Saccharomyces cerevisiae is the most relevant yeast species conducting the alcoholic fermentation that takes place during winemaking. Although the physiology of this model organism has been extensively studied, systematic quantitative physiology studies of this yeast under winemaking conditions are still scarce, thus limiting the understanding of fermentative metabolism of wine yeast strains and the systematic description, modelling and prediction of fermentation processes. In this study, we implemented and validated the use of chemostat cultures as a tool to simulate different stages of a standard wine fermentation, thereby allowing to implement metabolic flux analyses describing the sequence of metabolic states of S. cerevisae along the wine fermentation.S. cerevisiae EC1118 were performed using a synthetic must and strict anaerobic conditions. The simulated stages corresponded to the onset of the exponential growth phase, late exponential growth phase and cells just entering stationary phase, at dilution rates of 0.27, 0.04, 0.007 h−1, respectively. Notably, measured substrate uptake and product formation rates at each steady state condition were generally within the range of corresponding conversion rates estimated during the different batch fermentation stages.Chemostat cultures mimicking the different stages of standard wine fermentations of Moreover, chemostat data were further used for metabolic flux analysis, where biomass composition data for each condition was considered in the stoichiometric model. Metabolic flux distributions were coherent with previous analyses based on batch cultivations data and the pseudo-steady state assumption.S. cerevisiae corresponding to the different growth stages of a typical batch wine fermentation, thereby showing the potential of this experimental approach to systematically study the effect of environmental relevant factors such as temperature, sugar concentration, C/N ratio or (micro) oxygenation on the fermentative metabolism of wine yeast strains.Steady state conditions obtained in chemostat cultures reflect the environmental conditions and physiological states of  During the last decades concern on climate change has increased and it is nowadays well recognised as one of the most important environmental problems faced on Earth. Climate change is already having significant impacts on the world’s physicochemical, biological and human systems. Agriculture is one of the main sectors affected by this phenomenon -3, with Besides, although many of the wine properties and production methods are grape-related, there are numerous features that are dependent on the yeast strain used. These include fermentation performance (e.g. tolerance to stress and the ability to efficiently utilise carbon and nitrogen sources), downstream wine processing , modulation of alcohol content, levels of both desirable (e.g. resveratrol) and undesirable (e.g. ethyl carbamate) chemical compounds, as well as the modulation of the organoleptic properties resulting from the hundreds of metabolites and flavour compounds that are either produced or liberated from precursors in the grape juice during wine fermentation, including esters, higher alcohols, volatile acids, phenols and thiols .For these reasons, wine producers have launched different initiatives over the last years that aim on one side, to understand and mitigate the impacts of global warming on winemaking and, on the other, to improve their knowledge base on yeast physiology under winemaking conditions for the optimisation of production processes.S. cerevisiae. Nevertheless, the application of such tools to the understanding of yeast physiology under winemaking conditions is still limited [In the past recent years, systems biology tools have been extensively used to study the physiology of the model yeast  limited -14.Wine fermentations are operated in batch mode. Due to the intrinsic nature of this process, yeast metabolism undergoes a series of adaptive changes in response to the initial stressing conditions as well as to the continuous environmental variations that take place. Specifically, yeasts have to adapt to the characteristics of the grape must, that is, high osmolarity due to the high sugar concentration, low pH and presence of sulphites. Also, heat is generated and ethanol is accumulated to high concentrations (ca. 12 ~ 15%) as a result of the fermentative activity of yeast. Moreover, limited availability of assimilable nitrogen sources and oxygen leads to rapid nutrient deficiency after a first growth phase. Notably, most of the ethanol is produced during the later fermentation stages, i.e. at near zero growth rates and stationary phase.Systematic profiling of yeast metabolism under winemaking conditions is required in order to understand and predict the effect of environmental changes and distinct genetic backgrounds on wine fermentations, as well as to perform a rational optimisation of fermentation processes. Among the strategies for systems-level analysis of cell metabolism, Metabolic Flux Analysis (MFA) has been extensively applied in many physiological studies of yeast, for example to quantify the impact of growth conditions or genetic modifications on metabolic pathway activities -24.13C isotopic labelling. Moreover, characterisation of cellular metabolism using isotopic tracers such as 13C-labelled substrates is much more convenient in chemically defined media with one or two carbon sources at a relatively low concentration. Nevertheless, laboratory scale fermentations mimicking wine fermentations may be more complicated due to the higher complexity associated with the medium , as well as co-consumption and secretion of substrates and metabolites. To date, several experimental approaches have been proposed for MFA studies of yeast growing under wine making conditions. Varela and co-workers [Attaining metabolic steady states is crucial to investigate metabolic pathways using MFA methodologies, including MFA based on -workers  reported-workers ,26, alloAlternatively, chemostat cultures have been extensively used for quantitative physiology analyses of yeast cells. Nevertheless, their application to the study of wine fermentations has been so far very limited. For instance, this approach has been used to investigate the effect of growth parameters such as temperature  or dissoIn this study, we propose the utilization of classic chemostat cultures to obtain metabolic steady states mimicking different physiological states found in different time points (stages) along a classical wine-making fermentation process, operated in batch mode. This has allowed for the quantitative physiological analysis of each fermentation phase, as exemplified by the MFA performed with the obtained datasets.2 concentration in the exhaust gas was virtually zero. Fermentation evolution shows that glucose was the preferred carbon source since it was consumed and depleted quicker than fructose, following the behaviour already described by other authors [2 production, it evolved exponentially during the initial stage of the fermentation, followed by a period when started to slow down; this period was coincident with a substantial reduction of the nitrogen content of the medium. Biomass grew exponentially during the early stages of the process (8–17 h); after that first phase, growth started to slow down as a result of a substantial reduction of the nitrogen content (both in the form of NH4+ and as free α-amino acids (FAN)) of the medium, as shown in Figure Initially, the fermentation profile for strain EC1118 was studied in a standard batch fermentation at 28°C under strict anaerobic conditions with a synthetic must mimicking a typical natural must , pH 3.5, and sulphites) , as show authors ,20,30,312 and ethanol production slow down, max = 0.29 h−1 ± 0.01 was calculated as an average from four different batch replicates, while for the transition period –or late exponential growth phase- (20–35 h), a μtrans = 0.04 h−1 ± 0.01 was obtained. At the end of the transition phase the CO2 production rate (CER) peaked, gradually declining thereafter along the following fermentation stage (stationary phase).Next step was defining and choosing the phases from the batch process to be reproduced as a series of steady states in continuous cultures. As a first approach, the specific growth rates observed during the batch process were the criteria used for the selection of the two first stages to be simulated, corresponding to growing cells. In particular, Phase I corresponded to mid-exponential growth phase and Phase II to late exponential growth phase. Figure −1, along with the decline in CO2 production and accumulation of ethanol. An average μ of 0.007 h−1 was estimated for this phase . This value is slightly lower to that obtained in similar studies [Phase III corresponded to the onset of the stationary phase. During this period (35–106 h) growth rate gradually declined from 0.04 to 0 h studies  and largWith the exception of proline, which is not assimilated in absence of oxygen , all theS. cerevisiae increase transcription levels of stress-response genes and induce expression of proteins involved in the response to oxidative stress. Such response results in increased ROS scavenging ability of the cells, which is essential for the maintenance of their fermentative capacity. Therefore, the observed kinetics of ROS accumulation and scavenging are consistent with a transient oxidative stress during the initial phases of the fermentation process. The increase in the number of cells characterized by lower intracellular levels of ROS in Phase III might reflect the generation of subpopulations that were better adapted to unfavourable growth conditions during long-lasting batch cultures, as suggested by previous studies [Cell viability, cell size and accumulation of reactive oxygen species (ROS) were monitored along the fermentation by flow cytometry. Consistent with previous studies ,38, ther studies .S. cerevisiae strains  in stages I and II had a diameter in the range of 10–15 μm, this population fraction progressively decreased to about 50% along stage III, with a concomitant increase of the cell population in the 7–9 μm (up to about 45%) and 4–6 μm (up to about 5%). This observation is consistent with previous studies showing that cell size is negatively correlated with cell growth rate . Specifi ~ 6 μm, ). This merevisiae. Moreoveerevisiae. Taken tD = 0.27 h−1 defined as an approximation to μmax, and D = 0.04 h−1.The two first phases described on the basis of growth rate were subsequently reproduced in continuous cultures carried out at steady state conditions at dilution rates 2 concentration and by measuring the concentration of the main metabolites  at 3, 4 and 5 residence times.In these cultures, steady states were verified by on-line monitoring of the off-gas COmax), where exponential evolutions were observed, while linear adjustments were used for the second phase, since rates were markedly lower than during the first stage and their evolution close to linear.Batch phases and corresponding continuous cultures stages were compared in terms of specific growth, consumption and production specific rates  meant working at conditions with no substrates limitations, since it is known that residual substrate concentration in chemostats is only a function of the dilution rate. In particular, it increases slowly with D at low values but very rapidly as D approaches μmax[Table nt rates . The reaches μmax,50.D (0.25 h−1) and 24% glucose as single carbon source yielded glucose consumption and glycerol production rates consistent with those measured in batch fermentation [Unfortunately, glucose and fructose consumption rates in stage I could not be accurately calculated. This was due to the fact that sugar concentration in both the feed tank and the bioreactor were both very high and close to each other, as sugar consumption is very low, reflecting very low cell numbers. As a result, error propagation of the glucose and fructose measures from two independent chemostat cultivations resulted in very high standard deviation values for the corresponding calculated specific consumption rates. Besides this experimental limitation, one significant divergence was found in the glycerol production rate in stage I, which was substantially higher than that in the exponential phase of the batch fermentation. Interestingly, chemostat cultures carried out under identical conditions except for a slightly lower entation .−1. Therefore, as a first approach, a continuous culture reproducing this phase was performed at a dilution rate D = 0.007 h−1 using the same feeding medium as for experiments at D = 0.04 h−1. Comparison between specific rates obtained at these conditions and the equivalent batch phase (III) corresponding from 35 – 100 h approximately, showed a good correspondence  with a mean specific growth rate μ = 0.007 h−1, starting at around 60 h of fermentation , about 90% of the C consumption corresponds to glucose, while at the lower dilution rates of 0.04 and 0.007 h−1 (stages II and III) this fraction is reduced to about 70% and 60%, respectively. As expected, most of the carbon was used for energy production using the ethanol fermentative pathway; the fraction of assimilated C source used for ethanol production increased from stage I to stages II and III, from about 60% to 90%, with a concomitant decrease in the carbon source to glycerol as the D was reduced (from about 30% to 10%). That is, flux ratio between the ethanol and glycerol pathways increases when shifting from stage I to later stages. Notably, this effect was clearly observed despite the relative amino acid composition of the feed medium was the same for all chemostat cultures, in contrast to batch cultures where amino acids are consumed sequentially. It is well known that the nitrogen source profile influences product  yields [Overall, the metabolic flux distributions  yields . Convers13C-MFA studies of S. cerevisiae under anaerobic conditions, i.e. most of carbon flux from glucose + fructose (75 ~ 95%) was channelled to glycolysis [The calculated glycolytic and oxidative PPP branch split flux was also in agreement with previous MFA and ycolysis ,20. SpecAs already described in several MFA studies ,17,20,52Our first series of results, obtained from experiments simulating the three phases of wine-growing fermentations under standard conditions suggest that steady states obtained in chemostat cultures at defined growth rates reflect the major traits of the yeast physiological state observed in the corresponding growth phase of the batch fermentation. The experimental data obtained from these cultures has been integrated into a metabolic model, allowing for the quantitative description of the metabolic state of cells (metabolic fingerprint) under each growth condition. Notably, this study has used a synthetic most medium incorporating both glucose and fructose as carbon sources, as well as potassium bisulphite to mimic cellar conditions, in contrast to previous metabolic studies based on conventional continuous and multistage continuous cultures, where glucose is often used as single carbon source, and no sulphites were added to the growth medium.−1), consequently recreating both the growth and stationary phases [13C isotopic labelling techniques should allow the refinement of the metabolic flux analyses. Importantly, beyond identifying and characterising strain- and environmental-dependent physiological differences, our approach seeks to correlate physiological responses with transcriptional and metabolic changes in the future. As a first proof-of-concept of our approach, we have recently used chemostat cultures to investigate the effect of sugar concentration and temperature on exponentially growing yeast in wine fermentations [Moreover, these results proved that it is possible to define different wine-growing fermentation phases through chemostat cultures and, consequently, they have been further used to characterise metabolic changes due to temperature and increased sugar content , providiy phases . Hence, ntations .The final aim is to integrate all experimental data in a framework metabolic model that can be effectively used to describe and predict a wine fermentation, as well as facilitating the rational design of reliable fermentation processes. The model could additionally be used as a tool for characterizing the metabolic behaviour of different wine yeast strains (metabolic fingerprint or phenotype), as well as for the selection of the most appropriate yeast strain as a function of the grape must composition or, in the optimal design and usage of enological additives.Saccharomyces cerevisiae EC1118  was used in this work. This strain is considered as a model organism in the field and has been used in a wide number of physiological studies related to wine fermentations.A commercial yeast strain, 4Cl; 29 mg L-aspartic acid; 80 mg L-glutamic acid; 52 mg L-serine; 333 mg L-glutamine; 23 mg L-histidine; 12 mg L-glycine; 13 mg L-tyrosine; 50 mg L-threonine; 245 mg L-arginine; 97 mg L-alanine; 14 mg L-cysteine; 29 mg L-valine; 21 mg L-methionine; 116 mg L-tryptophan; 25 mg L-phenylalanine; 22 mg L-isoleucine; 32 mg L-leucine; 11 mg L-lysine and 400 mg L-proline. All the amino acids required for the medium, with the exception of tyrosine, were added in a 50× solution prepared, sterilised by filtration, aliquoted, and then kept at −20°C until required. Glucose and fructose were autoclaved separately and added to the rest of medium. Concentration of glucose and fructose into the fresh medium was checked by HPLC in order to have accurate concentrations and taking possible alterations of the glucose-to-fructose ratio due to isomeration. The pH was adjusted to 3.5. Feeding media for continuous experiments had the same composition except that NH4Cl and the amino acids composition was adjusted to the required experiment. The same medium but with 60 g/L glucose and fructose and without anaerobic factors  was used for inocula growth.Culture medium was a modification of the MS300 medium . It contSaccharomyces strain were used to inoculate 100 mL of YPD medium. The culture was grown for 48 h at 28°C and 150 rpm in a Multitron II incubator . 10 mL of this culture were then used to inoculate 100 mL of inoculum medium and incubated aerobically overnight at 28°C and 150 rpm. This culture was used to inoculate the bioreactor to an optical density (OD600) of 0.1. Operation parameters in the reactor were temperature 28°C, pH 3.5, and 100 rpm stirring rate. No pH control was used during batch processes, while in the continuous culture it was automatically controlled using 2 M NaOH. Data acquisition and control of the different variables was done using an in-house control software. Prior to inoculation, culture medium was sparged with 0.3 L/min of N2 to establish anaerobic conditions. After inoculation, N2 flow was diverted to the head-space to minimise the stripping of ethanol. With the same purpose, off-gas condenser was kept at 4°C throughout the process. N2 flow throughout the cultivation process (0.3 L/min) was controlled using a mass flow controller , and norprene tubing was used to avoid oxygen diffusion.Feed medium was also sparged with N2 throughout the experiments to maintain anaerobic conditions.All experiments were performed in 2 L bench-top bioreactors  with a working volume of 1.5 L for batch experiments and 1 L for continuous processes. Four replicates were performed for the batch fermentation, whereas duplicate replicates were performed for each continuous cultivation condition. For inocula development, 0.1 mL cryostock of the When required, samples were taken from the reactor in pre-chilled tubes kept on ice during processing. For elemental and macromolecular biomass composition analyses and extracellular metabolite analysis, samples were centrifuged 10 min at 10,000 rpm and 4°C. Supernatants were then filtered through 0.45 μm filters and kept at −20°C until analysis, while biomass pellets were washed twice, lyophilised and kept at −80°C until analysis. Triplicate samples were taken for all analytical measurements.600). For cell dry weight, a known volume of culture broth was filtered through pre-weighted filters that were then washed with 2 volumes of distilled water and dried to constant weight at 105°C for 24 h.Cell biomass was monitored by measuring optical density at 600 nm (ODAn Ultimate 3000 HPLC system (Dionex Corp) with an IC Sep ICE-Coregel 87H3 column (Transgenomic Inc. USA) equipped with an IR detector was used for the analysis of glucose, fructose, glycerol and ethanol while succinic, lactic, acetic and malic acids were analysed using the same equipment but with an UV detector. 15 mM sulphuric acid was used as mobile phase. Two process temperatures were used: 70°C for the analysis of fructose, and 40°C for the analyses of the other metabolites.2 sensor . The off-gas was passed through 2 columns containing silica gel to remove the humidity before entering the sensor.Production of carbon dioxide was monitored on-line in the exhaust gas of the bioreactor using a BCP-COYAN was determined using 2 different commercial kits : K-NOPA which measures the PAN (primary amino acid nitrogen) and K-LARGE which measures the contribution from the side chain of L-arginine and free ammonium ions. Results from these kits were combined to determine the FAN.Amino acids content of culture and feeding media was determined using a modification of the AccQ Tag method . Derivatisation was carried out using the AccQ Fluor reagent (6-aminoquinolyl-N-hydroxysuccinimidyl carbamate) according to the method specifications; hydrogen peroxide was added to the reaction mixture. Once derivatised, amino acids were separated and analysed using a Waters Nova-Pak C18  in a HPLC gradient system (Waters 600) equipped with an UV detector (Waters 2487). Detection was performed at 254 nm and α-amino-N-butyric acid (AABA) was used as internal standard.6 cells/mL. Cell suspensions were stained according to the following procedures. Propidium iodide, PI  was used to stain dead cells and dihydroethidium, DHE  was used for ROS accumulation. Cells treated with 20% ethanol for 30 min were used as positively DHE stained cells. PI staining: 1 μL PI stock solution in PBS was added to 1 mL cell suspension just prior to the analysis and was incubated for 5 min in the dark. DHE staining: 0.2 mL DHE stock solution was added to 1 mL cell suspension and incubated at 30 °C for 30 min. Stained cells were then centrifuged and resuspended in 1 mL of PBS. After the staining step, cell samples were sonicated at low power prior to the analyses  and further diluted in PBS to a concentration within the 50–500 cells/μL. 5000 cellular events were analysed for each sample . Fluorescence data for PI or DHE stained cells was collected in the channel FL2 (680 nm).Analyses were performed with a Guava EasyCite Mini cytometer (Millipore) with a 488-nm excitation argon-ion laser. Cell size calibration was performed using the Flow Cytometry Calibration Kit (Molecular Probes-Life Technologies) following manufacturer’s instructions. Yeast cells were harvested, washed and resuspended in PBS to a final concentration of 10Elemental composition of the biomass was analysed using an elemental organic analyzer Thermo EA 1108  following the the conditions recommended by the supplier of the instrument .Biomass samples were first hydrolysed at 105°C for 24 h with 6 M HCl in vacuum sealed glass ampoules. After hydrolysis, samples were evaporated under vacuum, re-dissolved in 20 mM HCl, and filtered. Amino acid content of an aliquot of the filtrate is then determined using the AccQ Tag method . Derivatisation was carried out using the AccQ Fluor reagent (6-aminoquinolyl-N-hydroxysuccinimidyl carbamate) according to the method specifications. Once derivatised, amino acids were separated and analysed using a Waters Nova-Pak C18  in a HPLC gradient system (Waters 600) provided with an UV detector (Waters 2487). Detection was performed at 254 nm and α-amino-N-butyric acid (AABA) was used as internal standard.Total protein content of the biomass was determined using the Lowry method as described in . BiomassTotal carbohydrate content of the biomass was determined using the phenol-sulphuric method, as described in . BiomassThe glycogen content was estimated according to the method described by , using 2The method described by  was used−1 h−1/mol gDCW−1 h−1) of a specific amino acid was ≥ 1, the biosynthetic pathway for that amino acid was included. Conversely, when this ratio was < 1, it was assumed that there was an excess of such compound in the cell and, therefore, the corresponding degradation pathway was included. The total cell content of each amino acid residue was estimated from the molar fraction of each amino acid in the total cell protein.The stoichiometric model used for metabolic flux analysis .Click here for file


Arabidopsis thaliana under a set of eight different light and temperature conditions. In a previous study, the gene expression data have already been integrated in a genome-scale metabolic network to predict pathways, termed modulators and sustainers, which are differentially regulated with respect to a biochemically meaningful data-driven null model. Here, we present a follow-up analysis which bridges the gap between flux- and metabolite-centric methods. One of our main findings demonstrates that under certain environmental conditions, the levels of metabolites acting as substrates in modulators or sustainers show significantly lower temporal variations with respect to the remaining measured metabolites. This observation is discussed within the context of a systems-view of plasticity and robustness of metabolite contents and pathway fluxes. Our study paves the way for investigating the existence of similar principles in other species for which both genome-scale networks and high-throughput metabolomics data of high quality are becoming increasingly available.Constraint-based approaches have been used for integrating data in large-scale metabolic networks to obtain insights into metabolism of various organisms. Due to the underlying steady-state assumption, these approaches are usually not suited for making predictions about metabolite levels. Here, we ask whether we can make inferences about the variability of metabolite levels from a constraint-based analysis based on the integration of transcriptomics data. To this end, we analyze time-resolved transcriptomics and metabolomics data from  Organisms are usually exposed to changing environments and balance these perturbations by altering their metabolic state. Gaining a deeper understanding of metabolic adjustment to varying external conditions is important for the development of advanced engineering strategies for microorganisms as well as for higher plants. One tool which is particularly suited for investigating these processes is genome-scale metabolic models. These large-scale representations of the underlying metabolic networks enable the integration of experimental data and application of constrain-based mathematical approaches to estimate flux rates through the chemical reactions of the network under different environmental scenarios. However, for most of these approaches the assumption of a steady-state  is indispensable and therefore precludes the prediction of metabolite concentrations. Here, we present a data-driven observation that relates results from a flux-centric constraint-based approach that is based on transcriptomics data to metabolite levels from the same experiments. Our observations suggest that constraint-based modeling approaches in combination with high-throughput data can be used to infer regulatory principles about the plasticity and robustness of metabolic behavior from the stoichiometry of the underlying reactions alone. We considered the distribution of CVs across all metabolites, across products only, and across substrates only, in the following six comparisons of groups: modulators vs. all metabolites, sustainers vs. all metabolites, differentially behaving functions  vs. all metabolites, modulators vs. non-modulators, sustainers vs. non-sustainers, and differentially behaving functions vs. non-differentially behaving functions. As shown in We calculated the variability of each considered metabolite over the time course following the perturbation by calculating the coefficient of variation (CV) as described in the i.e., high-light . Clearly, one has to keep in mind that our analysis is based on a generic compartmentalized network reconstruction. The connectivity values might vary in different tissues, due to the presence or absence of certain pathways. Nevertheless, we belief that the well-curated model we use in our study serves a good starting point for the analysis.Next, we investigated whether the group of substrates in differential metabolic functions shows distinct characteristics with respect to the network topology. For the analysis we neglected evidently ubiquitous cofactors, such as: To further investigate which attributes are typical for differentially behaving pathways, we next investigated the number of  substrates of the pathways. Cofactors of the considered reactions were neglected from the analysis see . CountinArabidopsis's metabolic acclimation to varying light and/or temperature conditions which was based on transcriptomics data i) for specific environmental conditions, differential metabolic functions have substrates, which on average show a lower CV than other metabolite groups tested, (ii) when considering the network topology, these substrates are on average more connected than the remaining metabolites and (iii) differential metabolic pathways have on average fewer substrates than the other metabolic functions investigated.In this study, we extended our earlier analysis of e.g., e.g., i.e., non-recovery. Therefore, we believe that the observed substrate robustness is an inducible genetic mechanism, both depending on the metabolic network structure and the specific environmental condition. Determining the range of conditions that permit the observed robust behavior would be an interesting undertaking for future experimental testing.Closer inspection of the environmental conditions that exhibit low substrate variability leads to the following hypothesis: substrate robustness can be observed under stressful environmental conditions. Yet, we do not observe substrate robustness, or in genetic terms canalization, under conditions which are not perceived as stress by the plant  rather than averaging laws. Here we observe that fewer input variables with smaller fluctuations, do not necessarily result in smaller fluctuations of the output  but in robust differential behavior. Furthermore, our findings also showed that for all metabolic functions for which substrate measurements are available, the CVs of their substrates are significantly lower than the CVs of the respective flux capacity profile. This further highlights the particularities of regulation, variability, and robustness of metabolic pathways.Our third finding concerning the smaller number of substrates in differentially behaving metabolic functions has wide implications on the interplay between plasticity and robustness in metabolism. Most notably, our findings differ from claims made with respect to evolution of robustness and cellular stochasticity of gene expression. In a recent study, the author proposed that the degree to which varying cellular components combine to determine robust phenotypes may be predictive of the amount of their inherent variability. The basis for this claim is the observation that averaging over multiple independent inputs is a general way to reduce variability of molecular phenotypes S. cerevisaeRobustness of certain pathway fluxes and specific metabolite concentrations have long been documented. The concept of network rigidity has initially been proposed in In our view, the high stability of a pool of primary metabolites, invariant to environmental heterogeneity, fulfills two major functions. On the one hand, it efficiently sustains a set of “core” reaction rates which are deemed essential for the plant's objective function across a wide range of different stresses. On the other hand, the observed substrate stability enables a tight conditional control on a set of metabolic functions to act as modulators or sustainers in response to specific stresses only.Finally, the fact that the robust metabolites may well be the most biologically relevant for metabolic regulation is an important point since it is at odds with the manner in which the majority of the metabolomics community assesses their data. This fact additionally highlights the potential difficulties and challenges in interpreting data from a single level of the cellular hierarchy and thus provides further grounds for integrated models such as the one we present here.Taken together, our findings show that the integration of large-scale modeling with high-throughput data can be used to infer regulatory principles from the stoichiometry of the underlying reactions alone. Furthermore, we presented an approach that bridges the gap between flux-centric and metabolite centric view of large-scale data. Therefore, our study paves the way for investigating the existence of similar principles relating plasticity of metabolic profiles and robustness of metabolic behavior across other species for which both genome-scale networks and high-throughput (time-resolved) metabolomics data of high quality are becoming increasingly available.Arabidopsis thaliana to changing light and/or temperature conditions Arabidopsis thaliana Columbia-0 plants were grown in soil under short-day-conditions for 4 weeks and then transferred to long-day-conditions for another 2 weeks. Subsequently, they were exposed to the following conditions: http://www.ebi.ac.uk/arrayexpress) under Arabidopsis light and temperature response ArrayExpress accession: E-MTAB-375 and they can be downloaded using the following link: http://www.mpimp-golm.mpg.de/Supplementary-Materials-for-Publications/Caldana-et-al_Filtered-Affymetrix-Gene-Expression-Data.zip. Metabolomics data are provided on the following website http://www.mpimp-golm.mpg.de/Supplementary-Materials-for-Publications/Caldana-et-al_Normalized-metabolic-data.zip.The investigated data set captures the time-resolved response of From the total of 82 measured metabolites, 65 can be mapped onto the model. It must be noted that the metabolomics data are not compartment-specific and 61 out of 65 mapped metabolites appear in more than one compartment in the model. Due to a lack of this information, for those non-unique metabolites we assigned the same profile to each compartment-specific compound in the model. The mapping dictionary is given in the i.e., 627 out of 1363 reactions can be constrained by transcriptomics data The mapping of the transcriptomics data from our previous study has a network coverage of 46%, e.g., the reaction stoichiometry, reversibility, and maximum uptake rates) and a putative biological objective of the organism under consideration . A central element of the approach is the assumption of a steady-state which implies that each internal metabolite e.g., amino acids, fatty acids, nucleotides, sugars) contribute to the objective function. For a detailed review of FBA and other related constraint-based optimization approaches see FBA is a constraint-based approach for predicting steady-state fluxes in a metabolic network independent of enzyme kinetics and metabolite concentrations The analysis presented here extends results recently presented in To determine the temporal variation of the metabolite profiles we used the coefficient of variation (CV) which is defined as the ratio of the standard deviation i.e., differential regulation of pathways involved in the response. To ensure that the categorization of differential metabolic functions is robust to the removal of this time-interval we repeated the analysis of our previous study. Reassuringly, we find our results, i.e., the classification as a sustainer or modulator of a given metabolic state, to be robust to the removal of up to six time points from the beginning of the time series.We applied this statistic to the mapped metabolite profiles for each condition separately. While doing so, we neglected the data for the first hour (first six time points) after the stress application during which the system experiences the strongest effect, Supporting Information S1List of tested metabolites. Given is the number of metabolites in the respective group for each condition on which the Wilcoxon-test is based.(XLS)Click here for additional data file.Supporting Information S2Additional figures. Figure S1: Schematic representation of the eight environmental conditions. Plants were grown under ambient conditions and then transferred into one of the eight indicted conditions. Figure S2: Condition-specific distribution of the coefficients of variation (CVs) for all mapped metabolite profiles. Given are the distributions of CVs for all measured metabolites (green) and those that participate as substrates in the metabolic functions that were previously identified as sustainer or modulator (red) for all eight investigated conditions separately.(DOC)Click here for additional data file.Supporting Information S3Metabolites regarded as cofactors or constant and neglected from the analysis. Given is the Metabolite ID, the AraCyc/PMN ID, the KEGG ID, the metabolite name, and the formula.(XLS)Click here for additional data file.Supporting Information S4Metabolite dictionary. Given is the mapping of the metabolites between that data and the model. Some metabolites have two possible metabolites IDs in the model. Note that a metabolite ID is not unique and the same metabolite can participate in reactions in different compartments.(XLS)Click here for additional data file.


S. cerevisiae. The thermodynamic approach allows to model passive ion fluxes driven by the electrochemical potential differences, but also primary or secondary active transport processes driven by the inter- play of different ions  or by ATP consumption (ATPases). The model—confronted with experimental data—reproduces the experimentally observed potassium and proton fluxes induced by the external stimuli KCl and glucose. The estimated phenomenological constants combine kinetic parameters and transport coefficients. These are in good agreement with the biological understanding of the transporters thus providing a better understanding of the control exerted by the coupled fluxes. The model predicts the flux of additional ion species, like e.g. chloride, as a potential candidate for counterbalancing positive charges. Furthermore, the effect of a second KCl stimulus is simulated, predicting a reduced cellular response for cells that were first exposed to a high KCl stimulus compared to cells pretreated with a mild KCl stimulus. By describing the generalized forces that are responsible for a given flow, the model provides information and suggestions for new experiments. Furthermore, it can be extended to other systems such as e.g. Candida albicans, or selected plant cells.Cationic and heavy metal toxicity is involved in a substantial number of diseases in mammals and crop plants. Therefore, the understanding of tightly regulated transporter activities, as well as conceiving the interplay of regulatory mechanisms, is of substantial interest. A generalized thermodynamic description is developed for the complex interplay of the plasma membrane ion transporters, membrane potential and the consumption of energy for maintaining and restoring specific intracellular cation concentrations. This concept is applied to the homeostasis of cation concentrations in the yeast cells of  Metals, and particularly their positively charged ions (cations), are an integral part of our environment, and all living organisms are exposed to metals in their natural habitat. Even though significant efforts have already been made by experimental and theoretical analysis of the individual components of transport systems and individual transport-mechanisms, such efforts did not result in an integration of the highly connected and complex system. The development of kinetic networks might well contribute to the understanding and visualization of cation homeostasis. However, such kinetic systemic analysis would require more detailed biochemical information than is currently available. We circumvented this problem by using an entirely phenomenological approach of the theory of non-equilibrium thermodynamics. The methodology does not require the detailed understanding of structure, function or kinetic parameters of individual constituents of the system but produces some unique parameters related to thermodynamic couplings between different ion fluxes and ATP consumption. These estimated phenomenological constants combine the kinetic parameters and transport coefficients and control the coupling of fluxes. The model predictions are in good agreement with the biological understanding of the roles of the transporter proteins. Our modeling approach might contribute to the development of new diagnostic and therapeutic purposes with cation-homeostasis as key-target. System responses to cation induced stress play a pivotal role in a wide range of essential cellular processes. A major challenge for the cell is to maintain optimum cytoplasmic concentrations of cations even under rapidly changing external conditions and perturbations such as salt, osmotic, or alkaline pH stress. The alkali metals such as sodium, potassium (or lithium) are considered as vitally important co-factors for a variety of enzymatic reactions and for structural and functional roles in cell metabolism ,2. HowevSaccharomyces cerevisiae most of the proteins responsible for uptake and extrusion of sodium, potassium, protons and chloride across the cellular membrane have been identified , single-celled organisms like e.g. some algae and fungi must tolerate a wide range of sometimes rapidly changing environmental conditions such as osmotic pressures, pH, or salt concentrations in their natural habitats. Moreover, yeast cells accumulate potassium from relatively dilute solutions to sustain a cytosolic Klyanions ,12.Besides supporting a stable and balanced intracellular cation content, monovalent cation transport is also required for other physiological functions such as maintenance of the cell volume and internal pH, the membrane potential, protein synthesis, and enzyme activation –15. To eThe paper is organized as follows: We first introduce a general thermodynamic concept for the description and analysis of cellular cation fluxes and concentrations. Second, we assign specific parameters, which were obtained from experiments with starved yeast cells. We then use the experimental data for parameter estimation and present model simulations predictive for scenarios not used for parameterization.via the MIFE method . At time 600 s, glucose is added. Potassium and proton fluxes are measured with specific electrodes thod see .Our description of ion fluxes and their mutual dependencies is based on the concepts of Non-Equilibrium Thermodynamics (NET). Since decades various theories and mathematical descriptions of active and passive transport executed by transmembrane proteins have been developed. These approaches are as different as complex and have already been extensively published –22 to meWhen modeling the behavior of living cells, the selective description of individual channels/transporters carries the risk of overlooking other ion transport processes by transporters that are not yet characterized or known transporters that have additional functions (e.g. non-specific transport) or membrane leakage. Thus, understanding the system’s behavior requires the integrative investigation of all transport processes, in addition to exploring individual transporters. Many features change simultaneously and should be integrated into a global model in order to obtain a comprehensive picture of the underlying physical processes. This includes transient pH, enzyme activities, cytosolic buffer capacities, chemical reactions, and changes in membrane potential or concentrations of other important ions. However, due to the complexity of the problem and the sparseness of data, typical kinetic network models that describe every reaction and transport step in detail are not yet feasible.σ denotes the local entropy production density, T is the temperature, i, ηi is the electrochemical potential of component i, i, Ai is the affinity of reaction i, and nf and nr are the numbers of compounds and reactions, respectively.The concept of Non-Equilibrium Thermodynamics, deployed to derive individual transport expressions, provides also a theoretical background to correlate driving forces and the resulting fluxes in cellular systems in a formal manner independent of specific kinetic or statistical models. The relevant forces are the differences in the electrochemical potential of the cations and reaction affinities of biochemical reactions. Fluxes are the resulting fluxes of cations in or out of the cell and the rates of biochemical reactions, respectively. All these irreversible processes lead to a production of entropy. The entropy production for a cellular system can be characterized by the entropy production density ,30σ=J→QXj. The fluxes are in general non-linear functions of these forces. However, at equilibrium all forces and fluxes vanish. Only in vicinity to equilibrium we can express the fluxes as linear combinations of all forces, based on a Taylor expansion until first order terms as follows:The various flows and forces are not independent of each other. A temperature gradient could, for example, induce the diffusion flux of a chemical compound besides the heat flux. Due to the constant temperature in the considered experiments, we can disregard temperature gradients and heat flux in the following reasoning. We take generalized forces as Lij. The Lii are referred to as the "straight coefficients" since they relate the flow Ji to its conjugate driving force Xi, in the analogy with either Ohm‘s or Fick‘s laws. The "cross coefficients" Lij, with j ≠ i, reflect to which extent the flux of species i is affected by the non-conjugate forces, Xj, in the system. The phenomenological coefficients have to fulfill a number of conditions. Since in the absence of other forces, a single force induces a positive conjugate flux, it holds:The partial derivatives of the fluxes with respect to the forces are called phenomenological coefficients and will be denoted with The fact that the dissipation function is positive implies further thatelation” ,32, and In the following we specify the relevant forces and fluxes for ion transport and biochemical reactions in the considered experiments. In general, these phenomenological coefficients combine kinetic parameters and transport coefficients and are functions of the parameters of the system but are independent of the flows and forces. Once determined from experimental data they provide an informative basis on the control exerted by the coupled fluxes. Specifically interesting for the maintenance of the intracellular cation concentration is the thermodynamic coupling of the individual fluxes. This enables that a flux may occur without or even against its conjugate thermodynamic driving force, which may be a gradient of the electrochemical potential or reaction affinity.+, Na+, Cl-, denoted as grad ηH, grad ηK, grad ηNa, and grad ηCl, respectively, as well as the affinity AAr of the reactions converting ATP into ADP or reverse. The conjugated fluxes are the fluxes of protons, JH, potassium, JK, sodium, JNa, and chloride, JCl, as well as the conversion of ATP to ADP or back, JAr. This resulted in the following phenomenological equation system:For the cellular response of starved yeast cells to the addition of KCl and glucose we considered the forces resulting from the electrochemical gradients of protons, Kci being the ion concentrations and zi being their charge number, F is Faraday‘s constant and φ is the membrane potential.Next, we replaced the electrochemical potentials with the expressionηi refers to the derivative of ηi with respect to the spatial direction normal to the cell surface. We approximated it with the difference of ηi between cellular environment  and cytoplasm , i.e. Since we assume homogeneity of concentrations inside and outside of the cell, the gradient of Combined, these considerations resulted in the following equation system:φ = φi − φo.The fluxes are considered as outward directed, i.e. Surf is the cellular surface, (Vin) is the internal volume added up over all cells of the system, and (Vout) is the volume of the extracellular compartment.The resulting internal and external concentration changes of the ions were calculated as:We followed this general description of concentration changes with two exceptions accounting for the specific experimental conditions. First, we assumed that the internal pH is buffered and the internal proton concentration changes with the proton flux as follows:Bf is a function depending on the pH, but it can be approximated by a constant for a wide range of intracellular pH values. This modification is equivalent to the proton buffering function as introduced before S. cereviSurf and the inner volume, Vin were calculated from the detected optical density (1.2 · 107 cells per ml OD 1) applied to achieve a cell monolayer and by assuming a single cellular surface of 63,6 μm2 (based on a round cell with a diameter of 4.5 μm) and a volume of 50 fL according to [out was obtained directly from the experimental setup.The surface of all cells, rding to . The valLiAr  were initially set to 0. It was assumed that only those parameters directly or indirectly involved in primary active transport LiAr  and Lii  can change after glucose and that the Onsager relation holds.ATP was estimated to be between 0 and 2.5 mM ahead of the glucose addition. The available ATP after the glucose stimulus was supposed to reach 2.5 mM, according to previous observations by , and deshttp://www.copasi.org.The model implementation, time course simulation and parameter estimation were performed in COPASI . COPASI Lii were allowed to be positive only, the “cross coefficients" Lij were allowed to be either positive or negative. The options iteration limit 400, swarm size 40, standard deviation 1e−6, random number generator Mersenne Twister [To minimize the problem of being trapped in local minima, a Python script was implemented to run the particle swarm algorithm 1000 times with random initial parameter values as well as random upper and lower parameter bounds. For the estimation of the initial conditions experimentally verified concentration ranges were used (see Tables  Twister  and rand Twister .S1 Text(DOCX)Click here for additional data file.S1 DataS. cerevisiae.Fluxes have been measured over time after addition of 10μM, 100μM, 1mM, or 10mM KCl to cells of (XLSX)Click here for additional data file.


C4 plants, such as maize, concentrate carbon dioxide in a specialized compartment surrounding the veins of their leaves to improve the efficiency of carbon dioxide assimilation. Nonlinear relationships between carbon dioxide and oxygen levels and reaction rates are key to their physiology but cannot be handled with standard techniques of constraint-based metabolic modeling. We demonstrate that incorporating these relationships as constraints on reaction rates and solving the resulting nonlinear optimization problem yields realistic predictions of the response of C4 systems to environmental and biochemical perturbations. Using a new genome-scale reconstruction of maize metabolism, we build an 18000-reaction, nonlinearly constrained model describing mesophyll and bundle sheath cells in 15 segments of the developing maize leaf, interacting via metabolite exchange, and use RNA-seq and enzyme activity measurements to predict spatial variation in metabolic state by a novel method that optimizes correlation between fluxes and expression data. Though such correlations are known to be weak in general, we suggest that developmental gradients may be particularly suited to the inference of metabolic fluxes from expression data, and we demonstrate that our method predicts fluxes that achieve high correlation with the data, successfully capture the experimentally observed base-to-tip transition between carbon-importing tissue and carbon-exporting tissue, and include a nonzero growth rate, in contrast to prior results from similar methods in other systems. C4 planpiration . The agrpiration , the imppiration ), the sipiration , detailspiration –12 and tpiration , 14.2 levels, and the rates of CO2 assimilation by leaves have been widely applied to infer biochemical properties from macroscopic experiments and explore the responses of C4 plants under varying conditions.  More recently, detailed kinetic models have been used to explore the optimal allocation of resources to enzymes in an NADP-ME type C4 plant [Mathematical modeling is a proven approach to gaining insight into C4 photosynthesis and will play an important role in addressing these questions. High-level, nonlinear models of photosynthetic physiology  relatingC4 plant  and the C4 plant .v1, v2, … vN by optimizing a biologically relevant function of the rates subject to the requirement that the system reach an internal steady state,S is determined by the network structure [vc of carbon fixation by Rubisco and the rate vo of the Rubisco oxygenase reaction, which depends nonlinearly on the ratio of the local oxygen and carbon dioxide concentrations ,SR is the specificity of Rubisco for CO2 over O2. In the C4 case, the CO2 level in the bundle sheath compartment is itself a function of the rates of the reactions of the C4 carbon concentration system and the rate of diffusion of CO2 back to the mesophyll.Large-scale constraint-based metabolic models offer particular advantages for the investigation of connections between the C4 system and a plant’s metabolism more broadly  and for interpreting high-throughput experimental data from C4 systems. The standard approach for predicting reaction rates in such models, flux balance analysis (FBA), determines predicted reaction rates tructure . HoweverWith the addition of PO2 and PCO2 are known and fixed vo/vc accordingly. This approach is suitable for mature C4 leaves under many conditions (as well as photosynthetic microorganisms with carbon-concentrating mechanisms), where vo/vc is approximately zero, or mature C3 leaves, where vo/vc can often be readily predicted from environmental conditions. It cannot be applied, however, to some of the most interesting targets for simulation: developing tissue, mutants, and C3-C4 intermediate species, where PCO2 in the bundle sheath compartment is not necessarily high.While a number of prior constraint-based models of plant metabolism have described photosynthesis in some detail  most quickly will have a fitness advantage over others in a population. As constraint-based models and FBA have been extended to the realm of multicellular organisms, or to particular subsystems , a challenge for the metabolic modeling field broadly has been to identify appropriate objective functions for use in FBA. In this work, we are using a metabolic model to explore the metabolism of a developing leaf. What is an appropriate objective function for this complex biological subsystem? The photosynthetically mature part of a leaf is presumably organized to some degree to assimilate COWith that preface, in this paper we attempt to use the combined results of enzyme assay measurements and multiple RNA-seq experiments to to infer the metabolic state at points along a developing maize leaf . AlthougA novel genome-scale metabolic model was generated from version 4.0 of the CornCyc metabolic pathway database  and is pBoth the comprehensive and high-confidence models can simulate the production of all major maize biomass constituents  under either heterotrophic or photoautotrophic conditions and include chloroplast, mitochondrion, and peroxisome compartments, with key reactions of photosynthesis (including a detailed representation of the light reactions), photorespiration, the NADP-ME C4 cycle, and mitochondrial respiration localized appropriately. Gene associations for reactions present in more than one subcellular compartment have been refined based on the results of subcellular proteomics experiments and computational predictions (as collected by the Plant Proteomics Database ) to assiTwo alternative sets of biomass production reactions are incorporated in the model. One system (based closely on iRS1563 ) allows 2 diffusion and metabolite transport through the plasmodesmata, and restricting exchange reactions appropriately . A schematic of the two-cell model is shown in A model for interacting mesophyll and bundle sheath tissue in the leaf was created by combining two copies of the high-confidence model, with transport reactions to represent oxygen and COBoth single-cell versions of the model and the two-cell model, designated iEB5204, iEB2140, and iEB2140x2 respectively , are avhttp://github.com/ebogart/fluxtools).To solve nonlinear optimization problems incorporating the constraints discussed above, we developed a Python package which—given a model in SBML format, arbitrary nonlinear constraints, a  objective function, and all needed parameter values—infers the conventional FBA constraints of 2 assimilation with nonlinear kinetic constraints [Eqs , nts [Eqs , 6),  a lower cost than a solution in which Ri has mean flux 100 μmol m-2 s-1 but is anticorrelated. The penalty term α set to 1. We require sa = sb if reactions a and b are mesophyll and bundle sheath instances of the same reaction.Allowing the scale factors k and segment jEjk is the measured maximal activity of the enzyme at that segment and the sum on the right hand side includes all the reactions which represent enzyme k in the mesophyll, bundle sheath, and subcompartments of those cells if applicable.To constrain the overall scale of the fluxes and further improve accuracy, we incorporated available enzyme activity assay data from  for seveSolving the optimization problem yielded predictions for reaction rates and other variables . Upper a2 uptake, with most of the assimilated carbon incorporated into sucrose and exported to the phloem. Near the base of the leaf, sucrose is predicted to be imported from the phloem and used to drive a high rate of biomass production, with some concomitant net release of CO2 to the atmosphere by respiration.As shown in 14C-labeling results of Li et al. [2 to leaf 2 (center image) or leaf 3 . Li et al. [2uptake rate.)This transition between a carbon-exporting source region and a carbon-importing sink region is well known, and the predicted transition point between the two, approximately 6 cm above the base of the leaf, can be compared to the i et al.  in the si et al.  identifiAgreement might be improved under a different assumption about net sucrose import or export by leaf 3 .2 assimilation predicted in the outer, most mature leaf segments, 8–11 μmol m-2 s-1, is lower than that typically measured in more mature maize plants , but phIn addition to sucrose, glycine and glutathione are predicted to be exported from the source region through the phloem and reimported by the sink region, consistent with our expectations that nitrogen and sulfur reduction will occur preferentially in the photosynthesizing region . Note th2 and O2 levels in the bundle sheath. As expected, the model predicts that a C4 cycle will operate in the source region of the leaf, elevating the CO2 level in the bundle sheath. The CO2 level is also elevated in the source region; this is an immediate consequence of respiration in the bundle sheath and 2 conductance gs ; in faco et al. , gs is pIn the Calvin cycle, most reactions are predicted to be bundle-sheath specific, but the reductive phase is active in both cells, with approximately half the 3-phosphoglycerate produced in the bundle sheath transported to the mesophyll and returned as dihydroxyacetone phosphate ; this is2 only to have it released again by the decarboxylases  in the chloroplast at a higher rate than necessary to sustain the C4 cycle; the excess is converted again to pyruvate by pyruvate kinase in the cytoplasm, with the resulting ATP consumed by the model’s generic ATPase reaction. Finally, in the bundle sheath, a modest rate of PEPC activity is predicted, recapturing COoxylases . Furtherr > 0.92 for more than half of the reactions in the model with associated expression data.For most reactions, the correlation between the base-to-tip expression pattern and the base-to-tip trend in predicted flux is high. The cumulative histogram in Differences in expression levels between different reactions, however, correlate only weakly with the differences in fluxes between those reactions, as shown for segment 15 in s4), imposed for technical reasons.)In si of 2 assimilation.) The C4 system is predicted to operate, but no source-sink transition is apparent, and typical data-predicted flux correlations are poor. Imposing a realistic biomass composition restores the source-sink transition and somewhat improves correlation between data and fluxes (d fluxes . Fluxes 2 assimilation) constrained by the experimental data in the E-Flux method, and fluxes predicted in an FBA calculation which ignores the data entirely  Both data-integration methods lead to predictions very different from the unconstrained FBA calculation.The expression of a gene encoding a metabolic enzyme need not correlate with the rate of the reaction that enzyme catalyzes. The relationship between transcription and degradation of mRNA and control of flux is indirect, mediated by protein translation, folding, and degradation, complex formation, posttranslational modification, allosteric regulation, and substrate availability. Indeed, as reviewed by , experimFor example, RNA-seq and quantitative proteomic data obtained from maize leaves at the same developmental stage studied here, harvested simultaneously from plants grown together, showed Pearson correlation approximately 0.6 across the entire dataset, but some significantly lower values were found when correlations were restricted to genes of particular functional classes, and measured mRNA/protein ratios for individual genes varied up to 10-fold along the gradient . A subseBrassica napus accessions that the authors concluded the inference of central metabolic fluxes from transcriptomics is, in general, impossible.The most comprehensive study of the issue in plants so far  found soE. coli and Saccharomyces cerevisiae where experimentally measured intracellular and extracellular fluxes were available for comparison. None of the methods consistently outperformed parsimonious FBA simulations which completely ignored transcriptomic data.In this light, it is not surprising that methods for integrating transcriptomic data with metabolic models to predict reaction rates have met with limited success. Machado and Herrgård  reviewedNonetheless, we hypothesized that in the leaf developmental gradient system in particular, expression levels would correlate enough with fluxes to allow usable predictions to be made with a careful choice of objective function. Our justification for this hypothesis is twofold.First, the metabolic transition between the heterotrophic sink region at the base and the photoautotrophic source region at the tip is particularly dramatic, involving a large number of reactions which are effectively absent in one region but carry high fluxes in the other ; so longSecond, although the developing maize leaf is biologically more complex than microbial growth experiments, the relationship between expression levels and fluxes may be actually be closer in the leaf. Leaf development is a stereotyped, frequently repeated, relatively slow, one-way process, in which the precise sequence of events is subject to evolutionary optimization. Coordination of transcription with required fluxes will lead to efficient use of resources. In contrast, the test cases of  involve Consistent with this hypothesis, in the present work the use of transcriptomic data (and a limited number of enzyme activity measurements) allowed the correct prediction of a metabolic transition from the base of the leaf to the tip, which could not have been expected based on FBA calculations alone: without such data, all points along the gradient would be identical, and the biomass-production-maximizing solution would be the same at each. The predicted position of the source-sink transition is not perfectly accurate, and the quantitative accuracy of the model cannot be evaluated until the predicted reaction rates are compared to detailed experimental flux measurements, but the results are encouraging and suggest that inference of fluxes from expression data may be more feasible in the specialized context of developmental shifts in metabolism than it is in general.Potentially further supporting this idea, we note that methods that did not constrain or maximize the growth rate predicted zero growth rates in almost all the test cases studied by Machado and Herrgård . In the Zea mays, and the first such reconstruction developed solely from maize data sources, rather than as a direct or indirect adaptation of the Arabidopsis thaliana model AraGEM [Our model is the fourth published genome-scale metabolic reconstruction of the major crop plant l AraGEM .Direct reaction-to-reaction comparison of iEB5204 with C4GEM , iRS1563Our computational methods, discussed below, should allow the incorporation of realistic Rubisco kinetics into any of the prior genome-scale models of C4 plant metabolism. However, for the specific goal of integration with transcriptomics data from the leaf developmental gradient, we found it useful to develop the present model, which has several advantages:Gene associations The gene associations included in iEB5204 are those presented in CornCyc [Arabidopsis genes to their best maize BLAST hits and manually selecting annotations for remaining maize genes from among BLAST hits in other species.) The entire set of gene associations in the FBA model may be readily updated based on improvements in the E2P2 prediction algorithm. CornCyc , which a CornCyc , a homolHigh-confidence submodel In developing the fitting algorithm we found that, to obtain plausible metabolic state predictions, a conservative reconstruction was preferable to a comprehensive one. For example, early tests with the comprehensive version of the model suggested that the fitting algorithm often found low-cost solutions involving high fluxes through reactions which, on investigation, we determined were unlikely to be active in maize. Because of the model’s connection to the CornCyc database, it was straightforward to create a reduced, high-confidence version of the model by preferentially excluding reactions not included in any manually curated plant metabolic pathway, even if candidate associated genes had been identified computationally, leading to more realistic results.Reproducibility In an effort to improve the reusability of the model and encourage its application to other data sets, we have provided the full source code . They are slower, are more sensitive to choices of starting point and problem formulation, are not guaranteed to converge to an optimal point even if one exists, and, when they do converge to an optimum, cannot guarantee that it is globally optimal.The software package we present allows the rapid and effective development of metabolic models with nonlinear constraints despite these complications. All necessary derivatives of constraint functions are taken analytically, and Python code to evaluate them is automatically generated. A model in SBML format may be imported, nonlinear constraints added and removed, and the problem repeatedly solved to test various design choices, solver options, and initial points, all within an interactive session, with a minimum of initial investment of effort in programming.2 assimilation and the predictions of classical physiological models confirmed that the true, globally optimal CO2 assimilation rate was found successfully. For the data-fitting calculations, where the true optimal cost is not known, we cannot exclude the possibility that there exist other optimal solutions, qualitatively distinct from the flux distributions and quasi-optimal regions presented above, with equivalent or lower costs. In practice, we encountered occasional cases in which reaction or pathway fluxes were initially predicted to be zero even when associated with nonzero data, despite the existence of a superior alternative solution with nonzero predicted fluxes. A step to detect and correct these situations was incorporated into the fitting algorithm.In the present case, agreement between nonlinear FBA calculations that maximized CO2 level at the Rubisco active site, and thus the Rubisco oxygenation/carboxylation ratio, is not known a priori. A published genome-scale metabolic reconstruction of the model alga Chlamydomonas reinhardtii, for example, was identified by the authors as being deficient in describing algal metabolism under low CO2 conditions due to the fact that the Rubisco carboxylase and oxygenase fluxes were treated as independent and not (as we have done here) competitive [Many future applications for the software are possible. Our approach to Rubisco kinetics may easily be extended to other models of C4 metabolism or, more generally, to any FBA calculation in a photosynthetic organism where the COpetitive .Ensuring that rates of Rubisco oxygenation, Rubisco carboxylation, and PEPC carboxylation are consistent with our knowledge of their kinetics is a special case of the more general problem of integrating kinetic and constraint-based modeling. Diverse approaches to this issue have been extensively developed, including dynamic FBA , k-OptFoNonlinear constraints may also be of use in enforcing thermodynamic realizability of flux distributions, and relaxing requirements of linearity or convexity may stimulate the development of novel objective functions—either for data integration purposes, as here, or as alternatives to growth-rate maximization.Large-scale metabolic models of interacting cells of multiple types first appeared in 2010, with C4GEM  and a moIn the most direct antecedent of the present work, Grafahrend-Belau and coauthors developed a multiscale model of barley metabolism  which reThe whole-leaf model presented here occupies an intermediate position between prior C4 models, with single mesophyll and bundle sheath cells, and multi-organ whole-plant models such as . It repra priori qualitative differences in the metabolic capabilities of their components . In contrast in the work presented here, in order to allow the metabolic differences between any two adjacent points to be purely quantitative, the same metabolic network must be used for all points. This simplifies the process of model creation but implies that meaningful predictions of spatial variation depend entirely on the integration of  experimental data. The ability of the model to capture the experimentally observed shift from sink to source tissue along the developmental gradient based on RNA-seq and enzyme activity measurements shows that this may be done successfully with high-resolution -omics data and careful model construction.Other interacting cell models incorporate A local copy of CornCyc 4.0  was obtaAn overall biomass reaction was adapted from iRS1563  with minCore metabolic pathways were assigned appropriately to subcellular compartments  and the intracellular transport reactions necessary for their operation were added.The model was thoroughly tested for consistency and conservation violations, confirming that no species could be created without net mass input or destroyed without net mass output The base metabolic model iEB5204 is provided in SBML format as To produce the higher-confidence version of the reconstruction, iEB2140 , reactioA model for leaf tissue  was creavc and vo in mesophyll and bundle sheath chloroplasts were constrained to obey Michaelis-Menten kinetic laws with competitive inhibition,vo, max/vc, max = kO/(kC ⋅ SR) was imposed, from which kC and kO and the Rubisco specificity SR were set to values typical of C4 species: kC, 650 μmol mol-1; kO, 450 mmol mol-1; SR, 2590 [Rubisco carboxylase and oxygenase rates SR, 2590 .kC,p .vpmax and vc,max representing the total amount of Rubisco and PEPC available may be fixed to permit comparison to models parameterized in those terms or allowed to vary.The parameters L and LO, were constrained to obey the relationshipgs, O set to 0.047gs, where gs is the bundle sheath CO2 conductance [2 conductance measured by [-2 s-1. While gs undoubtedly varies along the developmental gradient, its deviation from this value  is likely greatest below the region of high suberin synthesis identified 4 cm from the leaf base [Rates of oxygen and carbon dioxide diffusion from the bundle sheath to the mesophyll, ductance . All simsured by  for maizeaf base ; as the 2 diffusion from the intercellular airspace to the mesophyll cells was neglected; ref. [-2 s-1 in maize under a variety of conditions, suggesting the mesophyll and intercellular CO2 levels would differ only slightly at the rates of CO2 assimilation and release dealt with here. Similarly, all intracellular compartments were taken to have equal CO2 concentrations.Resistance to COed; ref.  reported−5, or 10−4 in FVA calculations. To solve purely linear problems  the GNU Linear Programming Kit, version 4.47 [The nonlinear modeling package uses the libsbml python bindings to read SBML files  and an iion 4.47 , was calion 4.47 .Python code used to calculate the predictions of the models of von Caemmerer  for compTo obtain mesophyll- and bundle-sheath-specific expression levels at 15 points, we combined the non-tissue-type-specific data of Wang et al. , measureThe full list of reaction rates constrained by enzyme activity measurements from  is givenThe objective function  optimizeS1 FigTransport of nitrogen (upper panel) and sulfur (lower panel) through the phloem in the best-fitting solution. Dotted lines indicate minimum and maximum predicted values consistent with an objective function value no more than 0.1% worse than the optimum.(PDF)Click here for additional data file.S2 FigDashed and dotted lines indicate minimum and maximum predicted values consistent with an objective function value no more than 0.1% worse than the optimum.(PDF)Click here for additional data file.S3 FigDotted lines indicate minimum and maximum predicted values consistent with an objective function value no more than 0.1% worse than the optimum.(PDF)Click here for additional data file.S4 Figsi = 0 for all reactions i. (a) Sucrose and CO2 uptake rates (compare to In (PDF)Click here for additional data file.S5 FigFor explanation of each panel, see (PDF)Click here for additional data file.S6 FigThe biomass composition is fixed to that used by iRS1563, as adapted see . For exp(PDF)Click here for additional data file.S7 FigFor explanation of each panel, see (PDF)Click here for additional data file.S8 Fig(PDF)Click here for additional data file.S9 Fig2 assimilation as predicted at the tip of the leaf in the fitting results. Left panel, FBA reaction rates vs. reaction rates predicted at the tip of the leaf in the best-fitting solution; right panel, FBA reaction rates vs. reaction rates predicted at the tip of the leaf by the E-Flux method. Axis limits exclude a small number of reactions of particularly large flux. Fluxes in μmol m-2 s-1.The FBA calculation minimizes total flux while achieving the same total rate of CO(PDF)Click here for additional data file.S10 Fig2 uptake rates  and and6) an(PDF)Click here for additional data file.S11 Fig(a) Predicted production of cellulose, amino acids, nucleic acids, and lipids and fatty acids all show a pronounced peak at the base of the leaf and are higher in the predicted heterotrophic source region, consistent with the interpretation of this region as an area of active cell growth and division. (b) In contrast, predicted chlorophyll production is relatively steady along the leaf, while ascorbate production increases from the source-sink transition to the tip of the leaf.(PDF)Click here for additional data file.S1 Appendix(PDF)Click here for additional data file.S2 Appendix(PDF)Click here for additional data file.S3 Appendix(TXT)Click here for additional data file.S1 TableIn addition to the reactions listed, transport capacities of pyruvate, PEP, alanine, aspartate and malate across the plasmodesmata and pyruvate, PEP, malate and oxaloacetate across the chloroplast inner membrane could limit this rate; the model currently associates no genes with these transport reactions.(PDF)Click here for additional data file.S2 TableTo assess the precision with which the model predicts the value of any variable requires a separate optimization calculation, which has been done only for the subset of variables for which upper and lower bounds are given in (TXT)Click here for additional data file.S3 Table(TXT)Click here for additional data file.S4 Tabledij in ms_active_pepc, the model’s internal term for vp,max of δij in Ejk in ms_active_rubisco and bs_active_rubisco, the model’s internal variables corresponding to vc,max in Sheet 1, RNA-seq data (FPKM) from the experiments of Wang et al  (noncons(XLSX)Click here for additional data file.S1 Model(XML)Click here for additional data file.S2 Model(XML)Click here for additional data file.S3 Model(XML)Click here for additional data file.S1 Protocol(GZ)Click here for additional data file.S2 Protocol(GZ)Click here for additional data file.


And that the switch to fermentation at high growth rates therefore is a consequence of a high ATP production rate, provided by a limited pool of enzymes. The catalytic efficiency is also higher for cells grown on glucose compared to galactose and ethanol, which may explain the observed differences in their growth rates. The enzyme F1F0-ATP synthase (Complex V) was found to have flux control over respiration in the model, and since it is evolutionary conserved, we expect the trade-off to occur in organisms from all kingdoms of life.Intermediary metabolism provides living cells with free energy and precursor metabolites required for synthesizing proteins, lipids, RNA and other cellular constituents, and it is highly conserved among living species. Only a fraction of cellular protein can, however, be allocated to enzymes of intermediary metabolism and consequently metabolic trade-offs may take place. One such trade-off, aerobic fermentation, occurs in both yeast (the Crabtree effect) and cancer cells (the Warburg effect) and has been a scientific challenge for decades. Here we show, using flux balance analysis combined with  E. coliTo generate energy, yeast can use both the, oxygen consuming, respiratory pathways and the, ethanol producing, fermentative pathways. The respiratory pathway generates 10 times more ATP per glucose molecule, and has a fivefold higher biomass yieldMany microorganisms and mammalian cells use glucose as their preferred carbon source, but can still utilize a range of alternative carbon sources. Catabolism of galactose through the Leloir pathway only involves a few additional enzymatic steps, but the growth rate is much lowerE. coli, has been found to cluster in to such biologically distinct sectors, with positive or negative relations to the growth rateTo understand these observations, we turned to the hypothesis that cells are constrained by the allocation of protein mass. This hypothesis has gained recent attention through the description of the cell as a self-replicating system6E. coli on different carbon sourcesE. coliS. cerevisiaein vitro enzyme activity for 15% of the reactions and the median for the remainingS. cerevisiae to avoid the use of simulated data and ensure complete in vitro enzyme data coverage.An extension of flux balance analysis12S. cerevisiae the size of the protein pool depends on the growth rate, and varies between 40–60% of the dry weight216S. cerevisiae can increase its protein content (g per g cell dry weight) by decreasing the glycogen reservesIn in vitro specific activities S. cerevisiae of approximately 50%To study the effects of protein efficiency, we implemented a stoichiometric model of the intermediary metabolism , includihe model . This alWe observed that fermentation requires less protein per produced ATP than oxidative phosphorylation . TogetheWe used the model to simulate yeast metabolism in a chemostat operated at different dilution rates , and found good agreement with experimental values . To bettChemostat experiments have shown that yeast produces acetate at high growth ratesTo gain mechanistic insight into the Crabtree effect we investigated how the critical and maximum growth rates depend on the specific activity parameter of each enzyme . The enzBecause of the high flux control of F1F0-ATP synthase, we expect that the cell regulates the amount of this enzyme tightly. Above the critical rate this is necessary, since it is the predicted decrease in F1F0-ATP synthase that allows more protein mass to be allocated to the glycolytic and fermentative enzymes. Proteomics of the mitochondria show that the relative abundance of proteins within the mitochondria is independent of respiratory or fermentative conditionss−1, was almost twice as high as the median turn over number in the model, We investigated the robustness of the Crabtree prediction by withholding each enzyme from the mass constraint in turn. F1F0-ATP synthase was the only enzyme that single-handedly changed the result. To verify the parameter value, we used the fact that F1F0-ATP synthase is evolutionary conservedd 55 kDa .K. marxianush−1. This might be explained by their high protein contentS. cerevisiaeK. marxianus grows faster than S. cerevisiae, it still grows slower than the fermenting S. kluyveri, 0.63 h−1 The evolutionary preservation of F1F0-ATP synthase likely explains the universality of low yield metabolism. A challenge to this are the Crabtree negative yeasts, e.g. S. cerevisiae and most other organisms is that the large hydrogen pumping protein complex, Complex I, 1000 kDa32E. coli at high growth rates, where the proton pumping Complex I is replaced by a non pumping variantA major difference between oxidative phosphorylation in When producing ATP under fermentative conditions, the NADH formed by glycolysis is balanced with the consumption from alcohol dehydrogenase (ADH). However, when the cell is growing, some of the carbon is diverted to biomass and there is a net production of NADHE. coliThe model assumes that all enzymes operate at 0.5 of their maximum specific activity. This assumption is based on the observation that most glycolytic enzymes are half saturated in One of the more striking under predictions occurred for alcohol dehydrogenase (ADH), this is likely due to product inhibition in the batch culture . AconitaDistinct metabolic pathways are utilized for growth on different substrates, e.g. glucose, galactose, acetate and ethanol. Using the model we predicted the maximum specific growth rates  and founThe model correctly predicts a significantly lower growth on ethanol and acetate compared with glucose. And the lower efficiency for these substrates is caused by a higher degree of respiration and thereby ATP generated through F1F0-ATP synthase, according to our analysis of flux control . The modWe investigated the effect of active glucose transport by adding a transport reaction for glucose requiring 1 mol ATP per mol glucose. This had only a a minor effect under respiratory conditions, the ATP produced per mass decreased by 6%. But for fermentation it reduced the efficiency by 50%, since the net production of ATP decreased to 1 ATP per glucose, which made it a less viable growth strategy than respiration. This may explain the dominance of glucose transporters using facilitated diffusion in yeastE. coli was linked to a limitation in respiration or the production of NADH by the TCA cycleh−1, and fermentation at growth rate 0.4 h−1, due to the simultaneous increase in ATP production A stoichiometric model of intermediary metabolism, iAN50, was implemented based on the genome scale iFF708 modelin vitro activity in vitro activities where collected from literature, and all though most of the studies were found using the enzyme database BRENDAS. A flux vector v is predicted that fulfills the constraints given by the upper, ub, and lower bounds, lb. An optimization using a vector of objectives, c, that normally contains only zeros, apart from for the biomass or substrate reactions.In extension to standard FBA, the total enzyme mass was estimated and constrained to the biologically observed level, using an approach equivalent to one taken before12S and an adjacency matrix was constructed by considering all reactions sharing a metabolite as adjacent. The network was visualized using CytoscapeFor the visualization of the model , the co S. cerevisiae of approximately 50%The reference enzyme mass distribution was calculated from proteomics data from literature. The proteomics dataO2 uptake and 1 mole ATP per mole fermentation product. The fitting of the ATP expenditure was inspired by the shifts in cellular protein content that followed a similar trend.The metabolic requirements for ATP production , were pro  until . The expin silico with different carbon sources as described above. The protein efficiency was calculated by dividing the estimated protein with the growth rate, at each point.For the prediction of carbon source dependent maximum growth rates , chemostFor the simulation of growth in batch , the groμ .