of YE to Yst is 50% better than the classical EMP pathway. The fact that the in vivo conversion of xylose into acetate by the engineered E. coli expressing the NOG pathway only reached 88% of YE was due to some by-products formation, notably succinate.In their Nature report, Liao and coworkers succeeded in demonstrating the E. coli strain that could grow while relying on NOG for carbon catabolism  from Zymomonas mobilis, the glucokinase (glk), and a AMP-insensitive PEP-activated FBPase (glpX) from E. coli  cycle Calvin,  for the in vitro pathway termed “Pentose-Bifido-Glycolysis” cycle (PBG) for the synthetic conversion of glucose into PHB via acetyl-CoA. This PBG cycle is divided in three metabolic parts. The first part is the phosphorylation of glucose into G6P which enters the cycle through the oxidative branch of the PPP and breaks down into Xu5P while producing NADPH. In a second phase, Xu5P is split into AcP and GAP by the phosphoketolase Fxpk. While AcP can be converted into acetyl-CoA by the CoA-phosphotransferase enzyme (Pta), GAP is recycled in a third phase into G6P. This occurs by the condensation of GAP and DHAP into FBP by the aldolase Fba, followed by a process involving a unique phosphofructokinase that catalyzes the ATP-dependent formation of F6P from FBP. At variance to the traditional phosphofructo-1-kinase reaction  and NAD+-dependent phosphogluconate dehydrogenase (Gnd) enzymes together with their native NADP+ dependent counterparts and a H2O-forming NADH oxidase (NoxE). While NADPH is reoxidized during PHB production, high level of NADPH would not penalize the cycle since it is taken over by the NAD+-dependent enzymes which continue to provide the precursor acetyl-CoA while NADH is readily reoxidized by NoxE. This original cell-free system production of bio-based chemicals from glucose turned out to be quite efficient as the authors reported a maximum productivity of the PBG cycle of 0.7 g PHB/L/h with a yield of 90%. There is great hope in developing such a process at an industrial scale since cell-free system can overcome common problems afflicting in vivo biological systems, such as building-up toxic intermediates, low productivities due to competing pathways and undesirable byproducts H at the cost of 1 ATP , fatty acids or mevalonate was moreover demonstrated by showing that the yield of these products was improved by 145, 56, and 48% respectively in engineered strains as compared to the control strains  from glucose (γs = 24) or from pentose (γp = 20) should be 4 and 3.3, respectively, whereas the maximal yield YS based on the pathway stoichiometry is 2 from glucose and 1.66 from pentose  isomerase and a class I aldolase, respectively. Even though these two genes are endogenous to E. coli, this pathway is not natural in this bacteria because the Kdsd enzyme is naturally implicated in the synthesis of 2-keto-3-deoxy-octulosonate (KDO), a constituent of the outer member of cell wall lipopolysaccharide  the blockage of the lower part of glycolysis by deletion of gapA encoding GADPH was detrimental for cell viability; (ii) all competitive pathways using the same intermediaries have not yet been dismantled in the engineered strains; and (iii) the carbon flux in the kdsD-fsaA pathway is not optimized yet  from C5 and C6 sugars without carbon loss . Accordi glucose  or 2.5 G glucose . This paPichia pastoris  that is present in methylotrophic bacteria and in some yeasts such as 0 = −44 kJ/mol), the glyoxylate cycle can only run in the acetyl-CoA condensation. However, running the cycle clockwise directly could be beneficial to supply acetyl-CoA from sugars by bypassing the decarboxylation step of pyruvate. As illustrated in in vivo by showing that a E. coli strain made auxotroph for glutamate (glu− strain) by deletion of gltA and prpC encoding citrate synthase was able to grow on glucose mineral medium supplemented with glyoxylate and succinate. In contrast, this glu− strain was unable to recover growth when glyoxylate was replaced by malate, even if dctA gene encoding a non-glucose repressible malate importer from B. subtilis had been overexpressed. These results confirmed that malate synthase reaction was not reversible in vivo. To get around this obstacle, they wished to express an ATP-dependent malate thiokinase (Mtk) encoded by mtkA and mtkB from Methylobacterium extorquens. In this methanotrophic bacterium, this enzyme contributes to C1 assimilation through the serine cycle . It can nevertheless be obtained by expressing an ATP-dependent citrate lyase encoded by acl which is present in several eukaryotic cells and in some archeabacteria  by deleting genes encoding all enzymes that produce its precursor OAA , as well as citrate synthase and citrate lyase (gltA and citE). As expected, the asp− strain recovered growth on a glucose minimal medium when supplemented with citrate. Although the thermodynamically unfavorable reactions were solved to potentially create a reverse glyoxylate cycle, it was also necessary to remove isocitrate dehydrogenase (icd) to avoid siphoning isocitrate obtained by condensation of glyoxylate and succinate into α-ketoglutarate. Then, the assembly of the complete pathway in asp− strain which was otherwise deleted for mdh, mqo, ppc, icd, and aceB consisted in the overexpression of BsdctA, McsuccD-2, Rsmcl, and Ctacl genes. This strain was shown to grow on glucose supplemented with malate and succinate, demonstrating the in vivo function of this rGS. Until now, the complete demonstration of the “in vivo” reversal of the glyoxylate cycle has not been fully demonstrated. It will require to connect OAA to malate which can be easily carried out by the reversible NAD+-dependent malate dehydrogenase encoded by mdh. However, cycling malate shall require also expression of a fumarase (Fum) and a fumarate reductase (Frd), both enzymes being preferentially active under anaerobic conditions  can be rescued upon the expression of mtkAB and mcl genes. Like NOG and rGS, the theoretical molar yield of acetyl-COA per glucose consumed is 3  cycling pathway allows the conversion of glucose into acetyl-CoA. As depicted in med is 3 . Anothermed is 3 . Hence, https://www.genome.jp/kegg/pathway.html) to generate carbon fixation pathways that are alternative to the 5 known to date. Criteria used in their modeling were (i) the enzyme's specific activity is equal or superior to that of RuBisCO which is used as the benchmark activity; (ii) a minimal energy cost of the pathway, which corresponds to the cost in NAD(P)H, ferredoxins, FADH2, and ATP in the production of one mole of products from CO2; (iii) thermodynamic feasibility of the pathway under a plausible physiological range of metabolites concentrations; (iv) topology of the pathway, which incorporates the number of enzymatic reactions the carbon fixation pathway can make as an independent unit and (v) the compatibility or integration of this synthetic pathway with the endogenous metabolic network. According to these criteria, they identified several cycling pathways containing four to six enzymatic steps leading to the production of the C2 compound glyoxylate. Although most of them were unrealistic because thermodynamically unfeasible or using oxygen-sensitive ferredoxin-oxidoreductase enzyme, these authors found that kinetically efficient pathways absolutely require a carboxylating enzyme with high activity and affinity toward CO2 or ppc gene) and pyruvate carboxylase (pyc gene) came at first in their listing, followed by acetyl-CoA and propionyl-CoA carboxylase. Accordingly, they designed a pathway family termed Malonyl-CoA-Oxaloacetate-Glyoxylate (MOG) cycle employing either PEP carboxylase or pyruvate carboxylase as the sole carboxylating enzyme and that has a higher carboxylating activity than the reductive pentose pathway (rPP). This MOG pathway resembles the natural C4 cycle in which the recuperation of CO2 arising from malate decarboxylation to pyruvate by RuBisCO is replaced by a PEP or pyruvate carboxylating enzyme. The net product of MOG is the C2-carbon glyoxylate, which can be converted into GAP by the bacterial-like glycerate pathway , the malyl-CoA lyase (mcl), the methylmalonyl-COA carboxytransferase (mct), the malonyl-CoA reductase (mcr), the β-alanine-pyruvate transaminase (bapta), and the alanine 2,3 aminomutase (aam). More importantly, the stoichiometry evaluation of this route from glucose indicated that it can produce 2 moles of glyoxylate and 2 moles of acetate, with the requirement of two mole of CO2. However, while globally thermodynamically favorable and redox balanced, this reaction can occur at the expense of 3 ATP, which can be obtained by consumption of acetate, and hence resulting in the reemission of 2 moles of CO2. Therefore, this route has likely no meaning to be expressed in a chemoorganotrophic system.In an elegant paper published in 2010, Bar-Even et al. . The methyl unit is afterwards transferred on serine cycle by a reaction involving glycine and catalyzed by serine hydroxymethyl transferase (Shmt). From these 13 enzymatic steps, seven  encoded by AGX1, serine dehydratase (Sdh) from Cupriavidus necator encoded by SdaA, malate thiokinase (Mkt), and malyl-CoA lyase(Mcl) from M.extorquens. For methanol oxidation and its conversion to 5–10 methylene tetrahydrofolate, a variant of the Cupriavidus necator methanol dehydrogenase (Medh) with higher specific activity was used together with formate-H4F ligase (Fhlfl) and 5,10-methylene tetrahydrofolase synthase (Mthfs) from Moorella thermoacetica. The NAD+-linked formadehyde dehydrogenase  from Pseudomonas putida was employed to oxidize formaldehyde to formate. All these genes were carried on 3 different plasmids and transformed into E. coli strain HY106, which was deleted for genes to avoid byproducts formation and shortage of intermediates in the cycle. Accordingly, aceB and glcB both encoding malate synthase were deleted to avoid competitive reverse reaction catalyzed by Mkt and Mcl. The gcl gene encoding glyoxylate carboxyligase was deleted to prevent shortage of glyoxylate into tartronate semialdehyde, as well as gcvP to avoid loss of glycine by decarboxylation. Genes encoding lactate dehydrogenase (ldhA) and fumarate reductase (frABCD) were also deleted in this strain to avoid shortage of pyruvate into D-lactate and malate into succinate. As indicated in 2 needs 3 moles ATP and 1 mole reduced equivalent per mole of acetyl-CoA produced. Hence, it cannot proceed without addition of another carbon source to provide this energy and cofactors. Thus, the in vivo function of the complete cycle was demonstrated using C13-methanol together with xylose to supply energy and PEP. In addition the pyruvate to malate flux was increased upon overexpression of pyc and mdh encoding pyruvate carboxylase and malate dehydrogenase in the engineered E. coli equipped with the Mser pathway. The engineered strain could produce acetate from which 33% came from methanol. When the same experiment was carried out with both C13 methanol and C13 bicarbonate, the amount of acetate produced was the same but the labeling of both C1 and C2- carbon of acetyl-moieties was enriched by 2-fold, indicating that bicarbonate has been also incorporated into acetyl moieties. To conclude, the construction of this synthetic serine cycle in E. coli enables the assimilation of C1 compounds such as methanol to increase the production of C2-compounds as precursor of bio-based products such as PHB, isoprenoid, fatty acids, etc. In addition, this cycle, combined with the glyoxylate shunt, is capable to support growth from pyruvate that is formed from two C1-carbon (formate or methanol) and one bicarbonate, unless the mole excess of NAD(P)H is reoxidized by respiratory chain coupled with ATP.In methylotrophic bacteria, the serine cycle is a natural pathway to assimilate C1 carbon such as methanol or methane into acetyl-CoA intermediate without loss of carbon  produced by the condensation of tetrahydrofolate with formaldehyde that originates from serine or glycine. To replace these amino acids as C1-donor, these authors devised a cyclic pathway in which the C1 compound  is obtained from the aldolytic cleavage of the non-natural intermediate 2-keto-4-hydroxybutyrate (HOB). As shown in E. coli possessing DNA in which thymine was replaced by the synthetic building block 5-chlorouracil  and 245 (Tyr to Glu). The HOB is then cleaved into pyruvate and formaldehyde which is readily transferred into H4F by the promiscuous hydroxymethytransferase (Mtf) encoded by panB. The cycle is then closed by converting back pyruvate into PEP, which implicates PEP synthase. Overall, the functioning of this cycle costs two moles of NADPH and three moles of ATP per mole of CO2 incorporated . The authors estimated that the CO2 assimilated in the biomass of E. coli expressing this HOB pathway is about 2 times more than in wild type strain  and ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO) onto ribulose 5-P (Ru5P) . In a second paper, the authors carried out several targeted metabolic engineering to optimize the fermentation kinetic, improving ethanol yield and reducing glycerol production. To achieve this goal, nine copies of the cbbM overexpression cassette along with a single expression cassette of E. coli groEL/groES chaperones were integrated at the SGA1 locus using CRISPR-Cas9 tool followed by the integration at X-2 locus of the PRK1 under the inducible anaerobic DAN1 promoter. The resulting engineered strain expressing a more robust Calvin-Benson cycle showed significant (31%) reduction of glycerol under glucose anaerobic condition. However, the contribution of the PRK/RuBisCO pathway to NADH reoxidation decreased with increased growth rate, with a concurrent higher contribution of the glycerol pathway. Therefore, a complementary strategy was to abrogate this pathway by removal of glycerol-3-P dehydrogenase encoded by GPD1 and GPD2. While GPD1 is essential for growth of Saccharomyces cerevisiae under osmotic stress  . In theiP (Ru5P) . This clP (Ru5P) . In the Saccharomyces cerevisiae with the two Calvin-cycle enzymes PRK and RuBisCO to enhance xylose fermentation with in situ CO2 fixation  and xylulose dehydrogenase (XDH) or the bacterial xylose isomerase (XI) have been heterologously expressed, together with upregulation of the native pentose phosphate pathway (PPP) to achieve efficient and rapid xylose fermentation  leading to a stable platform SR8C+ strain. Only RuBisCO activity was detected in yeast strain co-expressing cbbM and groEL/ES. Then, while the overexpression of PRK from Spinacia oleracea alone was toxic for growth on xylose but not on glucose, likely because of ATP depletion or consecutive hyperaccumulation of RuBP, expression of the PRK-RuBisCO module rescued complete growth on xylose, which was accompanied by a 24% reduction of xylitol and 10% increase of ethanol yield while glycerol yield was similar to the control strain. Moreover, it was demonstrated that this engineered S. cerevisiae carrying the Calvin-cycle enzymes released 7% less CO2 than the control strain during anaerobic xylose fermentation. In a more recent publication, Li et al.  and sugar consumption rate (+ 63%) with the engineered strain expressing heterotrophic form-I RuBisCO. Using 13C-labeled CO2 and a metabolic flux index MFI h−C02  or by deleting glucose-6-P dehydrogenase (zwf) encoding gene. These genetic actions resulted in a significant decrease of CO2 yield per glucose consumed. Genes encoding D-lactate dehydrogenase (ldh) and fumarate reductase (frd) were further deteled in this zwf mutant in order to favor recycling of in situ CO2 into fermentation products ethanol or acetate. However, while this reduced CO2 production proved the Calvin cycle pathway to work in vivo, and the expression of this cycle did not impede the growth on glucose, only 70% of carbon initially fed in the medium was recovered at the end of the fermentation. Moreover, there was no significant increase in C2-related compounds (Li et al., pflB encoding this enzyme due to the repression of its transcriptional activator encoded by arcA (Yang et al., Zymomonas mobilis were overexpressed in the Δzwf Δldh Δfrbd mutant strain equipped with the Calvin-cycle enzymes PRK and RuBisCO. This genetic intervention resulted in a yield of C-2 compounds from glucose 20% higher than that of theoretical fermentation value, which was due to a direct in situ CO2 recycling into these products by the RuBisCO system. In addition, a rate of 53 mg/L/h of CO2 consumption was evaluated, which was in the range of rate measured for CO2 fixation by microalgae (Gonzalez Lopez et al., 2 and converting it into bio-based products.The RuBisCO-based pathway was also investigated in 2 emission associated with human activities. Since carbon dioxide is an intrinsic by-product of carbon metabolism ensuring the irreversibility of metabolic pathways in which it is involved, the rewiring of carbon metabolism aiming to circumvent this carbon loss must take into account this cost. However, in most of the case that were presented here, this cost can be overridden by the benefit of a higher carbon yield achieved by these refractory or synthetic pathways. This higher carbon yield is the second advantage of this carbon management since it can in principle increase the practical performance of a product per carbon consumed, which is a decisive parameter for the economic evaluation of a biotechnology process. Nonetheless, the synthetic pathways aiming at reducing carbon loss or assimilate CO2 are still in their infancy. Substantial work is required to evaluate the potential for industrial application of some of them, such as NOG, MCG, rGS or glycoptimus, whereas others such as the MOG, MSer, and HOB will likely remain as elegant intellectual models illustrating the power of Synthetic Biology in its ability to reformat metabolic pathways.The carbon management during the metabolic conversion of renewable carbon sources such as sugars by heterotrophic organisms is an attractive, yet partial, solution to combat the acute problem of continuous CO2 is to equip these organisms with the two key Calvin cycle enzymes in order to capture CO2 produced during sugar fermentation, and meanwhile use it as an electron acceptor for NADH reoxidation. This dual function has been developed in yeast and E. coli and was shown to increase C2- products such as ethanol (Papapetridis et al., 2 and its carboxylation activity is antagonized by oxygen. Therefore, this engineering strategy could be implemented without major investment at the industrial scale owing to the fact that GMO's legislation is modified.While heterotrophic organisms are not naturally able to assimilate carbon dioxide, an attractive and complementary strategy to those developed elsewhere to capture CO2” in vivo. In addition of engineering specific pathways allowing this capture such as rGS or MCG, a great advantage of using heterotrophic organisms such as yeast or E. coli for CO2 fixation is their fast growth rates and capability to reach high cell density in bioreactors, both criteria contributing to CO2 assimilation rate that are higher than that of auxotrophic organisms. Therefore, engineering heterotrophic microbes for CO2 fixation can be a promising avenue to both reduce CO2 emission and in the meantime increase carbon yield as the fixed CO2 can be easily integrated into the central carbon metabolism. To be even more efficient, the next step will be to employ other energy source than sugar for CO2 fixation.Another promising strategy that is already attracting much interest is to exploit the high catalytic capacity of carboxylating enzymes such as the PEP carboxylase to capture “COAll authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Synechocystis sp. PCC 6803metabolism that spans a 12-hr light/12-hr dark cycle by segmenting it into 12Time Point Models (TPMs) with a uniform duration of two hours. The developedframework allows for the flow of metabolites across TPMs while inventoryingmetabolite levels and only allowing for the utilization of currently orpreviously produced compounds. The 12 TPMs allow for the incorporation oftime-dependent constraints that capture the cyclic nature of cellular processes.Imposing bounds on reactions informed by temporally-segmented transcriptomicdata enables simulation of phototrophic growth as a single linear programming(LP) problem. The solution provides the time varying reaction fluxes over a24-hour cycle and the accumulation/consumption of metabolites. The diurnalrhythm of metabolic gene expression driven by the circadian clock and itsmetabolic consequences is explored. Predicted flux and metabolite pools are inline with published studies regarding the temporal organization of phototrophicgrowth in Synechocystis PCC 6803 paving the way forconstructing time-resolved genome-scale models (GSMs) for organisms with acircadian clock. In addition, the metabolic reorganization that would berequired to enable Synechocystis PCC 6803 to temporallyseparate photosynthesis from oxygen-sensitive nitrogen fixation is also exploredusing the developed model formalism.Phototrophic organisms such as cyanobacteria utilize the sun’s energy to convertatmospheric carbon dioxide into organic carbon, resulting in diurnal variationsin the cell’s metabolism. Flux balance analysis is a widely acceptedconstraint-based optimization tool for analyzing growth and metabolism, but itis generally used in a time-invariant manner with no provisions for sequesteringdifferent biomass components at different time periods. Here we presentCycleSyn, a periodic model of  2 into organic carbon, due to which their metabolism isheavily influenced by light availability. The strongly diurnal nature of theirmetabolism is reflected in the presence of two distinct metabolic phases–alight-dependent anabolic phase tailored around the synthesis of storagecompounds and metabolic precursors and a light-absent catabolic period thatmetabolizes the previously manufactured compounds to release energy in theabsence of an external energy source. Due to these considerations, the analysisof phototrophic growth using constraint-based optimization methods isinsufficient and needs to be extended beyond time-invariant descriptions. Here,we introduce CycleSyn which models the periodic nature of metabolism inSynechocystis sp. PCC 6803. Our approach enables us toaccount for temporal metabolic shifts tailored around light availability whilestill allowing for the use of the pseudo steady-state assumption used inconventional flux balance analysis. This is achieved by exploiting the largedifference in time-scales between metabolic reactions and cell growth. We firstvalidate the biological fidelity of CycleSyn predictions by comparing them toexperimental observations for a diurnally culturedSynechocystis sp. PCC 6803 and to identify the majortemporal variations in its metabolic processes. Next, we demonstrate the abilityof CycleSyn to describe a temporally-varying metabolism by introducingdiazotrophy in Synechocystis and evaluating the genes that needto be upregulated/downregulated to enable nitrogen fixation in a photosyntheticorganism. Our study lays the foundation for subsequent analysis of systems withtemporal variations in metabolism using a constraint-based optimizationapproach.Phototrophic organisms such as cyanobacteria harvest the sun’s energy to convertatmospheric CO Flux balance analysis (FBA) has become a popular tool to analyze the metabolicfunction of organisms .FBA assIn their natural habitat, cyanobacteria are subject to a diurnal cycle of light anddark, leading to significant shifts and reorganization within their metabolicnetwork. Although several studies, both experimental and computational –10, havein silico knockout mutants or identifying essentialreactions/pathways under a varying light regime. In the absence of omics data frommutant strains, algorithms such as RELATCH . C. CSynechPCC 7942 .Synechocystis as an example cyanobacterium topredict the various metabolic pathways that would need to be regulated in aphotosynthetic organism so as to incorporate the two inherently incompatibleprocesses of photosynthesis and nitrogen fixation. The introduction of nitrogenfixation drew parallels from the non-heterocystous cyanobacteriaCyanothece ATCC 51142, which temporally separates the twoantagonistic processes. In doing so it fixes glycogen during the day and uses itas a respiratory product in the dark, thus also achieving the anoxic conditionsrequired for nitrogenase activity. This necessitates a reorganization of thecellular metabolic processes, with dominant flux-carrying pathways differingduring the light and dark periods. The model predicted changes in pathways ofcarbon fixation and amino acid synthesis upon introduction of diazotrophy inSynechocystis. The dark phase inCyanothece is known to have a high protein turnover, withupregulation of amino-acid biosynthesis pathways due to the increased nitrogensequestration. Pathways such as arginine and aspartate metabolism wereconsequently upregulated in the dark, due to the need to sequester the fixednitrogen. CycleSyn predicted the high-energy demands associated with nitrogenfixation to be met by increased flux through TCA cycle and the pentose phosphatepathway, maintained by higher glycogen synthesis and remobilization.Furthermore, oxygen scavenging reactions such as L-Aspartic acid:oxygenoxidoreductase were upregulated across dark TPMs, due to their oxygen-scavengingrole which is required to maintain the anaerobic conditions required fornitrogenase to function.We also treated The developed framework enables analyzing a time-variant GSM model whilepreserving the fundamental time-invariant assumption of conventional fluxbalance analysis. It improves upon existing techniques of diurnal simulations ofmetabolism while maintaining a linear programming problem resulting in lowcomputational costs. The formulation can readily be customized to accommodatequantitative measurements of reaction fluxes over a 24-hour cycle. This willalso constrain the feasible solution space and thereby improve the precision andaccuracy of model predictions . We expeiSyn731 genome-scale metabolic(GSM) model for Synechocystis sp. 6803 ’ to the metabolite name) in the base model.n to then+1 TPM using transfer reactions. A transfer reactionj for a metabolite i in a TPMk always operates in the forward direction from TPMk to TPM k+1 such that A single biomass reaction occurs in TPM12 to account for organism growth. Allmetabolites except photons and protons that are present in the cytosol andcarboxysome are transferred unidirectionally from the k if itcontains the necessary chlorophyll. The chlorophyll balance on a TPM equates thedifference between total chlorophyll synthesis and degradation fluxes to thedifference between the chlorophyll transfer fluxes that exit and enter the TPM.This is mathematically represented as: vPigment Transfer,k to k+1 refers to the flux through thechlorophyll transfer reaction from TPM k to TPMk+1.Photosynthesis is only allowed to occur in a TPM k to TPMk+1 represents the cumulative chlorophyll accumulation. We approximate this as a linearlyincreasing function with respect to time for a single TPM. Hence, the averageamount of chlorophyll made in a TPM k can now be calculated asThe chlorophyll transfer flux from a TPM MC is aconstant large enough not to constrain flux through photosynthesis reactions andk the Time Point Model.vPigment Transfer, k tok+1 refers to the flux through the chlorophyll transferreaction from TPM k to TPM k+1. This impliesthat amount of chlorophyll available to carry out photosynthesis is equal to thedifference between the amount transferred in to time point kand the amount transported out to point k+1, divided by two. Avalue of 1000 for MC predictsphotosynthetic oxygen evolution (estimated by the output flux through the oxygenexchange reaction during the light TPMs) ranging between 173 to 169 mmolO2 (gm chlorophyll)−1 whichis in the same order as that of wild-type Synechocystis. A widerange of values have been reported experimentally ranging from 225 mmolO2 (gm chlorophyll)−1(hr)−1 [mmolO2 (gm chlorophyll)−1(hr)−1 [The constraint levied on the model that couples photosynthesis to chlorophyllavailability is expressed as: 1(hr)−1 , precludSijk is thestoichiometric coefficient for metabolite i in reactionj and TPM k, j in TPMk.I,J, andK denote the sets of total metabolites, reactions, and TimePoint Models (TPMs), respectively, andJTransfer the set of alltransfer reactions. Constraints (4) and (5) refer to carbon (as CO2)and photons being supplied to only the light TPMs. The maximum amount of photonssupplied to a TPM are such that it is not growth-limiting but at the same timenot in excess so as to not trigger light-sensitive reactions. vPhontonuptake,k represent the carbon and photonuptake reactions, and vATPmaintenance,k is the ATP maintenancerequirement for a TPM k. Every transfer reaction j in TPMk is constrained to have a non-negative flux by Eq  throughout allTPMs, they may give rise to cycles that can carry unbounded flux. Hence, toprevent this cycling, the sum of transfer fluxes was set to a scalarSynechocystis, a protongradient is generated during photosynthesis across the thylakoid membrane thatdrives ATP formation. Transferring this gradient across time points would resultin an untenable way for storing energy outside of storage compounds. To thisend, protons and photons were not transferred across TPMs. The followingoptimization model formulation is used to carry out flux variability analysis(FVA): In photosynthetic organisms such as iCyt773 [Nitrogen fixation was included in the model with the addition of the nitrogenfixation reaction from iCyt773   relationships are evaluated for each reactionand the upper and lower bounds determined by flux variability analysis ofthe corresponding reactions are reduced by a factor corresponding to theexpression ratio [iSyn731 model wereused, so that the metabolic capacity of every TPM is equivalent beforeintroducing omics-derived flux constraints. Expression ratios of normalizedgene intensities were determined for every time point as the expressionlevel at a time point divided by the maximum expression of the gene acrossall time points, and not scaled using a non-linear transform such as thesigmoid scale. For reactions controlled by isozymes, the largest ratio amongall contributing isozymes was used, as when multiple enzymes have the sameenzymatic activity the one with the largest amount governs flux through thereaction. In the case of protein subunits the smallest ratio was used, asflux through the reaction is limited by the amount of the subunit componentpresent in the lowest concentration. This is incorporated into theoptimization framework presented earlier by modifying Eq  and thecorresponding change in biomass flux recorded (=Δvbiomass) and reportedusing flux control coefficients defined as: In our model, we determined the impact on the final biomass production fluxbrought about by a perturbation in the individual enzyme levels taken one ata time, taking mRNA expression to be a proxy for enzyme levels.Transcriptomic bounds constraining reactions in CycleSyn were perturbed by1%  is given asMMCA determines the interdependence between metabolite concentrations bycalculating pair-wise correlation coefficients between metabolite pairs.Here we used the non-parametric Spearman test  to calcuS1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.S6 Table(XLSX)Click here for additional data file.S7 Table(XLSX)Click here for additional data file.S1 Fig(PNG)Click here for additional data file.S1 File(JSON)Click here for additional data file.S2 File(ZIP)Click here for additional data file.


Constraint-based modelling (CBM) is a powerful tool for the analysis of evolutionary trajectories. Evolution, especially evolution in the distant past, is not easily accessible to laboratory experimentation. Modelling can provide a window into evolutionary processes by allowing the examination of selective pressures which lead to particular optimal solutions in the model. To study the evolution of C4 photosynthesis from a ground state of C3 photosynthesis, we initially construct a C3 model. After duplication into two cells to reflect typical C4 leaf architecture, we allow the model to predict the optimal metabolic solution under various conditions. The model thus identifies resource limitation in conjunction with high photorespiratory flux as a selective pressure relevant to the evolution of C4. It also predicts that light availability and distribution play a role in guiding the evolutionary choice of possible decarboxylation enzymes. The data shows evolutionary CBM in eukaryotes predicts molecular evolution with precision. Virtually all plants use energy from sunlight to convert carbon dioxide and water into oxygen and sugars via a process called photosynthesis. This process has many steps that each rely on different enzymes to drive specific chemical reactions. Most plants use a pathway of enzymes that is referred to as C3 photosynthesis.Plants absorb carbon dioxide gas from the atmosphere. However, the levels of carbon dioxide in the atmosphere are very low, so this limits the amount of photosynthesis plants can perform. To overcome this problem, some plants have evolved a different type of photosynthesis – called C4 photosynthesis – with a mechanism that increases the levels of carbon dioxide in the cells.Today, plants that use C4 photosynthesis  typically grow faster than other plants, especially in warmer climates. This gives C4 plants, such as corn, an advantage over their competitors and also helps them to colonize harsh environments that other plants struggle to thrive in. However, it remains unclear how C4 photosynthesis evolved in some plants living in wet habitats, or why other plants use forms of photosynthesis that are intermediate between C4 and C3 photosynthesis.C4 photosynthesis uses pathways containing enzymes that are found in all plants; therefore, C4 plants evolved by changing how they used enzymes they already had. To understand how these different enzyme pathways may have evolved, Blätke and Bräutigam used an approach known as constraint-based modelling. The researchers built a mathematical model of C3 photosynthesis and used it to predict the optimal enzyme pathways  for photosynthesis under particular conditions.The model predicted that, in addition to shortages in carbon dioxide, shortages in an important plant nutrient known as nitrogen may have driven the evolution of C4 photosynthesis. Furthermore, enzyme pathways that were intermediate between C3 and C4 photosynthesis were predicted to be optimal solutions under particular conditions. Together, the findings of Blätke and Bräutigam may explain why different variations of C4 photosynthesis exist in plants. These findings could be used to breed crops that use the most efficient type of photosynthesis for the conditions they are grown in, leading to better yields. Identifying specific evolutionary trajectories and modelling the outcome of adaptive strategies at the molecular levels is a major challenge in evolutionary systems biology . The evo2 concentration at the site of Rubisco to overcome a major limitation of carbon fixation , forming a C4 acid, oxaloacetate (OAA). After stabilisation of the resulting C4 acid by reduction to malate or transamination to aspartate, it is transferred to the site of Rubisco and decarboxylated by one of three possible decarboxylation enzymes, NADP-dependent malic enzyme (NADP-ME), NAD-dependent malic enzyme (NAD-ME), or PEP carboxykinase (PEP-CK) (Zea mays) (Sorghum bicolor) (Panicum miliaceum) (Gynandropsis gynandra) (Panicum maximum) (C4 photosynthesis evolved independently in at least 67 independent origins in the plant kingdom  and it afixation . Enrichmpiration . The ratin speed . Lower sin speed . In the (PEP-CK) . Speciesea mays)  and greabicolor)  use NADPliaceum)  and Afriynandra)  use NAD-maximum)  use mainmaximum) . After dmaximum) . All themaximum) . In its maximum) . Initialmaximum) .Escherichia coli, such as glycerol usage , and optimisation criteria for the algorithm which approximate the selective pressures the metabolism evolved under. In this context, inputs define the resources that need to be taken up by the metabolic network to fulfil a particular metabolic function, which is related to the outputs, for example the synthesis of metabolites part of the biomass or other specific products. In CBM, the objective is most likely related to the in- and/or outputs.Arabidopsis core model   . Light, ol/(m2s) , we set Arabidopsis phloem exudate design, simulate, validate cycles against known physiology with errors sequentially eliminated and a minimal set of constraints required for a C3 model recapitulating extant plant metabolism determined. After each change, the CBM predicted all fluxes which were output as a table and manually examined  and 4:1 (mitochondria)  . We assuhondria)  have shoone-cell model, since (https://github.com/ma-blaetke/CBM_C3_C4_Metabolism (https://github.com/elifesciences-publications/CBM_C3_C4_Metabolism).In preparation for modelling the C4 cycle, we ensured that all reactions known to occur in C4 , which are involved in 59 subsystems. The one-cell model requires a photosynthetic photon flux density (PPFD) of 193.7 μmol/(m2s)  of NO3- and 18.2 μmol/(m2s) of H2O. According to the assumed ratio of sucrose and amino acids in the phloem sap, the flux of sucrose predicted by the model is 0.5 μmol/(m2s) and of amino acids 0.3 μmol/(m2s). The rate of oxygen supply by the network is 20.9 μmol/(m2s). Part of the complete flux table is displayed in The ol/(m2s) . The one2 uptake rate and the phloem sap output have a positive linear relationship, see 2s)–200 μmol/(m2s), see 2s), the CO2 uptake rate acts as a limiting factor restricting the increase of phloem sap production. If either the PPFD or the CO2 uptake rate is zero, the phloem sap cannot be produced, compare The COone-cell model and connected the two network copies by bi-directional transport of cytosolic metabolites including amino acids, sugars, single phosphorylated sugars, mono-/di-/tri-carboxylic acids, glyceric acids, glycolate, glycerate, glyceraldehyde-3-phosphate, di-hydroxyacetone-phosphate and CO2, see Materials and methods for details. Since CBM is limited to static model analysis, we introduced two Rubisco populations in the bundle sheath network to approximate CO2 concentration-dependent changes in the oxygenation : carboxylation ratio of Rubisco  was allowed , that is all CO2 is funnelled through PEPC, for high photorespiratory fluxes. Concomitant with flux through PEPC, the activity of the decarboxylation enzymes changes (2 to the bundle sheath at up to 4.7 μmol/(m2s). Decarboxylation of C4 acids is initially mostly mediated by PEP-CK and is largely taken over by NADP-ME at high fluxes through photorespiration. Flux through NAD-ME is very low under all photorespiration levels. The decarboxylation enzymes dictate flux through the different Rubiscos in the model  to 1000 μmol/(m2s) and photon distribution in the range 2s) , the CO2 uptake rate is reduced, leading to a decreased activity of the decarboxylation enzymes (2s) or if at least twice as many photons are absorbed by the mesophyll. Excess light availability and a higher proportion of photons reaching the bundle sheath leads to optimal solutions which favour PEP-CK as the decarboxylation enzyme. In the case of very high light availability and an abrupt shift towards the bundle sheath, NAD-ME becomes the optimal solution –200 μmol/(m2s), see 2 evolution for a PPFD of 200 μmol/(m2s) is estimated to be 16.5 μmol/(m2s) in the literature  are shade plants which grow in the understory  may alsCBM of photosynthetically active plant cells revealed a major knowledge gap impeding CBM, namely the unknown protonation state of most transport substrates during intracellular transport processes. When photoautotrophic metabolism was optimised in a single cell for minimal metabolic flux and therefore, optimal resource use, C3 photosynthetic metabolism was predicted as the optimal solution. Under low photorespiratory conditions, a two-celled model which contains a CCM-dependent Rubisco optimised for resource use, still predicts C3 photosynthesis. However, under medium to high photorespiratory conditions, a molecularly correct C4 cycle emerged as the optimal solution under resource limitation and photorespiration reduction as objective functions which points to resource limitation as an additional driver of C4 evolution. Light and light distribution was the environmental variable governing the choice of decarboxylation enzymes. Modelling compartmented eukaryotic cells correctly predicts the evolutionary trajectories leading to extant C4 photosynthetic plant species.Flux balance analysis (FBA) is a CBM approach  to invesThe degeneracy problem, the possible existence of alternate optimal solutions, is one of the major issues of constraint-based optimisation, such as FBA . To avoihttps://github.com/ma-blaetke/CBM_C3_C4_Metabolism (https://github.com/elifesciences-publications/CBM_C3_C4_Metabolism).All FBA experiments in this study employ pFBA and are performed using the cobrapy module in a python 2.7 environment run on a personal computer . All FBA experiments are available as jupyter notebooks in the supplementary material and can also be accessed and executed from the GitHub repository one-cell model, is based on the Arabidopsis core model  (As in ol/(m2s) . TherefoEx_Suc is already included in the model. An additional export reaction Ex_AA represents the relative proportion of 18 amino acids in the phloem sap of Arabidopsis as stoichiometric coefficients in accordance to experimentally measured data from Ex_Suc and Ex_AA. Furthermore, it is known that the export of sucrose and the formation of starch is approximately the same , chloroplast (NGAM_h) and mitochondria (NGAM_m) in the form:The one-cell model ATP/ADP are not included as peroxisomal metabolites. The flux through the maintenance reactions is fixed to the determined maintenance costs given in An equivalent maintenance reaction cannot be formulated for the peroxisome since in the 2 and O2 partial pressures determine the ratio of the oxygenation : carboxylation rate of Rubisco (given by reactions RBO_h and RBC_h) and can be described by the mathematical expression:2 over O2. In the case of a mature leave and ambient CO2 and O2 partial pressures in temperate regions with adequate water supply, the ratio The COiCitDHNADP_h) and plastoquinol oxidase (AOX4_h) because .For enhanced compliance with the recent standards of the systems biology community, the two-cell model, comprises two copies of the one-cell model to represent one mesophyll and one bundle sheath cell. Reactions and metabolites belonging to the metabolic network of the mesophyll are indicated with the prefix [M], whereas the prefix for the bundle sheath is [B]. The separate mesophyll and bundle sheath networks are connected via reversible transport reactions of the cytosolic metabolites indicated with the prefix [MB], 2 concentrating mechanism steadily supplies Rubisco with CO2 in such a way that the oxygenation rate is negligible. Therefore, the bundle sheath network is equipped with two Rubisco populations. The native Rubisco population binds external CO2 and adheres to forced oxygenation : carboxylation ratios, where the optimised evolutionary population binds only internal CO2 and the carboxylation occurs independently of the oxygenation. External CO2 is defined as [B]_CO2_ex_{c,h} supplied by the mesophyll network. Internal CO2 given by [B]_CO2_{c,h,m} originates from reactions in the bundle sheath network producing CO2. External CO2in the bundle sheath network is only allowed to move to the chloroplast [B]_Tr_CO2h_Ex and to react with Rubisco [B]_RBC_h_Ex. The differentiation of two Rubisco populations binding either external or internal CO2 approximates the concentration-dependent shift of the oxygenation : carboxylation ratio.The generic model of C4 metabolism, short one-cell model, we assume photoautotrophic growth conditions, see 2 assimilation became more efficient allowing higher CO2 assimilation rates. Zea mays achieves up to 40 μmol/(m2s) ([M]_Im_CO2)  . We assuone-cell model are transferred to the mesophyll and bundle sheath network, as well as the corresponding flux ratios, see The outputs of the genC3 model are assigned to both cell types in the two-cell model. Due to declining CO2 concentrations over evolutionary time and/or adverse conditions which close the stromata, the oxygenation : carboxylation ratio of the native Rubisco population in the bundle sheath and the mesophyll is increased and can be predicted as 1 : 3, the corresponding flux ratios are adapted accordingly. Furthermore, we assume that the total photon uptake in the mesophyll and bundle sheath is in the range of 0 μmol/(m2s)to 1000 μmol/(m2s). Since they are more central in the leaf, the photon uptake by the bundle sheath must be equal or less compared to the mesophyll. The mesophyll and bundle sheath networks are connected by a range of cytosolic transport metabolites including amino acids, sugars , single phosphorylated sugar , mono-/di-/tri-carboxylic acids ; Amy Marshall-Colon (Reviewer #3).Thank you for submitting your article "Evolution of C4 photosynthesis predicted by constraint-based modelling" for consideration by The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.The main requests for clarity by the reviewers revolve around these three general areas.Arabidopsis that are lineage specific, and how existing physiological measures could be used to support the modeling.1) Commenting on how this model may or may not fit to reality. This includes issues of assumptions inherent to the CBM model, flux issues in 2) Noted issues with the Jupyter Notebook.3) Making the writing more accessible in how the data shows the claims and what are hypothesis generated by the models that need testing.Reviewer #1:The authors use a flux based optimization approach to investigate the C3/C4 transitions and the different C4 possibilities. Overall, this is a very interesting manuscript. As an editorial note, as a general biologist, I could understand the main conclusions due to the explicit statements making these conclusions. It would help however to walk the general biologists through the results and figures more to help them understand how the data makes these conclusions. I was able to divine this from the data but it did take effort that a general biologist may not put into the work.Arabidopsis flux model but I was unsure if this is the generic flux model or the one that incorporates specialized metabolism. It might make some sense to comment on how using the Arabidopsis C3 map as a resource from the flux model given that Arabidopsis has very different sulfate/sulfur fluxes in comparison to non-Brassicaceous plants. This links directly to sulfur-amino acids and glutathione metabolism due to the heavy requirement for glucosinolate metabolism as shown by the work of Conant, Pires and colleagues. At the very least some discussion about how large carbon sinks not in the model may or may not change the conclusions would be helpful especially to guide future modelling efforts.I do have one point of clarification. The model is built on the Reviewer #2:In this manuscript, the authors develop a constraint-based metabolic model (CBM) of C4 photosynthesis using known C3 metabolic models with additional constraints. They compare the C3 and C4 models to see if various evolutionary pressures can drive a metabolic shift from C3 to C4 photosynthesis. They find that selection for minimizing metabolic turnover will drive metabolism total the C4 solution with differing light conditions controlling the appearance of different classes of C4.I enjoyed reading this manuscript, and I commend the authors on their approach to an important and complex topic. However, I think that the manuscript could use improvement in two key areas.Arabidopsis core model predicts physiological results”, the authors give many numerical predictions of their model, but no comparative values from real plants. Obviously, many model parameters are not measurable . But if the model is reproducing physiology, the authors should clearly specify how and with what level of error. Note also that there are advanced approaches for fitting models such as these to real data on gene expression levels, trying to make models that more closely follow observed physiology (1). The authors certainly need not apply them, but the text  as written rather implies that CBMs have not been successfully used with eukaryotes, which is not true. (Also note that "eukaryote" is not synonymous with "multicellular" (2)).First, while the authors discuss at several points how their models are consistent with physiological data, these comparisons appear to be vague and qualitative. For instance, in the ninth paragraph of the subsection “The curated My second concern is that the authors do not make enough of an effort to guide the reader through the potential confounds of CBM for problems such as this one. For instance, in the last paragraph of the subsection “C4 modes with different decarboxylation enzymes result from different set of constraints”, the authors reject nitrogen-limitation as a driver of C4 evolution. However, if compounds that are composed of a good deal of nitrogen are used as catalysts in a CBM, the model will not predict a need for high levels of nitrogen because those compounds are regenerated. I believe that the various C4 carbon shuttles function in exactly this way, and a CBM that seeks only to synthesize sugars and amino acids and has no biomass component will not predict an increased nitrogen requirement for C4 even if that requirement exists, because the compounds requiring that nitrogen cycle in the model. To be clear, I suspect the authors are correct that light is a more likely driver of C4 evolution than nitrogen limitation. But I am not convinced the CBM proves this.Likewise, CBMs "overpredict" solutions to metabolic problems because they are not kinetic. Hence, the fact that the base 2-cell model does not differentiate between the C4 classes does not mean that there are not kinetic differences that are evolutionarily important.References:1) Shlomi T, Cabili MN, Herrgard MJ, Palsson BO, and Ruppin E (2008) Network-based prediction of human tissue-specific metabolism. Nature Biotechnology 26(9):1003-1010.Saccharomyces cerevisiae iND750, a fully compartmentalized genome-scale metabolic model. Genome Research 14:1298-1309.2) Duarte NC, Herrgård MJ, and Palsson BØ (2004) Reconstruction and validation of Reviewer #3:2 concentration in the model; this should either be more clearly explained how it was done and the results, or why it wasn't done. Finally, it is wonderful that the authors include their Jupyter Notebooks and source data for the reader; however, we identified a few issues that made it difficult to run the code. First, there is no Readme file to follow.The manuscript by Blätke and Brautigam provides a novel method using constraint based modeling to predict the selective pressures that resulted in C4 metabolism. The take-away from this study is that C4 metabolism emerged from increasing photorespiration with concomitant resource efficiency, and that light is a driver for different C4 states. The model presented here overcomes some of the limitations of previous flux models of C3 and C4 metabolism, and makes an important contribution to the field. However, the main take-aways of this study are not easy for the reader to pull out as they are buried within the manuscript. This very interesting manuscript could be improved by streamlining the text and more clearly summarizing the main results either in the section titles or as a couple of sentences at the end of each Results section. Much of the Discussion is redundant to the results, so can be shortened for clarity. Likewise, the Discussion would be more interesting if the authors took a deeper dive into the potential outcomes and applicability of their results; how can the information revealed in this study guide future efforts for engineering C4 metabolism into C3 crops? Are there potential transcriptional regulatory mechanisms that could be investigated to evolve C4 metabolism in C3 crops? It is also unclear if the authors altered exogenous COSecond, the code would not run with the current installations of the Cobra and Escher packages; this was resolved by changing cobra.io.sbml3.read_sbml_model to cobra.io.sbml.read_sbml_model in the load_sbml_model.py file as cobra.io.sbml3 does not appear to exist in the current version of the cobra package. The escher package returned a syntax error from the plots.py file in the initialization step of the jupyter notebook files. In order to run the files, we commented out (removed) any uses of the escher package in the code.eLife. Your revised article has been reviewed by three peer reviewers, including Dan Kliebenstein as the Reviewing Editor, and the evaluation has been overseen by Christian Hardtke as the Senior Editor.Thank you for resubmitting your work entitled "Evolution of C4 photosynthesis predicted by constraint-based modelling" for further consideration by The manuscript has been improved but there are some remaining issues that need to be addressed before final acceptance, as outlined below.There are a few suggestions where in a couple of places the writing could be tightened to improve the accessibility for the general reader.Reviewer #1:The authors have nicely addressed my previous concerns and I have nothing further to add.Reviewer #2:In this manuscript, the authors develop a constraint-based metabolic model (CBM) of C4 photosynthesis using known C3 metabolic models with additional constraints. They compare the C3 and C4 models to see if various evolutionary pressures can drive a metabolic shift from C3 to C4 photosynthesis.2 limitations confusing. The authors write "the optimal solution to the model predicted the same behavior" and "resulted in the same optimal solution as unlimited uptake with the differences of proportionally lower flux overall."The authors have addressed most of my concerns, but I still find the description of the effects of nitrogen, water and CO2O or CO2 limitation, which is common with FBA when a metabolite is not truly limiting. I think the authors' point is actually that the proportional fluxes are the same but with different magnitudes, but neither the text nor Figure 6 nor Figure 6—figure supplement 1 seem to me to be crystal clear on this point.A quick reading of these statements makes one believe that the optimal solution is unchanged with N, HIntroduction, second paragraph: "prohibitive" is a slightly odd word to use here. Lower speeds are very likely maladaptive, but are not lethal for growth.Arabidopsis core model predicts physiological results”, first paragraph: I would add a few words on what these inputs and outputs are.Subsection “The curated Reviewer #3:The authors addressed each of our comments to various extents. We appreciate the clear headings that provide the reader with the main findings of each section. However, we still find the summary at the end of each section to be lacking. That said, the authors did a good job of streamlining the section on the C4 cycle under resource limitation to reveal the key insights. This helped to reduce the redundancy of the Discussion section. Importantly, the authors corrected the Jupyter Notebooks issue such that now they can easily be run. The conclusion paragraph still needs work to achieve clarity and a logical flow of ideas. For example, the second sentence seems out of place. Otherwise we are satisfied with the revised version. Reviewer #1:The authors use a flux based optimization approach to investigate the C3/C4 transitions and the different C4 possibilities. Overall, this is a very interesting manuscript. As an editorial note, as a general biologist, I could understand the main conclusions due to the explicit statements making these conclusions.Reviewer 3 asked for streamlining the manuscript, and indeed, some sections between the Results and Discussion were repetitive. We have excised those Discussion elements from the Results and hope that the clarity has not suffered.It would help however to walk the general biologists through the results and figures more to help them understand how the data makes these conclusions. I was able to divine this from the data but it did take effort that a general biologist may not put into the work.Thank you for this comment. We have now added an introductory sentence for each figure that explains how the visualization is generated and why. In essence, all figures and tables are partial visualizations of the flux distribution predicted by the model under different constraints.I do have one point of clarification. The model is built on the Arabidopsis flux model but I was unsure if this is the generic flux model or the one that incorporates specialized metabolism. It might make some sense to comment on how using the Arabidopsis C3 map as a resource from the flux model given that Arabidopsis has very different sulfate/sulfur fluxes in comparison to non-Brassicaceous plants. This links directly to sulfur-amino acids and glutathione metabolism due to the heavy requirement for glucosinolate metabolism as shown by the work of Conant, Pires and colleagues.Arabidopsis core model from Arnold and Nikoloski, 2014, describes only the primary metabolism. We added two sentences to make explicit the absence of specialized/secondary metabolism. Our curation process based on the Arabidopsis core model did not add reactions part of the specialized metabolism. The duplicated two-cell model we are using to investigate C4 also contains no additional specialized metabolic routes; only transport reactions have been added.The At the very least some discussion about how large carbon sinks not in the model may or may not change the conclusions would be helpful especially to guide future modelling efforts.We agree that the current model is unable to integrate biotic interactions since it lacks specialized metabolism in both metabolic map and output function. We have inserted one sentence each in the discussion of the results of the single-cell model and the two-cell model to make this absence explicit for the reader.Reviewer #2:[…] I enjoyed reading this manuscript, and I commend the authors on their approach to an important and complex topic. However, I think that the manuscript could use improvement in two key areas.First, while the authors discuss at several points how their models are consistent with physiological data, these comparisons appear to be vague and qualitative. For instance, in the ninth paragraph of the subsection “The curated Arabidopsis core model predicts physiological results”, the authors give many numerical predictions of their model, but no comparative values from real plants. Obviously, many model parameters are not measurable . But if the model is reproducing physiology, the authors should clearly specify how and with what level of error.Thank you for making this point. The original plant model on which the single-cell model was based contained multiple reactions which lead to flux distributions through enzymes and transporters not known to carry large fluxes in plants. This included circular fluxes across membranes for simple transport processes since transport reactions were missing. All of these were corrected, leading to a state more in agreement with the physiological state and the biochemistry according to current textbooks.To our knowledge, MFA in plant leaves is currently limited to the Calvin Benson Bassham cycle (https://www.pnas.org/content/pnas/111/47/16967.full.pdf), and hence it is presently not possible for us to benchmark the model predictions against a known flux distribution.Hence, we limit our comparison to output from the model and make the comparison explicit in a table in Figure 1B, which includes the model predictions and the measured values. A more detailed interpretation and comparison to experimental measurements can be found in the Discussion section, for the particular case “One cell model reflects C3 plant physiology”. We now also include a flux distribution table. Using this table, one can check the fluxes against one’s own expectations of plant metabolism without having to re-run the model.Note also that there are advanced approaches for fitting models such as these to real data on gene expression levels, trying to make models that more closely follow observed physiology (1). The authors certainly need not apply them, but the text  as written rather implies that CBMs have not been successfully used with eukaryotes, which is not true. (Also note that "eukaryote" is not synonymous with "multicellular" (2)).We did not attend to leave the impression that CBM has not already been successfully applied to eukaryotic/multicellular systems. We instead aimed to say that we see potential in the applications of CBMs when it comes to systems more complex than single-celled bacteria. According to the comment of reviewer 3, we have rewritten the Abstract and rephrased the respective part in the new Abstract and in the Introduction.My second concern is that the authors do not make enough of an effort to guide the reader through the potential confounds of CBM for problems such as this one. For instance, in the last paragraph of the subsection “C4 modes with different decarboxylation enzymes result from different set of constraints”, the authors reject nitrogen-limitation as a driver of C4 evolution. However, if compounds that are composed of a good deal of nitrogen are used as catalysts in a CBM, the model will not predict a need for high levels of nitrogen because those compounds are regenerated. I believe that the various C4 carbon shuttles function in exactly this way, and a CBM that seeks only to synthesize sugars and amino acids and has no biomass component will not predict an increased nitrogen requirement for C4 even if that requirement exists, because the compounds requiring that nitrogen cycle in the model. To be clear, I suspect the authors are correct that light is a more likely driver of C4 evolution than nitrogen limitation. But I am not convinced the CBM proves this.We obviously were not clear enough in our writing. Indeed, the model predicts C4 evolution if we optimize for minimal total flux. To us, this indicates that C4 is predicted to evolve under conditions where resources (i.e. N) are limited. The C:N ratios of C4 plants and intermediates support this prediction.Light and its distribution “only” influences which decarboxylation path is favoured, while limited N uptake does not influence the decarboxylation path. Reviewer 3 criticized that the manuscript was not written clearly enough. The Results section was edited to clarify this issue in the text.Likewise, CBMs "overpredict" solutions to metabolic problems because they are not kinetic. Hence, the fact that the base 2-cell model does not differentiate between the C4 classes does not mean that there are not kinetic differences that are evolutionarily important.We agree that kinetic constraints are likely also critical. To avoid the impression that CBM provides a final solution, we have inserted a sentence in the Discussion, which points out the critical role of kinetic constraints.References:1) Shlomi T, Cabili MN, Herrgard MJ, Palsson BO, and Ruppin E (2008) Network-based prediction of human tissue-specific metabolism. Nature Biotechnology 26(9):1003-1010.2) Duarte NC, Herrgård MJ, and Palsson BØ (2004) Reconstruction and validation of Saccharomyces cerevisiae iND750, a fully compartmentalized genome-scale metabolic model. Genome Research 14:1298-1309.Reviewer #3:The manuscript by Blätke and Brautigam provides a novel method using constraint based modeling to predict the selective pressures that resulted in C4 metabolism. The take-away from this study is that C4 metabolism emerged from increasing photorespiration with concomitant resource efficiency, and that light is a driver for different C4 states. The model presented here overcomes some of the limitations of previous flux models of C3 and C4 metabolism, and makes an important contribution to the field. However, the main take-aways of this study are not easy for the reader to pull out as they are buried within the manuscript. This very interesting manuscript could be improved by streamlining the text and more clearly summarizing the main results either in the section titles or as a couple of sentences at the end of each Results section.We have removed the intermittent partial discussion in favour of single sentences at the end of each section. Section headers were also changed.Much of the Discussion is redundant to the Results, so can be shortened for clarity.Thank you for pointing this out. We have removed the intermittent discussion from the Results and limited interpretation in the Results to single sentences at the end of each section.Likewise, the Discussion would be more interesting if the authors took a deeper dive into the potential outcomes and applicability of their results; how can the information revealed in this study guide future efforts for engineering C4 metabolism into C3 crops? Are there potential transcriptional regulatory mechanisms that could be investigated to evolve C4 metabolism in C3 crops?Thank you for pointing out this oversight. We have now inserted into the Discussion an evaluation of C4 and intermediacy as breeding and engineering targets for agriculture.cis in the C4 cycle genes; in Kühlahoglu et al. we have proposed that the C4 genes are likely hooked into the photosynthetic regulon.With regard to the transcriptional regulation, we think CBM cannot reveal potential transcriptional regulatory mechanisms. In Mallmann et al., 2014, and in the review Bräutigam and Gowik, 2016, we point out that evolution most likely occurs in 2 concentration in the model; this should either be more clearly explained how it was done and the results, or why it wasn't done.It is also unclear if the authors altered exogenous CO2 concentration is reflected in changes to photorespiration. There are multiple factors  which alter CO2 availability in the plant. Hence we opted to converge them in altered photorespiratory flux. We now added a sentence to make this fact explicit.The COFinally, it is wonderful that the authors include their Jupyter Notebooks and source data for the reader; however, we identified a few issues that made it difficult to run the code. First, there is no Readme file to follow.Second, the code would not run with the current installations of the Cobra and Escher packages; this was resolved by changing cobra.io.sbml3.read_sbml_model to cobra.io.sbml.read_sbml_model in the load_sbml_model.py file as cobra.io.sbml3 does not appear to exist in the current version of the cobra package. The escher package returned a syntax error from the plots.py file in the initialization step of the jupyter notebook files. In order to run the files, we commented out (removed) any uses of the escher package in the code.Thank you for putting in the effort to run the code and point out the deficiencies in the documentation. We updated the file “READM.md” in the GitHub repository to link listed figure supplements in chronological order to the corresponding jupyter notebooks. In addition, we added a file “environment.yml” which contains detailed information about the used module versions to avoid any version conflicts. With the addition of the “environment.yml” the jupyter notebooks can now easily be executed at “https://mybinder.org/”, links are provided in the “READM.md”. Please be aware, that we provide the GitHub repository as zipped folder, but it is more convenient to view and access files in the GitHub repository itself:https://github.com/ma-blaetke/CBM_C3_C4_MetabolismWe added a short comment about the GitHub Repository to the end of the first Results section and to the “Materials and methods”.Reviewer #2:2 limitations confusing. The authors write "the optimal solution to the model predicted the same behavior" and "resulted in the same optimal solution as unlimited uptake with the differences of proportionally lower flux overall."[…] The authors have addressed most of my concerns, but I still find the description of the effects of nitrogen, water and CO2O or CO2 limitation, which is common with FBA when a metabolite is not truly limiting. I think the authors' point is actually that the proportional fluxes are the same but with different magnitudes, but neither the text nor Figure 6 nor Figure 6—figure supplement 1 seem to me to be crystal clear on this point.A quick reading of these statements makes one believe that the optimal solution is unchanged with N, HWe have edited the text passage to reflect our results better and now clearly state that the solutions result in reduced flux but proportionally identical solutions. We have also edited the figure legend of the figure in question to clarify the point further.Introduction, second paragraph: "prohibitive" is a slightly odd word to use here. Lower speeds are very likely maladaptive, but are not lethal for growth.Subsection “The curated Arabidopsis core model predicts physiological results”, first paragraph: I would add a few words on what these inputs and outputs are.We also corrected the typos and wording as suggested by the reviewers. As suggested by reviewer #2, we also added a short explanation on inputs and outs after introducing the basic set up of flux balance analysis.Reviewer #3:The authors addressed each of our comments to various extents. We appreciate the clear headings that provide the reader with the main findings of each section. However, we still find the summary at the end of each section to be lacking. That said, the authors did a good job of streamlining the section on the C4 cycle under resource limitation to reveal the key insights. This helped to reduce the redundancy of the Discussion section. Importantly, the authors corrected the Jupyter Notebooks issue such that now they can easily be run. The conclusion paragraph still needs work to achieve clarity and a logical flow of ideas. For example, the second sentence seems out of place. Otherwise we are satisfied with the revised version.The concern of reviewer #3 with the conclusion statement was addressed by rephrasing to improve the flow.


Mathematical models of biological networks can provide important predictions and insights into complex disease. Constraint-based models of cellular metabolism and probabilistic models of gene regulatory networks are two distinct areas that have progressed rapidly in parallel over the past decade. In principle, gene regulatory networks and metabolic networks underly the same complex phenotypes and diseases. However, systematic integration of these two model systems remains a fundamental challenge.In this work, we address this challenge by fusing probabilistic models of gene regulatory networks into constraint-based models of metabolism. The novel approach utilizes probabilistic reasoning in BN models of regulatory networks serves as the “glue” that enables a natural interface between the two systems. Probabilistic reasoning is used to predict and quantify system-wide effects of perturbation to the regulatory network in the form of constraints for flux variability analysis. In this setting, both regulatory and metabolic networks inherently account for uncertainty. Applications leverage constraint-based metabolic models of brain metabolism and gene regulatory networks parameterized by gene expression data from the hippocampus to investigate the role of the HIF-1 pathway in Alzheimer’s disease. Integrated models support HIF-1A as effective target to reduce the effects of hypoxia in Alzheimer’s disease. However, HIF-1A activation is far less effective in shifting metabolism when compared to brain metabolism in healthy controls.The direct integration of probabilistic regulatory networks into constraint-based models of metabolism provides novel insights into how perturbations in the regulatory network may influence metabolic states. Predictive modeling of enzymatic activity can be facilitated using probabilistic reasoning, thereby extending the predictive capacity of the network. This framework for model integration is generalizable to other systems.The online version of this article (10.1186/s12859-019-2872-8) contains supplementary material, which is available to authorized users. Advances in high-throughput technologies have made large-scale measurements of molecular traits possible. Mathematical and probabilistic models of networks have become instrumental in elucidating complex relationships among molecular traits from high-throughput data, e.g., –4. HowevThis work describes a novel approach to network integration that aims to understand how gene regulatory networks influence metabolism. Our approach interfaces two network-based approaches that have evolved largely in parallel: (1) constraint-based models of cellular metabolism  and (2) Gene regulatory networks play an important role in fundamental processes such as cell cycle, differentiation and signal transduction and metabolism . UnderstConstraint-based modeling has been widely used in systems biology as a computational tool to provide insights into cellular metabolism , 27. TheP(A=on∣B=off) is an estimate of the number of samples such the target gene A is on given transcription factor B is off. The effect of a knock out at the genome scale can then be assessed by building the probabilities associated with the target genes into upper bounds for FVA. PROM requires massive sample sizes to stably estimate the probabilities between target regulator pair interactions, and underlying these estimates is the need to discretize the gene expression into on and off states. Transcriptional Regulated FBA (TRFBA) [There have been several attempts to merge constraint-based models with regulatory constraints. Regulatory FBA (rFBA) , 44 and  (TRFBA)  also int (TRFBA) –51.Transcriptional abundance has also been utilized to derive context-specific metabolic models , 53. TheIn this work, we aim to integrate a gene regulatory network into a constraint-based metabolic networks model using probabilistic reasoning as the “glue” that binds these two systems. Specifically, probabilistic reasoning provides an underlying framework for predictions of the system-wide effects of genetic (node) perturbations in a regulatory network . These pX={X1,X2,…Xp}, in the graph that nodes (aka vertices) represent random variables [PGMs are a flexible class of models that encode probability distributions between a set of random variables, ariables , 61. In ariables , 62–66. Markov condition, which states that each variable, Xi, is independent of its ancestors, given its parents in graph, G. The conditional independencies between variables (nodes) is depicted in G, and can be used to express joint distribution in compact factored form. Under these assumptions, a BN encodes conditional independence relationships: pa(Xi) are the parent nodes of child node, Xi, and Θi denotes the parameters of the local probability distribution. The conditional probability of a child node given its parents, P(Xi∣pa(Xi),Θi), is often referred to as a local distribution. In our applications, these local models are Gaussian and are parameterized using gene expression data via local regressions on parent nodes [Briefly we provide an overview of BNs, see , 61 for evidence relates to changes in an upstream transcription factor. The probabilistic reasoning paradigm can be leveraged to predict updated probabilities and states of nodes in the network after taking new evidence into account. Probabilistic reasoning can be viewed as a tool to predict comprehensive system-wide responses of the network to new evidence, which is akin to an in silico experiment. Belief Propagation (BP) algorithms enable the absorption and propagation of evidence through a network [Probabilistic reasoning in a BN utilizes evidence about nodes in the network in order to reason (query) information about other nodes in the network . In our  network . BP in a network , 68, 69 This work utilizes the BP procedure in the BayesNetBP package, which implements the algorithms described in . The outC denotes the concentration of metabolites, E∈Rm×n is the sparse stoichiometric matrix and Φ∈Rn×1 contains the flux rates for the reactions in the model. When the system is at steady state the system of ODEs simplifies to a linear system, which is our underlying assumption. The addition of constraints can serve many purposes, e.g., to impose the irreversibility of certain reactions, to add a priori knowledge about flux rates or linear combinations of flux rates. Mathematically, the addition of constraints shapes the solution space for the flux estimation [Cellular metabolism can be modeled using the principals of mass balance  as a systimation . An objetimation , 40.The objective of FVA is to estimate feasible solutions to the constrained optimization problem , 42, whiEm×n is the stoichiometric matrix with rows representing m metabolites and columns for n fluxes, and Φ is a vector of fluxes. The concentrations of metabolites does not change under the steady state assumption. External metabolites participate in uptake or release to the extracellular environment, or are not fully accounted for in the model. Therefore, the net fluxes for these external metabolites can be non-zero. The inequality constraint GΦ≥h can be used to impose irreversibility of certain reactions as well as the capacity constraints that provide the upper limit of fluxes. The objective function, cTΦ, is a linear combination of the fluxes that are to be optimized. In our applications, we seek the maximization of net ATP production in the feasible space of Φ, because the brain has a very high requirement on energy production, which is critical for bioenergetics, function and neurodegeneration [b represent the measured fluxes and ε be the measurement errors, then the observation model is given as: where neration . This obneration . Equalitwhile still satisfying the constrains in Equation Model of brain metabolism: A core metabolic model for normal human brain was constructed using 89 metabolites, 71 biochemical reactions from core pathways, including the glycolytic pathway, Pentose Phosphate Pathway (PPP), the TriCarboxylic Acid (TCA) cycle, malate-aspartate shuttle, the glutamate and GABA shunt and oxidative phosphorylation. The model spans the extracellular space, cytosol and mitochondria. This core model was originally used to investigate the low oxygen to carbohydrate ratio in the brain during extreme endurance sports [e sports , and late sports . These iBayesian Network of the HIF-1 signaling pathway: The structure of the BN is constructed from the HIF-1 signaling pathway in the KEGG database [A→C←B, which would create additional independencies in the graph. The full network consists of 86 nodes and can be viewed in Additional file database . The R pdatabase  and pcaldatabase  were usedatabase  for detadatabase . This apTwo BNs were constructed with the identical structure of the signaling pathway  regulation, which is a connection between glycolysis and the TCA cycle. Pyruvate dehydrogenase kinase 1 (PDK1) is a known downstream target of HIF-1 regulation, which can inactivate PDH through phosphorylation , a post-Ax=b+ε was computed using the lsei  routine in the R LIM package [mirror algorithm that is implemented in the xsample function [xsample implements Markov Chain Monte Carlo (MCMC) sampling to uniformly sample the feasible region of the constrained optimization problem. The mirror algorithm for MCMC takes advantage of reflections that are guided by the inequality constraints, which improves acceptance rates and mixing for the chain when compared to hit-and-run samplers [https://github.com/hyu-ub/prob_reg_net.Taken together, ten constraints were added to the model. The system of equations is overdetermined, and thus the solution is not unique. The least square solutions of  package , 82. FVAfunction . The funsamplers . FVA modsamplers  and Gewesamplers . SpecifiThe integrated model consists of a signaling pathway represented by a BN and a constraint-based model of cellular metabolism in the brain. These models are interfaced through belief propagation Fig. , which eEnzyme abundance levels were estimated for control and AD models when ranging HIF-1A between low (8) and high 13) levels. These estimated abundance levels were subsequently utilized to derive fold changes between estimated basal and repressed/activated levels of HIF-1A for control and AD models. The predicted fold changes for the lowest  brain. Considering the side effects of HIF-1 activation, and its lower efficiency in rescuing deficient energy production, HIF-1 pathway is perhaps not an ideal therapeutic target for AD patients. Therefore, the therapeutic benefit of HIF-1 activator in AD patients is probably not through directly modulating intracellular energy metabolism. If data becomes available, it would be informative to reproduce this in silico experiment to characterize AD brains in early and late stage AD patients, as it is expected that the metabolic shift from healthy patients is more subtle in early-stage –95. ThusThere are several limitations in this approach that are inherited from the underlying representations of the gene regulatory and metabolic networks. Notably, the gene regulatory network is integrated into a metabolic network, and the modeling framework does not allow for other way around. Thus, the one-way integration of networks describes the impact of the genetics on metabolism , but wilLimitations outlined in Blazier et al.  that ariIn conclusion, the integration of probabilistic graphical models of gene regulatory networks into constraint-based models of metabolism networks provides a unique opportunity to assess the impact of in silico genetic perturbations to downstream metabolism. Moreover, leveraging probabilistic reasoning facilitates predictive modeling of enzymatic activity that extends beyond the gene expression data. Future work will be extending this paradigm to genome-scale models . In ordeAdditional file 1Supplemental figures. (PDF 110 kb)Additional file 2Supplemental table. (XLSX 17 kb)