Paenarthrobacter aurescens TC1 is one of the most studied degraders of this herbicide. Here, we developed a genome scale metabolic model for P. aurescens TC1, iRZ1179, to study the atrazine degradation process at organism level. Constraint based flux balance analysis and time dependent simulations were used to explore the organism’s phenotypic landscape. Simulations aimed at designing media optimized for supporting growth and enhancing degradation, by passing the need in strain design via genetic modifications. Growth and degradation simulations were carried with more than 100 compounds consumed by P. aurescens TC1. In vitro validation confirmed the predicted classification of different compounds as efficient, moderate or poor stimulators of growth. Simulations successfully captured previous reports on the use of glucose and phosphate as bio-stimulators of atrazine degradation, supported by in vitro validation. Model predictions can go beyond supplementing the medium with a single compound and can predict the growth outcomes for higher complexity combinations. Hence, the analysis demonstrates that the exhaustive power of the genome scale metabolic reconstruction allows capturing complexities that are beyond common biochemical expertise and knowledge and further support the importance of computational platforms for the educated design of complex media. The model presented here can potentially serve as a predictive tool towards achieving optimal biodegradation efficiencies and for the development of ecologically friendly solutions for pollutant degradation.Atrazine is an herbicide and a pollutant of great environmental concern that is naturally biodegraded by microbial communities.  Its residues are found in soil samples decades after it was last applied and were shown to chronically leach into local aquifers3. As such, efforts are being made to limit and monitor its use4. While atrazine was banned in the European Union and Switzerland since 2003, the United States Environmental Protection Agency still allows its wide use under monitoring6. Areas contaminated with atrazine and other hazardous herbicides are rapidly increasing worldwide introducing a need in remediation approaches. Bioremediation—an environmental bioprocess in which naturally occurring organisms are used for breaking down hazardous substances into less toxic or non-toxic substances—is increasingly acknowledged as a cost-effective feasible alternative for environmental cleaning9. Critical environmental bioprocesses are naturally carried out by bacteria and are related to removal of pollutants from water, soil or air10. Thus, bacterial bioremediation is widely applied for the degradation of various organic pollutants14 including herbicides18. Bioremediation may occur naturally or through the stimulating addition of fertilizers, electron acceptors, etc. These amendments encourage the growth of the degrading microbes within the medium or environment in a process termed biostimulation19. Microbial metabolism has been described as most influential on atrazine degradation, promoting the development of biodegradation strategies20. One of the well-known atrazine degraders is the gram-positive Paenarthrobacter aurescens TC125 (previously known as Arthrobacter aurescens TC1), reported to biodegrade atrazine more efficiently than most other known degraders including Pseudomonas sp. ADP26. The full hydrolytic pathway for atrazine degradation in P. aurescens TC1 was described and reported27. While P. ADP can only use the hydrolytic products of the ring cleavage as a source of nitrogen but not as a source of carbon; TC1 can use the side groups of atrazine as source of carbon, nitrogen and energy consuming up to 3,000 mg of atrazine per liter24. As such, P. aurescens TC1 is an ideal candidate for the study of atrazine bioremediation using a genome scale metabolic model reconstruction.Atrazine  is an herbicide employed to control broadleaf and grass mainly in crops such as rice, wheat, maize, and sorghum. It is also a well-known pollutant of great environmental concern. Atrazine has been shown to have negative effects such as DNA damage, gene expression shifts, cancer and endocrine disruption29. Generally, such approaches follow four key steps: (1) data acquisition—mainly genome sequencing information, basic cell-physiological and biochemical knowledge and some experimental data on cell growth; (2) model reconstruction—translating data into structured mathematical representation; (3) constraint-based optimization simulations—the prediction of growth rate, substrate uptake rates, and byproduct rates under different growth conditions or following knockout mutations, in the absence of kinetic information36; and (4) experimental validation. The potential of such models for the investigation of optimal processing is now acknowledged and practiced40. Examples for applicative use include the optimal production or utilization of industrial compounds such as xylose41, biofuels42, vitamins43 and drug development44. In bioremediation, genome scale metabolic modeling approaches were applied for the design of Geobacter sulfurreducens strain capable of increased electron transfer and a higher Fe(III) respiratory that was beneficial for environmental bioremediation of uranium-contaminated groundwater45. Application of genome scale metabolic modeling for strain design is often based on the Optknock algorithm46 and its derivatives which search for the optimal gene knockouts for a desired metabolic production. However, unlike industrial use of engineered strain for enhanced production in monoculture, introduction of exogenous species into natural habitat is far from trivial and hampers the application of modeling approaches towards bioremediation solutions. An alternative strategy is the use of modeling for the design of optimal conditions that will enhance processes (degradation or synthesis) carried by the endogenous community47. For example, interactions between Geobacter and Rhodoferax—a competitor Fe(III)-reducers in anoxic subsurface environments—were captured and described using metabolic modelling and allowed identification of optimal degradation conditions48. Models can also predict the benefits of cooperative and commensal interactions to degradation efficiency. Xu et al. have demonstrated the use of metabolic models for predicting interactions between P. aurescens TC1 and endogenous soil species49. Exchange metabolites secreted by non-degraders species contribute for enhancing P. aurescens TC1 growth and expediting degradation efficiency50. Here, we directly focused on modeling-based identification of media supplements that can enhance atrazine degradation. We hypothesize that the introduction of specific nutrients into the bacteria’s immediate environment can resemble metabolic exchanges between P. aurescens TC1 and non-degrader species in soil and can lead to an increase in the total biomass and a subsequent increase in the degradation activity. We describe the process of reconstruction of a genome-scale metabolic model of P. aurescens TC1 and its evaluation as a predictive tool for the fast and low-cost screening of potential nutritional supplements that can serve as bio-stimulators of degradation.Modern tools of genomics, transcriptomics, metabolomics, proteomics, signaling systems and synthetic biology have opened new avenues for biotechnological advances and are increasingly applied for promoting better understanding of complex biological systems. In recent years, constraint based metabolic modelling approaches have become widely used as an in silico tool for organism-level phenotyping and the subsequent development of metabolic engineering strategiesP. aurescens TC1 is composed of a circular chromosome of 4.6 Mb coding for 4,222 open reading frames (ORFs) as well as two plasmids, 0.3 Mb each, coding for additional ~ 600 ORFs51. The genome and plasmids were annotated and used to create a draft model reconstruction using the Model SEED pipeline52. The draft reconstruction included an automatic gap-filling step, using default  media options52. This initial reconstruction contained a list of gene-protein-reaction associations that were classified as exchange, transport, and cytosolic as well as a list of all relevant metabolites and a biomass reaction. Based on taxonomy, the biomass reaction was defined to describe a gram-positive bacteria52. The composition of the biomass reaction summarizes the fractional contribution of generalized microbial biomass precursors  to the synthesis of a new cell and is similar to the previously published genome scale reconstruction of Bacillus subtilis53. Unspecified non-metabolic consuming processes in the cell were defined as ATP maintenance and set similarly to Oh et al.53.The genome of 54 were carried out. The model's metabolic functions were compared to genome annotations of P. aurescens TC1 from four established and comprehensive public resources and databases  and missing reactions were added to the draft network. All reactions were screened to verify that they are stoichiometrically balanced. Errors in reaction elemental balance and directionalities were determined according to the KEGG scheme. Model Reactions involved in atrazine degradation pathway and its further conversion into the cellular building blocks were added manually  followed by two hydrolytic deamination reactions catalyzed by hydroxyatrazine hydrolase (AtzB) and N-isopropylammelide isopropylamino hydrolase (AtzC). These enzymes convert atrazine to cyanuric acid and release the alkylamines ethylamine and isopropylamine. Cyanuric acid accumulates stoichiometrically, whereas the alkylamines are further catabolized into cellular building blocks27. Ethylamine and isopropylamine are converted into acetaldehyde and l-alanine  and curation of reaction directionality.Initial simulations were carried for debugging and removing futile or erroneously energy generating loops. To this end, all external fluxes were blocked (upper and lower bounds set to zero). Next, a minimal medium was used, verifying that growth requires the supply of both carbon and nitrogen sources. After establishing no growth under infeasible conditions, we tested growth (biomass production) under experimentally verified conditions as described in Strong et al.C. difficile or B. subtilis (20%)60 and the overall number of reactions is similar to the number of reactions covered by gold standard, updated models of species with similar genome sizes such as iML151561. A detailed description of the network including the reactions, metabolites, genes, and compartments that comprise the network is provided in Supplemental Dataset 62 in Supplemental Dataset The reconstructed metabolic network presented here covers 25% of the ORFs present in the genome and includes 1,179 genes, 2,541 reactions, out of which 134 are exchange, and 2,848 metabolites. The coverage of the genome is similar to those of previously published reconstructed metabolic networks of gram-positive bacteria such as P. aurescens TC1 degrades atrazine and metabolizes its intermediates, isopropylamine and ethylamine that can both be used as sole carbon and nitrogen sources. In silico growth simulations in minimal mineral media supplemented by atrazine or one of its degradation intermediates as a sole carbon and nitrogen source confirm that the model captures these reported physiological capacities. Experimental growth measurements verify model simulations and show that atrazine and its degradation products isopropylamine and ethylamine can be used as sole carbon and nitrogen sources for P. aurescens TC1  and glucose as nitrogen and/or carbon sources respectively was tested. The effect of nutrient ratio on growth rate was predicted by optimizing the production of biomass across uptake gradients while constraining the fluxes through exchange reactions for carbon and nitrogen sources. As expected, increasing glucose uptake increased the growth rate  and high (11.3 h−1). Simulation indicated a media dependent effect of these amino acids , allowing the identification of the ranges of flux variability that are possible within a given mediaets see “”. Atraziets see “ but alsoets see “.Figure 4Arthrobacter sp. HB-5, a close relative of P. aurescens TC168. Phosphate has been previously shown to accelerate atrazine degradation8. To test the effect of phosphate, we used the model to simulate growth and atrazine degradation in high or limited phosphate conditions. In accordance with these reports, simulations showed similar trends, which were confirmed by experimental results. These indicate an effect of phosphate concentrations on P. aurescens TC1 growth . The in-silico simulations were carried on an array of minimal media using atrazine and its interim degradation products as alternative sole carbon and nitrogen sources supplemented by potential enhancers. Simulations predicting and prioritizing specific metabolites as enhancers of growth and degradation were confirmed by in vitro experimental validation. Several limitations of the analysis should be acknowledged. Though the model refinement process included key steps required for construction of high-quality model, further adaptations are required for the current version of iRZ1179 to meet the requirements of gold standard models54. Mainly, the biomass composition and energy maintenance requirements are approximations that rely on automatic protocols and genomic information53. Collection of currently lacking experimental data can be incorporated in future versions of the model to define an accurate biomass objective function using, for example, the BOFdat computational platform69. Another example for potential improvement is modification of maintenance demands and mass transfer regulation based on a recent detailed account of atrazine degradation in P. aurescens at very low concentrations59. Second, data used to construct the model are not consistent at their level of confidence and annotations were gathered from numerous databases. A detailed process of manual inspection of each reaction and determination of its substrate/co-factor specificity54, was not yet carried. Finally, accuracy of predictions is likely to be significantly improved by the addition of other layers of information including metabolomics, transcriptomics and reaction kinetics70. Continuation of the manual curation process, also based on added transcription information, is likely to improve the performances of future versions. Yet, despite limitations, the resulting predictions can successfully capture the relative effect of different media complements on growth and atrazine degradation, as seen in the in vitro experiments performed, hence supporting the use of iRZ1179 as a predictive tool.Here, we reconstructed a genome scale metabolic model, iRZ1179 as a predictive tool enables fast and low (no)-cost screening and ranking of a wide range of potential nutritional supplements that can serve as stimulators. Here, growth and degradation simulations were carried with more than 100 compounds consumed by P. aurescens TC1. In vitro validation confirmed the predicted classification of different amino acids as efficient, moderate or poor stimulators of degradation activity. Simulation outcomes cannot be pre-determined based solely on the C:N ratio of media supplements but rather consider the complementary stoichiometric effect of multiple chemical reaction cascades, or pathways, that construct the genome scale metabolic network. Thus, these describe the complexity of cellular processes and balance between different metabolic pathways contributing to growth. Simulations per se provide multiple optimal solutions for the internal fluxes involved in primary metabolism and hence are not sufficient for deciphering the mechanism of how environmental (media dependent) conditions affect atrazine degradation. However, integration of simulation data with `omics data  can reduce the solution space and shed light on the fine-tuning of cellular activity considering the need to balance between myriads of constrains. Beyond the current study, the model can serve the contextualization of results from a growing number of high throughput experiments describing the relative abundance of discrete elements  into a higher level understanding of cellular activity. For example, future integration of proteomic data as produced in a recent study exploring adaptation of P. aurescens TC1 to growth in atrazine-fed bioreactors59, can serve for both model refinement and as a predictive tool.Several key findings emerge from this study. First, simulations successfully capture previous reports on the use of carbon and other sources (glucose and phosphate) as bio-stimulators of atrazine degradation, supported by in vitro validation. Second, the confirmation of Finally, model predictions can go beyond supplementing the medium with a single compound. Here, we demonstrated that the efficiency of the combination of different amino acids as growth enhancers depends on other medium components (here –atrazine). Hence, the analysis demonstrates that the exhaustive power of the genome scale metabolic reconstruction allows capturing complexities that are beyond common biochemical expertise and knowledge and further support the importance of computational platforms for the educated design of complex media.iRZ1179 as a predictive tool and can be considered as a first step towards designing bio-stimulation strategies that can be further tested in vitro and in the field. Soil communities are complex in terms of composition and microbial consortia dynamics, hence imposing greater complexity. Despite the complexity of soil communities, supplementing soil with carbon sources is long known to induce a change in microbial community structure and function. In a recent study we demonstrated the usefulness of modeling approaches for deciphering metabolic complexities within indigenous soil community treated with atrazine49. The integration of species-specific models together with community-based modelling approaches is likely to contribute to our understanding of the biodegradation processes of atrazine in natural environments and promote the development of bioaugmentation and biostimulation strategies. More generally, soil contaminations caused by pesticides and herbicides are considered among the top ten environmental hazards, with no current solutions that support green and cost-effective soil detoxification processes71. Exploiting the exhaustive power of the computational modeling platforms allows for a relatively fast search for bioremediation solutions that optimize the degradation activity of the existing natural communities, by allowing screening of hundreds of thousands of possible solutions and scoring them. Simulations can be designed to screen for metabolites, microbial species and combinations of both. Finally, in order to develop realistic solutions, a potential bio-stimulator should not only be efficient but also cost effective, ruling out expensive degradation enhancing compounds such as dipeptides. The ultimate proof of concept for the advent of computational approaches should be the design of cost-effective bioremediation strategies that outperform solutions that can be found by standard ‘trial and error’ practices.The in vitro validation provides a proof of concept for the use of P. aurescens TC1 was reconstructed using automatic pipeline, as described in Henry et al.52. Briefly, the complete genome sequence of P. aurescens TC1 was retrieved from NCBI , uploaded into RAST55, spliced into genes and annotated. RAST annotations were put through the Model SEED pipeline52 and an initial metabolic network reconstruction was obtained. Model refinement included addition of reactions identified in the specific strain in literature and additional databases, validation of reactions’ elemental balance and directionality, removal of futile loops and gap filling. Simulation conditions were modified to reflect experimentally validated minimal media alternatives that support growth of P. aurescens TC124. All simulations were carried out in a Minimal Mineral Media , supplemented by alternative carbon and nitrogen sources including atrazine, ethylamine, isopropylamine, ammonium, glucose and selected amino acids. The model is available in SBML format and as excel sheet  typically exceeds the number of metabolites (m), the system is under-determined. In order to get a feasible solution space, linear programming (LP), subject to mass balance preservation and flux constraints, was used by introducing an optimization problem. Here, model growth was maximized by maximizing its biomass reaction, which was used as objective function. Specific fluxes for metabolites consumption and secretion were determined following fixation of the respective biomass reaction to its maximal value and then using Flux Variability Analysis (FVA)67, a linear programming method to find the minimal amount of metabolites needed to produce a preset amount of biomass. Dynamic modeling was used for the prediction of the profile of consuming metabolites typical to the biomass increase of P. aurescens TC1 and atrazine degradation across time. To this end, we simulated the behavior of our metabolic model across time. This was done as described in49 and illustrated in Supplemental Dataset 75. Briefly, the model works under the following assumptions: (1) a finite start amount of media components is available; (2) a maximal amount of uptake a single cell can acquire from the media in a given time point is defined ; (3) new substrate concentrations in time t, are determined by the predicted substrate concentration for the previous step augmented with any additional substrates provided or consumed in the current iteration. The maximum uptake was set to a ratio of up to 1 unit of each metabolite available in the media; (4) after each time tick, the biomass amount was updated according to the flux amount of the biomass reaction in the model at this time tick. As biomass production rate serves as a proxy for the size of the population in the simulated environment and substrate uptake/secretion is mainly affected by to population size, the model was used to evaluate the actual substrate uptake/secretion and growth rate given the supplied media across time. Simulations were carried until reaching a state where time cycles did not lead to an increase in biomass. Initial concentration values for all metabolites were set to a fixed amount of 50 units . Simulation parameters and defaults are available in Supplemental Dataset P. aurescens TC1 across time.Flux distributions in the metabolic model were determined using Flux Balance Analysis (FBA) value);  new subs76.All model simulations were done on an Intel i7 quad-core server with 32 GB of memory, running Linux. The development programming language of our simulators was JAVA, and our linear programming software was IBM CPLEX. Surface plots were created using the MATLAB 2019a . Pathway maps were created using Escher mapsPaenarthrobacter aurescens TC1 (ATCCBAA-1386) was grown on R medium  plates with glucose (0.2%) and atrazine  as sole nitrogen. Stock cultures were maintained in 15% glycerol at − 80 °C. Cultures were resuscitated on R medium agar plates (1.5% Difco bacto) and were used as starter colonies for liquid medium growth experiments. The growth of P. aurescens TC1 was tested in R media supplemented with different combinations of carbon and nitrogen sources, including Glucose (0.2%), Atrazine , ammonium chloride (37 mg/l), Ethylamine and Isopropylamine  and the amino acids Histidine, Isoleucine and Methionine . Concentrations of amino acids, ethylamine and Isopropylamine were calculated to provide the same nitrogen content as the atrazine. In addition to the carbon and nitrogen sources, growth in media supplemented by atrazine and atrazine together with glucose was tested under two phosphate concentrations (K2HPO4 in 0.45 and 0.045 g/l). Each substrate was added to sterile R medium and bacteria were grown in triplicate 250 ml flasks incubated at 30 °C with shaking in the dark. One flask contained only R medium and was used as control. A 200 µl sample was taken from each flask every 8 h for measurement of OD in microplate reader  and 1 ml was taken to study atrazine degradation rate using HPLC. The HPLC analysis was performed with Agilent HPLC  equipped with a DAD detector. Samples were separated on Kinetex C18 column  and the mobile phase consisted of 70% methanol flowing at 1 ml/min. Detection and quantitation of atrazine was done at 240 nm with detection limit of 0.1 mg/l. Total duration of each growth experiment was between 152 and 168 h.Supplementary Dataset 1.Supplementary Dataset 2.Supplementary Dataset 3.Supplementary Dataset 4.Supplementary Dataset 5.


Komagataella phaffii (Pichia pastoris) into an emerging cell factory for recombinant protein production (RPP). As a key step of the bioprocess development, this work aimed to demonstrate the importance of tailor designing the cultivation strategy according to the production kinetics of the cell factory. For this purpose, K. phaffii clones constitutively expressing (PGAP) Candida rugosa lipase 1 (Crl1) with different gene dosage were used as models in continuous and fed‐batch cultures. Production parameters were much greater with a multicopy clone (MCC) than with the single‐copy clone (SCC). Regarding production kinetics, the specific product generation rate (qP) increased linearly with increasing specific growth rate (µ) in SCC; by contrast, qP exhibited saturation in MCC. A transcriptional analysis in chemostat cultures suggested the presence of eventual post‐transcriptional bottlenecks in MCC. After the strain characterization, in order to fulfil overall development of the bioprocess, the performance of both clones was also evaluated in fed‐batch mode. Strikingly, different optimal strategies were determined for both models due to the different production kinetic patterns observed as a trade‐off for product titre, yields and productivity. The combined effect of gene dosage and adequate µ enables rational process development with a view to optimize K. phaffii RPP bioprocesses.Its features as a microbial and eukaryotic organism have turned  Komagataella phaffii (Pichia pastoris) recombinant protein production (RPP) of an industrial lipase in chemostat and fed‐batch cultures. Different optimal strategies were designed from a trade‐off for product titer, yields and productivity for two clone models with different gene dosage and production kinetics, from which further transcription analysis supported potential bottlenecks after transcription.The combined effect of strain and bioprocess engineering should be considered during a rational process development towards bioprocess optimization. The synergy between gene dosage and specific growth rate have been evaluated for the  Komagataella phaffii, formerly known as Pichia pastoris, is a widely used yeast for recombinant protein production (RPP), for both biopharmaceuticals and an increasing number of industrial enzymes of interest  has been widely used in K. phaffii bioprocesses by virtue of allowing a strong and tight regulation for the recombinant expression in the presence of methanol , which is involved in a key step of the glycolysis pathway, was the first to emerge as a benchmark for efficient protein expression on various carbon sources. Thus, by avoiding all methanol‐related drawbacks, PGAP‐based bioprocesses present relevant advantages for large‐scale production  and specific growth rate (μ), is considered a key factor to be considered in the bioprocess development. It reflects the equilibrium between the various steps until the product is secreted, as a balance of the different processes involved during the protein synthesis, folding and secretion. This relationship is crucial to bioprocess development and optimization  is one of the most promising lipase enzymes for biocatalytic applications  have been identified; also, all except CRL6 and CRL7 have been identified and sequenced  was selected as model protein to elucidate the differences in the rational design of optimal bioprocess strategies for two clones of K. phaffii with different gene dosage, as example of clone variability in terms of protein production. For this purpose, an accurate characterization of physiological parameters and the production kinetics was firstly performed on chemostat cultures. The obtained results allowed the selection of the optimal bioprocess strategy to maximize the RPP, in order to be applied further in fed‐batch cultivations, which is currently considered as the most used operational mode for industrial RPP , five copies, and to confirm the presence of only one copy of CRL1 gene in the single‐copy clone (SCC).Later, transformed clones were screened in order to identify the best producer clone, which was a clone that integrated five copies of the expression cassette. Thus, it was selected for further studies in which it was compared with a clone with a single copy of gene of interestD). The specific growth rates spanned the range of 0.025–0.15 h−1. The carbon and electron balances were verified and closure found to exceed 95% prior to reconciliation. Fig. D in both strains.The impact of gene dosage on clone production kinetics was assessed with two sets of chemostat cultures grown at different dilution rates (qS) increased linearly with increasing μ. Interestingly, there were no significant differences in qS between clones, which suggests that this rate was unaffected by gene dosage. On the other hand, the overall biomass substrate yield (YX/S) remained fairly constant with a value of about 0.5 gX gS–1, which is consistent with most reported values  possibly due to requirement of more energy for maintenance (ms) than the single‐copy strain (0.029 vs. 0.0023 gS gX–1 h–1). This factor strongly influenced YX/S, which is consistent with some previous studies where biomass production decreased with decreasing μ . This notable change could be related to the RPP. It exerts a strong effect on metabolic fluxes that often leads to an increase in the maintenance requirements  and CO2 production (qCO2) rates increased linearly with μ. Slight differences between both strains were observed at high μ. However, the proportion between these two specific rates are constant, and consequently, the respiratory quotient (RQ) was always about 1.15.In Fig. qS, qO2 and qCO2 showed also to be strongly coupled with μ, therefore, fit into a linear equation pattern , which describes how is distributed a determined bioprocess parameter (specific rate) for cell growth and maintenance.Similarly to qS  and the overall product‐to‐biomass yield (YP/X) were evaluated as main key production parameters. Both are shown in Fig. The specific product generation rate . Some studies have shown protein production to be correlated with gene dosage and hence suggest that the number of gene copies influences qP up an optimum number above which the synergistic effect usually is lost .Unlike SCC, the variation of K. phaffii strains in long‐run chemostats describing a high genetic stability of the recombinant strains .As shown in Fig. µ range that leads to the saturation effect observed in the production kinetic profile. This result is consistent with previous reports where the expression system seemingly saturated during transcription, protein synthesis, post‐translational modifications or even secretion , TDH3 relative transcript levels were essentially identical for the two strains, which suggest that the levels were influenced by D but not by CRL1 gene dosage.Figure r et al.  in whichCRL1 gene expression was initially greater in MC than in SC clones. In SCC, CRL1 relative transcript levels increased linearly with increasing D, which suggests coupling of µ, CRL1 relative transcript levels and qP. These results indicate that PGAP regulates genes TDH3 and CRL1 similarly and hence that the effects are strongly related with cell growth. This was not the case with MCC, however. Thus, although CRL1 gene expression was seemingly not affected by D, qP clearly saturated at high D levels. This may have resulted from CRL1 expression coupling with biomass growth and the total amount of product secreted being limited. Therefore, there might be a bottleneck after transcription precluding conversion of all CRL1 transcripts into proper folded and secreted Crl1.Consistent with the results of the enzymatic activity analysis, TDH3 and CRL1 for different µ is compared by means of plotting the quotient of the relative transcript levels between the MCC and the SCC, can be observed the above‐mentioned trends. Interestingly, while no effect was observed for the TDH3 quotient, the positive effect of CRL1 gene dosage in terms of transcription is confirmed for all the culture conditions tested. According to these results, therefore, no limitation in the transcriptional machinery for CRL1 can be stated. Nevertheless, and despite the CRL1 quotient of transcript levels remains constant regardless the different cultures conditions at different D, there is a significant decrease in the qP quotient when increasing µ. This would support the hypothesis that the relevant increases achieved in terms of transcript levels due to the higher gene dosage of the target gene cannot be therefore converted into functional protein of interest.In Fig. GAP‐driven example of protein expression differs markedly from that reported by Cámara et al. (AOX1‐driven Rhizopus oryzae lipase (Rol) recombinant expression. The increased number of cassettes in Rol attenuated transcription of methanol metabolism and decreased methanol consumption, cell growth and recombinant protein production as a result.Strikingly, the gene dosage effect observed in this Pa et al.  for PAOXK. phaffii may be limited in terms of protein folding, glycosylation and secretion, reduced product yields and productivity could be expected. These limitations were widely discussed by Puxbaum et al.  with MCC.As detailed in Table –1 was used to confirm that Crl1 production would peak at the lowest μ level. As hypothesized, lipolytic activity (1414 UA ml–1) was highest under those conditions and four times greater than the highest value for SCC. A systematic comparison based on the main production parameters obtained at the different operating conditions followed with the two producer clones is presented in Table Based on these results for MCC, an additional fermentation run at 0.025 hqP and YP/X for the fed‐batch cultures at different µ values are depicted. As expected for consistency with the chemostat results, qP increased linearly with increasing µ in SCC but exhibited saturation in MCC. The YP/X variation pattern was similar to that for the chemostat cultures; thus, YP/X decreased exponentially with increasing µ in MCC, but remained fairly constant in SCC.In Fig. qP was higher with MCC than with SCC, and their ratio (3–6) was dependent on the µ applied. Although the overall patterns for the two operational modes were similar, qP and YP/X were substantially higher for the fed‐batch cultures.As in the chemostat cultures, μ is, the longer a bioprocess can be extended to increase product titres until the termination criterion is fulfilled.Fed‐batch cultivation usually ends when biomass production reaches a critical concentration limit imposed by biological and physical restrictions. As a result, growth‐associated biomass in fermentation processes is an unavoidable by‐product and requires controlling the biomass growth in order not to exceed the limiting concentration. Thus, the lower µ and qP, and how these two specific rates affect the bioprocess efficiency.In Table μ on qP, it was demonstrated that the kinetic pattern is markedly different for the MCC and SCC. The MCC exhibited a 30% qP decrease when μ decreased from 0.15 to 0.05 h–1, by effect of its rather flat production kinetic curve at the highest μ, as shown in Fig. qP decreased by 70 % from 0.15 to 0.05 h–1. It is due to the more marked coupling of qP to the cell growth.Regarding the production kinetics, that is, how affects QP) varied on µ similarly to that observed for qP in MCC and SCC. Consequently, the rational selection of µ to optimize the bioprocess performance would require a trade‐off.As expected, productivities .On the contrary, for the MCC, product titre reached a 68 % increase when µ and gene dosage on PGAP‐based K. phaffii clones expressing CRL1 can be used to design optimal operating strategies.The results previously exposed support the idea that combined effect of qP increases linearly with increasing specific growth rate in SCC but exhibits a non‐linear pattern suggestive of saturation of the production kinetics in MCC. Interestingly, qP is considerably higher with MCC than with SCC . These results confirm that gene dosage impacts directly on the production kinetic profile, both in the levels of titre achieved as well as the profile pattern. From the transcriptional analysis performed, one can hypothesize the presence of a potential bottleneck after transcription.In this way, the results obtained from chemostat cultures reveal that μ on the bioprocess efficiency. Although trends were similar as those observed in the chemostat cultures, there were some differences, especially with MCC. Saturation was more marked than in the chemostat tests, and a plateau was reached in the higher µ range.The continuous cultures were used as tool to the design of optimized fed‐batch strategies, since this operational mode is the most widely operational mode used for industrial RPP. Therefore, a rational‐based bioprocess design can be carried out considering the effect of gene dosage and µ has a strong impact on specific production rates and yields (e.g. with SCC), a high µ level should be used to increase qP and YP/X. On the other hand, if the impact of µ is weak (e.g. with MCC), low‐to‐moderate µ values can help to extend the bioprocess time until the limit imposed by a critical amount of biomass is reached. In this case, these differences have been caused by the different gene dosage.When the data for the main production parameters in Table K. phaffii. This work presents how a comprehensively elucidation of the gene dosage effect on production kinetics towards an overall optimization of the RPP bioprocesses can be afforded. Hence, properly understanding these features and their correlation provides a more rational, robust knowledge of the behaviour of cell factories and allows bioprocesses to be engineered for greater efficiency.Summing up, it can be stated as main outcome of this contribution that the production kinetics of the cell factory and specific growth rate must be jointly considered to tailor operating strategies to production clones for maximizing expression in K. phaffii X‐33 from Invitrogen  expressing CRL1 regulated by the GAP promoter were obtained and used. A chimeric vector assembled with the restriction–ligation method was constructed by using commercial pGAPZαA plasmid from Invitrogen and a codon‐optimized synthetic CRL1 coding sequence from GeneScript . Different amounts of plasmid were transformed by electroporation in order to obtain clones with different numbers of integrated expression cassettes. However, only the clones containing 1 or 5 gene copies were used. Both clones can secrete Crl1 to the extracellular medium through the Saccharomyces cerevisiae α‐mating factor signal sequence.Two recombinant clones of et al.  was used to determine the number of cassette integrations in both clones, using a slightly modified version of the method of Cámara et al. . Actin get al. . The speTranscriptional analyses were only done on chemostat cultures, where steady‐state conditions ensured homogeneity in cell population.TM  and 200‐mg glass beads. Total RNA was extracted as per the manufacturer’s instructions. Then, RNA integrity and concentration were checked by agarose electrophoresis and Nanodrop analysis  respectively.Samples of 1 ml were withdrawn under different chemostat conditions and centrifuged at 4 ºC at maximum speed for 2 min. The resulting pellets were resuspended in 1 ml of TRIzolCRL1 (heterologous product); TDH3, which is the gene natively expressed under PGAP control (glycolytic); and PGK gene, phosphoglycerate kinase (glycolytic). Additional genes involved in the unfolded protein response (UPR) and the secretory mechanisms such as KAR2 and HAC1 were also studied. Transcription was assessed by qPCR amplification. For maximum accuracy, mixes were made by the robot EpMotion® . SYBR™ Select Master Mix was used as polymerase mix and a QuantStudio 12K Flex Real‐Timer from Thermo ScientificTM for amplification cycles and data acquisition.cDNA was synthetized by using the iScript™ cDNA Synthesis Kit from Bio‐Rad  according to the manufacturer’s instructions. A set of primers was designed to amplify cDNA for the target genes by qPCR. The set comprised MTH1 glucose‐responsive transcriptional factors, which code for a negative regulator of the glucose‐sensing signal transduction pathway, as housekeeping agents. Rebnegger et al.  and fed‐batch tests (glucose), and of potential fermentation by‐products (arabitol or ethanol), were all determined by HPLC. The column and procedure used for this purpose are described elsewhere . CO2 and O2 mole fractions were measured on‐line with provision for off‐gas pressure and humidity. The data thus obtained were used to estimate the oxygen uptake rate (OUR), carbon dioxide evolution rate (CER), specific rates (qO2 and qCO2) and the respiratory quotient (RQ). RSD was < 5% in all cases.p‐nitrophenyl butyrate (pNPB) % acetone. A volume of 980 µl of buffer was mixed with 20 µl of sample. The absorbance at 348 nm was measured on‐line at 30°C for 2 min on a Specord 200 Plus instrument from Analytic Jena . One unit of activity was defined as the amount of enzyme needed to release 1 mmol of p‐nitrophenol per minute under assay conditions. RSD was < 1%.Crl1 activity was determined by using a modified version of an existing enzymatic assay based on et al., et al., All equations derived from the mass balances used to calculate yields and rates in the chemostat (Garcia‐Ortega µ), glucose uptake (Sq), product generation (Pq), oxygen uptake (qO2) and carbon dioxide production (qCO2). The methodology used is described in detail in a previous paper (Ponte et al., .Measurement consistency was checked by using the standard test with carbon and electron balances as constraints. Both on‐line and off‐line measurements allowed five key specific rates in the black‐box process model to be calculated, namely biomass generation (None declared.Table S1. Primer pairs used for gene dosage and transcript‐level determination by means of ddPCR and qPCR respectively.Click here for additional data file.


Microbial metabolism is highly dependent on the environmental conditions. Especially, the substrate concentration, as well as oxygen availability, determine the metabolic rates. In large-scale bioreactors, microorganisms encounter dynamic conditions in substrate and oxygen availability (mixing limitations), which influence their metabolism and subsequently their physiology. Earlier, single substrate pulse experiments were not able to explain the observed physiological changes generated under large-scale industrial fermentation conditions.Escherichia coli culture in a time-scale of seconds. The regime was applied for several generations, allowing cells to adapt to the (repetitive) dynamic environment. The observed response was highly reproducible over the cycles, indicating that cells were indeed fully adapted to the regime. We observed an increase of the specific substrate and oxygen consumption (average) rates during the feast–famine regime, compared to a steady-state (chemostat) reference environment. The increased rates at same (average) growth rate led to a reduced biomass yield (30% lower). Interestingly, this drop was not followed by increased by-product formation, pointing to the existence of energy-spilling reactions. During the feast–famine cycle, the cells rapidly increased their uptake rate. Within 10 s after the beginning of the feeding, the substrate uptake rate was higher (4.68 μmol/gCDW/s) than reported during batch growth (3.3 μmol/gCDW/s). The high uptake led to an accumulation of several intracellular metabolites, during the feast phase, accounting for up to 34% of the carbon supplied. Although the metabolite concentrations changed rapidly, the cellular energy charge remained unaffected, suggesting well-controlled balance between ATP producing and ATP consuming reactions.In this study we applied a repetitive feast–famine regime in an aerobic E. coli under substrate dynamics, representative for large-scale fermenters, revealed the existence of several cellular mechanisms coping with stress. Changes in the substrate uptake system, storage potential and energy-spilling processes resulted to be of great importance. These metabolic strategies consist a meaningful step to further tackle reduced microbial performance, observed under large-scale cultivations.The adaptation of the physiology and metabolism of  Microorganisms are widely used for the production of chemicals, ranging from small organic acids to large proteins, including biopharmaceuticals, biochemicals and bulk biofuels –3. In orSubstrate gradients are frequently considered as a main reason for performance reduction. Commonly, the substrate concentration should be kept at low levels to avoid overflow metabolism –17. To aEscherichia coli cultures, cyclically circulating from high to low glucose levels, have shown decreased biomass yields and by-product formation  were quantified with GC–MS/MS , as described in  and/or aE. coli to repetitive, dynamic perturbations was evaluated with respect to short and long-term physiological and metabolic characteristics:Comparison between average metabolic rates and yields under repetitive dynamic conditions and steady-state (reference) conditions, at the same dilution rate.Comparison of the metabolic response between repetitive dynamics, single perturbations (pulse experiments) and steady-state levels.The adaptation of 2 and CO2) concentrations  and offgas O and CO2 mentclass2pt{minimKM = 10 μM) of the microorganism  and after glucose or oxygen perturbations [E. coli cultivations in glucose-containing medium, where acetate is produced even when the culture is fully aerated [The extracellular by-product  concentrations  [The biomass specific rates were reconciled using the approach described in , using e g/Cmol)  was used2 production were higher  for the intermittent feeding, compared to the reference continuous regime. More specifically, during the reference chemostat operation, the oxygen to substrate consumption ratio was 2.85 ± 0.05 glc, which is comparable to the values reported in literature for similar cultivation conditions, ranging from 2.74 to 3.62 glc [glc.The most evident observation is that the calculated rates for glucose and oxygen uptake and CO2/molglc , 59–61. Introducing potential cell lysis in the reconciliation, we observed that the lysis rate during the steady-state was calculated as negative (while positive by definition), with a high standard deviation and therefore the steady-state lysis was assumed zero.E. coli, when varying the substrate availability. Many studies attributed this phenomenon either to overflow metabolism, due to high growth rates (> 0.15 h−1) [Saccharomyces cerevisiae , subjected to an intermittent feeding (similar to the regime used here) [The intermittent feeding, resulted in decreased average cell dry weight concentration and subsequent 0.5 log2-fold decrease (− 30.3%) of the total biomass yield. The biomass yield was calculated as the ratio of the total biomass growth rate (including lysed biomass) over the glucose uptake rate. A decrease in biomass yield has also been reported in previous studies for .15 h−1) , 39, or .15 h−1)  observeded here) .2 produced per glucose consumed, during the steady-state regime, was 3.16 ± 0.05 glc, while for the feast–famine a value of 4.05 ± 0.08 glc (+ 28.1%) was observed. Together with the increase in O2 consumption, it indicates that more glucose was used for respiration, rather than biomass production, during the feast–famine cycles [The ratio of COE. coli cells with high time resolution and repeated measurements. Especially, samples can be obtained from repetitive cycles , among various combinations [Special focus was to obtain a high-resolution uptake profile as substrate uptake has a major impact on the intracellular metabolic behaviour of the microorganism. To calculate the short-term glucose uptake profile, a piecewise affine (PWA) rate approximation  was calcinations . The fluCDW/s) immediately after the beginning of the feeding and then decreased slightly until the end of the feeding, followed by significant decrease between 15 s and 18 s, i.e. from 4.40 to 1.04 μmol/gCDW/s.There was no obvious correlation between the glucose uptake rate and the extracellular glucose concentration. The rate reached its highest value (4.68 μmol/gE. coli under glucose excess (Km is in the range of 3–10 μΜ [This contradiction is explained by the activity of the phosphotransferase system (PTS) , which i 3–10 μΜ , 67). ThThe overshoot in the glucose uptake rate has been previously observed in cells exposed to excess of substrate after a starvation period, in different experimental setups , 60, 62.CDW/s), proving that the microorganism has a higher uptake capacity than the one observed under maximum growth. It is, however, puzzling that the glucose uptake rate was decreasing already (mainly after 18 s), while glucose was still in excess (above the glucose affinity constant). An additional test experiment was performed under the same cultivation conditions, with a shorter feeding phase (13 s) but the same cycle length (400 s) and the same total amount of glucose fed over the cycle. The glucose uptake rate calculated (data not shown) exhibited the same decreasing pattern 2 s before the end of the feeding phase (at 11 s), while glucose was still in excess. Raw observations of this test experiment are included in Additional file The highest estimated uptake rate in our work was significantly higher than the maximum observed during batch cultivations for the same strain  cycle, pentose phosphate pathway (PPP) intermediates and amino acids. These measurements originated from one experiment, but metabolites were sampled densely in time, over several cycles. The clear trends of the measurements showed high technical reproducibility .The highly dynamic glucose uptake rate, discussed in the previous section, was expected to result in significant fluctuations in the intracellular metabolite levels. Therefore, it is important to observe how E. coli strains redistribute their metabolic fluxes in such way to minimally divert from the wild-type metabolic network [The intracellular flux profiles over time were estimated by (dynamic) Flux Balance Analysis (FBA) for the glycolytic and pentose phosphate reaction steps. The stoichiometric network included reactions of central carbon metabolism, where the intermediates could be measured . The measured concentrations were significantly higher than the steady-state levels (e.g. up to 20 fold change for FBP), due to the short-term overshoot of carbon flux. The opposite trend was observed for the lower glycolytic metabolites , whose concentration immediately decreased in the first seconds of the feast phase (three to sixfold change from steady-state). The reason behind this drop is based on the PTS system. In order to import and phosphorylate glucose to G6P, PEP needs to be produced and then converted to pyruvate. Unfortunately, pyruvate could not be quantified in this experiment. PEP concentration showed negative correlation with G6P, as it reached its lower concentration after 12.5 s, the same time the maximum concentration of G6P was reached. This behaviour has been observed before in e pulses , 75–77. The metabolites of pentose phosphate pathway related well to the dynamics observed in glycolysis, as they exhibited the same behaviour of rapid accumulation in the beginning of the feast phase and later decrease to the initial levels. The pool of 6PG responded directly to the changes occurring in its precursor, G6P, reaching its maximum concentration at 20 s (7.5 s delay compared to G6P). This peak was observed slightly later in the rest of the metabolites, with the exception of Xyl5P, which responded equally fast.Looking at the flux profiles, we observed that the glucose uptake rate dynamics propagated through glycolysis. The peak observed in the PTS flux right at the beginning of the feeding, also occurred in the succeeding reactions towards the formation of PEP and they all decreased significantly after 15 s. After 110 s all metabolite pools remained constant, while there was no more flux running in glycolysis. The same trend was also observed in all the reaction steps of the pentose phosphate pathway.E. coli culture, which was used to further support the calculated increase in growth rate during the feast phase [E. coli [Compared to the steady-state levels, the immediate increase of the PTS flux (16 fold) led to a higher change in all the glycolytic fluxes (18–19 fold) and an even higher increase in the flux towards PPP (30 fold). This observation, together with the fact that 62.4% of the PTS flux was directed into glycolysis (less than the 70% assumed in steady-state), gives an indication that the cells may increase the flux to pentose phosphate pathway, under these dynamic conditions, therefore enhancing the production of NADPH, assumingly for redox balance purposes. Similar increase was observed after a single-pulse of glucose in an aerobic st phase . NADPH w[E. coli , 79 and [E. coli , 81.In the case of the TCA cycle, only a few metabolites could be precisely quantified, which are shown in Fig. Following glycolysis, also the TCA metabolites showed a dynamic profile over time. We observed that aKG and malate reached their highest concentration 30 s after the beginning of the feast–famine cycle Fig. , displayAmino acids are relevant precursors for protein synthesis. At the same time, several amino acids are closely connected with their respective central carbon metabolism precursor. For example alanine is only one (equilibrium) reaction step from pyruvate. Thus, on the one hand one could expect homeostasis to ensure balanced growth, on the other hand a high dependency on central carbon metabolism  for E. coli [Nucleotide responses to the feast–famine regime are of high interest and especially the ATP/ADP levels, which reflect the adenylate energy state (+ADP+AMP ) of a ce E. coli . Therefo E. coli –86. AMP E. coli K12, where the energy homeostasis was also reported during glucose excess (AEC ranging from 0.8 to 0.85 in the different studies). However, in these studies, the AEC was decreasing during the famine phase, sometimes reaching values even lower than 0.7 [Our findings are in agreement with results from single pulse experiments , 52, 87,than 0.7 , which wthan 0.7  also obsIn contrast to AxP’s, UDP and UTP were not homeostatic. They decreased over the feast phase and increased during the famine phase. Also, GDP and GTP were dynamic with a trend opposite to UxP’s Fig. .Fig. 6In2 was observed over the whole cycle (400 s). The specific glucose uptake rate was higher than at the reference steady-state and there was no significant accumulation of by-products. This suggests high intracellular accumulation of carbon during the feast phase and degradation during the (extracellular) famine phase.From the extracellular observations, it was observed that the carbon uptake and excretion were significantly shifted. While the substrate carbon was consumed only during the first 100 s, excretion in the form of COThe total amount of intracellular carbon during steady-state and feast–famine was calculated from the measured metabolites at every timepoint and is shown in Fig. CDW), at 30 s  until approximately 120 s. Then a constant decrease, until reaching the initial level, was observed. Significantly, the total amount of carbon in the measured metabolome was, at all timepoints, higher than the steady-state levels, resulting from the overshoot in the glucose uptake.The total amount of metabolites was changing over time, during the feast–famine regime. We observed a small decrease in the total metabolome during the first 10 s of the cycle, followed by an increase until the highest point  consumed by the cells in the first 100 s of the feast–famine cycle. In terms of electrons, this accumulation in the feast phase was 6.4 mEmol/LEC. If all the electrons were used during the famine phase, the maximum oxygen consumption observed would be 1.6 EC. In fact, we estimated, from the calculated EC were consumed during the famine phase. Therefore, all of the accumulated intracellular metabolites could have been used as electron donors and could explain the O2 uptake, while the substrate was depleted. Taymaz-Nikerel et al. [Looking at the rest of the intracellular intermediates, the total accumulation, in terms of carbon, during the feast phase was calculated to be 256 μCmol/gLEC Fig. -top. Thil et al.  reached Escherichia coli cultured under dynamic substrate conditions exhibited a different physiology compared to conditions supplying the same amount of substrate steadily. Namely, the average biomass specific consumption  and production rates (CO2) increased under the feast–famine regime, compared to the steady-state, while by-product synthesis remained unaffected. Consequently, biomass formation was adversely disturbed with 30% decrease in yield.These observations suggest that during the intermittent feeding, more glucose was used for respiration than biomass production. This would mean that the excess of ATP produced was used in other cellular processes. If the energy-spilling scenario is correct, it would imply an increase in maintenance or the presence of futile cycles.Alternatively, this change in physiology could be attributed to an increase in competitiveness. Fast consumption of the substrate generates an advantage compared to slow competitors, as an increasing share of the substrate will go to the faster consuming cells .E. coli, the most important maintenance processes described in literature, are protein turnover (synthesis and degradation), switches in metabolic pathways, proteome and RNA repair and cell motility [13C labeling of the amino acids pools and proteasome activity essays [Maintenance is defined as the energy-consuming processes “for functions other than production of new cell material” . In E. cmotility , 94–96. motility . The ATPmotility , 99. Proy essays , 101, whE. coli strain [−1.The reconversion of oxaloacetate to phosphoenolpyruvate by the gluconeogenic PEP carboxykinase . This ATi strain , as welli strain . The indi strain . Yang eti strain  demonstrThe reconversion of fructose-1,6-biphosphate to fructose-6-phosphate by fructose 1,6-bisphosphatase. Usually this futile cycle is tightly regulated by the cells and is therefore minimal under both glycolytic and gluconeogenic conditions , 108.E. coli wild-type on glucose [The reconversion of pyruvate to phosphoenolpyruvate by phosphoenolpyruvate synthase, with the involvement of Enzyme I of the PTS , 110. 10 glucose .The reconversion of acetate to acetyl-coA by acetyl-coA synthetase . ValgepeGlycogen formation and re-consumption. The formation of glycogen, by glycogen synthetase, requires one ATP per glucose, while its consumption does not form any ATP , 113.Futile cycles may also explain the ATP-spilling during the feast–famine regime. Some potential futile cycles, already described in literature, are:E. coli during the feast–famine conditions. It is well possible that the cells up-regulate the enzymes of these futile cycles, in order to rapidly switch the direction of the fluxes, when shifting from feast to famine conditions. The reasons behind this metabolic strategy can be the rapid re-initiation of growth and the tight regulation of the ATP levels in the cell. We indeed observed a constant energy cellular status over the intermittent regime, which enhances the hypothesis of this role of futile cycles. However, the identification and interpretation of these energy-spilling reactions, under alternating feast–famine conditions, has not been studied in literature. Measurements of the enzyme expression and 13C flux determination will be needed to confirm our hypotheses. In addition, knocking out some of the enzymes causing these futile cycles and growing the engineered strains under the same conditions would be a strategy to verify if they are key elements of the ATP homeostasis.All of the above-mentioned futile cycles could be active in E. coli (FBAwMC), including a constraint for the enzyme concentrations, considering the macromolecular crowding. With this model they predicted the maximum growth both in single-substrate, but also in mixed substrate media, accurately representing experimental observations, showing that the growth rate was influenced by the solvent availability in the cytoplasm. In a following study, Vazquez et al. [Based on high time resolution, extracellular glucose concentration measurements and PWA rate approximations, the glucose uptake rate was calculated over cycle time and showed an immediate increase after the feeding was switched on. This rate reached a maximum value, higher than batch maximum rates, and decreased before the concentration decreased. The fact that glucose was still in excess, but the uptake rate could not follow up, indicates the existence of an intracellular metabolic limitation. From our intracellular metabolic analysis, we showed that there was enough PEP during the whole cycle to drive glucose transport in the cell through the PTS, therefore, the import of substrate was not the limiting step. One hypothesis which could explain the switch in the uptake rate is the phenomenon of macromolecular crowding. Macromolecular crowding is occurring in all living organisms, as a large part of the volume of the cell is occupied by high concentrations of macromolecules, such as proteins. Thus, there is limited intracellular volume available for other molecules. This volume exclusion affects various enzymatic reactions, either by increasing or decreasing their rates, depending on the change in size of the reactants –117. Whiz et al.  applied z et al.  or enzymz et al. .Furthermore, we observed the high capacity of intracellular metabolism facing the substrate gradients applied. There was a rapid response in intracellular metabolite concentrations and fluxes, which generally deviated significantly from the steady-state. The dynamics observed were less pronounced moving downstream, from glycolysis to TCA and then to amino acid synthesis, with more modest changes over time.E. coli under nutrient-limited conditions.In addition, during the highly dynamic conditions, applied in this study, we demonstrated the ability of the cells to store an amount of carbon and electrons intracellularly during the feast phase, which were then used when substrate was depleted, therefore, explaining oxygen consumption during the famine phase. This strategy proves to be important for the survival and robustness of E. coli is aerobically cultivated in large-scale bioreactors, facing long-term substrate gradients. Fed-batch regimes are often preferred, since the substrate concentration or the specific growth rate can be controlled in such a way to avoid overflow metabolism [These observations are highly relevant in an industrial context, where tabolism , 125. Thtabolism . Howevertabolism .E. coli culture to substrate perturbations, highlights parameters to take into account for metabolic engineering and process design in relation to large-scale reactor operation.Cells responded immediately to an excess of substrate, by increasing their uptake rate and consequently the intracellular fluxes in tens of seconds. Carbon was stored in intracellular intermediates, during substrate feast and was consumed during a famine phase.Despite, the highly changing dynamics, energy charge homeostasis was observed, as a remarkable fitness characteristic of the response to perturbations, indicating rapid metabolic regulation.More important and highly relevant to industrial fermentations, was the 30% decrease of the biomass yield, occurring during the intermittent feeding, compared to a reference steady-state. Energy-spilling, was therefore, a trade-off for the adaptation of the microorganism in the dynamic environment, seeking for robust growth.Studying the physiological and metabolic responses of an adapted E. coli responds to stress, induced by substrate gradients, by launching a specific metabolic strategy. In order to improve productivity cost-effectively in large-scale bioprocesses, we need to further identify the mechanisms behind stress adaptation, limitations in substrate uptake and respiration, potential energy-spilling pathways and optimal growth targets of the cells, combining multi-omics approaches.The obtained results revealed some reasons for the reduced performance of cell factories during scale-up. Additional file 1. Additional file supporting the results discussed in the text.


Altered metabolism is associated with many human diseases. Human genome-scale metabolic models (GEMs) were reconstructed within systems biology to study the biochemistry occurring in human cells. However, the complexity of these networks hinders a consistent and concise physiological representation. We present here redHUMAN, a workflow for reconstructing reduced models that focus on parts of the metabolism relevant to a specific physiology using the recently established methods redGEM and lumpGEM. The reductions include the thermodynamic properties of compounds and reactions guaranteeing the consistency of predictions with the bioenergetics of the cell. We introduce a method (redGEMX) to incorporate the pathways used by cells to adapt to the medium. We provide the thermodynamic curation of the human GEMs Recon2 and Recon3D and we apply the redHUMAN workflow to derive leukemia-specific reduced models. The reduced models are powerful platforms for studying metabolic differences between phenotypes, such as diseased and healthy cells. The complexity of genome-scale metabolic networks (GEMs) hinders their application in specific physiological contexts. Here, the authors introduce a framework to reduce thermodynamically curated GEMs to the subnetworks of interest and demonstrate its application by deriving leukemia-specific models. Understanding the metabolic mechanisms that underlie this reprogramming guides the discovery of new drug targets and the design of new therapies. To this effect, tremendous efforts are now being made to use the large amounts of now-available multi-omics experimental data to gain insight into the metabolic alterations occurring in different phenotypes. Unfortunately, current mathematical models can be too complex for this analysis, rendering them too cumbersome to employ for many systems biology studies.An altered metabolism is a hallmark of several human diseases, such as cancer, diabetes, obesity, Alzheimer’s, and cardiovascular disorders5 and are valuable tools for studying metabolism7. The mathematical representation of GEMs through the stoichiometric matrix7 is amenable to methods such as flux balance analysis (FBA)8 and thermodynamic-based flux balance analysis (TFA)13, which ensure that the modeled metabolic reactions retain feasible concentrations and their directionalities obey the rules of thermodynamics, to predict reaction rates and metabolite concentrations when optimizing for a cellular function, such as growth, energy maintenance, or a specific metabolic task. Additionally, GEMs can be used for gene essentiality14, drug off-target analysis15, metabolic engineering18, and the derivation of kinetic models22.In the field of systems biology, genome-scale metabolic models (GEMs) integrate available omics data with genome sequences to provide an improved mechanistic understanding of the intracellular metabolism of an organism. GEMs have been reconstructed for a large diversity of organisms spanning from bacteria to mammals24. Since then, the scientific community has been working to develop high-quality human GEMs, including HMR 2.025, Recon 226, Recon 2.227, and Recon 3D28. The human GEMs used for the analysis in this article are Recon 2 and Recon 3D. Recon 2 is composed of 7440 reactions with 4821 of them associated to 2140 genes, and 2499 unique metabolites across seven compartments: cytosol, mitochondria, peroxisome, Golgi apparatus, endoplasmic reticulum, nucleus, and lysosome. Recon 3D is the latest consensus human GEM. It is an improved more comprehensive version of the previous GEMs consisting of 10,600 reactions, with 5938 of them associated with 2248 genes, and 2797 unique metabolites compartmentalized as Recon 2 with an additional compartment for the mitochondria intermembrane space.The first human GEM was reconstructed in 200729, for healthy and diseased cells31, and for cells growing under diverse extracellular conditions. Some examples of such methods are (1) GIMME32, mCADRE33, and tINIT34 to reconstruct tissue-specific models based on omics data and a set of tasks or a specific objective function; (2) redGEM–lumpGEM36 to reconstruct models around a specific set of subsystems of interest for the study; and (3) iMM38 to characterize the extracellular medium and the metabolites that are essential for growth under each condition. Context-specific metabolic models have been extensively used to understand the differences in metabolism between cancer cells and their healthy counterparts45.Human GEMs reconstruct the metabolic reactions occurring in several human cell types. However, a given cell type only leverages a portion of these reactions. This motivates the development of methods to generate context-specific metabolic models that can be used to study the differences in metabolism for different cell typesIn this article, we present redHUMAN, a workflow to reconstruct thermodynamic-curated reductions of the human GEMs Recon 2 and Recon 3D. We integrate the thermodynamic properties of the metabolites and reactions into the GEMs and use redGEM–lumpGEM to reconstruct reduced models around specific subsystems. Furthermore, we introduce redGEMX, a method to identify the pathways required to connect the extracellular compounds to a core network. redGEMX guarantees that the reduced models have all the feasible pathways that consume and produce the components of the extracellular environment of the cell. Finally, we use metabolic data for leukemia as an example of how to integrate experimental data to derive disease- and tissue-specific metabolic models.In order to generate reduced models from human GEMs, we developed redHUMAN, a six-step workflow that can be applied to any GEM or desired model system. The overall workflow is briefly described here and shown in Fig. − group). We observed that as the number of metabolites increases from Recon 2 to Recon 3D, the percentage of thermodynamic coverage increases as well. This is due to the improved annotation of the metabolite structures in Recon 3D. Using the thermodynamic properties of the compounds as constraints (see “Methods”), we estimated the Gibbs free energy for 51.3% of the 7440 reactions present in Recon 2 and 61.6% of the 10,600 reactions in Recon 3D. These constraints ensured that the reactions in the computed flux distributions operated in thermodynamically feasible directions.We first determine the directionality of the chemical reactions of the network, which is directly associated with their corresponding Gibbs free energy. The Gibbs free energy of a reaction can be estimated from the thermodynamic properties of its reactants and products. Therefore, we curated the GEMs Recon 2 and Recon 3D (see “Methods”) and integrated the thermodynamic properties for 52.4% of the 2499 unique metabolites from Recon 2 and 67.5% of the 2797 unique metabolites from Recon 3D Fig. . Three m49. Consequently, the core subsystems for our models were glycolysis, pentose phosphate pathway, citric acid cycle, oxidative phosphorylation, glutamate metabolism, serine metabolism, urea cycle, and reactive oxygen species detoxification. We have estimated the thermodynamic properties for the metabolites and the reactions in these initial subsystems. In the case of Recon 2, we provide an estimate for the Gibbs free energy of formation for 236 metabolites  and the Gibbs free energy of reaction for 143 reactions . In the case of Recon 3D, we provide estimated values of the thermodynamic properties for 288 metabolites (97.6%) and for 183 reactions (91.0%).A proper metabolic model contains the pathways that are essential for the survival of the cell as well as the pathways that are informative of a specific metabolic behavior. In this work, we were interested in the metabolism of cancer cells. Thus, we selected as core subsystems: (a) the central carbon pathways that provide the energy, redox potential, and biomass precursors, and (b) the subsystems that have been reported to be altered in cancer cellsSubsequently, to reconstruct the core network we pairwise connected the chosen subsystems using redGEM (see “Methods”). The algorithm first performed an intra-expansion of the initial subsystems. In this process, each initial subsystem was expanded to include additional reactions from the GEM whose reactants and products belong to that subsystem. These reactions can be assigned to different subsystems in the GEM which are not any of the initial subsystems and the core network would miss these additional reactions if we had considered the formal definition of the initial subsystems. The initial core subsystems of Recon 2 contained a total of 180 reactions. After the intra-expansion, 135 reactions from 21 subsystems were added. Examples of these added reactions included three from pyruvate metabolism that interconvert acetyl-CoA, acetate, malate, and pyruvate, which are all metabolites that participate in the citric acid cycle subsystem. For Recon 3D, 171 reactions from 24 subsystems were added to the 211 reactions from the initial core subsystems.D  between pairs of metabolites from the subsystems. Our final models included the connections for degree D = 1, that is, all the reactions that in one step connect two metabolites (excluding cofactors) belonging to any of the initial subsystems. A degree D = 1 was enough to pairwise connect all the initial subsystems , and Recon 3D simulated growth in a medium with glucose, the nine essential amino acids, the same inorganics as Recon 2, and one of the two essential fatty acids . The presence of the two essential fatty acids in the iMM of Recon 3D is a consequence of the improvement of the lipid metabolism28, where the essential fatty acids participate in the synthesis of phospholipids. This demonstrates how the algorithms and workflow can be used to compare and validate updated model reconstructions for the same organisms or between different organisms.Cells adapt their metabolism to the available nutrients in their extracellular environment. Consequently, a correct definition of the medium in the metabolic model is fundamental for an adequate representation of the intracellular metabolism. Given the complexity of the extracellular medium, it is particularly important to identify and classify the essentiality of the medium components and the pathways used for their metabolism. To this end, we curated the representation of the interactions of the cell with its environment into the human GEMs. First, we did not allow the exchange of intracellular metabolites lacking associated transport reactions or transport molecules containing P, CoA, or ACP (acyl carrier protein). Secondly, we allowed the synthesis of generic fatty acids from palmitate, with reactions from Recon 2 and Recon 3D . This algorithm finds the pathways from the GEM that are needed to connect the extracellular metabolites to the core network defined by redGEM. In this work, we considered a complex medium composition of 34 metabolites Fig. , and redl-histidine which affects many aspects of human physiology, including cognition functions and allergic reactions. The classical pathway to metabolize l-histidine consists of four steps that sequentially convert it into urocanate, 4-imidazole-5-propanoate, N-formimidoyl-l-glutamate, and ultimately, l-glutamate50. Interestingly, the resulting redGEMX subnetwork for l-histidine uses this classical pathway to connect it to the Recon 2 core metabolites l-glutamate and 4-aminobutanoate, both from the subsystem glutamate metabolism. The subnetwork is composed of 22 reactions, and it contains not only the classical pathway but also all the additional reactions required to balance the cofactors and by-products  to connect l-histidine to the core network of Recon 2. The alternatives emerge from the existence of different transport reactions for the extracellular metabolites. In the case of Recon 3D, l-histidine is connected to the core network using 20 reactions, and there exist two pathways of minimum size. The subnetworks connect l-histidine to the Recon 3D core metabolites l-glutamate, 5-10-methylenetetrahydrofolate, 2-oxoglutarate, and pyruvate using the classical pathway to metabolize l-histidine. The different topology of the Recon 2 and Recon 3D networks manifests in differences in the pathways used to metabolize and synthesize the compounds, thus, it is important to characterize which are the pathways used in the models. Following this approach, we added the reactions that compose all the alternative subnetworks of minimum size to the core networks to connect the 26 extracellular metabolites . Similarly to redGEMX, lumpGEM generates subnetworks that account for the synthesis, degradation, and balancing of all the by-products and cofactors required by the main pathway. The alternative subnetworks generated with lumpGEM can assess the flexibility of the cells to use alternative pathways to produce the BBBs, which can lead to survival in different conditions and drug resistance. Using lumpGEM, we calculated all the alternative subnetworks (set of reactions) of minimum size to capture the flexibility of the network for the biosynthesis of the BBBs , cholesterol, and the phospholipids and sphingolipids. The core network of Recon 2 contains a reaction that produces l-cysteine, however, the core network of Recon 3D requires two reactions to produce it. The subnetworks that produce dTTP have the same size in both models, but a different number of alternatives. The subnetworks to produce the purine nucleotides have one more reaction and more alternatives in Recon 3D. Cholesterol is another BBB whose subnetworks agree in size for both models, but Recon 3D has more alternatives than Recon 2. The explosion of alternatives in Recon 3D is due to the parallel description of the synthesis of cholesterol in three compartments, namely cytosol, peroxisome, and endoplasmic reticulum. The differences in the lumped reactions for the phospholipids and sphingolipids between both models are due to the introduction of the essential fatty acid in their synthesis in Recon 3D.The subnetworks generated with lumpGEM have the same size and number of alternatives in both Recon models for most of the BBBs, indicating that both models have the same level of flexibility for synthesizing the BBBs, with the exception of 54 for the synthesis of phosphatidylserine comprises four steps, wherein glycerol 3-phosphate is converted to lysophosphatidic acid, phosphatidic acid, CDP-diacylglycerol, and phosphatidylserine. In Recon 2, the subnetwork generated with lumpGEM for the synthesis of phosphatidylserine was composed of eight reactions. It included the KEGG pathway with the exception of the CDP-diacylglycerol intermediate, which was not connected to phosphatidylserine in the GEMs. Instead, phosphatidylserine was produced directly from phosphatidic acid by attaching serine. Additionally, the subnetwork contained the reactions required to generate from acetyl-CoA the fatty acids that would attach to glycerol 3-phosphate and to lysophosphatidic acid, which are important to consider for the final synthesis of phosphatidylserine. All the reactions involved in the synthesis of phosphatidylserine were lumped together in one reaction.As an example of the subnetworks that produce the BBBs, we show the synthesis of the phospholipid phosphatidylserine Fig. . The sta52.For Recon 3D, the phosphatidylserine synthesis subnetwork was generated with the same eight reactions, but in this case, four alternative subnetworks existed Fig. , indicatThe analysis performed with lumpGEM allows to characterize and classify the metabolic pathways and their alternatives, leading to an in-depth understanding of the flexibility of metabolism. In the context of GEMs, such detailed analysis of the subnetworks is often a difficult task due to their large size and interconnectivity.By applying the redHUMAN workflow, we reconstructed four reduced metabolic models for human metabolism Table . Two of 34. The four models captured 45 of the 57 tasks, including rephosphorylation of nucleoside triphosphates, uptake of essential amino acids, de novo synthesis of nucleotides, key intermediates and cholesterol, oxidative phosphorylation, oxidative decarboxylation, and growth  the model reconstruction, specifically the definition of the biomass, or (2) the reduction properties, that is, the subsystems included in the reduction and the representation of parts of the network as lumped reactions. To recover these tasks such that they are captured by the model, the following actions should be performed: the synthesis of proteins from amino acids and vitamin and co-factor metabolism can be recovered by modifying the biomass to account for their synthesis and utilization; the inclusion of lipid metabolism subsystems can recover the beta oxidation of fatty acids; and finally, the utilization of inositol can be recovered by adding the explicit reactions that compose the subnetworks, as it was found to be hidden in the lumped reactions of phosphatidyl-inositol. This demonstrates that redHUMAN allows to build reduced models consistent not only with the GEM but also with the metabolic tasks, and these models are suitable for targeted modifications and expansions.55. Additionally, we limited the maximal growth to the doubling time reported for leukemia cells, which is 0.035 h−1, and we constrained according to literature values the maximum uptake rate of oxygen to 2 mmol·gDW−1·h−1 40 and the ATP maintenance to 1.07 mmol·gDW−1·h−1 56  for the corresponding leukemia cell lines. We have identified that, in the four models presented in this study, over 99% of the enzymes with gene associations  are expressed in the NCI60 leukemia cell lines  on the common reactions between the GEM and the reduced model. The top 20 reactions whose rate ranges changed the most in absolute value included reactions from glycolysis, the pentose phosphate pathway, folate metabolism, and nucleotide interconversion among others Fig. . For real-glutamate 5-semialdehyde dehydratase (from arginine metabolism) and l-glutamate 5-semialdehyde:NAD+ oxidoreductase (from urea cycle) are bidirectional when flux variability is performed without thermodynamics and become unidirectional when their thermodynamic information is taken into account. Therefore, integrating thermodynamic information reduces the space of reaction directionality and the physiological solution space, and it eliminates thermodynamic infeasible reactions, excluding some pathways.redHUMAN helps to navigate large human genome-scale metabolic models to explore and classify the metabolic pathways that cells use to function and survive under specific conditions. The thermodynamic curation performed in the genome-scale models guarantees that the reactions obey the laws of thermodynamics, discarding possible pathways that would not be compatible with the bioenergetics of the cell. As an example of how thermodynamics reduces the space of solutions to the thermodynamically feasible pathways, we analyzed the flux variability with and without thermodynamic constraints in the Recon 3D reduced model that has all the alternative lumped reactions of minimum size (Smin). The reactions The leukemia-specific models generated in this study are powerful tools to analyze how the metabolic pathways are altered with respect to other cancer cells or normal cells. In particular, we can analyze how leukemia cells utilize the nutrients available in the microenvironment to biosynthesize the precursors required for growth and cellular functionality. As an example, we identified the minimal number of reactions that are required for the synthesis of phosphatidyl-serine in the reduced Recon 3D model with all the alternative lumped reactions of minimum size. We found that at least 76 reactions should be active for the production of phosphatidyl-serine including the interactions with the extracellular medium, i.e., for some alternatives the uptake of glucose, histidine, linoleic acid, oxygen, and phosphate, and the secretion of succinate, ammonia, carbon dioxide, and water. The main pathways active within the subnetwork of 76 reactions are glycolysis, the citric acid cycle, serine metabolism, and the electron transport chain. This type of analysis will enlighten our knowledge on how cells adapt their metabolism to the microenvironment allowing researchers to hypothesize how and why the cancer cells change their expression profile to adapt and survive.For a better understanding of the altered metabolisms that accompany many human diseases, we have herein presented a workflow to generate reduced models for common human GEMs that can reduce the complexity of these systems to the relevant processes to be studied, making detailed in silico analyses of metabolic changes possible.59 in redHUMAN allows to integrate endo- and exo-metabolomics in the models, constraining the concentration of the metabolites according to physiological data. The size of the model is directly related to the percentage of metabolites that need to be measured. Therefore, the continuous expansion in the size of genome-scale models increases the demand of larger sets of metabolomics, and such data are not always available. In addition, there is a community effort to expand constraint-based models to include information on enzyme abundancy relating the metabolic fluxes with enzymatic data and allowing to integrate transcriptomics and proteomics data into the models. These data are currently limited, but they can be continuously updated and integrated as they become available61.During the last years, there has been an increased generation of metabolomics data that better study what is happening in the physiology of cell metabolism compared to other omics data. This has created a need to expand the classical constraint-based modeling methods to include metabolomics information. Our thermodynamic formulation and application of TFA62. The main difficulty with these methods is the large amount of data required to fully characterize the initial set of reactions or core reactions. The lack of data could lead to unconnected parts and the impossibility to include reactions that could be important for the specific physiology, affecting the final model and the predictions.Moreover, most of the existing methods to build context-specific models are data-driven, that is, the reduced models are extracted from a GEM by considering only the enzymes associated to highly expressed data, or literature-based pathways. Then, they include additional reactions that are required to simulate growth and cellular functions62, tINIT34, mCADRE33, uFBA63, GECKO64, ETFL65, TEX-FBA66, and IOMA67.redHUMAN reconstructs reduced models considering only the pathways of interest and their stoichiometric connectivity. The reduced models are built unbiased from the data, guaranteeing thermodynamic feasibility and consistency with the GEM and the metabolic tasks. The reduced models can then be used to construct context-specific models by integrating omics data, accommodating to also integrate partial data without sacrificing reactions from the network. Overall, the reduced size of the new models and their conceptual organization overcomes some of the main challenges in building genome-scale context-specific models as for example, the barrier of data network coverage. The reduced models generated with redHUMAN are powerful representations of the specific parts of the network, and they have promising applications as they are suitable to use with existing methods including MBABased on our results, we propose the following approach to using these models as tools to explain and compare phenotypes. First, generate a reduced model around a desired set of subsystems and for a defined extracellular medium, and check that the model captures the metabolic tasks. Subsequently, build physiology-specific models by integrating experimental data into the reduced models. Then, test the consistency of the reduced network with respect to its parent GEM. Finally, integrate different sets of omics data, including expression, to compare different physiologies, such as diseased vs healthy or within several types of cancers. This approach will help to better investigate the alterations in metabolism that occur as diseases develop and progress. Moreover, the same procedure can be used to analyze systematically and consistently metabolic models for the same organism and to compare metabolic models of different organisms, enhancing our understanding of their similarities and differences.68.Throughout this paper, we have considered a specific set of subsystems, a specific medium, and the biomass definition from the GEMs. In the future, the reduced models could be further expanded to include other pathways, a more complex medium, or more biomass components. To introduce new subsystems or pathways into the core network, redGEM should be run to find the pairwise connections between the added pathways and the rest of the core. For an expansion of the medium, redGEMX would find the connections necessary for using the new extracellular metabolites. In a similar manner, a further curation of the biomass reaction could increase the number of BBBs, requiring lumpGEM to be run to find the biosynthesis pathways for those compounds. If a higher consistency was required between the GEM and the corresponding reduction, we could find the reactions missing in the reduced model to satisfy that condition. Moreover, we have selected a set of metabolic tasks to test the generated reduced model based on the definition within the original GEM. However, these sets of tasks can be expanded or redefined according to the needs of the specific studies, which can be based on expert knowledge or experimental data, as done in ref. Furthermore, in this study, we have used metabolomics, proteomics, and growth data from the NCI60 cell lines to define a generic physiology for leukemia cells. The core networks of the reduced models are structurally the same across growth conditions and depend only on the structure of the corresponding GEMs. Therefore, these generic models are robust to variations in growth or data for the same physiology, and thus data for individual leukemia cell lines can be used without changing the workflow. However, if there are important differences in the data, for example across different physiological conditions, the authors suggest running the lumpGEM workflow with data integration and generate alternative subnetworks and lumped reactions, which in turn will capture the different flux profiles for each physiological state.Overall, our analysis demonstrates how redHUMAN facilitates the characterization of differences in metabolic pathways across models and phenotypes.The thermodynamic curation of the human GEMs Recon 2 and Recon 3D aims to include thermodynamic information, i.e., the Gibbs free energy of formation for the compounds and the corresponding error for the estimation, into the model. The workflow to obtain this information is as follows.http://www.metanetx.org)69 to annotate the compounds of the GEMs with identifiers from SEED70, KEGG54, CHEBI71, and HMDB72. We then used Marvin  to transform the compound structures  into their major protonation states at pH 7 and to generate MDL Molfiles. We used the MDL Molfiles and the Group Contribution Method to estimate the standard Gibbs free energy of the formation of the compounds as well as the error of the estimation59.We first used MetaNetX  problem that incorporates the thermodynamic constraints to the original FBA problem. The Gibbs free energy of the elemental and charge balanced reactions is calculated as a function of the standard transformed Gibbs free energy of formation (depending on pH and ionic strength) and the concentrations of the products and reactants.TFA estimates the feasible flux and concentration space according to the laws of thermodynamicsm metabolites and n reactions, the Gibbs free energy,i is:ni,j is the stoichiometric coefficient of compound j in reaction i; j; xj is the concentration of the compound j, R is the ideal gas constant, T is the temperature. In this case, T = 298 K.Considering a network with The value of the Gibbs free energy determines the directionality of the corresponding reaction and the thermodynamically feasible pathways. With this formulation, we included the concentrations of the metabolites as variables in the mathematical formulation. TFA allows the integration of metabolomics data into the model.38. iMM identifies the minimum number of boundary reactions (uptakes and secretions) that need to be active. The method defines new binary variables in the TFA problem that represent the state of each boundary reaction, active or inactive. New constraints link the new binary variables to the corresponding reaction rates such that if the reaction is inactive, then it should not carry flux. The objective of the problem is to maximize the number of inactive reactions.iMM is formulated as a MILP problem that introduces new variables and constraints to the TFA problem to find the minimum set of extracellular metabolites necessary to simulate growth or a specific metabolic task with the GEMm metabolites and n reactions, the mathematical formulation of the iMM problem is the following:nb is the total number of boundary reactions in the model, zk are new binary variables for all the boundary reactions, S is the stoichiometric matrix, v are the net fluxes for all the reactions and M is a big constant  and C is an arbitrary large number. In this case, if k is active.Assuming a network with The redGEM, redGEMX, and lumpGEM algorithms seek to generate systematic reductions of the GEMs starting from chosen subsystems , based on the studied physiology and the specific parts of the metabolism that are of interest.35 that extracts the reactions that pairwise-connect the initial subsystems from the GEM, generating a connected network named the core network.redGEM is a published algorithm35 for further details). For example, for a degree equal to 2, it will connect the metabolites from the starting subsystem that are one and two reactions away in the GEM.The inputs for redGEM are (i) the GEM, (ii) the starting subsystems or an initial set of reactions, (iii) the extracellular medium metabolites, (iv) a list with the GEM cofactor pairs, and (v) the desired degree of connectivity. The algorithm then performs an expansion (by graph search) of the starting subsystems by finding the reactions that pairwise-connect the subsystems up to the selected degree  nor (b).Classify the extracellular metabolites of the GEM into 3 classes:Those that belong to the inter-connected subsystems network (core-reactions),those that do not belong to the inter-connected subsystems network (non-core reactions).Classify the reactions from the GEM into 2 classes:Block the flux through the reactions in the GEM that involve only extracellular metabolites.Block the flux through the boundary reactions of other metabolites in the GEM (1c). Steps (3) and (4) guarantee that the subnetwork reaches the core network.Force the uptake of a medium metabolite  and minimize the number of non-core reactions (2b) required to connect this extracellular metabolite to any core metabolite participating in a core reaction (2a). Note that the subnetwork will contain any reaction required to balance the by-products secreted by the subnetwork and/or the core network.The redGEMX method involves five steps:(i)Consider the TFA problem of the model that we want to reduce.(ii)zi for each non-core reaction (2b). Non-core reactions are denoted as Rnc.Create binary variables (iii)bF and bR are the binary variables for the forward and reverse fluxes of all the reactions (coupled to the TFA constraints); when zi = 1, the corresponding reaction is inactive.Generate a constraint that controls the flux for each non-core reaction:(iv)Build the following MILP problem for each extracellular medium metabolite (1a)veM,j is the flux of the jth extracellular medium metabolite (1a), and c is a small number.The redGEMX is a MILP problem that is formulated as follows:36 that generates elementally balanced lumped reactions for the synthesis of the biomass building blocks (BBBs). Using a MILP formulation, lumpGEM identifies the smallest subnetwork (minimum number of reactions from the GEM) required to produce each BBB from metabolites that belong to the core network using reactions from the GEM that are not part of the core. With this formulation, we can identify all the alternative subnetworks  for the synthesis of each BBB (one by one). lumpGEM generates, for each BBB, an overall lumped reaction by adding all the reactions that constitute each subnetwork (see ref. 36 for further details). Note here, different subnetworks can give rise to the same overall lumped reaction. This implies that although we produce all the alternative subnetworks with their associated lumped reactions, only the unique lumped reactions will be added to the final reduction.lumpGEM is a published algorithm73 has been used to draw the subnetworks in the figures.The simulations of this article have been done with Matlab 2017b and CPLEX 12.7.1. EscherFurther information on research design is available in the Supplementary InformationSupplementary Data 1Supplementary Data 2Supplementary Data 3Reporting SummaryDescription of Additional Supplementary Files