The key feature of the theory is that it does not require knowledge of the regulatory network, only of the metabolic part. We derive that maximal metabolic flux can be maintained in the face of varying N environmental parameters only if the number of transcription-factor binding metabolites is at least equal to N. The controlling circuits appear to require simple biochemical kinetics. We conclude that microorganisms likely can achieve maximal rates in metabolic pathways, in the face of environmental changes.One of the marvels of biology is the phenotypic plasticity of microorganisms. It allows them to maintain high growth rates across conditions. Studies suggest that cells can express metabolic enzymes at tuned concentrations through adjustment of gene expression. The associated transcription factors are often regulated by intracellular metabolites. Here we study metabolite-mediated regulation of metabolic-gene expression that maximises metabolic fluxes across conditions. We developed an adaptive control theory,  qORAC for specific flux (q) Optimisation by Robust Adaptive Control. It considers that external changes are sensed by internal “sensor” metabolites that bind to transcription factors in order to regulate enzyme-synthesis rates. We show that such a combined system of metabolism and its gene network can self-optimise its metabolic activity across conditions. We present the mathematical conditions for the required adaptive control for robust system-steering to optimal states across conditions. We provide explicit examples of such self-optimising coupled metabolism and gene network systems. We prove that a cell can be robust to changes in K parameters, e.g. external conditions, if at least K internal metabolite concentrations act transcription-factor binding sensors. We find that the optimal relation of the enzyme synthesis rates of self-optimising systems and the concentration of the sensor metabolites can generally be implemented by basic biochemistry. Our results indicate how cells are able to maintain maximal reaction rates, even in changing conditions.To attain high growth rates, microorganisms need to sustain high activities of metabolic reactions. Since the catalysing enzymes are in finite supply, cells need to carefully tune their concentrations. When conditions change, cells need to adjust those concentrations. How cells maintain high metabolism rates across conditions by way of gene regulatory mechanisms and whether they can maximise metabolic activity is far from clear. Here we present a general theory that solves this metabolic control problem, which we have called  Microbes need to grow fast to outcompete others. They therefore have to maintain high growth rates in changing environments. To achieve this specific metabolic fluxes (metabolic rates per unit of expended enzyme) need to be kept as high as possible. Since metabolic enzymes are a limited resource, cells should behave economically: synthesise the right enzymes in the right amounts, and adapt their levels when conditions change. In this paper we show how cells can achieve this in the case when the growth rate itself is fixed, but a limited protein pool needs to be optimally distributed over metabolic pathway reactions to maximise its steady-state rate.Experimental evidence is mounting that cells are indeed able to tune enzyme levels to maximise the growth rate , a glycolytic intermediate, binds to the transcription factor Cra to regulate genes involved in glycolysis  will cause an increase in [Galin], which is therefore indicative for the external change. Galin can thus act as a signal for the adjustment of enzyme concentrations of the pathway: the transporter concentration should decrease and the others should increase.Depending on the external galactose concentration, less or more enzymatic resources should be invested in the galactose import reaction. This leaves a correspondingly smaller or larger pool of enzymatic resources for the remaining pathway reactions. An increase in ) and the metabolic enzymes as the input-output relation of the gene circuit. qORAC specifies this relation for robust maximisation of specific pathway flux. Whether a gene circuit with realistic biochemical kinetics can be found that can implement this input-output relation then still needs to be determined. Since the gene network for the galactose pathway in yeast is known, the optimal input-output relation may be found by fitting parameters in this network, which we achieved in an earlier paper  is an external concentration which may change value periodically, as shown in vi = eifi(x), i = 1, …, 4, and the kinetics functions fi(x) are defined byj = 1, … 4, whereξ(x2) is defined byA toy metabolic network, with two external parameters and one output flux, is shown in qORAC, consider the complicated branched example network in To illustrate the general applicability of qORAC framework is able to start from nearly any initial condition. As an extreme example, with no enzymes present, and only the sensor concentration and no other internal metabolite, the qORAC-controlled pathway still steers to optimum  Optimisation by Robust Adaptive Control (qORAC) to describe the regulatory mechanism that we study. ‘Robust’ signifies that attaining optimal states is independent of  parameter values—the system is robust to them. ‘Adaptive’ means that the control system steers the metabolic system to optimality without direct knowledge of external changes, contrary to the more widely studied problem of ‘optimal control’, in which the steering mechanism works using external changes as inputs to the controller [We use the term Specific Flux (ntroller .O(x) is also absent. Our approach is therefore more suitable to isolated pathways then to all of metabolism. For such smaller pathways, it is more reasonable to assume that there is a fixed amount of enzyme resources to distribute, and that the cellular growth rate is considered constant. Recent work does suggest, however, that the objective function O(x) studied here in fact matters to cells also on a more global metabolic level [It is important to note that the growth rate itself is not optimised in our approach. Maximising steady state growth rate rather than specific flux requires a fundamentally different approach. The modelling framework should be extended to Metabolite-Enzyme models in which enzymes are made from precursors , 37. In ic level .E. coli seems to be controlled by just three sensors, FBP, cAMP and F1P [An important finding of our work is that the number of sensor metabolites must be (at least) equal to the number of parameters for which the metabolic pathway is robustly optimal. In other words, if the metabolic pathway always achieves states of maximal specific flux, regardless of the values of three (independently changing) environmental parameters, such as, for example, osmolarity, temperature and some nutrient concentration, then the number of sensors is expected to be three. This is a general result that follows from the associated mathematics of this control problem. Finding the sensors experimentally is difficult, and the number of known sensors is still quite small. However, it is telling that the whole of central carbon metabolism in  and F1P .O with x the set of metabolites between the sensors xS). The remaining variables, including the external concentrations, then need to be determined using the optimum The identity of suitable sensors does not follow immediately from the optimisation problem. In general, one needs to make sure that the Implicit Function Theorem applies to the optimum qORAC-controlled networks show remarkably simple dynamics and input-output relations. One would expect that biochemical systems are capable of evolving those, and that synthetic biologists are capable of designing them.An important question is whether the adaptive control can be achieved by molecular circuits, given our understanding of biochemical kinetics and molecular interactions. The explicit example from galactose metabolism in yeast  gives hoThe parameterisation of the optimising circuit is completely determined by the kinetics and the wiring of the metabolic pathway that it controls, since the objective function The internal model principle, applied to metabolic pathway control, suggests a new perspective on the larger problem of understanding metabolic regulation. The theory presented here indicates that knowledge of the metabolic pathway, including properties of catalysing enzymes, is sufficient to understand how this pathway needs to be controlled to maximise flux. It is not necessary to know the controlling regulatory pathway in advance. This offers hope for situations in which this circuit has not been characterised yet, or for which it needs to be designed synthetically.E. coli [Technological advances have spurred recent interest in studying control properties of gene regulatory networks in cellular metabolism. One line of work involves characterising a particular gene control system and studying its theoretical properties. Examples are the perfect adaptation in the chemotaxis network in E. coli , 39, theE. coli  and of tE. coli . SeveralE. coli , deFBA [E. coli , and forE. coli , robustnE. coli , and noiE. coli . In manyE. coli , e.g..The approach taken here differs principally from most previous works in the following respect. The objective  is defined in advance, and the optimal input-output relations are characterised later. The framework is also analytic rather than computational: the input-output relations are obtained by solving the optimum equations qORAC. FCR also explicitly relies on making estimates at each time point under the assumption of steady state. When the system is in fact in steady state, it has reached the desired objective. The principle difference between FCR and qORAC lies in the objective. The input-output relations in FCR come from measurements and ensure steady state properties only. qORAC, however, solves a steady state optimisation problem, and constructs input-output relations directly from the kinetic rate laws of the metabolic pathway itself. Another recent example of a coarse-grained model of cellular physiology including gene expression control can be found in [E. coli. The free amino acid concentration acts as a sensor to ppGpp, which downstream influences gene expression. Two models have been proposed that are based on optimal synthesis of ribosomes so as to maximise growth rate [qORAC, but are designed by hand to approximate maximal growth rates in different conditions.A few recent papers have used adaptive controls similar to ours. So-called Flux Control Regulation  comes cfound in . Two othwth rate , 16. TheqORAC control follows logically from the design objective, it is not easy to decide which intermediate metabolites make it controllable. We cannot expect completely general mathematical theorems. Apparently, some choices of sensors do work, and others do not, for the same pathway, using the same initial conditions. A second, mathematical reason why one cannot expect convergence to optimal states is that if time would be reversed, the control would remain the same, but dynamics would be reversed. The control is based on steady state properties of the system, and these do not change upon time reversal.The choice of sensors sometimes matters for the control to steer the pathway to optimum Figs  and S4. qORAC has direct applications in synthetic biology. To achieve maximal production rates in a biotechnological-product producing pathway requires a controller that qORAC provides. The only ingredient to design such a controller are the enzymatic rate laws in the pathway. qORAC then immediately makes predictions about the optimal enzyme synthesis rates, as a function of one or more intermediate metabolites. As the synthetic biology field advances, synthetic circuits with the required input-output relationships for the constituent enzymes of the pathway can be designed and built. qORAC therefore does not only contribute to the general understanding of steering mechanisms to optimal states, but provides direct operational relevance for microbiology, synthetic biology and biotechnological applications.S1 TextqORAC. We prove that many pathways with qORAC control only have one steady state, the actual optimum. We also give additional illustrations of the qORAC formalism, give details on the numerical integration of qORAC-controlled pathways, and fully describe the kinetics of the pathways considered in this paper.We also give a detailed explanation which and how many sensor metabolites may be used in (PDF)Click here for additional data file.S1 Figdaes_CN_minimal_ICs.m for the code.The pathway is still steered to the optimal specific flux steady state. A: the pathway; B: metabolite concentrations over time , and predicted optimal external metabolite concentration (orange); C: reaction fluxes over time; D: enzyme concentrations over time. See Box 2 in main text for details of the pathway, and the matlab file (TIF)Click here for additional data file.S2 Figx1 to x7; B: dynamics for the predicted optimal metabolite concentrations (ξ). The intersection point of all the curves is thermodynamic equilibrium; C: reaction flux dynamics. Note that the fluxes do not pass through v1 = ⋯ = v6 = 0. Three do, and the others do not, in this example. See SI text for details of the pathway, and the matlab file daes_linearchain_reversal.m for the code.Although the requirements for sensor control are not upheld in this point, the predicted optimum moves smoothly through this singular points and the system adapts as it should. A: linear chain pathway, with external conditions such that flow is initially from (TIF)Click here for additional data file.S3 Figx3 is swapped with x4. B/C: The dynamics of metabolites (B) and predicted K3 values (C) do start to change. However, the dynamics converge to a singular point, and the dynamical system can not continue. This second choice of sensors does not yield a gene expression control system which steers the pathway to optimal specific flux. See matlab code daes_extra_param_wrong.m for the code.A: The pathway, which is identical to that in (TIF)Click here for additional data file.S4 Figf.The left one shows the master pattern, the middle and right figure show two alternative patterns that yield the constant term in the denominator of (TIF)Click here for additional data file.


The human gut microbiome is a complex ecosystem, in which hundreds of microbial species and metabolites coexist, in part due to an extensive network of cross-feeding interactions. However, both the large-scale trophic organization of this ecosystem, and its effects on the underlying metabolic flow, remain unexplored. Here, using a simplified model, we provide quantitative support for a multi-level trophic organization of the human gut microbiome, where microbes consume and secrete metabolites in multiple iterative steps. Using a manually-curated set of metabolic interactions between microbes, our model suggests about four trophic levels, each characterized by a high level-to-level metabolic transfer of byproducts. It also quantitatively predicts the typical metabolic environment of the gut  in approximate agreement with the real data. To understand the consequences of this trophic organization, we quantify the metabolic flow and biomass distribution, and explore patterns of microbial and metabolic diversity in different levels. The hierarchical trophic organization suggested by our model can help mechanistically establish causal links between the abundances of microbes and metabolites in the human gut. Trillions of microbial inhabitants of a human gut play a crucial role in human health and disease. This ecosystem is composed of hundreds of individual species and shaped by extensive nutrient exchange. The network of such cross-feeding interactions between microbes has been extensively studied and shown to be staggeringly complex. Here we propose an algorithm to arrange this network in multiple trophic levels guiding the flow of nutrients from lower to higher levels. This organization is reminiscent of macroscopic food webs converting the biomass from plants to herbivores and ultimately to carnivore predators. We build a simplified model, providing quantitative support for a multi-level organization of the human gut microbiome. It allows us to predict the typical metabolic environment of the gut  in individual patients that is in approximate agreement with the experimental data. The hierarchical trophic organization suggested by our model can help establish causal links between the abundances of microbes and metabolites in the human gut. The human gut microbiome is a complex ecosystem with several hundreds of microbial species , 2 consuMore generally, the construction of mechanistic models has been hindered by the complexity of dynamical processes taking place in the human gut, which in addition to cross-feeding and competition, includes differential spatial distribution and species motility, interactions of microbes with host immune system and bacteriophages, changes in activity of metabolic pathways in individual species in response to environmental parameters, etc. This complexity can be tackled on several distinct levels. For 2-3 species it is possible to construct a detailed dynamical model taking into account the spatial organization and flow of microbes and nutrients within the lower gut , 14, or For around 10 microbial species, and a comparable number of metabolites, it is possible to construct a consumer-resource model (CRM) taking into account microbial competition for nutrients , the genHowever, modeling 100s of species and metabolites, typically present in an individual’s gut microbiome, requires thousands of parameters, which cannot be estimated from the current experimental data. Therefore, any such model must instead resort to a few “global parameters” that appropriately coarse-grain the relevant ecosystem dynamics. Here, we propose such a coarse-grained model of the human gut microbiome, hierarchically organized into several distinct trophic levels. In each level, metabolites are consumed by a subset of microbial species in the microbiome, and partially converted to microbial biomass. A remainder of these metabolites is excreted as metabolic byproducts, which then form the next level of metabolites. The metabolites in this level can then be consumed as nutrients by another subset of microbial species. Our model needs two global parameters: (1) the fraction of nutrients converted to metabolic byproducts by any microbial species, and (2) the number of trophic levels into which the ecosystem is hierarchically organized.While previous studies have suggested that such cross-feeding of metabolic byproducts is common in the microbiome, the extent to which this ecosystem is hierarchically organized has not been quantified. Our model suggests that both, the gut microbiome, and its relevant metabolites, are organized into roughly 4 trophic levels, which interconnect these microbes and metabolites in quantitative agreement with their experimentally measured levels. We also show that this model generates new predictions for the distribution of biomass and flow of metabolites through these trophic levels, quantify the relative contribution of the observed microbes and metabolites to these levels, and thereby describe the effective diversity at each level.f, one of the two key parameters of our model, as the fraction of nutrients secreted as byproducts. The complementary biomass fraction, 1 − f, is the fraction of nutrient inputs converted to microbial biomass. The metabolic byproducts produced from the nutrients entering the gut, can be further consumed by some species in the microbiome, in turn generating a set of secondary metabolic byproducts. We call each step of this process of metabolite consumption and byproduct generation, a trophic level. Due to factors such as limited gut motility, and a finite length of the lower gut, we assume that this process only continues for a finite number of levels, Nℓ, the second key parameter of our model. At the end of this process, metabolites left unconsumed after passing through Nℓ trophic levels are assumed to leave the gut as a part of the feces  human individuals . This flhe feces .In order to quantitatively describe all the steps of this process, our model requires the following information:The metabolic capabilities of different microbial species in the gut, i.e., which microbes can consume which metabolites, and secrete which others. For this, we used a manually curated database connecting 567 common human gut microbes to 235 gut-relevant metabolites they are capable of either consuming or producing as byproducts [The nutrient intake to the gut, which is the first set of metabolites that are consumed by the microbiome. Since the levels of these metabolites in a given individual are generally unknown, we first curated a list of 19 metabolites likely to constitute the bulk of this nutrient intake, and subsequently fitted their levels to best describe the observed microbial abundances in the gut of each individual see . We collThe kinetics of nutrient uptake and byproduct release, i.e., the rates we refer to as λ’s, at which different microbial species obtain and secrete different metabolites in the gut environment see .f) of the total consumed metabolites to their biomass. The remaining fraction, f  was converted to byproducts for the next level. Here, we assumed that each of the species produced all the byproducts it was capable of in equal amounts. After Nℓ such iterative rounds , we assumed that this process ends. We added up all the biomass accumulated by each microbial species across all trophic levels as their total biomass, and added up all the unconsumed metabolite levels as the total fecal metabolome. Finally, we normalized, both the microbial biomass and metabolite amounts separately, to obtain the relative microbial abundances and relative metabolome profiles, respectively.Our model describes the transit of nutrients from the lower gut to the feces of a specific human individual. As the nutrients transit through the gut, the microbial species in the gut consume, digest and convert them to microbial biomass and metabolic byproducts. For a specific individual, our model comprises multiple iterative steps of metabolite consumption by microbes and the subsequent generation of metabolic byproducts, with each step constituting a trophic level. At each level, all metabolites produced in the previous level could be consumed by all microbial species detected in the specific individual’s gut. Note that at the first level, these metabolites were given by the nutrient intake to the gut, as described above. Any metabolite that could be consumed by multiple microbial species, was split across those species in proportion to their experimentally measured relative abundances . Note that, while the agreement between the experimentally observed and predicted microbial abundances shown in P-value 0.05 which did not clear the commonly used threshold of P < 0.05 . For all individuals, the Pearson correlation is 0.44 ± 0.2 and the median of their corresponded P-value 0.046. Taken together, our simplified model supports the organization of the human gut microbiome into roughly four trophic levels with byproduct fraction around 0.9.An example of the agreement between predicted and experimentally observed fecal metabolome in a single individual  consisted of a cohort of 380 human individuals from the Human Microbiome Project (HMP) and the MetaHIT study. We carried over this calibration for three reasons: (1) the lack of availability of simultaneous metabolome measurements for the latter dataset; (2) the fact that both datasets are derived from the human gut; and (3) the similarity in the level of metagenome variability in both datasets.With a well-calibrated and tested model we are now in a position to apply it to a broader set of human microbiome data. To this end we chose data for 380 healthy adult individuals from several countries , while the remaining fraction f = 0.9 is excreted as metabolic byproducts. Some fraction of these metabolic byproducts (blue bar) cannot be consumed by any of the microbes in individuals microbiome and hence ultimately it leaves the individual as part of their fecal metabolome. The metabolic byproducts that can be consumed by the microbiome (turquoise bar) serve as the nutrient intake for microbes in the next level . This scenario repeats itself over the next levels until the level 4, beyond which we assume all the byproducts enter the fecal metabolome. Note that, even though some of these byproducts can be consumed by gut microbes, our previous calibration  and metabolites, averaged over our 380 healthy individuals. The microbes first appear in the second trophic level feeding off the nutrient intake metabolites in the first level. We found that the α-diversity (the average number of abundant entities weighted by their contribution to each level) systematically increases with the level number for both microbes and metabolites. There is no clear trend in the γ-diversity of microbes grouped at the species level .γ− and α-diversity is the highest (∼ 4) in the first level, while being considerably lower (∼ 2.5) in the next two levels. The β-diversity addresses the following important question: how variable are the abundant species between individuals?Finally the beta-diversity of microbial species, defined as the ratio between β-diversity of microbial species could be as large as 4  and lower in the next three levels (∼ 1). While this declining trend was similar to that observed for microbial diversity, surprisingly, the value of β diversity for nutrients was much smaller than for microbes . This suggests the picture of functional stability—in spite of taxonomic variability—in all trophic levels of the human gut microbiome, namely that even though the species composition of the microbiome can be quite different for different individuals, their metabolic function is quite similar. These results supplement similar findings of the HMP project [We also quantified the diversity of metabolites across 4 trophic levels. We found that the levels ∼ . While tAbove we introduced and studied a mechanistic, consumer-resource model of the human gut microbiome quantifying the flow of metabolites and the gradual building up of microbial biomass across several trophic levels. What distinguishes our model is its ability to simultaneously capture the metabolic activities of hundreds of species consuming and producing hundreds of metabolites. Using only the metabolic capabilities—who eats what, and makes what—of different species in the microbiome, we uncovered roughly four trophic levels in the human gut microbiome. At each of these levels, some microbes consume nutrients, and convert them partially to their biomass, while the remainder gets secreted as metabolic byproducts. These metabolic byproducts can then serve as nutrients for microbes in the next trophic level.Understanding such a trophic organization of microbial ecosystems is important because it helps identify causal relationships between microbes and metabolites at two consecutive trophic levels and helps to separate them from purely correlative connections, either at the same or at more distant levels. Thus it extends the previously introduced concept of a “microbial metabolic influence network”  by highlThe concept of trophic levels has been widely used in macro-ecosystems to make sense of flow of nutrients and energy in large food webs , 25, 26,Further, there are several well-known ecological factors that constrain the number of trophic levels in an ecosystem, such as ecological energetics and population dynamics  and acetogenic bacteria , as well as their byproducts, are typically assigned to the lower trophic levels by our model. One can also see that, towards the lower trophic levels metabolites are either very simple and energy-poor, like CO2, H2, H2S, or are those that cannot be consumed by any gut microbial species, such as various amines, short-chain fatty acids (SCFAs), and secondary bile acids. We expect these latter set of metabolites to therefore be present in an individual’s fecal metabolome.The human gut microbiome is notorious for several complex and interlinked metabolic cross-feeding interactions between its resident microbial species , 33. Eve acetate . This acBy assuming such a fluid multi-level trophic organization, our model is able to independently predict the fecal metabolome of individual humans, in quantitative agreement with experimental measurements, comparable to or better than the state of the art. For example, Ref.  used intβ-diversity of microbial species combined with a low to moderate β-diversity of microbial genera to which they belong and low β-diversity of their metabolic byproducts.Our model also allows us to quantify the diversity of both species and metabolites contributing to different trophic levels. One conclusion we made was that the functional convergence of the microbiome holds roughly equally across all trophic levels. Indeed, at each level we observed the microbial diversity across different individuals was considerably higher than their metabolic diversity. Our model also provides additional support to the “lottery” scenario described in Ref. , especiaf and the number of trophic levels Nℓ, assumed to be common to all species. This very small number of parameters has been a conscious choice on our part. We are perfectly aware that species differ from each other in their byproduct ratios, and that the metabolic flows are not equally split among multiple byproducts. This can be easily captured by a variant of our model in which different nutrient inputs and and byproduct outputs of a given microbial species are characterized by different kinetic rates. However, this would immediately increase the number of parameters from 2 to more than 3, 600. To calibrate a model with such a huge number of parameters one needs many more experimental data than we have access to right now. However, we tested the sensitivity of our model to variation in these parameters by repeating our simulations for 100 random sets of nutrient kinetic uptake and byproduct release rates (λ’s in our model), and found that this did not qualitatively change our central result . Surprisingly, our metabolome predictions were also relatively insensitive with respect to varying these parameters  from NJS16. Moreover, we constrained our analyses to microbes only, and therefore removed the 3 types of human cells from NJS16. This left us with a database with 567 microbes, 235 metabolites and 4,248 interactions connecting these microbes with corresponding metabolites , and assigned them to all unmapped species in that genus . This allowed us to map an additional 20 microbial species from the abundance data, and incorporate into our model. Note that we did this additional mapping, only for those genera, where species metabolic capabilities were identical.We then mapped these species names to those listed in the NJS16 database. We found an exact match for 110 species out of 208 in this table. In order to improve the species coverage from the abundance data, we manually mapped the remaining species in the following manner. For those genera in NJS16, whose member species had identical metabolic capabilities, we assumed that the capabilities of other, unmapped species from these genera were the same as these species. For several well-studied bacterial genera, such as To quantify the metabolome levels in each individual, we used the available quantitative metabolome profiles (obtained via from CE-TOF MS) corresponding to the 41 individuals whose metagenomic samples we had. Here, we mapped the reported metabolites to our database of metabolic capabilities using KEGG identifiers, which revealed 84 such measured metabolites.To make predictions about metabolic flow and effective diversity from our model, we used additional metagenomic datasets, namely those from the Human Microbiome Project (HMP)  and MetaThe inputs of our model are the experimentally measured relative abundances of microbial species in each individual, which are known (and described above), and the levels of various nutrients reaching their lower gut, which we fit using the model. Note that we always used the experimentally measured relative microbial abundances, which simplified calculations and made the model easy to run. This also removed the model’s dependence on the initial relative abundances, and the need for a new set of parameters to represent them. Moreover, this assumption is valid; our model’s calculated abundances are very close to the experimentally observed abundances see . This iscnut,i represents the amount of one of the 19 metabolites entering the lower gut of that individual. We inferred these amounts through a fitting procedure described in the next section. Throughout this description, we use the subscript i to refer to metabolites, and α to refer to microbial species.Our model incorporates a set of observed microbial species abundances and the known metabolic cross-feeding interactions between these species, to calculate and predict both the step-wise metabolic flow through the lower gut, and the resulting fecal metabolome. The model does this on an individual-to-individual basis. We started simulating the model with the various levels of nutrients entering the lower gut, represented by the 19-dimensional vector α, as follows:f) represents the fraction of consumed metabolites converted to biomass, and f represents the fraction of input nutrients converted to metabolic byproducts. Ain is a matrix which represents how each species takes up and consumes the nutrients it is capable of. Each term of this matrix, (Ain)α,i was set to zero if species α was incapable of consuming metabolite i as a nutrient α,i was set as follows:In the first trophic level, we calculated how these nutrients entering the gut were consumed by the gut microbiome and converted to microbial biomass, α,i represents the rate at which species α takes up nutrient i, α, and κi is a normalization constant such that, for any nutrient i, the (Ain)α,i for all microbial species α sum up to 1, i.e., α,i = 1 for all values of α and i; this is because we lacked knowledge of the precise rates at which each species takes up different nutrients, and had insufficient data about microbial growth to fit them using our model. To verify that this assumption did not significantly affect the predictions of our model, we repeated our metabolome predictions 100 times by assigning each value of λα,i randomly, chosen from a uniform distribution between 0 and 1 i,α was set to zero if species α could not secrete metabolite i as a byproduct i,α was set as follows:α was capable of secreting.After calculating the contribution of nutrient consumption to microbial biomass, we computed the relative levels of the first level of metabolic byproducts produced by them, as follows:Nℓ such steps, we calculated the final microbial abundances, In the second trophic level , we calculated how the byproducts secreted by the microbes in the previous step were consumed by the gut microbiome and converted to further biomass and byproducts. After Nℓ and the byproduct fraction, f, by comparing the model’s predicted fecal metabolome with the individual’s experimentally measured metabolome. The number of levels and byproduct fraction that best matched the experimentally observed metabolomes, averaged over all individuals, were the ones that were considered to best represent their gut microbiome. To measure the best match, we used two different measures: (1) the Pearson correlation coefficient between the predicted and experimentally measured fecal metabolomes omes see , i.e., 1evel see , as follWe split the byproducts at each level, P-value) gives an indication of the similarity in the trends predicted by our model with the experimentally observed metabolome, the logarithmic accuracy actually calculates the average error (measured in orders of magnitude) between the predicted and experimentally observed metabolomes. In both cases, we used the log-transformed values because we were interested in comparing the quality of our predictions with the experimental measurements at the level of resolution of an order of magnitude. This avoided overfitting in the model. Moreover, note that the nutrient input to the model  resulted in a predicted set of microbial abundances, Note that while the Pearson correlation  t-statistic: the adjusted t-statistic was obtained by dividing the original t-statistic by n was the number of metabolites (or points) that were used to measure the correlation, and p was the number of adjustable model parameters ; (2) t-test: typically the one-tailed t-test with degree of freedom n − 2 is used to compute of P-value for the Pearson correlation coefficient. Here the one-tailed t-test with degree of freedom n − 2 − p was used to account for adjustable model parameters.For each metabolome correlation coefficient that we calculated, we also corrected its associated lsqnonlin in MATLAB R2018a, Mathworks Inc.). We initially chose a random set of nutrient inputs, each chosen randomly from a uniform distribution between 0 and 1, and normalized so that all nutrient inputs summed up to one. For this random set of nutrient inputs, we calculated the predicted microbial abundances using pα is the predicted relative abundance of species α, and mα is the experimentally measured abdunace of species α. We then let the nonlinear optimization routine vary and choose that set of nutrient inputs, which minimized this error. We assumed that this set of nutrient inputs, which best explained the observed microbial abundances, given the microbial cross-feeding interactions, as the nutrient intake to the lower gut, or first trophic level, of that individual. Note that this is only step where we perform fitting in the model. All other subsequent steps, especially the prediction of the fecal metabolome, is an independent prediction from the model. Typically, we fit 19 metabolite amounts for each human individual, who had roughly 80 microbial species.Simulating the model required us to know the nutrient intake to the gut, for which there are no available experimental measurements. Therefore, we inferred the amounts of these 19 intake metabolites by fitting the microbial abundances predicted by our model with those measured from each individual’s microbiome. We used a nonlinear optimization technique for this  i in a specific individual j is given by pi normalized by α-diversityj represents taking the average across 380 individuals used in our analysis.To quantify the diversity of microbes and metabolites at each trophic level across the 380 individuals we studied, we used three measures popular in the ecosystems literature: namely the iversity , 40. Forγ-diversity of microbes and metabolites in their gut, which quantified the “global” diversity across all individuals, as:pi(ℓ) = 〈pi〉j is the mean relative abundance of species (or metabolite) i at the trophic level ℓ across all individuals used in our analysis.Across all individuals, we calculated the β-diversity, which is the ratio of the global to local diversity, as:Finally, to quantify the between-individual variability in microbial and metabolite diversity, we calculated the overall https://github.com/eltanin4/trophic_gut.All computer code and extracted data files used in this study are available at the following URL: S1 Figx = y. Red squares indicate the predicted metabolome for the default set of kinetic parameters used, i.e., when all of λ’s were set equal to 1.Scatter plot of the measured and predicted metabolome where, instead of considering equal specific nutrient uptake and byproduct release rates, λ’s in our model, we take several random sets (in black). Error bars (in black) indicate standard deviation in the predicted levels of specific metabolites for different sets of λ’s. The solid line represents (EPS)Click here for additional data file.S2 Figf and Nℓ. The logarithmic accuracy quantifies the average order-of-magnitude error in our predicted fecal metabolome, when compared with the experimentally measured one Click here for additional data file.S3 Figf, values 0.95 and 0.99. Higher values on the y-axis means worse predictions. This suggests that at 4 trophic levels, f = 0.9 gives the best calibration.Logarithmic accuracy of the model’s predictions between the metabolomes (see (EPS)Click here for additional data file.S4 FigP-values , 3 (orange), 4 (yellow), 5 (purple) and 10 (green).Adjusted lues see  at diffe(EPS)Click here for additional data file.S5 FigBlue nodes correspond to metabolites, red nodes to the microbes. Blue edges show metabolite consumption, red—production.(EPS)Click here for additional data file.S6 Figf and Nℓ. The correlation coefficient is averaged over 41 individuals in Ref. [f = 0.95 and Nℓ = 4. (B) Heatmap of the logarithmic accuracy between experimentally measured and predicted metabolomes for different combinations of parameters f and Nℓ. For this case, the best average logarithmic accuracy 0.69 is given by f = 0.1 and Nℓ = 10.(A) Heatmap of the average Pearson correlation between experimentally measured and predicted metabolomes for different combinations of parameters  in Ref. . For thi(EPS)Click here for additional data file.S7 Figα are drawn from a Dirichlet distribution. (A) A frequency distribution of the highest average Pearson correlation coefficients between the predicted metabolome and the experimentally measured metabolome. The dashed line corresponds to the best mean Pearson correlation coefficients 0.678 (Nℓ = 4 and f = 0.9) achieved in the heatmap shown in The byproduct production abilities of a microbial strain (EPS)Click here for additional data file.S8 FigNℓ = 4 and f = 0.9) achieved in the heatmap shown in (A) A frequency distribution of the highest average Pearson correlation coefficients between the predicted metabolome and the experimentally measured metabolome. The dashed line corresponds to the best mean Pearson correlation coefficients 0.678 ((EPS)Click here for additional data file.S9 FigNℓ = 4 and f = 0.9) without any shuffling, the same as in in (A) A frequency distribution of the highest average Pearson correlation coefficients between the predicted metabolome and the experimentally measured metabolome, when the microbe names are shuffled in the microbial metabolic capabilities. We show here results from 100 such shuffling attempts, where each correlation coefficient in the distribution corresponds to one shuffling attempt. The dashed red line corresponds to the best mean Pearson correlation coefficients 0.678 ((EPS)Click here for additional data file.S10 Figf, the byproduct fraction, and (B) Nℓ, the number of trophic levels, using the same procedure as described in Methods, but on 100 synthetic datasets, each with 41 individuals, constructed by sampling the 41 original individuals used in the main text with replacement. The resulting distributions provide a measure of statistical uncertainty in the calibrated model parameters, with the level of uncertainty in f being approximately 0.05 , and that in Nℓ being negligible .Distribution of resulting calibrated model parameters (A) (EPS)Click here for additional data file.S11 FigResults from all 41 model fitted metagenomes, an example of which was (EPS)Click here for additional data file.S12 FigResults from all 41 model fitted metagenomes, an example of which was (EPS)Click here for additional data file.S1 TableTable of all 4,248 interactions between microbes and metabolites used in the model, from Ref. .(XLSX)Click here for additional data file.S2 TableList of all 19 metabolites used to fit the gut nutrient intake in the model.(XLSX)Click here for additional data file.S3 Tablef = 0.9 and Nℓ = 4 for all 380 individuals are listed.All metabolites in metabolome predicted by the model with global parameters (XLSX)Click here for additional data file.


Non-alcoholic fatty liver disease (NAFLD) is a serious public health issue associated with high fat, high sugar diets. However, the molecular mechanisms mediating NAFLD pathogenesis are only partially understood. Here we adopt an iterative multi-scale, systems biology approach coupled to in vitro experimentation to investigate the roles of sugar and fat metabolism in NAFLD pathogenesis. The use of fructose as a sweetening agent is controversial; to explore this, we developed a predictive model of human monosaccharide transport, signalling and metabolism. The resulting quantitative model comprising a kinetic model describing monosaccharide transport and insulin signalling integrated with a hepatocyte-specific genome-scale metabolic network (GSMN). Differential kinetics for the utilisation of glucose and fructose were predicted, but the resultant triacylglycerol production was predicted to be similar for monosaccharides; these predictions were verified by in vitro data. The role of physiological adaptation to lipid overload was explored through the comprehensive reconstruction of the peroxisome proliferator activated receptor alpha (PPARα) regulome integrated with a hepatocyte-specific GSMN. The resulting qualitative model reproduced metabolic responses to increased fatty acid levels and mimicked lipid loading in vitro. The model predicted that activation of PPARα by lipids produces a biphasic response, which initially exacerbates steatosis. Our data support the evidence that it is the quantity of sugar rather than the type that is critical in driving the steatotic response. Furthermore, we predict PPARα-mediated adaptations to hepatic lipid overload, shedding light on potential challenges for the use of PPARα agonists to treat NAFLD. Novel computational modelling approaches predict the liver’s metabolic response to dietary fat and sugar. A multi-disciplinary team led by Dr. J. Bernadette Moore at the University of Leeds has used novel computational modelling and simulation approaches to understand the livers response to dietary sugars and fats, and the development of non-alcoholic fatty liver disease. Simulations of the team’s multi-scale models, along with their experimental findings, show it is the quantity, not type (e.g. fructose vs. glucose), of sugar that drives fat accumulation in liver cells. Furthermore, they model the behaviour of PPARα, a critical regulator of fat metabolism in the liver, providing cautionary insights into its potential as a therapeutic target. This work demonstrates the potential of systems approaches to elucidate mechanisms underpinning the role of diet in non-alcoholic fatty liver disease. While still potentially reversible, NASH is associated with increased incidence of fibrosis, hepatocellular carcinoma, liver failure and the need for liver transplant.1 Despite the high prevalence of this disease, particularly in obese individuals, the pathogenesis of NAFLD is complex and not well understood, limiting the development of effective treatments. Currently, there are no pharmaceutical agents licenced for the treatment of NAFLD with weight loss, dietary and lifestyle modifications underpinning clinical management.3 Whether or not a low-sugar or low-fat diet should be recommended for NAFLD is controversial and we consider these dietary factors here.Non-alcoholic fatty liver (NAFLD) disease is a major public health concern associated with obesity and the metabolic syndrome. Prevalence is estimated at 30–45% of the adult population in many countries, although NAFLD is typically underdiagnosed due to its asymptomatic nature in its initial stages. Pathogenesis begins with steatosis, the accumulation of lipid droplets within the hepatocytes of the liver. Although steatosis can be reversible and may be viewed as relatively benign clinically,4 Fructose has been scrutinised in part due to its extensive use in beverages such as fizzy and fruit-flavoured drinks for which children and adolescents are major consumers. High fructose intakes have been shown to alter hepatic insulin sensitivity, increase lipogenesis and ectopic lipid disposition in human and rodent studies.5 Hepatic fructose metabolism bypasses a key rate-limiting step in glycolysis leading to the provision of increased substrates for de novo lipogenesis (DNL) and the increased synthesis of long chain fatty acids, triacylglycerol (TAG) and other, often inflammatory, lipid intermediates.6 In addition, fructose regulates the activity of multiple transcription factors involved in the regulation of both lipogenesis and fatty acid oxidation including the carbohydrate response element binding protein (ChREBP), the sterol response element binding protein (SREBP1) and the peroxisome proliferator activated receptor alpha (PPARα).7 However, the impact of fructose at lower, ‘normal consumer’ levels is debatable, and it is unclear if there is a differential impact on lipogenesis and NAFLD beyond the provision of, typically, excess energy.Dietary sugars, in particular fructose, have been implicated in the development and progression of NAFLD and other chronic metabolic diseases.9 The critical point frequently neglected in the, often polarised, debates around whether sugar or fat is the nutrition villain of the day,11 is the key observation that, at a population level, identifying individual culpable nutrients is problematic. While almost no one consumes a low-fat diet (US12 and UK13 adults consume an average of 34–35% of daily energy intake from fat), the vast majority of adults in developed countries consume excess energy from foods high in both sugar and fat, fundamentally contributing to increasing obesity and NAFLD.Recent focus on the negative metabolic effects of a high-sugar diet has led to debate over historical dietary guidelines, which recommend low-fat (considered <35% of daily energy from fat with an ‘acceptable distribution’ of 20–35%) and low-saturated fat diets  for the prevention of cardiovascular disease.14 Computational systems biology has advanced considerably in the last decade, including the reconstruction of human genome-scale metabolic networks (GSMNs), comprehensive models incorporating the metabolic and transport reactions mediated by the proteins encoded within the genome.17 These models can be further constrained to reflect specific tissues, or even specific organelles, using transcriptomic data.20 Recently GSMNs have been utilised for the mechanistic interpretation of clinical NAFLD data.22 However, these models are static and do not reflect the dynamic reprogramming of global metabolism and metabolic adaptation to maintain homoeostasis during sugar and lipid loading. Increasingly, GSMNs are being integrated with detailed gene regulatory and/or physiologically based pharmaco/toxico-kinetic models in the emergent fields of quantitative systems pharmacology/toxicology.23While it is generally accepted that high-sugar and high-fat diets disrupt metabolic homoeostasis and the regulation of lipogenesis, thereby contributing to NAFLD, the molecular mechanisms and temporal order of key metabolic and signalling events are unclear. Here in silico models and systems biology approaches may offer insights into disease mechanisms, generating hypotheses for subsequent experimental testing.25 to study how disruption of metabolic adaptation contributes to NAFLD pathogenesis. We examine two important questions in NAFLD; the differential impact of glucose and fructose on lipogenesis, and the role of the PPARα regulome in liver adaptation to lipid loading.Here we adopt a multi-scale approach, coupling GSMNs to dynamic models of regulatory networks5 specifically, whether or not fructose is more lipogenic than glucose. Utilising the QSSPN24 method, we reconstructed a dynamic, quantitative model of monosaccharide transport and fully parameterised insulin signalling;26 and integrated this to a hepatocyte-specific GSMN19 with an external nutrient exchange set27 representing in vitro conditions constrained by in vitro consumption and secretion rates  was observed , whereas the effect of insulin on glucose uptake disappeared  cells were first treated with physiological and supraphysiological concentrations of insulin and sugars to mimic the human hepatic overfed state in vivo. We confirmed the responsiveness of HepG2 cells to insulin stimulation by measuring the phosphorylation ratio of the RAC-alpha serine/threonine-protein kinase (pAKT/AKT) protein, which transduces signalling from the insulin receptor. In response to a postprandial-like dose of 1 nM insulin, a 1.7-fold increase in pAKT/AKT  was set as the objective function and dFVA was used to explore the maximal and minimal TAG production possible for a given monosaccharide. With an initial concentration of 25 mM glucose, maximisation of TAG production resulted in a rapid production of TAG over time  for TAG was 2300 and 2332 mM.h/g DW for glucose (48.2 h) and fructose (48.5 h), respectively. As expected, minimisation of TAG production resulted in no production of TAG, regardless of monosaccharide  is the predominate lipid species within the neutral lipid core of macrovesicular droplets,ide Fig. . The simide Fig. . InsulinTo confirm the in silico predictions, HepG2 cells were used to detect the influence of the type of monosaccharide, with and without insulin, on hepatic intracellular lipid in vitro. HepG2 cells, with or without 100 nM of insulin, were exposed to either 25 mM of glucose or fructose and measured every 24 h over 72 h by Nile red staining Fig. . Consist31 The prior identification of disruption and activation of PPARα signalling in pilot experiments in palmitate-treated hepatocytes (HuH7 cells),28 was confirmed independently here in a combined pathway enrichment analysis of both the proteomics31 and microarray data sets.28 Enriched pathways identified as statistically significant (P < 0.05) were ranked by clustering coefficient and presented with results from both datasets using hive plots32 , and high-fat fed murine models.s32 Fig. . Enriche19 This allowed examination of the dynamic cellular response behaviours to lipid loading. Although previous reconstructions of the PPARα regulatory network have been published,33 we believe our resulting model to be the most comprehensive model of PPARα-regulated metabolism described to date.With these data as our rationale, a PPARα regulome reconstruction was manually curated from a thorough search of the peer-reviewed literature and online databases Fig . The finP = 0.0003; Fig. PPARα mRNA transcript and protein levels were measured in HepG2 cells treated with 400 μM oleic acid (OA) over 24 h Fig. . Intrace24 the gene regulatory model we employ here is rule-based and has three stable levels of gene expression, allowing for genes expressed at basal steady-state to be reversibly induced or inhibited  and genetic susceptibility, the underlying mechanisms remain unresolved. This lack of understanding has limited the ability to predict progression along the NAFLD spectrum for an individual, or to design effective therapeutic interventions and/or dietary advice. With this motivation, in this work we address two of the outstanding questions within the NAFLD field: does fructose, commonly used as a sweetener, have a greater lipogenic potential than glucose; and, what is the biological impact of activation of PPARα by fatty acids during NAFLD? To address these questions, we have reconstructed hepatic regulatory models for both monosaccharide signalling and transport and the PPARα regulatory network, then integrated these to a genome scale model of hepatic metabolism utilising QSSPN.Associated with the exponential rise in obesity, NAFLD has quickly become the most common chronic liver disease in many countries. Often undetected for many years, NAFLD increases the risk of chronic diseases such as type 2 diabetes and cardiovascular disease, and alters drug metabolism in the liver.34 Studies using supra-physiological doses of single monosaccharides suggest some differential effects, but are difficult to reconcile with the diets of free-living humans. In addition, meta-analyses of studies with blood lipid and liver-related end points show no effect in trials that controlled for energy.37 Studies in vitro also present conflicting conclusions: some studies showing differential effects of fructose at remarkably low (0.72 mM) concentrations of total monosaccharide with increasing fructose:glucose molar ratios;38 other studies show no differential effects until higher (25 mM) doses of fructose were used.39 Such concentrations are generally supra-physiological doses, being significantly higher than concentrations observed in portal blood, which rarely exceed 2 mM. As recently shown by Jang and colleagues (2018),40 the majority of fructose is metabolised in the intestine with extensive fructose-derived glucose, lactate and glycerate found in portal circulation. While we did not simulate this metabolic interconversion in our kinetic model, such metabolic fates are captured within the hepatic model. We did not explore if these metabolic fates were realised in silico by tracing the full metabolic fate of fructose. An interesting future direction would be to expose the cell lines to this mixture of metabolites and compare the response to when the parent (fructose) is given. Additionally, in studies where very small positive effects of fructose on intracellular lipid in HepG2 cells have been shown,42 there is uncertainty about the minimal limit of detection of the lipid assay used.The potential differential effects of glucose and fructose on TAG metabolism were investigated with a reconstruction comprising monosaccharide transport, insulin signalling and hepatic metabolism. The resulting multi-scale, hybrid model was used to perform predictive, dynamic simulations of minimum and maximum flux rates. No differential lipogenic effects were predicted between fructose and glucose, a result verified by experiments in HepG2 cells. These results are important in the context of ongoing disagreement in the literature about potential differential effects of fructose on health and NAFLD.43 The model of Fouget and colleagues was parametrised with 13C labelled glucose and fructose based experimental (GC-MS) data from primary rat hepatocytes treated with 20 mM of glucose supplemented with either 3 or 20 mM of fructose for 2 h. The results show that while 20 mM of fructose inhibited glycogen synthesis, the addition of 3 mM of fructose, a physiological relevant portal concentration (0.2–2 mM44), showed no adverse effects on intracellular energy status. Moreover, the authors observe there was very little flux going through fatty acid synthesis in both experimental models of 3 and 20 mM fructose. The authors attributed this outcome to isolating primary hepatocytes from fasted rats, plus the short experimental incubation time. While the in vitro experiments performed here did not take into account glycogen synthesis; similarly, our experimental HepG2 cells fed glucose and fructose had no differential effects in intracellular lipid over longer periods of exposure. It might be of interest to implement the stoichiometric data produced from Foguet and colleagues43 into our metabolic model in order to incorporate specific rates of hepatic fructose and glucose metabolism. However, whereas our data are from a human hepatoma cell line, the Foguet data are derived from rat primary hepatocytes; ultimately human kinetic data would be preferable. In summary, through the use of a biologically realistic computational model encompassing the key mechanistic modules of monosaccharide processing, we conclude that there is no differential effect on lipogenesis between glucose and fructose.Supporting our results are data from a recently published kinetic model comprising 88 reactions and 81 metabolites of hepatocyte core metabolism capable of simulating energy and redox metabolism.45 Activation of PPARα induces genes involved in fatty acid binding, transport, and β-oxidation, thereby promoting the uptake, utilisation, and catabolism of fatty acids. In NAFLD patients, liver PPARα gene expression negatively correlates with NASH severity, visceral adiposity and insulin resistance.46 The serum lipid lowering fibrates are established weak agonists of PPARα used to treat atherogenic dyslipidaemia. However, fibrates have had disappointing results in trials examining their use in NAFLD, with no improvement in histological NASH observed in several pilot studies.47 Moreover, animal studies show that fenofibrate treatment increases hepatic TAG synthesis and hepatic steatosis suggesting an adverse effect of fibrates and PPARα activation in NAFLD.49The identification of PPARα as a key regulatory network module in liver adaptation to lipid loading was interesting given the potential clinical role for PPARα activation in NAFLD treatment, with dual and selective PPAR modulators currently in phase 2 and phase 3 clinical trials.51 However, the specific role of PPARα in the pathogenesis and progression of steatosis is confounded by conflicting reports in the literature. The finding that PPARα activation appears to have a detrimental role in hepatic steatosis may go some way to explaining the lack of success in trying to exploit PPARα as a therapeutic target in NAFLD treatment.53 However, if one considers that the function of the complement of genes regulated by PPARα is largely associated with fatty acid metabolism, de novo lipogenesis and lipid transport it becomes clear that a PPARα naive system would have a reduced capacity for TAG accumulation. Activation of PPARα results in the induction of expression of multiple genes with direct and indirect roles in TAG synthesis. As such, the regulatory competent model adapts to the increased concentrations of fatty acids in such a way that it can store this excess as relatively safe TAG within lipid droplets.54The reconstruction of the PPARα regulatory network permitted dynamic insights into the role of the PPARα regulome in both fatty acid metabolism and NAFLD. Simulation of lipid loading using just the GSMN (i.e. without PPARα-mediated regulation of gene expression) showed no increase in flux towards TAG synthesis. In contrast, addition of PPARα signalling to the GSMN predicts an increase in TAG synthesis. Such data is consistent with previous studies identifying PPARα as a key regulatory node in lipid metabolism and in diseases manifesting steatosis.55 Future work to reconstruct other critical regulatory systems will allow us to explore the role of each of these transcription factors through simulations such as those shown here with PPARα. However, a significant advantage of the use of modelling and simulation, and the QSSPN approach, is the facility to not only study these regulatory factors in isolation, but also as integrated, cross-talking networks of transcription factors.The in vitro experiments, designed to test the hypothesis generated by the in silico experiments with the PPARα regulome model, are in agreement with simulated results. In the presence of the PPARα antagonist GW6471, a reduced accumulation of lipid droplets in the early stage of the steatotic response was observed in the cultured hepatocytes. We note that while the model simulations show a stark difference between the regulated and unregulated systems, the in vitro cell system exhibits a subtler, but statistically significant, difference. This is not unexpected given the qualitative nature of this model, driven by the scarcity of kinetic parameters to describe the induction and turnover of 91 PPARα target genes. As such, the in silico model accurately reproduces the behaviour of the network, but not the absolute quantitative changes. The endpoints that are being monitored in both the in vitro and in silico models are subtly different but allow us to compare the response of the two systems. Finally, while our in silico model is limited to PPARα-mediated regulation of gene expression, our in vitro system is regulated through the activity of an interlinking network of transcription factors. PPARα is not the only mediator of an adaptive response to excess fatty acid in hepatocytes.55 However, two conclusions from our work suggest that this is not the case for PPARα signalling during the hepatocyte response to lipid stimulation. First, the in vitro data shows that although PPARα pathways are identified in our omics pathway analysis, this is due to activation of these pathways and not due to regulation of PPARα protein expression itself. Second, the in silico simulations integrating the PPARα regulatory network cause an increased flux towards TAG. Rather than the traditional interpretation of dysregulation, we suggest that, in the case of lipid loading, dysregulation of PPARα signalling is a result of persistent and repeated activation of the receptor. Given that the model predicts a continuing regulatory ‘ripple effect’ even after the clearance of the agonist, it is clear that regulation is not simply an ‘on’ ‘off’ response limited by interaction of agonist and receptor. It should be noted that the presented simulations are not in real time and so it is not possible to determine how long the reconstitutive phase persists. However, if this phase persists sufficiently that the basal state is not reached before the next signalling event, then repeated signalling would result in a form of dysregulation that could lead to disease.56 The current model only simulates regulation through a single transcription factor. In reality, nuclear receptors form a complex interactome that acts to coordinate the biological response to chemical challenge. As such, expansion of the current model to include multiple transcription factors may enhance the prediction robustness. Likewise, both in silico and in vitro models represent isolated hepatocytes; hence, their ability to reproduce a systemic disease that affects other tissues as well may be limited. Future work should replicate the interplay of multiple cell types that reside in the liver, such as hepatic stellate cells and Kupffer cells, as well as the interaction between different organs.It is often considered that the emergence of NAFLD is the result, at least in part, of dysregulation of critical metabolic/transporter mechanisms. Dysregulation implies that the system is no longer being regulated correctly either through interference in agonist binding to the transcription factor or through suppression of transcription factor expression.In summary, this work demonstrates that QSSPN permits both integration of qualitative and quantitative regulatory models with GSMNs. The multi-scale models herein, reproduce sugar and fat metabolism in silico, generating hypotheses that can be confirmed in vitro. Our data supports the absence of a differential lipogenic effect between glucose and fructose. In addition, we have provided mechanistic insight into the role of the PPARα regulome in the early metabolic reprogramming of hepatocytes following lipid loading.19 biologically realistic monosaccharide transport kinetics, and insulin signalling.26 To represent in vivo-like transportation of glucose and fructose, Michaelis–Menten kinetics were utilised to map substrate concentrations to fluxes within the activity list of the monosaccharide constraint places. All parameters for the kinetics were sourced from the literature with a greater weight given to values derived from whole-cell uptake experiments, as opposed to recombinant systems; further detailed in the This model integrated three components: a hepatocyte-specific GSMN,26 using the Petri net editor software Snoopy 257  software.25 As described previously,23 specific adjustments were made to better detail metabolic pathways of interest accurately . PPARα-regulated genes were represented using a rule-based model of gene expression, expanding on our previously described gene expression model Figure .24 PPARαes Table . As desces Table .The reconstructed QSSPN model was used to simulate a dynamic, PPARα competent regulatory model and a fixed gene expression model. The number of simulation steps was optimised so that the metabolic network returned to a basal, steady-state flux after treatment.2 air, humidified environment and regularly confirmed mycoplasma-free through a PCR assay. Cells were routinely seeded at 30,000 cells/cm2 and sub-cultured in Dulbecco’s modified Eagle’s medium (DMEM) supplemented with 10% foetal bovine serum, 1% non-essential amino acids, 2 mM l-glutamine, and 100 U/mL penicillin and 100 U/mL streptomycin  for 72 h prior to treatment, and passaged by trypsin treatment to represent independent experiments. After supplementation, final glucose concentrations of the media were estimated as 0.87 g/L (4.8 mM) and 3.92 g/L (21.7 mM) representing low and high glucose exposure, respectively. For the monosaccharide assays, glucose-free DMEM was supplemented with either 25 mM glucose or 25 mM fructose, with and without 100 nM insulin. In addition to the routine supplements listed above, these media also contained 1 mM sodium pyruvate .Human hepatocellular carcinoma-derived cell lines  were maintained at 37 °C in a 5% COn = 3), 1, or 100 nM of insulin (n = 4) in serum-free DMEM for 15 min. For the fatty acid treatments, fatty acids were first solubilised in dimethyl sulfoxide (DMSO) and conjugated to 5.56% (v/v) fatty acid-free bovine serum albumin in a 1-h incubation at 37 °C with periodic vortex mixing prior to addition to serum-free DMEM. Final concentrations of DMSO in treatment media were maintained at 2% (v/v); a dose determined experimentally not to be cytotoxic by both LDH and MTT assays  were concomitantly treated with 400 µM OA in the presence or absence of 10 µM PPARα antagonist GW6471  for 2 h.For pAKT measurements, cells were treated with vehicle (n = 5). Briefly, an automated cell counter  was used to count and collect 500,000 cells after trypsin treatment. Cells were centrifuged for 5 min at 500 × g at room temperature and the supernatant was removed. Cells were re-suspended in 500 μL of 1 μM Nile red in PBS pre-warmed to 37 °C and incubated for 10 min in darkness at 37 °C. Cells were centrifuged again and the supernatant removed before adding 500 μL of pre-warmed PBS. Three technical replicates of 100 μL of Nile red stained cells suspended in PBS per well were incubated for 2 min and shaken for 30 s at 37 °C before reading fluorescence  on a multi-mode plate reader .The fluorescent, lipophilic dye, Nile red  was used to detect intracellular lipid after OA and sugar treatments  and at 24 and 48 h of 25 mM glucose (n = 5) and fructose  containing media, or after OA treatment (n = 3); and quantified by using glucose and fructose assay kits .Sugar consumption was monitored by sampling the culture media at 0 h (n = 3) were homogenised in Trizol  and total RNA isolated as per the manufacturer’s instructions. Quantity and purity was assessed by absorbance spectroscopy ; integrity was confirmed via gel electrophoresis. RNA samples were DNase treated prior to first strand synthesis  and SYBR green based PCR run using custom designed primers  were homogenised in radio immunoprecipitation assay buffer  containing protease and phosphatase inhibitors . Cell homogenates in RIPA buffer were spun through a Qiashredder column  to break up insoluble cellular debris. Protein was quantified by a BCA assay  and 20 µg from each sample subjected to SDS-PAGE and subsequent immunoblot analysis. Blots were probed for PPARα , COXIV , pAKT or AKT . Immobilised proteins were quantified using secondary antibodies conjugated to near infra-red flurophores and visualised using the odyssey system . All blots within each respective experiment were processed in parallel.For protein isolation, treated cells , unless otherwise specified. One-way ANOVA with Tukey’s or Dunnett’s test post hoc; two-way ANOVA with either Tukey’s or Bonferroni’s test post hoc; and two tailed t-test with Welch’s correction were performed, as appropriate, to detect statistical significance between groups. The level of statistical significance was set at http://www-dssz.informatik.tu-cottbus.de/DSSZ/Software/Snoopy) and implemented by QSSPN . All files that support the findings of this study are available from the corresponding author upon reasonable request.All models were built using the Petri net edition software Snoopy  via the PRIDE partner repository with the dataset identifier PXD001442.31 All other data that support the findings of this study are available from the corresponding author upon reasonable request.The MS proteomics data have been deposited to the ProteomeXchange Consortium (Supplemental Information


A recurrent problem in genome-scale metabolic models (GEMs) is to correctly represent lipids as biomass requirements, due to the numerous of possible combinations of individual lipid species and the corresponding lack of fully detailed data. In this study we present SLIMEr, a formalism for correctly representing lipid requirements in GEMs using commonly available experimental data.Saccharomyces cerevisiae, we can represent accurate amounts of lipid species, analyze the flexibility of the resulting distribution, and compute the energy costs of moving from one metabolic state to another.SLIMEr enhances a GEM with mathematical constructs where we Split Lipids Into Measurable Entities (SLIME reactions), in addition to constraints on both the lipid classes and the acyl chain distribution. By implementing SLIMEr on the consensus GEM of https://github.com/SysBioChalmers/SLIMEr.The approach shows potential for better understanding lipid metabolism in yeast under different conditions. SLIMEr is freely available at The online version of this article (10.1186/s12918-018-0673-8) contains supplementary material, which is available to authorized users. Genome scale metabolic models (GEMs) are widely used to model and compute functional states of cellular metabolism  and as sA requirement for formulating the biomass pseudo-reaction are abundance measurements of every single constituent; however, this is seldom available for individual lipid species. Instead, it is more common to measure separately (i) a profile of all different lipid classes, for example by high-performance liquid chromatography , 7; and The most common approach to represent lipid metabolism in GEMs is to enforce a specific distribution of each individual lipid species, either by using detailed experimental data , 11 or bA second common approach is to allow any specific lipid to form a corresponding generic lipid class  and to only constrain those classes with experimental abundances from lipid profiling , 16. TheSaccharomyces cerevisiae (budding yeast), a model that has undergone iterative improvements  of the corresponding amino acids in yeast. In this study we focus on the lipid pseudo-reaction, which becomes more challenging to formulate, because there are so many different individual species. One option is to define an equivalent reaction to Eq.i coefficients are fractions inferred from FAME data. This generic Acyl – CoA is then used to form each generic lipid species, forcing then every lipid class to have the same acyl chain distribution. The latter is an important limitation of this approach, considering that the acyl chain distribution can vary significantly across lipid classes  can be directly transformed to the stoichiometric coefficient in Eq.Split Lipids Into Measurable Entities and are hence referred to as SLIME reactions. As the name suggests, these pseudo-reactions take each specific lipid and split it into its basic components, i.e. its backbone and acyl chains:ij is a lipid of class i and chain configuration j, Bi the corresponding backbone, Ck the corresponding chain k, and si and sjk the associated stoichiometry coefficients. These reactions replace any pseudo-reaction of the sort of Eq.In this study we solve all the problems presented above through two new types of pseudo-reactions, to account for both constraints on lipid classes and on acyl chains. The first pseudo-reactions mentclass2pt{minimThe second type of pseudo-reactions are new lipid pseudo-reactions, which will in turn replace Eq.i would be equal to 1 and sjk would be equal to the number of repetitions of the corresponding acyl chain k in lipid j. However, as the abundance data often comes in mass units, si must be equal to the molecular weight [g/mmol] of the full lipid, and sjk must be equal to the molecular weight of the corresponding acyl chain k, multiplied by the number of repetitions of k in configuration j. By choosing these values we allow the SLIME reactions to convert the molar production of the lipid [mmol/gDWh] into a mass basis [g/gDWh], which in turn will be converted to a lipid turnover [1/h] by the lipid pseudo reactions.For the new reactions to be consistent, we need to choose adequate stoichiometric coefficients for Eq.We implemented SLIMEr in the consensus genome-scale model of yeast version 7.8.0 , a modelFor the reference model, we used both lipid profiling and FAME data at low growth rate and no stress conditions . The lipWith the enhanced model we also studied in how many ways lipid requirements can be satisfied spending the same amount of energy, by performing flux variability analysis (FVA) Fig. b. ComparTo validate model predictions, we used reported data  includinComparing these in silico lipid distributions to the original in vivo measurements Fig. a, the enS. cerevisiae depending on the genetic background and environmental conditions [It should be noted that even though SLIMEr improved the model’s lipid composition predictions, many other distributions are still predicted to be equally likely for all simulated conditions /gDW more than the enhanced model. Also in this condition, the simulated growth-associated ATP maintenance (GAM) without accounting for known polymerization costs of proteins, carbohydrates, RNA and DNA  was of 3As previously mentioned, we did not see a significant reduction in flux variability of predictions compared to the permissive approach , as conventions for naming lipids vary a great deal between different databases and models. Introduction of standardized metabolite ids [Even though developed for the consensus GEM of lite ids , 29 can With SLIMEr we can now correctly represent biomass requirements from lipid metabolism in genome-scale metabolic models. The approach allows the model to satisfy at the same time requirements on the lipid class and acyl chain distributions, which is a significant improvement compared to only being able to constrain lipid classes , 16. We S. cerevisiae, strain CEN.PK113-7D, growing on minimal media at a growth rate of D = 0.1 h− 1 was used [2 production.All data used in this study was collected from literature. For the initial model analysis and the analysis of lipid metabolism under increasing levels of stress, aerobic glucose-limited chemostat data of was used . The menS. cerevisiae grown aerobically on SD media at maximum growth rate (shake flask cultures), under 8 different conditions: four different BY4741 strains (a wildtype plus three knockout strains), each cultivated at both 24 °C and 37 °C [− 1, based on previous batch simulations of the yeast GEM [For model predictions of specific lipid distributions, we used published data of nd 37 °C . In thatnd 37 °C  and conseast GEM .Add pseudo-metabolites representing each specific backbone, each specific acyl chain, the generic backbone and the generic acyl chain.Add for each specific lipid species a SLIME reaction. These reactions replace the previous ones of the sort of Eq.Add all three new lipid pseudo-reactions Fig.  using thScale either the lipid class or the acyl chain abundance data so that they are proportional, as the approach is based on exact mass balances. For this, an optimization problem is carried out where the coefficients of the corresponding pseudo-reaction are rescaled to minimize to zero the excretion of unused backbones and acyl chains


Saccharomyces cerevisiae show a drastic decrease in ATP concentration under oxidative stress, together with a decrease in concentration of other tri- and diphosphates. This raises a question if hydrolysis of 5-fluoro-2-deoxyuridine diphosphate (FdUDP) under oxidative stress could not lead to the presence of FdUMP and the activation of so-called ‘thymine-less death’ route. We attempted to answer this question with in silico modeling of 5-FU metabolic pathways, based on new experimental results, where the stages of intracellular metabolism of 5-FU in Saccharomyces cerevisiae were tracked by a combination of 19F and 31P NMR spectroscopic study. We have identified 5-FU, its nucleosides and nucleotides, and subsequent di- and/or triphosphates. Additionally, another wide 19F signal, assigned to fluorinated unstructured short RNA, has been also identified in the spectra. The concentration of individual metabolites was found to vary substantially within hours, however, the initial steady-state was preserved only for an hour, until the ATP concentration dropped by a half, which was monitored independently via 31P NMR spectra. After that, the catabolic process leading from triphosphates through monophosphates and nucleosides back to 5-FU was observed. These results imply careful design and interpretation of studies in 5-FU metabolism in yeast.The cytotoxic effect of 5-fluorouracil (5-FU) on yeast cells is thought to be mainly via a misincorporation of fluoropyrimidines into both RNA and DNA, not only DNA damage via inhibition of thymidylate synthase (TYMS) by fluorodeoxyuridine monophosphate (FdUMP). However, some studies on  Modeling and analysis of metabolic pathways have received an increasing amount of attention over the past two decades . This inSaccharomyces cerevisiae is a convenient and inexpensive model to test the response of anticancer compounds [ompounds , due to ompounds ,12 nor tompounds , therefoompounds ,15. Thisompounds . Dephospompounds  in human2O2 (0.05–1.0 mM) to the yeast cultures with low (0.025%) and high (2%) glucose concentration resulted in a sharp decrease in ATP and a less extensive decrease in GTP, CTP, UTP and ADP levels, respectively, [Bakers’ yeast can metabolize glucose using the fermentative or oxidative pathway, depending on the concentration of glucose . Both coctively, ,19 in fectively, , who looS. cerevisiae cytoplasm using NMR spectroscopy. We observed the increase in FdUMP concentration already during the drop in ATP concentration, and even sharper increase in FdUMP once ATP has been completely depleted.A decrease in triphosphates in response to oxidative stress raises a question if the shift toward catabolic processes caused by absence of ATP could be the source of FdUMP in 5-FU metabolism in yeast. Here, we simultaneously followed levels of 5-FU metabolites and ATP in the S. cerevisiae W303, , [The strain used in this work was the wild-type n1-100),  transforn1-100), . Yeast cThe growth rate and survival of yeast cells in the presence of 0.0, 0.1, 0.2, 0.4 and 0.8 mM 5-FU was measured to determine the optimal 5-FU concentration in the growth medium, which slightly affected the growth rate and allowed to follow its concentration in the cells. Cells growth in the presence of 5-FU was followed by measurement of optical density at λ = 600 nm. Cell viability was assessed after 4-h incubation with 5-FU (0–10 mM) by plating serial dilutions of the yeast cultures on YPD plates , and counting the colonies formed after incubation at 28°C for 2 days.2O and directly subjected to NMR measurement or stored at −80°C. After each centrifugation, including washing of the cells, the samples of supernatant were collected to determine the 5-FU content.To prepare samples for NMR measurements, exponentially growing yeast cells (1 L) were treated with 0.1 mM 5-FU for 12 h. Yeast cells were then pelleted by centrifugation, washed twice with water, resuspended in 0.2 mM Tris buffer at pH 7.5 (12 ml) and disrupted with glass beads of 0.5 mm diameter) by vortexing at the top speed of a tabletop mixer for 10 periods of 1 min separated by 1-min periods of cooling on ice. Cell debris was removed by three rounds of centrifugation (8000 rpm for 15 min and twice at 14000 rpm for 15 min). Resulting supernatant was divided into 600-µl portions, mixed with 10 µl ml D19F spectra, each acquired for 1 h, were analyzed in the pseudo 2-D mode to minimize possible disruptions. All these spectra were collected at 376.32 MHz on a spectrometer equipped with a 5-mm inverse broadband pfg probe at 25°C using an s2pul pulse sequence with a spectral width of 8.0 kHz, 16000 data points and 488 scans. The recycle time of 7.4 s (i.e. relaxation delay of 5.4 s) was used as a compromise between the standard qNMR approach [All NMR spectra of the samples of yeast cytoplasmic fraction were recorded on Varian Inova-400 MHz spectrometer, and processed with MestreC 4.5 . Seventeapproach  and maxi31P spectra was additionally recorded at 1-h intervals for a part of the same sample, which was temporarily stored at −80°C to minimize uncontrolled spontaneous catabolic reactions. 31P NMR spectra of cytoplasm samples were collected at 161.897 MHz. Fourteen spectra were acquired in 1-h intervals at 25°C using an s2pul pulse sequence with a spectral width of 6.5 kHz, 20802 points and 384 scans. Since only the time evolution of a particular resonance was monitored, the repetition time was reduced to 10 s to enhance S/N ratio. Additional inspection of the intensity of H1′ and H8 resonances of ATP/ADP (6.17/8.47 ppm) and GTP/GDP (5.93/8.13 ppm) [To monitor the balance of ATP and its metabolites, a series of .13 ppm)  in the s.13 ppm) .S. cerevisiae (budding yeast), listed in in silico model of 5-FU metabolism in yeast.Twenty-two reactions and sixteen species for pyrimidine metabolism in S. cerevisiae, but were used in the proposed model as the hypothetical analogs that mimic return pathways.The presumed physiological directions of the investigated metabolic reactions have been chosen according to the Kegg pathway maps (sce00240) indications. Chosen species and moieties (19F NMR spectrum (e.g. 5-FUrd and 5-FdUrd). The experimental 31P NMR data collected in the period 1–14 h were extrapolated to the range of 0–17 h using the scale-free approximation with the relative ATP level (t = 0) set to 1.The kinetic model of 5-FU metabolism was fitted to the experimental data representing the evolution of 5-FU metabolites and ATP concentrations over time. All the data for 5-FU metabolites recorded during the period 1–17 h were used in the simulations. The time-evolution of particular metabolite concentration was fitted individually, and then summed for groups of compounds indistinguishable in In general, the properties of the same enzyme acting on different species were distinguished and the specific attributes marked by the successive natural numbers , e.g. 2.7.4.9 (1) and 2.7.4.9 (2), for dUMP and dTMP kinase.Km, for the phosphohydrolase 3.6.1.5 (1)-(4) was fixed (according to Brenda database) to Km = 12.5 µM  and Km = 15 µM . However, to seriously reduce the number of investigated items and this way the error of the estimation, the parameters of the other enzymes, acting for different substrates, were treated as invariant. Analyzed reactions are listed in To avoid the fitting ambiguity, the well-documented value of Michaelis constant, The Copasi 4.22 simulator for biochemical networks  were useKm, apparent Michaelis conts. ; Ki, inhibition const., Keq, equilibrum constant.where symbols meant: V, maximum rate ; −6. Finally, only the five most accurate attempts were considered. For each investigated parameter, the best fit value (bfv), the average value of analyzing attempts (avg), the standard deviation of the sample (stds) and the dev/stds ratio  were analyzed.After the preliminary tests with different parameter estimation methods, start values and the bounds, the Hooke and Jeeves heuristic method , and the respectively wide enough parameter ranges, were chosen to pre-minimize the objective function (weighted least squares) below arbitrary value 0.15, to ensure the freedom, and the initial precision, in the following parameter search. Then, several consecutive attempts using the same method and the previous adjustments as starting points were performed till the variation in the value of the objective function was less than 10The question how much a change in a concentration of a given substrate can modify the reaction rate of an isolated enzyme, or how much the change in an activity of a given enzyme can modify a given pathway flux or a concentration of a metabolite was resolved by the metabolism control analysis (MCA).The effect of 5-FU concentration on cell growth was monitored by means of the optical density at λ = 600 nm OD in . The inhS. cerevisiae is highly susceptible to the 5-FU treatment , the concentration of which was approximately 1 mM seemed to guarantee penetration of 5-FU into the cell interior and the relative robustness of the cellular metabolism. Consequently, 1 mM 5-FU was used in all further experiments.The dose–survival curve  clearly 19F NMR spectra obtained for yeast after a short (1-h) incubation with low concentration (1 mM) of 5-FU. The spectra recorded immediately and 11 h (marked in red) after the incubation, both demonstrate that 5-FU efficiently penetrates the yeast cell interior. Contrary to the Parisot study on Nectria haematococca [atococca , beside It should be noted that extreme resonance broadening that results from inhomogeneous and variable distribution of cells spontaneously sedimenting in the NMR tube precluded any quantitative analysis of the data. This could be, however, overcome by either immobilization of cells or sole analysis of extracted cytoplasmic fraction.31P NMR spectra recorded in pseudo-2D model (not shown). The concentration of ATP drops within 4 h, nearly to zero . During the next 13 h, we did not observe any process leading to the production of ATP.Relative changes in the ATP concentration were analyzed in 19F NMR spectra, 1 h each, were recorded successively for 17 h.19F NMR spectra 5-FU, its nucleosides, and corresponding mono-, di- and triphosphates were assigned (c) fails in the range of 1–10 ns, the value of which is characteristic for small RNA (20–30 nt), while for tRNA τc was estimated to be ∼23 ns [19F spectrum recorded of poly(FU)  [In all recorded assigned . Both rie ∼23 ns . Locatiohia coli ,34), whihia coli  or 5-FU hia coli , which ihia coli . Summarior tRFs) ,39, but 19F spectrum [We also observe weak signal . Theoretical predictions of the best fit model, i.e. the kinetics of changes in flux, and concentration, at the time range, both, the same as for the experiment , and in the long time scale , were also presented in Supplementary Material.The quality of the fit was illustrated in Supplementary Figure S2, presenting the linear regression analysis of the trend in the plot of the fitted variables: predicted vs observed values , flux control coefficient (FCC) and concentration control coefficient (CCC) were presented in 19F NMR spectroscopy already in the late seventies [in vitro and in vivo attempted to understand the complexity of the metabolism of fluorinated compounds.The absence of endogenous fluorinated compounds in living cells serves a chance to follow a metabolic pathway of potential drugs that are fluorinated. In case of 5-FU, its incorporation into tRNA was observed with eventies . Since tIn the present study, we attempted to resolve a certain incongruence in the body of knowledge about 5-FU metabolism in yeast. The absence of key enzymes in yeast (sce00240 in ) capableKeq = 4.689, Successful fitting of the proposed theoretical model of 5-FU metabolism  and 4 toKma, for the reaction ATP and FUDR  there have been seen still effective FRNA and FDNA upload, and the upload of FdUDR hypothetically corresponding to FdUMP. In the next phase of ∼3 h, there was transfer of metabolites from FRNA and FUTP+ level down to FUDP+ level and the balance of fluxes through 2.7.4.14 and 3.6.1.5 (2) . After 6 h, in the ATP-free phase, metabolites started accumulating at the FUMP+, FUDR+ and 5-FU levels . Then in later (after approximately 9 h) phase 5-FU deoxy-form processing by 1.17.4.1 stopped . Discussed model also predicts the long-term behavior of the system with the asymptotic steady state flux around the triangle 2.4.2.9, 3.1.3.5 (2) and 3.2.2.3  and stable nonze-ro concentration of ADP, 5-FU, FUDR . Other metabolites in the model vanished down to the relatively very small values.Km (irr. Michaelis–Menten model), for three essential enzymes  fall in the range reported by Brenda database, for three other enzymes they are up to two orders of higher magnitude. In a case of 2.1.1.45, Km is 2-order lower, and for hypothetical pathways through 3.1.3.5, Km is extremely low. It may indicate the toxic effect, the molecular crowding resulting in the difficult accessibility of enzymes and metabolites, or the inadequate modeling requiring further studies. Not enough confirmed activity of 3.1.3.5 in S. cerevisiae by leading databases, but demonstrated by a non-zero flux in the performed simulations, may indicate that the functional role of this 5′-nucleotidase could take over 3.1.3.1 and 3.1.3.2. Further, more detailed investigation a kinetic model with the toxic inhibition and a possible replacement taking over the important catalytic function, should be considered.The bfv of the parameters of the model fall in the distance dev < 2 stds from the average for the five most accurate attempts, what indicates the reasonable fitting. In overall, estimation of the initial concentrations of species (Supplementary Table S1) is worse (stds @ 0.8) than the estimation of the other parameters (As Osorio and co-workers had shown ,19, defiDue to differences in the enzymatic repertoire between human and yeast, our results cannot be directly used when studying 5-FU metabolism in human. However, Shin and co-workers  had implClick here for additional data file.