Cells can sense changes in their extracellular environment and subsequently adapt their biomass composition. Nutrient abundance defines the capability of the cell to produce biomass components. Under nutrient-limited conditions, resource allocation dramatically shifts to carbon-rich molecules. Here, we used dynamic biomass composition data to predict changes in growth and reaction flux distributions using the available genome-scale metabolic models of five eukaryotic organisms (three heterotrophs and two phototrophs). We identified temporal profiles of metabolic fluxes that indicate long-term trends in pathway and organelle function in response to nitrogen depletion. Surprisingly, our calculations of model sensitivity and biosynthetic cost showed that free energy of biomass metabolites is the main driver of biosynthetic cost and not molecular weight, thus explaining the high costs of arginine and histidine. We demonstrated how metabolic models can accurately predict the complexity of interwoven mechanisms in response to stress over the course of growth. As the three main requirements for growth, the principal drivers of metabolic shifts are carbon, nitrogen, and energy sources. Several studies have focused on identifying the response mechanism of organisms to the depletion of each of the sources2. Metabolic adaptation has been associated with changes in the production or degradation rates of biomolecules. These profiles are observed in various heterotrophic and photoautotrophic microorganisms, increasing their resistance to stress conditions and nutrients limitation12. Depletion of carbon and energy sources directly reduce the synthesis of all biomass precursors since carbon is the backbone of nucleic acids, proteins, lipids, and carbohydrates and all anabolic pathways consume energy. On the other hand, nitrogen depletion has been proven to selectively decrease the synthesis of proteins and nucleic acids, triggering a metabolic response that upregulates the synthesis of carbon-rich compounds13. Previous studies on the metabolic response mechanism to nitrogen depletion have identified key signal metabolites13 and global biomass composition trends15. However, an in-depth analysis at the genome scale has not yet been employed to understand how metabolic pathway use changes to survive in nutrient-deplete conditions.Perturbations in environmental conditions require organisms to withstand transient phases from nutrient abundance to nutrient depletion. Adequate physical and metabolic responses enable microorganisms to survive under these dynamic environments16. Using a reduced number of known uptake rates, or constraints17, M-model simulations predict growth and flux distributions (phenotypes) under diverse genetic and environmental conditions, identifying the main drivers of metabolism14. In this approach, the formulation of the biomass objective function (BOF) is highly important to obtain biologically relevant flux distributions. Each biomass precursor in the BOF pulls resources from the network depending on its stoichiometric coefficient; ideally each coefficient is experimentally determined. Considering this dependence, we devised a strategy to compute dynamic flux distributions by using time-course biomass composition data, thus expanding the scope of M-models from a steady state to several pseudo-steady states encompassing growth under stress conditions and in time-dependent processes1.M-model simulations allow to identify main metabolic reactions driving growth phenotypes under diverse genetic and environmental conditions18. We used time-course composition data to define BOFs at six timepoints of culture for five eukaryotic microorganisms . High quality and validated M-models exist for all five organisms22. Then, flux balance analysis (FBA) using the COBRA Toolbox23 was employed to calculate flux distributions at each timepoint and growth mode (heterotrophic or photoautotrophic). We predicted variations in flux distributions that reveal time-specific metabolic activities across compartments, thus describing the metabolic response of different organisms to nitrogen depletion. We further explain how flux distributions are shaped by changes in the biomass composition by calculating the component-specific impact on growth simulations, which is referred to in this work as sensitivity. The sensitivity of a component was calculated as the variation of growth rate due to a change in its abundance in the biomass. Our results show that sensitivity holds a tight relationship with the biosynthetic cost of each component, which placed lipids of high molecular weight as the most impactful on growth. However, we showed through a deeper look into the biosynthetic cost of amino acids that molecular weight does not entirely explain the cost of biomass components, as was the case for arginine and histidine. Rather, we found that the underlying driver of cost is the free energy contribution of the chemical groups contained in the biomass components.We employed this dynamic simulation procedure to study the metabolic effect of nitrogen depletion, a common and important phenomenon in nature and various biotechnology processesC. vulgaris, iCZ8433, and P. tricornutum, iLB102724, and the heterotrophic cell factories Chinese Hamster Ovary cell, iCHOv119, S. cerevisiae, iMM90422, and Y. lipolytica, iYali420 . We included time-course metabolomics data in the M-models of the phototrophs 420 Fig. . The genC. vulgaris, data were collected under both heterotrophy and photoautotrophy, and for P. tricornutum under mixotrophy and photoautotrophy. All datasets were aligned in six timepoints , phospholipids , and other lipids , such as pigments, sulfolipids, and glycolipids. We used experimental measurements of components present in the BOF, predicting dynamic variations in flux distributions as well as in total organelle activity and metabolite exchange across compartments . In Fig. 15. This metabolic trade-off affects the middle growth stage of all cells, but in CHO cells takes place at the early stage (timepoints 1–2). Consequently, the nitrogen-depletion threshold that triggers lipid synthesis appears to be much more sensitive for this organism. CHO cells are not capable of synthesizing some proteinogenic amino acids such as asparagine, arginine and aspartate, among others. Hence, the depletion of carbon and nitrogen is intertwined as a result of these amino acids being provided in the medium. Our simulations of biomass yield show that non-glucose carbon input can amount to 45% of the biomass c-mol at the highest . We determined carbon Fig.  and nitr26. Moreover, we identified a common decrease after nitrogen depletion in the transport of amino acids, as well as their precursors, e.g., α-ketoglutarate (AKG). In the non-steady-state of living cells, a lower transport rate of AKG would mean its accumulation in the cytosol, which has been reported to be a consequence of nitrogen depletion13. The direct link of AKG levels to nitrogen availability rendered it one of the principal signal metabolites of low nitrogen to carbon availability ratio13. Other amino acid precursors whose transport rates were found to decrease were succinate, fumarate, and O-acetyl carnitine (phosphoketolase pathway in P. tricornutum), and tetrahydrofolate (THF).Moreover, a significant share of the global mitochondrial activity variation was associated with change of the activity of other organelles. The reduction of fast-growth-related fluxes induced a decrease in metabolite transport rates among the mitochondria, cytosol, and the chloroplast. This mitochondrial communication with other organelles has previously been reported to help regulate several energetic cellular functionsP. tricornutum and in C. vulgaris (during heterotrophic growth), the cytosol and chloroplast carbon and nitrogen load increased. For C. vulgaris, simulations show that the increase of cytosol and chloroplast activity is mainly due to highly active symport of asparagine and protons between these two compartments. Protons are transported from the chloroplast to the cytosol, where they are subsequently used for ATP regeneration in this compartment, as well as in the mitochondria.We predicted that in most cases the cytosol activities exhibited a long-term (through the timespan of culture) decrease, and at the same time amino acid biosynthetic reactions were downregulated in all organisms Fig. . DespiteP. tricornutum, activity increase represents the fraction of upregulated reactions  and the change of a response variable. With growth rate as the response variable, the sensitivity of metabolite i represents the variation of the predicted growth rate caused by a change in the composition of i. The sensitivity of a metabolite is not constant across metabolic networks, as different biomass compositions affect the flux distributions and responsiveness of the whole network. Therefore, we performed a codependence analysis in which hundreds of sensitivities were calculated for a single metabolite, so that the mean of the distribution could be used as a representative value of the sensitivity (see Methods for a complete definition of sensitivity and codependence).A sensitivity analysis was conducted to analyze the effect of changes in stoichiometric coefficients of the BOF on predicted growth rates of all organisms. This analysis was based on the definition of sensitivity as the relationship among the change in a controlled variable  and heterotrophic  growth, meaning that regardless of growth condition and organism, sensitivity was driven by biosynthetic cost  are competitive drivers of growth, comparable to the most expensive amino acid tryptophan30, which has been identified as the most expensive amino acid of bacterial metabolism31. In previous reports, arginine and histidine exhibited unexceptional costs of merely 27 and 38% of the biosynthetic cost of tryptophan (73–75.5 mole ATP/mole Trp)33, as opposed to our results of more than 70%.Amino acids with higher carbon and nitrogen bounds, such as tryptophan and phenylalanine (nine carbons), can affect growth roughly four to five times more than low molecular weight amino acids such as glycine (two carbons), as shown in Fig. To gain insight into this finding, we evaluated the effect of simultaneous variations in nitrogen content and molecular size on biosynthetic cost. Supplementary Fig. C. vulgaris  and Supplementary Fig. 34, the amino groups contained in the chemical structures of histidine and arginine lie among the most energetic: =NH, >NH (nonring), >NH (ring), and -N= (ring). Since most amino acids contain low free energy -NH2 groups, carbon groups tend to have a higher contribution to This exception to the rule led us to assess the underlying phenomena using the standard Gibbs free energy of formation , causing cells to prioritize higher-energy nitrogen-free biomolecule synthesis, such as those for lipids, carbohydrates, and sterols. Here, we developed a metabolic modeling approach that uses as dynamic constraints time-course metabolomics data to study the effect of biomass composition on flux distributions of five eukaryotic organisms. Simulations predicted the metabolic response of each microorganism to dynamic constraints at organelle and pathway levels. Our calculations showed that nitrogen deprivation caused a major decrease in energy metabolism and the synthesis of nitrogen-rich compounds, as expected.26. It has been shown that the cross-talk of the mitochondria with adjacent organelles holds a central role in the signaling for the initiation and completion of apoptosis through the production and transport of signal metabolites, causing an increase of mitochondrial abundance for the synthesis of Bax/Bak proteins36. However, this change in mitochondrial abundance does not appear to have a basis in metabolic flux demands, since we found that energy metabolism and amino acid precursor synthesis in the mitochondria is expected to decrease in the late stages of culture. Our results showed this reduction is partially due to the high interconnection of the mitochondria through several metabolic functions with the cytosol and the chloroplast (namely the reduction in amino acid synthesis and energy metabolism), that caused the decrease of cytosol and chloroplast activity to affect the mitochondria.The mitochondria have been recognized as central hubs of communication among compartments for metabolic and regulation purposes33. Free energy and molecular weight are not independent, as bigger molecules tend to have higher free energies associated to a larger number of bonds. Rather than discarding molecular weight as a contributor of cost, our results shed light on free energy being the true driver.The sensitivity analysis unraveled individual contributions of each biomass precursor to growth of all studied organisms. We determined the biosynthetic cost of all metabolites and showed that the growth was the most sensitive to metabolites with higher biosynthetic cost. Even though we showed that amino acids have some of the lowest biosynthetic costs Fig. , their mC. vulgaris, P. tricornutum, Y. lipolytica, and S. cerevisiae are capable to produce arginine and histidine. Intriguingly, differential compartmentalization of arginine biosynthesis does not seem to affect its sensitivity and cost across organisms. On the other hand, flux simulations showed that pathways involved in histidine biosynthesis tend to remain unchanged among phylogenetically distant organisms, in accordance with previous reports39. Specifically, it is necessary to generate precursors in other pathways, such as the PPP, TCA, acetyl cycles, and nucleotide biosynthetic pathways. In all organisms, arginine biosynthesis consumes ornithine and glutamine, a main nitrogen carrier, which induces an additional cost for the network, considering its high connectivity with the biosynthesis of other amino acids, pigments and nucleotides. Glutamine, specifically, has been identified as one of the most important contributors to carbon and nitrogen metabolism40, and a drastic decrease 7 in its abundance is a common response under nitrogen starvation41. Moreover, the consumption of ornithine fully activates the acetyl cycle, thus adding nitrogen and energy costs by consuming glutamate and ATPs.The high free energies of arginine and histidine are reflected in the complexity and energy requirement of their biosynthetic pathways. Among the studied organisms, 33. Interestingly, arginine and histidine have been associated with metabolic exchange in syntrophic microbial communities42. The predicted flux exchange may be linked to their high free energy and nitrogen content.For both amino acids, the high free energy of their nitrogen groups translated into the activation of relatively complex pathways, often meaning the consumption of highly connected intermediates and precursors, such as main nitrogen carriers and nucleotide precursors. Arginine requires the full activation of the acetyl cycle, whereas histidine synthesis activates nucleotide synthesis pathways to generate its side chain. In addition, main carriers are principal reactants in the production of both amino acids in all organisms, namely glutamate, glutamine, and ammonium itself. The burden of synthesizing histidine through these pathways is reflected in histidine having some of the lowest abundances in the proteomes of the included organisms , as it has been reported that cells  prefer thermodynamic favorability over other efficiency criteria such as cofactor use efficiency15; however, the determination of the impact of nitrogen stress at the biochemical reaction-scale had not been addressed. The lack of attention to this phenomenon is mainly caused by the difficulty of quantitative determination. Experimentally, the quantification of intracellular metabolic changes and transport levels is done through microscopy-based methods that have limited quantitative capacity and speed43, thus precluding them from analyzing reactome-wide variations. From a modeling perspective, accounting for intracellular transport is still a major challenge, as gene–protein-reaction association data is frequently missing for transporters1, thus relegating the addition of transport reactions to gap-filling methods. This issue is only amplified in eukaryotes, where even more information is missing for transporters in organelle membranes. Among other modeling limitations, it is worthy to note that our calculations could be used to reverse-engineer the time-course phenotype adjustment, but could not account for other known responses to nutrient starvation previously identified for phototrophs such as the depletion of pool-like nitrogen reserves1 and the breakdown of nitrogen-containing molecules through autophagy44 and chlorosis46. In the case of CHO cells, modeling approaches are not able to account for the increase in mitochondrial number47, as well as lipid composition variations in close proximity to cellular death48.With these results, we demonstrated how nitrogen deprivation shapes the metabolic phenotype in organisms, as well as the underlying phenomena driving these variations. This field has been studied extensively in the past from both experimentation and modeling standpointHere, we showed how condition and time-course composition data can be employed to understand the metabolic processes that an organism undergoes in stress conditions. We analyzed the interplay of metabolites in these processes and identified key drivers in these responses. However, with increased development of novel strategies to obtain more refined omics data, the approach shown in this study can be greatly complemented and can be used to elucidate further time-course pathway coupling and variations that were not captured in the present study due to the aforementioned modeling and data limitations.49. FBA was used for flux distribution calculations, and GUROBI 7.5.2 was employed as a solver for the linear optimization problems. Metabolic network visualization was performed using Escher50.All simulations were carried out within the MATLAB 2016b (MathWorks Inc.) environment and using the COBRA Toolbox v3.051.In order to ensure phylogenetic diversity, we included five genome-scale metabolic models under different growth modes: heterotrophy, mixotrophy and/or photoautotrophy, yielding seven organism- and condition-specific simulations. Information regarding genome-scale metabolic model characteristics and growth modes are presented in Table C. vulgaris1, P. tricornutum12, Chinese Hamster Ovary cells5, S. cerevisiae6, and Y. lipolytica7 . We calculated the range of variation of Si as a measurement of the codependence Di .2\documSensitivity and codependence were correlated with both connectivity and biosynthetic cost. Connectivity was calculated as the number of reactions in which the biomass component appeared with a nonzero stoichiometric coefficient.i, its biosynthetic cost was defined as the amount of ATP moles necessary to produce one mole of i. The algorithm to calculate this parameter was taken from Du et al.33. The growth rate was first predicted using the existing model. Then, flux through the biomass reaction was set to 95% the predicted value, and the objective function was set to an ATP hydrolysis reaction. A demand reaction was added for each biomass component and a minimal flux of 0.0001 was set for it. The relative decrease in the ADP flux through this reaction after forcing the production of this minimal flux was set as the biosynthetic cost of the metabolite, in units of (mmol ATP) (mmol metabolite)−1. The mathematical definition of biosynthetic cost (A) for a metabolite i is shown in Eq. (For any metabolite R). Element loads were defined as the molar flux of the element flowing into a certain compartment at a given time, as shown in Eqs.  loads, being carbon and nitrogen loads referred to as activity. Since FBA is a pseudo steady-state method, accumulation as a measurement of load could not be determined. Since all elemental mass that enters a compartment is secreted from it, we estimated carbon and nitrogen loads by the flux of these elements being transported into each compartment by all transport reactions ( in Eqs.  and 5)  R). Elem23 in close proximity to the optimal solution space by constraining the LP problem to a minimum of 90% the optimal solution53, with a sample size of 5000 points for each timepoint. Reactions were considered to be upregulation or downregulated if the paired one-tailed (right and left respectively) Student’s t test rejected the null hypothesis with a p value lower than a significance level of 0.05, with reaction flux distributions at the initial and final time points as inputs.To assess significant upregulation and downregulation of reactions, we sampled the solution space for each model and timepoint. Sampling was carried out using the gpSampler function of the COBRA ToolboxSupplemental MaterialDataset 1Dataset 2Dataset 3Dataset 4Dataset 5


E. coli strain, producing a heterologous protein, is sided by a second E. coli strain engineered to scavenge toxic byproducts, thus favoring the growth of the producer at the expense of diverting part of the resources to the growth of the cleaner. The simplicity of the consortium is ideal to perform an in depth-analysis and draw conclusions of more general interest. We develop a coarse-grained mathematical model that quantitatively accounts for literature data from different key growth phenotypes. Based on this, assuming growth in chemostat, we first investigate the conditions enabling stable coexistence of both strains and the effect of the metabolic load due to heterologous protein production. In these conditions, we establish when and to what extent the consortium outperforms the producer alone in terms of productivity. Finally, we show in chemostat as well as in a fed-batch scenario that gain in productivity comes at the price of a reduced yield, reflecting at the level of the consortium resource allocation trade-offs that are well-known for individual species.Synthetic microbial consortia have been increasingly utilized in biotechnology and experimental evidence shows that suitably engineered consortia can outperform individual species in the synthesis of valuable products. Despite significant achievements, though, a quantitative understanding of the conditions that make this possible, and of the trade-offs due to the concurrent growth of multiple species, is still limited. In this work, we contribute to filling this gap by the investigation of a known prototypical synthetic consortium. A first  In nature, microorganisms occur in communities comprising a variety of mutually interacting species. Established through evolution, these interactions allow for the survival and growth of microorganisms in their natural environment, and give rise to complex dynamics that could not be exhibited by any of the species in isolation. The richness of microbial community dynamics has been leveraged to outperform individual species in biotechnological production processes and other processes of high societal value. Yet, in view of their complexity, natural communities are difficult to study and control. In order to overcome these issues, a rapidly growing research field concerns the rational design and engineering of synthetic microbial consortia. Despite the great potential of synthetic microbial consortia, and significant efforts devoted to their mathematical modelling and analysis, a detailed understanding of how enhanced production can be achieved, and at what cost, is still unavailable. In this work, based on a quantitative model of a prototypical synthetic microbial consortium, we determine precise conditions under which a consortium outperforms individual species in the production of a recombinant protein. Moreover, we identify the inherent trade-offs between productivity and efficiency of substrate utilization. Escherichia coli strains has been shown to significantly increase the production of muconic acid, a commodity chemical, from a mixture of glucose and acetate . Acetate overflow at a rate −1 h−1] occurs when the glucose uptake rate reaches a threshold level  and converted into biomass with a yield coefficient Ya [gDW g−1]. Accumulation of acetate in the medium inhibits bacterial metabolism and growth  is the sum of the concentration of heterologous protein H [gDW L−1] and the concentration of biomass actively involved in cellular growth and maintenance, the autocatalytic biomass B [gDW L−1]. The fraction of biomass production assigned to the synthesis of heterologous protein is determined by the (dimensionless) product yield constant Yh. The total biomass Btot [gDW L−1] decays at a rate kdegBtot, with degradation rate constant kdeg [h−1]. In other words, non-growth-related maintenance of the biomass requires an expenditure of resources equal to kdegBtot  and a glucose concentration Gin [g L−1] in the inflow. This gives rise to the following dynamical system of Ordinary Differential Equations (ODEs):The producer strain is assumed to grow in a bioreactor operating in continuous mode , that isB.The term μ [h−1] to be explicitly defined in terms of the reaction rates. By definition, the rate of change of the total biomass in the bioreactor equals the biomass produced due to the growth of the bacterial culture (μBtot) minus the biomass flushed out due to dilution (DBtot):The model of Eqs μ represents the sum of the rate of change of total biomass per total biomass unit and the dilution rateTherefore, the specific growth rate From Eqs Btot = B, and the growth rate is given by the balance between substrate assimilation and dissimilation and biomass degradation. Heterologous protein production, however, puts a burden on the growth of the population, by drawing away resources from catalytic biomass. H leads to a smaller ratio B/Btot lowering the specific growth rate. At steady state, as shown in the Methods section, we find from Eqs In the absence of heterologous protein production Yh, as well as on the glucose and acetate uptake rates.This formulation emphasizes that, at steady state, the growth rate linearly depends on the product yield The rate equations are functions of the nutrient concentrations and express the regulatory mechanisms at work. The rate laws are motivated by a combination of modeling assumptions and experimental evidence as explained below.The uptake rates are defined in such a way that, when inserted into kg, ka [g gDW−1 h−1] denote maximal uptake rate constants and Kg, Ka [g L−1] half-maximal saturation constants. The inhibition term with the constant Θa [g L−1] in g [g gDW−1 h−1] in n and m shape the nonlinear effect of acetate inhibition and carbon catabolite repression, respectively.l [g gDW−1 h−1], E. coli produces and secretes acetate as a fermentation by-product , kPTSΔ < kg, in kAcs [g gDW−1 h−1], kAcs > ka, and half-maximal saturation constant KAcs [g L−1].The only modifications with respect to the producer strain are the replacement of Next, we assemble the model for the protein producer and the acetate cleaner to obtain the model of the consortium . The twoThe dynamics of the system are thus characterized by the following system of ODEs, where the dependency of the rate expressions on the concentrations has been dropped for clarity:μP, and μC analogously to The growth rates of the producer and cleaner strains are defined by the following equationsD must not exceed the maximal growth rate of either of the species. At the same time, acetate, the primary substrate for cleaner growth, is only available upon overflow in the producer. Since the latter occurs when Yh, this range must depend on Yh as well. In order to quantitatively pinpoint the effects of all these factors on the stability of the consortium, in the following paragraphs we perform steady-state analysis of Eqs When can the species composing the consortium stably coexist? To answer this question, we study the consortium model developed above in chemostat, that is, we investigate the existence and nature of the (stable) steady states of the model. First of all, setting both derivatives in rate see , it follYh = 0, that is, in absence of heterologous protein synthesis. All other parameters of the consortium are fixed as in Yh > 0 will be considered below.For ease of illustration, in this section, we consider the system with D, Gin)∈ h−1× g L−1. Assuming that both biomasses are initially present, we first used a numerical integration approach , unique steady-state biomass concentrations We sought the  steady states of the system for a grid of values of the bioreactor inflow parameters in the region , the entire consortium is washed out.For onod law , this thYh = 0.2, which is the value of product yield reported in D and Gin, see Yh = 0 are also obtained, as shown in D and Gin supporting coexistence are observed.How is coexistence affected by the synthesis of a heterologous protein? To address this question, we repeat the analysis of the previous section for the case where D > 0.25 h−1. This value is smaller than the corresponding value for the case where Yh = 0. This is explained by the fact that, for larger Yh, the necessary acetate overflow to support cleaner existence starts at lower growth (dilution) rates  are required to observe coexistence at some suitable dilution rate.Coexistence occurs for wth rate  as well YH drastically reduce the ability of the producer to grow, to the detriment of the whole community. In fact, it can be seen that when the burden is so heavy that the cleaner outperforms the producer in growth on glucose, regimes where only the cleaner survives are possible  rates. Does coexistence improve performance of the heterologous protein production process? Presence of the cleaner has the potential to favor growth of the producer due to the scavenging of acetate. At the same time, however, growth of the cleaner also consumes glucose, thus taking away resources from the producer. The effects of this resource utilization trade-off on heterologous protein production performance are a priori unclear. In the following, we focus on two main questions: When does a consortium achieve the highest production rates? Does the consortium outperform a producer population alone in the synthesis of H? As we will see, based on further anaysis of our model in continuous culture conditions in the chemostat (with product yield fixed to Yh = 0.2), the answer to these questions will unveil further trade-offs between different notions of production performance.We have shown in the previous section that coexistence of the producer and cleaner strains in a chemostat is possible and even favored by a nonzero yield D and Gin. Productivity is defined as the steady-state rate of outflow of protein H through the chemostat effluent (DH*). Productivity is indeed maximal in a coexistence regime. Highest values are obtained near the maximal dilution rates before the cleaner washout, and for high input glucose concentrations (D ≃ 0.5 h−1). This is the result of a sudden decrease of the producer population , we compare productivity of the consortium and of the producer species in isolation as a function of the dilution rate D. For the intermediate dilution rates where coexistence is possible, two subdomains can be distinguished. For D between 0.26 h−1 and 0.36 h−1, productivity grows with D for both the consortium and the sole producer. However, since part of the resources are devoted to maintain the cleaner species, the producer species alone outperforms the consortium. For values of D between 0.36 h−1 and 0.48 h−1, because of the larger overflow at higher growth rates, the toxic effect of acetate becomes dominant. In absence of the cleaner, this results in a sudden drop of productivity due to a reduced size of the producer population (see D. The net result is an increase in productivity (−1 h−1 at D ≃ 0.44 h−1) is about 14% larger than that of the producer alone (about 0.6 g L−1 h−1 at D ≃ 0.36 h−1). In summary, the consortium outperforms the producer species alone in terms of productivity. As seen before, maximal productivity is obtained for high values of Gin. It is worth noting that the maximum is obtained at a dilution rate strictly smaller than the maximal rate supporting coexistence. For applications, this warrants persistence of the cleaner in spite of fluctuations of the system and modelling inaccuracies. Results along the same lines are obtained for all other values of Gin supporting coexistence.In tion see . For theuctivity , up to tcont stands for continuous bioreactor, to distinguish from later analysis in fed-batch). D for the same value of Gin as in D ≃ 0.26 h−1), thus in particular, in absence of cleaner. Intuitively, this is because at that point, the largest producer biomass is obtained before resources are partly redirected into acetate overflow. For the consortium, this overflow sustains the cleaner growth. At rates above D ≃ 0.26 h−1, for the producer alone, biomass loss is initially less pronounced than in the consortium, since no other species consumes glucose. However, at higher dilution rates, this results in strong acetate accumulation, whence a sharp loss of biomass and yield. Compared with How efficient is the conversion of substrate into product by the consortium? How does this relate with productivity? To address this point we computed the yield of the process, defined asotP* see , it hold compare . The samThe productivity of the community is expressed as the rate at which biomass and thus the protein of interest flow out from a bioreactor operating in continuous mode. From a methodological point of view, continuous culture in a chemostat has the advantage of allowing productivity and yield to be analyzed under well-defined steady-state conditions. However, in many biotechnological applications today, fed-batch cultures are still the standard mode of operation . MoreoveG, is kept constant by a suitable time-varying input flow; (ii) there is no outflow; (iii) the total volume in the bioreactor is constant. These assumptions are reasonable over a suitable finite time-horizon and for large ratios between bioreactor volume and input volume. The design of the (time-varying) control input parameters D and Gin to meet these assumptions is beyond the scope of this paper. For the consortium, the model describing this scenario is provided by Eqs G fixed and D = 0 h−1. A similar adaptation holds for the model with producer only.To simplify the analysis and focus on production performance, we analyze the model under the following assumptions: (i) glucose concentration in the bioreactor, G = 20 g L−1, also referring to more general theoretical results reported in the Methods section. G is kept constant. We can thus refer to constant proportions and constant rates in exponential growth (indicated with a superscript “+”) to investigate productivity and yield.How does production performance of a consortium and of a producer alone compare in fed-batch? What are the trade-offs involved in this case? We illustrate simulation results for μ+ is constant and equal to the constant rate of increase of H, that is, (d log H/dt)+ = (H−1dH/dt)+. Moreover, the ratio between the product concentration and the total producer biomass concentration at any point of the exponential growth regime is precisely equal to Yh . In exponential growth, this yield reaches a constant value The same index can be defined for the producer alone , like in [et al., however, is also supported by experimental data . The discrepancy between the studies might be due to the use of different E. coli strains, different media compositions, or other details of the experimental procedures.A key challenge for constructing synthetic consortia is to guide their design by mathematical modeling and analysis, before the actual implementation enotypes . Like in like in , 46, tha like in , predict like in . The max like in , 56. TheThe model predicts that coexistence of the protein producer and acetate cleaner strains is possible over a range of dilution rates . While cOne of the main conclusions from this study is that coexistence of the producer and the cleaner strains may lead to a productivity gain . CoexistHigher productivity in the consortia comes at the price of a lower process yield, that is, the outflow rate of heterologous protein divided by the inflow rate of substrate decreases as the productivity increases . This isRalstonia eutropha and a Δ manA mutant of Streptomyces coelicor for the production of biodiesel [S. coelicor ΔmanA produces fatty acid methyl esters, while secreting acetate and citrate into the medium, resulting in growth inhibition and a lower pH. R. eutropha utilizes the fermentation acids, thus promoting growth of the producer strain and increasing pH. Another example is the consortium consisting of a S. cerevisiae strain carrying an enzyme for the production of methyl halides and the cellulolytic bacterium Actinotalea fermentans [A. fermentans growth. Note that in this consortium, the cleaner produces the metabolite of interest, whereas the producer provides the growth substrates. We expect that our conclusions, for example, that metabolic load influences producer and cleaner coexistence, or that higher productivity comes at the price of lower yield, will also apply, with appropriate qualifications, in these and other cases.While our modeling study has focused on a specific synthetic consortium of protein producers and acetate cleaners , the coniodiesel . S. coelrmentans . The latYH and kAcs, to give but two examples. Moreover, appropriate control laws may be needed to stabilize the consortium against fluctuations of the bioreactor operating conditions, modelling errors, etc., or, in case of multistability, to drive the system to the appropriate steady state. When considering the consortium from a dynamical perspective, one can formulate optimal control problems for the maximization of heterologous protein production in finite time and/or dynamical conditions, instead of maximizing productivity at steady state [In the current analysis of the consortium we have assumed that the only control inputs we dispose of are the dilution rate and the glucose concentration in the inflow, and we have determined productivity and yield only at steady state. The question under which conditions the consortium can achieve higher productivity can also be addressed with a larger range of control inputs, such as the possibility to change dy state . The actdy state , 65. ThiE. coli wild-type strain K-12 MG1655 in minimal medium with (i) glucose as the sole carbon source, (ii) acetate as the sole carbon source, and (iii) glucose with different concentrations of acetate added. The growth conditions of the experimental data set (wild-type strain in batch) imply that Yh and D must be set equal to 0.The model of the producer strain is given by Eqs kdeg [l [Kg [Ka [kdeg was computed from experimental quantification of the maintenance coefficient Cm [kdeg = CmYg  in the absence of acetate uptake, and (ii) in the absence of glucose and therefore acetate overflow  above, by means of an optimization procedure that minimizes the sum of squared errors between the predictions and measurements of the growth rate (μ+), the glucose uptake rate .The consortium model, the parameter identification procedure as well as the identifiability analysis are implemented in the accompanying code .Results section features a number of expressions showing the relation between the product yield Yh and other quantities at steady state in continuous culture  and the rate of the outflow is set to D = 0 h−1. The relationships we derive again apply to the producer alone or in consortium with the cleaner. The relevant condition to study in this case is exponential growth  and log H(t). From BP(t) is given bySecond, we consider the fed-batch case where the bioreactor glucose concentration r+. From H(t) is then given bySetting this to zero implies that the sum of rates BP/H is a constant which we denote by (BP/H)+ . Then log(BP/H) is also a constant. By the same relationships employed above, one hasSetting this to zero implies that the ratio r+ ≠ 0 (that is G > 0), the above implies Yh = (1 + (BP/H)+)−1. Since (1 + BP/H)−1 = H/(H + BP) and 1−(1 + BP/H)−1 = BP/(H + BP) for any H and BP, when BP/H is constant, H/BtotP and B/BtotP are also constant, given by (H/BtotP)+ = (1 + (BP/H)+)−1 and (B/BtotP)+ = 1−(1 + (BP/H)+)−1. In summary, for this case,Restricting attention to the nontrivial case where x =  taking values in Eqs θ is the vector of parameters that are varied in the study of the system, that is, θ = , while the other system parameters are fixed as in θ, we employ the following two methods.Here x(0) = x0, a (strictly) stable equilibrium of the dynamical system is given by the asymptotic value of the corresponding solution x0 = 0 by the Matlab ODE solver ode15s over a sufficiently long time horizon (T = 107 h), see θ. However, for any given θ, if the system has several stable steady states, then the steady state eventually reached will depend on x0. This has motivated the parallel use of a second, algebraic approach.In this approach, stable steady states of the system are sought by numerical integration of θ, the possible stable steady states of x of the equationF(x|θ) = ∂f(x|θ)/∂x is strictly stable . In the interest of clarity and simplicity, in what follows we drop θ from the notation, and instead write rates as functions of x. It can be verified by inspection of Eqs f(x) is a piecewise rational function. Indeed, the piecewise linear structure of Eqs X into the four subsetsFor any given Xi, f(x) = Ni(x)/Di(x), where Ni(x) and Di(x) are two multinomial functions determined by the relevant form of Eqs X2 imply that i, the solutions of Xi correspond to the roots in Xi of Ni(x). Out of these solutions, for i = 1, …, 4, the steady states sought are the real nonnegative solutions such that F(x) is strictly stable.Over each F(x) and the Ni(x) can be computed explicitly or symbolically at little cost. This suggests the following algorithm:Multinomial root finding is a well explored problem and specialized tools for enumerating all solutions exist . In addiNi(x), with i = 1, …, 4, and F(x);Compute i = 1, …, 4:For Ni(x) = 0;Find the real nonnegative solutions of x as a system stable steady state if and only if x ∈ Xi and F(x) is strictly stable.Record solution BP = 0 or BC = 0, symbolic calculations (step 1) are performed in Wolfram Mathematica, while multinomial root finding (step 2) is performed by the Matlab  routine psolve available at NAClab [x agrees with the rate conditions defining Xi, thus avoiding the explicit calculation of the latter. In view of the complexity of the multinomials Ni(x), which comprise terms of order up to 33, this method is computationally intensive, yet it returns all possible steady states within the precision of the routine psolve.In our implementation, which is optimized by suitable simplifications for the exploration of steady states with t NAClab , 81. In S1 Fig(PDF)Click here for additional data file.S2 Fig(PDF)Click here for additional data file.S3 Fig(PDF)Click here for additional data file.S4 Fig(PDF)Click here for additional data file.S5 Fig(PDF)Click here for additional data file.S6 Fig(PDF)Click here for additional data file.S7 Fig(PDF)Click here for additional data file.S8 Fig(PDF)Click here for additional data file.S1 Text(PDF)Click here for additional data file.S1 SoftwareThe code is accompanied by a description, instructions of usage and a summary of the implemented model.(ZIP)Click here for additional data file.


On the basis of scientific literature and experimental data for 14,931 bacterial phenotypes, we demonstrate that gapseq outperforms state-of-the-art tools in predicting enzyme activity, carbon source utilisation, fermentation products, and metabolic interactions within microbial communities.Genome-scale metabolic models of microorganisms are powerful frameworks to predict phenotypes from an organism’s genotype. While manual reconstructions are laborious, automated reconstructions often fail to recapitulate known metabolic processes. Here we present gapseq . Anything you have to do repeatedly may be ripe for automation.— Doug McIlroy Metabolism is central for organismal life. It provides metabolites and energy for all cellular processes. A majority of metabolic reactions are catalysed by enzymes, which are encoded in the genome of the respective organism. Those catalysed reactions form a complex metabolic network of numerous biochemical transformations, which the organism is presumably able to perform .In systems biology, the reconstruction of metabolic networks plays an essential role, as the network represents an organism’s capabilities to interact with its biotic and abiotic environment and to transform nutrients into biomass. Mathematical analysis has shown great potential for dissecting the functioning of metabolic networks on the level of topological, stoichiometric, and kinetic models , which tIn the process of genome-scale metabolic network reconstruction, the genomic content of an organism is linked to biochemical processes, including enzymatic reactions and cross-membrane metabolite transport . TherefoThe feature to directly obtain network models that can be used for FBA-based growth simulations is especially powerful in situations where large numbers of new microbial genomes are assembled from high-throughput metagenomic datasets . In suchEscherichia coli K12 or Bacillus subtilis 168. The overall performance of reconstruction tools, particularly for non-model organisms, is therefore insufficiently assured. Yet, accurate phenotype predictions for a wide range of organisms is crucial for the broad application of automated network reconstruction pipelines in research. For instance, genome-scale metabolic network reconstructions are increasingly applied to simulate complex metabolic processes in microbial communities b, which Rall is the set of all reaction in the universal model, Rdraft are the reactions, which are already part of the draft network before gap-filling, vj is the flux through the objective reactions (e.g. biomass production), vi the flux through reaction i, wi the weight for reaction i, v the flux vector for all reactions, and c a scalar factor that determines the contribution of the absolute reduction of weighted fluxes to the overall FBA solution (default: c=0.001). Moreover, a maximum weight value wmax (default: 100) is assigned if the reaction’s highest bitscore is smaller than a threshold l (default: 50). A minimum reaction weight wmin (default: 0.005) is assigned to reactions with a bitscore higher than u (default: 200) or if the reactions are already part of the draft model. S is the stoichiometric matrix and lb and ub the lower and upper flux bound vectors.where vj together with the reaction evidence scores in a single objective function.Two other LP-based gap-filling algorithms that incorporate reaction evidence scores have been formulated by Dreyfuss et al. 2013)  and Medl3  and MeIn gapseq and following the solution of the LP Eq. , reactioBiomass production: To ensure that the model is able to produce biomass under the given nutritional input (gap-filling medium) the gap-filling algorithm is applied while the objective is defined as the flux through the biomass reaction. This step will add all missing reactions that are essential for in silico growth and are not part of the model yet.Individual biomass components: It is checked whether the model supports the biosynthesis of individual biomass components. Therefore, the model is re-constrained to a M9-like minimal medium with a carbon source for which an exchange reaction is found (default: glucose if available). The objective function is set to the production of one biomass component at a time and the gap-fill algorithm is performed using only reactions with sequence support as source. This gap-filling step is repeated for each biomass component metabolite twice, with and without oxygen to potentially allow aerobic and anaerobic growth for facultative anaerobes.Alternative energy sources: gapseq attempts to gap-fill likely metabolic pathways, which enable the utilisation of alternative energy sources, which might not be part of the defined growth medium from step (1). To this end, the model is re-constrained to a M9-like minimal medium containing a single carbon source of interest at the time. Next, three temporary reactions were inserted into the model that recycle common reducing equivalent carriers . As objective function, the summed flux of the temporary reactions ESP1, ESP2, and ESP3 is used. Again, the gap-filling of this step only employs those reactions having sequence support. By this, the capacity of a potential carbon source to function as electron donor can be evaluated. This test can be considered as an in silico simulation of the commonly used BIOLOG carbon source utilisation test arrays [t arrays  in whicht arrays . This gaMetabolic products: Finally, the same list of compounds (dat/sub2pwy.csv), is used to check whether the network can be gap-filled to allow the formation of these metabolites given the original medium. For each compound the gap-filling algorithm is applied with the production of the focal compound as objective function. As for step 2–3, only reactions with sequence evidence are considered for gap-filling.Gap-filling of a draft model in gapseq requires only for the first step a user-defined growth medium that is ideally known to support growth of the organism of interest in vivo. If no growth medium is specified by the user, a complete medium (dat/media/ALLmed.csv) is chosen by gapseq . Thus, these so-termed core reactions represent only reactions, for which gapseq has found genomic sequence evidence. Gaps in the specific metabolic functions  are only resolved if all required additional reactions are core reactions. The gap-filling steps (2–4) are implemented to reduce the impact of a gap-filling medium on the final metabolic model. Thus, these steps aim to increase the versatility of gapseq reconstructions for downstream metabolic simulations of the models in growth environments that are potentially different to the chemical composition of the actual gap-filling medium. This could be especially of relevance for dynamic community metabolism simulations, where the nutritional environment changes over time due to the release of by-products by certain community members that serve as resources for others. In case gapseq users prefer to perform gap-filling solely for biomass production on a defined gap-filling medium, the argument -q can be passed on to the gap-filling command ./gapseq fill. The number of reactions added during gap-filling is given as output during runtime. In addition, detailed information on why a specific reaction was added to the model is provided in the reaction attributes table (@react_attr) of the model’s S4 R-object of class sybil::modelorg [’gs.origin’ states an integer number between 0 and 10 where 0 indicates that the focal reaction was directly included in the draft model due to predicted sequence homology (see While step (1) considers all reaction from the universal model as potential candidate reactions for gap-filling, steps (2–4) allow only the addition of candidate reactions to the model with a corresponding bitscore from the pathway prediction  higher tmodelorg . In thislogy see ; 1–4 corThe validity of genome-scale metabolic model files was checked with MEMOTE (0.10.2) . For allhttps://github.com/kblin/ncbi-genome-download). If multiple genomes were available for one type strain, ‘representative’ and ‘complete’ (NCBI tags) genomes were preferred and, in case there were still multiple candidate genomes available, the most complete genome was selected. Genome completeness was estimated using the software BUSCO (3.0.2) [https://www.vmh.life) and for ModelSEED and gapseq the ModelSEED (http://modelseed.org) reaction database was used to match reactions and EC numbers. Only those EC numbers were considered for testing for which a matching from EC number to reaction IDs exist. For the EC numbers 3.1.3.1, 3.1.3.2, the corresponding reactions were the same, and thus unspecific, so that both EC numbers were from the validation analysis. In general, the enzymatic data in the BacDive database has the entries enzyme name, EC number, and experimentally measured enzyme activity  but some entries were ambiguous (e.g. ‘+/-’). These ambiguous entries were omitted from the analysis. If an enzyme was measured to be active according to the BacDive database and the corresponding reaction also present in the metabolic network, then the enzymatic test was called a true positive. In contrast, if the reaction was not present in the network the test was called false negative . Sampling of enzymatic data was performed in order to preclude a potential bias due to over-representation of certain EC numbers. All EC numbers with at least 100 tests were considered for sampling. For each EC number, 100 tests were randomly chosen. The re-sampling was repeated 500 times to estimate the variation of true positives, true negatives, false positives, and false negatives.Enzyme activity tests are commonly performed for characterisation and identification of microbial isolates. In those tests, microbial cell cultures or extracts from the cultures are exposed to the substrate of the focal enzyme and it is measured whether the substrate is transformed. While the experimental culture and test conditions can vary between microorganisms tested and the specific enzymes of interest, the experiments are generally designed to invoke the expression of the specific enzyme, if the organism harbours the respective gene(s). The Bacterial Diversity Metadatabase (BacDive) is a large curated database for, among other data, results from laboratory enzyme activity tests . We used (3.0.2) . In totahttp://protraits.irb.hr/data.html) as a tab-separated table. For organisms which had at least one high-confidence carbon source utilisation trait, the corresponding genome assembly was obtained from NCBI RefSeq [In order to predict accurate growth phenotypes using genome-scale metabolic models, it is crucial that the network reconstructions possess the metabolic capability to utilise the specific carbon sources, which the organism can also use in their natural environment. Here, we used microbial phenotypic trait data for the validation of carbon source utilisation from the ‘atlas of prokaryotic traits’ database (ProTraits) . In brieI RefSeq  if availEscherichia coli str. K-12 substr. MG1655 (RefSeq assembly accession: GCF_000005845.2), Bacillus subtilis substr. subtilis str. 168 (GCF_000789275.1), Shewanella oneidensis MR-1 (GCF_000146165.2), Pseudomonas aeruginosa PAO1 (GCF_000006765.1), and Mycoplasma genitalium G37 (GCF_000027325.1). The analysis was performed on the basis of the models’ Gene-Protein-Reaction (GPR) mappings and according to the protocol by Thiele and Palsson, 2010 [-1. The growth-media compositions for growth predictions were defined as M9 with glucose as carbon- and energy source for E. coli, lysogeny broth (LB) for B. subtilis and S. oneidensis, M9 with succinate as carbon and energy source for P. aeruginosa, and a complete medium  for M. genitalium. Experimental data for gene essentiality was obtained from [Genome-scale metabolic models are commonly used to predict if essentiality of genes for cellular growth. In order to further evaluate our gapseq approach, we compared gene essentiality predictions with previously reported growth phenotypes of single gene-knockout experiments. To predict the essentiality of genes, we performed in silico single gene deletion phenotype analysis for the network reconstructions of on, 2010 . To thisned from –110. In To evaluate the potential of our approach to predict bacterial metabolism in anaerobic environments, we simulated the anoxic growth of bacterial model reconstructions and compared the predictions with fermentation end products reported in primary literature. The release of by-products from anaerobic metabolism was predicted using Flux Balance Analysis (FBA) coupled with a minimisation of total flux  to avoidW−1∗h−1, by the predicted growth rate of the respective organism which has the unit h−1. Thus, we report the amount of fermentation product production in the quantity of the metabolite that is produced per unit of biomass: mmol∗gDW−1.Since the amount of fermentation product release depends on the organism’s growth rate, we normalised the outflow of the individual fermentation products, which has the unit mmol∗gDThe pathway analysis was done by comparing predicted pathways of soil and gut microorganisms. For this means, genomes were downloaded from a resource of reference soil organisms  and gut 2, CH4, ethanol, H2S, succinate), and carbohydrates  was used for gap-filling. Furthermore, a published model of Methanosarcina barkeri was added to the community [M. barkeri model. Subsequently, the community was simulated for seven time steps, which corresponds to seven hours simulation time. The metabolite uptake and production rates were analysed after the third time step for CarveMe and gapseq models and after the fifth time step for ModelSEED models, in which all organisms were growing exponentially and reached similar total population density.Microbial strains rarely live in isolation but usually coexists with other strains in multi-species communities. In such communities, metabolic processes in one organism may affect the metabolism of other cells and vice versa . It is aommunity  to repreommunity . All orgommunity . A virtuD) [TSGB: Genomes assembled from metagenomic data via ‘binning’ are often fragmented and incomplete. For the reconstruction of metabolic models from such genomes, it is important to estimate how missing genetic fragments may affect final model quality. 4930 species-level genome bins (SGBs) assembled from shotgun metagenome sequencing reads were obtained from the study of Pasolli et al. 2019) . Only thD)  were belD) . Only SG019 . OnlRSGB is the set of reactions part of the SGB’s model reconstruction. bi is the frequency of reaction i among the ten SGB’s reference models. Completion of the genome sequence of SGBs was estimated by using BUSCO  using tThe pathway prediction part of gapseq is implemented as Bash shell script and the metabolic model generation part is written in R. Linear optimisation can be performed with a different solvers (GLPK or CPLEX). Other requirements are exonerate, bedtools, and barrnap. In addition, the following R packages are needed: data.table , stringrAdditional file 1 Supplementary figures S1-S5.Additional file 2 Supplementary tables S1-S7. OpenDocument spreadsheet (ODS) fileAdditional file 3 Review history.


Cutaneotrichosporon oleaginosus ATCC 20509 is a fast-growing oleaginous basidiomycete yeast that is able to grow in a wide range of low-cost carbon sources including crude glycerol, a byproduct of biodiesel production. When glycerol is used as a carbon source, this yeast can accumulate more than 50% lipids (w/w) with high concentrations of mono-unsaturated fatty acids.To increase our understanding of this yeast and to provide a knowledge base for further industrial use, a FAIR re-annotated genome was used to build a genome-scale, constraint-based metabolic model containing 1553 reactions involving 1373 metabolites in 11 compartments. A new description of the biomass synthesis reaction was introduced to account for massive lipid accumulation in conditions with high carbon-to-nitrogen (C/N) ratio in the media. This condition-specific biomass objective function is shown to better predict conditions with high lipid accumulation using glucose, fructose, sucrose, xylose, and glycerol as sole carbon source.C. oleaginosus ATCC 20509 can effectively convert crude glycerol waste streams in lipids as a potential bioenergy source. Performance simulations are essential to identify optimal production conditions and to develop and fine tune a cost-effective production process. Our model suggests ATP-citrate lyase as a possible target to further improve lipid production.Contributing to the economic viability of biodiesel as renewable fuel,  Yarrowia lipolytica, Rhodotorula glutinis, Rhodosporidium toruloides, Cutaneotrichosporon oleaginous, and Lipomyces starkeyi . For growth rates smaller than 0.2 h−1, we fixed the biomass to the maximal predicted values at the corresponding C/N ratio. A specific biomass reaction for each C/N ratio was used. Lipid formation happens when the cell was subjected to sudden depletion of other nutrients such as nitrogen after growing maximally  mmol · gDCW−1 · h−1 for nitrogen.To study effects of different carbon sources on growth and lipid production, lower bound and upper bound of each exchange reaction for glucose, fructose, xylose, sucrose, ethanol and glycerol was constrained in each study. To generate different C/N ratio the uptake rate was increased gradually in the range of − [0.1: 5: 100] 10 and 1 thread was used. Sampling results were analyzed as described in [Z scores for each reaction in the central metabolic network. A C/N ratio of 6 (g/g) was used as the reference point to calculate Z scores for fluxes in other C/N ratio.To study how flux distribution change when changing C/N ratio, we sampled the solution space at steady state for each C/N ratio. Based on , 46 we sribed in . In shorC. oleaginosus ATCC 20509, we sampled the solution space at steady state for each C/N ratio. The C/N ratio data from experiment in [gDCW−1 · h−1. Carbon was gradually increased to generate the desired C/N ratio.To study the main source of acetyl-coA for lipid synthesis in iment in  were useAdditional file 1. C. curvartum ATCC 20509 genome annotation.Additional file 2. Details on lipid synthesis pathways.Additional file 3.C. oleaginosus and Y. lipolytica orthologsAdditional file 4. Condition-specific biomass generation.Additional file 5. List of up and down-regulated genes under high and low C/N condition.Additional file 6. Biomass component at glucose and unlimited nitrogen condition.Additional file 7.iNP636_Coleaginosus_ATCC20509 model.


Managing and organizing biological knowledge remains a major challenge, due to the complexity of living systems. Recently, systemic representations have been promising in tackling such a challenge at the whole-cell scale. In such representations, the cell is considered as a system composed of interlocked subsystems. The need is now to define a relevant formalization of the systemic description of cellular processes.Biological interlocked Process Ontology for metabolism) an ontology to represent metabolic processes as interlocked subsystems using a limited number of classes and properties. We explicitly formalized the relations between the enzyme, its activity, the substrates and the products of the reaction, as well as the active state of all involved molecules. We further showed that the information of molecules such as molecular types or molecular properties can be deduced by automatic reasoning using logical rules. The information necessary to populate BiPOm can be extracted from existing databases or existing bio-ontologies.We introduce BiPOm (BiPOm provides a formal rule-based knowledge representation to relate all cellular components together by considering the cellular system as a whole. It relies on a paradigm shift where the anchorage of knowledge is rerouted from the molecule to the biological process.https://github.com/SysBioInra/SysOntoBiPOm can be downloaded at  Studying and determining the characteristics of world entities and their causal relationships is at the core of many scientific endeavours, including the modern biological sciences. Managing and organizing biological data and knowledge have remained a major challenge for decades, mainly due to the high complexity of living systems. Moreover, advances of technologies in biology lead to perform high throughput experiments, that generate thousands of genes or gene products descriptions in one experiment . The datglutamate synthase complex GltAB of Bacillus subtilis, composed of two subunits GltA and GltB. The available information is rich [GltAB is an aggregate of four catalytic active heterodimers, consisting of a large GltA subunit and a small GltB subunit) and the cofactors , FMN (Flavin mononucleotide)). The presence of iron-sulfur clusters implies that the complex requires dedicated chaperones to be folded [GltA, GltB, are considered and annotated but not the enzymatic complex GltAB, even though GltAB is the active compound mediating the enzymatic reaction. It may result in ambiguities, especially for the cofactors definition, and redundant information since the enzymatic complex does not exist as a cellular component by itself in repositories like Uniprot [The central issue is now to find an effective and efficient way to ensure the integration of biological data originating from heterogeneous sources, while providing a formal, generic, and unambiguous representation of biological data and knowledge. For instance, let us consider the  is rich : we may e folded . Althoug Uniprot . Such liTo address this complex issue, ontologies have been widely acknowledged as a successful formal knowledge representation in many application domains including biology and many others such as geography, astronomy, medical domain and cultural heritage . Indeed,Tiger is-a Animal expresses that all the instances of the class Tiger are also instances of the class Animal: ∀x:Tiger(x)⇒Animal(x). Therefore the instance Tigger of the class Tiger (denoted by Tiger(Tigger)) is an Animal. Moreover, to capture even more the constraints and the semantics of a given application domain, logical rules can be defined. These rules can be used by reasoners to infer new assertions from existing ones, thus enriching knowledge. For instance, the rule ∀x,y:Animal(x)∧Animal(y)∧eats⇒Carnivore(x) means that every animal that eats another animal is a carnivore. Therefore, if we have Tiger(Tigger) ∧Giraf(Ernestine) ∧eats, we can automatically deduce that Tigger is also a carnivore that is Carnivore(Tigger).Additional knowledge and constraints on entities and relations can be represented by domain-specific relations and/or complex logical axioms such as disjointness between classes (e.g. Oxygen is-disjoint-with Carbon), functionality and cardinality restrictions on properties (e.g. a Cell has only one Nucleus). The underlying ontology semantics is formalized as set-based logical assertions that can be either manually declared or automatically generated (i.e. inferred). Classes may have instances that must fulfill the logical axioms defined in the ontology. For instance, the statement In biology, various bio-ontologies have been developed and stored in public repositories , 9. MostRecently, the systemic description of the cell was shown to be very effective in tackling the complexity of the cell . In systArabidopsis thaliana’s “reductive pentose-phosphate cycle” , and show how properties of the cell components participating in this metabolic pathway can be automatically inferred from the formal description of a process. This example highlights how BiPOm contributes to a richer semantic description of the biological knowledge. Then, we show on a second use case that BiPOm can support the scaling up and can be instantiated with the metabolic network of the Gram negative bacterium Escherichia coli [We previously showed in  that thehia coli , 27.typing of molecules: for example, molecule A is a metabolite; molecule B is a kinasemolecular composition of a complex: molecule A is composed of molecules B and Cinteraction between molecules: molecule A interacts with molecule Bmolecular function of molecules: molecule A has a function of kinase activity.contribution of a molecule to a molecular function: molecule A contributes to kinase activity.This work seeks to show the substantial benefits of using a concise and highly expressive  ontological model to describe metabolic processes  using only few knowledge of molecules. Our model was edited with Protégé  editor aA. thaliana’s reductive pentose phosphate cycle (RPPC) available2 fixation and composed of 10 chemical reactions. Each chemical reaction is catalyzed by an active enzyme or enzymatic complex. The process of enzyme activation involves many different post-translational modifications, chaperoning, and complexations. In particular, the Ribulose Bisphosphate CarbOxylase (RuBisCO) enzyme that catalyzes the first reaction is an enzymatic complex composed of 16 subunits encoded by 5 genes. The activation of RuBisCO is achieved through many steps  [As a use case, we considered the g, etc.) . Other eWe collected information on the metabolic reactions and on the different steps of protein complex formation and activation using Uniprot and literature to complement the description of Plant reactome. Information was structured in a table  is also automatically linked to the enzyme (Phosphoglycerate kinase 1) by the property has_function. Finally, the molecule Mg-ATP is automatically linked to its subcomponents (Mg2+ and ATP) by the property has_molecular_part. Compared to the static annotation given in Additional file The metabolic process (phosphorylation of 3PGA), the substrates , the products , the enzyme (Phosphoglycerate kinase 1) and the enzyme activity (Phosphoglycerate kinase activity) are instances of BiPOm and are related by properties onents Mg+ and ATPhas_input and has_output properties, the protein complex and their subunits or coenzyme are formally related with the has_molecular_part property.In the standard gene-centered annotation, knowledge is anchored manually to protein complex subunits. Current annotation of subunits merged information on the protein itself, and on the full complex. For instance, in Amigo2, the ribulose bisphosphate carboxylase large chain  is annotated as a magnesium dependent (magnesium(2+): CHEBI: 18420) protein (GO:0000287). This information is specific and relevant for this subunit. RBCL is further annotated 1) by the functions of the RuBisCO: Ribulose-bisphospate carboxylase activity (GO:001698) and Monooxygenase activity (GO:0004497) and 2) by the process involving RuBisCO: Reductive pentose-phosphate cycle (GO:0019253) and Photorespiration (GO:0009853)  the accuracy of the metabolic reconstruction, (ii) the quality of annotations and cross-references of reactions, metabolites and gene products [iii) the description of enzymatic complexes (including cofactor recruitment and subunit structures), all of this information being available in standardized files [E. coli information was performed with 10055 instances (3653 declared class assertions and 16093 declared property assertions). After a reasoning step using logical rules, we obtained 71990 inferred class assertions and 82774 inferred property assertions. This example highlights that automatic reasoning on a large metabolic network can be achieved while allowing a substantial enrichment of the initial knowledge.Finally, we investigated the capability of BiPOm to describe a large metabolic network composed of more than 1500 reactions: the cytosolic metabolic network of the Gram negative bacterium products , 30, anded files , 31. Theed files , 27, 30,A. thaliana’s RPPC is representative of the complexity of metabolic processes and highlights the added value of BiPOm representation. Thanks to BiPOm rules, the classical annotations stored in public repositories such as Amigo2 or Uniprot were automatically inferred as new properties. By dealing with different aggregation levels of biological processes, BiPOm can take into account heterogeneous levels of knowledge on biological pathways. Moreover, BiPOm includes GeneProductModificationProcess classes that are able to describe post-translational modification processes. Thus, in addition to metabolic pathways, BiPOm is already capable of describing a large set of non-metabolic processes involving post-translational modifications of proteins and protein complexes. In particular, post-translational modifications are commonly encountered in signalling pathways or cascades processes  by information from literature. Our approach takes advantage of existing public repositories to finely describe biological processes and benefits from the ontological reasoning to infer new types and properties. The use case of bacteria , 32 and bacteria .Due to its flexibility, the extension of BiPOm to the subcellular localization of components should be straightforward since different localizations of a molecule can be managed as different states. This requires to integrate additional classes for the fine description of subcellular compartments. However, enriching the ontology with precise information of molecule localization may be difficult, because the localization of molecules may not be well characterized experimentally, especially for eukaryotic cells. In addition, our ontology could be extended with other biological processes such as the gene-expression  using thThere exist other attempts of biological process formalism, and especially BioPAX . BioPAX Recent releases of knowledge-based repositories such as Reactome  or diseaIn conclusion, BiPOm is based on a minimal and generic ontological model and aims to take maximum advantage of automatic reasoning to limit the number of assertions and enrich initial knowledge. Logical reasoning has already been exploited by other bio-ontologies mainly for the automatic classification of molecules , 42 or pNotation: For the sake of readability of this section, we use the following notation. Names of classes are written in lower-case and first letter capitalized  and properties are written in lower case and in italics (e.g. has_input refers to the property named “has_input").Elementary by its inputs and outputs and possibly by a specific mediator and/or by an activity;Aggregated by a set of elementary processes.In systems biology, the cell is considered as a system composed of interlocked subsystems having their own dynamics of operations. In this approach, a subsystem is a biological process . A process can be independently defined as see Fig. a:ElemenFurthermore, a metabolic reaction is defined as an elementary biological process having molecular entities in inputs (i.e. the reactants) and in outputs (i.e. the products) Fig. a. A metahas_participant and its subproperties has_input, has_ouput, mediated_by define the relations between the classes BiologicalProcess, Participant, and ActiveEntity. The property requires defines the relation between the class BiologicalProcess and the class Activity. Finally, the class Pathway is defined by successive biological processes. The first, last and intermediate biological processes within a pathway are set up using the has_subprocess subproperties start_with, end_with and has_intermediary_process respectively. We further detail in the next subsections the BiPOm core-ontology classes, properties and rules.This representation relies on a limited set of classes, cardinalities and properties presented in Fig. Our aim is to easily represent any biological process involved in metabolic networks. By definition, such processes gather the metabolic biochemical reactions and the post-translational processes involved in the activation of molecular machineries, protein complexes or enzymes of the metabolic network. We described the subclasses of BiologicalProcess  as a metabolic reaction having only metabolites in inputs and outputs. In contrast, a gene product modification process is defined such that it has at least one gene product as input of the process. Finally, the class MolecularInteraction is decomposed into the two disjoint classes Non-covalentBinding and Dissociation, to describe molecule association and dissociation.Then, specific biological processes are defined according to the role of their participants. Two examples of description are given in Additional file Altogether our model contains 65 processes’ classes with a maximum depth of 7.The class Participant describes the entities that are inputs, outputs or mediators of biological processes . Moreover, some SWRL rules infer both properties as well as instance typing, i.e. to which class an instance is belonging to , and if proc has also for input a simple protein pi, then p0has_molecular_part the participant pi, and pi is a ProteinComplexSubunit. This can be expressed in the SWRL rule R10 presented in Additional file contributes_to: let us assume that the participant p0 mediates the reaction r which requires a as activity, and that p0 is composed of several molecular parts. Then, each molecular part of p0contributes_to the activity a. This can be expressed in the SWRL rule R26 presented in Additional file interacts_with: using SWRL rules, we designed properties that define transient interaction between proteins. The property interacts_with is particularly used to describe processes of post-translational modifications: If a process proc has a protein prot as an input and is mediated by another participant p0 then protinteracts_withp0. This can be expressed in the SWRL rule R25 presented in Additional file precedes and its inverse property preceded_by) to provide information on the relative order of biological processes. They are able to order reactions in a pathway. The properties precedes and preceded_by are used to infer participants of a pathway, while excluding those that are produced and consumed by consecutive reactions  or the metabolic network of E. coli). Briefly, each instance of processes of the studied application domain has to be typed by one class among the 65 different processes’ classes in BiPOm. Each instantiated process is then described by highlighting its links with the instances of its inputs, its outputs, its mediators (if any) and its activity through has_input, has_output, mediated_by and requires properties, respectively. The whole pathways can therefore be described by their links to the starting, intermediate and ending processes through the starts_with, has_intermediary_process and ends_with properties, respectively. The instances of the participants have to be typed by the class Gene, GeneProduct or Non-geneProduct. The manual typing of an instance by a class is called a declared class assertion. The manual assertion of a property between two instances is called a declared property assertion hereafter. For example, the biological process "phosphorylation of 3-PGA" and the metabolite "Mg-ATP" are typed manually by the class MetabolicTransference and the class Non-geneProduct respectively (and thus correspond to declared property assertions). In addition, we specified manually the declared property assertion that phosphorylation of 3-PGA has_input Mg-ATP  from the instances [https://github.com/SysBioInra/SysOnto. The different steps of instantiation and reasoning are summarized in Additional Table 3 for the RPPC of A. thaliana and in Additional Table 6 for the metabolic network of E. coli.Information on instances could be easily structured in a table  an enzymatic metabolic reaction and B) a protein complex assembly) are described by classes and properties of BiPOm.Additional file 2 The phosphoglycerate kinase of A. thaliana. Available information on the phosphoglycerate kinase of A. thaliana in public repositories such as Uniprot or Amigo2Additional file 3 Guidelines. This additional file aims at assisting the creation of the instantiation table for BiPOm feeding, such as Additional Table 5.Additional file 4 List of BiPOm properties. Additional Table 1 contains the properties of BiPOm that can be (i) asserted, (ii) defined as the inverse of an asserted property, or (iii) defined by a SWRL rule.Additional file 5 Table of BiPOm instantiation for the rPPC of Arabidopsis thaliana. Additional Table 2 contains the instances of BiPOm classes necessary to describe the RPPC of A. thaliana.Additional file 6 Metrics of BiPOm before and after reasoning on the rPPC of A. thaliana. Additional Table 3 contains the metrics of BiPOm (i) before and (ii) after instantiation, and finally (iii) after automatic reasoning.Additional file 7 Quantitative comparison of inferences in BiPOm and in bioPAX. Additional Table 4 contains the number of class/property axioms before and after reasoning in both BiPOm and BioPAX.Additional file 8 Table of BiPOm instantiation for the metabolic network of Escherichia coli. Additional Table 5 contains the instances of BiPOm classes necessary to describe the metabolic network of E. coli.Additional file 9 Metrics of BiPOm before and after reasoning on the metabolic network of E. coli. Additional Table 6 contains the metrics of BiPOm (i) before and (ii) after instantiation, and finally (iii) after automatic reasoning.