During the last decades, we face an increasing interest in superior plants to supply growing demands for human and animal nutrition and for the developing bio-based economy. Presently, our limited understanding of their metabolism and its regulation hampers the targeted development of desired plant phenotypes. In this regard, systems biology, in particular the integration of metabolic and regulatory networks, is promising to broaden our knowledge and to further explore the biotechnological potential of plants.Arabidopsis thaliana provides an ideal model to understand plant primary metabolism. To obtain insight into its functional properties, we constructed a large-scale metabolic network of the leaf of A. thaliana. It represented 511 reactions with spatial separation into compartments. Systematic analysis of this network, utilizing elementary flux modes, investigates metabolic capabilities of the plant and predicts relevant properties on the systems level: optimum pathway use for maximum growth and flux re-arrangement in response to environmental perturbation. Our computational model indicates that the A. thaliana leaf operates near its theoretical optimum flux state in the light, however, only in a narrow range of photon usage. The simulations further demonstrate that the natural day-night shift requires substantial re-arrangement of pathway flux between compartments: 89 reactions, involving redox and energy metabolism, substantially change the extent of flux, whereas 19 reactions even invert flux direction. The optimum set of anabolic pathways differs between day and night and is partly shifted between compartments. The integration with experimental transcriptome data pinpoints selected transcriptional changes that mediate the diurnal adaptation of the plant and superimpose the flux response.The thale cress Arabidopsis thaliana can bring systems-biological interpretation of plant systems forward. Using the gained knowledge, metabolic engineering strategies to engage plants as biotechnological factories can be developed.The successful application of predictive modelling in The online version of this article (doi:10.1186/s12918-016-0347-3) contains supplementary material, which is available to authorized users. Firstly, in silico metabolic modelling has proven impressively successful in guiding systems metabolic engineering of other biological systems, including bacteria and fungi [in silico based analyses, such as elementary flux mode analysis [13C-metabolic flux analysis (13C-MFA) [in silico simulation appears particularly interesting due to its high speed, given e.g. the relatively long time of experiments with growing plants.Increasing world population, shortage of arable land and the resulting growing demand for food, feed and raw materials are major drivers to create plant lines with increased performance, e.g. better resistance to disease and drought . In addind fungi –14. Second fungi  provide nd fungi –18. And nd fungi . Among tanalysis , 21 and analysis , 23, as 13C-MFA) –26, high13C-MFA) , flux ba13C-MFA)  and meta13C-MFA) . Among tin silico analysis of plant central carbon metabolism. We use A. thaliana as a widely applied model plant to study plant biology and biotechnology, reflected also by the fact that it was the first plant sequenced [A. thaliana leaf was constructed, which represented 511 reactions and 1567 metabolic genes. Its reactions and pathways were localized in different subcellular compartments: cytosol, plastid, mitochondrion and peroxisome. Through simulation, relevant physiological scenarios of plant metabolism were studied. This involved the detailed investigation of the diurnal metabolism through comparison of metabolic capabilities in the light and in the dark. In addition, the modelling results were integrated with previous experimental fluxomic and transcriptomic data of A. thaliana leaves in order to explore the systems-wide regulation of the metabolism. This provides an enhanced understanding of plant metabolic pathways and their contribution to growth and product formation.Here, we conduct detailed equenced . In shorA. thaliana leaves. For re-construction, the initial draft of the network built on recent genome-scale models of the organism [http://www.genome.jp/kegg), MetaCrop [http://metacrop.ipk-gatersleben.de/) and AraCyc [http://pmn.plantcyc.org). This provided state-of-art gross information on the genomic pathway repertoire. Where needed, the network was updated with experimental data and primary literature as described in detail below. Individual additions and specifications considered enzyme localization, cofactor usage, and inter-compartmental transport. Subsequently, the model was condensed, which, however, did not reduce its information content , which were added. Both models, the detailed version and the condensed version, used for the simulations, are provided as SBML files in the Additional files The metabolic network used in this study comprises the central carbon metabolism of organism –32. The organism   and an absolute log2-value > 0.5.Elementary flux modes (EFMs) were calculated with efmtool, based on the null space approach and recursive enumeration with bit pattern trees . The EFMA. thaliana rosettes [Experimental transcriptome data were taken from a recent study on the shift of gene expression between day and night in rosettes . In thisA. thaliana rosette [−1 to enable a straightforward comparison with the respective flux modes, obtained in this work, also given in (C-mol) (C-mol)−1.The experimentally measured metabolic fluxes of an illuminated  rosette  were conArabidopsis and of other C3 plants under ambient atmospheric conditions at different light intensity [The quantum yield of photosynthesis was derived from previous measurement of the rate of photosynthesis of ntensity –43. Due ntensity . This prA. thaliana’s core carbon pathways reflected 511 metabolic conversions in total . The chosen topology is specific for green leaf tissue. The network contained the Calvin-Benson-Bassham (CBB) cycle for CO2 assimilation and photosynthesis, the gluconeogenesis, the glycolytic Embden-Meyerhof-Parnas (EMP) pathway, the oxidative and the non-oxidative pentose phosphate (PP) pathway, the tricarboxylic acid (TCA) cycle, the reactions of photorespiration, of starch biosynthesis and degradation, of energy metabolism, as well as the anabolic pathways for biomass synthesis  (http://pmn.plantcyc.org) [http://metacrop.ipk.gatersleben.de) [The network reflected the four major compartments of plant leaves that contribute to biochemical conversions: cytosol, peroxisome, mitochondrion and plastid (cyc.org) , 45–48. cyc.org) , the oxicyc.org) . The placyc.org) , the oxicyc.org) . The TCAcyc.org) . The phocyc.org) . Additioeben.de) . Pyruvateben.de) , whereaseben.de) . The supeben.de) . Malic eeben.de) .2 was assumed to freely diffuse within the cell [The separation of the metabolic routes in distinct organelles requires the translocation of specific compounds across cellular membranes. Based on experimental evidence, unidirectional or bidirectional transport between cytosol and mitochondrion was assumed for pyruvate, malate, inorganic phosphate, glycine and serine, respectively, whereas antiporters were considered for malate/oxaloacetate, citrate/oxaloacetate and ATP/ADP , 52–55. the cell , photonsthe cell  and inorthe cell .Redox, energy and phosphate metabolism were compartmentalized across the different organelles. This included the confinement of the photosynthetic light reactions to the plastid and of the oxidative phosphorylation system to the mitochondrion. A vacuolar storage pool for inorganic phosphate was considered . InorganA. thaliana leaves was collected from previous work , and for metabolism in the dark using internal starch (dark-metabolism). The solution space consisted of 1.2 million elementary flux modes for the light-metabolism and of 5.7 million elementary flux modes for the dark-metabolism  (C-mol substrate)−1 closely resembles experimental values for A. thaliana leaves of about 25.2 (g biomass) (C-mol substrate)−1 [2 assimilation, deducing that degradation of a heterotrophic substrate, such as starch, is the only feasible phenotype in the dark.The full sets of elementary flux modes, which span the entire space of feasible flux distributions, were calculated both for metabolism in the light using COtrate)−1 . The max2)−1. This corresponds to a quantum yield between 0.09 - 0.12 (mol CO2) (mol photons)−1, obviously supporting optimal photosynthesis.The computed set of elementary modes was used to investigate the impact of the light influx on growth in more detail. First, energetically inefficient modes that included massive cycling of resources were eliminated. Although stoichiometrically possible, these modes involve futile cycling of carbon across the internal membranes to dissipate energy , as compared to light-metabolism (5 %), whereby overall, both values were rather low. It was interesting to note that also the origin of the released CO2 differed. Under both conditions, the carbon loss by photorespiration was negligible, whereas the largest contributors to CO2 release were the TCA cycle and pyruvate and malate dehydrogenase. During the dark, additional carbon was released during the generation of NADPH in the oxidative PP pathway, whereas during illumination, previously assimilated CO2 was lost via PEP carboxykinase.As shown in the previous section, the metabolism in the dark recruited all compartments to supply ATP and reducing power, whereas the plastid was the dominant compartment in the light Fig. . Next, wThe striking differences in the localization of energy and reducing power supply among the cellular compartments now suggested to also inspecting anabolic metabolism. Therefore, the metabolic pathways, responsible for the synthesis of each anabolic precursor, were investigated and compared between the optimum growth modes in the light and in the dark . Interestingly, the biosynthetic origin of many of the twelve anabolic precursors strongly depended on the physiological growth mode, i.e. light and carbon acquisition Fig. . As examIt is generally accepted that cyclic and non-cyclic electron flow both contribute to the in vivo photosynthetic light reaction –67. HoweA. thaliana, such as growth and photosynthetic efficiency, which can be taken as indication of its high quality and validity  a diurnal expression pattern was identified, however only the former two are linked to the observed flux changes. This indicates that At3g49160 likely has a functionally different purpose from mediating the pyruvate phosphorylation in central carbon metabolism. For instance, pyruvate kinase could also catalyze several metabolic conversions in ribonucleotide and nucleotide biosynthesis. As isoenzymes might have distinct functions , correlain silico through modelling [Plants adapt to changes in light intensity through photo protection and optimization of energy conversion . In thisodelling . Likely,odelling . When anArabidopsis can operate close to theoretical pathway optimum and that this is mediated by a fine-adjustment of metabolic flux, strongly under transcriptional control. In this light, the present work is one of the very few examples so far, which link in-vivo with in-silico flux data to a higher-level understanding [The created condensed network model adequately described leaf physiology, and thus, because of its reduced network size as compared to genome-scale models, permits straightforward, comprehensive analysis of the entire elementary flux mode solution space. Taken together, the metabolic simulations provide detailed molecular insights into plant functioning. standing , 115. It


Hybridoma cells are commonly grown for the production of monoclonal antibodies (MAb). For monitoring and control purposes of the bioreactors, dynamic models of the cultures are required. However these models are difficult to infer from the usually limited amount of available experimental data and do not focus on target protein production optimization. This paper explores an experimental case study where hybridoma cells are grown in a sequential batch reactor. The simplest macroscopic reaction scheme translating the data is first derived using a maximum likelihood principal component analysis. Subsequently, nonlinear least-squares estimation is used to determine the kinetic laws. The resulting dynamic model reproduces quite satisfactorily the experimental data, as evidenced in direct and cross-validation tests. Furthermore, model predictions can also be used to predict optimal medium renewal time and composition. Therapeutic products  are subject to exponential demands and cost-lowering process improvements, leading to the intensification of growth conditions in the bio-pharmaceutical industry and the sharp increase of the related market economy. For instance, monoclonal antibody (MAb) market amounts to several billion dollars and is still increasing.To improve bioprocess yield and repeatability, monitoring and control tools are required. The latter implies the availability of dynamic models, which can predict the process trajectory and support the design of software sensors or control strategies. Previous optimization studies of hybridoma cell cultures for MAb production were usually conducted using simple mathematical models based on macroscopic reaction schemes such as in ,2.More recently, a macroscopic model with kinetics accounting for overflow metabolism, where glucose and glutamine are the main substrates, was proposed in . Indeed,A more practical alternative is to directly deduce the model structure from the available data, assuming that the data sufficiently cover the process operating range. In , PrincipA simple dynamic model of cultures of hybridoma cells in SBR is developed and validated with experimental data. Confidence intervals for the parameters and the estimated trajectories are provided.A systematic model identification procedure, based on rigorous yet simple to use tools—MLPCA to determine the stoichiometry, nonlinear least squares to identify the parameters of the kinetic laws, sensitivity analysis and Monte Carlo analysis to infer the confidence intervals—is assessed in a real case study, showing good performance and promise for future applications.The simple dynamic model is further exploited to optimize the medium renewal strategy in the sequential batches.The main contribution of this study is threefold:This paper is organized as follows. This section first reviews the basic concept of overflow metabolism and then presents a systematic procedure to infer candidate macroscopic models from principal component analysis of the data at hand.The glycolysis which is a series of degradation reactions of glucose (the main substrate) taking place in the cytoplasm and leading to a final product, i.e., pyruvate.TCA) cycle or citric acids cycle, which takes place inside the mitochondrions and uses pyruvate to product the cells energy units (Adenosine triphosphate or ATP) and reduced cofactors .The Krebs cycle, also called the tricarboxylic acids  principally used for cell growth and division. This limitation comes from the capacity to oxidize the main nutrients: glucose (main carbon source) and glutamine (main nitrogen source). The excess amounts of these nutrients are assumed to follow other metabolic pathways more commonly known as “fermentation”, producing a side byproduct.This “Overflow Metabolism” or “short-term Crabtree effect” ,9,10,11,The byproduct formation usually inhibits the oxidative capacity of the cells, slowing down growth for increasing concentrations. In turn, it depends on the oxidative capacity of the cells and on the medium composition. A generic mechanistic model that would, in principle, allow the representation of the culture of different strains presenting overflow metabolism, can be described through the following main reactions:jth substrate consumption:jth substrate overflow:jth byproduct consumption:X, jS and jP are the concentrations of cell biomass, jth substrate and jth side byproduct, respectively. The nik coefficients represent the yield (or pseudo-stoichiometric) coefficients of component n in reaction i. Overflow metabolism assumption involves that, for each concerned substrate, these reactions take place in pairs (1a and 1b) or triplets (1a–1c) if the considered byproduct can be reconsumed by the biomass as a substitute substrate source when the oxidative capacity is not fully exploited.S < critS and Sφ < Smaxφ), substrate is consumed with biomass growth and a relatively low metabolite byproduct production (1a) without overflow, which is defined as respiratory metabolism and the consequent remaining respiratory capacity can be used to oxidize byproduct as substitute carbon source as in (1c). Indeed, Sonnleitner and Käppeli  assume tS > critS and Sφ > Smaxφ), the respiratory capacity is saturated, resulting in overflow metabolism towards excess metabolite production (reactions (1a) and (1b)). The state at which overflow metabolism is initiated (S = critS and Sφ = Smaxφ) is referred to as critical metabolism. For instance, yeast metabolism is described by the bottleneck assumption of Sonnleitner and Käppeli , i.e., is the medium renewal time trenewal and the glucose and glutamine concentrations in the medium Grenewal and Gnrenewal. Fmincon also allows to specify box constraints for trenewal Є [3 14] days. These values are selected in accordance with the previous experimental results: medium renewal should on the one hand not occur too soon and on the other hand before the end of the experiment set at day 14. Grenewal Є [1 15] g/L and Gnrenewal Є [0.1 1] g/L so as to avoid cell starvation or growth inhibition through the accumulation of byproduct.This section intends to provide the best medium renewal time and composition to maximize the monoclonal antibody production and substrate savings. Using the validated model of renewal and Gnrenewal are respectively set to 6 and 0.4 g/L . Moreover, the MAb production, defined as the sum of the final batch concentrations, amounts to 60.92 µg/mL which represents a production gain of 30% with respect to the experiments of refresh is reached. Indeed, when G is depleted, Gn still limits biomass decay and therefore maintains an efficient MAb production rate. However, since ammonium production (byproduct formed by glutamine overflow) is not considered in the model obtained in refresh are not recommended.Even when considering substrate savings, the upper bound of GnInterestingly, approximately the same renewal time as in Since MAb production clearly appears as a function of substrate saving penalization, new optimizations considering α in the range 0 to 500 with incremental steps of 50 are achieved in order to assess the impact of α on MAb production and select a good compromise. Results displayed in In this work, a simple dynamic model of hybridoma sequential batch cultures is developed, which can be used to optimize the production of monoclonal antibodies. Maximum likelihood principal component analysis allows assessing the information content of the experimental data, providing the minimum number of reactions and the corresponding stoichiometry by solving an optimization problem under a few a priori biological constraints. An original formulation of the method is presented, allowing biomass to occur in several reactions. Advantages of the method are (a) to limit the number of reactions, i.e. to avoid a useless complication of the model with respect to the experimental field and the involved biological phenomena ; (b) to offer the possibility to proceed to a quick first estimation of the stoichiometry independently of the kinetics, in turn reducing the number of unknown parameters ; (c) to provide a “divide and conquer” approach where the stoichiometry and kinetics can be estimated separately or simultaneously, in an iterative way, starting from estimates obtained at the previous step.The procedure can be supplemented by parametric sensitivity analysis, which allows further model simplification, whenever needed, by isolating parameters with low sensitivities.A Monte-Carlo study, where parameter variations are considered in accordance with the resulting estimation error variances, shows that model trajectories are globally kept inside a corridor defined by measurement confidence intervals . As a practical illustrative outcome of the present study, the obtained dynamic model is used for a two-sequential batch process optimization . The results show that the importance of substrate savings drives the location of the optimum. A renewal time scheduling can therefore be established based on the user will to save medium components such as substrates. Further experimental validations of the optimization method are important perspectives of this still on-going work as well as estimation and on-line control issues.


Yarrowia lipolytica has great potential due to its oleaginous characteristics and unique ability to utilize hydrophobic substrates. However, Y. lipolytica should be further engineered to make it more competitive: the current approaches are mostly intuitive and cumbersome, thus limiting its industrial application.Recently, there have been several attempts to produce long-chain dicarboxylic acids (DCAs) in various microbial hosts. Of these, Y. lipolytica. At the outset, we reconstructed genome-scale metabolic model (GSMM) of Y. lipolytica (iYLI647) by substantially expanding the previous models. Subsequently, the model was validated using three sets of published culture experiment data. It was finally exploited to identify genetic engineering targets for overexpression, knockout, and cofactor modification by applying several in silico strain design methods, which potentially give rise to high yield production of the industrially relevant long-chain DCAs, e.g., dodecanedioic acid (DDDA). The resultant targets include (1) malate dehydrogenase and malic enzyme genes and (2) glutamate dehydrogenase gene, in silico overexpression of which generated additional NADPH required for fatty acid synthesis, leading to the increased DDDA fluxes by 48% and 22% higher, respectively, compared to wild-type. We further investigated the effect of supplying branched-chain amino acids on the acetyl-CoA turn-over rate which is key metabolite for fatty acid synthesis, suggesting their significance for production of DDDA in Y. lipolytica.In this study, we proposed model-guided metabolic engineering strategies for enhanced production of DCAs in In silico model-based strain design strategies allowed us to identify several metabolic engineering targets for overproducing DCAs in lipid accumulating yeast, Y. lipolytica. Thus, the current study can provide a methodological framework that is applicable to other oleaginous yeasts for value-added biochemical production.The online version of this article (10.1186/s12918-018-0542-5) contains supplementary material, which is available to authorized users. Candida sp. [Yarrowia lipolytica [Pseudomonas aeruginosa [Cyptococcus neoformans [Escherichia coli [Y. lipolytica has attracted great attention as a cell factory to manufacture DCAs [Long-chain dicarboxylic acids (DCAs) are widely used in the manufacturing of polyamides and polyesters as the monomeric intermediates . The mosdida sp. , 4, Yarrpolytica , Pseudomruginosa , Cyptocooformans , and Eschia coli . Of thesure DCAs  since thure DCAs –13. In ωure DCAs .Y. lipolytica as oleaginous yeast has huge potential to become a model organism to produce fatty-acid derived products including DCAs. In order to make it industrially competitive, its productivity should be further enhanced, which can be achieved by modification of relevant target genes. However, metabolic engineering of Y. lipolytica has been mainly focused on over-producing lipids, e.g., triacylglycerols (TAGs) with only a handful of studies for the increased DCAs production [in silico genome-scale metabolic model (GSMM) have been developed and successfully applied to several industrial hosts including E. coli [S. cerevisiae [in silico methods using GSMM of Y. lipolytica which was newly reconstructed by substantially expanding the previous models, thus allowing us to identify various genetic engineering targets for overexpression, knockout, and cofactor modification towards DCA overproduction.Indeed, oduction . In addioduction . In this E. coli , 18 and revisiae , 20. SimY. lipolytica for designing DCA overproducing strains. Initially, four existing Y. lipolytica GSMMs  were col iND750  by addinY. lipolytica appeared to not degrade leucine and other BCAA into acetyl-CoA, but there are reports implicating the biosynthetic capacity of leucine as an effector of lipogenic capacity in oleaginous organisms [With the aim of building an objective-oriented model for simulating DCAs production, we first added 9 biosynthetic reactions which are sequentially catalyzed by hydroxylase, oxidase and dehydrogenase enzymes within the ω-oxidation pathway, thus capturing the oxidation of fatty acids to DCAs. The 27 DCAs degradation reactions were also included to represent β-oxidation pathway together with 6 dicarboxylic acids transport and an exchange reaction pertaining to DDDA secretion. Based on the scaffold model, rganisms ; a putatY. lipolytica. Additionally, we corrected the elemental balance and directionality of 45 reactions. For example, the directionality of THRA representing the threonine aldolase mediated breakdown of threonine to glycine and acetaldehyde, was changed to opposite direction favoring acetaldehyde formation based on the direction reported in S. cerevisiae [in silicoY. lipolytica model (iYLI647) consists of 1347 reactions and 1152 metabolites encoded by 647 genes  file  was also constrained according to the experimental data wherever provided. For the biomass maximization in iMK735, biomass equation corresponding to 5% lipid was used. The maximum specific growth rate was determined for all models simulated under same constraints and the results were compared  also provide mitochondrial acetyl-CoA. The most interesting finding from tSOT is GLUDy, which apart from regeneration of NADPH; also plays key role in maintaining the balance of carbon and nitrogen. There is considerable evidence of the presence of GLUDy shunt in plants, which returns the carbon in amino acids biosynthesis back into reactions of carbon metabolism and TCA cycle [Considering that fatty acid biosynthetic pathway is very tightly regulated, transcriptomic data can provide some useful insight into the ON/OFF state of the reactions in a particular condition. To identify the overexpression targets for increasing the DCAs production, we implemented tSOT by resorting to time-course transcriptomic profile of the ry phase . A nitrory phase . AlthougCA cycle  which isCA cycle , making Y. lipolytica which apparently takes the flux away from DCAs production which requires free fatty acid [GDLS algorithm was used to search for growth-coupled solutions for DCA production, identifying up to 5 reaction deletion candidates. Basically, GDLS propose the pathway design which couples the product formation with the cell growth, making its production necessary to reach optimal growth. The strain design strategy deciphered by GDLS combined the simultaneous knockout of DESAT16 (Stearoyl-CoA desaturase) and MI1PS (Myo-inositol-1-phosphate synthase). DESAT16 is the enzyme that catalyzes the conversion of saturated fatty acid to monounsaturated fatty acids. The overexpression of this enzyme is shown to increase lipid accumulation in tty acid , deletinY. lipolytica which lacks acyl-CoA oxidases can more efficiently convert n-alkanes and fatty acids or their derivatives to their corresponding DCAs [Furthermore, formed DCAs can get degraded via β-oxidation pathway. Therefore blocking it by deletion of acyl-CoA oxidase encoded by POX1–6 genes can further enhance the titer of DCAs. ing DCAs .Y. lipolytica involves several unique reactions and is commonly controlled by the supply of precursors and cofactors. Earlier part of this study has focused on overexpression and downregulation of some key enzymes regulating the ω-oxidation pathway. However, cofactors are very important to achieve improvement in productivity. NADPH, as a reducing equivalent, usually plays an important role in coupling catabolism with anabolism and energy generation during metabolism. Several metabolic engineering approaches have been implemented to manipulate the cofactors level to increase the product yield in other microorganisms [Streptococcus mutants gapN gene which encodes a GAPDH to increase the L-lysine production [Kluyveromyces lactis [Similar to other biosynthetic pathways, the DCAs biosynthesis via ω-oxidation pathway in rganisms , 45 Incroduction ; enginees lactis ; overexps lactis , are a fY. lipolytica. This excessive cofactor demand is mainly satisfied through the pentose phosphate pathway (PPP) reactions. But, the increased usage of the PPP through overexpression is suboptimal as one mole of carbon is lost as CO2 for every two moles of NADPH produced [Fatty acid biosynthesis and ω-oxidation pathway are NADPH demanding oxidative pathway in produced . To circTo achieve a high-level production of DCA in yeast, we propose to enhance the supply of NADPH to the ω-oxidation pathway. Hence, a multi-step metabolic engineering strategy can be devised to simultaneously modify the glycolysis step, optimize the NADPH supply and to enhance the activity of some NADPH producing enzymes.Y. lipolytica that lipid accumulation can occur de novo without exogenous supply of hydrophobic substrate, laying the grounds for a possibility to be used for de novo DCAs production as well, from primary carbon sources, i.e., glucose or glycerol [S. cerevisiae [Y. lipolytica [Y. lipolytica, we sought to explore the effect of BCAA supplementation on acetyl-CoA pool, which can be produced via degradation pathway of BCAA. In order to theoretically analyze the flux distribution and flux-sum changes that occur when BCAA is supplemented, we maximized the DDDA production using glucose as the primary carbon source supplemented with 10 C-mmol/gDCW-hr of leucine, isoleucine, or valine. To elucidate the difference in pathway utilization and metabolite turn-over in different amino acids during DDDA production, we prepared the heat map of flux distribution and flux-sum as shown in Fig. Y. lipolytica. This is the first report implicating a prominent role of valine degradation as an alternate route of acetyl-CoA biosynthesis in Y. lipolytica, experimental validation of which can give insight to intricate correlation between fatty acid biosynthesis and amino acid degradation.In most recombinant DCAs production studies, the hydrophobic substrates such as alkane and fatty acid methyl ester (FAME) were used for the biotransformation . As suchglycerol . In addirevisiae  and Y. lpolytica . Taking Y. lipolytica, iYLI647, was reconstructed using iMK735 as a scaffold and the relevant information from other available Y. lipolytica models. iYLI647 consists of 1347 reactions and 647 genes. The biomass equations were carefully formulated with various experimental information of Y. lipolytica, which is perhaps the reason for accurate model prediction. The potential of de novo DCAs production in Y. lipolytica combined with a model–driven strain design for metabolic engineering and media optimization strategies were then evaluated using the reconstructed iYLI647. The flux towards DDDA production was increased following the overexpression and deletion of few reactions and the model-based strain design gives us a good starting point to explore the metabolic capabilities of Y. lipolytica to produce fatty acid derived products. Moreover, the workflow and procedure presented in this analysis can be utilized as a platform to perform similar analyses with different organisms.The GSMM of iNL895, iYL619, iMK735, and iYali4, to compare and select the best suited as scaffold model. Following our qualitative and quantitative comparison, we chose iMK735 as a scaffold model and proceeded to manual curation to expand the model coverage and characteristics. To do this, using literature data, we verified the presence of reactions and relevance in Y. lipolytica metabolism. Then, we added ω-oxidation pathway to convert fatty acids to DCAs, and also the subsequent degrading β-oxidation pathway. Following the literature evidence and its established importance in fatty acid metabolism, we also included BCAA degradation pathways. Furthermore, we checked the mass balance of reactions and made appropriate changes to make stoichiometrically balanced reactions. In addition, we derived the biomass equation in carbon and nitrogen limited conditions using updated and relevant literature sources. Using refined biomass equation, we simulated the model to identify the loops, and missing link reactions using GapFinder [We chose all four separately developed publicly available metabolic network reconstructions, apFinder . Loops wY. lipolytica was simulated under varying environmental conditions using constraints-based flux analysis. The biomass reaction was maximized to simulate the growth under various culture conditions as described elsewhere [Sij refers to the stoichiometric coefficient of metabolite i involved in reaction j, vj denotes to the flux or specific rate of metabolic reaction j, j, respectively; and Z1 corresponds to the cellular objective as a linear function of all the metabolic reactions where the relative weights are determined by the coefficient cj. In this study, the constraints-based flux analysis problems were solved using COBRA toolbox [The cellular metabolism of lsewhere –56. The  toolbox .in silico strain design approaches have been employed to identify metabolic engineering targets for overproducing DCA from glucose.Four GDLS strain design algorithm  was implfj, is defined as the absolute value of reaction flux, vj [To identify the upregulation and downregulation gene/reaction targets which lead to the enhanced production of desired compound, we first needed to quantify the flux activity of all reactions in the wild-type strain. Flux activity, flux, vj . This caSubject to:αj and βj are upper and lower bounds of fluxes, respectively. The fj+ and fj− are the positive two variables into which the flux, vj, is decomposed. It is observed that fj+ or fj− is equal to zero. This condition was introduced by new binary variables Ij+ and Ij− which are when multiplied with a large integer which should be larger than the flux of experimentally measured value, M, will be always lesser than fj+ and fj−, respectively. Additionally, the constraint fj+ or fj− are equal to zero.Where, Once the reference flux activities are established, i.e. wild-type, maximum and minimum values, we then solve the below mentioned MILP problem to analyze the effects of perturbing a particular flux activity on cellular growth.Subject to:ORkatt and kint are gradually varied between 0 and 1 in steps of 0.1 to analyze the effect of reaction upregulation between minimal and wild-type values, and reaction downregulation between the wild-type and maximal values, respectively.Where, constraints (C1) and (C2) are applicable for upregulation and downregulation problems, respectively. Parameters Finally, the objective value obtained from the solution of Eq.  is used Subject to:Bj,k is the maximum biomass obtainable while solving problem  database using accession number GSE29046 [Since optimality assumption based FBA algorithms ignores the regulatory consideration while strain designing, we implemented transcriptomics-based strain optimization tool (tSOT)  to identGSE29046 .Since the ω-oxidation pathway is an oxidative process and requires cofactor optimization to maximize theoretical yield, we used CMA to identify the cofactor specificity engineering target which can increase the yield of DDDA. CMA was implemented as described in our previous work . MathemaSij, except the reactions which involve either NAD(H) or NADP(H). These reactions are swapped for cofactors in the k and which is fixed at 1 for all simulations in this work. The bi-level MINLP problem was reformulated as a single-level MINLP problem using the primal dual transformation as implemented earlier [Where,  earlier . The MILi can be formulated as Φi = 0.5 ∑ |Sijvj|. Each term in this summation series gives us the absolute rate of consumption/generation of metabolite i due to reaction j and thus by halving the sum of these terms, we can obtain the overall turnover rate for metabolite i.In the constraints-based flux analysis, there is no accumulation of intermediate metabolites due to the steady-state condition. However, the turnover rate, which is also equivalent to the total consumption or production rate, of the intermediates can be nonzero, which is defined as their flux-sum . Since tAdditional file 1:iYLI647 model in comparison with iMK735 scaffold model. (XLSX 22 kb)Changed, added and deleted reactions in Additional file 2:iYLI647. (XML 2312 kb)SMBL file of Additional file 3:Y. lipolytica in C- and N- limited conditions and GAM and NGAM calculations. (DOCX 52 kb)Biomass composition of


Clostridium butyricum. However, despite the increasing role of Clostridium butyricum as a bio-production platform, its metabolism remains poorly modeled.The increase in glycerol obtained as a byproduct of biodiesel has encouraged the production of new industrial products, such as 1,3-propanediol (PDO), using biotechnological transformation via bacteria like iCbu641, the first genome-scale metabolic (GSM) model of a PDO producer Clostridium strain, which included 641 genes, 365 enzymes, 891 reactions, and 701 metabolites. We found an enzyme expression prediction of nearly 84% after comparison of proteomic data with flux distribution estimation using flux balance analysis (FBA). The remaining 16% corresponded to enzymes directionally coupled to growth, according to flux coupling findings (FCF). The fermentation data validation also revealed different phenotype states that depended on culture media conditions; for example, Clostridium maximizes its biomass yield per enzyme usage under glycerol limitation. By contrast, under glycerol excess conditions, Clostridium grows sub-optimally, maximizing biomass yield while minimizing both enzyme usage and ATP production. We further evaluated perturbations in the GSM model through enzyme deletions and variations in biomass composition. The GSM predictions showed no significant increase in PDO production, suggesting a robustness to perturbations in the GSM model. We used the experimental results to predict that co-fermentation was a better alternative than iCbu641 perturbations for improving PDO yields.We reconstructed Clostridium strain to propose new scenarios for PDO production, such as dynamic simulations, thereby reducing the time and costs associated with experimentation.The agreement between the predicted and experimental values allows the use of the GSM model constructed for the PDO-producing The online version of this article (doi:10.1186/s12918-017-0434-0) contains supplementary material, which is available to authorized users. Clostridium butyricum or Klebsiella spp. [Clostridium species are the more attractive alternative because they are safer and achieve higher yields than Klebsiella [Clostridium butyricum could therefore shed light on a better ways to promote glycerol transformation to PDO in this organism.The rising biodiesel industry has resulted in a major overproduction of glycerol as a byproduct, which now threatens the economic viability of this industry , 2. Thislla spp. , 7. Closebsiella . Howeverebsiella –11. Therebsiella . A more Clostridium butyricum have generally focused on its central metabolism, which is composed of oxidative and reductive branches [Clostridium strain, indicating the functioning of 77 reactions and 69 metabolites. The model, in addition to the oxidative and reductive branches, also included simplified synthesis reactions for amino acids, macromolecules, and biomass. However, at present, metabolic models based on genome annotation information, also known as genome-scale metabolic (GSM) models [Clostridium butyricum.Metabolism studies of glycerol by the anaerobic bacterium branches . The oxibranches , 9, 15. branches  reported) models , 18, areClostridium sp. IBUN 158B cultured in glycerol [Clostridium butyricum 5521 cultured in glycerol. Nevertheless, despite this experimental information and the computational tools available, the prediction of PDO production by Clostridium based on its metabolic behavior is still limited.A proteomics study of the native Colombian strain glycerol  has provglycerol  also useOne computational tool commonly employed for metabolic modeling is flux balance analysis (FBA). FBA allows the use of a steady state assumption of defined culture conditions to predict the phenotype of one microorganism based on its GSM model –25. HoweIn general, predictions using GSM models assume biomass yield maximization as the objective function, based on the assumption that cells have evolved to select the most efficient pathways that achieve the best yields . NeverthClostridium strain. The biological model selected was the Colombian strain Clostridium sp. IBUN 13A, a strain isolated by our Bioprocesses and Bioprospecting Group. This strain is a natural PDO producer and has been employed over the last 20 years in several studies aimed at understanding PDO production, including the annotation of its genome [For these reasons, the initial purpose of the present research was to construct the first GSM model of a PDO producer s genome –42. AddiClostridium sp. IBUN 13A strain was constructed based on RAST annotation [Clostridium butyricum cultured in glycerol [C. beijerinckii GSM [C. acetobutylicum [C. thermocellum [C. ljungdahlii [C. cellulolyticum [1.624O0.456N0.216P0.033S0.0047.A draft metabolic model for the notation . The dranotation  analysisglycerol , 19, 44 glycerol , 45–52. utylicum . This exmocellum , C. ljunolyticum  include iCbu641 GSM model included 641 genes, 891 reactions, and 701 metabolites. Table Clostridium strains showed 11 unique enzymes, including as PDO dehydrogenase (EC.1.1.1.202) and glycerol dehydratase (EC.4.2.1.30). These two enzymes function in lipid metabolism but are associated with the reductive branch of glycerol metabolism [After curation, elemental balancing, and loop deletion, the constructed tabolism .Table 1MiCbu641 metabolic network is the first GSM model curated for a PDO producing Clostridium strain [iCbu641 model also includes all the enzymes associated with glycolysis and the pentose phosphate pathway and most of the enzymes involved in the TCA cycle. The enzymes from the TCA cycle that were not included are malate dehydrogenase (EC.1.1.5.4), succinate-CoA ligase (EC.6.2.1.4 - EC.6.2.1.5) and fumarate reductase (EC.1.3.5.4), which were not detected in the genome. Therefore, additional experimentation is required to verify the presence or absence of genes encoding these three enzymes in the genome of Clostridium sp. IBUN 13A. The model is able to synthesize de novo all the precursors involved in the biomass reaction .The m strain , 18, 49 iCbu641 GSM model and FBA were employed to predict the flux distribution of Clostridium butyricum cultured in glycerol. FBA was solved using linear programming (LP) with biomass maximization as an objective function. When compared with the experimental data, FBA predicted a biomass overestimation and no PDO production  and PDO yield (YPDO/S) errors of 300% and 100%, respectively [Clostridium butyricum does not grow optimally in glycerol. This can be explained mathematically, because the objective function and all constraints  used were linear. This means that the optimum found is indeed a vertex of the feasible solution space [The constructed ectively . Therefoon space , where nClostridium sp. IBUN 13A is related to dha operon expression and the enzyme activity of both PDO dehydrogenase (EC.1.1.1.202) and glycerol dehydratase (EC.4.2.1.30), which have been experimentally detected in the presence of glycerol as main carbon source [C. butyricum to produce formic acid and hydrogen (H2) [Clostridium butyricum is an anaerobic bacterium, so according to the redox balance, the substrate must act simultaneously as an acceptor and donor of electrons [2 formation, which would require no substrate as an electron acceptor to produce reduced compounds such as PDO. In other words, in the vertex predicted by LP optimization, the substrate is used mainly as an electron donor due to the formation of formic acid and H2, and no PDO is produced.Contrary to FBA predictions, PDO production in n source , 53, 54.gen (H2) . Clostrilectrons . However2 were overproduced instead of reduced products like butanol or ethanol, which have been detected experimentally (data not shown) [Clostridium butyricum, which is capable of producing formic acid or H2. Nevertheless, LP optimization is commonly employed in solventogenic Clostridium strains, although all of them are able to produce at least hydrogen [2 secretion in LP optimization; however, no linear trend was observed, especially in H2 secretion [Similar results were observed using glucose as a substrate, where formic acid and Ht shown) . Consequhydrogen , 50, 51.ecretion .Clostridium butyricum cultured in glycerol as a mechanism to control acetyl-CoA/CoA and ATP/ADP ratios [X/S and YPDO/S errors of nearly 4.5%, and 1.5%, respectively, when compared with the experimental values obtained under limiting conditions of glycerol (<15 g/L) [2. It also suggests that Clostridium butyricum indeed minimizes enzyme usage and prefers short pathways (PDO production) to maximize its growth under limiting nutrient conditions.A new objective function of maximizing biomass yield per flux unit Equation  was therP ratios . The new<15 g/L) . TherefoIdentical phenotypic predictions were also observed using both LP and NLP optimizations when the production of hydrogen and formic acid were blocked as additional constraints (data not shown). This validates, on the one hand, the effect of these products in the lack of prediction using LP optimization. On the other hand, NLP optimization indeed predicts global optima, as suggested Schuetz et al. .X/S under glycerol-excess conditions (without reaching inhibition conditions) [Clostridium butyricum grows under sub-optimal conditions when the substrate is present in excess, as is also observed in E. coli [growth < 0). Growth Gibbs free energy can be expressed as a function of biomass yield and the Gibbs free energies for catabolism and anabolism, as shown Eq. However, the new objective function overestimated Yditions) , suggest E. coli . This bew) that minimizes both the enzyme usage and ATP production of the network , where the average experimental errors were minimal [X/S and YPDO/S errors were 5.3% and 2.5%, respectively, as shown Fig. Clostridium butyricum cultured anaerobically in glycerol; additional experimental data would validate its usage.The sub-optimal behavior was accounted for in the objective function of Eq. Equation . The ATPp to 98% , 39. On  minimal . The ave2 and less PDO than is observed under the excess condition, where ferredoxin reductase produces reducing equivalents. Consequently, Zeng quantified ferredoxin reductase directionality by calculating the ratio between hydrogen and reduced ferredoxin formed . The remaining 24 non-predicted enzymes correspond only to directionally coupled growth and most of them (21 enzymes) are involved in carbohydrate metabolism and the synthesis of nitrogenous compounds (amino acids and nucleotides). The absence of a prediction for these enzymes could be due the presence of alternate pathways and isozymes, as is the case for asparagine synthase (EC.6.3.5.4), isocitrate dehydrogenase (NADP) (EC.1.1.1.42), and glycerol-3-phosphate dehydrogenase (EC.1.1.1.94), where the alternative enzymes are asparagine synthetase (EC.6.3.1.1), isocitrate dehydrogenase (NAD) (EC.1.1.1.41), and glycerol kinase (EC.2.7.1.30), respectively. Another possible cause is the inability of FBA to predict regulation mechanisms , as is tiCbu641 was further tested by comparing the experimental and simulated data using other substrates at optimal conditions, Eq. Clostridium butyricum W5 cultured in glucose [The robustness of  glucose , as showClostridium butyricum TM-9A using different carbohydrates. Our comparison of the experimental yields with the predicted yields obtained through FBA is shown in Table X/S agree with the experimentally obtained values, showing smaller yields for pentoses and the highest yield for the trisaccharide raffinose, while the yields using monosaccharides were lower than those obtained using disaccharides. However, some differences are observed between the experimental and predicted values. First, ribose and xylose had considerably higher experimental than predicted yields. Second, the experimental yield for cellobiose was much lower than the predicted yield. Finally, although the simulations predicted the same yields for arabinose and ribose, their experimental yields differed. The first case could be a result of an incomplete curation of iCbu641 related to pentose consumption; therefore, more experimental information is needed. The second and third cases could be due to miscalculation of the experimental yields of arabinose and cellobiose, since these substrates were not consumed completely, as can be inferred from their pH reports [Clostridium was not well adapted to these substrates and may have needed to undergo more generations to reach its optimal growth [H2/S) showed experimental values that were mostly within their respective predicted feasible ranges. The only unpredicted YH2/S corresponded to arabinose, which supports the necessity of complementing iCbu641 for consumption of pentoses. Consequently, iCbu641 has the capacity to be employed to predict Clostridium butyricum growth using different carbohydrates as substrates.Junghare et al.  also eva reports . The lasl growth . The hydC. butyricum strain CWBI 1009 cultured in glucose [We also assumed a qualitative correlation between the enzyme flux and mRNA expression and compared FBA predictions and experimental transcriptomics results for the  glucose . Of the  glucose .  reduction was also predicted for the mutant strain. By contrast, the experimental reduction of hydrogen yield in the mutant was not predicted; however, this is not conclusive since the FVA ranges of the wild type and mutant strains did agree with their experimental values.Finally, the chnology  was emplPDO/S using iCbu641. The first strategy was to use ROOM to predict single and double mutants through in silico enzyme deletion. The 145 enzymes associated with reactions directionally coupled to growth at culture conditions, as reported by Comba et al. [PDO/S by up to 1% in relation to the wild type strain. One of the best mutant predicted had simultaneous deletion of lactate dehydrogenases (EC.1.1.1.27 and EC.1.1.1.28), which increased YPDO/S only to nearly 1.2% , lactate dehydrogenase (ΔldhA-508 s), and 3-hydroxybutyryl-CoA dehydrogenase (Δhbd-414 s), corresponding the lack of production of hydrogen, lactic acid, and butyric acid, respectively. Montoya [Single BUN 158B  to impro Montoya  reportedknockout is an inadequate strategy for improving PDO yields. Similar results were obtained using Optknock, with up to 3 deletions [Optknock maximum PDO yield value was 17.4% higher than the predicted value under glycerol limitation, but it was only 0.4% higher than the predicted value under glycerol excess, which reinforces that blocking reactions are useless. This can be understood by considering that PDO is a primary metabolite and its production is associated with growth [The experimental values for PDO yields agreed with the predicted range, validating the ROOM simulations. Moreover, the FVA of the wild type strain indicated a PDO maximum flux that was 11.6% higher than the flux predicted by FBA; therefore, none of the mutants would show an increase in the PDO yield greater than this value without affecting biomass yield. This validates the single and double mutant predictions and suggests that mutant elaboration by eletions , 74, wheh growth , 75.X/S and YPDO/S correlation values, indicating low correlation with the precursors  but a higher correlation with macromolecules, especially proteins . This could suggest that a low protein content in the cell could improve YX/S and reduce the YPDO/S, due their negative and positive correlations, respectively. However, the relative standard deviations obtained for YX/S and YPDO/S were 3.2% and 0.45%, respectively, meaning that the model is sufficiently stable to perturbations in biomass composition. These predictions suggest that changes in culture media aimed at modifying biomass composition and enhancing PDO yields would be unnecessary. However, modifications in the culture media could reduce PDO yield, as Dabrock et al. found using iron in excess [The second strategy evaluated was perturbation in the biomass composition by simultaneous random variation of stoichiometric coefficients of 44 precursors and 8 macromolecules. This strategy was evaluated since modifications in the culture media can affect biomass composition, such as accumulation of lipids during nitrogen starvation or protein accumulation with excess of nitrogen in the culture medium . Normal n excess .Fig. 3PePDO/S values than obtained using glycerol as single substrate [PDO/S at different glucose and glycerol uptake fluxes, as shown Fig. PDO/S = 0) in the absence of a glycerol uptake flux. The results also show the complete transformation of glycerol to PDO (YPDO/S = 1), using ratios of at least 0.375 between uptake fluxes of glucose and glycerol. Therefore, these predictions permit the proposal that co-fermentation is the best alternative for improving biomass and PDO yields. However, a priori prediction of the molar ratio between these substrates that could allow these flux ratios is difficult.The third strategy evaluated was to use two substrates simultaneously: glucose and glycerol. Glucose is used as carbon source, while glycerol is used to maintain redox balance, therefore generating higher Yubstrate . Figure iCbu641, the first curated genome-scale metabolic model for a PDO producer Clostridium strain. During iCbu641 validation, we solved flux balance analysis using LP optimization; however, according to the experimental data, the model predicted errors of nearly 300% for biomass yield and failed to predict PDO production. Therefore, NLP optimization was employed in FBA simulations, and the new objective function maximized biomass yield per flux unit [Clostridium butyricum growth and PDO production under limiting and excess glycerol conditions. Additional validations were developed using proteomics and transcriptomics data, as well data from knockout mutants, which allowed verification of the accuracy of predicting perturbations of iCbu641. All validations were completed using experimental data from different Clostridium butyricum strains and suggested that iCbu641 is an agnostic GSM model at the state steady, but the differences may be observed during dynamic predictions.We generated lux unit . The valiCbu641 allows the proposal of this GSM model for predicting dynamic cultures (i.e. batch and fed-batch fermentations) capable of increasing PDO production, thereby minimizing the need for direct experimental efforts.Subsequently, perturbations in the metabolic network and biomass composition were proposed to increase the PDO yield predictions. However, these perturbations predicted no significant increments. We also evaluated glucose-glycerol co-fermentation as a strategy to improve PDO yields. We found that a ratio of glucose and glycerol uptake fluxes greater than or equal to 0.375 would allow the complete conversion of glycerol to PDO; however, experimental analysis is needed to find the molar ratio that allows the achievement of this flux ratio. Finally, predictions of PDO production in state steady cultures using Clostridium sp. IBUN 13A, isolated and stored by the Bioprocesses and Bioprospecting Research Group from the Institute of Biotechnology of the Universidad Nacional de Colombia. This draft genome was previously sequenced and annotated and is available in GenBank with the accession no NZ_JZWG00000000.1 [Clostridium strains C. acetobutylicum [C. thermocellum ATCC 27405 [C. beijerinckii NCIMB 8052 [C. ljungdahlii ATCC 55383 [C. cellulolyticum H10 [The draft genome was obtained for the Colombian-native strain 000000.1 . The str000000.1 ; automat000000.1 . The GSMutylicum –49, C. tCC 27405 , C. beijIMB 8052 , C. ljunicum H10  were useicum H10  was usedClostridium acetobutylicum ATCC 824 by Lee et al. and are 40 mmol·ATP·g−1 and 5 mmol·ATP·g−1·h−1, respectively [−1 h−1 as initial and maximum values, respectively, and −0.0879·g·h·mmol−1 as the accumulation rate, as shown in Eq. The values for growth-associated maintenance (GAM) and non-growth–associated maintenance (NGAM) were reported for ectively . An alloectively  and Papaectively . The kinxi involved in N reactions is described in Eq. Sij is the stoichiometric coefficient of metabolite i in reaction j, and vj is the flux value in which this reaction occurs [M metabolites; however, since N > M, the prediction of fluxes vj can be achieved using FBA, which maximizes or minimizes an objective function Z , both according to the glycerol uptake flux (vGlycerol). The robustness analyses were made using different objective functions for both glycerol limited and glycerol excess conditions. The objective function employed under glycerol limitation was biomass maximization per enzyme usage. Under glycerol excess, the biomass was maximized, while both enzyme usage and ATP production were minimized, where ATP production corresponds only to thermodynamically feasible reactions able to produce ATP. According to KEGG nomenclature, these reactions are R00156, R00158, R00200, R00315, R00332, R00512, R00570, R00722, R01512, R01547, R01665, R01688, R01724, R02090, R02093, R02094, R02098, R02326, R02331, R03005, R03035, R03530, and R03920. The predicted values were compared with the experimental values reported for the Clostridium butyricum DSM 5431 strain cultured in glycerol limited and glycerol excess conditions [The experimental validation used two robustness analyses, as reported by Price et al. : the fornditions .iCbu641 and the experimental proteome of the strain Clostridium butyricum DSM 10702 cultured in glycerol [. The enzymes in the model were classified as blocked or directionally, partially or fully coupled to growth using FCF, according to the methodology reported by Burgard et al. [The prediction capability of enzyme expression was also evaluated by comparing the enzymes present in both metabolic model glycerol . The enzd et al. . BlockedClostridium butyricum strains in substrates other than glycerol, such as glucose [C. butyricum CWBI 1009, was also used for validation; this organism had been cultured in glucose using batch fermentation with uncontrolled pH. The mRNA detected in the transcriptome coded a total of 913 enzymes (532 unique and 381 redundant), where values at the exponential growth phase were used in a similar way to those from the proteomic data.Validation was also obtained using data from experimental cultures of  glucose  and othe glucose . The tra glucose  for straknockout of enzymes directionally coupled to growth. In total, 145 single mutants were evaluated. Double deletion was also studied by simultaneously blocking two enzymes, excluding enzymes previously detected as essential in the single deletion; this led to evaluation of almost 7900 double mutants.Regulatory on/off minimization (ROOM)  was empliCbu641. A total number of 10,000 simulations were made, where 965 of them were excluded because at least one of the concentrations was negative. Coefficients of correlation were calculated for biomass and PDO yields using the remaining 9035 biomass precursor combinations.We also made perturbations in the biomass composition expressed by the variation of stoichiometric coefficients of 8 macromolecules, 7 fatty acids, 20 amino acids, 8 nucleotides, 3 polar lipids, and 6 cofactors. FBA was performed using different compositions randomly generated using normal distributions with standard deviations equivalent to 30% the values used in GSM model FBA, FVA, and ROOM were computer simulated using GAMS  software V.24.2.2 r44857 for Linux. Linear and Nonlinear Programming (LP and NLP) were developed with solver CONOPT v3.15 N, and Mixed Integer Programming (MIP) was developed with solver CPLEX 12.6.0.0. Data were analyzed using Microsoft Excel® 2010.Additional file 1:iCbu641Genome Scale Metabolic Model. (XLSX 203 kb)Excel format of Additional file 2:iCbu641Genome Scale Metabolic Model. (XML 2250 kb)SBML format of Additional file 3:Proteomic and transcriptomic comparison results. (XLSX 30 kb)Additional file 4:Results of modeling scenarios with PDO yield increment. (XLSX 5507 kb)


TPC) for metabolic rate—that metabolic rate is a unimodal function of temperature often with maximal values in the biologically relevant temperature range and that activation energies are temperature dependent. We show that the temperature dependence of metabolic rate in ectotherms is well described by an enzyme‐assisted Arrhenius (EAAR) model that accounts for the temperature‐dependent contribution of enzymes to decreasing the activation energy required for reactions to occur. The model is mechanistically derived using the thermodynamic rules that govern protein stability. We contrast our model with other unimodal functions that also can be used to describe the temperature dependence of metabolic rate to show how the EAAR model provides an important advance over previous work. We fit the EAAR model to metabolic rate data for a variety of taxa to demonstrate the model's utility in describing metabolic rate TPCs while revealing significant differences in thermodynamic properties across species and acclimation temperatures. Our model advances our ability to understand the metabolic and ecological consequences of increases in the mean and variance of temperature associated with global climate change. In addition, the model suggests avenues by which organisms can acclimate and adapt to changing thermal environments. Furthermore, the parameters in the EAAR model generate links between organismal level performance and underlying molecular processes that can be tested for in future work.A mechanistic understanding of the response of metabolic rate to temperature is essential for understanding thermal ecology and metabolic adaptation. Although the Arrhenius equation has been used to describe the effects of temperature on reaction rates and metabolic traits, it does not adequately describe two aspects of the thermal performance curve ( The product kT is the average kinetic energy of the reactants, such that as temperature increases, the energy of the reactants increases, reducing the value of the exponent and raising e−Ea/kT toward 1.The Arrhenius factor varies between 0 and 1 Figure , giving Topt)  on temperature (T). Most of these models were originally developed to describe enzyme‐catalyzed reactions, rather than metabolic rate per se, but model 4 was developed to describe population growth rate and model 3 originally dealt with development rate. Nonetheless, they all have potential as descriptions of the temperature dependence of metabolic rate. All of the models begin with a monotonically increasing function of temperature, either the Eyring or the Arrhenius equation, the difference being that the Eyring model explicitly includes temperature in the constant. All of the models invoke a reduction in enzyme performance at low and/or high temperature due to the decreased probability of enzymes being in an active state. A key difference between the EAAR model and models 1‐5 is that in the EAAR model, enzymes increase reaction rates over some baseline rate, while in models 1‐5, reduced enzyme performance lowers the reaction rate from a maximal rate .A range of models have been developed to describe the dependence of a reaction rate  enzymes are inactive at high temperature, (2) enzymes are inactive at low temperature, (3) active state is given by a three‐state transition process, (4) active state is given by a protein stability process, (5) substrate supply is unlimited, (6) the proportion of enzymes that are in an active state is at equilibrium, (7) enzymes denature through time, (8) the activation energy of the catalyzed reaction is equal to the free energy of the catalyzing enzymes, (9) heat capacity is negative, (10) activation energy corresponds to maximal enzyme activity level, (11) there is no activation energy in the absence of enzymes, (12) the activation energy of the reaction is lowered as a function of the free energy of the catalyzing enzymes.H, enthalpy change of folding the enzymes, relative to a reference or melting temperature, subscripted A for active state and L for lower temperature inactive state; ΔS, entropy change of an enzyme with temperature, relative to the melting temperature, subscripted A for active state and L for lower temperature inactive state; ΔCp, the difference in heat capacity between the folded and unfolded state of the enzymes, relative to the melting temperature; Tm, melting temperature. The Schoolfield model includes three summary parameters: ρ(25°C), rate at 25°C assuming no inactivation; T1/2, the temperature at which the enzyme is half active and half inactive, subscripted L for low‐temperature inactive and H for high‐temperature inactive. The equilibrium model includes four parameters: Teq, the temperature at which the concentration of active and inactive enzymes is equal; ΔHeq, the change in enthalpy associated with the equilibrium; ΔGcat, activation energy for the reaction; and ΔGinact, activation energy for enzyme inactivation. The EAAR model introduces Eb, the baseline activation energy, the change in activation energy associated with the change in enthalpy of the catalysts (ECpΔ), and the change in activation energy associated with the change in heat capacity of the catalysts (EHΔ). The physical constants are k, Boltzmann's constant, R, the gas constant, and h, Planck's constant.The common parameters in these models are ΔA model that describes and predicts metabolic rate TPCs based on more realistic biological mechanisms is therefore urgently needed Schulte, . Here, w2Ea in the Arrhenius equation, as it is used to describe biological rates, will be set by enzymes. However, it is more precise to say that the realized Ea represents the difference between the kinetic requirements of a reaction as it would occur outside of an organism  and the enzymatic contribution (Ec) of the organism to the reaction , then, is the kinetic hurdle that remains after enzymes have done their job (Eb − Ec).The observed activation energy  and rewrite Equation Biochemical reactions within organisms require sufficient kinetic activation and the catalytic contribution of enzymes Segel, . Protein Feller, . As indiSubstituting Equation H is by definition zero at the melting point and increases below the melting point, meaning that the colder it gets, the more stable the enzyme is and the more effectively it can contribute to a reaction  and the change in activation energy associated with the change in heat capacity of the catalysts (EHΔ).The thermodynamic parameters in Equation n Figure c. ΔCp sTopt), where the top of the unimodal TPC is reached:Taking the derivative of Equation Topt through acclimation or adaptation potentially involves changes in the activation energy of the reaction as well as the thermodynamic properties of enzymes, EHΔ, ECpΔ, and Tm.This expression shows that modifying Cp—the difference in heat capacity between the folded and unfolded state of enzymes—directly affects the spread or breadth of the TPC, so one clear route to becoming a thermal generalist is to lower enzymatic ΔCp. The model predicts that lowering ΔCp not only broadens the curve, but also elevates the curve, suggesting that we might not predict a specialist—generalist trade‐off for all TPCs. Enzymes with higher ΔH are predicted to elevate the TPC due to increases in the enzyme contribution to Eb and to shift Topt to lower temperatures, while increases in Tm will lower the curve and move the Topt to the right. Any potential genetic correlations among parameters, however, could constrain the options for acclimation or evolution of the curves with changing thermal environments  acclimated to two different temperatures  using a fit of a quadratic function to the right side of the data. This step is essential because the model is defined with respect to Tm, and otherwise attempting to fit Tm in the overall fitting process can provide poor estimates of both Tm and the remaining parameters. In step (2), we fit the EAAR model to the rest of the data with the Tm set at the value identified in step (1). For each modeled data set, we also calculated the Topt using Equation Tm, and Topt.As an initial assessment of the model's ability to describe real data, we fit the model to metabolic rate TPCs for three species of amphipod , although there is some variation among taxa . The EAAR model uses the thermodynamics of protein stability to describe how enzymes increase and then decrease in effectively lowering the activation energy as temperatures rise, and the model describes well the dependence of metabolic rate on temperature for diverse organisms  for metabolic rates represents an average activation energy for the rate‐limiting enzyme‐catalyzed biochemical reactions that govern metabolism . Protein stability may be modified by extrinsic changes in pH, thermoprotectant osmolytes, protein concentration, and, in the case of membrane‐localized proteins, the membrane architecture. Additionally, a variety of stressors including temperatures near and above thermal optima activate the heat‐shock protein response  via regulation of flux in response to temperature may be a critical component of thermal responses of metabolic rate , the sharing of similar thermal dependencies of the many enzymes that underlie metabolic rate within an organism, or whether it is the average of many enzymes which share control of metabolism, each of which may differ somewhat in their thermal optima , but other parameters, such as substrate levels (A0), EHΔ, and ECpΔ were unchanged. One possibility for such changes is that acclimation of mitochondrial membranes to temperature may be a factor determining the thermal stability of the membrane‐embedded protein oxidative phosphorylation complexes, which may play a critical role in how thermal acclimation shapes TPCs for aerobic metabolic rate (Dahlhoff & Somero, In addition, the model makes useful connections between whole‐organism rates and underlying mechanisms by building on fundamental, thermodynamic aspects of all protein stability curves Feller, . Thus, oThe molecular evolution underlying divergence in intrinsic protein stability across the range of temperatures inhabited by life appears to be shaped by a common set of thermodynamic rules that govern protein folding Feller, . NonetheTm, where by definition the enzymes are no longer contributing to the reaction and the organism is near death. Above this point, however, the reactant kinetic effect of temperature is still increasing, which suggests that the remaining reactants present in an organism that is pushed above this temperature should react at a faster rate, even if the organism has died, at least until the reactants decline in availability. Surprisingly, this outcome has been observed in what is known as thermolimit respirometry, where the metabolic rate of an organism is measured as the temperature is ramped up, and an increase in the rate of metabolism is observed after the organism dies (Lighton, The right column of Figure Lighton, . AlthougLighton, .In summary, the EAAR model captures the empirical patterns and incorporates the minimum necessary processes shaping the temperature dependence of metabolic rate in a relatively simple and useful manner. It resolves long‐term problems with the Arrhenius equation and other reaction models and provides a way to move forward with temperature in metabolic ecology. In particular, the EAAR model will facilitate more comparative analyses to elucidate mechanisms involved in acclimation and adaptation to different thermal environments. Furthermore, the many biological processes that depend on metabolic rate can be understood as extensions of the EAAR process. For example, the EAAR model should apply equally well to photosynthesis, which also shows a unimodal response to temperature (Padfield, Yvon‐Durocher, Buckling, Jennings, & Yvon‐Durocher, The authors declare no conflict of interest.The data used in this article are previously published and available in the original sources. Our digitization of the data will be made available on Data Dryad upon acceptance of the manuscript.All authors were involved in the conception of the paper and contributed to the collection of data. JPD and JPG developed the model. JPD and TML analyzed the data. All authors contributed critically to the drafts and figures and gave final approval for publication. Click here for additional data file.


Mis-annotation aside, it is unclear whetherin silico reconstructions of metabolic structure fromcomponent parts accurately captures the higher levels of network organizationand flux distribution. For this approach to provide accurate predictions, onemust assume that the conservation of metabolic components leads to conservationof metabolic network architecture and function. This assumption has not beenrigorously tested. Here we describe the implications of a recent study : e01840-15), which demonstrated that conservation of metabolic componentswas not sufficient to predict network structure and function.For decades, experimental work has laid the foundation for our understanding ofthe linear and branched pathways that are integrated to form the metabolicnetworks on which life is built. Genetic and biochemical approaches applied inmodel organisms generate empirical data that correlate genes, gene products andtheir biological activities. In the post-genomic era, these results have servedas the basis for the genome annotation that is routinely used to infer themetabolic capabilities of an organism and mathematically model the presumedmetabolic network structure. At large, genome annotation and metabolic networkreconstructions have demystified genomic content of non-culturablemicroorganisms and allowed researchers to explore the breadth of metabolisms Salmonellaenterica has served as a model system to probe metabolic integration anddefine network architecture in vivo. When this system is constrained,it is highly sensitive to slight changes in the metabolic network, and subtle changes incarbon flux can be monitored using growth analyses. A large part of our work has focusedon defining metabolic redundancy and recruited pathways that can produce the firstshared purine/thiamine synthesis intermediate, phosphoribosylamine (PRA). PRA issynthesized by phosphoribosylpyrophosphate amidotransferase (PurF)  and in apurF mutant, six alternative mechanisms for synthesizing PRAsufficient for thiamine synthesis have been defined experimentally. As PurF is feedbackinhibited by purines, bypassing PurF with alternative or recruited pathways woulddecouple thiamine synthesis from regulation by purines. Such a scenario is significantwhen the natural habitat of S. enterica is expected to have substantiallevels of purines due to lysed cells and degraded DNA. However, the extent to whichthese alternative pathways contribute to thiamine synthesis in wild type S.enterica has remained elusive. The following fundamental questions aroseduring the course of the aforementioned studies: i) are metabolic network structuresdissected by mutational analysis biologically relevant? ii) if metabolisms containidentical components, is the network structure and function predetermined? In otherwords, does the conservation of metabolic components demand the conservation of thenetwork? To begin to address these questions we took a comparative approach and queriedthe metabolic network surrounding PRA synthesis in Escherichia coli, aclose relative of S. enterica with conserved metabolic pathways andregulatory paradigms. Importantly, all metabolic components relevant for PRA synthesisin S. enterica are present and are > 95 % identical in E.coli.Biosynthesis of the coenzyme thiamine pyrophosphate (TPP) in S. enterica and E. coli were recently reportedin mBio : e01840-15) and are summarized and expanded here. As expected,deletion of purF in either E. coli or S.enterica results in a requirement for exogenous purines for growth.However, the purF mutants of E. coli and S.enterica differ in their ability to synthesize thiamine. Both organismsmaintain thiamine synthesis due to non-enzymatic formation of PRA fromribose-5-phosphate (oxidative pentose phosphate pathway) and ammonia. When thenon-enzymatic mechanism is eliminated, E. coli retains PRA synthesis,while growth of S. enterica becomes dependent on exogenous thiamine.Further experimentation showed that E. coli utilizes an unusual pathwaystitched together from isoleucine and tryptophan biosynthetic enzymes. We learned thatin E. coli, threonine is converted to 2-aminocrotonate (2-AC) byserine/threonine dehydratase , which is then condensedwith phosphoribosylpyrophosphate by anthranilate synthase component II  to form PRA . Importantly, results of labeling studies([15N]-threonine) showed that, in E. coli, IvA/TrpD-dependent synthesiscontributes significantly (~ 35 %) to the thiamine pool in a wild type strain.Therefore, the pathway described for canonical thiamine synthesis contributes littlemore than half of the cell’s total thiamine under some growth conditions. This findingwas unexpected since it was not apparent from the knowledge of metabolic componentspresent. This work demonstrated that S. enterica and E.coli do not use the same set of pathways to synthesize thiamine, andhighlighted the fact that there is something fundamentally different about the networkdeterminants of the two organisms. We can then conclude that even in closely relatedorganisms, conserved metabolic enzymes do not guarantee conserved structure and functionof the metabolic network.Our initial results from a study to address the conservation of metabolic structurebetween S.enterica as a pathway activated by a suppressor mutation(ridA) in a purF strain. ridAencodes the reactive intermediate deaminase, RidA, a universally conserved metabolicstress protein. RidA protects critical PLP enzymes  by quenching the reactive enamine 2-aminoacrylate (2-AA)generated by other PLP enzymes such as IlvA (when serine is the substrate). Thethreonine-derived product of IlvA, 2-AC, that is utilized by the IvA/TrpD-dependent PRAbiosynthetic pathway is also a substrate of RidA . The fact that this pathwayis active in wild type E. coli, but must be activated by aridA lesion in S. enterica, suggests that 2-ACdoes not accumulate in S. enterica because of the presence of RidA.Then the question is, why does 2-AC accumulate in E. coli, which alsohas a functional RidA? In other experiments we have shown that diverse phenotypes causedby 2-AA damage in a S. enterica ridA strain are not observed in anE. coli ridA strain (unpublished data). Together our observationssuggest that wild type E. coli makes more 2-AC and less 2-AA thanS. enterica, implicating IlvA activity as the key difference. Wehypothesize that a metabolite balance  is responsible for the multiple phenotypic differences  between the two organisms. Calculations of kinetic parameters suggestthis is a feasible explanation. Advantageously, we have the genetic tools to manipulateboth E. coli and S. enterica. Future efforts willattempt to “switch networks”, that is, convert the E. coli network intothe S. enterica network (with respect to PRA synthesis) and viceversa.The IvA/TrpD-dependent pathway for PRA synthesis was first identified in A natural extension of metabolic studies is the implementation of mathematical models tocapture the inherent complexity of biological systems. One of the current challenges inthis effort is to move beyond a focus on high-flux metabolic pathways and incorporatethe subtle intricacies of a metabolic network into a series of mathematical models withincreasing validity. These intricacies are often responsible for the plasticity that ischaracteristic of metabolic networks, and they are critical for the responsiveness anetwork has to perturbations by external and internal signals. To accurately predict thephenotypes we observe, a productive modeling approach has to be rigorously applied to asmall-scale network. Toward this end, in collaboration with Eberhard Voit and colleagues(Georgia Tech), we are developing the metabolic node that includes the purine, histidineand TPP biosynthetic pathways into a single system that can be experimentally andtheoretically queried. This node is composed of low and high flux pathways and extensivepoints of metabolic crosstalk. We envision developing the purine/histidine/TPP node ofmetabolism as a model system to integrate mathematical modeling, quantitative metabolitemeasurements and experimental approaches that will uncover fundamental properties of themetabolic network. The integration of experimental and theoretical approaches plannedmay provide dynamic models to address critical questions at the interface of thephysical and biological sciences. We expect to pinpoint network behaviors with a levelof detail that is not yet possible for a metabolic system at a whole-cell level.E. coli was originally characterized in mutant analysis ofS. enterica, a strategy that is sometimes dismissed as lackingphysiological relevance. The biochemical and genetic characterization of this pathwayidentified hallmark behaviors that were easily detected in E. coli andled to the quick identification of the relevant pathway. The resultant metabolicinsights, that transcend the organism of discovery, underscores that the role of geneticanalysis of mutants is to better understand wild type cell behavior and uncovermetabolic paradigms. The most dramatic point made by this work is the recognition thatmetabolisms that contain the same components do not necessarily configure them the sameway. This study emphasized the value in going beyond the cataloging of component partsas we strive to understand network structure, and the critical role that experimentalapproaches still have in deciphering cellular metabolism.The IlvA/TrpD-dependent PRA pathway that contributes to TPP biosynthesis in wild type