Xantusia vigilis) confers direct reproductive success and survival advantages and that thermal benefits of winter huddling disproportionately benefit small juveniles, which can favor delayed dispersal of offspring and the formation of kin groups. Using climate projection models, however, we estimate that future aggregation in night lizards could decline more than 50% due to warmer temperatures. Our results support the theory that transitions to group living arise from direct benefits to social individuals and offer a clear mechanism for the origin of kin groups through juvenile philopatry. The temperature dependence of aggregation in this and other taxa suggests that environmental variation may be a powerful but underappreciated force in the rapid transition between social and solitary behavior.Social aggregation is a common behavioral phenomenon thought to evolve through adaptive benefits to group living. Comparing fitness differences between aggregated and solitary individuals in nature – necessary to infer an evolutionary benefit to living in groups – has proven difficult because communally-living species tend to be obligately social and behaviorally complex. However, these differences and the mechanisms driving them are critical to understanding how solitary individuals transition to group living, as well as how and why nascent social systems change over time. Here we demonstrate that facultative aggregation in a reptile (the Desert Night Lizard,  Few topics within evolutionary biology have inspired more excitement and controversy than the origin and evolution of social behavior Social aggregation is thought to evolve though adaptive benefits to group living, but hypothesized benefits of communal behavior can be difficult to quantify, compare, and interpret in natural systems. Most empirical research on social evolution has focused on taxa with obligate sociality  and highly complex social interactions, precluding comparison to solitary individuals and limiting insights to the maintenance of sociality rather than its origins Comparative studies across social insects Xantusia vigilis) provides both survival and reproductive success advantages, test a physiological mechanism driving these fitness benefits, and predict changes to social behavior with changing environmental conditions. Xantusia vigilis is a very small (1.5 g), long-lived (at least 8–10 years), viviparous lizard that lives at high densities under fallen logs (Yucca sp.) in the Mojave Desert of California, USA Here we show direct empirical evidence that social group participation in a reptile  and a trend in the same direction for juveniles  and adult males  and were not an artifact of small-scale fluctuations in daytime temperature , the strong temperature dependence of social behavior , our data support the idea that social group formation may be a very dynamic process in species that maintain reproductive independence of individuals All methods were approved by the Chancellor’s Animal Research Committee at the University of California, Santa Cruz (Sine00.02-1) and California Department of Fish and Game (SC-05560 to ARDR).Yucca brevifolia) log in this plot once per season.We conducted a mark-recapture survey of 2,332 lizards from 441 social groups every summer and winter from August 2003 - January 2008 on a 36 hectare plot in the western Mojave Desert, approximately 16 km from Pearblossom, CA, USA . We hand-captured lizards by turning every fallen Joshua tree , and tail condition  of each lizard. We sexed each lizard by shining a light through the base of the tail to visualize hemipenes in males N = 34 females, 24 males, all from separate aggregations). Summer-recaptured females were kept in the laboratory until parturition to determine litter size and then returned with their offspring to their exact log of capture. We used general linear models (GLMs) to test for the potential confounding effect of body size (SVL) on litter size (P = 0.56) and to assess the effect of winter sociality on litter size.To assess the reproductive success of social and solitary lizards, we analyzed only adults for which we knew aggregation status in the winter directly preceding summer reproduction  to assess the effect of winter sociality on male reproductive success. There was no significant effect of male body size (SVL) on reproductive success (P = 0.36).To assign paternity, we genotyped 369 females, 249 males, and 624 juveniles at seven unlinked, highly polymorphic microsatellite loci ark v6.0 by coding encounter histories as A (solitary state), B (aggregated state), or 0 (not captured) over the 10 sampling occasions . We constructed four main models with constant but state-specific survival , time-dependent state transition probabilities , and all four combinations of constant and time-dependent capture probabilities by aggregation state . To minimize over-parameterizing models, we independently analyzed adult males, adult females, and juveniles. Our sampling occasions were not equally spaced across the year, as winter observations were taken in December/January and summer observations in August/September during late stages of female pregnancy (see Ψ): ΨA→B was fixed to 0 and ΨB→A was fixed to 1 for all four winter to summer transitions.To estimate survival of social and solitary lizards, we used multi-state models in M2 = 113.3, df = 11, P<0.0001; males: χ2 = 42.6, df = 3, P<0.0001; juveniles: χ2 = 101.5, df = 9, P<0.0001).We ran all models with the logit link function, 2ndPart variation estimation, and identity design matrix options. We then weight-averaged the real survival parameter estimates from our four models to obtain robust estimates of survival  and compN = 640 females, 389 males, 507 juveniles). We then used residuals from class-specific regressions as an index of body condition and used linear models to compare aggregated and solitary lizards within each class. All individuals with incomplete tails were excluded from analysis, and pregnancy does not occur in the winter.To compare body condition of aggregated and solitary lizards, we log transformed (for linearity) mass and SVL of all winter-caught lizards at time of capture and regressed log mass against log SVL by age/sex class  from the NOAA National Climatic Data Center (NCDC) database for all available years (1986–2009). We compiled summary statistics for annual number of nights below 0°C and annual extreme Tur study .To assess the effect of field temperature on aggregation, we averaged maximum and minimum daily temperature data for each collection day from the PWS. We analyzed only days for which we caught more than 30 lizards to avoid small sample biases (N = 17 winter and 9 summer days). We then fit a self-starting three parameter logistic model to generate predicted aggregation values by temperature and used a Spearman rank test on the 17 winter collection days to assess the effect of temperature on winter aggregation.To quantify the thermal stability of social groups, we measured heat flux of 26 naturally solitary lizards, 55 natural aggregations, and 27 experimentally isolated lizards originally found in aggregations. We placed lizards inside 59 ml cylindrical airtight plastic arenas filled across the bottom by a 2 cm diameter heat flux disk  Coupled Model Intercomparison Project phase 3 (CMIP3) multimodel dataset, stored and served at the LLNL Green Data Oasis. As per the setup of this online database’s access capabilities, we queried the closest geographic approximation of our field site, which was a 156 kmains see  so as noΔAIC = 62.78; CM3.1-B1: ΔAIC = 83.71; PCM1.1-A2: ΔAIC = 115.15; CM3.1-A2: ΔAIC = 170.86).After acquiring average monthly temperature projections for the four climate models, we used the three parameter logistic model generated from observed aggregation by mean temperature  to prediP<0.05. For parametric analyses, normality of residuals was assessed using Shapiro-Wilk tests, linearity by visual assessment of residual by predicted plots, autocorrelation with Durbin-Watson tests, and homogeneity of variance with Levene’s test for all relevant analyses. Nonparametric tests were chosen where described for data that violated assumptions of parametric analyses. Unless otherwise noted, only significant effects are reported.Unless otherwise stated, we performed all statistical tests in R v2.13.1 and assessed significance at Figure S1Night lizard aggregation and Joshua tree habitat. (A) In situ night lizard (Xantusia vigilis) aggregation of three adults and two juveniles demonstrates winter huddling behavior. The lizard above is walking away from the aggregation after being disturbed by the rolling of the cover log. (B) Joshua tree (Yucca brevifolia) habitat at the field site shows both living trees and fallen logs, the site of winter aggregation.(TIF)Click here for additional data file.Figure S2Fallen log microhabitat characteristics do not predict aggregation. (A) None of the following habitat variables vary between sites with aggregations versus solitary lizards (left to right): Under log temperature , buffer from air temperature, log decomposition , log size, nearest fallen log, or nearest living tree. (B) Evaporative water loss (EWL) rates are the same in aggregated and solitary lizards, and EWL rates do not scale with aggregation mass as expected if water loss needs were driving social behavior. Comparison graphs show means ±1 s.d.(TIF)Click here for additional data file.Figure S3Daily temperature profiles underneath fallen logs. Microhabitat temperatures measured by HOBO data loggers underneath five fallen logs are remarkably similar to environmental temperatures at the Pearblossom weather station, especially underneath preferred logs of medium decomposition (top row). Sheltering logs can weakly buffer lizards against extreme temperatures, but the maximum effect of this buffer is no more than a few degrees C and subzero temperatures are encountered as late as March.(TIF)Click here for additional data file.Figure S4Lack of aggregation capture bias during daily temperature fluctuation. (A) Typical temperature profile from sunrise to sunset (3 March 2002) from a HOBO data logger underneath fallen log of medium decomposition. (B) Group size by daily capture order (sunrise to sunset) show that lizards caught at the beginning of the day (the coldest temperatures) were not more likely to be aggregated. Aggregations were found throughout each collection day. Collection dates and average daily temperatures are at the top of each graph.(TIF)Click here for additional data file.Figure S5Arenas for laboratory measurements of heat flux. We measured heat flux in 26 naturally solitary lizards, 55 natural aggregations, and 27 experimentally isolated lizards originally found in aggregations by placing them inside plastic arenas filled across the bottom by a heat flux disk. We then placed these arenas inside an environmental chamber at 16°C before the temperature dropped to 1°C for 12 hours to simulate natural daytime and nighttime winter temperatures. We recorded changes in heat flux over time to generate heat loss curves for which we then calculated decay rate and half-life to compare the thermal stability of solitary and aggregated lizards.(TIF)Click here for additional data file.Table S1ark.Multi-strata survival model output from M All four main models for each class , with constant survival (Φ) for each state , time-dependent transition probabilities between states , but variable capture probability (p) parameters . The weighted model averages are bolded, and the fully time-constant and time-dependent models are italicized for comparison. Estimates of survival are remarkably robust to changes in model structure; in all cases, the aggregated state is associated with higher survival than the solitary state.(DOC)Click here for additional data file.Table S2Historical weather data for Pearblossom, CA, USA. Annual average and extreme minimum temperatures and number of nights below freezing from 1986–2009 (subset 2003–2008 is the duration of this study). Source is NOAA National Climatic Data Center (NCDC) for the Pearblossom weather station (#046773).(DOC)Click here for additional data file.Text S1Supporting text.(DOC)Click here for additional data file.


Although all brain cells bear in principle a comparable potential in terms of energetics, in reality they exhibit different metabolic profiles. The specific biochemical characteristics explaining such disparities and their relative importance are largely unknown. Using a modeling approach, we show that modifying the kinetic parameters of pyruvate dehydrogenase and mitochondrial NADH shuttling within a realistic interval can yield a striking switch in lactate flux direction. In this context, cells having essentially an oxidative profile exhibit pronounced extracellular lactate uptake and consumption. However, they can be turned into cells with prominent aerobic glycolysis by selectively reducing the aforementioned parameters. In the case of primarily oxidative cells, we also examined the role of glycolysis and lactate transport in providing pyruvate to mitochondria in order to sustain oxidative phosphorylation. The results show that changes in lactate transport capacity and extracellular lactate concentration within the range described experimentally can sustain enhanced oxidative metabolism upon activation. Such a demonstration provides key elements to understand why certain brain cell types constitutively adopt a particular metabolic profile and how specific features can be altered under different physiological and pathological conditions in order to face evolving energy demands. aerobic glycolysis and was first observed in cancer cells. Since then, it has also been described in several normal tissues including the central nervous system. The biochemical basis of aerobic glycolysis has remained elusive until now. Taking advantage of a modeling approach, we unraveled the main metabolic characteristics that determine whether a cell will be strictly oxidative or rather will exhibit aerobic glycolysis. When applied in the context of the central nervous system, our findings not only provide a theoretical demonstration of why neurons and astrocytes differ in terms of metabolic profile, but also suggest that such complementarity forms the basis for metabolic cooperation between the two cell types.In an environment with appropriate oxygen levels (normoxia), most eukaryotic cells produce energy by oxidizing glucose into carbon dioxide and water. In this process, glucose is transformed into pyruvate, which then fuels oxidative phosphorylation in the mitochondria. Interestingly, Otto Warburg reported back in the 1920's that some eukaryotic cells prominently process glucose-derived pyruvate into lactate, hence “avoiding" the mitochondrial oxidation despite adequate oxygen concentrations. This phenomenon was termed  A central question in biology concerns the biochemical characteristics that determine the metabolic profile (glycolytic vs. oxidative) of a particular cell type. Indeed, since the experimental description of aerobic glycolysis (i.e. the conversion of glucose into lactate despite the presence of sufficient oxygen levels to carry out oxidative metabolism) by Warburg Such considerations acquire additional interest in the context of cell-cell interactions and metabolic cooperation. Indeed, in several tissues including muscles +, which is converted into NADH. For glycolysis to proceed, the excess NADH needs to be “recycled" back into NAD+. One way to do this is to convert pyruvate into lactate (Li), a reversible reaction catalyzed by lactate dehydrogenase (LDH). The produced lactate can then be transported outside the cell via the monocarboxylate transporters (MCT). The consumption of glucose for lactate production mainly is considered a glycolytic phenotype  and the rate of the PDH reaction (JPDH).In order to better understand the importance of distinct energy substrate sources for brain cell energetics, we considered a simple model taking into account glucose and lactate supply as well as their metabolism. This model describes the dynamics of lactate and glucose in brain cells. via this reaction). The intracellular lactate dynamics is therefore described by the following equation: outside the cell) and a priori assumption is made about the sign of In this model, lactate is taken up (or released) by brain cells via MCTs and further metabolized by LDH into pyruvate , while it is “recycled" back into NAD+ by the mitochondrial shuttles for the transfer of reducing equivalents:Shuttlek is a constant). The NADH mitochondrial shuttle therefore plays an essential role in determining the direction of the LDH reaction. .We note that the baseline steady state values (subscript 0), obtained by equating to zero the right-hand side of all the differential equations, obey toSome of the parameters in our equations, or a combination of them, have been measured or are known to lie within some range All the figures presented in this work except  were obtvia MCTs, of 80% based on the data of Pierre et al. obtained in cultured neurons in vivo increase in the extracellular lactate concentration eL of 80% as reported by Hu and Wilson eL of the same magnitude. Simulations allowed to determine the resulting fluxes for lactate transport, max,glycov, shuttlek and max,PDHv alone (ctrl-bar). Further activating lactate transport capacity, stimulated cell yields a slight increase in oxidative metabolism to +33%. Note that the increase in lactate flux remains relatively modest (+13%) in this condition. If instead an increase in the extracellular lactate concentration eL is taken into account, oxidative metabolism is further enhanced (+42%), with a significant increase in lactate flux (+34%). A combination of enhanced lactate transport capacity and extracellular lactate concentration leads to a 47% increase in oxidative metabolism with a concomitant 45% increase in lactate flux. It is noteworthy that in this last case, the contribution of each metabolic pathway approaches the basal state contributions (r = 0.73). Based on these metabolic responses, such a behavior appears characteristic of oxidative cells.The model presented above was used to determine the changes in lactate flux across the plasma membrane as well as in the glycolytic and pyruvate dehydrogenase-catalyzed fluxes, when switching conditions from a basal to a stimulated state. For the basal state, the contribution of lactate-derived and glycolysis-derived pyruvate was set to 43% and 57%, respectively .It is well known that a certain fraction of brain cells do not respond to a stimulation by importing lactate but rather by producing and releasing lactate. In order to reproduce this specific behavior, some of the parameters had to be modified. We found that reducing both the initial PDH reaction rate and the activity of the mitochondrial NADH shuttles leads to a strikingly different type of response. fixed glycolytic conditions. Four scenarios were studied combining two lactate/glycolysis-supplied pyruvate ratios, MCTJ/glycoJ = r, at basal state, and two distinct levels of activation of the oxidative rate, r = 0.75, +30% r = 0.75, +70% r = 2.2, +30% r = 2.2, +70% Choice of parameters). As can be seen, a rather wide range of increased oxidative rates can be accounted for by altering lactate transport capacity and extracellular lactate concentration. Importantly too, we see that increasing the PDH maximal capacity max,PDHv by 30% (respectively 70%) is not sufficient to yield an increase in oxidative metabolism JPDH of 30% (respectively 70%). Hence, in order to be efficient under fixed glycolysis, the cell should not rely exclusively on the regulation of the PDH activity to increase its production of energy. In parallel, it should also enhance lactate transport, meaning that the latter could become limiting upon activation.It could be observed in the previous simulations that lactate metabolism can significantly contribute to an enhancement in oxidative metabolism in cells with a predominantly oxidative phenotype . In thes5, +30%  ; r = 0.75, +70%  ; r = 2.22, +30%  ; and r =2, +70%  . In eachalone can satisfy physiological increases in oxidative rate, we varied the lactate/glycolysis-supplied pyruvate ratio, MCT,0J/glyco,0,J = r, between extreme cases (0.1 to 3.4 with increments of 0.3) together with increases γ in lactate flux of up to 80% , between 10% and 29% (light gray), or even above 29% (dark gray) can be easily accounted by physiological increases in lactate flux for a wide range of basal conditions which encompasses most published values Evaluation of model validity with in vitro and in vivo experimental data).In order to better delineate under which range of basal conditions a change in lactate metabolism r = MCTJ/glycoJ = 0.69/0.31 = 2.2 as determined in vivo by Hyder et al. MCTJ, glycolysis, glycoJ, and oxidative metabolism, PDHJ . Reducing the glycolytic flux by 60% yielded a pyruvate concentration of 0.036 mM : intracellular lactate concentrations PDH-metabolic flux as a function of the mitochondrial NADH shuttling rate (TIF)Click here for additional data file.Figure S2JPDH fluxes upon stimulation . (B) Same as (A), but glycolysis is also enhanced upon stimulation . Cf. NALS at rest, ANLS upon activation. (A) In the basal state (black), parameters are chosen such that lactate is taken out of the cell ((TIF)Click here for additional data file.Figure S3−3.6; 10−4.8] mM; for the other parameters, refer to Choice of parameters in the main text): intracellular lactate concentrations Effect of pH on transport, glycolysis and PDH-metabolic flux. All the rates are normalized relative to their maximum. The intracellular proton concentration (TIF)Click here for additional data file.Figure S4Choice of parameters in the main text): intracellular lactate concentrations total = 3.2 mM, cf. total = 0.064 mM . In the basal state (black), both glycolysis and lactate transport contribute to JPDH (57% and 43% respectively). We show the resulting transport, glycolytic and JPDH fluxes upon stimulation .Changing the LDH pool. (A) Effect of the total LDH pool on transport, glycolysis and PDH-metabolic flux. The simulations in the gray area did not match the following physiological constraints (cf. (TIF)Click here for additional data file.Figure S5JPDH . (B) Glycolytic phenotype: In the basal state (black), parameters are chosen such that lactate is taken out of the cell . See Supp. Effect of MCT parameters (transport equation in (TIF)Click here for additional data file.Table S1Parameters used in our simulations to compute the basal state of a typical oxidative cell cf. . For the(DOC)Click here for additional data file.Text S1Model description.(DOC)Click here for additional data file.Text S2Model robustness.(DOC)Click here for additional data file.


Escherichia coli. The incorporation of spontaneous and enzymatic reactions, as well as damage and repair of biomolecules, allowed for a detailed analysis of how NO• distributes in E. coli cultures. The model was informed with experimental measurements of NO• dynamics, and used to identify control parameters of the NO• distribution. Simulations predicted that NO• dioxygenase (Hmp) functions as a dominant NO• consumption pathway at O2 concentrations as low as 35 µM (microaerobic), and interestingly, loses utility as the NO• delivery rate increases. We confirmed these predictions experimentally by measuring NO• dynamics in wild-type and mutant cultures at different NO• delivery rates and O2 concentrations. These data suggest that the kinetics of NO• metabolism must be considered when assessing the importance of cellular components to NO• tolerance, and that models such as the one described here are necessary to rigorously investigate NO• stress in microbes. This model provides a platform to identify novel strategies to potentiate the effects of NO•, and will serve as a template from which analogous models can be generated for other organisms.Nitric oxide (NO•) is generated by the innate immune response to neutralize pathogens. NO• and its autoxidation products have an extensive biochemical reaction network that includes reactions with iron-sulfur clusters, DNA, and thiols. The fate of NO• inside a pathogen depends on a kinetic competition among its many targets, and is of critical importance to infection outcomes. Due to the complexity of the NO• biochemical network, where many intermediates are short-lived and at extremely low concentrations, several species can be measured, but stable products are non-unique, and damaged biomolecules are continually repaired or regenerated, kinetic models are required to understand and predict the outcome of NO• treatment. Here, we have constructed a comprehensive kinetic model that encompasses the broad reactivity of NO• in  Escherichia coli that includes NO• autoxidation, respiratory inhibition, enzymatic detoxification, and damage and repair of biomolecules. Using this model, we investigated the control of NO• dynamics in E. coli cultures, and found that the primary aerobic detoxification system, NO• dioxygenase (Hmp), functions as a dominant NO• consumption pathway under microaerobic conditions (35 µM O2), and loses utility as the NO• delivery rate increases. We confirmed these predictions experimentally, thereby demonstrating the predictive power of the model. This model will serve as a quantitative platform to study nitrosative stress, provide a template from which models for other organisms can be generated, and facilitate the development of antimicrobials that synergize with host-derived NO•.Nitric oxide (NO•) is a highly reactive metabolite used by immune cells to combat pathogens. Since the biological effects of NO• are governed by its broad reactivity, it is desirable to determine how NO• distributes among its many targets inside a cell. A quantitative understanding of this distribution and how it is controlled will facilitate the development of novel NO•-potentiating therapeutics. Here, we have constructed and experimentally validated a comprehensive kinetic model of NO• biochemistry within  However, the NO• biochemical network is complex  for use in signaling and defense  complex , contain2, O2•−, and peroxynitrite (ONOO−) in idealized mammalian cell cultures using a reaction–diffusion model, and explored the effect of varying the rates and locations  of their generation. Their results suggested negligible spatial variation in species concentrations, and identified conditions under which the different cellular compartments serve as dominant sources or sinks. However, their model did not include the reactions of numerous intracellular metabolites that either directly react with NO•, or its autoxidation products . Lancaster et al.in vivo and used to estimate steady-state intracellular concentrations of different reactive nitrogen species (RNS), in addition to identifying their major sources and sinks in the cytosol and membrane compartments of mammalian cells. Interestingly, none of these models considered the interaction of NO• and its autoxidation products with [Fe-S] clusters, cytochromes, or DNA, and their treatment of the relevant enzymatic processes was limited to NO• dioxygenase and superoxide dismutase. Recently, Tórtora et al.2•− and NO•. Since their focus was specifically on the inactivation of aconitase, they did not consider much of the extensive reaction network of NO•, O2•−, and their products. Bagci et al.2O3, NO2• and ONOO−, as well as their interactions with GSH, non-heme iron, and mitochondrial cytochrome c. However, their attention was primarily on the dynamics of the apoptotic response, and many RNS-related reactions and biological species that were not directly involved in apoptosis were omitted. Though previous models provide a firm foundation for modeling NO• in biological systems, none are sufficiently comprehensive to quantify the distribution of NO• among its many intracellular consumption pathways.A number of kinetic models have been developed to simulate NO• chemistry in biological contexts Escherichia coli. This model includes NO• autoxidation, enzymatic detoxification, [Fe-S] damage, thiol and tyrosine nitrosation, DNA base deamination, tyrosine nitration, and the repair steps responsible for regeneration of RNS targets. A model of NO• stress with this level of detail has not been previously recognized for any organism. Using this model, we quantitatively explored the distribution of NO• consumption in E. coli, and predicted that the utility of the major aerobic NO• detoxification system (Hmp) depends on the NO• delivery rate and extends to environments with O2 concentrations as low as 35 µM (microaerobic). We went on to experimentally confirm these predictions, thereby demonstrating the utility of this model to the study of NO• metabolism. This computational model will serve as a platform to quantitatively interrogate the kinetic competition of NO• with its many targets in E. coli, and assess the influence of various parameters on its distribution.Here, we describe the construction, experimental validation, and utility of a comprehensive model of NO• metabolism in E. coli, NO• may be consumed directly through enzymatic detoxification , or reactions with [Fe-S] clusters, O2•−, or O2 , [2Fe-2S] and [4Fe-4S] damage and repair, thiol nitrosation and denitrosation, DNA base deamination and repair, enzyme expression and degradation, tyrosine nitration, and reversible cytochrome inhibition are included  and quantification of the impact these alterations have on NO• metabolism. To substantiate the utility of the model, we first validated that the model could reproduce experimentally-measured NO• dynamics and make accurate predictions of experimental outcomes.Upon diffusing into included . The modincluded , Text S1included . An overE. coli cultures. Since extracellular NO• loss, including autoxidation and gas phase transport, was non-negligible, we bridged the intracellular model to the experimental system by adding an extracellular (growth media) compartment that accounted for autoxidation and gas-phase transport  were determined from experimental NO• and O2 measurements in the absence of cells (E. coli were treated with 0.5 mM dipropylenetriamine (DPTA) NONOate, and the concentration of NO• in the culture was monitored over time , and Hmp expression  parameters were the most influential, whereas the oxidation of NorV (kNorV-O2) was of minor significance, but exhibited a greater effect than the remaining parameters, which were all negligible (less than a 5% increase in SSR)  . This prcultures . As depiE. coliE. coli treated with DPTA using the optimized parameter values (2 and O2•−. Reduction by anaerobic detoxification enzymes (NorV and NrfA) and nitrosylation of [Fe-S] clusters was predicted to account for less than 0.03% and 0.04% of the cellular NO• consumption, respectively. To provide additional experimental evidence in support of these intracellular distributions, we experimentally validated that a mutant lacking the NorV enzyme (ΔnorV) consumed NO• at the same rate as wild-type under the experimental conditions tested  after DPTA delivery, it started to diverge rapidly as Hmp began to dominate the consumption of NO• in the wild-type culture   , validathmp culture, we simulated the corresponding intracellular distribution of NO•  and [Fe-S] nitrosylation accounted for the remaining 14.1% and12.6%, respectively  to 1.35×10−3 s−1 , the measured rate for the NO• donor propylamine propylamine (PAPA) NONOate , Δhmp entered this regime after 1.2 h when treated with PAPA, compared to the 6.4 h predicted for DPTA. We simulated the corresponding NO• distributions for PAPA-treated cultures to examine the participation of the different pathways in NO• removal. The elevated NO• concentrations simulated for the faster-releasing PAPA greatly increased flux through various consumption pathways, where over 99% of the total NO• consumption was predicted to occur within the first hour after dose for both wild-type and Δhmp , highlighting the decreased utility of Hmp under conditions of more rapid NO• release. These results demonstrate that the model can accurately identify parameters that control the distribution of NO• in bacterial cultures, and quantify the impact of their manipulation.To experimentally validate the prediction that the utility of Hmp decreases as the delivery rate of NO• increases, we measured and compared the ability of wild-type and Δrameters . The pearameters , suggestbd inhibition (kNO•-[Fe-S]), the parameter value was varied across this range when predicting the extent of [Fe-S] damage. Simulated exposure of wild-type and Δhmp E. coli to 0.5 mM DPTA predicted a 2- to 4-fold reduction in the total concentration of [Fe-S] clusters damaged as a result of Hmp activity. When simulations were repeated for PAPA, however, the total [Fe-S] damage predicted for wild-type and Δhmp cultures differed by a maximum of 5%, in agreement with the predicted dependence of Hmp utility on NO• release rate. Furthermore, the duration of NO•-mediated cytochrome bd inhibition following DPTA treatment was predicted to greatly increase for the Δhmp culture relative to wild-type, requiring over 9 h (compared to 0.7 h for wild-type) for the concentration of NO•-bound cytochromes to drop below 50% of the total. Treatment with PAPA resulted in more similar cytochrome inhibition between the strains, with durations of 0.6 h and 1.5 h predicted for wild-type and Δhmp, respectively. Collectively, the results from these damage descriptors, in addition to the rate and distribution of NO• consumption, predicted a greater similarity in recovery from bacteriostasis between wild-type and Δhmp when treated with PAPA than with DPTA. To test the prediction, we monitored the optical density (OD600) of each strain following treatment with 0.5 mM DPTA or PAPA , and found to capture the data very well , whereas Hmp was identified as the major NO• sink. These predictions were experimentally validated, and the results are presented in 2 concentrations.Hmp is considered the major aerobic enzyme responsible for NO• detoxification periment . This coery well . We notehmp, and ΔnorV under microaerobic conditions were simulated, and are presented in norV, respectively, and 95% for Δhmp), due to the increased air-liquid surface area caused by the bubbling of N2 through the culture, as well as the reduced rate of autoxidation. Autoxidation was predicted to have negligible NO• consumption activity compared to the cellular and gas transport pathways , owing to the reduced O2 concentration, as well as the lower peak NO• concentration  than was achieved under aerobic, non-bubbling conditions using DPTA (∼8–10 µM). Cellular consumption of NO• was still predicted to be the greatest sink of NO• for the wild-type and ΔnorV strains , but only a minor pathway in the Δhmp culture (3.8%). The intracellular distributions (norV cultures were still predicted to be dominated by Hmp detoxification (both exceeding 98% of intracellular NO• consumed by Hmp), as was seen under aerobic conditions. The NO• consumed by Δhmp cells, however, was now predicted to occur primarily through NorV reduction (93% of the intracellular NO•), compared to the 14% contribution predicted for Δhmp in aerobic conditions. Overall, the simulation results predicted Hmp to be the primary mode of NO• consumption under O2 concentrations as low as 35 µM, but suggested an increased role of NorV reduction in the event that Hmp detoxification becomes unavailable.The corresponding extracellular and intracellular NO• distributions for wild-type, Δibutions  for wild2 and O2•− to yield the reactive nitrogen species, NO2•, N2O3, N2O4, and ONOO−NO• is a critical antimicrobial of the innate immune response whose utility originates from its ability to diffuse through cellular membranes E. coli cultures. Oxidation of NO• has been shown in the past to be a major contributor to the consumption of NO• under certain conditions 2 concentrations as low as 35 µM (microaerobic). Both of these predictions were validated experimentally, thereby demonstrating the utility of the model for the study of NO• metabolism. Specifically, when treated with a fast-releasing NO• donor (PAPA), the consumption of NO• and recovery from bacteriostasis was far more similar between wild-type and Δhmp E. coli than with a slower NO• donor (DPTA). This effect arises from substrate inhibition of the Hmp active site caused by high NO•/O2 concentration ratios and the time required to synthesize Hmp 2 concentrations as low as 35 µM. This effect originates from the strong induction of Hmp expression upon NO• exposure even under anaerobic conditions 2-mediated deactivation of NorV, the alternative NO• detoxification system that has been previously identified as critical for resisting NO• stress under anaerobic conditions 2 concentrations at infections sites/in macrophages and neutrophils are typically hypoxic  would be measured and both metabolic databases and the organism's genome would be mined for model additions capable of capturing the experimental data. Potential additions would then be experimentally validated by measuring in vitro kinetics of samples purified from cultures of interest. Execution of these steps will produce models of NO• metabolism in pathogens, that will mirror utility and capabilities achieved by the kinetic platform described here.The work presented here demonstrates the predictive accuracy and utility of a comprehensive model of NO• metabolism in E. coli K-12 MG1655. The Δhmp and ΔnorV mutants were obtained from the Keio collection hmp primers used were 5′-CCGAATCATTGTGCGATAACA-3′ (forward) and 5′-ATGATGGATACTTTCTCGGCAGGAG-3′ (reverse) for accurate integration, and 5′- TCCCTTTACTGGTGGAAACG-3′ (forward) and 5′-CACGCCCAGATCCACTAACT-3′ (reverse) for gene duplication. The norV primers used were 5′-CCAGCACATCAACGGAAAAA-3′ (forward) and 5′-ATGATGGATACTTTCTCGGCAGGAG-3′ (reverse) for accurate integration, and 5′-GACTGGGAAGTGCGTGATTT-3′ (forward) and 5′-CGGAAGCGTAAACCAGTCAT-3′ (reverse) for gene duplication.All strains used in this study were NO• donors (Z)-1-[N-(3-aminopropyl)-N-(3-ammoniopropyl)amino]diazen-1-ium-1,2-diolate (DPTA NONOate) and (Z)-1-[N-(3-aminopropyl)-N-(n-propyl)amino]diazen-1-ium-1,2-diolate (PAPA NONOate) were purchased from Cayman Chemical Company. All other chemicals and reagents were purchased from Sigma Aldrich or Fisher Scientific, unless otherwise noted.E. coli from a frozen −80°C stock were inoculated into 1 ml of fresh LB broth and grown for 4 hours at 37°C and 250 r.p.m. 10 µl of the LB culture were used to inoculate 1 ml of MOPS minimal media (Teknova) containing 10 mM glucose. The minimal glucose culture was grown at 37°C and 250 r.p.m. overnight (16 h) and used to inoculate 20 ml fresh MOPS glucose (10 mM) in a 250 ml baffled shake flask to a final OD600 of 0.01. The flask culture was grown at 37°C and 250 r.p.m. to exponential phase (OD600 = 0.2), at which point 4 ml was transferred to separate microcentrifuge tubes in 1 ml aliquots and centrifuged at 15,000 r.p.m. for 3 min at 37°C. To remove the culture media, 980 µl of the supernatant was removed and cell pellets were resuspended in 1 ml of pre-warmed (37°C) 10 mM MOPS glucose media. Samples were combined in a 15 ml Falcon tube, and returned to the shaker . After 5 minutes, the resuspended culture was diluted to an OD600 of 0.03 in fresh, pre-warmed (37°C) MOPS glucose (10 mM) in a 50 ml Falcon tube with a final culture volume of 10 ml. The culture was stirred with a sterilized magnetic stirring bar, and immersed in a stirred water bath to maintain the temperature at 37°C. Growth was monitored until the OD600 reached a value of 0.05 (approximately 45 minutes after diluting to OD600 of 0.03), at which time the NO• donor solution (DPTA or PAPA) was added. On the day of use, the NONOate powder was dissolved in a chilled (4°C), sterile solution of 10 mM NaOH in deionized H2O, and stored on ice prior to delivery. After NONOate delivery, every half-hour (DPTA) or twenty minutes (PAPA), 75 µl aliquots were removed to measure the OD600 . The concentration of NO• in the culture was monitored continuously over the course of the experiment using an ISO-NOP NO• sensor . The electrode was calibrated daily, prior to use, according to the manufacturer's specifications.2 bubbling was included to reduce the dissolved O2 concentration. Immediately following the dilution of cells to an OD600 of 0.03 in the 50 ml Falcon tube, N2 gas (99.998% pure) was bubbled into the culture through a sterile pipet tip at a constant flow rate of 1 ml/s. The O2 concentration was observed to drop quickly and stabilize at approximately 19% air saturation (35 µM) within 15 minutes of initiating the N2 bubbling, where it remained for the duration of the experiment. The concentration of O2 was monitored continuously to ensure stable conditions throughout the assay . The sensor was calibrated according to the manufacturer's specifications, and the signal was automatically compensated for temperature fluctuations using the TDIP15 temperature sensor (PyroScience GmbH) during all O2 measurements.The concentration of dissolved O2− and NO3− were measured using the Nitrate/Nitrite Colorimetric Assay Kit from Cayman Chemical Company, following the manufacturer's instructions. Briefly, Griess reagents were added to diluted samples to convert the NO2− to a purple azo compound, and quantified by measuring the absorbance at 540 nm using a microplate reader 2− solution. The total NO2−+NO3− concentration of the samples were obtained by first converting the NO3− to NO2− using nitrate reductase, and then treating with Griess reagents. The NO3− concentration in the samples was calculated as the difference between the total NO2−+NO3− concentration and the NO2− concentration. All samples were measured in triplicate.The concentration of NOX is the vector of species concentrations, and S is a matrix of stoichiometric coefficients describing all model reactions. Reaction rates, defined by vector r, are a function of the relevant species concentrations x, and the associated kinetic parameter(s) p. r = k[A][B]), while The model simulates the dynamics of intracellular metabolites and cellular components upon exposure to NO• using a system of differential mass balances,2 to diffuse freely across membranes, we assumed equal intracellular and extracellular concentrations 2 mass balances were scaled according to their relative volumes,V is the total or compartment-specific volume, rgen is the rate of generation of NO• in the media, and rmedia and rcell are the rates of extracellular and intracellular NO• consumption, respectively. The volume fractions were calculated as a function of OD600, assuming an OD-specific cell concentration of 11.1±1.1×108 cells.ml−1.OD−1, and a single-cell volume of 3.2×10−15 L 600 of 0.05, which corresponds to a cell volume fraction of 1.78×10−4.The model was partitioned into intracellular and extracellular compartments to facilitate experimental validation, as measurements inherently involve the culture media. Given the ability of NO• and OThe intracellular pH was assumed to be 7.6, reflective of bacteria growing in a neutral medium The delivery of NO• to the system was modeled as originating from an NO• donor (such as DPTA or PAPA), where the initial concentration of the donor species (in the extracellular compartment) was set accordingly. The release of NO• from the NONOates was modeled according to first-order decay kinetics, releasing two moles of NO• per mole of parent compound 2 to generate nitrogen dioxide (NO2•), which may combine with another molecule of NO• to form nitrous anhydride (N2O3) In aqueous solutions, NO• will undergo autoxidation at a rate that is second-order in NO• and first-order in OE. coli are NO• dioxygenase (Hmp) 3−22O at a rate orders of magnitude greater than the Hmp-mediated reduction 22−; however, NrfA has also been shown to catalyze the 5-electron reduction of NO• to NH4+ in the presence of NO2− or NO3−2-responsive regulator FNR, restricting its role to anaerobic environments The main enzymatic NO• detoxification systems identified in 2• and N2O3) that are primarily responsible for the nitrosation of thiols E. coli, can serve as a protective sink for RNS Protein-bound and low molecular weight (LMW) thiols are subject to modification upon exposure to NO•, forming products such as S-nitrosothiols and thiyl radicals bo and bd in E. coli) makes it a potent inhibitor of respiratory function, which can cause bacteriostatic effects even at low NO• concentrations The high affinity of NO• for the terminal quinol oxidases .All simulation calculations were performed using Matlab (R2012a). The governing set of differential mass balances was integrated using the stiff numerical ODE integrator  between the experimentally-measured and model-simulated NO• concentration profiles. Since the nonlinearity of the minimization problem gives rise to local minima, we performed 100 independent optimizations, each initialized with a random set of parameter values .Optimization of model parameters was performed in Matlab using the kNONOate), transfer of NO• to the gas phase (kLaNO•), and the rate of NO• autoxidation (kNO•-O2). Cell-free growth media was treated with 0.5 mM DPTA under conditions identical to the aerobic NO• consumption assay, and the resulting NO• concentration profile and final (10 h) NO2− and NO3− concentrations were measured. The optimization yielded values of 1.34×10−4 s−1 , 4.74×10−3 s−1, and 1.80×106 M−2s−1 for kNONOate, kLaNO•, and kNO•-O2, respectively  NO• consumption assay, uncertain parameters were re-optimized for the low-O2 environment due to expected changes in cellular properties and the effect of N2 bubbling on gas transfer rates. We note that differences in N2 bubble properties (such as bubble size and lifetime) caused by the presence of cells prevented the use of cell-free NO• measurements in determining extracellular parameters for this experimental setup. Instead, the simulated O2 concentration was fixed to 35 µM based on experimental observations  were found to strongly influence the predicted NO• dynamics. Parameters governing the rate of NONOate dissociation (kNONOate) and NO• transfer to the gas phase (kLaNO•) also demonstrated substantial control of the [NO•] curve upon variation. Finally, NorV expression  and inactivation (kNorV-O2) parameters were found to have a significant impact on the SSR.For the microaerobic  were added to the adapted model. For Lancaster's model, the NO• formation and disappearance reactions, as well as the disappearance of NO2• and •OH, were not included because the rates of the disappearance reactions are user-defined, and the formation of NO• is accounted for by the NONOate dissociation reaction. The model described by Nalwaya and Deen contains a simplified reaction representing the consumption of NO• by a heme- and flavin-dependent dioxygenase, analogous to Hmp detoxification in E. coli. The reaction was included in the adapted model, and the associated bimolecular rate constant was allowed to vary during parameter optimization. Additionally, the rate parameters governing ONOO− and ONOOH reactions used by Nalwaya and Deen were adjusted for a pH of 7.6, where the fraction of ONOO− in protonated form was calculated to be 12% Three existing models of NO• chemistry, developed by Lim n+) in the model of Lim et al. were allowed a range of 5–8 mM and 1–500 µM, respectively. The protein concentration range was selected based on typical protein content reported for E. colin+ was allowed the same concentration range as [Fe-S] clusters in the present model, which assumes ∼5% of proteins contain [Fe-S] clusters Species concentrations in the alternative models were set to the same values or ranges used in the present model, except for a few minor differences. The concentrations of proteins and transition metal centers  and 70-fold  greater than the SSR achieved by the present model , where parameters classified as uncertain were varied to minimize the SSR between the predicted and experimental [NO•] curves. Ultimately, none of the three adapted models were able to capture the dynamics of NO• measured in wild-type nt model .E. coli cultures  are not shown.tein see . Enzymes(TIF)Click here for additional data file.Figure S2Reaction network diagram of DNA deamination and base excision repair. Shown are the model reactions for N2O3-mediated deamination of DNA bases, and the subsequent process of damaged base removal and repair mediated by the BER system, where N represents DNA base A, G, or C, and Ndeam is the respective deamination product hX, X, or U. The surrounding DNA strand is simplified and drawn in blue, except for the newly inserted base, which is colored in red to aid in visualization. Enzymes involved in a reaction are shown above or below the reaction arrow in bolded italics. For simplicity, protons are not shown.(TIF)Click here for additional data file.Figure S3Determination of extracellular parameter values. Shown are the experimentally-measured and predicted (A) NO• concentration curves and (B) 10 h NO2− and NO3− concentrations following addition of 0.5 mM DPTA to cell-free media. Measured values are the mean of 3 independent experiments, with error bars (light green for NO• and black for NO2− and NO3−) representing the standard error of the mean. The extracellular parameters kNONOate (NO• donor dissociation), kLaNO• (NO• transfer to the gas phase), and kNO•-O2 (NO• autoxidation) were optimized to reproduce the experimentally-measured [NO•] curve and NO2− concentration at 10 h post-dose (when it was predicted that over 99% of the DPTA had dissociated). The red line in (B) depicts the NO3− assay limit of detection, where the asterisk (*) indicates that the measured NO3− concentration was not significantly different from the detection limit .(TIF)Click here for additional data file.Figure S4Comparison of model performance with previous NO• models. Shown is the NO• concentration  measured following addition of DPTA (0.5 mM) to a wild-type E. coli culture, along with the [NO•] curve predicted (dashed black line) by the present model (A), and the models of (B) Lim et al.(C) Lancaster (D) Nalwaya and Deen (TIF)Click here for additional data file.Figure S5Sensitivity analysis of uncertain model parameters under aerobic conditions.(A) Effect of varying uncertain parameters on NO• dynamics. Each uncertain parameter was varied among 5 equally-spaced values spanning its range ((B) For comparison, the NO• concentration profiles obtained when varying the maximum Hmp expression rate parameter  are shown (red lines).ts range , and the(TIF)Click here for additional data file.Figure S6Effect of ΔnorV on NO• dynamics in aerobic E. coli cultures. Shown are the measured and predicted NO• concentrations measured following the addition of 0.5 mM DPTA to (A) cell-free growth media, (B) wild-type E. coli culture, and (C) ΔnorV E. coli culture. Error bars  represent the standard error of the mean for 3 independent experiments. We note that these measurements were obtained with a separate ISO-NOP NO• sensor than the one used to generate (TIF)Click here for additional data file.Figure S7Determination of PAPA NO• release rate. Shown is the NO• concentration following addition of 0.5 mM PAPA to MOPS glucose media measured experimentally (solid green line) or predicted by the model (dashed black line) after optimizing the NO• donor dissociation rate parameter, kNONOate, to reproduce experimental [NO•] curve. Experimental measurements were performed under identical conditions to those of the NO• consumption assays .n assays , except (TIF)Click here for additional data file.Figure S82 concentration during microaerobic NO• consumption assays.Measured O Shown are the dissolved O2 concentration profiles of the culture (average of at least 3 independent experiments for each curve) measured following addition of DPTA to wild-type, ΔnorV, or Δhmp E. coli cultures during N2 bubbling, which remained constant at approximately 35 µM (∼19% air saturation). Error bars  represent the standard error of the mean. For comparison, the dashed black line depicts the O2 concentration of air-saturated growth media at 37°C in the absence of N2 bubbling (185 µM).(TIF)Click here for additional data file.Figure S9Parametric analysis under microaerobic conditions. Fold increase in the SSR between the experimentally measured and predicted NO• concentration  under microaerobic (35 µM O2) conditions is plotted as a function of parameter value for the 8 of 42 optimized parameters (rameters  exhibiti(TIF)Click here for additional data file.Figure S10Effect of individual parameter variation on the predicted NO• distribution under aerobic conditions. Shown are 175 vertical bars representing the predicted final (t→∞) distributions of (A) intracellular and (B) total NO• consumption after treatment with 0.5 mM DPTA for each parameter set during parametric analysis. Parameter sets were generated by varying each of the 35 uncertain parameters found to have negligible influence on the NO• concentration profile among 5 logarithmically-spaced values spanning their allowed range Click here for additional data file.Figure S11Effect of combinatorial parameter variation on the predicted NO• distribution under aerobic conditions. Shown are 100,000 vertical bars representing the predicted final (t→∞) distributions of (A) intracellular and (B) total NO• consumption after treatment with 0.5 mM DPTA calculated for each parameter set during randomized combinatorial parametric analysis. The plots are similar to those in (TIF)Click here for additional data file.Figure S122 volumetric mass transfer coefficient (Measurement of OkLaO2).(A) The concentration of O2 was measured in stirred MOPS glucose media at 37°C in contact with air after degassing with N2. (B) The O2 concentration data was re-plotted as ln([O2]sat – [O2]) vs. time (black line) to calculate the value of kLaO2  corresponds to the kLaO2.(TIF)Click here for additional data file.Figure S132 concentration prior to NONOate addition.Measurement of O The dissolved O2 concentration in an aerobic wild-type E. coli culture was measured during the period of growth prior to addition of NONOate. Conditions were identical to those used for the aerobic NO• consumption assays Click here for additional data file.Figure S14Estimation of the rate constant governing cysteine-mediated removal of protein-bound DNIC. Experimental EPR data tracking the cysteine-mediated removal of DNICs from proteins was obtained from literature kDNIC-rem value is shown (dashed red line) (see (TIF)Click here for additional data file.Table S1Biochemical species included in the model. All metabolites, enzymes, and biomolecules are listed with their initial concentrations.(XLSX)Click here for additional data file.Table S2Model reactions governed by elementary-type rate expressions. Reactions are listed along with the value of their associated rate constant.(XLSX)Click here for additional data file.Table S3Model reactions with complex rate expressions. Reactions are listed with their associated rate expression and rate constants. Reaction numbering is continued from (PDF)Click here for additional data file.Table S4Uncertain model parameters. “Reaction #s” are the numbers of the reactions governed by the rate parameter, and correspond to the numbering in E. coli treated with DPTA under aerobic conditions. Confidence intervals (C.I.) are provided for parameters that were informed by the optimization, and were calculated as the range of optimal parameter values obtained for the top 10% of optimization outcomes .(PDF)Click here for additional data file.Table S5Minimum biochemical reaction network necessary to simulate NO• dynamics in aerobic, wild-type E. coli cultures.(A) Reactions. Reaction numbers correspond to those used in (B) Biochemical Species. Species numbers and initial concentrations (M) correspond to those reported in (C) Kinetic parameters. “Reaction #s” are the numbers of the reactions governed by the rate parameter, and correspond to the numbering in (PDF)Click here for additional data file.Table S6Experimentally-accessible model parameters varied during parametric analysis. “Reaction #s” are the numbers of the reactions governed by the rate parameter, and correspond to the numbering in (PDF)Click here for additional data file.Table S7Model parameters optimized for microaerobic conditions. “Reaction #s” are the numbers of the reactions governed by the rate parameter, and correspond to the numbering in E. coli treated with DPTA under microaerobic (35 µM O2) conditions. Confidence intervals (C.I.) are provided for parameters that were informed by the optimization, and were calculated as the range of optimal parameter values obtained for the top 10% of optimization outcomes .(PDF)Click here for additional data file.Text S1Additional details on model development and analysis. Detailed model description, parametric analysis of model parameters with uncertain values, measurement of extracellular NO• kinetic parameters, measurement of O2 volumetric mass transfer coefficient (kLaO2), determination of O2 concentration prior to NO• stress, Hmp reaction mechanism and kinetics, O2-mediated inactivation of NorV, enzyme expression and degradation, and protein-bound DNIC removal and degradation.(PDF)Click here for additional data file.


Pichia pastoris. In particular, growth under mixed feed conditions appears to alleviate the metabolic burden related to stress responses triggered by protein overproduction and secretion. Yet, detailed analysis of the metabolome and fluxome under mixed carbon source metabolizing conditions are missing. To obtain a detailed flux distribution of central carbon metabolism, including the pentose phosphate pathway under methanol-glucose conditions, we have applied metabolomics and instationary 13C flux analysis in chemostat cultivations.Several studies have shown that the utilization of mixed carbon feeds instead of methanol as sole carbon source is beneficial for protein production with the methylotrophic yeast 13C-based metabolic flux analysis using GC-MS and LC-MS measurements in time allowed for an accurate mapping of metabolic fluxes of glycolysis, pentose phosphate and methanol assimilation pathways. Compared to previous results from NMR-derived stationary state labelling data  more fluxes could be determined with higher accuracy. Furthermore, using a thermodynamic metabolic network analysis the metabolite measurements and metabolic flux directions were validated. Notably, the concentration of several metabolites of the upper glycolysis and pentose phosphate pathway increased under glucose-methanol feeding compared to the reference glucose conditions, indicating a shift in the thermodynamic driving forces. Conversely, the extracellular concentrations of all measured metabolites were lower compared with the corresponding exometabolome of glucose-grown P. pastoris cells.Instationary 13C flux analysis resulted in fluxes comparable to previously obtained from NMR datasets of proteinogenic amino acids, but allowed several additional insights. Specifically, i) in vivo metabolic flux estimations were expanded to a larger metabolic network e.g. by including trehalose recycling, which accounted for about 1.5% of the glucose uptake rate; ii) the reversibility of glycolytic/gluconeogenesis, TCA cycle and pentose phosphate pathways reactions was estimated, revealing a significant gluconeogenic flux from the dihydroxyacetone phosphate/glyceraldehydes phosphate pool to glucose-6P. The origin of this finding could be carbon recycling from the methanol assimilatory pathway to the pentose phosphate pool. Additionally, high exchange fluxes of oxaloacetate with aspartate as well as malate indicated amino acid pool buffering and the activity of the malate/Asp shuttle; iii) the ratio of methanol oxidation vs utilization appeared to be lower (54 vs 79% assimilated methanol directly oxidized to CO2).The instationary 13C-based metabolic flux analysis to P. pastoris provides an experimental framework with improved capabilities to explore the regulation of the carbon and energy metabolism of this yeast, particularly for the case of methanol and multicarbon source metabolism.In summary, the application of instationary  Pichia pastoris has become an important yeast cell factory platform for the production of recombinant proteins [P. pastoris system is the use of the strong AOX1 promoter from the alcohol oxidase 1. The conceptual basis for this expression system stems from the observation that some of the enzymes required for methanol metabolism are present at substantial levels only when cells are grown on methanol [proteins -3 and haproteins ,5. Moreoproteins -11 has iproteins , as wellmethanol ,14.P. pastoris based bioprocesses [P. pastoris) and fungi [Mixed-carbon substrate feeding strategies  have been extensively investigated for rocesses . Such strocesses -19. In fnd fungi -22. Most13C-based metabolic flux analysis has become a highly relevant tool for systems biology of microbial metabolism. Usually, 13C flux analysis relies on the detection of 13C patterns of proteinogenic amino acids using NMR or GC-MS. This approach requires long labelling phases as isotopic steady-state is required. Only then the enrichment of carbon backbones of key precursor metabolites is also present in the amino acids of the cell protein [ protein -26.P. pastoris cells growing on glucose [The direct measurement of isotopic enrichments of intracellular primary metabolites allows for shorter labelling experiments and additionally more information, and consequently a more accurate estimation of fluxes, including fluxes beyond central carbon metabolism ,28. Howe glucose , opening13C-based flux analysis methods. Currently, the approach is mostly used to determine steady-state fluxes in microbes grown on single-carbon substrates, typically glucose. Under single-carbon conditions, different approaches have been compared [13C quantification techniques and mathematical formalisms may generate more accurate metabolic phenotype descriptions [The use of more than one carbon source is also interesting in the context of compared . For co-riptions .P. pastoris growing on glucose-methanol mixtures using 13C-labelling patterns of proteinogenic amino acids (measured by NMR) as constraints [Recently, we extended the classic formalism for flux analysis of straints . Neverth13C-labelling information from primary metabolism has been used for the first time to estimate flux patterns of yeast cells growing on glucose-methanol substrate mixtures. Compared to previous studies [13C-MFA based on the MS dataset allowed to validate the existing NMR-based methodological development for MFA.In addition,  studies , we coulBased on the obtained results, the cofactor balances were studied and novel hypotheses for the mixed substrate condition are derived.P. pastoris X-33 (Invitrogen) derived strain harbouring pGAPαA (Invitrogen) as a mock plasmid [A recombinant  plasmid  was used4)2HPO4, 0.5 g/l MgSO4.7H2O, 1.5 g/l KH2PO4, 0.02 g/l CaCl2 · 2H2O, 5 ml/l trace salt solution, 2 ml/l Biotin solution (0.2 g/l). The composition of the chemostat medium was 7.04 g/l Glucose monohydrate, 1.6 g/l Methanol, 0.915 g/l citric acid, 2 g/l (NH4)2 HPO4, 0.3 g/l MgSO4.7H2O, 1.4 g/l KH2PO4, 0.01 g/l CaCl2 · 2H2O, 0.5 ml/l trace salt solution, 0.3 ml/l biotin (0.2 g/l). The composition of the trace salts solution was the same as described previously [Duplicate chemostat cultivations were performed in a 2-l bioreactor  with a working volume of 1 l, using the Sartorious Biostat B + controller. The culture media were the same as described in . In parteviously .2 profile, approximately 24 h after inoculation), the feed was switched on. Cells were growing under carbon limited conditions at a dilution rate of 0.09 h-1. The aeration rate was set to 1 vvm, controlled by mass flow meters . The pO2 was maintained above 40% ensuring fully aerobic conditions. The O2 and CO2 concentrations in the bioreactor off-gas were measured on-line using a combined paramagnetic/infrared analyser . Pressure, pH, stirring speed and temperature were maintained at 1.2 bars, pH 5 (with 20% v/v NH3), 490 rpm and 25°C, respectively.A one litre shake flask containing 200 ml of YPD medium  was inoculated with 1.5 ml of cryostock. The culture was grown for approximately 20–24 h at 30°C (shaking at 250 rpm), and used to inoculate the bioreactor. After termination of the batch phase  were pipetted on top of the filter cell cake. The 13C cell extract contained all relevant metabolites as U-13C-labeled isotopes and was obtained from a S. cerevisiae fed-batch culture grown on 100% U-13C-labelled glucose and U-13C ethanol [Samples for intracellular metabolites and amino acid concentration measurements were taken one hour before the switch to the labelled feed using a dedicated rapid-sampling setup . For que glucose  was used pastoris – theref pastoris. Since n pastoris was used pastoris,37, 120  ethanol .12C samples compared to 13C-labelled cell extract were used to confirm the metabolite fragments. The obtained mass isotopomer distributions were corrected for derivatization-based as well as non-carbon isotope mass-shifts using the MS correction tool [The metabolite extraction was performed with 75% (v/v) aqueous ethanol at 95°C. Concentrations were measured from two independent chemostat experiments in triplicate. The labelling enrichment was measured from one wash-in experiment by sampling at 20 time-points. The sampling times were selected based on the theoretical calculations by Nöh and co-workers , exponenion tool .13C-based metabolic flux analyses was derived from the metabolic model described in [P. pastoris. As discussed in the Results section, this initial model was further extended to include trehalose metabolism and the pyruvate dehydrogenase bypass reactions, as well as reversible reactions for Ala, Asp and Glu synthesis. Additionally, an alternative stoichiometry of the pentose phosphate pathway (PPP) was included to evaluate the impact of the mechanisms proposed by Kleijn [The metabolic network used for ribed in  for P. py Kleijn . BecauseThe expanded metabolic model established in this study contains 37 metabolites and 79 metabolic reactions ,  the measured substrates and products uptake/secretion rates (three fluxes),P. pastoris biomass and growth rate [2) a series of biomass synthesis fluxes which were determined from the composition of the wth rate  (nine fl3) a set of fluxes that have symmetrical products ) – a split of 1:1 for each form of the product was applied,4) one constraint flux (emp11C = emp11D) for an unknown unlabelled pyruvate source (and sink). Source and sink were set equal to maintain the carbon balance.Thus a total of 24 metabolic fluxes are required to solve the complete flux distribution. The mass isotopomer measurements, used for parameter estimation, are presented in Figure For the simulation of the labelling enrichments, the instationary approach using the cumomer concept  was applThe parameter estimation routine implemented in gPROMS is based on maximum likelihood . The accuracy of the measurements was described by a constant relative variance, For mass isotopomer measurements a constant relative variance of 2% was used (based on previous experience).χ2 at a 95% confidence level for the corresponding degrees of freedom. The degrees of freedom were calculated as the total number of experimental points  minus the number of parameters (34 in the expanded model). As a result of the fitting gPROMS provides the determined parameters together with the standard deviations and 95% confidence intervals .For all results presented in this work a flux fit was considered acceptable when the obtained minimal weighted residual was below the CDW), different values of cell volume were tested due to the lack of information of its real value for P. pastoris in the experimental conditions tested. Specifically, a range of cell volumes were tested, based on reported data for S. cerevisiae, ranging from 1.4 to 2.0 ml/gCDW[CDW to perform all NET analysis. Cytosol was the only cellular compartment considered in this analysis, as no information on the specific volumes of the different compartments was available. Thus, the metabolic pathways included in the NET analysis and the intracellular metabolites were considered to be located in this compartment, including the methanol utilization reactions.The consistency of the measured intracellular metabolite concentrations was verified with a method that is based on the second law of thermodynamics, A reaction can only run in the direction of a negative change of the Gibbs free energy . This ne0 ml/gCDW. HoweverThe feasible ranges of the quantified intracellular metabolites were calculated using the respective experimental mean and standard deviation. The lower and upper limits were defined according to a Student’s –T distribution with a confidence interval of 0.80. In addition, for the unmeasured metabolites ranges were defined Figure a. From tP. pastoris cytosol was 0.15 M [P. pastoris cytosol . This value is slightly higher than that reported for S. cerevisiae[+/NADH minimum ratio, as expected (see Results section).The assumed ionic strength of the s 0.15 M , while terevisiae. NeverthBiomass Analyses, The cell concentration was monitored by measuring the optical density of cultures at 600 nm (OD600). For cell dry weight (CDW) measurement, 5 ml of culture broth was filtered using pre-weighed dried glass fibre filters (Millipore). Cells were washed twice using the same volume of distilled water and dried overnight at 100°C. Triplicate samples (5 ml) were taken for all optical density and cell dry weight measurements. The macromolecular and elemental composition, used to derive the biomass equation for 13C-constrained metabolic flux analysis was previously obtained in cultures growing in analogous conditions as previously reported [reported . In all reported -50, undeQuantification of extracellular metabolites, Triplicate samples (5 ml) for extracellular metabolite analyses were centrifuged at 6,000 rpm for 3 min in a micro centrifuge  to remove the cells, and subsequently filtered through 0.45 mm-filters (Millipore type HAWP). Glucose, methanol, and other extracellular compounds were analyzed by HPLC analysis using an ionic exchange column, . The mobile phase was 6 mM sulphuric acid.P. pastoris cells were grown in aerobic, glucose-methanol limited chemostat cultures at a dilution rate of 0.09 h-1, resulting in comparable conditions to our previous study [us study , except P. pastoris cells grown on glucose as sole carbon source at the same growth rate [In general, the intracellular levels of central carbon metabolites and free amino acids Figures  were comwth rate . DiffereTricarboxylic acid (TCA) cycle intermediates and several metabolites from the pentose phosphate pathway (PPP) -Xul5P, erythrose-4-P (E4P) and sedoheptulose-7-P (Sed7P)- were higher under glucose-methanol conditions, indicating a shift in the thermodynamic driving forces.As explained above, to validate the metabolite measurements, their thermodynamic consistency was checked using the Network-Embbeded Thermodynamic (NET) analysis described by ,45, whicS. cerevisiae[P. pastoris[S. cerevisiae[Remarkably, concentrations of metabolic intermediates resulted to be thermodynamically consistent with the flux directionalities of the metabolic network reactions, with the exception of the metabolites involved in the non-oxidative branch of the pentose phosphate pathway Figure . Thermoderevisiae,52 and P pastoris growing The metabolite mass action ratios (MAR) of other reactions included in the central carbon metabolism and expected to operate close to equilibrium  were calP. pastoris growing on the mixed carbon source were compared with those previously measured for the same strain growing with glucose as a sole carbon source. Although amino acids pools sizes show the same overall profile found in glucose-grown cells, generally lower amino acid pools sizes were found in cells grown on glucose-methanol. Nevertheless, such differences were only statistically significant  for Tyr, Met, His, and Glu.The free amino acid pools measured for P. pastoris cells growing under analogous conditions but using glucose as sole carbon source. Exceptions are the residual glucose and, to a lesser extent, trehalose, which were significantly higher in the glucose-methanol cultures.Strikingly, the extracellular concentrations of all measured metabolites were very low compared with the corresponding exometabolome of The dynamics of the measured mass isotopomer distributions are shown in Figure 13C enrichment in Glc6P is higher than expected from the direct precursor, extracellular glucose. Based on the feed composition  the C3-C6 Glc6P fragment should be unlabelled (80%) resp. fully labelled (20%). Besides the m + 0 fraction, also the m + 1 (m + 2 and m + 3) fraction of this fragment shows unexpected values, especially by reaching a value of nearly 14%  at isotopic steady state. The origin of the masses +1, +2 and +3 is 13C carbon from methanol fixation. Especially DHAP shows a fast increase of the m + 1 mass fraction that via GA3P and the reversible pentose-phosphate pathway enters to Fru6P and finally Glc6P (reversible PGI reaction). Alternative to this route, the m + 1 (m + 2) can originate from metabolic activity of fructose-bisphosphatealdolase together with FBPase that can ‘re-scramble’ the C1 labelling into a C6 labelling of FBP (C1 labeled DAHP - > C3 labeled GA3P - > C1 or C6 labeled FBP). FBPase further carries this pattern to Fru6P [The measurements of Glc6P are based on a fragment containing carbon atoms C3-C6. Two observations need to be highlighted for Glc6P, In contrast to other experimental conditions, the to Fru6P . Fru6P iD = 0.09 h-1), indicating a simultaneous synthesis and degradation of trehalose.Although the labelling dynamics of Glc6P are fast, an exchange with carbohydrate storage pools  needs to be introduced - Trehalose show a clear enrichment profile, that is faster compared to a pure synthesis flux  together with additional, yet unknown exchange fluxes or pyruvate bypass reactions in the mitochondria. This is consistent with the finding that the other amino acids connected to the mitochondrial pyruvate node  show a slower enrichment than alanine and  pyruvate enrichments.CDW/h. Without this reaction, the measured enrichment of pyruvate could not be reproduced.Following the hypothesis of unknown exchange reactions, an unlabelled in-flux producing mitochondrial pyruvate was introduced together with a pyruvate efflux. Although this approach is not mechanistic, it allows to estimate the exchange with e.g. biomass components at this node . This unNote that this flux could also have an impact on the ATP balance, e.g. amino acid synthesis and degradation like the ones from the valine family would represent an ATP consuming cycle.The reproduction of the measured enrichments in the TCA cycle were improved by including:1) Reactions for the pyruvate dehydrogenase (PDH) bypass (emp9 and emp12),2) Exchange fluxes α–ketoglutarate ↔ Glu (aa_glu) and oxaloacetate ↔ Asp (aa_asp), that reflect a buffer capacity of amino-acid pools  and are maybe also involved in the activity of the Malate/Aspartate redox shuttle ,4 formation and could reflect the activity of transamination reactions and cell protein turnover. This flux is not well determined as there is also a parallel route in the TCA cycle (tca7 and tca6).3) Asp ammonia lyase reaction which converts Asp into fumarate (tca8), resulting in NHAlthough the flux through the PDH bypass was not considered in the initial metabolic model , its acS. cerevisiae does not synthesise carnitine de novo, which is essential for carnitine acetyltransferase-mediated transport of cytosolic Acetyl-CoA (ACCoA) to the mitochondria. In contrast, a complete carnitine biosynthesis pathway has been characterised in Candida albicans, and the corresponding 4 genes have been identified [P. pastoris genome contains putative homologues to these genes [entified . Interesse genes ,59 and pse genes .13C-labelling experiments in chemostat cultivations of S. cerevisiae[The TCA cycle metabolites do show a more pronounced delay to reach isotopic steady state Figure . Besideserevisiae.13C-labelling transients between each of their corresponding substrate and product, suggesting high exchange fluxes. As discussed above, Fru6P and FBP labelling patterns suggested that both phosphofructokinase and fructose-1,6-bisphosphatase reactions were active in glucose-methanol grown cells. Therefore, the observed exchange reactions were also incorporated into the metabolic network model.Several glycolytic, non-oxidative pentose phosphate pathway and TCA cycle reactions, known to be reversible under physiological conditions, showed basically identical 2 criteria as described in the material and methods section. More specifically, a total of 1600 experimental measurements (80 mass isotopomers * 20 time points) were available for the determination of 34 parameters, (24 fluxes and 10 concentrations). This results in 1566 degrees of freedom for the statistical χ2 test. The weighted residual of the best fit of the extended model was 1508.54 which is in the bounds of the chi-square distribution , indicating an acceptable flux fitting.To analyse the impact of the network extensions and reversibility assumptions  for the determination of 27 parameters, (17 fluxes and 10 unmeasured concentrations).In the case of the previous model, a weighted residual of 5540.2 was obtained for the best fit, which is above a 95% confidence level χP. pastoris fed with mixed substrates. In the following steps, 13C-based MFA was performed using the LC-/GC-MS datasets and the expanded stoichiometric model , the experimental results do only reflect whole cell amounts and labelling enrichments. Following our primary focus of determining fluxes of glycolysis, pentose-phosphate pathway and methanol assimilation we did not include complex, assumption based, approaches to fully include compartmentation. This simplification does not bias the estimation of fluxes in glycolysis, PPP or methanol utilization. Notably, quantification of labelling patterns of xylulose-5-P, dihydroxyacetone and glyceraldeyde phosphate, which are directly linked to methanol metabolism, could be measured by first time.The simulation results for the two different models discussed previously, shown in Figure 13C-labelling patterns of proteinogenic amino acids  A major part of Glc6P is entering the oxidative branch of the PPP ;2 - lower than that calculated in our previous study (79%).2) Most assimilated methanol (54%) is directly oxidized to CO3) High exchange fluxes for oxaloacetate, malate, Asp and Glu, indicating amino acid pool buffering and the activity of a Malate/Aspartate shuttle (not determined previously).4) Trehalose recycling accounts for about 1.5% of the glucose uptake rate (not determined previously).MetOH). This rate was lower in the cultures performed in the present study compared with those from [CDW/h vs -1.15±0.06 mmol/gCDW/h, respectively), resulting in a lower qMetOH/qGluc ratio. Since immediate oxidation of methanol to CO2 has also been considered a “detoxification pathway” to eliminate formaldehyde and formate, lower methanol consumption rates could result in lower relative activity of the dissimilatory pathway [The difference observed for methanol redistribution could be explained by the observed difference between the two experiments with respect to the specific methanol consumption rates , which was not possible to discriminate using steady-state flux analysis based on Importantly, MS-based flux analysis provided novel insights regarding parallel resp. bidirectional reactions. In particular a gluconeogenic flux from dihydroxyacetone phosphate (DHAP) and glyceraldehyde phosphate (GA3P) back to Glc6P was observed based on the MS transient data. Moreover, such gluconeogenic flux resulted to be thermodynamically consistent with the measured glycolytic pool sizes Figure a and 2b.Also, by combining the metabolomic and MS-based flux analysis, we could more precisely determine the flux directionalities/reversibilities and stoichiometry in the non-oxidative branch of the PPP, which have been proven difficult to estimate accurately in previous studies on methanol co-assimilation . Fluxes 13C-based flux estimation , the co-factor balances are reconstructed using a stoichiometric model including the co-factors ATP, NADH, NADPH.Based on the vs 0.85±0.04 mmol/gCDW/h, respectively). In principle, since the PPP is the main pathway for cytosolic NADPH formation, the flux through the oxidative branch of the PPP is generally directly correlated to the biosynthetic demand for NADPH [CDW/h. Although not statistically significant, this value was slightly lower than the total generated NADPH. In contrast, the NADPH biosynthetic demand for cells grown on glucose as sole carbon source exactly matched with NADPH generation. Interestingly, some Crabtree negative yeasts appear to have alternative mechanisms involved in the reoxidation of the NADPH produced in the PPP, e.g. by mitochondrial external alternative dehydrogenases that use NADPH [Pichia angusta batch cultures growing on glucose, about 40% of the NADPH was produced in the PPP in excess of the biomass synthesis requirements, suggesting the presence of a yet unidentified NADPH reoxidation mechanism in this yeast [P. pastoris cells co-assimilating methanol e.g. via the observed exchange fluxes between α-ketoglutarate and glutamate. Another potential sink for such excess of NADPH generated maybe related with the NADPH requirements for glutathione regeneration a key metabolite involved in the direct oxidation of methanol to CO2.As previously observed , methanoor NADPH . Howeveror NADPH . This suse NADPH . Also, iis yeast . It is tAdditionally, protein turnover might have an impact here. The flux estimated for Asp lyase could indicate protein turnover and in its consequence NADPH consumption.CDW/h, i.e. within the range of the values previously calculated from the 13C-NMR based metabolic flux analysis [O2 - no significant imbalance that would suggest major NADPH dehydrogenase or NADPH → NADH transhydrogenase activities.The rate of NADH regeneration was calculated from the reaction network stoichometry and calculated net fluxes as 4.37 ± 3.62 mmol/ganalysis . Assumin+/NADH minimal ratio calculated on the basis of the thermodynamic analysis of the metabolome data using the anNET software was about 1300 (assuming an intracellular pH of 7.2), which is over 13-fold higher than the one calculated for P. pastoris growing on glucose under equivalent conditions [Strikingly, the NADnditions , . Both terms can be calculated from the reaction stoichiometry and the net flux data. As a result, the fraction of ATP generated through respiration was about 75% of the total ATP generatedThe metabolic flux distributions calculated above allow to estimate the amounts of ATP generated or consumed either for growth or maintenance. Thus the total specific rate of ATP being generated by CDW/h. The efficiency of oxidative phosphorylation, i.e. the P/O ratio, was defined as 1.48 mol ATP/molO based on previous studies in yeast [CDW/h for P. pastoris growing on glucose and glycerol-methanol mixed media, respectively. These data can be compared with similar estimations from literature. Recent P. pastoris calculations based on a genome-scale model, [CDW was calculated for glucose and glycerol and a significantly higher one for methanol (ca. 150 mmolATP/gCDW). Mixtures of glycerol with methanol showed intermediate values. Based on these calculations, the specific ATP generation rates for P. pastoris cells growing in a chemostat at a D of 0.1 h-1 can be calculated to be in the range between 7 and 15 mmolATP/gCDW/h for glucose and methanol respectively, a range that includes the value of 8.6 mmolATP/gCDW/h calculated for the present case. Therefore, from a general point of view the above calculated energetic features of P. pastoris grown in chemostats using different combinations of glucose/methanol as carbon source are in agreement with previous estimates for yeasts.The maintenance requirements (non growth associated maintenance energy) was estimated to be 2.7 ± 3.6 mmolATP/gin yeast . Considee model,  reported13C-MFA approach has been applied for the first time to P. pastoris co-assimilating glucose and methanol. Most notably, the flux distributions obtained with this methodology were coherent with those previously determined using 13C-labelling data of proteinogenic amino acids [13C-MFA methodology, the in vivo metabolic flux estimations were expanded to a larger metabolic network and, reversibility of glycolytic/gluconeogenesis, TCA cycle and non-oxidative PPP reactions were determined. Besides, this approach allowed an improved accuracy for the calculation of fluxes through methanol assimilating pathways, as labelling patterns of some metabolite intermediates of these pathways  could be directly accessed.In this study, an MS-based INST no acids . By usin13C-labelling information from metabolites involved in compartment-specific reactions (used as “sensor reactions”) should provide improved accuracy to the current INST 13C-MFA approach, as well as providing new insights on the redox and energy metabolism. Especially the pyruvate node remains challenging and requires for an yet unknown exchange flux. This missing knowledge hampers also the precise reproduction of the TCA cycle derived amino acids, aspartate and glutamate at later time-points. Nevertheless, this does not influence the flux estimation of glycolysis and pentose-phosphate pathway because there is no exchange with these pools.Combination of GC-MS and NMR datasets and additional Combined analysis of metabolome and fluxome data showed their thermodynamic consistency, further validating the obtained results. The estimated flux directionalities were thermodynamically consistent when an alternative topology for the non-oxidative branch of the PPP  was used.15 N could be applied to further investigate the cellular physiology under these conditions.The surplus of NADPH generation, together with the gap in the NADH balance as well as increased ATP requirements for maintenance under glucose-methanol conditions could be an indication of increased protein turnover. Specific experiments, e.g. using MetabolitesαKG: α-ketoglutarate; GA3P: Glyceraldehyde-3-phosphate; PG2: 2-phosphoglycerate; PG3: 3-phosphoglycerate; GA3Pper: Glyceraldehyde-3-phosphate peroxisome pool; DHA: Dihydroxyacetone; DHAP: Dihydroxyacetone phosphate; E4P: Eritrose-4-phosphate; Rib5P: Ribose-5-phosphate; Rul5P: Ribulose-5-phosphate; Xul5P: Xylulose-5-phosphate; Man6P: Manose-6-phosphate; Fru6P: Fructose-6-phosphate; Glc6P: Glucose-6-phosphate; Sed7P: Sedoheptulose-7-phosphate; FBP: Fructose-1,6-biphosphate; T6P: Trehalose-6-phosphate; Treh: Trehalose; Pyr: Pyruvate; Glc: Glucose; Pep: Phosphoenolpyruvate; MAL: Malate; SUCC: Succinate; CIT: Citrate; ICIT: Isocitrate; FUM: Fumarate; ACCoA: Acetyl coenzyme; Glux: Glucose intra/extra; FullyGlu: Fully labelled Glucose; CGlu: First carbon labelled Glucose; Metoh: Methanol; MetohL: Labelled Methanol; Xbio: Biomass formation; NPyr: Not labelled Pyruvate; Pyrt: Total Pyruvate pool; Form: Formaldehyde; FOR: Formate; OAA: Oxaloacetate; ACALD: Acetalehyde; PRPP: Phosphoribosyl pirophosphate; MTHF: Methylenetetrahydrofolate; THF: Tetrahydrofolate; CHOR: Chorismate; Pi: Inorganic phosphate; PPi: Inorganic pyrophosphate; 13dpg: 1,3 Diphophoglycerate; G1P: Glucose 1-phosphate; Glyc3P: Glycerol 3-phosphate; SUCCoA: Succinyl coenzyme A; Kval: Ketovalerate; DHF: Dihydropholate.Othernd: not determined; sd: standard deviation.The authors declare that they have no competing interests.13C-labelling experiments, macroscopic data processing and metabolic flux analysis calculations. CS assisted in the bioreactor cultivations and the 13C extract preparation. MC assisted in the bioreactor cultivations and performed the thermodynamic analysis of metabolite datasets with the anNET programme. JJ together with AP, performed the concentration and 13C metabolite analyses. JJ, AW and JA extended the metabolic network, performed flux estimations and interpreted the results. PF, JA, JJH, WG participated in the overall conceptual and experimental design, interpretation of results and drafted the manuscript. All authors read and approved the final manuscript.JJ performed bioreactor cultivations and Comparison of the ‘classical’ and the PPP stoichiometry proposed by Kleijn and co-workers [.-workers .Click here for fileMetabolic models of the central carbon metabolism of P. pastoris. (1.1) Reactions in the expanded stoichiometric model of the central carbon metabolism of P. pastoris, applied in the 13C-MFA. Note that CO2, O2 and cofactors were not used for flux balancing. (1.2) Reaction network used for anNET analysis. (1.3) Reaction- and atom transition network used in 13C flux analysis, following the notation of [ation of .Click here for fileMeasured mass isotopomer fractions during the wash-in experiment.Click here for fileMeasured extra- and intracellular concentrations at steady-state (D = 0.09 h-1).Click here for fileTables of the all Intracellular concentrations and Gibbs energy in P. pastoris cells growing on glucose-methanol chemostat.Click here for fileResults from the INST 13C flux analysis. Estimated intracellular fluxes under methanol-glucose condition with the calculated standard deviations. The network description can be found in Additional file 2 (1.1).Click here for file