Chlamydomonas reinhardtii under varied CO2 inputs. The metabolic network model of Chlamydomonas was updated based on the genome annotation data and sensitivity analysis revealed CO2 sensitive reactions. Biological experiments were performed with cells cultivated at 0.04% (air), 2.5, 5, 8, and 10% CO2 concentration under controlled conditions and cell growth profiles and biomass content were measured. Pigments, lipids, proteins, and starch were further quantified for the reference low (0.04%) and high (10%) CO2 conditions. The expression level of candidate genes of sensitive reactions was measured and validated by quantitative real time PCR. The sensitive analysis revealed mitochondrial compartment as the major affected by changes on the CO2 concentrations and glycolysis/gluconeogenesis, glyoxylate, and dicarboxylate metabolism among the affected metabolic pathways. Genes coding for glycerate kinase (GLYK), glycine cleavage system, H-protein (GCSH), NAD-dependent malate dehydrogenase (MDH3), low-CO2 inducible protein A (LCIA), carbonic anhydrase 5 (CAH5), E1 component, alpha subunit (PDC3), dual function alcohol dehydrogenase/acetaldehyde dehydrogenase (ADH1), and phosphoglucomutase (GPM2), were defined, among other genes, as sensitive nodes in the metabolic network simulations. These genes were experimentally responsive to the changes in the carbon fluxes in the system. We performed metabolomics analysis using mass spectrometry validating the modulation of carbon dioxide responsive pathways and metabolites. The changes on CO2 levels mostly affected the metabolism of amino acids found in the photorespiration pathway. Our updated metabolic network was compared to previous model and it showed more consistent results once considering the experimental data. Possible roles of the sensitive pathways in the biomass metabolism are discussed.The development of microalgae sustainable applications needs better understanding of microalgae biology. Moreover, how cells coordinate their metabolism toward biomass accumulation is not fully understood. In this present study, flux balance analysis (FBA) was performed to identify sensitive metabolic pathways of  BiomassChlamydomonas reinhardtii has been extensively considered as a model organism to the study of different cellular mechanisms under distinct environmental conditions . This approach takes in consideration a linear programming strategy to solve and describe the fluxes in a systems at steady state   enzyme by increasing the cellular inorganic carbon (Ci) pools favoring the carboxylase activity of RubisCO; thus, carbon fixation through photosynthesis. Moreover, some Ci transporters located in the plasma membranes and chloroplast have been suggested as main proteins on the carbon uptake process  were retrieved from NCBI database  and the CO2 fluxes modified to evaluate the effects of different conditions of CO2 supply at the steady state of the cell metabolism and other parameters were established as previously described  is the objective function (biomass).Where 2 level response was performed through the identification of reactions affected under different CO2 fluxes through FBA simulations. FBA was resolved at five different CO2 conditions  and the resulting magnitudes defined the CO2-sensitive reactions by the flux variation coefficient ρ  in a R'ALF Plus solo 6.7 L bioreactor  in constant and continuous illumination with cool-white LED (average 400 μE·m−2·s−1). The cultures remained in a batch mode with starting culture volume of 4 L, in open system with automatic controlled CO2 gas flow in air, no pH control and continuous stir at 60 rpm. Cell inoculation was carried out with a 10 mL pre-inoculum taken from a sample at steady state. Cells were harvested by centrifugation at the late exponential phase of cell growth (O.D.750nm ≈ 0.9) for biomass characterization.The Cell growth monitoring was performed daily with measurements of O.D. at 750 nm and cell counting using Neubauer chamber. Growth rates were calculated as previously described  or two biological replicates , each one with three technical replicates, were considered for statistical analysis.Cell pellets from 50-mL cell culture aliquots at the late exponential phase were washed three times with 2 mL of de-mineralized water to remove inorganic salts and the final cell suspension was transferred to previously weigh empty Petri dishes. Plates containing the biomass were kept overnight at 90°C, and the dry weight was measured. Three (0.04 and 10% CO2 (10%) were harvested in 50-mL aliquots  and centrifuged at 3000 × g in a swing rotor bench centrifuge for 5 min at 4°C. Cell pellets were kept at −80°C until further processing. Frozen cell pellets were macerated until conversion into a light green powder. Protein extraction was performed using a buffer containing 100 mM Tris pH 7.5, 4 mM EDTA, 5 mM 2-mercaptoethanol, 10% glycerol, and 0.05% Triton X-100. Protein content was determined by Bradford assay  and high CO2 changes [low CO2  and high CO2 (10% CO2)] were selected to further gene expression analysis through the relative quantification by qRT-PCR. These candidate genes were previously annotated to the following routes and mechanisms: CCM, Calvin cycle, Glycolysis/Gluconeogenesis metabolism, and Glyoxylate/dicarboxylated.Based on our results on the sensitivity analysis using FBA approach on the model described by Chang et al.  and litewww.quantprime.de) following the criteria as follows: Tm = 60 ± 1°C, length 18–25 bases, preferentially on exon-exon junctions. When possible, primers were designed to have a GC content of 45–55%, generating a single PCR product sizing between 60 and 150 bp. Primers were synthesized by Macrogen .Cells for RNA extraction were harvested in 2-mL aliquots by centrifugation for 2 min, 3000 × g, at 4°C, and the cell pellets were immediately frozen and kept at −80°C until further use. Total RNA extraction was performed using the RNeasy Plant Mini Kit  as previously described  as primer for the synthesis of the first complementary DNA strand. Two genes [Actin (ACT) and Ubiquitin protein ligase (UBQ)] were selected as reference genes. All the cDNA samples were amplified in 96-well plates in an Applied BioSystems ABI7500 FAST system. The qPCR reaction was carried out in 10 μL containing 1 μM primers and SYBR Green qPCR Master Mix (Roche). The primer sequences used in this study are presented in Supplemental Table 2) were performed.Three micrograms of total RNA were used for cDNA synthesis employing the SuperScript III First Strand System  according to the manufacturer's instructions, using oligo-(dT750 ≈ 0.9) at low (0.04%) and high CO2 concentration (10%). Metabolites were extracted with methanol-chloroform-water HPLC grade (2.5:1:1.4) mixture and three biological replicates for low CO2 (0.04%) and two biological replicates for high CO2 (10%) were considered. Samples were immediately frozen in liquid nitrogen and lyophilized for storage. Extraction and derivatization of metabolites were performed as outlined previously , coupled to an Agilent 7890 A gas chromatograph—Leco Pegasus HT time-of-flight mass spectrometer . Identical chromatogram acquisition parameters were used as those previously described  or PMN (http://pmn.plantcyc.org/CHLAMY/) that report proteins and curated metabolic data, showed that only a small group of enzymes of Chlamydomonas has been discovered and functionally characterized. Considering this, our homology analysis was performed comparing all annotated proteins in KEGG database to identify the EC numbers and the associated reactions. In order to simplify the reconstruction, only the reactions with reported reactants in Chang et al.  were associated. After removing the reactions that already exist in the work of Chang et al. , 1803 neChlamydomonas. These results indicated that manual curation is still necessary and mandatory to guarantee feasible models.We found that some reactions and metabolites have generic names in KEGG database, especially those associated to lipid and starch metabolism. This inconsistent information provides new reactions and metabolites that cannot be interconnected affecting viable results from the FBA analysis. Gaps within the different pathways were observed when looking at the rows of the stoichiometric matrix and manual interconnection had to be assumed to consume products based on metabolic maps. Furthermore, unlikely reactions were found associated to homology parameters, reactions belonging to penicillin, and cephalosporin biosynthesis were rejected because no information was confronted with 2 input fluxes. However, in our complemented reconstruction, more, and novel sensitive reactions appeared related to the amino acid metabolism of alanine, threonine, tryptophan, and propionate metabolism  , and transport of compounds such as ethanol, ammonia, and O2. The mitochondria is important to the maintenance of intracellular redox gradients, impacting the rates of photorespiration, and efficiency of photosynthesis , reaching the highest content when evaluated at 10% ; this information corroborate previous results  and high (10%) CO2 conditions, showed a positive increase at high CO2 concentration. However, no significant changes were found for starch . Moreover, we observed that cell culture at 5% CO2 produced similar amounts of total biomass than cells cultured at 10% CO2, suggesting the existence of a saturation trend in the biomass production once cells are cultivated in CO2 concentration higher than 5%.Cell growth was measured daily Figure  and a si% Figure . Therefo2 conditions  showed similar profiles but cellular density was higher and statistically different from those cell cultures under low CO2 (0.04%). Thus, the exposure to high CO2 lead to an increased number of cells per culture volume and enhanced cellular capability to accumulate biomass, likely affecting mitosis-related cell cycle and energy metabolism.Furthermore, the cell growth curves observed on high CO2 sensitive metabolic reactions included gene expression analysis of selected genes and a metabolomics approach focused in the identification and relative quantification of the main metabolites of primary metabolism.The experimental validation of our results on the identification of CO2 related mechanisms may be determinant to biomass accumulation and CAHs play an important role on cellular carbon uptake . Similar results were shown by previous studies on the Carbon Concentrating Mechanism , glycine cleavage system, H-protein (GCSH), NAD-dependent malate dehydrogenase (MDH3), low-CO2 inducible protein A (LCIA), low-CO2-inducible protein 23 (LCI23), mitochondrial pyruvate dehydrogenase complex, E1 component, alpha subunit (PDC3), fructose-1,6-bisphosphate aldolase (FBA2), glyceraldehyde-3-phosphate dehydrogenase (GAP1), dual function alcohol dehydrogenase/acetaldehyde dehydrogenase (ADH1), and phosphoglucomutase (GPM2), were defined as sensitive nodes in the metabolic network simulations and found to be responsive to the changes in the carbon fluxes in the system.In Figure As discussed previously, the sensitivity analysis may generate different outputs depending on the completeness of the metabolic network used as input for simulation. Genes coding for GLN1, CIS1, ATP2, PRK1, and FBP1, which were found to be sensitive in Chang et al. , showed 2 concentrations. The metabolomics analysis performed using GC-TOF-MS permitted the quantification of 67 metabolites in the two compared CO2 concentrations  and high (10%) CO2 sensitive reactions of 13 out of the 67 metabolites identified. Our model was able to predict the behavior of these 13 metabolites at high and low CO2 concentrations regarding the amount and presence within the cells, being consistent with experimental results at the two growth conditions, except for the measurements of glycine, isocitrate, and sucrose, which were not good represented by the FBA.We further explored the CO2) and 50% of these did not show any alteration through FBA. From this perspective, it is shown that the model assumptions in general terms seem to be consistent with real behavior of maximizing biomass. However, others mechanisms may be activated resulting in saturation trends for CO2 processing and constraints.Other 50 metabolites quantified did not show significant differences between the two growth conditions  in order to satisfy the model constraints. The magnitude of the fluxes are >0 and are contributing to maximize the biomass function. Special attention to those magnitudes were taken into account for glycine transport from chloroplast to mitochondria, serine transport from mitochondria to chloroplast, hydroxypyruvate production, glycerate, and 3-phospoglycerate production in the chloroplast. All these processes may be related to photorespiration and showed positive fluxes in both Chang et al. and our complemented metabolic network models. Although genomic-scale restriction was not considered in the FBA, it is shown that these routes contribute to maximize biomass production.FBA analysis indicated that at low and high CO2 concentrations in the biomass composition of C. reinhardtii cells. Moreover, we identified candidate genes sensitive to the variations on the CO2 concentrations through the use of FBA in an extended metabolic network model presented here. Further experimental validation through gene expression analysis and metabolomics was performed. Our experimental results suggested that cells at high CO2 have increased capability toward biomass production. However, it also indicated that cells cultivated at CO2 concentrations higher than 5% achieved a saturation trend on total biomass accumulation. Although our FBA model was unable to describe this saturation trend, the magnitudes of the growth rate values were consistent between the different CO2 concentrations compared. This may be explained by the fact that the model was resolved using linear optimization and a change in input values, such as any external metabolite, represents a proportional increase in the objective function.In the present work, we compared the effects of varying CO2 concentrations. For the new sensitive routes and genes identified by our FBA, it was noted that many reactions were associated with energy metabolism. These sensitive routes have a number of genes which expression may be affected. Therefore, these genes may be interesting candidates on further biotechnological applications focused in the enhancement of biomass production. Reactions associated to the transport of amino acids, pyruvate, and carboxylate species into the mitochondria and chloroplast were shown to be the most sensitive ones. Moreover, mitochondria resulted as the most sensitive compartment as most reactions detected in our sensitive analysis may occur inside this organelle. Mitochondria presents a fundamental role in growth and biomass production, through its role on energy metabolism.Our results on the FBA sensitivity analysis of the two metabolic reconstructions showed a significant increase of flux in metabolic routes occurring in the chloroplast and mitochondria transport systems, including TCA cycle, glycolysis/gluconeogenesis, and amino acids biosynthesis in cells under high COSensitivity analysis also revealed a high dependence on the metabolic network quality and completeness on the identification of key routes. These routes can vary in differing models making it difficult to achieve consistent results; however, consensus in some main nodes were found and validated by qRT-PCR. Thus, our results revealed novel biochemical routes and candidate genes that may be relate to biomass production, through the modulation of the rate of biosynthetic processes.2 (10%) concentrations suggest that high CO2 concentration in microalgae cell culture may trigger mechanisms that are able to control the carbon fixation by the alternative synthesis of compounds that may have an inhibitory effect on the photosynthesis, or may enhance energy losses through photorespiration. These processes may have a role in the control of the cell biomass content and microalgae cell population, even under non-limiting availability of CO2. Further experiments are now necessary to provide more evidences of these effects.The changes observed in the metabolite profiles of cells at low (0.04%) and high CO2 concentrations. It was observed that many CCM-related genes are overexpressed at low CO2, indicating, as expected, that cells change their metabolism to produce enzymes involved in enhanced carbon uptake and carbonic acid conversion, instead of redirecting energy to build biomass precursors. A previous transcriptomics analysis compared Chlamydomonas cells at high (5%), low (0.05%), and very low (0.02%) CO2 concentrations  was found highly expressed at low CO2 concentration  itself does not depend on the CO2 conditions, we further compared which metabolites were modulated in the two CO2 concentrations (0.04 and 10%). Our metabolomics analysis indicated that the concentration of metabolites possibly related to photorespiration or other alternative route is modulated in response to high CO2 concentration.Besides the identification and validation of the expression of the main CA's under low and high CO2 concentration, indicating possible enhanced needs for light absorption and carbon fixation. However, starch content showed no significant changes which imply that the continuous light conditions may lead cells to control their carbohydrate stocks, probably due to the absence of a dark period and reduced need for starch accumulation or through the activation of alternative processes of carbon usage.Our results on the experimental biomass characterization showed that the pigment content per cell is the most sensitive component and its amount is almost duplicated at high CO2. The control of biomass accumulation may be closely connected to the regulation of biochemical pathways occurring in the mitochondria and the use of energy sources toward the accumulation of proteins and pigments.Altogether, these findings suggest that biomass accumulation does not enhances indefinitely with the enhanced availability of COFW, AG: conceived and designed the work; FW, DP, MM: performed experiments; FW and DP: drafted the manuscript; CC: performed metabolomics analysis; FW, DR, DP, AG: performed data analysis. All authors have read and approved the final version of the manuscript.This project was funded by Universidad de los Andes and FAPESP.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.


Constraint-based analysis of genome-scale metabolic models has become a key methodology to gain insights into functions, capabilities, and properties of cellular metabolism. Since their inception, the size and complexity of genome-scale metabolic reconstructions has significantly increased, with a concomitant increase in computational effort required for their analysis. Many stoichiometric methods cannot be applied to large networks comprising several thousand reactions. Furthermore, basic principles of an organism’s metabolism can sometimes be easier studied in smaller models focusing on central metabolism. Therefore, an automated and unbiased reduction procedure delivering meaningful core networks from well-curated genome-scale reconstructions is highly desirable.NetworkReducer, a new algorithm for an automated reduction of metabolic reconstructions to obtain smaller models capturing the central metabolism or other metabolic modules of interest. The algorithm takes as input a network model and a list of protected elements and functions (phenotypes) and applies a pruning step followed by an optional compression step. Network pruning removes elements of the network that are dispensable for the protected functions and delivers a subnetwork of the full system. Loss-free network compression further reduces the network size but not the complexity (dimension) of the solution space. As a proof of concept, we applied NetworkReducer to the iAF1260 genome-scale model of Escherichia coli  to obtain a reduced model that (i) allows the same maximal growth rates under aerobic and anaerobic conditions as in the full model, and (ii) preserves a protected set of reactions representing the central carbon metabolism. The reduced representation comprises 85 metabolites and 105 reactions which we compare to a manually derived E. coli core model. As one particular strength of our approach, NetworkReducer derives a condensed biomass synthesis reaction that is consistent with the full genome-scale model. In a second case study, we reduced a genome-scale model of the cyanobacterium Synechocystis sp. PCC 6803 to obtain a small metabolic module comprising photosynthetic core reactions and the Calvin-Benson cycle allowing synthesis of both biomass and a biofuel (ethanol).Here we present NetworkReducer algorithm provides a valuable tool for the application of computationally expensive analyses, for educational purposes, as well to identify core models for kinetic modeling and isotopic tracer experiments.Although only genome-scale models provide a complete description of an organism’s metabolic capabilities, an unbiased stoichiometric reduction of large-scale metabolic models is highly useful. We are confident that the The online version of this article (doi:10.1186/s12918-015-0191-x) contains supplementary material, which is available to authorized users. Escherichia coli (E. coli). The first E. coli genome-scale model (iJE660) was published in 2000  and added then also a reaction to “export” this biomass compound. This configuration makes it easier to configure biomass synthesis as a protected function and to keep track of the stoichiometric coefficient of the biomass compound during network compression. The final stoichiometric matrix of the genome-scale model (in the following denoted by ColiGS) was thus slightly extended to 2384 x 1669. Flux constraints in the ColiGS model were specified such that glucose serves as the only carbon substrate.We considered the network spanned by the reactions contained in the ColiCore model contains uptake reactions for glucose but also for some other substrates (including some amino acids). Since we aimed to focus on glucose as the sole carbon substrate, we removed all reactions and metabolites from the ColiCore model that are involved in uptake of these substrates. Analogously to the ColiGS model, we also included a biomass metabolite in the biomass synthesis reaction and a corresponding “biomass export” reaction. With these changes, the final dimension of the ColiCore model was 88 reactions and 69 internal metabolites. Key properties of ColiGS and ColiCore are summarized in Table The ColiGS network could be started. Phenotypes and elements of the genome-scale model to be maintained in the reduced model were specified as follows. All 88 reactions of the ColiCore model were marked as protected reactions (PR ) in the ColiGS model and we also demanded that all these reactions should be feasible (unblocked) in the reduced network. Since all metabolites involved in these reactions are implicitly protected as well we did not explicitly specify protected metabolites (PM = ∅). Concerning protected phenotypes, we demanded that (i) at least 99.9 % of the maximal growth rate  at least 99.9 % of the maximal growth rate in the ColiGS model under anaerobic conditions (0.2309 h−1) should be reachable in the reduced network ))ColiGS nColiPruned) which already decreased the dimension of the genome-scale network from 2384 reactions / 1669 internal metabolites to 455 reactions / 438 internal metabolites. As demanded, the maximal growth rates under aerobic and anaerobic growth in ColiPruned are identical (anaerobic) or very close (aerobic) to the respective maximal rates in the genome-scale model. The dof of ColiPruned (26) is significantly smaller than in ColiGS (753) and already close to the dof of ColiCore (24) indicating a similar complexity of the solution spaces of ColiPruned and ColiCore. Even though ColiPruned still contains more than 400 reactions, the  elementary modes of this network can be fully enumerated.Network reduction without applying network compression in postprocessing (only pruning) yielded a reduced network model  is much smaller compared to ColiPruned (455 reactions) while neither the dof nor the number of elementary modes and the possible phenotypes changed. The dimension of ColiPrunedComp is now very similar to ColiCore  of these additional elements arises due to a different description of exchange reactions. The ColiCore considers two compartments where metabolites are balanced (cytoplasm and extracellular space) plus (implicitly) an environment. Thus, 3 reactions and 3 balanced species are needed to describe the import of a metabolite M (Menvironment ➔ Mextracellular space ➔ Mcytoplasm) in the ColiCore model . In contrast, ColiGS contains additionally a periplasm compartment, hence, uptake of an exchange metabolite M involves 4 exchange reactions and 4 species (Menvironment ➔ Mextracellular space ➔ Mperiplasm ➔ Mcytoplasm). Since 15 metabolites can be exported/imported to/from the environment in ColiCore, 15 additional species and reactions (for the periplasmic space) must be maintained in the ColiPrunedComp model; they can also not be compressed because they are surrounded by protected reactions.ColiCore model for which we identified two reasons. First, different stoichiometries for biomass synthesis may lead to different biomass yields (discussed below). Second, we found that the remaining two additional (non-exchange) reactions in the ColiGS model not contained in the ColiCore model allow for higher maximal growth rates; these reactions were kept by the pruning algorithm to maintain the protected phenotype of maximal growth in the ColiPrunedComp model . The first of these two reactions is related to hydrogen production which turns out to be necessary to attain the maximal anaerobic growth rate. The second reaction is related to respiratory pathways. The ColiGS model contains two cytochrome oxidases (cytochrome bd and cytochrome bo3 oxidase). Both oxidize ubiquinol but with different stoichiometry for the translocated (pumped) protons:Another observation is that the genome-scale network and its derived reduced models allow higher maximal growth rates than the ColiCore model contains only reaction (ColiCore) was protected when reducing ColiGS, however, to allow maximal growth, the second reaction had also to be kept in ColiPrunedComp. In fact, integration of reaction .Clearly, the second reaction  will leareaction  translocreaction  in the CColiCore and ColiPrunedComp. For the case of ColiCore, the stoichiometric coefficients of the precursor metabolites  in the BSR had to be calculated manually from the known requirements of monomers  in the genome-scale BSR. Accordingly, Orth et al. wrote [Since most of the subunits of the cellular macromolecules, such as nucleic acids and amino acids, are not present in the core model, they could not be directly accounted for the biomass reaction. The metabolites in the core model that those macromolecular subunits are synthesized from are included instead. These are precursor metabolites. For example, the amino acid L-alanine is synthesized from pyruvate and L-glutamate, so both of these metabolites are consumed in the biomass reaction.”These remaining discrepancies can be attributed to different stoichiometric coefficients in the biomass synthesis reaction (BSR) of l. wrote : “Since ColiCore and ColiPrunedComp to identify and understand possible sources of different stoichiometries.Hence, molecules such as amino acids contained in the genome-scale BSR must be translated into a stoichiometric demand for compounds present in the reduced model. Making this translation manually in a genome-scale model is an error-prone and tedious task and an automated approach as ours supports this step and provides a rigorous approach to obtain a BSR in the compressed network that is consistent with the BSR of the full model. We directly compared the BSRs of ColiCore and of the ColiPrunedComp model , it is one advantage of our algorithm that these condensed material balances are automatically calculated and still visible in the reduced model. Note that the (cumulative) amount of periplasmatic protons (H_p) consumed in the condensed BSR of ColiPrunedComp is related to antiport uptake of trace elements.One major difference is that the BSR of ColiCore uses glyceraldehyde-3-phosphate (G3P) as a precursor (− 0.129) whereas ColiPrunedComp uses instead dihydroxyacetone-phosphate with a similar amount (−0.141). Since both metabolites can be converted into each other by a triose-isomerase reaction, both metabolites can in fact be used as precursors. A similar relationship exists for Ribose-5-phosphate (R5P) and Ribulose-5-phosphate (Ru5P). Ru5P occurs only in the BSR of ColiPrunedComp but, due to a simple isomerase reaction between both metabolites, could also be integrated in the value of R5P which is consumed in both BSRs.Further differences in the BSRs may arise by non-unique ways of representing precursor stoichiometries due to different reference points. For example, ColiCore seems to slightly underestimate the demand for most precursors and, to a larger extent, for energy (ATP). On the other hand, the core model consumes a significantly larger amount of NADPH and NADH which, in the final balance and biomass yield, could partially compensate the lower demand for some precursors. As mentioned above, would we add the high efficiency oxidase reaction  would be slightly higher than in the ColiPrunedComp model (0.9288 h−1). We emphasize that we do not claim that the BSR of ColiPrunedComp is necessarily “better” or more realistic than the BSR of the ColiCore model in [ColiCore model which may have led to discrepancies with the condensed BSR calculated herein. Nonetheless, the condensed BSR obtained with the NetworkReducer algorithm is consistent with the full model and allows for quantitative comparisons. Our algorithm thus facilitates the unbiased and reproducible calculation of condensed BSR stoichiometries in reduced network models from their genome-scale representation.Despite those explainable differences, the BSR of reaction  in the Cmodel in . It is pColiPrunedComp we exemplarily perfomed flux variability analyses for three different growth scenarios and compared the results with the original genome-scale model . Such a strongly reduced model may be useful to study basic principles and stoichiometries of, for example, coupled synthesis of biomass and biofuels . The gesee e.g.  (in the see e.g. ) served μmax is the maximal growth rate for a photon uptake of 100 mmol/gDW/h), andrmaxEthanol is the maximal ethanol production rate for a photon uptake of 100 mmol/gDW/h).Since the goal was to extract a network module that represents the Calvin cycle and enables maximal phototrophic growth as well as maximal production of ethanol we protected all reactions of the Calvin Cycle, the pathway to ethanol, biomass and ethanol excretion, and light uptake  is much lower than in the NetworkReducer, a new algorithm for automated reduction of large-scale metabolic network models to obtain meaningful small- or medium-scale models, typically representing the central metabolism or certain modules of interest. The algorithm consists of (i) a pruning step followed by (ii) network compression. Network pruning removes elements of the network that are dispensible for a user-defined set of protected properties and parts. Our algorithm accepts various criteria for specifying protected features. In particular, inequalities as in eqs.  if these are not protected. Network compression works loss-free, that is none of the feasible phenotypes and functions is lost, however, the resulting network is generally not a proper subnetwork of the full system and a mapping of flux distributions (and reactions) between the compressed and the full network can be cumbersome. It will depend on the application whether network compression is applied to the pruned network or not. If, for example, elementary modes are to be calculated in a network, loss-free compression algorithms are commonly used in a preprocessing step , 17. In Whereas network compression delivers always a unique result, the outcome of the network pruning step can be unique or non-unique, depending on network structure, input parameters, and protected functions and parts. Although reactions are removed in the order of their flux range , reactions with identical flux ranges may exist  from which then one is chosen randomly.E. coli case study demonstrated the applicability and potential of our approach. We reduced the genome-scale reconstruction iAF1260 of Feist et al. [E. coli core model. The reactions and metabolites to be maintained were taken from the core model proposed by Orth et al. [iAF1260 serving as a basis. With the protected phenotype that the maximal growth rates of iAF1260 under aerobic and anaerobic conditions must be achievable also in the condensed model, we used our algorithm to reduce the iAF1260 model to its core and compared it with the model of Orth et al. We found a generally good agreement between the manually and the automatically derived model but also some discrepancies. Essentially, two reactions of the iAF1260 not contained in the Orth model were retained by NetworkReducer to ensure that the maximal growth rates can be achieved. Furthermore, the stoichiometries in the condensed biomass synthesis reactions (BSRs) showed some differences. With our algorithm we can ensure that the condensed BSR fully reflects the stoichiometries of the BSR of the original network thus leading also to the same maximal growth rates and biomass yields. The E. coli case study demonstrated the value of our approach for obtaining a fast , unbiased, and exact network reduction.The t et al.  to an E.E. coli study as a typical application scenario for our method, namely to reduce a genome-scale network to its core  thereby protecting important properties such as  biomass or/and product yields. In the general case, a prerequisit is the careful delineation of the central metabolism (to be protected) in the genome-scale network which, however, should be possible for many organisms from prior biological knowledge. Many other reduction problems can be defined as well by using appropriate criteria for protected functions and parts. For example, instead of (or in addition to) the central metabolism, certain modules of a large-scale model  might be maintained in a high resolution while the rest is condensed. The presented case study of extracting a subnetwork of the cyanobacterial metabolism that comprises the Calvin cycle and allows for biomass and biofuel (ethanol) synthesis demonstrated that such an application is also supported by our algorithm. Such extracted subnetworks are also useful for the construction of kinetic models of specific parts of metabolism, while preserving consistency with a genome-scale reconstruction.We consider the NetworkReducer would be to compress the full network of an organism to just one single overall reaction consuming external metabolites  and synthesizing biomass with maximal yield. To simulate this maximal reduction, we again specified maximal aerobic biomass synthesis in E. coli as desired phenotype (ATP maintenance demand was not considered) and protected (only) the biomass export reaction. As a result, a “network” with only one overall reaction was maintained which exclusively converts external substrates and nutrients to external products The stoichiometry of this fully condensed BSR with one degree of freedom (ColiPrunedComp_DOF1) can be found in the An extreme application of NetworkReducer represents a valuable tool for stoichiometric and constraint-based modeling of metabolic networks.Although only genome-scale models can provide a complete view on the full functionality of a metabolic network there are several reasons why reduction of large-scale models can be useful or even necessary. First, computationally extensive analyses, such as full enumeration of elementary modes for metabolic pathway analysis, may only be tractable in smaller models. Methods of metabolic flux analysis seeking to calculate internal metabolic fluxes based on measurements of extracellular fluxes or/and on data from isotopic tracer experiments are able to resolve metabolic fluxes for smaller (core) networks only. Smaller models are also useful for didactic or educational purposes  and, in


Lactococcus lactis, subject to perturbations and brief periods of starvation. Supplementing existing methodologies, we show that it is possible to acquire a detailed understanding of the control properties of a corresponding metabolic pathway model that is directly based on experimental observations. In particular, we delineate the role of enzymatic regulation to maintain metabolic stability and metabolic recovery after periods of starvation. It is shown that the feedforward activation of the pyruvate kinase by fructose-1,6-bisphosphate qualitatively alters the bifurcation structure of the corresponding pathway model, indicating a crucial role of enzymatic regulation to prevent metabolic collapse for low external concentrations of glucose. We argue that similar probabilistic methodologies will help our understanding of dynamic properties of small-, medium- and large-scale metabolic networks models.Metabolic pathways are complex dynamic systems whose response to perturbations and environmental challenges are governed by multiple interdependencies between enzyme properties, reactions rates, and substrate levels. Understanding the dynamics arising from such a network can be greatly enhanced by the construction of a computational model that embodies the properties of the respective system. Such models aim to incorporate mechanistic details of cellular interactions to mimic the temporal behavior of the biochemical reaction system and usually require substantial knowledge of kinetic parameters to allow meaningful conclusions. Several approaches have been suggested to overcome the severe data requirements of kinetic modeling, including the use of approximative kinetics and Monte-Carlo sampling of reaction parameters. In this work, we employ a probabilistic approach to study the response of a complex metabolic system, the central metabolism of the lactic acid bacterium  Lactococcus lactisin-silico representation of the pathway is obtained. Despite considerable efforts, however, the construction of such models is still hampered by the extensive data requirements necessary to parametrize each enzymatic step. Several approaches have been suggested to alleviate this problem, including the use of approximative kinetics Lactic acid bacteria (LAB) are industrially important microorganisms used in the fermentation of milk, meat, and certain vegetables Lactococcus lactis. In particular, we seek to understand how allosteric regulation, together with its associated feedback and feedforward loops, influence the control exerted by the various enzymatic steps. Making only minimal assumptions about rate equations and kinetic parameters, and data from direct experimentation, we show that it is possible to study and elucidate the control properties of a metabolic pathway. In a second step, we investigate the dynamics of a corresponding kinetic pathway model in periods of starvation and show that allosteric control and regulatory interactions are crucial to maintaining metabolic viability in times of nutrient scarcity. Our probabilistic approach directly builds upon measured properties, such as the concentrations of metabolic intermediates and flux distributions, rather than enzyme-kinetic parameters, to constrain the possible dynamics of a metabolic pathway. We demonstrate that (i) the control coefficients of biochemical network models show intelligible patterns and trends that are accessible without detailed knowledge of enzyme-kinetic parameters; (ii) the regulatory structure of a biochemical network models has profound effects on the possible dynamics that are largely independent of specific kinetic parameters; and (iii) more specifically, that the topology of the regulation network is instrumental to ensure the stability of an observed state and to enable the patwhay to survive periods of starvation. We expect that our methodology will be of high utility to elucidate and understand the dynamic and regulatory properties that enable large-scale metabolic networks to function reliably in uncertain environments.Building upon these methods, we aim to elucidate and understand the regulatory properties of the central metabolism of the lactic acid bacterium Lactococcus lactis, defined here as the carbon and energy metabolism of this organism that generates most of its free-energy and C3 carbon precursors during fermentative growth. Drawing upon earlier kinetic models L. lactis was selected. A graphical overview is shown in The starting point of our analysis is a stoichiometric representation of the central metabolism of L. lactis central metabolism. Fructose 1,6-bisphosphate (FBP) activates the formation of pyruvate (PYR) by the pyruvate kinase (PYK), activates the conversion from PYR to LAC by the lactate dehydrogenase (LDH), and inhibits the phosphotransferase system (PTS). A potentially important regulator is the concentration of free phosphate. In our model, the total pool of phosphate is constant, therefore the concentration of free inorganic phosphate (Pi) is an (inverse) measure of the amount of the glycolytic intermediates plus ATP. Further reactions that are under regulatory control include the pyruvate dehydrogenase (PDH), as well as the alcohol dehydrogenases (ADH). A complete list of all regulatory interactions is summarized in Beyond the reaction stoichiometries, our model incorporates the currently known regulatory features found in flux control coefficientsTo quantify the extent to which a system property, such as a specific flux or metabolite concentration, is influenced by a specific enzymatic step, we make use of the concepts of Metabolic Control Analysis (MCA). The control coefficient The resulting distribution of flux control coefficients allows us to assess, qualitative and fairly independent of the precise values of the enzyme kinetic parameters, the potential effects of perturbations in enzyme levels on the system flux at the metabolic state. Most importantly, the distributions of the control coefficients were not arbitrarily. Rather, the results shown in L. lactisWe emphasize that the probabilistic distributions shown in las operon, were shown to have no significant control on the glycolytic flux in exponentially growing cells E. coliL. lactis do seem to be consistent with the bulk of the respective distribution.Using a series of mutants with altered GAPDH activity, Solem et al. (2003) As a rather counter-intuitive finding, the distribution of control coefficients indicates that for most sets of parameters the PTS would exert a negative control on flux through the pathway. This finding is in contrast to our expectation that an increase in PTS activity results in higher glucose uptake, hence an increased flux through glycolysis. These results emphasize that the control coefficients are indeed systemic properties of the pathway and may exhibit non-intuitive patterns, depending on the specific metabolic phenotype and details of the pathway stoichiometry and regulation. To verify that the non-intuitive distribution of the influence of the glucose transport upon the glycolytic flux is indeed a true feature of the pathway model, we varied the maximal velocity  the inhibition of PYK by inorganic phosphate, (ii) the activation of PYK by FBP and (iii) the inhibition of PTS by FBP. We showed that in cases of non-recovery the zero-flux metabolic state is an attractor for the system. In the presence of regulation the ability of the system to escape metabolic death is, in the overwhelming number of cases, mirrored by the absence of such attractor.In this sense, we argue that our approach has led to increased understanding of principles of metabolic regulation in typical, given no further knowledge about specific constraints the system is subject to – a tremendously useful information when interpreting experimentally observed data. In this respect, some of the probabilistic distributions are in line with what we expect given the topology of the network, while other properties are counter-intuitive and therefore point the direction for further investigation. Our approach is particularly suited to investigate the qualitative effects that result from changes in pathway topology, in particular from the presence or absence of regulatory interactions. Our computational approach is straightforward to implement and numerically efficient even for large systems. We therefore expect it to be of high utility also in other studies of metabolic, gene-expression and signal transduction systems.In summary, sampling unknown kinetic parameters for a kinetic model of a metabolic pathway, such that all sampled parameters give rise to the same metabolic state, can lead to fundamental insights into the control properties of the underlying system. In particular, the emergent control profile exhibits a structure that helps us to draw conclusions about the possible behavior of the system. The probabilistic control profile represents what dynamics we should expect as Our approach consists of a series of well-defined steps and is based upon related strategies that utilize Monte-Carlo sampling in the study of metabolic networks The probabilistic approach used within this work has been described previously The control coefficients are only evaluated for stable metabolic states, characterized by an invertible Jacobian with all real parts of the eigenvalues below zero. The information required to evaluate the control coefficients therefore consists of: (i) The stoichiometry of the system, as encoded by Our probabilistic evaluation of the system is then based on the fact that the metabolic state is often directly experimentally accessible, whereas information about kinetic parameters, and hence the elasticities, is generally lacking. We therefore evaluate the possible values of the unscaled elasticities by drawing random instances of parameters and evaluating the equations for the control coefficients. In particular, we proceed along the following steps: First, each reaction is associated with a kinetic reaction equation. We adopt general Michaelis-Menten kinetics of the form The number of unknown reaction parameters typically equals the number of associated substrates, products and modifiers  was added and samples were taken at regular time intervals. 400 Bacterial dry weight was measured as described previously Fluxes for lactate, acetate, formate, pyruvate and ethanol were calculated using their fermentation broth concentration, dilution rate Click here for additional data file.Text S2A pdf document providing additional information about computational methods and results.(PDF)Click here for additional data file.File S1A zip file providing all code used in the analysis.(ZIP)Click here for additional data file.


Biotechnology and Bioengineering Published by Wiley Peiodicals, Inc.This paper investigates the scaling‐up of cyanobacterial biomass cultivation and biohydrogen production from laboratory to industrial scale. Two main aspects are investigated and presented, which to the best of our knowledge have never been addressed, namely the construction of an accurate dynamic model to simulate cyanobacterial photo‐heterotrophic growth and biohydrogen production and the prediction of the maximum biomass and hydrogen production in different scales of photobioreactors. To achieve the current goals, experimental data obtained from a laboratory experimental setup are fitted by a dynamic model. Based on the current model, two key original findings are made in this work. First, it is found that selecting low‐chlorophyll mutants is an efficient way to increase both biomass concentration and hydrogen production particularly in a large scale photobioreactor. Second, the current work proposes that the width of industrial scale photobioreactors should not exceed 0.20 m for biomass cultivation and 0.05 m for biohydrogen production, as severe light attenuation can be induced in the reactor beyond this threshold. Biotechnol. Bioeng. 2015;112: 2429–2438. © 2015 The Authors.  Spirulina and Chlorella have been consumed as a food supplement in Mexico since antiquity, and are currently being cultivated for the commercialization of nutrient products in China, the United States and Thailand  greatly restricts the application of microalgae in both biofuels and biomass production  was supplied to enhance biomass growth rate, recent work found that green algae such as Nannochloropsis sp. can only peak at a density of 2.48 g L−1 in a 1000 L flat plate PBR with a width of 0.10 m, and 1.20 g L−1 in a 500 L flat plate PBR with a width of 0.17 m  h−1 from green alga Chlamydomonas reinhardtii, and 2.33 mL L−1 h−1 for cyanobacterium Cyanothece sp. in a 1 L flat plate PBR with a width of 0.025 m  sufficiency. Because the main focus of the current study is on the effects of light intensity and reactor configuration, temperature in the current experimental research is fixed at 35°C and its effects on cyanobacterial growth and decay rates are not considered. The detailed model is shown in Equations (1–3), and the parameters in the model are listed in Table cτ is the light absorption coefficient by cyanobacteria. max,aμ and d,aμ are the maximum specific growth rate and decay rate, respectively. I is the local light intensity and I0 is the incident light intensity. X is biomass concentration. sk is a light saturation parameter for cell growth, and ik is a photoinhibition parameter for cell growth.A previous study  and temporal variations as they constitute a dynamic model. To eliminate the spatial variation, the Trapezoidal rule is used to replace Equation (3) by Equation (4) in  are the same as those in Table h¯(I), given in Equation (5h), and represents the effect of light intensity on hydrogen production.μmax,h and μd,h are the maximum specific photo‐heterotrophic growth and decay rate, respectively. q is the normalized nitrogen quota. kq denotes the normalized minimum nitrogen quota. N, C, H2, and O2 are the concentration of nitrate, glycerol, hydrogen, and oxygen, respectively. KN and KC are the half‐velocity constant of nitrate and glycerol, respectively. Yq/X, YN/X, YC/X, YO/X. YH/X, YC, YOd are the yields of nutrients and products as indicated by the respective subscripts of the symbols used. ks,H2 and ki,H2 are the light saturation and photoinhibition terms, respectively, for hydrogen production.In this model, parameters in Equation (5g) have been estimated in previous work , the oxygen generation rate is assumed to be a function of nitrate concentration instead of nitrogen quota. This is because the cyanobacterial nitrate uptake process requires a high amount of ATP which has to be synthesized through the photosynthesis pathway where molecular oxygen is generated , the orthogonal collocation method is selected to discretize the current model. The implementation for the optimization problems shown in this work is done in Pyomo, a Python‐based optimization environment. Specifically, Pyomo , as shown in Figure In the current research, the laboratory scale photobioreactor is a 1 L flat‐plate photobioreactor with a width of 0.025 m  with respect to the normalized change of the parameters (x). A positive sensitivity value indicates that an increase in x results in an increase in y, while a negative sensitivity value indicates that increasing x will lead to a decrease in y.y is the model output and x is any parameter in the overall process model.Sensitivity analysis is widely used in this work to explore the variability of model outputs (process substrates and products) with respect to changes in model inputs (parameters in dynamic models)  even if biomass concentration is low (0.5 g L−1). Figure Light attenuation in a PBR is mainly caused by bubble scattering and cell absorption , the distributions of the cyanobacterial growth rate and the hydrogen production rate in the reactor are relatively uniform , both the cell growth rate and the hydrogen production rate are higher than those at low biomass concentration in the major part of the reactor, since more cells are exposed to illumination. However, because of the increased light attenuation , both rates are significantly improved in the front part of the reactor. This is due to the fact that local illumination intensity in the front part of the reactor is not much affected by light attenuation as it is proximity to the light source. As biomass growth and hydrogen production rates depend on the biomass concentration , both rates increase with the increasing biomass concentration. The major volume of the reactor, however, is subject to the severe photo‐limiting environment, and both rates are much lower than those at the low biomass concentration , the photo‐autotrophic growth culture is mainly selected for biomass cultivation. Therefore, in the current study, for biomass cultivation the photo‐autotrophic growth model will be selected and for hydrogen production the photo‐heterotrophic growth model will be chosen.Dunaliella tertiolecta have been isolated recently  is proportional to the mass fraction of chlorophyll in cells, its value will also be reduced in a low‐chlorophyll mutant.σ is the cross‐section of PSU unit, m2 J−1; v is the equivalent turnover time of PSU, s−1; K is the ratio of the protein damage constant to the protein recovery constant, s−1.Previous research has demonstrated that parameters in the Aiba model have their specific biological meaning  can enhance cell growth rate, which accelerates the consumption of nitrogen quota. As a result, cell decay due to the lack of nitrogen source will be enhanced and the hydrogen production rate will be reduced. Therefore, a laboratory scale PBR might not show the potential enhancements possible at industrial scale, that is, the potential benefits might be simply overlooked as there is usually no scale‐up assessment carried out when collecting laboratory data. This fact is also consistent with the conclusion from sensitivity analysis that identifying the optimal operating conditions is more important for a small‐scale process.To explore further the effects of PBR configuration on biomass cultivation and hydrogen production, the current work calculates the maximum biomass concentration and average hydrogen production rate in different configurations of PBRs and compares them in Table For biomass cultivation, it is found that the reactor width should not exceed 0.2 m, as the maximum biomass concentration is severely reduced . With regards to incident light intensity, using a low intensity on two exposure surfaces is a better strategy to enhance biomass concentration and save lighting costs. For hydrogen production, very similar observations are made. However in this case the width should not be greater than 0.05 m  as the metabolic pathway of hydrogen production is more energy demanding and a uniform light distribution is vital.This contribution presents the detailed modelling of cyanobacterial photo‐heterotrophic growth and hydrogen production. To the best of our knowledge, it is the first time a dynamic model is presented, which is capable of simulating all phases of this bioprocess, and also includes the effects of limiting nutrient concentration, light intensity, and light attenuation.Based on a sensitivity analysis, it is shown that identifying the optimal operating conditions is more effective than developing mutants for increasing hydrogen production in a laboratory scale reactor.Cell absorption has been determined to be the primary limiting factor for light attenuation in the present laboratory scale PBR. It is found that cultivating a low‐chlorophyll mutant is an efficient way to enhance both biomass and hydrogen productions in a large‐scale PBR, although this effect might not be observed at laboratory scale. Finally, for the design of pilot‐scale PBRs, the present research calculates the maximum biomass concentration and the average hydrogen productivity in different configurations of PBRs. It is concluded that using lower incident light intensity but double exposure surfaces is a better strategy for the simultaneous production of biomass and biohydrogen.D. Zhang gratefully acknowledges the support from his family. P. Dechatiwongse is supported by a scholarship from the Royal Thai Government, Thailand. The Solar Hydrogen Project was funded by the UK Engineering and Physical Sciences Research Council (EPSRC), project reference EP/F00270X/1. E. A. del Rio‐Chanona is funded by CONACyT scholarship No. 522530 from the Secretariat of Public Education and the Mexican government.


In this paper a new model of growing and dividing protocells is described, whose main features are (i) a lipid container that grows according to the composition of the molecular milieu (ii) a set of “genetic memory molecules” (GMMs) that undergo catalytic reactions in the internal aqueous phase and (iii) a set of stochastic kinetic equations for the GMMs. The mass exchange between the external environment and the internal phase is described by simulating a semipermeable membrane and a flow driven by the differences in chemical potentials, thereby avoiding to resort to sometimes misleading simplifications, e.g., that of a flow reactor. Under simple assumptions, it is shown that synchronization takes place between the rate of replication of the GMMs and that of the container, provided that the set of reactions hosts a so-called RAF  set whose influence on synchronization is hereafter discussed. It is also shown that a slight modification of the basic model that takes into account a rate-limiting term, makes possible the growth of novelties, allowing in such a way suitable evolution: so the model represents an effective basis for understanding the main abstract properties of populations of protocells. Protocells are cell-like structures that are simpler than present-day biological cells, but that are nonetheless able (i) to grow by some form of rudimentary metabolism, (ii) to reproduce giving rise to new protocells that are similar to their parents and (iii) to undergo evolution.While viable protocells do not yet exist, these structures are supposed to have played a key role in the self-organizing processes leading to the emergence of life; moreover their study could be important in order to create new “protolife” forms which are able to adapt and evolve . This eni.e., the “protogenetic material”) and the fission rate, evolution could in principle take place, so it would be appropriate to speak of a true protocell . The entire set of number of copies of the different species of the system is denoted by X = .The model describes a system in which simplified chemical species, cleavage, the cutting of a species made of more than one brick into two shorter species  and (ii) condensation, the concatenation of two species in a longer polymer . Reactions can occur only if catalyzed by reaction-specific catalysts, so no spontaneous reactions are allowed (by assuming a sufficiently high activation energy for each reaction). Condensation requires an intermediate step with the creation of a temporary complex between one of the substrates and the catalyst. Finally, the presence of backward reactions is also neglected, by assuming a sufficiently high Gibbs energy ∆G for each reaction . Thus, the reaction scheme can be summarized as follows:Cleavage: AB + C → A + B + CCondensation: (whole reaction: A + B + C → AB + C)○Complex formation: A + C → A C○Complex dissociation: A:C → A + C○Final condensation: A:C + B → AB + Cwhere A and B are two substrates involved in a specific reaction, C is the specific catalyst for that reaction and A:C represents the transient complex. The kinetic equations can be obtained by applying the law of mass action to this reaction scheme, as detailed in Only two kinds of reactions are allowed in the system, namely: (i) X and, in particular, each species i has a certain (fixed) probability ip of being the catalyst for a reaction chosen at random . Following Kauffman , catalyssion see ). In thesion see .The dynamics of the system is stochastic and simulated by means of an extension of the Gillespie algorithm ,38, descAppendix AThe dynamic behavior of catalytic reaction networks has been classically investigated in the case of a continuous stirred-tank reactor (CSTR) ,43,44,45i.e., those species that are shorter than an arbitrary length permL. Conversely, species longer that permL remain entrapped inside or outside the protocell. Another key modeling choice is that the concentration of the permeable molecules is assumed to be homogeneous inside and outside the protocell, by hypothesizing infinitely fast diffusion, both in the bulk phases and across the membrane . Then the equation for the growth rate of the container takes the form: rV is the internal volume of the protocell (where reactions occur) and [ix] is the concentration of catalysts in the internal aqueous phase; the kinetic coefficients ik are zero for all those species that do not contribute to the container growth. The kinetics of lipid formation are first-order with respect to the concentration of catalyst, because an infinite supply of lipid precursors is considered available inside the protocell; any lipids produced inside the protocell are assumed to go instantaneously to the membrane and not occupy the internal volume.Let C be a measure of the mass of the container, Protocells can grow and divide: during these processes their form and shape can change . HoweverrV is equal to: This hypothesis allows one to determine the relationship between C and the volume, so that Equation (1) provides a rule to determine the volume growth rate. Under the assumptions made, one can show see  that theAs discussed in Since the volume of the daughter protocell is approximately Different researchers have suggested several interesting models ,50,51,52A nice way of identifying the sets of chemical species able to catalyze their own growth is that of using a digraph representation  “comple where ciThis structure is therefore a possible component of a dynamic engine able to grow and reproduce ,29,30. HA RAF is the union of all the reactions allowing the complete self-reproduction of the involved chemical species, so it may be composed of several separate subparts each one able to separately self-replicate: if these subparts cannot be further decomposed they are called irreducible RAFs (irrRAFs) . IrrRAFsi.e., RAF sets, or strongly connected components, i.e., SCCs. Indeed, both depend upon the probability p that a molecule chosen at random catalyzes a reaction chosen at random: if this probability is very low, neither are observed, while, if it is high, the system is full of both. Apart from these trivial regimes, there is an interesting region of intermediate values. It has been observed  and [Miint] are the concentrations of the chemical i outside and inside the protocell, respectively.However, as has already been proposed in In this case, irrRAFs having growth rates equal to that of the already present ones but starting from very low concentrations have the possibility of increasing their presence and reach the already present irrRAFs a. MoreovWe believe that the model presented here could provide a convincing picture, at an abstract level, of the main features of the relevant processes involved in protocell growth and division. The model can be improved in different ways, some of which will be summarized below, but it can also be used in its present version to address some important issues in protocell research.First of all, let us recall that a population of units of evolution is “any population of entities with the properties of multiplication (one entity can give rise to many), variation , and heredity (like begets like)” . The proi.e., those that cannot be generated by the catalysts that are included in the “chemistry”, and that may come from outside or from rare spontaneous reactions) and make them grow—if the growth limiting terms are taken into account as it has been proposed in It is interesting to observe that the results shown above prove that not only protocells can be different, but that they may also host new types of molecules  possible answers to the question concerning the necessity of compartments: (a) the smallness of the vesicle; or (b) a possible active role of the membrane. The first one has already been discussed above: small vesicles can have an internal composition that is very different, not only from that of other protocells (thus ensuring heterogeneity), but also from that of the bulk, thus allowing different reaction pathways to dominate their internal environments.As far as alternative (b) is concerned, it is indeed highly plausible that the lipid membrane creates a local environment close to its boundaries that is markedly different from the bulk and that these surface effects modify the chemistry, by favoring some reactions and inhibiting others. In this case the membrane would itself act like a kind of catalyst, and would create a local environment different from the bulk. This would happen on both sides, but here the advantage of a closed vesicle is apparent: the molecules generated inside it will be trapped (if non permeable) in a small volume, so their concentrations will increase, while those that are generated on the outer side will freely diffuse in the bulk, without significantly affecting the external concentrations (at least until there are not very many protocells). It has also been shown that some superconcentration phenomena can appear in these cases . The actFinally, note that the presence of high protein concentrations in small vesicles are also experimentally reported, as for example in ; these dAs far as model improvements are concerned, there are of course many important directions. Indeed, we think that the picture that has been outlined above represents a rich class of models and opens up an interesting agenda for further research.A major topic concerns the robustness of our analysis  in different protocell architectures, like the Los Alamos Bug or the GARD models. Previous works on synchronization with different equations for the replicators makes us confident that the results can actually be robust, but this has of course to be proven.The appearance of novelties represents a major research topic: it would be important to better determine under which conditions the novelties are actually likely to survive and spread.p. Other improvements  involve considerations of backward reactions and the introduction of energy constraints.The model of the reactions could also be significantly improved, e.g. by considering a structure-dependent catalytic activity, instead of using a uniform probability of catalysis Let us recall, from the above discussion, that there are at least two different  explanations of the importance of closed containers: heterogeneity due to smallness, and an active role of the membrane. Both should be explored with appropriate versions of the model in order to understand their features.Other improvements are of course also possible. The model presented here can be the basis for a set of explorations of different alternatives, and it can be useful to cast basic questions about protocells in a precise form, amenable to analysis and simulation.


Such features are directly tailored to the more common experiment that performs only relative quantitation and compares fluxes between two conditions. We call our extension rKFP. Moreover, we examine the effects of common missing data and common modeling assumptions on (r)KFP, and provide practical suggestions. We also investigate the selection of measuring times for (r)KFP and provide a simple recipe. We then apply rKFP to 13C-labeled glucose time series data collected from cells under normal and glucose-deprived conditions, estimating the relative flux changes of glycolysis and its branching pathways. We identify an adaptive response in which de novo serine biosynthesis is compromised to maintain the glycolytic flux backbone. Together, these results greatly expand the capabilities of KFP and are suitable for broad biological applications.Fluxes are the central trait of metabolism and Kinetic Flux Profiling (KFP) is an effective method of measuring them. To generalize its applicability, we present an extension of the method that estimates the relative changes of fluxes using only relative quantitation of  Metabolism underlies all biological processes, and its quantitative study is crucial for our understanding. The central trait of metabolism, metabolic fluxes, cannot be directly measured and are estimated usually through modeling. Existing modeling methods, however, are limited by poorly-characterized parameters, crude precision, or labor-intensiveness. Motivated by these limitations, and recognizing a most common goal in the field of comparing the fluxes between two conditions, we develop an extension of an existing method that takes in time-series relative-quantitation data of isotope-labeled metabolites (a kind of data that modern metabolomic technologies readily generate), and outputs the relative changes of fluxes in the metabolic networks of interest. We also carefully examine some issues on model construction and experimental design, and improve the reliability and strength of the method. We apply our method to data collected from cells in normal and glucose-deprived conditions, demonstrate the efficacy of the method and arrive at new biological insight. PLOS Computational Biology Methods article.This is a In recent years there has been renewed interest in metabolism resulting from discoveries of its connections to gene regulation Among the isotope-based methods, Kinetic Flux Profiling (KFP) The basic idea of KFP can be illustrated using a toy metabolic network. Consider a system of only one metabolite tate so  . KFP worThe two terms ques see . Its soland geometrically corresponds to a family of curves parameterized by  and  .why KFP should work in this case. First, it is easy to see from Eq. 2 that parameter scale and rate. To highlight this, we define a rate parameter, identifiable when applying KFP to the system in With some measurements of en when  . Measureth  and  . The disApplying KFP to systems of arbitrary size and network topology and with multiple influxes is less straightforward and requires care absolute quantitation of metabolites, meaning that their absolute concentrations have to be measured, while many experimental techniques such as mass spectrometry can only perform relative quantitation readily, meaning that the measurement output is scaled from the absolute concentration by a metabolite-specific unknown constant; going from relative quantitation to absolute quantitation typically requires performing relative quantitation on some reference samples whose absolute concentrations are known, which can often be a challenge due to the increased effort of both additional experiments and procurement of reference samples. Second, often it is the relative changes of fluxes  between two conditions that are of interest or biological relevance  and the absolute quantitation measurements (concentrations) for the two conditions:where an upper-case letter denotes concentration and lower-case signal, more natural in this situation: although relative quantitation leaves us oblivious to the scale, we can still normalize the measurements to uncover the rate.The above two equations highlight a simple but important fact: Defining the relative changes of pool size Since tifiable , so is .To summarize the mechanics of rKFP for the system, one sets up the following two equations:which form a model that is parameterized by For larger networks consisting of single-substrate reactions arranged in linear pathways and branch points, rKFP proceeds in a similar way: equations like Eq. 7 are constructed for each metabolite in the network, and relative quantitation measurements of the metabolites allow for estimating the relative changes of all the independent fluxes with precision. However, for metabolic networks involving reactions of multiple substrates, especially cycles .Formally, one can plug some metabolites  use a reduced model where the network components corresponding to the missing data are removed; (2) use a full model where all components are kept and the part of the model corresponding to missing data represents additional degrees of freedom unconstrained by data; (3) use the full model but incorporate prior information for the part of model uncovered by data; (4) spend additional effort to collect all data and use the full model. We observe that a common practice in applying KFP is to choose the first option and use reduced models when there is missing data e.g., . We ackni.e., how well one a priori knows the missing piece. Hence it has to be judged on a case-by-case basis and cannot be discussed generally. We therefore exclude option (3) in our subsequent analysis, and only note that in the limit of a correct tight prior the case converges to option (4) of completing the data, and in the limit of a loose prior the case converges to option (2) of effectively having no prior information.Consider the following example. missing metabolite, and the corresponding procedure of constructing reduced models metabolite removal. We identify and name three additional common scenarios of missing data with their associated reduction procedures: first, missing pathway, where a branching pathway has poor data coverage with most metabolites unmeasured, associated with pathway removal, where the branching pathway is removed from the model; second, undistinguished metabolites, where the individual identity of a set of metabolites in a measurement cannot be resolved, associated with lumping, where the undistinguished metabolites are lumped into a single pool; third, unknown reversibility, where the extent of reversibility of a reaction is unknown, associated with assuming irreversibility, where potentially reversible reactions are modeled as irreversible for simplicity. In the remainder of this section, we describe in details the effects of metabolite removal on both KFP and rKFP, for this case is the simplest and hence most illustrative, and also for this case turns out to be important (see below); after that we briefly describe the results on pathway removal and lumping, leaving the details to the supplementary text; results on assuming irreversibility are discussed in the next section.We call this scenario of missing data in underestimateBack to vs. the green error bars). These observations suggest the following three summary statistics:bias, defined as cost, the cost of fitting using the reduced model.error ratio, defined as a priori to have small pool sizes, one should use full models in KFP.These statistics summarize the effects and pitfalls of missing data: error ratio quantifies their adverse effects on parameter estimation , and bias and cost quantify the harm of using reduced models. We next examine how metabolite removal affects rKFP . We haveelasticity regimes flux controlmore robust to metabolite removal than KFP. However, we also note in To summarize, we have demonstrated above the effects of missing metabolites on (r)KFP and the pitfalls of removing them; we suggest that unless one has good prior knowledge about the missing pool size or its relative change between two conditions that ensures a small bias, full models should be used. The approach we use for the demonstration is an intuitive and computational one, and in supplementary flux-force relationship: Biochemical reactions often operate close to equilibrium This suggests another potential issue in setting up models for KFP or rKFP: ignoring the reversible fluxes when the reaction is close to equilibrium, as is commonly done, might introduce bias. To check this, we again use a toy system  and, simvice versa. Second, if   in KFP , if the We naturally wonder how likely the change of unlike the case of metabolite removal, the bias increases slowly as the relative pool size changes of different metabolites diverge . We therefore conclude rKFP should be robust to assuming irreversibility and reduced models can be used.In other words, the change in We last note that, like the case of pathway removal discussed in the supplementary text, using the full model in this case and incorporating In addition to the issues on setting up models as discussed in the previous two sections, we have also investigated the experimental design issue of selecting measuring times for a metabolic pathway in (r)KFP. We list below the main conclusions, and leave the derivation details to the supplementary text.First, we note that the problem can be formulated as a classical experimental design one sticness .We choose to adopt an alternative approach for which there is a physical intuition: since the dynamics of the metabolites in a pathway are linear combinations of exponential functions , and in We show that for the first metabolite in a pathway, if a late time has been measured so that its (relative) scale is estimated, the optimal measuring time would be around We also show by using a similar reasoning that for the second metabolite in a pathway the optimal measuring time is around We last note that a typical metabolic network exhibits strong separation of concentration scales. For the example of glycolysis, one source reports that the most abundant metabolite (glucose) is about 35 times more than the second most abundant one and the full range of variation spans over three orders of magnitude In this last section, we apply rKFP to experimental data collected on glycolysis and its two main branching pathways  from cells in normal (5 mM glucose) and glucose-deprived (0.5 mM glucose) media conditions, and estimate the relative changes in the fluxes of the three pathways.We set up three computational models for rKFP, corresponding to three different choices of treating missing data as discussed in earlier sections, and the estimation results of all three models are shown in e.g., The observations support our recommended choice. The shifted green histograms relative to the blue suggest that metabolite removal introduces significant bias, likely because the pool sizes of the missing metabolites change differently from the other metabolites. The flattened red histograms relative to the blue suggest that keeping in the model the missing pathways with no data leaves the estimation greatly underconstrained; on the other hand, their similar averages suggest that the bias introduced by pathway removal is small in this case, likely because the missing pathways have much lower fluxes than the main glycolysis pathway (see the supplementary text) which is consistent with some previous studies  construct the Jacobian of the model, Generating posterior distribution: assuming Gaussian-distributed measurement noise, the measurement of sensitivity analysis or delta method, and is computationally cheap but less accurate; the second one is also known as ensemble methodNote that the last two points constitute the two standard ways of estimating parameter uncertainties: the first one also goes by the name of Experimental procedures of cell culture, metabolite extraction, mass spectrometry, liquid chromatography and data processing follow those in Text S1A file containing three supplementary figures, a derivation of the solution for KFP applied to a linear metabolic pathway, a discussion on applying (r)KFP to metabolic cycles, the description of an analytical approach to studying the effects of removing metabolites and pathways, and effects of pathway removal in KFP and rKFP, and some detailed results on the effects of missing data and selecting measuring times.(PDF)Click here for additional data file.Dataset S113C-labeled relative-quantitation data collected from cells in normal and glucose-deprived media used for the analysis.(CSV)Click here for additional data file.