K-ras transformed cell line we experimentally assessed glutamine-induced metabolic changes. We validated computational results through an extension of Flux Balance Analysis that allows prediction of metabolite variations. Taken together these findings offer new understanding of the logic of the metabolic reprogramming that underlies cancer cell growth.Cancer cells share several metabolic traits, including aerobic production of lactate from glucose (Warburg effect), extensive glutamine utilization and impaired mitochondrial electron flow. It is still unclear how these metabolic rearrangements, which may involve different molecular events in different cells, contribute to a selective advantage for cancer cell proliferation. To ascertain which metabolic pathways are used to convert glucose and glutamine to balanced energy and biomass production, we performed systematic constraint-based simulations of a model of human central metabolism. Sampling of the feasible flux space allowed us to obtain a large number of randomly mutated cells simulated at different glutamine and glucose uptake rates. We observed that, in the limited subset of proliferating cells, most displayed fermentation of glucose to lactate in the presence of oxygen. At high utilization rates of glutamine, oxidative utilization of glucose was decreased, while the production of lactate from glutamine was enhanced. This emergent phenotype was observed only when the available carbon exceeded the amount that could be fully oxidized by the available oxygen. Under the latter conditions, standard Flux Balance Analysis indicated that: this metabolic pattern is optimal to maximize biomass and ATP production; it requires the activity of a branched TCA cycle, in which glutamine-dependent reductive carboxylation cooperates to the production of lipids and proteins; it is sustained by a variety of redox-controlled metabolic reactions. In a  in vitro—utilization of glutamine by reductive carboxylation and conversion of glucose and glutamine to lactate confer advantage for biomass production. Redox homeostasis can be maintained through the use of different alternative pathways. In conclusion, this paper offers a logic interpretation to the link between metabolic rewiring and enhanced proliferation, which may offer new approaches to targeted drug discovery and utilization.Hallmarks describing common key events in initiation, maintenance and progression of cancer have been identified. One hallmark deals with rewiring of metabolic reactions required to sustain enhanced cell proliferation. The availability of molecular, mechanistic models of cancer hallmarks will mightily improve optimized personal treatment and new drug discovery. Metabolism is the only hallmark for which it is currently possible to derive large scale mathematical models, which have predictive ability. In this paper, we exploit a constraint-based model of the core metabolism required for biomass conversion of the most relevant nutrients—glucose and glutamine—to clarify the logic of control of cancer metabolism. We newly report that, when available oxygen is not sufficient to fully oxidize available glucose and glutamine carbons–a situation compatible with that observed under normal oxygen conditions in human and in cancer cells growing  Cancer is a network disease  resultinThis property requires an extensive reorganization of metabolic fluxes –9, charaIn order to integrate sets of experimental data and to formulate new testable hypotheses, complex biological systems–such as human metabolism that involves thousands of metabolites and reactions—need to be formally described by mathematical models. In this regard, constraint-based modeling and in particular Flux Balance Analysis (FBA), which is based on the definition and manipulation of stoichiometric matrices and was originally developed for the optimization of microbial strains, is rapidly gaining popularity within life sciences . FBA allFBA may be applied to genome-wide metabolic networks , 24, whiin-vivo nutrient utilization rates. Moreover, when the aim is to investigate the plethora of admissible wirings, rather than to determine optimality, their computation becomes demanding and may give origin to a combinatorial explosion of different flux patterns, which fuels mere details while masking the major regulatory connections. Manually curated core models including hundreds of metabolites, selected for the specific purpose of the analysis, help to overcome the problems above [Being highly detailed, genome-wide models require many assumptions on ms above , 30. We K-ras transformed fibroblasts, grown in high glucose together with either low or high glutamine availability.In this study, we aim to identify the regulatory principles that link the utilization of glucose and glutamine in originating the Warburg effect, and ultimately in driving cancer cell growth. We manually reconstructed a core stoichiometric model designed to evaluate the contribution of glucose and glutamine to enhanced growth, hence the name ENGRO1 (ENhanced GROwth). By exploring the space of admissible wirings of the ENGRO1 model, we newly identified and rationalized intense aerobic glycolysis and glutamine reductive carboxylation as the fittest emergent strategy that supports cancer cell growth under conditions reported to be generated by oncogenic activation: sustained glucose and glutamine uptake. This emergent phenotype is observed only when the available carbon exceeds the amount that could be fully oxidized by the available oxygen, a condition that is entirely physiological. We validated our predictions by analyzing the metabolic behavior of murine uptake flux or by specifying the maximal rate allowed for nutrient consumption reactions. We will refer to the latter case as a constraint on nutrient availability, bearing in mind that it should be interpreted as a constraint on intracellular rather than on extracellular nutrient availability, the relationship between the two being non-linear and controlled by complex signaling networks [In the context of FBA, nutritional conditions are simulated either by imposing a specific networks .in vivo is undetermined, we wanted to systematically evaluate the typical response of a human metabolic network to different boundary conditions. For the sake of feasibility, we limited our analysis to glucose and glutamine—the most abundant nutrients in plasma [Given that the actual consumption rate of each individual nutrient n plasma  as well The metabolic network ENGRO1, designed to evaluate the contribution of glucose and glutamine to biomass formation, was therefore manually reconstructed. The network includes the catabolic pathways of glucose and glutamine and the anabolic reactions necessary for the main building blocks of biomass: amino acids and fatty acids , together composing 80% of the dry cellular weight . We focuAlthough cancer cells proliferate under conditions that restrain growth of normal cells, their growth rate does not necessarily coincide with the global optimum: indeed, it has been argued that a 5% improvement in growth rate would suffice to provide a selective advance to cancer cells . We haveInstead of focusing on the optimal response to a nutrient change (standard FBA), we examined the typical properties of the ensemble of theoretical wirings whose generic properties statistically match those of cancer cells, an approach similar to the one first applied to the study of gene regulatory networks . To effein vivo and in vitro are largely variable and mostly unknown, with special regard to oxygen consumption rates, we simulated the response of 50,000 wirings to a modulation of either the glucose or glutamine uptake flux, while the maximal oxygen consumption rate  was kept constant across all the experiments.Because the precise boundary conditions of cancer cells in silico cells displayed considerable variability in flux patterns, Although the 50,000 Despite the high utilization of nutrients, ENGRO1 wirings on the average do not exhibit biomass production . Therefore, lacking a prerequisite for cell proliferation, these simulated cells would not be classified as tumorigenic . The disWe thus partitioned the total population into distinct sub-populations that respond differently to nutritional conditions. Based on the interest raised by aerobic production of lactate, a first filter was applied to investigate the mode of utilization of glutamine: the cyclic mode of TCA cycle was reduced by glutamine in 98% of cell types : the experimental concentration of these metabolites is indeed increased in low glutamine , but we failed to predict the slight increase in the level of serine. This minor inconsistency may derive from the fact that in our simulation we did not supply external serine.We did not predict ornithine and putrescine to be significantly changed because these metabolites display a large variability in our sample. Efflux of ornithine and putrescine are indeed energetically equivalent in ENGRO1 network (cofactors are not involved in the step from ornithine to putrescine). We did not predict glucose to be significantly changed, as experimentally detected.Hence, the extended computational analysis was able to capture with a good degree of accuracy how the levels of many metabolites respond to glutamine shortage, giving support to the reliability of the ENGRO1 model and of our ensemble approach. A similar pattern of response has been obtained by a biochemical interpretation of the experimental findings see .In the previous sections we used a random sampling approach coupled with parameter scan of glutamine and glucose uptake rates to highlight that in the presence of glutamine there is a trend  to increase the amount of glucose that is converted to lactate. After having validated most model predictions using a murine cancer cell line, in this and the following sections we use standard FBA to understand, from a theoretical point of view, if the preference for glutamine is related to ATP and/or biomass optimization and how this preference is affected by the boundary conditions, i.e. the relative availability of oxygen, glucose and glutamine.2GR) of at least 6  all extra glucose supplied will decrease the O2GR and will thus be fermented to lactate  value  value . Resultsy) value .Notably, although we simulated the modulation of oxygen consumption by altering the boundary on oxygen intracellular availability, comparable effects were observed when constraining the capacity of Complex I to carry flux, and thus to accept NADH electrons, to mimic mitochondrial dysfunction .Although cancer cells divert most—but not necessary all—glucose to lactate, to better understand the principles governing the utilization of glutamine carbon in cancer cells, we focused on the extreme condition identified above in which all glucose is preferentially redirected to lactate . Without loss of generality, we arbitrarily picked a critical oxygen boundary conditions. Notice that similar conclusions would be derived for different values of the ratio between glucose and glutamine consumption, by accordingly adjusting the utilization of oxygen .2GR. It can be observed that the TCA “cycle” works in a branched non-cyclic mode, in which the α-ketoglutarate (AKG) originating from glutamine  takes a reverse path to isocitrate and then fatty acid biosynthesis (for about 20%) and a clockwise path to malate (for about 80%) which is eventually converted to pyruvate and then lactate. Excess TCA intermediates not contributing to biomass (including part of the OAA derived from the synthesis of citrate that fuels fatty acid biosynthesis) are preferentially disposed via conversion to lactate. The pentose-phosphate pathway is not active, reflecting the fact that our model does not account for synthesis of nucleic acids, a small fraction of cellular biomass. The electron transport chain is nearly equally distributed between oxidation of FADH and NADH, which also generates hydrogen peroxide (H2O2). H2O2 is totally removed by the coordinated action of glutathione peroxidase and glutathione reductase, with NADPH serving as an electron donor, despite the possibility to remove H2O2 without energy costs via a demand reaction. Besides lactate, another major toxic product is excreted: the ammonia that is not used for protein synthesis is removed as such, without using the ATP-costly urea cycle.The overall flux pattern that maximizes growth, hereinafter referred to as branched TCA cycle even though TCA is not working as a cycle, is in line with literature reporting experimental findings. Conversion of most glucose to lactate in spite of oxygen availability has been observed in many cancer cell lines or tumors , 7, as wWe examined if the flux pattern in When enumerating optimal solutions, we found that 44 alternative metabolic paths, sharing the same boundary conditions, produce the same maximal growth rate. Remarkably, all of them follow the branched TCA cycle mode described above.It has been already reported that variability in the optimal solution space is captured by a small number of sub-networks constituted by reactions with variable flux . AccordiIt can be observed that the four sub-systems involve redox factors and may therefore influence one another . For insA role for redox control in CMR has been anticipated in . The preWe have shown that glutamine utilization makes aerobic glycolysis optimal for growth. Nevertheless, the results of our ensemble approach  indicateTo investigate this hypothesis, we compared the previously obtained flux distribution at critical oxygen that maximizes growth Figs  and 6A aWe wanted to verify that a cyclic TCA mode was still possible for ENGRO1 at critical oxygen, so we forced it by inhibiting lactate secretion . In thisNoteworthy, the preference for a branched TCA cycle is maintained when glutamine is the unique carbon source , even wh2 yield. The glutamine to lactate flux mode improves the ATP production over oxygen consumption ratio by 5% as compared to the glucose to CO2 mode. Glutamine to lactate coupled with glutamine driven fatty acids synthesis improves the biomass production rate by 5% with respect to glucose to CO2 and glucose driven fatty acids synthesis. The correlation between lactate secretion and the ATP cost to make biomass further supports this contention (Taken together these observations indicate that glutamine is the preferred precursor for biomass production because it optimizes the ATP/Ontention .The strength of this preference for glutamine seems to depend on the ATP/oxygen ratio (P/O) ratio for FADH and NADH, and thus on the fraction of the electrons flowing through Complex I that ends up in superoxide anion , as was In this work, we exploited a novel constraint-based approach, based on the systematic evaluation of the possible wirings of the metabolic network required for the formation of biomass from glucose and glutamine, under different nutritional conditions. The first discovery presented in this paper is the identification of boundary conditions that taken together promote the emergence of cancer metabolic rewiring.2 molecules per glucose molecule may be typical for cancer cells. Detailed calculations—based on oxygen consumption rates reported in [in vivo the oxygen to glucose ratio in the blood supply is at least 3 times less than the 6 required for complete respiration  all activities it does not depend upon.in silico flux distribution that sustains CMR. We were able to integrate and rationalize the role of the various pathways observed in independent studies on cancer metabolism, as follows:Following the agreement with a wealth of literature, as well as experimental validation, of main ENGRO1 model predictions, we analyzed the global Glutamine utilization follows a branched TCA cycle, which proceeds clockwise from glutamine/AKG to oxaloacetate and malate, or counter-clockwise from AKG to citrate, then to acetyl-CoA going to fatty acids plus oxaloacetate going to malate.Glucose is almost fully fermented to lactate even in the presence of oxygen.Glutamine is not completely respired, but it is rather converted to lactate or pyruvate.By exploiting FBA, we investigated the relationship between different flux modes and their associated growth capability. We discovered that CMR is characterized by the following novel design principles:A large number of different metabolic routes may generate a CMR, by differential use of redox potential, while fatty acid synthesis gains a significant role as an acceptor of electrons, mostly coming from the assimilation of glutamine.Glutamine utilization promotes aerobic glycolysis, making the latter advantageous for growth, because it makes it energetically more favorable. This effect is enhanced by Reactive Oxygen Species (ROS) production by Complex I, with a stricter preference for the use of glutamine as an anaplerotic precursor when ROS production increases.in silico at limiting oxygen is not simply the fermentation of spare glucose, but a competition for oxygen between glutamine and glucose. The limiting amount of oxygen is preferentially used for the oxidation of the NADH and FADH2 generated when glutamine is converted to building blocks and lactate. As all available glucose is converted to lactate, we put forward a novel interpretation to what is classically understood as the ‘Warburg effect’.Aerobic production of lactate from glucose does not utilize all chemical potential of its substrate, thus it is generally regarded as unfit. Our results indicate that this is not the case. The phenomenon we observed in vivo, if the tumor environment imposes different constraints. In particular, we showed that fermentation of glutamine to lactate  is able to sustain growth even when glutamine is the exclusive simulated carbon source, suggesting how WarburgQ cells would be able to evade therapies that target only glycolysis.As boundary conditions change, so do the flux distributions of virtual cells that allow–possibly sub-optimal—biomass accumulation under a variety of conditions, suggesting how cancer cells might be able to follow different metabolic routes In conclusion, our paper offers for the first time a “logic” to the central role of the metabolic hallmarks in cancer biology, logic that was envisioned in . As the p to produce ATP and a probability pROS = (1 − p) to produce ATP to NADH oxidation in the respiratory chain. Biomass formation is expressed in terms of ATP, non-essential amino acids and palmitate requirements. Thermodynamically infeasible loops were first identified with the algorithm presented in [Once the pathways to be included were selected, we checked that each reaction in the model was able to carry flux. We included a minimal set of exchange reactions. We avoided compartmentalization of metabolites, paying attention that this simplification would not affect the energetic requirements for biomass. We associated a probability ented in  and thenThe resulting ENGRO1 model includes 84 reactions and 67 metabolites belonging to the following pathways: glycolysis and lactic acid fermentation (10 reactions); TCA cycle (9 reactions); oxidative phosphorylation and mitochondrial ROS generation (2 reactions); glutamine reductive carboxylation (4 reactions); glutathione biosynthesis and oxidation (10 reactions); urea cycle (5 reactions); fatty acid synthesis (2 reactions); pentose phosphate pathway (5 reactions) and biosynthesis of the main non-essential amino acids (13 reactions). The complete network definition together with the biomass composition is given in the S and a set of constraints that impose the upper and lower bound of fluxes. The steady state constraint is defined by the equation dx/dt = S · v = 0, where dx/dt are time derivatives of metabolite concentrations represented by the product of the m×n matrix S times the vector of fluxes v = , where vi is the flux of reaction i, n is the number of reactions, and m is the number of metabolites. The ensemble of functional states that the system can reach given a boundary condition I determines the feasible solutions space Φ = Σ∩I. By exploiting linear programming, FBA allows for optimization of the flux through a weighted sum of fluxes. In particular, we used the COBRA Toolbox [FBA requires a stoichiometric matrix  Toolbox  and the Because FBA only returns a single solution, we exploited Flux Variability Analysis  to assesTo analyze the complete set of flux distributions that maximize growth, we identified all the extreme points that lie at the intersection of the convex polytope given by the linear constraints and the hyperplane of the optimal objective function value, which correspond to alternate optima, as in . The proAs a complement to classic FBA, Monte-Carlo approaches are emerging with the aim of exploring the entire region of feasible flux distributions . The domIn , random τ of considered reactions is randomly drawn with uniform probability in  and then filtered them according to Boolean  expressions which must return true for each ensemble member. We define a metabolic response as the modification in fluxes resulting from a specific nutritional perturbation . The perturbation is simulated by varying the flux boundaries of the corresponding reaction. As an example, a metabolic response pertains to Ensemble E if and only if the biomass production flux is greater than 0 for at least one of the simulated glutamine and/or glucose uptake rates. For a more formal description of the method, the reader is referred to .K-Ras-transformed NIH3T3-derived cells [2. Cells were plated at a density of 3000 cells/cm2 in 6-well plates in normal medium. Culture medium was replaced after 18 hours with a normal medium containing 4 mM Gln or a low Gln medium (0.5 mM glutamine). The cells were collected and counted after 54, 72 and 144 hours. Media and serum were purchased from Life Technologies Invitrogen .Mouse embryonic fibroblast ed cells –42, 72 wKit for assay of acetyl-CoA and enzyme activities were purchased from BioVision  and used according to the manufacturer’s protocols. Raw data are provided in The total ROS levels were measured using the DCFDA Cellular Ros Detection Assay Kit from Abcam  according to manufacter’s instructions. Mitochondrial ROS levels were measured using 5 μM MitoSOX Red mitochondrial superoxide indicator (Molecular Probes) in HBSS/Ca/Mg for 10 min at 37°C. Fluorescence was measured at excitation/emission wavelengths of 510/580 nm, respectively, using a Cary Eclipse Fluorescence Spectrophotometer. Raw data are provided in l of ice-cold acetonitrile was added to 40 μl of media and vortexed at 4°C for 2 minutes, and the mixture was incubated on ice for 5 minutes and centrifuged at maximum speed for 10 minutes. A 100-μl volume of the aqueous phase was collected in a new tube and evaporated under nitrogen flow at 37°C. Derivatization was performed as described [l volume of sample was injected in a 1:10 split mode at 250°C. The GC was performed as previously described [After 144 hours of growth, the metabolites were extracted and analyzed by gas chromatography-mass spectrometry (GC-MS) as previously described  and the escribed . A GC/MSescribed . The GC/The following metabolites were detected: glutamine, glutamate, aspartate, glycine, serine, alanine, trehalose, methionine, lysine, tyrosine, cysteine, ornithine, putrescine, glucose, pyruvate, lactate, citrate, succinate, fumarate, malate, acetyl-CoA. Raw data are provided in −13 to 3.5*10−13 mMol per cell per second. We measured a glucose consumption rate of 5.8*10−13 mMol/sec per cell, while Jain et al. [−13 mMol/sec per cell which would require 12.10−13 for complete respiration. Oxygen consumption is not 6 times as much as glucose, and thus–according to our terminology–an oxidative bottleneck is apparent for cancer cells growing in vitro.According to the oxygen uptake rates catalogued for a variety of cells  in , the celn et al.  reportedThe condition of limiting oxygen should also prevail in vivo. Let us approximately evaluate the molar ratio between oxygen and glucose in human blood:V of 20 ml of oxygen gas at a pressure P of 760 mmHg [T = 310K°)The concentration of oxygen in the blood  corresponds to a volume 760 mmHg  and at aP*V = n*R*T, where R is the universal gas constant 62 L*mmHg K-1*mol-1, we can obtain the moles n of oxygen per liter of blood.By using the ideal gas law n = P*V/(R*T) = (760 * 0.2)/(62*310) ~ 8 mMol/liter.n is to start form the hemoglobin concentration in blood, which we found in literature [Another procedure to compute terature  to be 15−03 mol/litre.Because the molar weight of hemoglobin is 64, the concentration of hemoglobin in blood is 2.3*10If we assume a maximal saturation for oxygen, we have 4 oxygen molecules bound to each hemoglobin.−04 *4 ~ 9 mMol/liter.Therefore, n = 2.3*10The two alternative procedures return a similar order of magnitude for the maximum concentration of oxygen in blood (in the range 8 to 9 mMol/liter). The level of glucose in blood is around 5 mol/liter . TherefoBoth glucose and oxygen are ultimately delivered to the tissue (extracellular environment) not by diffusion but by convection by the blood. Therefore, at maximum consumption of glucose from the blood, at most 2 molecules of oxygen would be available per glucose molecule. If one hypothetical cell were to consume avidly all the glucose that is supplied by the blood in a given unit of time, that cell would not have enough oxygen to completely oxidize such glucose in that unit of time.S1 Fig2GR. The level of O2GR for which a plateau is reached  increases with the QGR (purple dots). For high O2GR a plateau is not reached within the considered range. 2GR. Red dots highlight the value of the ratio when O2GR is critical. Full glutamine utilization takes place at Critical O2GR (panel C), when the PDH flux is 0 and the respiratory chain is fed exclusively by glutaminolysis leading to almost equal NADH (Complex I) and FADH (Complex II) oxidation, the ratio of NADH oxidation over FADH oxidation being around 1.2. C) Glutamine uptake (z-axis) and ammonia efflux –scaled on glutamine availability and consumption respectively–as a function of QGR and O2GR. Red points highlight the minimum level of O2GR for which full glutamine consumption is observed. The increased glutamine uptake needs to be balanced by a comparable ammonia efflux that get closer to 2 when glutamine is plentiful and oxygen is low (coloring of the mesh). D) Aconitase flux  as a function of QGR and O2GR. 2GR is critical. At Critical O2GR, pyruvate dehydrogenase is not working, TCA cycle cannot work in a cyclic mode and production of citrate by the citrate synthase is therefore not possible. The citrate required to feed biosynthesis of fatty acids (required for biomass production) must derive from reverse carboxylation of glutamine derived AKG, as indicated by a negative flux of aconitase. E-H) The optimal flux value of serine synthesis (panel F), PDH (G), aconitase (H) and LDH (I) as a function of QGR for the standard non-essential amino acid (NEAA) composition of biomass NEAAA STD  Growth rate (z-axis) and oxygen uptake  scaled on glucose uptake as a function of QGR and O(PDF)Click here for additional data file.S2 Fig2GR (panel A) and as a function of the Complex I capacity over glucose uptake ratio (CGR in panel B) for three different levels of glutamine abundance (QGR). Purple dots highlight the growth rate when O2GR or CGR is optimal (oxygen not limiting for biomass). C-D) Lactate efflux scaled on glucose uptake as a function of O2GR (panel C) and CGR (panel D) for three different levels of QGR. Red points highlight the level of O2GR or CGR for which maximum lactate secretion is observed . E-F) Aconitase flux as a function of O2GR (Panel E) and CGR (Panel F). Red dots highlight the flux when O2GR or CGR is critical.Note that because of the reaction stoichiometry, Complex I flux is proportionally higher than the corresponding oxygen consumption rate. A-B) Growth rate scaled on glucose availability as a function of O(PDF)Click here for additional data file.S3 FigThe first sub-network  includes PEP carboxykinase; pyruvate kinase, NADP and NAD dependent malic enzyme and malate dehydrogenase. Because the TCA cycle is working in a non-cyclic mode, this set of reactions allows to maintain the steady state by removing glutamine-derived TCA cycle intermediates: OAA produced by reductive carboxylation of AKG and not used for fatty acids biosynthesis and malate deriving from fumarase, which, by means of the reactions in this subnetwork, can be converted into pyruvate and then secreted as lactate. The main options to remove OAA and malate are reported in (TIFF)Click here for additional data file.S4 FigpROS that emulates the level of production of reactive oxygen species in the respiratory chain . Glucose availability: 10; glutamine availability: 40; oxygen availability: critical level 38. B) Same experiment in panel A but with a P/O ratio of 2.5 and 1.5 considered for NADH and FADH2 respectively. C) Optimal biomass and FVA centroid of lactate secretion as a function of the ATP coefficient in the biomass forming reaction.A) Maximum and minimum value for lactate secretion across optimal growth solutions according to FVA, as a function of the parameter (PDF)Click here for additional data file.S5 FigA) Standard deviation of the model fluxes (represented with different colors) as a function of the sample size. B) Zoom in on fluxes of panel A with low standard deviations. The fluxes with high standard deviations correspond to those with high variability when running FVA. C) Relative standard error of the mean of each flux as a function of the sample size.(PDF)Click here for additional data file.S1 TableThe optimal flux value obtained with FBA, the minimum and maximum value as well as the range size, obtained with FVA, are reported for each reaction.(XLSX)Click here for additional data file.S2 TableThe optimal flux value obtained with FBA, the minimum and maximum value as well as the range size, obtained with FVA, are reported for each reaction.(XLSX)Click here for additional data file.S3 Table2 consumed (column 5), ATP produced form substrate (column 6) and ATP produced by oxidation of NADH and FADH2 produced in the respiratory chain (column 7). Complex I generates ROS that may be detoxified by glutathione in a mechanism that costs one NAD(P)H per 2 molecules of superoxide anion produced. If a fraction of the electrons flowing through complex I ends up in superoxide anion, the effective P/O ratio of NADH oxidation becomes 3(1−pRos)/(1+pRos). In this computations, we assume that a mere 25% of the electrons in Complex I flow to ROS; this implies a reduction of the effective P/O for NADH from 3 to 1.8 (against a 2 P/O for FADH2). This lowers the P/O of the Gln to lactate conversion, from 3.0 to 2.2. This effect is smaller than the effect on the P/O ratio of the glucose respiration-rather-than-fermentation, i.e. from 3.0 to 2.0, explaining the preference for the flux from glutamine to lactate when so much ROS is produced by Complex I (see above). The 10% difference in P/O ratio may seem small, but as maintenance metabolism may well consume more than half the ATP produced, the difference in ATP availability for anabolism might well exceed 20%. The table considers a value of infinity (computed as 100) for the P/O ratio of the fermentation of glucose to lactate, reflecting that no oxygen is consumed in that process. When oxygen is limiting, this process comes for free and therefore glucose has a preference for this. When we compare glucose catabolism to glutamine oxidation, we correct for the phenomenon that any glucose respired comes at the cost of one glucose fermented, hence our focus on P/O ratios for glucose respiration rather than fermentation. Should lactate dehydrogenase be incapacitated, then the next best strategy is glucose respiration to CO2 at a P/O. Should glucose uptake be impossible but lactate dehydrogenase active, the table shows that the best flux pattern for the fittest cells is glutamine to lactate again. In none of these cases pyruvate production should be better than lactate production, but if lactate production is blocked, pyruvate production from glutamine should occur in optimal fittest cells because it is more profitable (P/O = 2.10) than complete respiration of glutamine (P/O = 2.07). These two numbers exceed the P/O of 1.82 for glucose to pyruvate rather than lactate, i.e. glucose carbon would not leave as pyruvate. The table also shows that the P/O ratio for glucose being converted to cytosolic acetyl-CoA, which serves as carbon substrate for the lipids in the biomass synthesized rather than being converted to lactate (-0.80), is more negative than that for Gln being converted to acetyl-CoA (-0.60). The clockwise pathway (at P/O = -1.8) and the combined clockwise and counterclockwise pathway for synthesis of 2 acetyl-CoA (at -1.0) from glutamine are even less favorable.For different possible flux routes (table rows), the P/O ratio (column 8) of as well as the moles of acetyl-CoA deriving form one mole of substrate (column 10) following the considered route is computed. In some cases, the row indicates the difference between the computations of two possible routes . Intermediate steps of the computation are also reported: moles of NADH (column 3) and FADH2 (column 4) obtained, moles of O(PDF)Click here for additional data file.S1 TextDetails on ENGRO1 model reconstruction.(PDF)Click here for additional data file.S2 TextBiochemical interpretation of experimental results.(PDF)Click here for additional data file.S1 FileExcel file of the model compliant with the RAVEN Toolbox.(XLS)Click here for additional data file.S2 FileExcel file of the model compliant with: RAVEN Toolbox and FAME.(XML)Click here for additional data file.S3 FileScalable Vector Graphics image of the model, compliant with the software FAME.(SVG)Click here for additional data file.S4 FileRaw data  used to build graphs in (XLS)Click here for additional data file.


The scope of physiologically based pharmacokinetic (PBPK) modeling can be expanded by assimilation of the mechanistic models of intracellular processes from systems biology field. The genome scale metabolic networks (GSMNs) represent a whole set of metabolic enzymes expressed in human tissues. Dynamic models of the gene regulation of key drug metabolism enzymes are available. Here, we introduce GSMNs and review ongoing work on integration of PBPK, GSMNs, and metabolic gene regulation. We demonstrate example models. Physiologically based pharmacokinetic (PBPK) modeling has delivered considerable impact in drug development and has become the industry standard for prediction of drug‐drug interactions (DDIs), formulation effects, and pharmacokinetics in human populations. As a bottom‐up, literature‐based, mechanistic computer simulation approach, it shares general methodology with the computational systems biology, in which molecular biology knowledge is assimilated into molecular network models. In particular, reconstruction of genome scale metabolic networks (GSMNs) has led to mechanistic models incorporating a whole set of metabolic enzymes expressed in human tissues. Moreover, dynamic models of the expression of key drug metabolism enzymes are available. Currently, PBPK models account for about 20 genes involved in drug metabolism, already allowing prediction of the impact of genetic variability on drug population pharmacokinetics (PKs) as well as identification of individual genetic backgrounds leading to drug concentrations outside of the therapeutic window. The scope of this pharmacogenetic modeling can be naturally expanded by assimilation of GSMNs as mechanistic models of tissue intracellular space compartments within PBPK. Genetic polymorphism in thousands of metabolic enzyme genes accounted for by GSMN can be mechanistically linked to drug PKs, bringing PBPK to the pharmacogenomic domain. Mechanistic models of the intracellular space can be further expanded by assimilation of the dynamic models of gene regulation, which increasingly becoming available for key drug metabolism enzymes. Although these models add only a few genes, they account for complex dependencies of drug metabolism enzyme activities on endogenous metabolites, such as cortisol. Moreover, drug‐drug interactions (DDIs) involving compounds, such as pregnane X receptor (PXR) ligands, which bind to transcription factors rather than metabolic enzymes, can be modeled with more mechanistic detail.In this tutorial, we will describe how the scope of PBPK models can be extended by accounting for whole‐cell metabolism and gene regulation of key drug metabolism enzymes. We assume that the reader is familiar with ordinary differential equations (ODEs) and we will introduce PBPK very briefly. The PBPK tutorial has been previously published.in vitro data – some model parameters are intrinsic properties of tissues or enzymes that can be measured in vitro without the need of animal or clinical studies. Furthermore, increasing the granularity of the model may be essential when a particular application requires the presence of certain variables that influence the compound PKs being investigated. For example, simulation of DDI requires a resolution of individual enzymes and transporters that compounds bind to. Last but not least, mechanistic detail allows incorporation of parameter values and their distributions in populations for subsequent prediction of compound PK variability in the specific target population. For example, the model that resolves liver and kidney clearance can be used for simulation of populations with liver or kidney impairment. Correlations among body weight, age, and blood flows can be used to simulate virtual clinical trials and improve experimental design. Therefore, although the level of abstraction in a mathematical model is an arbitrary decision of its authors, an increase of granularity increases the scope of questions the model can potentially address. It is also generally accepted that mechanistic models are more likely to extrapolate and predict beyond the data used for parameter estimation than abstract phenomenological models.The wide adoption of PBPK in drug development demonstrates the value of bottom‐up, whole‐system scale, and the literature‐based mechanistic modeling approach. Current PBPK models are composed of hundreds of ODEs assimilating literature knowledge and data on the physiological processes involved in drug absorption, distribution, metabolism, and excretion. For example, simulation of full PBPK model available in the Simcyp simulator involves about 450 ODEs, which have been defined and parameterized by research and development teams scrutinizing about 17,000 publications since 2012. The PBPK models provide whole‐system scale description in a sense of including all major physiological compartments in the body. The granularity of this description is being continuously increased by versions of the model expanding mechanistic detail of selected compartments. For example, to model oral drug administration, the gut compartment may be split into lumen (unabsorbed drug) and enterocyte (absorbed drug). As the models advance, each compartment is further split into a number of subcompartments describing different regions of the gastrointestinal tract, such as the stomach, duodenum, jejunum, ileum, cecum, and colon. Likewise, other compartments, such as the liver and the lungs may be further divided. Incorporation of additional mechanistic detail into the model poses a challenge, as the values for additional parameters need to be determined either from literature or parameter estimation from available data. On the other hand, mechanistic detail enables extrapolation from in vitro. Therefore, data on allele frequencies in the population can be used in virtual trial simulation. In personalized medicine context, patient's genotype can be used to inform decisions about individual dosing regimen. This in turn opens an avenue for future assimilation of the wealth of information resulting from genomics revolution, such as the 100,000 genomes project already funded by the United Kingdom government.The PBPK models, as the name implies, are concerned with physiological rather than molecular level variables. The notable exception is drug metabolizing enzymes and drug transporters, which are described by mechanisms of compound binding, transport, and enzymatic reaction, familiar to a biochemist. Apart of application in DDI, mentioned above, molecular level mechanistic detail enables accounting for genetic polymorphism. For a number of molecular variants, the binding constants and maximal velocities have been determined The reconstruction and constrained‐based modeling of GSMNs is an area of computational systems biology, which to a remarkable extent shares methodology of the PBPK. Like PBPK models, the GSMNs are large, whole‐system scale models created by assimilation of scientific literature describing mechanistic detail. In the case of GSMNs, the system under consideration is metabolism of a living cell . Although quantitative parameterization of the ODEs representing whole‐system models involving several thousands of chemical reactions is still not possible, the constraint‐based modeling (CBM)et al.et al.The GSMN is a system of thousands of coupled chemical reactions involving thousands of metabolites. Metabolism is the best studied organization level of the cell and there is sufficient knowledge to write chemical reaction formulas defining connectivity and stoichiometry of this system. However, quantitative parameterization of the ODE model, simulating time evolution of each metabolite concentration is still not possible. The flux balance analysis (FBA)Figurei,j is a stoichiometric coefficient of metabolite i in reaction j. The variables of an FBA model are reaction fluxes in concentration per time units, rather than metabolite concentrations. Let v be a vector of M reaction fluxes and vi the flux of reaction i. At steady state, the FBA model is defined by the following equation:To introduce the mathematical formulation of FBA, let us consider the system of N coupled chemical reactions involving M metabolites Figure. Chemicai is an objective function coefficient for reaction i, l is a vector of lower bounds of N reactions, and u is a vector of upper bounds of N reactions. The LP solver finds maximal value of z given flux balance constraints defined by Eq. In most applications, the linear system defined by Eq. in silico essentiality screen, in which each reaction is removed from the model and feasibility of biomass synthesis is tested.The objective function z represents metabolic function of interest defined as a linear combination of reaction fluxes. For example, z could be a sum of fluxes producing adenosine triphosphate, bile acid secretion flux, or biomass reaction flux. Even if there is no quantitative information about any of the fluxes, LP maximization of z would test stoichiometric feasibility of the metabolic function of interest. The existence of the feasible solution where z ≠ 0 would indicate that metabolic function can be realized. Otherwise, metabolic function is not possible in the system of stoichiometric balanced, coupled chemical equations. This qualitative simulation can be already used to make useful predictions. For example, “druggable” metabolic vulnerabilities of cancer cell lines or bacterial pathogens can be identified by The LP is the most frequently used approach to explore a solution space defined by Eq. FigureThe GSMN is created in the reconstruction process Figure, in whicThe first draft of the model based on genome annotation alone usually fails to reproduce known metabolic functions and does not represent feasible cellular metabolism. This prompts an iterative process of model refinement. The most common refinement step is gap filling. Due to errors in genome annotation, some of the reactions are missing and metabolic conversions reported in literature cannot be reproduced. The gaps are filled by introducing additional reactions, which are not associated with enzymes. These should be supported as much as possible by literature evidence on the particular metabolic step, but arbitrary assumptions are inevitable. The list of GSMN reactions for which enzymes and genes are not known in itself represents a useful set of experimental leads. Further experimental studies can be conducted to identify the enzymes and transporters catalyzing hypothetical metabolic steps.All reactions in the GSMN, for which enzymes or transporters are known, are linked to genes in the genome by Boolean statements using gene names as variables. If the reaction is catalyzed by a multisubunit protein, the genes encoding individual subunits enter Boolean expression as terms of AND operator. If the reaction can be catalyzed by alternative enzymes, the genes are connected by OR operator. More complex Boolean expressions can be used to describe the reactions that can be catalyzed by many different multisubunit enzymes or transporters. Some modeling groups prefer to create multiple copies of reactions that can be catalyzed by multiple enzymes and use only AND statement. Some models use more complicated rules, in which genes are associated with proteins and proteins are associated with reactions. In general, we will refer to the Boolean rules describing the association between genes and reactions as gene‐protein‐reaction association rules.A major component of the body's strategy to survive in a complex chemical milieu is the use of gene regulation to allow metabolic adaptation. The body has a base metabolic state that corresponds to healthy physiology. Exposure to external chemicals, or changes in levels of endogenous chemicals, will lead to deviations from this base state, increasing the risk of adverse health outcomes. The body's response to this chemical challenge is to alter the metabolic state such that the body moves back to the base state, usually referred to as homeostasis.Sampling of the chemical environment within a cell is achieved through a number of protein sensors. A major class of these sensor proteins is the ligand‐activated transcription factors, which only activate gene transcription upon binding of their specific ligands. In addition, as ligand binding is an affinity‐driven process, receptor occupancy is a determinant of the impact on the gene regulatory network (GRN). Genes encoding drug‐metabolizing enzymes and drug transporters have their expression controlled by members of the nuclear receptor family of ligand‐activated transcription factors, and these have some unique properties.et al.et al.There are numerous examples of ODE‐based models that reconstruct chemical‐mediated alterations in gene expression of drug‐metabolizing enzymes. Of particular relevance to drug metabolism are interactions with the nuclear receptor PXR, which regulates the expression of many drug‐metabolizing enzymes (both phase I and II) as well as drug transporters.The examples above demonstrate how the use of ODE‐based models of the gene regulation of drug‐metabolizing enzymes can lead to biological insights into how the body responds to chemical challenge. In addition, robustly parameterized ODE models allow the accurate reproduction of concentration‐time curves for the response to chemical challenge. This is important for predicting the body's response to both individual and concomitant exposure scenarios.et al.The reconstruction of ODE‐based networks requires a high degree of parameterization, and this may limit the scale of generated models. In addition, the time required to build such highly detailed mechanistic models is not inconsequential, and may be an important factor for individuals beginning a project. An alternate approach to highly detailed ODE models is the use of approaches that represent network connectivity in a more qualitative manner. Perhaps the simplest way to qualitatively model GRNs is through the use of the Boolean network.et al.An alternative, or at least complimentary, approach to the use of Boolean GRNs is bipartite graph approaches, such as Petri nets. They provide both an established graphical notation and formal mathematical semantics that are ideal for describing GRNs. In a Petri net, places represent species , whereas transitions represent reactions . Places are connected to transitions via arcs, which indicate the nature of the interaction; one transition may have one or more inputs (pre‐places) and products (post‐places). Places contain tokens, with the number and location of these tokens across the network indicating its current state (or marking).TableFigureet al.et al.,FigureFigureIn recent years, several successful multiscale modeling approaches connecting PBPK with GSMNs have been published Table.43, 44, Gene regulation happens in timescales of hours and quasi‐steady‐state assumption has been extensively used in the systems biology field to couple dynamic models of gene regulation to GSMNs. The original, regulatory FBA method coupled Boolean GRN to FBA.Table43–46 presents multiscale models that integrate PBPK and GSMN or GSMN and GRNs in human tissues. The example introduced below represents the first prototype of a PBPK model being integrated with both whole‐cell tissue‐specific metabolic model and ODE system describing gene regulation of drug metabolism enzyme.et al.et al.per se, it did include physiological level variables describing blood concentrations, GSMN, and notably gene regulation of drug metabolism enzyme. The CBM and multiscale approaches discussed in this tutorial, together with their applicability under different circumstances, are summarized in TableKrauss FigureSupplementary Material.We demonstrated the multiscale model consisting of three different modules: PBPK, GSMN, and gene regulation. We show the potential of this model to analyze the PK properties of the drug and its toxic metabolite in the context of various perturbations, such as exposure to chronic stress and patient‐specific liver metabolism Figure. The mulFigureWe have used the human PBPK model with an example drug, as described in the previous tutorial of Jones & Rowland‐Yeo.Supplementary Text.We have further constrained HepatoNet1 to increase quantitative accuracy of predictions. We have used a high throughput metabolomics dataset, published after original publication of HepatoNet1, in which consumption and release fluxes for over 200 metabolites were measured in all cancer cell lines in the NCI‐60 collection.Supplementary Table S3. In this particular case, the scaling factor was proportional to maximal GSH availability. The GSH conjugation rate in the PBPK model was then scaled using the following formula:max) is a scaling factor proportional to the objective function value GSHmax calculated by LP of the GSMN model.The FBA allows the simulation of various liver functions, such as glutathione (GSH) production or conversion of ammonia to urea. In our example, the HepatoNet1 liver model was coupled to the PBPK model via GSH production flux, due to the GSH playing a crucial part in the detoxification of drugs activated by the phase I metabolism. We set GSH production as an objective function and, therefore, used unique maximal value calculated by LP. This value has been translated into scaling factor using the lookup table presented in in silico screening simulation, each reaction in turn was inactivated by setting flux bounds to  and objective function was re‐evaluated. Reactions for which the objective function value was different from the value in the unperturbed model are shown in TableTable43–46 constitutes a hypothesis that certain intracellular enzyme affects GSH availability if subjected to inhibition by a drug or xenobiotic or if its activity is affected by genetic polymorphism. These reactions are potential targets for safety or DDIs. Their influence on the PBPK results can be further examined by creating a feedforward link between PBPK and GSMN.At this stage, the model involved only a feedback integration: result of FBA was used to scale parameters in the PBPK model. Because there was no change to the GSMN reaction flux bounds during dynamic simulation, only one evaluation of objective function was needed. Therefore, we could apply a reaction essentiality scan to identify reactions that affect GSH availability. In this et al.To demonstrate multiscale simulation involving both feedback and feedforward steps, we have assumed that toxic metabolite in the PBPK model inhibits one of the reactions limiting GSH availability. We established a further link between PBPK and GSMN modules by creating the competitive inhibition link of formyltetrahydrofolate dehydrogenase (FTHLDH) reaction (HepatoNet1 reaction name is r0027) using the formula below, which is further detailed by Krauss To calculate r0027 activity, we assumed the substrate concentration to be equal to the Km value and implemented Ki of 50 mM. The calculated reaction activity state was set to constrain r0227 reaction by implementing proportional reduction in the upper bound reaction flux rate to the corresponding reaction activity level .FigureFigurea shows production of toxic metabolite under the unperturbed conditions (wild type). The inhibition of FTHLDH and methenyltetrahydrofolate cyclohydrolase (MTHFC) increases the concentration of the toxic metabolite via reduction of the GSH flux rate. Additionally, the inactivation of reaction methylenetetrahydrofolate dehydrogenase (MTHFD) completely blocks the production of the GSH in the liver model and, as a result, severally impacts the detoxification of the toxic metabolite . These results should prompt further examination of genetic polymorphism in FTHLDH, MTHFC, and MTHFD to consider whether there are genetic backgrounds particularly vulnerable to administration of the drug. In addition, compounds inhibiting FTHLDH, MTHFC, or MTHFD are likely to interact with the drug by increasing the concentration of its toxic metabolite.Simulation results of the multiscale model are shown in e Figureb. TheseFigurec). In contrast, the perturbation of CYP3A4 homeostatic regulation by simulating chronic stress led to the drastic increase of the toxic metabolite concentration . Chronic stress conditions increases and sustains higher blood cortisol concentration, which impacts nuclear receptor signaling. As a result, the increased cortisol signaling pathway leads to the perturbation of homeostatic CYP3A4 concentration (increase) and in turn elicits an impact to the metabolism of the drug.In the second example, we further enhance the PBPK‐GSMN model by adding the GRN, which controls liver CYP3A4 concentration in response to the cortisol‐induced signaling. Previously established dynamic ODE‐based CYP3A4 regulatory network was connected with the PBPK model to regulate the rate of the phase I metabolism by controlling CYP3A4 levels in response to cortisol signaling.n Figured. ChronIn this tutorial, we have reviewed pioneering literature describing multiscale models integrating PBPK and two classes of models from the systems biology field: GSMNs and quantitative dynamic models of GRNs. We have constructed example models and made them available in free software. We note that although most applications of quantitative systems pharmacology focus on pharmacodynamics, this tutorial shows how legacy of systems biology can be used to increase mechanistic scope of literature‐based, bottom‐up PK modeling.We believe that the area of multiscale modeling presented here will expand in the future due to the following motivation. First, the advent of next generation sequencing brings full genome sequencing of individual patients closer to clinical reality. This will motivate identification of intracellular metabolism enzymes that indirectly affect PK to fully use patient's genetic information in personalized medicine context. Our example model shows identification of reactions that affect toxic metabolite dynamics indirectly through limitation of GSH production in liver cells. In population context, meta‐analysis of data collected in genomewide association studies can be used to determine distribution of genetic polymorphism in the population.in vitro metabolomics dataset. We hope that development of genome‐scale mechanistic models relevant to pharmacology, toxicology, and health will motivate quantitative biology research, leading to increased quantitative accuracy of the models. We note that the CBM approach is particularly suitable in this context as it allows to gradually increase quantitative detail as new data become available.The success of quantitative, mechanistic modeling depends on availability of quantitative experimental data. Here, we show how advances in ∼omics technologies can be already used to quantitatively parameterize mechanistic models of unprecedented scale. In our example, we use the HepatoNet1 model that has been made liver‐specific by analysis of gene expression data. We have further constrained this model by providing biologically realistic, quantitative, consumption, and release flux bounds for over 200 metabolites, based on In conclusion, we are convinced that multiscale models integrating PBPK and GSMNs operating in human tissues will gain importance in the near future. We hope that our tutorial provides a useful introduction to this exciting field.Supporting InformationClick here for additional data file.Supporting InformationClick here for additional data file.


Our simulation results predicted luminal sodium as a limiting factor for active glucose absorption; necessity of apical localization of glucose transporter GLUT2 for absorption of all glucose in the postprandial state; potential for gluconeogenesis in enterocytes; and the requirement of oxygen for the formation of endogenous cholesterol needed for chylomicron formation under luminal cholesterol-free conditions. In addition, for a number of enzymopathies related to intestinal carbohydrate and lipid metabolism it was found that their effects might be ameliorated through dietary interventions. In conclusion, our improved enterocyte-specific model was shown to be a suitable platform to study effects of dietary interventions on enterocyte metabolism, and provided novel and deeper insights into enterocyte metabolism.The small intestine serves as gatekeeper at the interface between body and diet and is thought to play an important role in the etiology of obesity and associated metabolic disorders. A computational modelling approach was used to improve our understanding of the metabolic responses of epithelial cells to different diets. A constraint based, mouse-specific enterocyte metabolic model (named  The average diet in Western countries, such as the United States and the Netherlands, provides approximately 16%, 48%, and 33% of total energy intake in the form of protein, carbohydrate and lipid, respectively6. Upon ingestion, the three macronutrients i.e. carbohydrates, lipids and proteins are broken down in the gastrointestinal tract to their basic units , which in turn are absorbed by the enterocytes. These monomers are subsequently used as substrates for cellular energy production, interconversions or stored for shorter or longer time period not only in enterocytes but also in other body cells via shuttling into the circulation.Obesity and related disorders, such as cardiovascular diseases, insulin resistance and type 2 diabetes, have become major public health issues7. It is well accepted that glucose and galactose are transported across the brush border membrane into the enterocyte by the Na+ dependent glucose cotransporter 1 (SGLT1). SGLT1 has high affinity for these substrates and uptake is driven by the Na+ electrochemical gradient across the brush border membrane that is maintained through the basolateral Na+/K+ ATPase pump. Whether or not the facilitated transporter GLUT2 is involved in the apical glucose uptake remains controversial8. Fructose is absorbed at the apical side by the facilitated fructose transporter 5 (GLUT5). All three hexoses exit the enterocyte at the basolateral membrane via GLUT2, although it has been suggested that fructose may also use the basolaterally located GLUT5. These carriers deliver these monosaccharides to the capillaries and portal blood.After ingestion, dietary di- and polysaccharides are degraded into monosaccharides that can be absorbed7. FFA and MAG are subsequently either absorbed by specific carrier molecules including FATP and CD36 or diffuse into enterocytes. Since both products are potentially toxic due to their detergent-like properties, especially FFA at higher concentrations, they must be rapidly neutralized after absorption9. This can be achieved by binding to fatty acid–binding proteins , which also prevents their transport back into the intestinal lumen and facilitates their intracellular transport. FFA may also be catabolized by oxidation in the mitochondria or peroxisomes, a process involving various enzymes including CPT1, ABCD1/ALDP, ACOX1, and ACAD. However, quantitatively most important is the re-esterification of FFA with MAG by MGAT and DGAT in the endoplasmic reticulum (ER) which results in the formation of di- and triacylglycerol respectively. Alternatively, FFA are esterified with free cholesterol by ACAT. These resynthesized lipids either become part of cytosolic lipid droplets and stored, or are transported to the ER for secretion into the lymph system as chylomicrons10. The formation of chylomicrons occurs in the ER in two steps involving APOB-48 and MTTP. Chylomicrons consist of different types of TAG (~95%), phospholipids (~4%), cholesterol or cholesteryl esters (~1%) and proteins (~2%)11 and are typically synthesized during postprandial periods. During post-absorptive and fasting periods, intestinal very low-density lipoprotein (VLDLs) are synthesized that consist of TAG (~40%), phospholipids (~15%), cholesterol (~15%) and proteins (~10%)11. Chylomicrons as well as VLDLs leave the enterocyte by exocytosis and reach the lymphatic circulation through the lateral intercellular spaces.Triacylglycerols (TAG) represent the largest component (>90%) of the dietary lipids. TAG predominantly contain long-chain fatty acids esterified to a glycerol backbone. Hydrolysis of TAG into 2-monoacylglcyerol (MAG) and free fatty acids (FFA) occurs mainly in the duodenum7, a detailed understanding of many aspects of intestinal nutrient metabolism is lacking. Such detailed understanding is needed in view of the important role the intestine is thought to play in the development of chronic metabolic diseases13, and to explore possibilities of developing dietary strategies to prevent this and protect against enterocyte malfunctioning. Unresolved questions remain regarding the involvement of GLUT2 in luminal glucose uptake8 and whether the small intestine can act as a site for gluconeogenesis14. In addition, interactions between carbohydrate and lipid absorption and metabolism remain largely unknown. These and other issues require a systems level approach where all the metabolic interconversions and pathways are simultaneously examined to uncover possible relationships between seemingly unrelated pathways.Although the general metabolic functions of enterocytes are known15. In silico reconstruction of metabolic networks and consequent analysis of genome-scale metabolic models through constraint-based modelling helps in investigating physiology and metabolism of any cell type. Constraint-based models have been constructed using growth phenotype data for various organisms including Saccharomyces cerevisiae, Homo sapiens, Mus musculus, and these models predict the response of the cell or tissues to environmental and genetic perturbation and to simulate known and hypothesized phenotypes. Constraint-based modelling aims at helping researchers to get a better insight into the complex system of metabolism16. One of the most common approaches to constraint-based model is the use of flux balance analysis22 which can predict optimal  flux through a selected reaction using linear programming with the knowledge of reaction stoichiometry, biomass composition and additional constraints, such as limits on uptake/excretion rates and thermodynamic constraints on reaction directionality. To this end a murine enterocyte-specific constraint-based metabolic model was constructed by extensively curating and expanding a published model of human small intestinal epithelial cells23. Our model was then integrated with experimental data corresponding to four precisely defined dietary interventions performed in mice to study nutrient absorption and metabolic capability of enterocytes. Finally, the integrated model was used to explore the synergies between diet and enzymopathies, and to identify dietary interventions that might alleviate the effects of enzymopathies.A computational model able to reflect specific dietary conditions and their impact on the enterocytes provides a framework for such a holistic approach23, a murine enterocyte-specific constraint-based metabolic model was developed with dedicated pathways representing TAG absorption and metabolism. Four diets, that differed in the lipid to carbohydrate ratio, were precisely quantified in terms of their nutritional composition24. Dietary uptake rates were used to constrain the model of enterocyte metabolism. The model was deployed to investigate the absorption of dietary TAG and carbohydrates by enterocytes and to analyze the changes that occurred when enterocytes were exposed to different dietary carbohydrate to lipid ratios while dietary protein remained unchanged in a cholesterol free diet. Changes in absorption and secretion profiles of carbohydrates and lipids were investigated. Finally, the effects of enzymopathies were studied as well as the extent to which their effects could be counterbalanced through dedicated dietary interventions.Building on an already published modelhs_sIEC611)23 was first combined with mouse specific information as described in mouse reconstruction iSS139225. The resulting model was extensively curated and expanded, especially regarding lipid metabolism, resulting in a model comprising 708 unique metabolites that are involved in 1830 reactions and has 717 genes associated  and most importantly, a 63% increase in the number of metabolites accounted for  and two extracellular compartments , which all have different (metabolic) roles. The consistency of our model was tested and no holes in the structure of the network were identified. In addition, the model was used to recapitulate known biological functions of small intestine enterocytes. These functions relate, mostly, to the secretion of selected metabolites and were the same as listed in and used by Sahoo & Thiele23 for the construction of their human small intestinal epithelial cell metabolic model (hs_sIEC611). Our model was successfully challenged to perform these (and other) tasks, and this was an important validation and quality criterion. Simulations regarding these tasks are available in Supplementary file in vivo measurements of secretion rates. In this study, the model was used to explore avenues of nutritional physiology.To investigate the adaptability of nutrient absorption and metabolism in murine enterocytes when exposed to different diets, we required an enterocyte-specific computational framework. To this end a previously published human small intestinal epithelial cell metabolic model with 611 unique genes . These values were used to constrain the 39 exchange reactions in the model that represent uptake of components in the diets.Nutrient absorption and metabolic capability of enterocytes was investigated using the composition of 4 well-defined, semi-synthetic diets that were used previously to study the role of the small intestine during diet-induced obesityios Fig. . The amoios Fig. . Moreoveios Fig. . The onl8. A schematic overview of the monosaccharide metabolism in enterocytes that was modelled is given in Fig. +, we used the model to compute maximal possible glucose absorption with varying Na+ availability in the presence and absence of apical GLUT2  and TAG secretion as chylomicron (CHYLOMGE) were calculated for the 10en% fat diet. These values were considered as reference values and the effect of a possible impairment of each reaction present in the model was iteratively investigated. With regard to both glucose and TAG secretion, three types of behavior were observed that enabled the classification of reactions into the following three types: Type I: reactions that upon impairment did not affect the chosen task; Type II: reactions that upon impairment lead to complete blockage of the desired task; and Type III: reactions whose impairment lead to reduced performance (i.e. >5%) regarding the task but could be to some extent recovered by modifying the composition of the simulated diet. All reactions and their impact on glucose and TAG secretion are listed in Supplementary File mmu_ENT717 model is ideally suited to study carbohydrate and lipid metabolism as well as trans epithelial exchange from apical to basolateral side. It contains a very extensive representation of TAG/FFA metabolic reactions in enterocytes, specifically with regards to six different types of fatty acids that were present in different amounts in the considered experimental diets containing soybean and palm oil. The lipid reactions have been added following a standardized approach, using precisely defined metabolite identifiers. This set of reactions can therefore be adapted to any other metabolic model, thereby increasing the accuracy of the model. Moreover, our approach can also be easily extended to other TAG types which would allow the study of the impact of other dietary lipid compositions.In this study, we report on a comprehensive and improved murine enterocyte metabolic model. Compared to previous models, our Constraint-based metabolic models require uptake rates to produce meaningful predictions. However, such detailed biochemical characterizations of dietary interventions are often lacking and in the past, population-wise averages have been used. Instead, here we have used detailed characterizations of specific diets fully representing an experimental set up; thus, these diets accurately represent actual intake levels of individual mice. The diets used represent a broad range of lifestyles as the energy derived from fat ranges from 10en% up to 45%, the latter which in humans represents an unhealthy Western-style diet. Availability of such dietary datasets greatly expands applicability of constraint-based metabolic models and we believe that the data presented in Supplemental file 26. Our model showed that in the absence of apical GLUT2, cells can only absorb all the luminal glucose provided when abundant luminal sodium is present, representing SGLT1 functionality. This is in line with recent functional findings that demonstrated a reduction in luminal sodium availability after Roux-en-Y gastric bypass surgery, which in turn impaired intestinal glucose absorption27. We found that for full absorption of luminal glucose by only SGLT1, Na+ requirements were more than 10 times the amount present in the diet. However, owing to the complex physiology of the gastrointestinal tract it should be realized that luminal Na+ is not only derived from dietary sources, but also, and in larger quantities, from pancreatic and biliary juices28. Our model also revealed the potential for gluconeogenesis, which was associated with amino acid availability in the diet. Indeed, it has been suggested that gluconeogenesis from glutamine may occur in the small intestine29. This might also be a way to dampen the influx of amino acids into circulation, thereby controlling blood pH.We used the model to confirm the traffic of GLUT2 to the apical membrane upon high luminal glucose concentrationsde novo cholesterol biosynthesis is needed for adequate chylomicron secretion. Indeed, feeding mice a cholesterol-free diet leads to upregulation of genes encoding enzymes involved in cholesterol biosynthesis in small intestinal cells30, and inhibition of cholesterol biosynthesis resulted to reduced production of very low density lipoprotein (VLDL) particles by the liver31. Here, we have also shown that increased chylomicron synthesis/secretion is associated with an increased demand of ATP and thus oxygen in the intestine, which represents at least part of intestinal tissue oxygen consumption. It is estimated that the gastrointestinal tract contributes to about 7%-11% of standard metabolic rate in adult rat and humans, respectively32.Our model also enabled computation of oxygen requirements for chylomicron secretion in the absence of biliary cholesterol levels. Of note, the model does not incorporate uptake of cholesterol from circulation at the basolateral side; thus by absence of luminal cholesterol, cellular It was found that in most cases the modelled fluxes were proportional to the dietary carbohydrate or lipid content 23 was improved by performing a thorough search of the current literature and various enzyme and pathway databases  to obtain reactions known to occur in enterocytes, and reactions that were missing were added. Murine homologues of human genes were retrieved from the Homologene database38. Gene-protein-reaction (GPR) relationships associated with reactions were defined by the Boolean rules ‘and’ and ‘or’, where ‘and’ represents that all gene products are required while ‘or’ represent requirement of any of the listed gene products to catalyze the corresponding reaction. The model was, in particular, expanded with respect to lipid metabolism. In the human sIEC model the different triacylglycerols (TAG) are grouped as a single compound  that reflects the total amount of dietary TAG present. In our model we broke down the dietary TAG into 6 individual fatty acid species  and their corresponding diacylglycerols (DAG) and 2-monoacylglcyerols (MAG), since these metabolites represent the full fatty acid profile of the experimental diets given to the mice24. In addition, the human sIEC model was expanded with reactions for absorption, (re)synthesis, oxidation and secretion for each FA species, which resulted in the addition of 18 reactions for lipid absorption, 36 reactions for de novo synthesis of MAG, DAG and TAG, and 6 reactions for FA esterification with cholesterol. All unspecific reactions in the sIEC611 model that did not differentiate between the FA species were substituted by specific reactions. All different TAG were formulated based on a uniform fatty acid profile; that is all TAG molecules were composed of 3 identical fatty acid species. This was done for reasons of simplicity, because the possible number of different TAG molecules including enantiomers is n3, where n is the number of fatty acids present. This number will be very large even when a limited number of fatty acids is considered11. Taking into account the fact that before being absorbed, the TAG molecules have to be hydrolyzed by luminal lipases resulting in the formation of the building blocks of TAG, i.e. free fatty acids and glycerol, we believe this simplification is warranted. Our final mmu_ENT717 model is comprised of a total of 1830 reactions and 717 metabolic genes. 843 reactions had no gene associated of which 164 are diffusion reactions, whereas the remaining 565 reactions are orphan reactions. Information from the KEGG database and mouse whole genome model25 was used to determine candidate reactions to fill gaps in the non-compartmentalized draft model. The gap filling method from the COBRA toolbox39 was set to run 40 iterations. Each solution was then manually checked for applicability, such as the feasibility of the suggested directionality, before choosing a proposed solution. The Cobra model mmu_ENT717 model is available in. mat format as supplemental file The previously published human sIEC model . The fatty acid profiles of the dietary oils  that were used in our study were provided by the supplier, and were in very close agreement with the values reported by the worldwide food standards commissions 40. Casein (milk protein) was used as the sole protein source of the diet. Amino acid composition of the casein was derived from Pennings et al.41. Uptake rates of all these 39 nutrients were then converted into moles mouse−1 day−1 43. Such an approach is not uncommon as for example the parametrization of the virtual physiological rat and mouse heart models include data from other species as well45. The average wet weight of the mouse small intestine was reported to be 1.094 g, of which 76% was water46. The dry weight (dw) of the enterocytes per mouse equaled thus 1.094 g × 0.24 × 0.552 = 0.1449 g. The factor, A, to convert the intake of the nutrients from moles mouse−1 day−1 to mmol (gdw enterocytes)−1 h−1 is thus The composition of the diets and daily feed intake calculated from weekly intake levels has been reported previouslyS) of size m × n (where ‘m’ represents the number of metabolites and ‘n’ represents the number of reactions in the network). In this way Sij is the stoichiometric coefficient of metabolite i in reaction j; positive and negative Sij values indicating metabolite production or consumption respectively. Under steady state conditions the sum of input fluxes equals the sum of output fluxes for metabolite concentration (x) over time (t) i.e. dx/dt = 0, so the steady state equation can be written as n × 1 which represent the flux through all reactions. Flux values (vi) are limited with a set of constraints that indicate reaction reversibility: li ≤ vi ≤ ui for i ∈ {1, …, n}. The vectors li values. Additionally, li and ui values can be further constrained by experimentally determined values. Reactions representing luminal or basolateral uptake or secretion rates are termed exchange reactions. The usual convention of writing exchange reactions was followed in such a way that uptake and secretion are represented by negative and positive flux values, respectively. Here we have imposed the constraints derived from the analysis of the dietary intervention to the exchange reactions present in the metabolic model to mimic the specific conditions. Specifically, (negative) uptake rates of the dietary nutrients were set as lower bounds of the exchange reactions representing luminal uptake of the corresponding components. Flux balance analysis (FBA) seeks to optimize (by either maximizing or minimizing)23 a given objective function under a specific condition. In this study, metabolic tasks were defined for glucose and lipids on absorption from apical and secretion at basolateral side of the cell, for all four dietary conditions. To identify the effects on metabolism of enterocytes after deletion of a reaction, we used the cobra function to delete model reaction and optimize the corresponding objective39. All model calculations were done in MATLAB version 2014b (The Mathworks Inc.) using the COBRA toolbox and Gurobi solver version 647.In a constraint-based metabolic model, reactions are represented by the stoichiometric matrix (Supplementary informationSupplementary dataset 1Supplementary dataset 2


While a few studies on the variations in mRNA expression and half-lives measured under different growth conditions have been used to predict patterns of regulation in bacterial organisms, the extent to which this information can also play a role in defining metabolic phenotypes has yet to be examined systematically. Here we present the first comprehensive study for a model methanogen.Methanosarcina acetivorans growing on fast- and slow-growth substrates to examine the regulation of its genes. Unlike Escherichia coli where only small shifts in half-lives were observed, we found that most mRNA have significantly longer half-lives for slow growth on acetate compared to fast growth on methanol or trimethylamine. Interestingly, half-life shifts are not uniform across functional classes of enzymes, suggesting the existence of a selective stabilization mechanism for mRNAs. Using the transcriptomics data we determined whether transcription or degradation rate controls the change in transcript abundance. Degradation was found to control abundance for about half of the metabolic genes underscoring its role in regulating metabolism. Genes involved in half of the metabolic reactions were found to be differentially expressed among the substrates suggesting the existence of drastically different metabolic phenotypes that extend beyond just the methanogenesis pathways. By integrating expression data with an updated metabolic model of the organism (iST807) significant differences in pathway flux and production of metabolites were predicted for the three growth substrates.We use expression and half-life data for the methanogen M. acetivorans employs extensive post-transcriptional regulation to optimize key metabolic steps, and more generally that degradation could play a much greater role in optimizing an organism’s metabolism than previously thought.This study provides the first global picture of differential expression and half-lives for a class II methanogen, as well as provides the first evidence in a single organism that drastic genome-wide shifts in RNA half-lives can be modulated by growth substrate. We determined which genes in each metabolic pathway control the flux and classified them as regulated by transcription (e.g. transcription factor) or degradation . We found that more than half of genes in metabolism were controlled by degradation. Our results suggest that The online version of this article (doi:10.1186/s12864-016-3219-8) contains supplementary material, which is available to authorized users. The stability of an RNA molecule, as measured by its half-life, is a critical factor in defining timescales for cellular events. It also sets the correlation time of transient adaptations relative to a cell’s growth rate, when compared to its more long-term “basal” phenotype. For example, rapid, high-fidelity responses to extreme external stimuli are mediated through small RNA  whose function depends largely on search time and efficiency of stimulated co-degradation, sequestration or stabilization when in complex with the target mRNA . On longEscherichia ) control coefficients, which describe the relative change in mRNA due to relative changes in transcription rate ktrn and degradation rate γ . In contrast to the previous single substrate experiments in L. lactis and E. coli, our analyses show that between 16 and 28% of the changes in steady-state transcript levels are due to degradational control . Our procedure correctly predicted the increase of coenzyme M in acetate grown cells compared with MeOH grown cells [Additional Modeling Methods and Results”.The question then arises: How does the regulation of metabolic genes affect metabolism and what role does degradation play in defining metabolic state? To connect the regulation to metabolic function, we integrated the differential expression data with the updated genome-scale metabolic model to predict change in fluxes through metabolic pathways when the organism grows on different substrates. Briefly, the coefficients of biomass components, which describe a cell’s physiological requirement for that molecule, were allowed to vary between growth substrates and fitted such that the deviation of the metabolic flux ratio from gene expression ratios of DEG in those pathways were minimized  genes where the hydrogenotrophic methanogens lack significant portions of genes that are responsible for enabling the utilization of growth substrates beyond carbon dioxide. Despite the metabolic differences, a large fraction of all differentially expressed genes are still conserved across all the methanogens, especially those for translation. The problem that remains is to discover the structure and elements of the regulatory network and explore how they evolved.The similarity of mRNA degradation rates among related species grown under similar conditions—as evidenced by comparison of our results to the limited studies on M. mazei  and findM. mazei , 14—suggMethanosarcina acetivorans, with genes all across the genome affected especially those involved in growth  and metabolism . We found that while mRNA half-lives scale with doubling time, the effect was not uniform across functional classes, suggesting that the cell prioritizes certain capabilities at lower growth rates most likely to account for lower available energy. By combining the expression data with the half-life data we were able to identify genes that were likely targets of transcriptional regulation (e.g. transcription factors) or degradational regulation , providing testable hypotheses that can direct molecular studies of regulation within the organism. For example, we identified ∼32 putative regulators and their targets in Methanosarcina acetivorans and found that about 6 of the transcription factors and their targets were highly conserved across the order of Methanosarcinales and some were conserved across among all the methanogens. We hypothesized functions for those regulators, based on similarly conserved genes, which can be readily tested with molecular biology experiments.In this study we have demonstrated that the carbon source regulates significantly more than just methanogenesis in M. acetivorans may make extensive use of sRNAs and riboswitches to fine-tune the degradation of mRNAs that encode metabolic proteins according to their environment. We tuned coefficients of the biomass reaction of our metabolic model to increase correlation between fluxes and expression data for each carbon source. By doing so we could determine how the metabolite demand along certain pathways varies with growth substrate. This procedure allows us to account for the differential expression of genes in those pathways. Altogether the half-life, differential expression, and correlated fluxes data allows us to build a richer picture of regulation than possible with transcriptome-only studies.We found that most differentially expressed genes were involved in metabolism and about half of them were under degradation control. This is the first study to find such a prominent effect of degradation control in metabolism. As the RNases are not differentially expressed, this suggests that This work reveals many new features about regulation and metabolism in methanogens that inspired several hypotheses for further testing. Molecular genetic studies with corresponding transcriptomic information will be necessary to clarify the role of the differentially expressed transcription factors. Future bioinformatic and genetic studies will be required to confirm the presence and define the function of post-transcriptional regulators, especially any sRNAs. Additional proteomics data could confirm the changes in pathway fluxes that we predict for growth under various substrates. Such studies will allow the construction of a combined regulatory/metabolic network model that can predict how methanogens impact everything from the gut microbiome to the global carbon cycle.M. acetivorans C2A strain .e, WWM82  at 37 °Ce, WWM82 , 84. HanM. acetivorans C2A wild type was adapted to grown, TMA or acetate for 33 generations. Cells were grow in batch cultures tubes. The total RNA was isolated from mid-exponential phase cultures  using TRIzole  and the Zymo Direct-zol RNA MiniPrep kits . Specifically, at mid-exponential phase 2 mL of culture were added to 2 mL TRIzole and 4 mL ethanol was added. Samples were processed with the Zymo Direct-zol RNA MiniPrep kit and RNA was eluted at 50 muL. The RNA samples were depleted of the 16s- and 23s-rRNA through hybridization to complementary biotinylated oligonucleotides and were subsequently removed with streptavidin-magnetic beads . SampleμM of actinomycin D to cultures growing in exponential phase . At 6 or 7 times after transcription was halted 2 mL of culture was withdrawn . RNA was isolated as described above. All half-life experiments were performed with three biological replicates.In order to estimate half-lives for RNA transcripts, a series of RNAseq experiments were performed at timepoints after halting transcription. Transcription was halted by addition of 1 mL of ∼ 80 Additional Methods and Materials” and Table S1 for details. Additionally, three RNAseq datasets were taken from the GEO database accession GSE64349.Construction of cDNA libraries and high-throughput sequencing of RNA were carried out by the Roy J. Carver Biotechnology Center at University of Illinois at Urbana-Champaign using an Illumina HiSeq2500. All sequence data generated in this report are available online in the GEO database (accession number GSE77738). See Additional file Quality of the RNA reads in each experiment were assessed using the FastQC tool (http://www.bioinformatics.babraham.%20ac.uk/projects/fastqc/). Individual reads with systematic sequencer error  were removed, and then reads were trimmed. The adapter sequence was trimmed, constituting between 6 and 12 bases off the head or tail of the read. In some cases 2 bases were trimmed from the end of the read when the Sanger Phred quality score at that base had a score below 20. Trimmed reads were mapped to the reference genome (accession number NC_003552 ) using RMapped reads were further processed by normalization and averaging. Two normalization schemes will be considered: 1) reads are normalized per kilobase (gene length) then per one million reads (referred to as RPKM), and 2) reads are normalized per kilobase (gene length), then averaged across operons , which has been characterized as having one of the longest known half-life in the archaeon Sulfolobus solfataricus [S. solfataricus. The degradation of each gene was fit to a first-order decay reaction: For each distinct experimental growth condition RPKM values for genes were normalized so that the superoxide dismutase  was estimated for each gene by folding the open-reading frame, as annotated in the genome NCBI genome NC_003552, using the RNAFold package  using boAdditional Methods and Materials” and code to reproduce the results can be found in Additional file p-value ≤ 0.01 were considered to be differentially expressed. Differentially expressed genes can be found in the Additional file Differentially expressed genes (DEG) were computed using three statistical models: edgeR v3.8.5 , PoissonM. acetivorans were considered. One set was predicted by Rockhopper [Four sets of putative polycistronic operon structures for the genome of ckhopper , and thrckhopper , ProOpDBckhopper , and DOOckhopper . Mapped −5 for nucleic acids and proteins, respectively; MCL clustering was run with the maxbit option with inflation and score cutoffs of 2.0 and 0.4, respectively). For each differentially expressed gene in M. acetivorans, the top scoring homolog in each other methanogen was identified, if one exists. These were ordered by degree of conservation and plotted on a phylogenetic tree that is rooted at Methanopyrus kandleri using the Python ETE Toolkit [The Integrated Toolkit for Exploration of Microbial Pan-genomes (ITEP) was used to compare conservation of differentially expressed genes . ITEP wa Toolkit   so that the ratio of fluxes between the two predictions matches the ratio of messenger expression for differentially expressed genes. The metabolite requirement in the new condition is then classified as being higher, lower or unchanged with respect to the reference growth substrate, suggesting targets for further experiment.A new method was developed to integrate differential expression data with the metabolic model, as existing methods to integrate expression data into genome-scale metabolic networks have been shown to perform relatively poorly unless metabolomic data was also available and integrated . We reasMore specifically the method attempts to minimize an objective function; that is: bj. In the equation NDE is the number of differentially expressed genes, n in growth condition c, r that has a gene-protein-reaction rule that contains gene i in growth condition c. In order to do this, the the list of biomass coefficients is ordered randomly, and the new optimal biomass coefficient bj,opt is found in order from the beginning to the end of the list. For each biomass coefficient, the uptake rate is varied such that the experimentally measured growth rate is achieved. This whole process is performed multiple times with permuted ordering for optimizing biomass coefficients and the final biomass coefficients are selected as the best for that round of optimization.for each biomass coefficient p<0.01, t-test) the biomass coefficient is considered significantly different. If the new coefficient is larger  it indicates that metabolite is required in higher (lower) amounts than in the reference condition. A large standard deviation indicated that many different selections for that biomass coefficient could give equally good scores (Eq. The average and standard deviation of these biomass coefficients are computed. If the original biomass coefficient is different from the range of newly sampled biomass coefficients (ores Eq. .We used 96 random orderings of the 67 biomass coefficients found in Fig.