Pichia pastoris. This yeast has a tightly regulated methanol-induced promotor, allowing a good control over the recombinant protein production. Great efforts have been undertaken for improving the yields and purities of thaumatin productions, but a further optimization is still desired. This review focuses on (i) the motivation for using and producing sweet proteins, (ii) the properties and history of thaumatin, (iii) the production of recombinant sweet proteins, and (iv) future possibilities for process optimization based on a systems biology approach.There is currently a worldwide trend to reduce sugar consumption. This trend is mostly met by the use of artificial non-nutritive sweeteners. However, these sweeteners have also been proven to have adverse health effects such as dizziness, headaches, gastrointestinal issues, and mood changes for aspartame. One of the solutions lies in the commercialization of sweet proteins, which are not associated with adverse health effects. Of these proteins, thaumatin is one of the most studied and most promising alternatives for sugars and artificial sweeteners. Since the natural production of these proteins is often too expensive, biochemical production methods are currently under investigation. With these methods, recombinant DNA technology is used for the production of sweet proteins in a host organism. The most promising host known today is the methylotrophic yeast,  Food manufacturers are in constant search for alternative sweeteners for their products in accordance with the change of consumer perception on the intake of sucrose. Most of the times, the development of these alternatives poses certain difficulties in terms of meeting all the requirements for replacing sucrose. Due to the complex combination of properties existing within sucrose in terms of its taste and texture characteristics, it is often seen as a challenging task replace it with a low-calorie or non-caloric sweetener.Sugars are extensively used ingredients in numerous applications especially in food and pharmaceuticals. It is a disaccharide which consists of one unit of glucose and one of fructose linked by glycosidic bonds and gets easily hydrolyzed into these simple sugars upon digestion. Due to the increased demand for sucrose, the production of these ingredients has elevated over the years and lingers as an important part of the diet worldwide.The fragmentation of sugar into constituent monosaccharides occurs within the small intestine in the presence of the digestive enzymes and eventually gets transported into the bloodstream from the intestines. This leads to the elevation of blood glucose level until it gets transported by insulin . The breFurthermore, several other studies also point toward the fact that high intake of sugars can instigate risk factors such as high blood pressure  and card1.As a food ingredient, table sugar has played a paramount role until its value began to subside due to the public awareness which surfaced over the past years. This in turn triggered the development of alternative sweeteners that could effectively produce a similar effect in applications but have less impact on the overall health. The decrease in consumption of table sugar is evident from the data acquired on the changing trends in the consumption of low-calorie sweeteners . MoreoveThe awareness on the health issues among the acknowledged has imposed the need for alternative solutions that have less impact on human health. Since the 1800s many sweeteners, both natural and artificial have been identified for various applications. The potency of these sweeteners is most often higher than that of sucrose.2. A more detailed discussion on artificial and natural NNS is provided in Section “Artificial Sweeteners” and “Natural Sweeteners.”Sweeteners can be classified as caloric, low-calorie, and non-caloric. The caloric sweeteners are also known as nutritive sweeteners which provide energy in the form of carbohydrates. These can be seen naturally occurring in foods such as fructose in fruits or added to foods such as sucrose to drinks. This class of sugars also includes sugar alcohols such as sorbitol, lactitol, xylitol, mannitol, erythritol, trehalose, and maltitol. They provide calories which possibly contribute to health conditions on consumption in high quantities. In the case of sugar alcohols, consumption can also lead to other effects, i.e., irritable Bowel syndrome (IBS) and abnormal flatulence . SpecifiThe selected alternative sweetener should withhold certain important properties that make it ideal for similar applications as sucrose. For instance, Artificial sweeteners can be described as non-caloric or low-calorie sweeteners because they provide very few calories when compared with sucrose due to lesser absorption by the digestive system. Unlike the caloric or nutritive sweeteners, they provide no calories or hardly any calories but possess a much higher sweetness than sucrose. These intense sweeteners are usually mixed with bulking agents such as polydextrose and maltodextrin to enhance their applicability. Although the influence of artificial sweeteners on health aspects has been discussed widely in the past, there are still some uncertainties revolving around these sweeteners in terms of usage limitations . ExampleOut of these artificial sweeteners, aspartame is a prevalent ingredient around the globe and is used in a considerable number of food products . Despite3. It is therefore not surprising that the Apart from this, several other studies on artificial sweeteners have developed severe concerns among the consumers regarding its usage. For instance, these artificial sweeteners can enter the environment and undergo degradation thereby resulting in toxic products. The authors In this context, the plant-derived sweeteners such as stevioside, glycyrrhizin, osladin, etc. come into the limelight with the added advantage of not imposing any health issues. For example, stevia which is a natural sugar substitute was not seen to increase the blood glucose levels compared to sucrose with the findings of Apart from the previously mentioned sweeteners, there are several sweet compounds that are found in nature belonging to three classes namely terpenoids, flavonoids, and proteins . Most prUntil now, eight sweet proteins are identified namely, thaumatin , monelliOne of the most crucial factors to take into account while considering sugar replacers is the sweetness. The sweetness factor is measured with reference to sucrose. Sweetness perception occurs when sugar dissolves with the saliva and bind with the receptors on the tongue. Therefore, humans perceive sweet taste through the T1R2–T1R3 receptor which are heterodimers belonging to the family of G-protein-coupled receptors (GPCRs) . These rThe increasing awareness among the public over the adverse effects of sucrose and artificial sweeteners is creating opportunities for the exploration of naturally derived alternatives, such as plant-derived sweeteners. In this review, the advances in the production of the sweet-protein thaumatin will be discussed. Section “Thaumatin” summarizes the current relevance of thaumatin based on its characteristics and possible applications. Also, a detailing will be done on the aspects related to the production of this protein via the various routes that have been studied. Section “Bioproduction” focuses on the bioproduction aspects involved in the production of thaumatin with a focus given to the selection of strains, DNA construction for protein expression, production process and downstream processes. The final section summarizes on the possibility to integrate knowledge from systems biology for the optimization of thaumatin bioproduction.Thaumatococcus daniellii (Benth) belonging to the family Marantaceae , or Joint Expert Committee on Food Additives (JECFA) of the FAO/WHO have provided an acceptable daily intake. Considering the health aspects related to thaumatin, it does not instigate any tooth decay and can be suitable for the diabetic, unlike artificial sweeteners . MoreoveApart from being a low-calorie sweetener, thaumatin can also act as a flavor modifier in food applications. Hence, such unique properties of this sweet-protein make it an attractive ingredient for the food industry. The major applications of thaumatin are seen as an additive in chewing gum, dairy, pet foods, and animal feeds . It alsoEscherichia coli . The sweetness of the aqueous solution of thaumatin obtained during the experiment was seen to decrease when heated above 75°C and also at a pH below 2.5 at room temperature. Initially, thaumatin was produced in 1972 by van der Wel and Loeve from the fruits of The product attained upon aqueous extraction from the Katemfe fruit was first found as a mixture of proteins. In the following year thaumatin I was crystallized from which the physical attributes and diffraction data of the crystals were attained . AlthougDue to the increasing awareness of the public over artificial sweeteners, natural sweeteners gained popularity. For instance, thaumatin is favored by the public to replace sucrose in food products. However, the fact that thaumatin is produced from a tropically grown plant limits its availability while the demand is high. Moreover, the production process can be greatly affected with respect to the source material availability and quality. In order to attain a more stable production of the protein to meet the demand, a series of studies has been performed involving its production through genetically engineered microorganisms and transgenic plants .E. coli expression and bioreactor systems have facilitated the ease of production of these proteins. Currently, more than 400 protein drugs achieved from recombinant technologies have been approved and marketed worldwide and more than 1300 of them are undergoing the process of attaining approval 4. In 2016, the recombinant protein market witnessed a value of US$ 347.2 million globally. According to information provided by the Coherent Market Insights company (2018), a compound annual growth rate of 6.2% is expected for the period 2017–20255.Commercially, proteins can be produced using techniques such as genetic and protein engineering. These proteins are used by the biopharmaceutical industry, enzyme industry and agricultural industry within the fields of medicine, diagnostics, food, nutrition, etc. In the early 1900s, the microbial fermentation industry came into the scene through the production of chemicals such as acetone, butanol, and citric acid. The first protein pharmaceutical that was produced through recombinant DNA technology and approved by the FDA was Human Insulin, in 1982. Some examples of other recombinant proteins are albumin, human growth hormone (HGH) and factor VIII. Furthermore, advancement in the technologies for production processes has contributed to the growth of the recombinant protein market. For example, the evolution in mammalian cell expression, baculovirus expression, Numerous factors have to be considered for an efficient and low-cost production of recombinant proteins. Understanding the mechanism and metabolic pathway of thaumatin production can help in improving the yield and productivity. Since this protein has great potential as a substitute for the less safe sweeteners or sugar alternatives, an improved and commercially viable production is required. However, there is still much work to be done for the development of novel methods that can be utilized for the production of such recombinant proteins.The two major factors that need to be taken into account for the expression of recombinant proteins are cloning of the desired DNA and the amplification of the protein in the chosen expression system. Selection of the expression system can be based on certain characteristics such as; quality of the protein, functionality, productivity, and yield . Also, fAn approach toward the usage of transgenic plants has also been tested in a number of studies for the synthesis of sweet proteins. The usage of plant cells or tissue culturing has certain advantages in various applications such as (i) post-translational modification similar to mammalian cells, (ii) no health issues on humans and (iii) simplified large-scale production . HoweverEscherichia coli is one among the earliest and most commonly used host organism for protein expression , auxotrophic mutants that are defective in histidinol dehydrogenase , mutants that are defective in genes involved in methanol utilization  and protease-deficient strains   . P. pastP. pastoris are derived from the wild-type NRRL Y-11430   . In addisylation . Additiosylation .Pichia pastoris also has the capability to produce from milligram-to-gram quantities of proteins, making it suitable for both laboratory research and industrial manufacturing . This stage will be then followed by the fed-batch phase (transition or induction/production phase) which is initiated by the addition of glycerol-methanol mixture and later by pure methanol . During S. cerevisiae prepro α-mating factor secretion signal and a kanamycin resistance gene which can be used for G418 selection  promoter, election . Followi protein . P. pastP. pastoris strain for recombinant protein production is GS115, which is obtained from the wild-type strain NRRL-Y 11430 and has a mutation in the histidinol dehydrogenase gene (HIS4)  . S. cereynthesis . The forP. pastoris is that it secretes limited amounts of endogenous proteins and the culture medium does not contain any added proteins. Hence, the largest fraction of the obtained proteins in the medium will be thaumatin  which is functional in all yeast strains . The advhaumatin .P. pastoris for the production of thaumatin utilizing specific plasmids. P. pastoris strain. Natural mature thaumatin II was produced at a yield of about 25 mg/L and was found to elicit a sweet taste, comparable to that of thaumatin from the natural source. Four years later, the thaumatin I variant was produced in P. pastoris by 2 and H2O. Following this step, the formaldehyde either gets oxidized to CO2, thereby giving rise to two molecules of NADH, or gets condensed with xylulose 5-phosphate and then is converted to dihydroxyacetone and glyceraldehyde 3-phosphate within the methanol utilization pathway (P. pastoris contains two genes AOX1 and AOX2 that encodes two enzymes with AOX activity (P. pastoris consists of three phenotypes which are involved with the methanol utilization. These include (i) methanol utilization plus (Mut+), where both genes are active and intact, (ii) methanol utilization slow (Muts) where AOX1 is knocked out and (iii) methanol utilization minus (Mut-), where both AOX genes are knocked out when methanol is used as the sole carbon source (- strain methanol acts more like an inducing agent for the production of the recombinant proteins since they are unable to metabolize it + strains showcased a maximum specific growth rate of 0.15 h-1 at an excess concentration of methanol as substrate and a temperature of 30°C (Alcohol oxidase (AOX) is the enzyme that catalyzes the first step in the methanol utilization pathway . In this pathway . P. pastactivity . The foractivity . P. pastn source . In the  of 30°C .P. pastoris system would be proteolysis of the secreted proteins and cell death within the bioreactor. This can result in lower quality of the product after the downstream processing  sequence and a 66-residue (pro) sequence consisting of N-linked glycosylation sites and a Kex2 endopeptidase processing site (A simplified purification process can be applied when using secreted production. This secreted production is often possible for foreign proteins that are secreted naturally by their native hosts. This comes with the requirement for a signal sequence to guide the protein through the secretory pathway. The native secretion signal sequences have been used extensively. However, the most successful has been identified as the ing site . Brake eSeveral papers discuss on the possible analytical methods that can accommodate the characterization of thaumatin. For instance, S-transferase, maltose binding protein, etc. The tags can be positioned at the N- or C- terminus of the protein of interest. However, placing them at the N-terminal comes with the advantage of solubilizing the target proteins (One of the common methods adopted for the purification of recombinant proteins is through chromatography, specifically affinity chromatography because of their high specificity. Tags are used for improving the solubility and for facilitating affinity purification. These tags are small structures with short sequences of just 3–4 amino acids that can be added to the recombinant protein and hence allows to capture the proteins with ease. Apart from these, some fusion tags can be useful for a range of applications such as labeling for imaging studies, localization studies, detection, quantification, protein–protein interaction studies, subcellular localization or transduction and many others . Hence, proteins  and the P. pastoris and the designing of metabolic pathways for the enhanced production of the heterologous proteins have been seen in recent years. Today, P. pastoris is extensively utilized as a successful expression system for both industrial and research purposes (P. pastoris. As such, there is a plethora of opportunities for the production of protein of interest with this emerging technique. The metabolism includes several coupled and interconnecting reactions. The term metabolism refers to a reaction comprising the conversion of a molecule into another molecule or molecules within a defined pathway. A cell includes numerous pathways of such reactions which are independent and that can be coordinated with the presence of enzymes. Understanding the metabolic reactions gives insights on the information related to the fluxes. This information leads a path for the establishment of the metabolic model which can serve as a tool for setting up an optimized bioreactor process. Such a tool can be advantageous to predict the parameters influencing the process or genetic modifications on strain behavior (Several biopharmaceuticals are nowadays produced by the utilization of technologically advanced microbial and mammalian cell biosystems. This technique provides advantages for the production of important recombinant pharmaceuticals in a safe and abundant quantity. The utilization of a high number of engineered strains of purposes . The usebehavior .P. pastoris, methods for increasing the production of recombinant proteins with this host are of high relevance (P. pastoris, there are still some limitations persisting for the engineering of this non-conventional yeast, due to a lack of genome editing tools and incomplete knowledge on their cell behavior when compared with the yeast platforms such as S. cerevisiae. As such, this line of work comes with the limitations of time consumption, high cost and production of noisy data. Therefore, another method to be adopted can be the development of mathematical models which have the ability to characterize the various phenotypes their culturing behavior (Considering the increased interest in elevance . This cabehavior .P. pastoris during culturing can be predicted. Therefore, the key factors influencing microbial growth and protein production should be determined and the relationships between them should be captured in a mathematical model. An appropriate model structure should describe effects that limit recombinant protein production such as cell viability, metabolite accumulation, metabolite toxicity, substrate requirement, and substrate inhibition.Even though genetic engineering is a valuable first step, on a large-scale production of these compounds, a further optimization of the process based on carbon and nitrogen sources, feeding profiles, aeration levels and so on will be necessary as well. In order to perform this optimization in a systematic manner, it is necessary to learn how the behavior of in vitro studies (Systems biology is an approach which helps in studying the interactions within biological systems. It facilitates in understanding the behavior of systems involving several enzymes, metabolites and metabolic pathways or signaling networks. This understanding is obtained with the aid of mathematical models and computational techniques . Hence,  studies . This apThe utilization of microbial cell factories within industrial microbiology involves a constant process of strain engineering and optimization of the bioprocessing conditions. The main target with respect to the production of thaumatin would be to accommodate the maximum microbial production rate. For this, an optimal environment needs to be provided toward the culturing of the microorganism on one hand and the production of thaumatin on the other. With this respect, the media composition has a major influence on the overall performance of the bioprocess. Systems biology provides highly effective tools such as flux balance analysis and metabolic flux analysis for the optimization of media composition. However, both require that information on the metabolic network of the microorganism and the latter also requires a significant amount of experimental data. There has been sufficient data available already from studies depicting that an optimized nutritional medium is required for the organism to enhance the recombinant protein production. However, in order to obtain a deeper knowledge on the actual effect of media composition on cell growth and product formation, additional data is still required. The data itself can be from cell physiology , extraceP. pastoris, has been studied over the years, many parts of it still remain unclear. For instance, the secondary metabolism is very diverse in addition to the complexity existing between the connections in the various reactions thereby resulting in an extremely dense biological network. The in silico reconstructions of the metabolism can be achieved from the genome-scale metabolic models. Such a model helps in the linkage between the genotype and metabolic capability.The inclusion of microscopic models has the advantage of resulting in more mechanistic and generic predictive models when compared to the macroscopic models that do not take into account the underlying mechanisms that cause a certain response. For example, macroscopic models will simply describe the production rate of the end-product based on some key influencing factors whereas microscopic models will consider in more detail the metabolic reactions that lead to the production of this product. Despite the fact that the metabolism of, e.g., P. pastoris. These classical approaches are based on a system with ordinary differential equations or their explicit form. However, this information alone does not provide mechanistic knowledge on the cell. Further advancements have taken place with respect to model development through the integration of information on the metabolic level. These types of studies have been performed as well for P. pastoris strains. As such, the emergence of the implementation of genome-scale metabolic models has magnified the knowledge on the cell behavior. The first such model constructed for a eukaryotic organism was for S. cerevisiae. Now, there have been many studies involved in the reconstruction and expansion of the metabolic networks for yeasts. The various reconstructions of the genome-scale metabolic network models for P. pastoris are given in When looking into the traditional techniques used for modeling bioreactor processes, they are derived from mass balances of biomass and growth limiting carbon source. Similar model types can be utilized for the bioproduction of P. pastoris today. A full metabolism involves numerous reactions and hence, utilizing mathematical models contributes toward a better understanding of this complex process.The use of metabolic models helps in improving the production of target compounds and for uncovering new information on the biological systems. Hence, these models play a significant role in the design and optimization of bioprocesses. This way, a more quantitative and systematic framework that has the potential to improve the value and reliability can be achieved. It is noticed from recent literature that the engineering approach toward cell metabolism boosts the productivity of recombinant proteins. This is evident from the high number of pathway designs and engineered constructs that are available for P. pastoris are based rather on the influence of protein production on the metabolism than the prediction on specific efficiency. Hence, the genome-scale metabolic models seem to be a very valuable tool for the optimization of biochemical production processes that are still not used to their full potential.The optimization of fermentation processes requires the selection of numerous conditions such as pH, temperature, oxygen concentration and nutrient supply . The useSweet proteins are seen to a have great potential today in various applications and are expected to rise to a level capable enough to replace sucrose in several applications. Due to their low-caloric feature and great qualities as a sugar replacer, the consumers have perceived these natural sweeteners with a positive outlook. Thaumatin specifically is emerging as a strong alternative to sucrose and other synthetic replacers in the market today. Although thaumatin has been studied by various researchers over the past 30 years, there is still much work to be done in order to improve its production via the biochemical routes. It is evident from the literature that biological products are emerging as a promising applicant within the food industry. Hence, there is great potential for future research that focuses on the use of advanced computational techniques for the optimization of thaumatin bioproduction.JJ delivered the main contribution in reviewing literature and writing, in close collaboration with SA and PN. JI supervised the writing of this review. The general content and lay-out of this publication were determined by all authors.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Acetobacter pasteurianus 386B is a candidate functional starter culture for the cocoa bean fermentation process. To allow in silico simulations of its related metabolism in response to different environmental conditions, a genome-scale metabolic model for A. pasteurianus 386B was reconstructed. This is the first genome-scale metabolic model reconstruction for a member of the genus Acetobacter. The metabolic network reconstruction process was based on extensive genome re-annotation and comparative genomics analyses. The information content related to the functional annotation of metabolic enzymes and transporters was placed in a metabolic context by exploring and curating a Pathway/Genome Database of A. pasteurianus 386B using the Pathway Tools software. Metabolic reactions and curated gene-protein-reaction associations were bundled into a genome-scale metabolic model of A. pasteurianus 386B, named iAp386B454, containing 454 genes, 322 reactions, and 296 metabolites embedded in two cellular compartments. The reconstructed model was validated by performing growth experiments in a defined medium, which revealed that lactic acid as the sole carbon source could sustain growth of this strain. Further, the reconstruction of the A. pasteurianus 386B genome-scale metabolic model revealed knowledge gaps concerning the metabolism of this strain, especially related to the biosynthesis of its cell envelope and the presence or absence of metabolite transporters. Acetic acid bacteria (AAB) are obligately aerobic bacteria that play an important role in several food fermentation processes, such as vinegar production and cocoa pulp-bean mass fermentation, although they are undesired in wine, cider, and most beer fermentation processes . AAB canThe cocoa bean fermentation process is fundamental to obtain well-fermented dry cocoa beans, from which cocoa products, such as chocolate, can be made . Next toAcetobacter pasteurianus is an AAB species that has been isolated consistently from cocoa bean fermentation processes around the world  associations  have been reconstructed for many organisms, ranging from bacteria and archaea to fungi, plants, and even human cell lines . For AABproducer . The curA. pasteurianus 386B was sequenced and annotated previously, using a local installation of the bacterial genome annotation system GenDB v2.2  available on BioCyc . For the latter three bacterial strains, genome-scale metabolic models have been reconstructed before  numbers were assigned to each reaction, based on the ExplorEnz database , were excluded from the analysis, as these reactions inherited different EC numbers from their gene constituents.The presumed increase in functional annotation quality of the genes included in iAp386B454 was evaluated based on the EC numbers of enzyme-encoding genes, as the EC system provides a defined enzymatic reaction classification . EC numbA. pasteurianus 386B GEM was compared to GEMs obtained from a number of automatic GEM reconstruction tools. These included the RAST and ModelSEED tools in the KBase software . For RNA, molar fractions of building blocks were estimated using their respective frequencies in rRNA-, tRNA-, and mRNA-encoding genes. RNA mass fractions were taken from E. coli (Acetobacter species (E. coli (A biomass reaction was defined for ure data . Proteinla RZS01 . Stoichid before . For DNA E. coli . The fat species . The ave species . Energy (E. coli . Genes wA. pasteurianus 386B in a modified defined medium (4)2SO4, 5 g; KH2PO4, 1.375 g; MgSO4.7H2O, 0.5 g; EDTA, 15 mg; ZnSO4.7H2O, 4.5 mg; CoSO4.7H2O, 0.35 mg; MnCl2.4H2O, 1.0 mg; CuSO4.5H2O, 0.3 mg; CaCl2.2H2O, 4.5 mg; FeSO4.7H2O, 3.0 mg; MoO3, 0.24 mg; H3BO3, 1.0 mg; KI, 0.1 mg; and 30 mM phosphate buffer (pH 6.0). The pH of the medium was set to 5.0. A filter-sterilized vitamin mixture was added after heat sterilization  of the medium. The final vitamin concentrations were (per liter): biotin, 0.0005 mg; calcium pantothenate, 0.01 mg; nicotinic acid, 0.01 mg; myo-inositol, 0.25 mg; thiamine-HCl, 0.01 mg; pyridoxine-HCl, 0.01 mg; and para-aminobenzoic acid, 0.002 mg. Eight different carbon sources  were used at a final concentration of 60 mM to assess if they could sustain growth. The pH of the citric acid, lactic acid (both by using NaOH to increase the pH), and sodium acetate (using HCl to decrease the pH) stock solutions was set to 5.0. To prepare the inocula, A. pasteurianus 386B was grown overnight at 30°C in 10 ml of an undefined medium (pH 5.5), which contained (per liter): lactic acid, 5 g; sodium acetate, 10 g; granulated yeast extract, 5 g; MgSO4.7H2O, 1 g; NH4H2PO4, 20 g; and K2HPO4, 10 g. The stirring rate was set to 160 rpm. The overnight culture was centrifuged  and washed with a filter-sterilized saline solution . The cells were resuspended in the sterile saline solution and inoculated in 2 ml of the defined medium mentioned above at an optical density at 600 nm (OD600) of 0.01 in triplicate in test tubes with a total volume of 20 ml. A. pasteurianus 386B was allowed to grow at 30°C without shaking for 48 h as the test tubes contained only 2 ml culture medium, resulting in a relatively large surface to medium ratio. A threshold value for the OD600 of 0.1 was used to identify whether or not the strain had grown.Growth experiments were performed with d medium . This meIn silico growth experiments were performed using flux balance analysis (FBA). With FBA, an optimization of the flux distribution of a GEM can be performed to maximize an objective function, typically the biomass reaction, thus predicting the specific growth rate of a bacterial cell population  or cytochrome c (EC 1.1.2.4), thus linking this reaction directly to the respiratory chain (A. pasteurianus 386B GEM (E. coli (A gene encoding a lactate permease (TC 2.A.14), more precisely a lactate:H E. coli . Most prry chain . Overflory chain . Therefo386B GEM . Finally+-dependent dehydrogenases  and which was homologous to the E. coli SatP transporter , phosphate acetyltransferase (EC 2.3.1.8), and acetate CoA ligase (EC 6.2.1.1).ogenases . Periplansporter . Alternansporter . A react(E. coli . PutativAcetobacter species is their modified tricarboxylic acid (TCA) cycle , interconverting malate and pyruvate, and phosphoenolpyruvate carboxylase (EC 4.1.1.31) that could carboxylate phosphoenolpyruvate to oxaloacetate. However, in the NCBI 2017 genome annotation version of A. pasteurianus 386B, the latter enzyme-encoding gene was annotated as a pseudogene, containing a frameshift mutation.A major metabolic adaptation of acetic acid-resistant A) cycle , containA) cycle . Two enzA. pasteurianus is an obligate aerobe that has evolved a truncated aerobic respiratory chain  was found that encodes cytochrome ba3 ubiquinol oxidase . This heme-copper terminal oxidase probably contains a heme A moiety, since the genes encoding heme O  and heme A  synthase, which are remnants of a cytochrome c oxidase gene cluster, have been shown to be still functional in A. pasteurianus  and its homolog, cyanide insensitive oxidase . Since the reaction catalyzed by both of these terminal oxidases has the same stoichiometry, an identical reaction (EC 7.1.1.7) was added to the GEM. However, it has been shown that these enzymes have different kinetic parameters, indicating a physiological distinct role (bc1 complex (E.C. 7.1.1.8) were found in the genome of A. pasteurianus 386B, as is also the case for A. aceti  and one that is not (EC 1.6.5.9). Furthermore, a membrane-bound proton-translocating NAD(P)+ transhydrogenase (EC 7.1.1.1) was present in the genome. Finally, the genes encoding ATP synthase (EC 7.1.2.2) were present in two gene clusters (APA386B_1266 – APA386B_1270 and APA386B_1604 – APA386B_1608), which is also the case for Rhodospirillum rubrum m rubrum .in vitro growth experiments, A. pasteurianus 386B was only able to grow on a defined medium containing lactic acid as the sole carbon source added. Thus, except for the possible need for some micronutrients, A. pasteurianus 386B had no specific auxotrophies and was able to form all its biomass compounds from ammonium as the sole nitrogen source, sulfate as the sole sulfur source, phosphate as the sole phosphate source, and lactic acid as the sole carbon source.From all carbon sources tested during the A. pasteurianus 386B GEM and for which there was genetic evidence based on the genome re-annotation. These pathways allowed to simulate the growth of A. pasteurianus 386B in silico using the defined medium conditions mentioned above. Focus is on those steps of the pathways for which there was evidence that the gene-protein-reaction associations in A. pasteurianus 386B were different from the reference pathways described in the literature.In what follows, biosynthesis pathways are described that were included in the Acetobacter are cis-vaccenic acid (C18:1), palmitic acid (C16:0), and stearic acid (C18:0) (Acetobacter from the genus Gluconobacter (A. pasteurianus 386B was similar to the one described in E. coli (E. coli (cis-vaccenic acid (C18:1) was the major fatty acid in the fatty acid profile of A. pasteurianus, the genes encoding FabA and FabB could not be found in the A. pasteurianus 386B genome. Even though unsaturated fatty acid biosynthesis in A. pasteurianus 386B seemed to be unclear, reactions of the FabA/FabB pathway were nonetheless added to the model (cis-vaccenic acid (C18:1).The major fatty acids in bacterial cells of the genus  (C18:0) . Furthernobacter . The fat E. coli . For uns or NAD(P)+-dependent (EC 1.1.1.94) glycerol-3-phosphate dehydrogenase. The A. pasteurianus 386B genome encoded the PlsX/PlsY/PlsC system for phosphatidic acid biosynthesis, as described before -dependent methylation pathway forming phosphatidylcholine from phosphatidylethanolamine were most probably catalyzed by the same enzyme, namely phosphatidylethanolamine N-methyltransferase , as the enzyme from A. pasteurianus 386B (encoded by the gene with locus tag APA386B_612) belonged to the same family as the one in Rhodobacter sphaeroides and shared high sequence identity to the Pmt enzyme in A. aceti . Two genes were retrieved that encoded potential ammonium ion channels . In addition, an ammonium assimilation pathway for de novo biosynthesis of proteinogenic amino acids was assumed to be present. In E. coli, two pathways are known for ammonium assimilation (via a NADP+-dependent glutamate dehydrogenase (EC 1.4.1.4) that allows to form L-glutamate directly from 2-oxoglutarate and ammonium, the other via the formation of L-glutamate and L-glutamine through a cycle of reactions involving glutamine synthetase (EC 6.3.1.2) and glutamate synthase (EC 1.4.1.13), which produces a net amount of L-glutamate. Only the latter pathway was found in the A. pasteurianus 386B genome  but shared considerable sequence identity with curated SwissProt sequences from other bacteria with identical function (>50% identity). The gene encoding glutamate-pyruvate aminotransferase  was a predicted ortholog of the gene in E. coli . Finally, the genes encoding aspartate 4-decarboxylase  had no E. coli homolog but were related to a bifunctional aspartate aminotransferase and aspartate 4-decarboxylase of Comamonas testosteroni. However, the enzyme characterized had only a minor activity as an aminotransferase  was linked to three genes, likely encoding this enzyme . These were not predicted to be homologous to the nsferase . Thus, tA. pasteurianus 386B genome contained three genes, which likely encode the enzymes for these reactions. The genes with locus tags APA386B_835 and APA386B_836 were most likely involved in amino acid biosynthesis, since these genes each had an E. coli ortholog encoding subunits of a bifunctional acetolactate synthase/acetohydroxybutanoate synthase enzyme complex . However, the gene with locus tag APA386B_1863 was closely related to two “catabolic” acetolactate synthases, identified in Klebsiella pneumoniae and Lactococcus lactis  catalyzes the formation of (2S)-2-acetolactate and (S)-2-hydroxy-2-ethyl-3-oxobutanoate, the latter metabolite only involved in L-isoleucine biosynthesis . The A. s lactis . This evG. oxydans 621H (locus tag GOX0437) that has been identified as encoding a periplasmic enzyme involved in the oxidation of quinate (G. oxydans 621H (locus tag GOX1351) could not be found in the A. pasteurianus 386B genome. In the last reaction step of the biosynthesis of L-tyrosine and L-phenylalanine, an amino group transfer occurs with glutamate as amino group donor. In E. coli, three enzymes have been identified that could catalyze this reaction, namely the aromatic aminotransferase (TyrB), the aspartate aminotransferase (AspC), and the branched-chain amino acid aminotransferase (IlvE), whereby the latter is only involved in the biosynthesis of L-phenylalanine . Thus, the L-tyrosine-forming reaction was tentatively associated to the aspartate aminotransferases encoded in the genome .The aromatic amino acids L-phenylalanine, L-tyrosine, and L-tryptophan share a common initial pathway, which produces chorismate from erythrose 4-phosphate . Compara quinate . The cytlalanine . In A. pA. pasteurianus 386B was able to grow in a defined medium containing sulfate as the sole sulfur source, sulfate assimilation was assumed (via a sulfate permease (TC 2.A.53) as well as a probable ortholog of the E. coli cysPUWA ABC sulfate transporter. However, since the stoichiometry of the anion:H+ symporter is not known in Acetobacter, only the ABC transporter was added to the A. pasteurianus 386B GEM. The enzymes of the assimilatory sulfate reduction pathway, which reduce sulfate to hydrogen sulfide, were encoded in the genome. One exception was the flavoprotein subunit of sulfite reductase (EC 1.8.1.2), which was not found in the genome re-annotation. Whereas L-methionine is produced by the transsulfuration pathway in E. coli, only cystathionine 𝛽-lyase (EC 4.4.1.8), but not homoserine O-succinyltransferase (EC 2.3.1.46), could be identified in A. pasteurianus 386B. In Corynebacterium glutamicum, next to the transsulfuration pathway, a direct sulfhydrylation pathway is present that produces L-methionine, of which the key enzyme is O-acetylhomoserine sulfhydrylase (EC 2.5.1.49) (O-acetylhomoserine sulfhydrylase (EC 2.5.1.49)/O-succinylhomoserine sulfhydrylase (EC 2.5.1.48). However, the presence of a homoserine O-acetyltransferase  upstream in the direct sulfhydrylation pathway gave additional evidence to annotate the gene APA386B_753 as encoding an O-acetylhomoserine sulfhydrylase (E.C. 2.5.1.49). Since this pathway was complete, the direct sulfhydrylation pathway was added to the A. pasteurianus 386B GEM instead of the transsulfuration pathway. Finally, L-methionine could be synthesized from L-homocysteine by methionine synthase (EC 2.1.1.13). SAM could be formed from L-methionine by methionine adenosyltransferase (EC 2.5.1.6). This reaction is part of the SAM cycle, which links L-methionine biosynthesis to glycerophospholipid biosynthesis, and involves the key reaction catalyzed by adenosylhomocysteinase (EC 3.3.1.1)  . The gen3.3.1.1) .A. pasteurianus 386B PGDB, the nucleotide biosynthesis pathways were curated and added to the A. pasteurianus 386B GEM . The precursor for purine biosynthesis is 5-phospho-α-D-ribose 1-phosphate (PRPP), which is also the starting point of histidine biosynthesis and involved in tryptophan biosynthesis .Based on the 386B GEM . A broadproducts . Similarynthesis . From PRvia CTP synthase (EC 6.3.4.2) or deoxythymidine triphosphate (dTTP) by a dedicated pathway (Uridine diphosphate (UDP) production is the result of a linear pathway, in which aspartate is the substrate for pyrimidine biosynthesis and which could be converted into cytidine triphosphate (CTP)  pathway . CytidinE. coli were used as a reference for their reconstruction in A. pasteurianus 386B (N-acetylglucosamine (UDP-GlcNAc). UDP-GlcNAc is subsequently converted into UDP-N-acetylmuramic acid (UDP-MurNAc) and used as a basis to attach the first alanine residue by UDP-N-acetylmuramate L-alanine ligase (EC 6.3.2.8), which was previously not annotated in the A. pasteurianus 386B genome. In the next reactions, D-glutamate, meso-diaminopimelate, and D-alanyl-D-alanine are successively attached to UDP-MurNAc  could form the intermediary lipid X. In contrast to E. coli that has the lpxH gene, in A. pasteurianus 386B and other α-proteobacteria this enzyme is encoded by the lpxI gene, which has a different reaction mechanism  pathway . In A. pechanism . Lipid Xr growth , A. past lipid A . Here, tormation . Genes eIn vitro and in silico growth experiments were compared to validate the A. pasteurianus 386B GEM  pathway. Due to the absence of a phosphofructokinase enzyme, fructose-6-phosphate was converted into glucose-6-phosphate, leading to a reaction flux cycle involving the pentose phosphate pathway and the upper part of the EMP pathway. A high NADPH+H+ production flux had to be balanced to allow growth, which was mainly performed by a proton-translocating NAD(P)+ transhydrogenase. The contrasting results obtained for D-glucose and D-mannitol might be explained by the fact that no specific transporter could be identified for these metabolites or their oxidation products. In general, functional annotation of transporters is difficult because a limited number of transporters have been functionally characterized  was defined as being reversible. Here, a glycerol facilitator could be identified in the genome of A. pasteurianus 386B. No apparent reason for the absence of in vitro growth could be identified in the flux distribution. However, the assumption of the presence of a catabolic glycerol-3-phosphate dehydrogenase may be faulty or glycerol catabolism was not efficient enough for the bacterial cells to grow on glycerol as the sole carbon source.A similar discrepancy for A. pasteurianus 386B GEM was performed based on different information sources. Hereto, EC numbers were used, as these provide a defined classification of enzymatic reactions. However, GPR associations may be complex and it is thus expected that curation will reveal inconsistencies in the functional annotations provided by the different annotation sources. For genes linked to reactions in the GEM, the differences between the manually curated EC numbers and the EC numbers provided by each annotation source were compared . The latter highlighted the subtleties of the manual curation process in defining the substrate and co-factor specificities.Manual curation of GPR associations in the compared . Some anA. pasteurianus 386B GEM, the curated A. pasteurianus 386B PGDB, and the models of the automatic reconstruction tools are summarized in A. pasteurianus 386B GEM presented in the current study, as this reconstruction was performed manually and because some pathways were deliberately not included, such as the co-factor biosynthesis pathways. This latter decision was taken based on the assumption that the biosynthesis and degradation fluxes of the reaction co-factors were small compared to their involvement in the metabolic redox reactions. In contrast, the number of orphan reactions was much lower for the A. pasteurianus 386B GEM compared to the other models, providing causal links between reactions and enzyme-encoding genes in the genome. Also, the number of dead-end metabolites was low compared to the automatic reconstructions. Although dead-end metabolites could be an indication of redundancy in the reconstruction, their presence may also reflect the uncertainty in the reactants and products of the different enzymatic reactions in the models, thus providing a compendium of possible reactants and products, as for example in the curated A. pasteurianus 386B PGDB.The properties of the resulting A. pasteurianus 386B, the functional annotation of predicted enzymes and transporters was targeted, as these are critical for an accurate genome-scale metabolic network reconstruction. To improve the quality of the re-annotation, information from multiple, different annotation sources was combined, which proved to be a good strategy to guide manual curation of GPR associations. This methodology was combined with the prediction of orthogroups, using genomes of related species, which was further fine-tuned with information from the literature. Finally, using the Pathway Tools software allowed to set the annotation content in a metabolic pathway context. In this way, possible links between the different biosynthesis pathways, necessary for the biomass formation, were identified.During the genome re-annotation of A. pasteurianus 386B genome was used to compile a curated GEM, named iAp386B454, containing 454 genes, 322 reactions, and 296 metabolites embedded in two cellular compartments. The GEM is available in SBML level 3 format and as a curated Pathway Tools PGDB and represents the first in silico genome-scale metabolic network reconstruction of a species of the genus Acetobacter. The reconstructed model was validated by performing growth experiments in a defined medium, which revealed that lactic acid as the sole carbon source could sustain growth of this strain.The re-annotated A. pasteurianus.Nevertheless, it became clear that some knowledge gaps remained, for example for the reconstruction of the biosynthesis pathways of cell constituents, especially for the cell envelope. Also, the combination of genome re-annotation and growth experiments could not resolve the presence of all metabolite transporters. The results obtained in this study will help to guide future research to close these knowledge gaps in A. pasteurianus 386B PGDB of the current study can be found in the BioCyc Tier-2 repository.The curated RP and SW designed the study. RP performed the metabolic reconstruction and wrote the manuscript. DG and SW supervised the study, discussed the results, and edited the manuscript. BT contributed to the discussion of the results. LD contributed to the study and edited the manuscript. All authors approved the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


E. coli metabolic system were simulated. They presented the threshold response or digital switch-like function that steeply shift metabolic status.Many metabolic cycles, including the tricarboxylic acid cycle, glyoxylate cycle, Calvin cycle, urea cycle, coenzyme recycling, and substrate cycles, are well known to catabolize and anabolize different metabolites for efficient energy and mass conversion. In terms of stoichiometric structure, this study explicitly identifies two types of metabolic cycles. One is the well-known, elementary cycle that converts multiple substrates into different products and recycles one of the products as a substrate, where the recycled substrate is supplied from the outside to run the cycle. The other is the self-replenishment cycle that merges multiple substrates into two or multiple identical products and reuses one of the products as a substrate. The substrates are autonomously supplied within the cycle. This study first defines the self-replenishment cycles that many scientists have overlooked despite its functional importance. Theoretical analysis has revealed the design principle of the self-replenishment cycle that presents a threshold response without any bistability nor cooperativity. To verify the principle, three detailed kinetic models of self-replenishment cycles embedded in an  The elementary network can be regarded as the minimal or small subnetwork responsible for particular functions such as ultrasensitivity, amplification, adaptation, noise filtration, pulse generation, oscillation, and bistability. As well as LEGO blocks, the elementary networks can be assembled in a hierarchical manner to synthesize a large-scale network with a high-level or complex function. An understanding of the elementary networks and their combined networks provides insight into a rational guidance for how a robust biological circuit is synthesized to carry out a specific function. A database of such biological networks4 was presented to cover a broad range of elementary networks, as well as their derivatives and combined networks.To analyze or design a biochemical network, it is critically important to understand fundamental relationships between network structure and function, or design principles by which elementary networks, called building blocks and network motifs, generate a variety of biological functions5, and coenzyme  recycling8  cycle, glyoxylate (GX) cycle, Calvin cycle, urea cycle, carnitine cycle, substrate cyclesg8 Table . Those c15. Many substrate cycles are seen in metabolism, such as the L-lactic dehydrogenase-L-lactate oxidase (PYR-LAC) cycle3, alanine transaminase-L-glutamate oxidase (2KG-GLU) cycle16, malate dehydrogenase-malate oxidase (OAA-MAL) cycle17, and glutamine synthetase (GS)-glutamate synthase (GOGAT) (GLU-GLN) cycle18. Since the substrate cycles, which are typically coupled with coenzymes, consume chemical energy or reducing power, they were early called futile cycles19. At present, however, these substrate cycles are known to amplify or accelerate a response against a weak stimulus5. The amplifier function can be strengthened by coupling two substrate cycles so that one cycle supplies a substrate to the other cycle17 (Supplementary Table 15. A substrate cycle with a zero-order reaction provides ultrasensitivity or a switching device (formate/lactic dehydrogenases model cycle)20.Substrate cycles often consist of two antagonist enzymes. One enzyme catalyzing a reaction is opposed by the other enzyme that catalyzes its opposite reaction21. These can be classified into two types: the coenzyme recycling cascade with conservation of coenzymes22 and those with accumulation of coenzymes, where the coenzymes are supplied from neighboring pathways11. The coenzyme recycling cascade with coenzyme conservation shows slow relaxation to the steady state in response to external changes and provides robust properties to external and internal fluctuation10. The coenzyme recycling cascade with accumulated coenzymes presents turbo design, where the accumulated coenzymes enhance the cascade reaction in a positive feedback manner. The turbo design is exemplified by the yeast glycolysis pathway that a catabolic pathway begins with an ATP-requiring activation step and the subsequent metabolism yields a surplus of ATP11.Coenzyme recycling is ubiquitous and involved in many reactions to supply chemical energy or reducing power  was proposed that combines a competitive inhibition with the conserved total level of substrate and inhibitors and a positive feedback loop, exemplified by yeast Spt-Ada-Gcn5-acetyltransferase (SAGA) histone acetylation complex27. It linearly responds to substrate above a threshold.Design principles of such a biological switch have been extensively investigated. A shifted Michaelis-Menten relationship responds to substrate above a threshold but does not any response below the threshold. This threshold function was generated by multiple modificationsE. coli are numerically simulated to verify the proposed design principle.To date studies on metabolic cycles have focused on various functions such as amplification, acceleration and robustness, while they underexplored or overlooked any essential function of the self-replenishment cycles. The objective of this study is to first define the self-replenishment cycle and to theoretically reveal the design principle that presents a threshold response and all or nothing response. Three established, detailed kinetic models of vr > 0). To drive the cycle, substrates are typically supplied from the outside. On the other hand, the self-replenishment cycle , y(2) and y(3) are the molecular concentrations of y1, y2 and y3, respectively, km the merge (input) rate constant, ks the split rate constant, kr the removal (cataplerotic) rate constant, km1 the Michaelis constant for y1 for the merge reaction, km2 the Michaelis constant for y2 for the merge reaction, and ks3 the Michaelis constant for y3 for the split reaction. The steady state levels of y(2) and y(3) were obtained with respect to ks, as follows.NA indicates that no positive, steady-state solution exists. The flux of the self-replenishment cycle is given by:Two molecules of NA, indeed, y(3) diverges with time, while y(2) approaches a limit value. By settingy(2) is given by:In the region of va is the external replenishment flux or called the anaplerotic reaction flux, ke the conversion rate constant, and ke3 the Michaelis constant for y3 for the conversion reaction. Generally, the recycled products are supplied from the outside to run the cycle. The steady-state concentrations of y(2) and y(3) were obtained asNA means that there is no positive steady-state solution. The steady-state flux of the elementary cycle is given byAs a reference model, an elementary cycle with the external replenishment flux was built Fig. . By assuy(2) diverges with time; y(3) approaches to a limit value. By settingy(3) is given by:Indeed, va = 0), as shown in Fig. Ks1 is the Michaelis constant for y1 for the split reaction. The steady states of y(2) and y(3) were obtained with respect to the self-replenishment cycle reaction constant ks asThe self-replenishment cycle Fig.  was combThe fluxes of the self-replenishment and elementary cycles are given byNA, indeed, y(3) diverges with time; y(2) approaches to a limit value. By settingy(2) is given byIn the region of E. coli central carbon and nitrogen metabolism, and mapped them on the simplified cycles used in theoretical analysis  and allosteric metabolites. Here, I identified three real, self-replenishment cycles: the GS-GOGAT cycle, glucose Pts with glycolysis, and GX cycle in the sis Fig. , as showE. coli requires ammonia for synthesis of GLU and GLN, from which almost all nitrogen-containing compounds including amino acids and nucleotides are synthesized35. Based on detailed experimental data, Bruggeman et al. (2005) developed a detailed dynamic model of GS-GOGAT-GDH pathways that combine metabolic circuit with regulation by signal transduction through the covalent modification of PII and GS by UTase and ATase28 to produce glucose-6-phosphate (G6P) and pyruvate (PYR)  is a complex group translocation system present in many bacteriaR) Table . Kurata et al.42, provides a simple and efficient strategy for converting acetyl-CoA into anaplerotic and gluconeogenic compounds when complex sources such as glucose are not available43. If some intermediate metabolites of the TCA cycle are degraded or removed, the TCA cycle flux cannot be maintained without any anaplerotic (phosphoenolpyruvate carboxylase (Ppc)) reactions. In a Ppc knockout mutant of E. coli, however, OAA seemed to be supplied to drive the TCA cycle45. Intensive analysis suggested that the GX cycle forms a self-replenishment cycle .All numerical simulations were carried on Matlab . The simulation programs of the self-replenishment cycle, elementary cycle, and self-replenishment and elementary cycles are registered in the BioFNet databasey(2), y(3), and vself. The solutions, given by Eqs. (km* (Eq. (y(2), y(3), and vself were stable zero in region I. The steady-state levels of y(2), y(3), and vself steeply increased in region II. Molecule y(2) presented threshold response to specific parameter km*. The threshold value of km* was given by the derivative discontinuity point as follows.To reveal a distinct function of the self-replenishment cycle Fig. , Eqs 1,,1, 2 wery(2), y, and vse by Eqs. , were thkm* (Eq. )  and with a decrease in the synthesis rate of y(2), determined by the balance between the removal and synthesis rates. The existence of the zero region (region I) demonstrated that the self-replenishment cycle generates a play or clearance to switch on the cycle. In region III, they had no positive, steady-state solution, because the accumulator function surpassed the removal one. Indeed, y(3) diverged with time, while y(2) approached the limit value given by Eq. , y(3), and velem. The solutions, given by Eqs.  accumulated due to a low input reaction rate. Indeed, y(2) diverged with time, while y(3) approached the limit value given by Eq. (y(3), given by Eq. , y, and veln by Eq.  and the n by Eq. , was theva = 0, vr > 0). Since the self-replenishment and elementary cycles , y(3), and the fluxes of both the cycles. The solutions are given by Eqs  by the three critical points  and y(3) and the steady-state fluxes of both the cycles were stable zero in region I, because the removal reaction surpassed the self-replenishment cycle-based accumulation reaction. They simultaneously increased in region II, showing a threshold response, where both the removal and accumulation were balanced. It demonstrates that the self-replenishment cycle works as the anaplerotic reaction to run the elementary cycle. Region III had no positive, steady-state solution, where y(3) diverged; y(2) approached the limit value given by Eq. (y(2), y(3), and the fluxes of both the cycles returned to the steady-state level again, because a large value of ks decreased y(3). The steady state level of y(3) decreased with an increase in ks; y(2) gently increased. The first critical point or the threshold value of ks was given byThe elementary cycle typically stops without any anaplerotic reaction, when a removal reaction occurs , the st= 0 (Eq. ). The se→ 0 (Eq. ). The stn by Eq. . Both thke and the removal reaction with kr. An increase in removal rate constant kr increased the threshold value. An increase in rate constant ke increased the threshold value, because the elementary cycle took y(3) from the self-replenishment cycle, decreasing the flux of it.The existence of a zero concentration/flux region showed that the self-replenishment cycle generates a play or clearance to switch on both the cycles. The threshold value was determined mainly by the elementary cycle with et al.28, was simulated to investigate how the GS-GOGAT cycle is implemented into real biochemical networks. The GS flux was simulated for 1,000 min, while changing the environmental ammonium concentration (constant variable)  of km*, the simulation result can be compared to the theoretical analysis  Fig. . Since asis Eqs –5). The . The et E. coli central carbon metabolic system was simulated with respect to a change in environmental glucose concentration40. Since glucose concentration corresponds to y(1) of km*, the simulation result can be compared to the theoretical analysis . The . The E. sis  or malate synthase (MS) enzymes, directly responsible for the GX cycle  to drive the TCA cycle. This raises a question of how the Ppc knockout mutant drives the TCA cycle. Previous experimental studies suggested that the GX cycle supplied OAA to the TCA cycle45. This study simulated the detailed kinetic model of the Ppc knockout mutant40 to demonstrate that the GX cycle works as an anaplerotic reaction to drive the TCA cycle . The sma in Eq. , where ta in Eq.  showed m47. Cooperativity provides ultrasensitivity to an enzyme reaction and gene expression in the form of the Hill equation. A high Hill coefficient presents a sigmoidal response or a digital switch-like behavior. Bistability caused by positive feedback loops, such as mutual activation/repression and positive autoregulation47, are critically responsible for a digital switch-like response showing two distinct output levels. Importantly, the digital-like response of the self-replenishment cycles neither involves the bistability mechanism nor cooperativity. To intelligibly understand its design principle, the self-replenishment cycle  is given byAssuming that the concentration of yThis shows a ReLU or threshold response with respect to α  knockout mutant45, where the activities of Icl/Ms enzymes were increased. To demonstrate the digital switch-like response of the TCA and GX cycles  and reducing powers (NADPH) for each turn of cycles. The glucose Pts with glycolysis consumes PEP with a high energy phosphate bond, although the glycolysis pathway generates ATP and NADH. Those cycles may evolve as the nutrient uptake regulator that can completely stop the uptake of a very low concentration of ammonia or glucose to avoid wasting energy or reducing power. On the other hand, the GX cycle evolves as the internal anaplerotic pathway, which is formed by connecting the three metabolites of AcCoA, OAA and ICIT within the TCA cycle (Supplementary Fig. The threshold response is useful in biological functions that should ignore low levels of inputs and respond over a wide range of them. The threshold response has a desirable property to present a distinct threshold that separates a non-nutrient uptake state from a nutrient uptake oneSupplementary figuresSupplementary figures


Flux balance analysis (FBA) is a widely-used method for analyzing metabolic networks. However, most existing tools that implement FBA require downloading software and writing code. Furthermore, FBA generates predictions for metabolic networks with thousands of components, so meaningful changes in FBA solutions can be difficult to identify. These challenges make it difficult for beginners to learn how FBA works.To meet this need, we present Escher-FBA, a web application for interactive FBA simulations within a pathway visualization. Escher-FBA allows users to set flux bounds, knock out reactions, change objective functions, upload metabolic models, and generate high-quality figures without downloading software or writing code. We provide detailed instructions on how to use Escher-FBA to replicate several FBA simulations that generate real scientific hypotheses.https://sbrg.github.io/escher-fba.We designed Escher-FBA to be as intuitive as possible so that users can quickly and easily understand the core concepts of FBA. The web application can be accessed at The online version of this article (10.1186/s12918-018-0607-5) contains supplementary material, which is available to authorized users. The constraint-based modeling approach to studying metabolic networks has led to a great variety of applications, from understanding metabolic gene essentiality, stress tolerance, and gene regulation to designing microbial cell factory . The simThe metabolic networks that are used for FBA simulations are represented by genome-scale models (GEMs). GEMs are available for many model organisms, with the number growing rapidly . StandarThe most popular software packages for FBA simulation require computer programming skills. COBRA Toolbox  and COBREscher-FBA meets these needs by extending the Escher application for pathway visualization with on-the-fly FBA calculations. Escher-FBA adds functionality so users can modify parameters in the FBA simulation—including flux bounds, objective function, and reaction knockouts—with immediate visualization of the results. Escher-FBA constructs the network and reaction data using the same input files as Escher. Additionally, since Escher-FBA is a web application, it works across platforms, including mobile devices. These features make Escher-FBA an ideal choice for academic labs and classrooms where students and researchers need a cross-platform visualization tool for learning and exploring FBA simulations.Escher-FBA is built upon Escher , a versahttps://github.com/hgourvest/glpk.js). The slider control in the tooltip adjusts both the upper and lower flux bounds of the reaction, while also displaying the current flux through the reaction. Value fields for upper and lower flux bounds allow the users to enter precise values. A Knockout button can be used to simulate a knockout of the associated reaction by setting both the upper and lower bounds of the reaction to zero. There is also a Reset button to reset the bounds to their original values from the loaded model. Finally, the Maximize and Minimize buttons can be used to change the FBA objective function to maximize or minimize the flux through the current reaction. The current objective and flux through that objective are displayed along the bottom-left corner of the screen, and buttons to reset the entire map back to its original data and to view a help menu are in the bottom-right corner of the screen. Perturbing the system with these controls produces immediately visible effects within the system. There is no need to manually re-run the simulation as Escher-FBA produces a new solution in response to user input.Escher-FBA extends Escher with interactive tooltips that appear when a user hovers the mouse over (or taps on a touchscreen) any reaction in the pathway visualization Fig. . These thttp://bigg.ucsd.edu) [E. coli K-12 MG1655 (available at http://bigg.ucsd.edu/models/e_coli_core). This model is small enough that the user can see everything happening in the simulation within a single pathway map. Escher-FBA also supports full GEMs. Any GEM in the COBRA JSON file format can be imported in Escher-FBA directly. Models in other formats can be converted to JSON using COBRApy [Escher-FBA supports upload of custom maps and models, using the same upload functionality and file format as Escher . Users ccsd.edu) . The def COBRApy . COBRApy COBRApy . The JSO COBRApy .E. coli, so they are ready to be implemented as soon as the Escher-FBA webpage is opened. Make sure to click the Reset Map button between each example. If you are having trouble finding a reaction, simply click the Find option in the View menu (or the “f” key on your keyboard) to open up a search bar.In order to demonstrate the use of Escher-FBA for real applications, we present four key FBA examples that can be executed directly in the browser. These are adapted from a review of FBA and its applications . These eE. coli includes a simulated minimal medium with D-glucose as the carbon source. Here, we will switch the carbon source from D-glucose to succinate. First, mouse over the succinate exchange reaction EX_succ_e, and change the lower bound to − 10 mmol/gDW/hr., either by dragging the slider or by entering − 10 into the Lower Bound field. Next, mouse over the D-glucose exchange reaction EX_glc_e, and either raise the lower bound to 0 or click the Knockout button. The default objective is still to maximize growth, so these two changes will instruct the program to calculate the maximum growth rate while using succinate as the carbon source instead of D-glucose. You should see that the maximum predicted growth rate decreases from 0.874 h− 1 to 0.398 h− 1, reflecting the lower growth yield of E. coli on succinate  are currently supported. To go back to single objectives, just click the Compound Objectives button again.Escher-FBA supports setting of multiple objectives in the Compound Objectives mode. In the default model, setting a new objective always disables the previous objective. To enable the mode, first click the ATPM) reaction is one such example. In order to determine the maximum production of ATP, simply mouse over the ATPM reaction and click the Maximize button. Setting up the objective this way works because, in order for the system to maximize flux through the ATPM reaction, it must first produce ATP in the highest possible quantity. When ATPM is maximized in the default core metabolism model of E. coli, the objective value is 175 mmol/gDW/hr.  and set the upper and lower bounds to slightly less than the current flux value . Next, mouse over a reaction of interest and click the Maximize and Minimize buttons to see the maximum and minimum flux through that reaction given the optimal growth rate. For example, maximizing and minimizing flux through GAPD in glycolysis yields a feasible flux range of 15.44–16.68 mmol/gDW/hr., indicating that glycolytic flux is highly constrained at high growth rates. On the other hand, maximizing and minimizing flux through MALS in the glyoxylate shunt yields a feasible flux range of 0–2.64 mmol/gDW/hr., indicating that the glyoxylate shunt can be activate or inactive at high growth rates. This procedure can be done with any set of reactions and the user can constrain their system to any number of flux values to see the range of solutions available to a particular reaction.Analyzing alternate optimal solutions in metabolism is another useful application of FBA . Since tE. coli core model is not the only system that can be simulated. For example, if one wishes to run simulations on a yeast cell, a model and map for Saccharomyces cerevisiae can be downloaded from http://bigg.ucsd.edu/models/iMM904. On that page, click the download button for the model (iMM904.json) and the map . Load these in Escher-FBA by clicking Load Map JSON in the Map menu and Load Model JSON in the Model menu to load both JSON files. Once loaded, the map is ready to edit and simulate with any of the tools in Escher or Escher-FBA , and a single map of central metabolism is provided that is compatible with both models .To provide an example of a research hypothesis that can be tested using Escher-FBA, we loaded genome-scale models of  strains . The fir strains . The sec strains . Each moMaximize), set the lower bound for excretion to 99% of the maximum, then minimized the flux through the first committed step of the pentose phosphate pathway, glucose 6-phosphate dehydrogenase (G6PDH2r). The resulting maps demonstrate that the synergistic pathways for 1-propanol production are stoichiometrically balanced with glycolysis, so they do not require PPP activity  and an iterative development process [While Escher-FBA can already be used for many FBA simulations directly in the web browser, a number of the examples presented by Orth et al. cannot currently be accomplished with Escher-FBA . As of r process  to eventEscher-FBA can perform interactive FBA simulations without any software installation or knowledge of computer programming. Additionally, even though it does not perform the advanced analysis available in popular libraries like the COBRA Toolbox and COBRApy, Escher-FBA can serve as an entry point for new users of FBA, for teaching FBA to students, and as a research tool for experts who want to visually explore simulations.Project name: Escher-FBA.Project home page:https://sbrg.github.io/escher-fbaOperating system: Platform independent.Programming language: JavaScript.Any restrictions to use by non-academics: none.Additional file 1:iJO1366 Atsumi2008.json. The genome-scale model of E. coli that contains the 1-propanol production pathway reported by Atsumi et al. [i et al. . (JSON 1Additional file 2:iJO1366 Shen2013.json. The genome-scale model of E. coli that contains the 1-propanol production pathway reported by Shen and Liao [and Liao . (JSON 1Additional file 3:iJO1366.Central metabolism 1POH.json. The Escher map that is compatible with both models (Additional files


Growth rate is a near-universal selective pressure across microbial species. High growth rates require hundreds of metabolic enzymes, each with different nonlinear kinetics, to be precisely tuned within the bounds set by physicochemical constraints. Yet, the metabolic behaviour of many species is characterized by simple relations between growth rate, enzyme expression levels and metabolic rates. We asked if this simplicity could be the outcome of optimisation by evolution. Indeed, when the growth rate is maximized—in a static environment under mass-conservation and enzyme expression constraints—we prove mathematically that the resulting optimal metabolic flux distribution is described by a limited number of subnetworks, known as Elementary Flux Modes (EFMs). We show that, because EFMs are the minimal subnetworks leading to growth, a small active number automatically leads to the simple relations that are measured. We find that the maximal number of flux-carrying EFMs is determined only by the number of imposed constraints on enzyme expression, not by the size, kinetics or topology of the network. This minimal-EFM extremum principle is illustrated in a graphical framework, which explains qualitative changes in microbial behaviours, such as overflow metabolism and co-consumption, and provides a method for identification of the enzyme expression constraints that limit growth under the prevalent conditions. The extremum principle applies to all microorganisms that are selected for maximal growth rates under protein concentration constraints, for example the solvent capacities of cytosol, membrane or periplasmic space. The microbial genome encodes for a large network of enzyme-catalyzed reactions. The reaction rates depend on concentrations of enzymes and metabolites, which in turn depend on those rates. Cells face a number of biophysical constraints on enzyme expression, for example due to a limited membrane area or cytosolic volume. Considering this complexity and nonlinearity of metabolism, how is it possible, that experimental data can often be described by simple linear models? We show that it is evolution itself that selects for simplicity. When reproductive rate is maximised, the number of active independent metabolic pathways is bounded by the number of growth-limiting enzyme constraints, which is typically small. A small number of pathways automatically generates the measured simple relations. We identify the importance of growth-limiting constraints in shaping microbial behaviour, by focussing on their mechanistic nature. We demonstrate that overflow metabolism—an important phenomenon in bacteria, yeasts, and cancer cells—is caused by two constraints on enzyme expression. We derive experimental guidelines for constraint identification in microorganisms. Knowing these constraints leads to increased understanding of metabolism, and thereby to better predictions and more effective manipulations. Fitter microorganisms drive competitors to extinction by synthesising more viable offspring , 2. The Tuning all enzyme expression levels appears to be a highly complex task. First, the genome of a microorganism encodes for thousands of reactions with associated enzymes. Second, a change in expression level of one enzyme not only affects the rate of its associated reaction, but also changes intracellular metabolite concentrations. These metabolite concentrations influence the activities of many other enzymes in a nonlinear fashion. In mathematical terms, microorganisms thus have to solve a high-dimensional nonlinear optimization problem.Surprisingly, experiments on many different microorganisms often show simple linear relations between growth rate, enzyme expression levels and metabolic rates –12, and We found an evolutionary extremum principle: growth-rate maximization drives microorganisms to minimal metabolic complexity. We provide the mathematical proof of this principle in the Methods section. It is derived from basic principles, more specifically from (i) mass conservation, i.e., steady-state reaction-stoichiometry relations, and (ii) enzyme biochemistry, i.e., the linear dependence of enzyme activity on the amount of enzyme and its nonlinear dependence on substrate and product concentrations. Our results provide a novel perspective on metabolic regulation, one in which the complexity is not determined by the size of the network or the rate equations, but by the constraints acting on the enzyme concentrations.In this section we will introduce the class of models that we studied, and mathematically prove our main result: the extremum principle. Readers that would like to skip the mathematical proof are strongly suggested to read the biological summary of the results at the end of the section.N, indicating which metabolites (rows) are consumed or produced in each reaction (columns). Because we can split reversible reactions in two irreversible reactions  is the cost vector matrix. The relation D(x) ⋅ λ ≤ 1 shows that the optimal λ vector indeed depends on the metabolite concentrations x, as was indicated below The x = x0, so that the enzyme saturations fj(x0) are constant. This will give us a fixed cost vector for each EFM. The remaining optimization problem is then visualized in M vectors in a K-dimensional cube.Largely following Wortel et al. , we now K constraints lead to the usage of at most K EFMs since all K linearly-independent vectors form a basis of a K-dimensional space. We can thus always take a combination of K vectors to reach the point where all constraints are met with equality. However, we should be careful because we could end up with negative λ’s for some of the EFMs. We continue with the proof by rewriting the problem in a Linear Programming (LP) form,In the general case, it might seem intuitive that vr = 1 ⋅ λ,Maximize subject toAλ ≤ z,M of the K + M constraints with equality. Therefore at most (K + M) − M = K constraints can be satisfied with strict inequality. These K inequalities could be concentrated in the λi ≥ 0 part, which means that the corresponding K Elementary Flux Modes are used. Thus, an optimal solution can use no more EFMs than there are active constraints in the system, thereby proving the theorem for any arbitrary vector of metabolite concentrations x.whereK EFMs are used in the optimum: EFMK, has an equivalent EFM, say EFMK+1, then we can replace the usage of EFM K by any convex combination of EFMs K and K + 1 and the solution will still be optimal. So, in the case that the costs of several EFMs are the same, the optimal flux vector could consist of more EFMs than the number of constraints. That’s why the theorem only tells us that no more than K non-equivalent EFMs are used in the optimal solution.There is one possible exception to the above reasoning. Let’s say that x, it is of course also true for the optimal set, Finally, it follows that, since the theorem is true for any set of metabolite concentrations xE. Which specific EFMs are the optimal ones, thus does not follow directly from the theorem.We note that the optimal internal concentrations, the choice of EFMs, and thereby the optimal enzyme concentrations, all depend on the external concentrations We think that the case where several EFMs are equivalent is not very common in biology. First, the constraints on enzyme expression are due to biophysical limits and we expect these to act on many enzymes together. This reduces the chance of having several EFMs that use exactly the same enzymes within the constrained pool of enzymes. Second, even if several EFMs would use the same enzymes, then the enzyme costs depend on the enzyme saturations, and these depend on the optimal metabolite concentrations. These optimal concentrations depend on the rest of metabolism, such that the non-overlapping part of the EFMs can still influence the enzyme costs. For these two reasons, we will assume in the rest of this work that EFMs are generally not equivalent.The previously published theorem that maximal specific flux, n an EFM , 25 is aThe following corollary can be used to find out how many constraints are active when we observe a certain number of active EFMs. It is the contrapositive of Theorem 1 and therefore mathematically equivalent. The reason that it is stated separately is the difference in biological applicability: the theorem is a predictive statement while the corollary is descriptive. As we will see in the Results section, the theorem tells us that metabolic complexity is low because the number of enzymatic constraints is typically low. The corollary however, enables us to infer from experimental data how many constraints must be active, and thus gives us physiological insight from population-level data.Corollary 2. r is optimized and K non-equivalent Elementary Flux Modes are used, then at least K linear enzymatic constraints must be activeIf a flux v.K EFMs.EFMs are not the only set of building blocks that we could have used. In the context of Flux Balance Analysis, constraint-based rate maximization can be studied by calculating Elementary Flux Vectors (EFVs) , 27, whiThe extremum principle, stated in Theorem 1, is a statement about all metabolic networks, independent of the network size, topology, or the specific enzyme kinetics. All microorganisms are subjected to a small number of enzymatic constraints, and all metabolic networks have Elementary Flux Modes as their building blocks: minimal pathways that make all cellular components from external sources. The fluxes through the participating reactions in an EFM can only be rescaled with one overall factor. We concluded that the use of an additional EFM thus only adds one flux degree of freedom, so that experimental data will show low complexity if few EFMs are used. We then proved the extremum principle, stating that the number of flux-carrying EFMs in the maximal growth rate solution is always bounded by the number of constraints on enzyme expression. As a whole, this leads to the prediction that microbial behaviour will show low complexity.K constraints, we also have K different costs for which we need to compare the different EFMs. We showed that the optimal solution is a combination of up to K of these EFMs. This is in accordance with the intuition that one EFM can be selected for each constraint because it has a low cost with respect to this constraint.In the proof, we compared the costs and benefits of the different EFMs. To be precise, we rescaled the EFMs such that the benefit of each EFM was equal: they all give one unit of objective flux. If we have To find the proof, we developed a framework using cost vectors. In We called an EFM a minimal unit of metabolic complexity because the ratios between the fluxes through all participating reactions are fixed, and none of its reactions can be removed. Consequently, a microorganism that uses one EFM can only change all reaction rates with the same factor. In other words, there is only one regulatory degree of freedom, instead of many if all reaction rates could have been tuned separately. In this case, flux values can be described by only one straight line. This becomes more complex when the number of flux-carrying (active) EFMs increases. Using this knowledge, the number of active EFMs can be estimated from flux measurements.We re-analysed data from carbon-limited chemostats and indeed observed that uptake rates of glucose and oxygen could be described by a straight line for a large range of growth rates, testimony of single EFM usage , lactate by cancer cells (Warburg) or acetate by hia coli , 38, 39.According to our theory, an additional enzymatic constraint must have become active at the critical growth rate see . Below tWe can gain more insight on overflow metabolism by applying the cost vector formalism on a coarse-grained model . Note hoWe think that many published explanations of overflow metabolism are unified by the extremum principle. The added value is not that it gives yet another model that qualitatively captures overflow metabolism, but rather that it explains why published models are successful by offering an overarching theory. Indeed, we show in We can predict the effect of experimental perturbations on metabolism with the cost vector formalism. Examples of such perturbations are the expression of non-functional proteins or the inhibition of enzymes, which can respectively be interpreted as reducing a limited enzyme pool, or lengthening the cost vectors. The effect of such perturbations on growth, when two EFMs are expressed, was analysed in the cost vector formalism . ChlorL. lactis from mixed-acid fermentation to homolactic fermentation. Since they found constant protein expression as a function of growth rate, they concluded that this metabolic switch cannot be explained from protein cost considerations. However, in E. coli at low growth rates [Under-utilization of enzymes appears to be in conflict with optimal resource allocation. For example, Goel et al.  studied th rates . This isE. coli only co-consumes carbon sources when this increases its growth rate  and theThe extremum principle is a null hypothesis about the course of a particular evolutionary process . It has Our theory suggests that metabolism has only a few operational degrees of freedom. By shifting perspective on rate maximization from the entire metabolic network to its representation in the cost vector formalism, we have reduced the problem to its essential dimensions, equal to the number of growth-limiting biophysical constraints. Together with the extremum principle, this work provides a species-overarching, molecular, constraint-based perspective on microbial metabolism.S1 AppendixIn this text we present our results in full mathematical detail. The harder mathematical steps are illustrated with figures.(PDF)Click here for additional data file.S2 AppendixIn this short text we analyse a core model of overflow metabolism using the extremum principle. Code for running the model is also provided.(PDF)Click here for additional data file.S3 AppendixL. lactis using the extremum principle. Code for running the model is also provided.In this short text we analyse a core model of overflow metabolism in (PDF)Click here for additional data file.S4 AppendixIn this short text we first explain how we found EFMs that simultaneously take up several carbon sources in a genome-scale model. We then present the method and results of our own experiments on co-consumption.(PDF)Click here for additional data file.S1 Source codeAll raw data and the Matlab-code used for data analysis can be found in the compressed folder attached to the supplements.(ZIP)Click here for additional data file.S2 Source codeThe Matlab-code used for modeling overflow metabolism is attached in a compressed folder as a supplement. In the compressed folder, we have also added a text-file with instructions.(ZIP)Click here for additional data file.S3 Source codeL. lactis is attached in a compressed folder as a supplement. In the compressed folder, we have also added a text-file with instructions.The Matlab-code used for the kinetic model of (ZIP)Click here for additional data file.S4 Source codeThe Python and Matlab-code used for finding co-consuming EFMs are attached in a compressed folder as a supplement. In the compressed folder, we have also added a text-file with instructions.(ZIP)Click here for additional data file.S1 DatasetEstimated growth rates from separate biological replicates.(TXT)Click here for additional data file.S2 DatasetFor all different growth media, we include an excell-sheet. Shown are the measured concentrations of carbon sources , with the corresponding Optical Density (OD). The letters that indicate the conditions denote the available carbon sources in the medium: S = Succinate, L = maLtose, M = Mannose, X = Xylose, G = Glucose.(XLSX)Click here for additional data file.S3 DatasetShown are the estimated uptake rates (mean and standard deviation) of different carbon sources  on the different growth media. The letters that indicate the conditions denote the available carbon sources in the medium: S = Succinate, L = maLtose, M = Mannose, X = Xylose, G = Glucose.(XLSX)Click here for additional data file.


Streptomyces clavuligerus (S. clavuligerus) is a Gram-positive bacterium which produced clavulanic acid (CA) and cephamycin C (CephC). In this data article, a curated genome scale metabolic model of S. clavuligerus is presented. A total of eighteen objective functions were evaluated for a better representation of CA and CephC production by S. clavuligerus. The different objective functions were evaluated varying the weighting factors of CA and CephC between 0, 1 y 2, whereas for the case of biomass the weight factor was varied between 1 and 2. A robustness analysis, by mean of flux balance analysis, showed five different metabolic phenotypes of S. clavuligerus as a function of oxygen uptake: (I) and (II) biomass production, (III) biomass and CephC production, (IV) simultaneous production of biomass, CA and CephC and (V) production of biomass and CA. Data of shadow prices and reduced cost are also presented. The objThe objective function No. 6 was the only one that included a metabolic phenotype that produced CA and CephC, simultaneously. S. clavuligerus as a function of oxygen uptake: (I) and (II) biomass production, (III) biomass and CephC production, (IV) simultaneous production of biomass, CA and CephC and (V) production of biomass and CA. See also supplementary material 2.22.1https://www.genome.jp/kegg/) and enzyme database (https://www.enzyme-database.org/). The improved metabolic model encompassed 1534 reactions  and 1199 metabolites . Cytoscape was used to visualize unconnected reactions in the metabolic network The genome scale metabolic model reported by Ramirez-Malule et al. (2018) was used as starting point 2.2Flux balance analysis (FBA) was used to determine metabolic states 2.3Metabolic fluxes were quantified by means of a two-stage optimization approach, which is a combination of the maximization of the objective function and minimization of the overall flux Stage oneStage two:−6, while the second stage was solved using the MATLAB's built-in fmincon solver, with a first order optimality and a maximum constraint violation within 10−6.The first stage optimization problem was solved using a Gurobi solver, with a feasibility tolerance of 10Different objective functions were evaluated varying the weighting factors of CA and CephC between 0, 1 y 2, whereas for the case of biomass the weight factor was varied between 1 and 2 see .2.4A robustness analysis was carried out to evaluate the functionally of the objective function when the optimal flux of oxygen was varied 2.5® as programing environment, and the Gurobi optimizer 7.5.2 was used to solve all optimization problems COBRA Toolbox v.3.0 synchronized with Matlab