Metabolomics can be applied for comparative and quantitative analyses of the metabolic changes induced by microorganisms during fermentation. In particular, mass spectrometry (MS) is a powerful tool for metabolomics that is widely used for elucidating biomarkers and patterns of metabolic changes. Fermentation involves the production of volatile metabolites via diverse and complex metabolic pathways by the activities of microbial enzymes. These metabolites can greatly affect the organoleptic properties of fermented foods. This review provides an overview of the MS-based metabolomics techniques applied in studies of fermented foods, and the major metabolic pathways and metabolites  derived from their metabolism. In addition, we suggest an efficient tool for understanding the metabolic patterns and for identifying novel markers in fermented foods. Omics tools can be used as a platform to provide strategies for controlling and changing the qualities of fermented foods. The various types of omics can be divided according to the target compounds, such as genes (genomics), mRNA (transcriptomics), proteins (proteomics), and metabolites (metabolomics). In particular, metabolomics is a comprehensive and quantitative approach for determining dynamic metabolic changes, being a powerful tool that can be efficiently applied in diverse scientific fields, such as food science, biochemistry, and drug discovery , steaming step (1 day), drying (2 days), meju fermentation , brining , and aging (81 and 141 days). Metabolic data sets obtained from GC-time of flight (TOF)/MS and ultra-performance liquid chromatography (UPLC)-TOF/MS indicated the major metabolic changes associated with each process. A metabolomics approach can also be used evaluate the metabolic activity, which is related to the levels of specific metabolites produced. For example, knowledge of the profiles of metabolites produced during fermentation could be useful when attempting to enhance the functional properties of cheese. , and stir bar sorptive extraction (SBSE)] and solvent based extractions [simultaneous distillation extraction (SDE) and solvent-assisted flavor evaporation (SAFE)]. Solvent-based extraction can require further sample preparation, such as solid phase extraction (SPE), solvent evaporation, and chemical derivatization, in order to optimize them for instrumental analytical techniques.Metabolomics data sets are commonly very large, and so diverse data-mining analysis techniques such as, principle component analysis (PCA), partial least squares (PLS), PLS- discriminant analysis (PLS-DA), and orthogonal projection to latent structures (OPLS), are often used to extract relevant information. Applying such statistical data-mining analysis methods in metabolomics research can identify treatment differences or patterns in large data sets.  can provide a global view of the metabolism and a list of the involved pathways  and the synthesis of micromolecules (e.g. volatile metabolites) by microorganisms. The microbial metabolic processes that occur during fermentation include a series of catabolism and anabolism steps involving the breaking down and synthesis of diverse metabolites. In the primary stage of fermentation, microorganisms grow rapidly on the surfaces of surrounding ingredients and usually make some metabolites associated with the growth phase, such as the synthesis of DNA, RNA, and vitamins, the degradation of macromolecular compounds, , and the generation of energy  for their survival  related to other metabolic pathways . Lactic acid fermentation is the simplest type of fermentation, which involves the production of lactic acid from pyruvate. Lactic acid can influence the flavor of fermented foods by the production of acids and the lowering of pH, which increases sourness  is mainly observed in the fermentation of certain microorganisms, such as Amino acids are common precursors involved in the production of higher alcohols  as well as sulfur- and nitrogen-containing volatile metabolites. The Ehrlich pathway is the main biological catabolism process involving branched-chain amino acids , aromatic amino acids , and sulfur-containing amino acids (cysteine and methionine), leading to the formation of fusel aldehydes, alcohols, acids, and esters. The Ehrlich pathway comprises three stages: (i) transamination, (ii) decarboxylation, and (iii) oxidation/reduction Fig. . In the Cheonggukjang   aliphatic aldehydes, acids, alcohols, and esters can be generated by the degradation of amino acids via the Ehrlich pathway as well as the degradation of fatty acids.  and different degrees of unsaturation  , and lactones. Fatty acids-derived volatiles are mainly generated from β-oxidation or lipoxygenation of fatty acids  in synthetic must. They compared transcriptome and flavor-active metabolite profiles, and some of the differentially expressed genes appeared to respond to chemical changes during fermentation. The up- and down-regulated genes were also determined, and the impacts on fermentation kinetics associated with the produced flavors and aromas were explained. Afshari et al.  (Fondi and Liò, i et al.  investigi et al. .In general, the connection between gene expression and produced metabolites is estimated based on hypothesized cause-and-effect relationships. However, this approach can be challenging when interpreting data obtained using different technologies. Fondi and Liò  proposed


Streptomyces xiamenensis. To fulfil the requirements of pharmaceutical investigations, a high production of xiamenmycin is needed. In this study,, the authors present a kinetic metabolic model to evaluate fluxes in an engineered Streptomyces lividans with xiamenmycin‐oriented genetic modification based on generic enzymatic rate equations and stability constraints. Lyapunov function was used for a viability optimisation. From their kinetic model, the flux distributions for the engineered S. lividans fed on glucose and glycerol as carbon sources were calculated. They found that if the bacterium can utilise glucose simultaneously with glycerol, xiamenmycin production can be enhanced by 40% theoretically, while maintaining the same growth rate. Glycerol may increase the flux for phosphoenolpyruvate synthesis without interfering citric acid cycle. They therefore believe this study demonstrates a possible new direction for bioengineering of S. lividans.Xiamenmycins, a series of prenylated benzopyran compounds with anti‐fibrotic bioactivities, were isolated from a mangrove‐derived  Streptomyces xiamenensis [. Streptomyces are well‐known microbial cell factory for bioactive secondary metabolites based on various biosynthetic pathways [Xiamenmycins, a series of prenylated benzopyran compounds, were isolated from a mangrove‐derived menensis –3. Streppathways . The natpathways , anti‐hepathways , and antpathways . It is rpathways –3. Sincepathways , 9. Thusin silico model which can guide the enhancement of production. In this paper, we present a kinetic model for benzopyran production in Streptomyces.It is well known that the production level of most secondary metabolites is always too low to satisfy the industrial production . To fulfin silico works on metabolic network modelling based on flux balance analysis (FBA) have been applied to the bacteria aiming for strain improvement with desired properties [Streptomyces. We use a new kinetic metabolic modelling approach in the present paper [Some operties –12. Althnt paper , 13.in vivo and predict the flux in various circumstances. Most importantly, it tests the time‐dependent dynamics of metabolites against the steady solutions obtained in the modelling. Traditionally, kinetic modelling is hindered by the numerous unknown enzymatic parameters. In this paper, we have employed two methods to overcome the main obstacles. We first use generic enzymatic rate equation which standardises and reduces the parameters needed to construct a model. We then further imposed on the metabolic network a stability requirement by introducing regulations on the reaction parameters. The metabolic network is thus regulated in such a way that it adjusts to a set of parameters that guarantee its stability.Kinetic modelling of metabolic network is a potential useful tool to simulate the biological processes Streptomyces lividans with glucose feed that are not only stable against metabolic fluctuations but show a reasonable amount of xiamenmycin. To further verify the in silico solution, we also simulated the strain growing on a combination of glucose and glycerol media. We found that xiamenmycin production rate is significantly higher in the combination, which is consistent with experiments.We are able to successfully obtain a set of parameters for genetically engineered S. lividans with xiamenmycin‐oriented genetic modification aiming to enhance xiamenmycin production.The links between primary and secondary metabolisms in the biosynthesis can be explored. Phosphoenolpyruvate (PEP) is the key intermediate supporting xiamenmycin biosynthesis because the flux increases of PEP synthesis from 2‐phosphoglycerate (2‐PG) associates with the output flux of xiamenmycin. Adding glycerol as an extra carbon source is predicted to enhance xiamenmycin production. Calculations show glycerol may provide another carbon source for PEP without interfering TCA cycle. The framework established in this paper sets the foundation for more difficult tasks in the research. It can provide a blue print and ways to evaluate engineered Streptomyces is known for producing novel secondary metabolites and for highly effective processing of bioactive compounds. Xiamenmycin is one of the leading anti‐fibrotic compounds isolated from S. xiamenensis [Xim A–E [menensis , 15. The[Xim A–E . It was [Xim A–E . The linOur purpose is to understand the bioprocess of secondary metabolites and provide guidance for optimising the production of xiamenmycin biosynthesis including the flux distribution and identification of the key reactions. From our kinetic simulation, the flux distributions feed on various carbon sources were predicted Table  and the Streptomyces metabolism which can support the fastest growth rate for S. lividans [in silico since S. xiamenesis also contained the glpCABX genes for glycerol utilisation. Thus, glycerol may serve as another carbon source when we try to improve the compositions of medium. We simulated the flux distribution when growing on mixture carbon sources A1+Aeactions , 21, 22.f1 and f2 have the following properties, see (VF and VB), and the Michaelis–Menten‐like parameters (iK).A generic enzymatic rate equation can be written in the general form of (2)uAi,ies, see –5)(3)(3)(2)We introduce a mathematic method to stabilise a dynamic network with a simple and straight forward form of regulation constructed based on Lyapunov function derived from stochastic dynamics, see supplementary material II.N metabolites whose dynamics can be described by dxdtboundary . We usedptomyces .W is a positive‐definite modulation matrix and φ is a Lyapunov function for the metabolites dynamical network [Vf and Vb [ψ, in which S scales inversely with diffusion matrix D. In our calculation, we assumed a simple diagonal form of D and S, by assuming smaller metabolite compounds having bigger D, inversely linked to the number of carbon chain. We used Vf = 0.4, Vb = 0.4 as initial values. In this range, different initial values result in slightly output fluxes of slightly different carbon efficiencies. In  for calculation represented in Table We found that the regulatory dynamics, as given by  and 8)8)7)W network . Here W network , 22. TheW networ and Vb , 22. ThiVf and Vb for reactions were optimised by calculations using ,,Vf and in silico that a significant improvement on the production of xiamenmycin can be obtained when adding glycerol feed as an additional carbon source. The flux distributions of genetically engineered S. lividans were calculated. In addition, our modelling offers a practical approach to deal with unavailable kinetic parameters for metabolic network modelling.The primary focus of metabolic engineering is on enhancement of productions. On the basis of an optimised kinetic metabolic modelling, we demonstrate


Escherichia coli (eciML1515) by directly adding a total enzyme amount constraint in the latest version of GEM for E. coli (iML1515), considering the protein subunit composition in the reaction, and automated calibration of enzyme kinetic parameters. Using eciML1515, we predicted the overflow metabolism of E. coli and revealed that redox balance was the key reason for the difference between E. coli and Saccharomyces cerevisiae in overflow metabolism. The growth rate predictions on 24 single-carbon sources were improved significantly when compared with other enzyme-constrained models of E. coli. Finally, we revealed the tradeoff between enzyme usage efficiency and biomass yield by exploring the metabolic behaviours under different substrate consumption rates. Enzyme-constrained models can improve simulation accuracy and thus can predict cellular phenotypes under various genetic perturbations more precisely, providing reliable guidance for metabolic engineering.Genome-scale metabolic models (GEMs) have been widely used for the phenotypic prediction of microorganisms. However, the lack of other constraints in the stoichiometric model often leads to a large metabolic solution space being inaccessible. Inspired by previous studies that take an allocation of macromolecule resources into account, we developed a simplified Python-based workflow for constructing enzymatic constrained metabolic network model (ECMpy) and constructed an enzyme-constrained model for  Accurate prediction of metabolic phenotypes of an organism is a key goal of computational biology and has attracted more and more attention from researchers. For this purpose, many genome-scale metabolic models have been developed ,2 and suE. coli [S. cerevisiae using GECKO and made an accurate prediction of several metabolic phenotypes [S. cerevisiae [, Bacillus subtilis [Bacillus coagulans [E. coli [Streptomyces coelicolor [In recent years, researchers proposed several new methods that introduced new constraints such as cell volume limitation , proteinE. coli . Adadi eE. coli . In 2017E. coli . They deenotypes . Howeverrevisiae , Bacillusubtilis , Bacilluoagulans , E. colielicolor , which helicolor ,20,21.E. coli (eciML1515) based on its latest metabolic model iML1515 [iML1515 could simulate the sub-optimal metabolism such as overflow metabolism and the maximal growth rates under different carbon sources. The whole process for model construction and simulation is available at GitHub  for users to easily reproduce the results and use it as a reference to build enzyme-constrained models for other organisms.In the current study, we propose a simpler workflow called ECMpy by explicitly introducing an enzyme constraint without modifying existing metabolic reactions or adding new reactions. Using ECMpy workflow, we constructed a high-quality enzyme-constrained model for  iML1515 , high co iML1515 , and autiML1515 model in this study) was used as the initial model for the construction of enzyme-constrained models according to the workflow shown in catk values. The stoichiometric constraints (Equation (1)) and reversibility constraints (Equation (2)) used were the same as in flux balance analysis [ptot and f represent the total protein fraction in E. coli and the mass fraction of enzymes, respectively. The enzyme mass fraction f was calculated based on Equation (4) where iA and jA represented the abundances (mole ratio) of the i-th protein (p_num represented proteins expressed in the model) and j-th protein (g_num represented proteins expressed in the whole proteome). iMW and catki, were molecular weight and turnover number of an enzyme catalyzing reaction i. For reactions catalyzed by multiple isoenzymes, a reaction can be split into multiple reactions. For reactions catalyzed by enzyme complex, using the minimum value of protein in complex (m is the number of proteins in complex). i-th enzyme.A metabolic network , similar to the way in GECKO and AutoPACMEN [13C flux consistency) to adjust the original catk values, as follows: First, a reaction with an enzyme usage exceeding 1% of the total enzyme content requires parameter correction; Second, a reaction with the catk multiplied by 10% of the total enzyme amount (13C experiment needs to be corrected. All the catk data used for correction comes from BRaunschweig ENzyme DAta base (BRENDA) and System for the Analysis of Biochemical Pathways - Reaction Kinetics databases (SABIO-RK) .Generally, enzyme-constrained models need model validation  format, as the Systems Biology Markup Language (SBML) format cannot save enzyme constraints due to COBRApy  limitatiiML1515′s ability to predict growth rates, we compared the predicted results of iML1515 and eciML1515 with experimental results performed by Adadi et al. [E. coli’s growth rates on 24 single carbon sources . For comparison of each method on 24 single carbon sources, the model and experimental results were used to calculate the estimation error of the growth rate (Equation (5)) [To evaluate ecion (5))  and normion (5)) .(5)estiE. coli. Especially, the growth rate is fixed (from 0.1 h−1 to 0.65 h−1) and glucose is supplied infinitely. Besides, we calculated the reaction enzyme cost (Equation (7)), energy synthesis enzyme cost (Equation (8)) and oxidative phosphorylation ratio (Equation (9)) to explore the adjustment strategy of E. coli’s overflow metabolic pathway.In addition to the maximal growth rates under different carbon sources, we also explored the overflow metabolic behaviours of To obtain the trade-off between yield (ous FBA) . When siiML1515 model was used as the initial model for the construction of the enzyme-constrained model. During the process, we observed that some errors in iML1515  and corrected them based on information from the Encyclopedia of Escherichia coli genes and metabolism database (EcoCyc) [iML1515 into two irreversible reactions and split reactions catalyzed by multiple isoenzymes into different reactions . We found that the subunit composition of different proteins in E. coli differed significantly (iML1515 were obtained from EcoCyc. GECKO and sMOMENT (AutoPACMEN for E. coli) used the in vitro catk which was obtained in labour-intensive, low-throughput in vitro assays and resulted in only a small fraction of cellular enzymes having a measured catk even in model organisms [catk values derived from machine learning methods performed by Heckmann et al. [catk values were assigned to 2432 enzymatic reactions, and the coverage exceeds 60% , which is larger than the GECKO and sMOMENT (the number of reactions that matched EC number and substrate at the same time was only about 387). The protein fraction ptot was set at 0.56 g gDW−1 based on the experimentally measured macromolecular composition of E. coli cells [E. coli protein abundance values were obtained from the Protein abundance database (PAXdb)  [f was calculated to be 0.406 g enzyme/g protein.The (EcoCyc)    and the −1, but the conversion of phosphoenolpyruvate to the TCA pathway was still abnormal  is low, which is mainly caused by the subunit composition of these two reactions is complicated and the protein molecular weight is very large. After calibration using 13C data . As shown in iML1515 model  in addition to acetate could also be produced at the maximal growth rates. The predicted results were in good agreement with previously reported experimental results [iML1515 (the substrate uptake rates were set as the same as those for eciML1515) were significantly higher than the measured values  from eciML1515 were closer to (estimation error is 0.01 and 0.03) experimental values than those from the iML1515 model. In a stoichiometric model such as iML1515, the substrate uptake rate needs to be preset to calculate the growth rate and there is a linear relationship between the growth rate and substrate consumption rate. Whereas in the enzyme-constrained model, the maximal growth rate is limited by enzyme resources and thus there is no need to preset a substrate consumption rate. This means that at the maximal growth rate, a considerable quantity of substrates was utilized through the fermentation pathways with the secretion of fermentation products. Therefore, the predicted growth rates from the enzyme-constrained model were significantly lower than those from iML1515 but much closer to the experimental findings. One exception for acetate as the carbon source is that the predicted results were the same for both models as no acetate producing fermentation pathway was activated in this case. From the results shown in catk values of enzymes in the uptake pathways of these two substrates may be underestimated. Besides, we found that ECMpy is better than GECKO and sMOMENT for the simulation of growth rate on 24 different carbon sources , and the simulation results of all enzyme-constrained models are also better than non-enzyme-constrained models (We simulated the maximum growth rates of  results  as shownd models a–d. ThisE. coli at different substrate (glucose as an example) uptake rates. As shown in E. coli ME-model [In addition to the maximal growth rates under different carbon sources, we also explored the metabolic behaviours of ME-model , indicatiML1515 for E. coli using the simplified Python-based ECMpy workflow. The new model was validated with various experimental data from literature including metabolic overflow data and the growth rates under different carbon sources. The prediction results were better than GECKO and sMOMENT, and those enzyme-constrained models were also better than the original iML1515, indicating in these conditions enzyme availability rather than network stoichiometry is the key constraint. The enzyme-constrained model also showed a clear trade-off between biomass yield and enzyme usage efficiency. Switching from a high yield pathway to a high-rate pathway could be a general principle in metabolic regulation. This provides new insight into engineering organisms for the production of valuable biochemicals. In organisms using a high yield and high enzyme cost biosynthesis pathway, improving enzyme-specific activity could be more effective than enzyme overexpression.We constructed a genome-scale enzyme-constrained model ecE. coli enzyme constraint model (using GECKO or sMOMENT), which set the number of each of the protein subunits to one, we defined the number of subunits for each protein in detail based on the EcoCyc. For example, pyruvate dehydrogenase consists of three subunits, AceE, AceF and Lpd, and its molecular weight is about 216.43 kD if the number of subunits is 1:1:1. However, the true number of subunits is 24:24:12 in EcoCyc, which means that the final molecular weight is 4586.16 kD. The large difference between the molecular weight of the same reaction would certainly cause a big difference in the flux results. The whole model construction and simulation processes were written in Jupyter Notebook files available from GitHub. This enables people from anywhere to reproduce the work and construct their enzyme constrained models for other organisms.Different from GECKO and sMOMENT, our method for enzyme constrained model construction just adds a constraint on the total amount of enzyme does not need to modify the reaction equations  and introduce over a thousand new enzyme exchange reactions (like GECKO). This greatly reduces the complexity in model construction and the model can be solved using COBRApy or other freely available python packages for constrained optimization. Besides, compared to the existing E. coli, the enzyme kinetic data coverage is low in databases such as BRENDA and kinetic parameters from different researchers are often inconsistent. In this study, we make use of the predicted data from machine learning [catk values to some extent to improve the agreement of model predictions with experimental data [catk adjustment and automated catk calibration, and there are some unreasonable places, such as the manual correction is simply expanded by 10 times or reduced by 10 times. In recently, GECKO 2.0  provided an automatic procedure, in which the top enzymatic limitation on growth rate is identified and its correspondent catk is then iteratively replaced by the highest one available in BRENDA for the given enzyme class until the growth rate fit is normal [13C flux consistency, see method) to update the catk for a small number of reactions to achieve a better growth rate fit. This new calibration process will facilitate the construction of high-quality enzyme constraint models.As we have shown that the quality of the enzyme constrained model depended largely on the quantity and accuracy of enzyme parameters. Even for learning  to improtal data . A systetal data , which hs normal . CurrentThe ECMpy also has some areas that need improvement. First, ECMpy currently obtains protein subunit composition data manually, while a large amount of protein composition data are distributed in databases, such as BioCyc , UniprotiML1515 for E. coli. By introducing the enzyme constraints, the model can predict the overflow metabolism and growth under different carbon sources more precisely than the stoichiometric model iML1515. The construction method can be applied to construct enzyme constrained models for other organisms and the optimization framework can be extended to integrate other constraints such as thermodynamic feasibility to further reduce the solution space and subsequently improve model prediction accuracy.We presented ECMpy, a simple open-source Python-based workflow, for constructing enzyme-constrained models based on enzyme kinetic parameters and proteomics data. Using this method, we constructed an enzyme constrained model ec


This technical note addresses the need to consider uncertainties when using experimental procedures to extract a geometry that is consequently used for computational simulations. Many uncertainties enter the process in both the experimental and computational techniques.Imaging subject-specific heart valve, a crucial step to its design, has experimental variables that if unaccounted for, may lead to erroneous computational analysis and geometric errors of the resulting model. Preparation methods are developed to mitigate some sources of the geometric error. However, the resulting 3D geometry often does not retain the original dimensions before excision. Inverse fluid–structure interaction analysis is used to analyze the resulting geometry and to assess the valve’s closure. Based on the resulting closure, it is determined if the geometry used can yield realistic results. If full closure is not reached, the geometry is adjusted adequately until closure is observed. Leonardo da Vinci’s later work (≈1506 until his death in 1519) encompasses studies on the heart (among other organs) from the perspective of an architect–engineer and is permeated with recognition as to how mechanics relate to human pathology. Half a millennium later, with the progress of scientific research and development in the field of mechanics, we enjoy new ways to study how mechanics relate to human pathology. Moreover, the urgency to continue exploring the mechanics of heart valves and new products and procedures related to their repair/replacement continues to be relevant. Artificial heart valves and their delivery systems are so complex that they often culminate in subsequent recalls of the related products . The useThe computational assessments of these systems are associated with their own set of challenges . For exaμCT) and assumes that a geometric error occurs in the resulting 3D model acquired from the medical images. For example, as described in [This study uses a heart valve (HV) scanned with micro-computed tomography  approach [The computational platform for establishing HV geometry is based on approach . The folTo develop a “valve-specific” geometry for the FSI simulation of the heart valve, a locally sourced ovine mitral valve is obtained to avoid rigor mortis. The process of model development includes: (1) CT scanning, (2) image processing to develop a 3D model, and (3) high quality, robust mesh generation . As explSeveral approaches can be adopted to simulate the HV function using FSI. In this study, an approach based on smoothed particle hydrodynamics (SPH) is adopted, i.e., the fluid domain is modeled as a collection of discrete particles . The flu® while large deformation in the solid domain, i.e., the HV, is simultaneously solved with the IMPETUS Afea Solver®. Both the solvers use GPU parallel processing. The contact, i.e., particle to structure contact, is very simple, which is why SPH is ideal for these complex applications. It can easily account for movement in any direction, unlike finite element fluid solvers, which involve more complicated contact and usually require re-meshing of the fluid domain during the simulation. The ability of IMPETUS to achieve a very high resolution in terms of particle density results in a very accurate particle to structure contact, especially in regards to a structure as detailed and complex as MV.The combination of SPH methods (used to simulate the fluid domain flow) with a high-order finite element method (used to simulate the solid domain deformations) is ideal for simulating FSI when complex geometries are included . Using SμCT imaging, the “bunching” effect can be observed.As mentioned above, one of the many uncertainties to consider, the “bunching” effect of leaflets and chordae tendineae, happens when the excised HV specimen is mounted onto the annulus plate of pulsatile CLHS . PapillaμCT dataset are used to develop the “valve-specific” geometry, it has to be confirmed how effective these in vitro preparation methods are. However, the “bunching” effect is just one of many uncertainties to consider, many of which are unknown and, therefore, impossible to address using preparation methods.The “bunching” effect can be partially counteracted by using appropriate fixation techniques and preparation methods. Even then, after the medical images from the Confirming the effectiveness of preparation methods used can be done in silico by performing an FSI simulation of the HV closure. Suppose the HV closure cannot be reached computationally. In that case, it is assumed that the preparation methods did not effectively counteract the uncertainties and the 3D model needs to be adjusted to further account for the discrepancies between the experimental and computational procedures. In this study, the model is elongated in the z-direction, and multiple FSI simulations are performed until the HV closure is observed and validated.μCT imaging, many uncertainties can occur during the exposure to air. Consequently, the original model developed directly from the μCT dataset cannot achieve closure, and a large non-zero regurgitant orifice area (ROA) can be seen . Even when approved, the number of recalls is increasing. Hence, developing well-validated computational (in silico) testing that assists in the development of novel medical devices is desirable. More effective medical devices yield improved patient quality of life and ultimately decreased cost of treatment.μCT), it is confirmed that, for this specific specimen and methods used, the 30% elongation of the original model  represents more realistic HV dimensions. This computational platform has been previously validated and used in several of our studies. Our group has studied the mitral valve function in both healthy [When HV is excised from the heart for further processing, it no longer possesses its properties compared to when it is in a living, beating heart.  The tissue of HV is susceptible and quickly suffers changes when not submerged in a liquid. For example, it is known that HV tissue experiences the “bunching” effect when exposed to air, causing leaflets to appear smaller and thicker while chordae tendineae appear bulkier with minimal branching. In addition to the changes in the tissue when exposed to air, many more uncertainties enter the process from excision to securing a realistic 3D model used for predictive simulations. Even when the same dataset is used, different users will produce differing geometries . When ex healthy ,8,11 and healthy ,15,16. O healthy .In most cases, especially when the geometry being extracted  is complex, in vitro and in silico procedures are accompanied with uncertainties. The entire process includes many experimental and numerical procedures, and every step introduces uncertainty. These uncertainties need to be carefully balanced to ensure that the resulting geometry and, consequently, the results of the computational simulations are realistic. In this study, with the procedures as described, elongation was used as the factor which, when adjusted, leads to more realistic geometry with HV closure validated against experimental data. However, depending on the procedures used in vitro and in silico, other factors might have to be considered. For example, the fixation techniques to prevent the “bunching” effect need to be studied to confirm their efficiency. On the in silico side, our choice of numerical algorithms used affects the resulting geometry. There is more work to be done exploring these uncertainties.


Metabolomics has been applied to measure the dynamic metabolic responses, to understand the systematic biological networks, to reveal the potential genetic architecture, etc., for human diseases and livestock traits. For example, the current published results include the detected relevant candidate metabolites, identified metabolic pathways, potential systematic networks, etc., for different cattle traits that can be applied for further metabolomic and integrated omics studies. Therefore, summarizing the applications of metabolomics for economic traits is required in cattle. We here provide a comprehensive review about metabolomic analysis and its integration with other omics in five aspects: (1) characterization of the metabolomic profile of cattle; (2) metabolomic applications in cattle; (3) integrated metabolomic analysis with other omics; (4) methods and tools in metabolomic analysis; and (5) further potentialities. The review aims to investigate the existing metabolomic studies by highlighting the results in cattle, integrated with other omics studies, to understand the metabolic mechanisms underlying the economic traits and to provide useful information for further research and practical breeding programs in cattle. The omics, such as genomics, transcriptomics, epigenomics, proteomics and metabolomics, have emerged, whereas the terms genome, transcriptome, epigenome, proteome and metabolome are used to address the objects of such studies, respectively ,2,3,4,5.Currently, the applications of metabolomics have increased to measure metabolic responses dynamically, identify biologically relevant candidate metabolic markers, reveal potential genetic architecture and understand the systematic networks underlying the economic traits for cattle ,11,12,13Given the previous findings in different traits , it is essential to summarize the major results of metabolomic analysis for further research and applications in cattle, as well further ingratiation analysis with other omics. Therefore, this review aims to investigate the existing metabolomic studies by highlighting the results from five aspects in cattle, integrated by other omics studies, e.g., genomics, transcriptomics, epigenomics, microbiomics, etc., to understand the metabolic mechanisms underlying the economic traits in cattle and to provide useful information for further cattle research and practical breeding programs.The diversities of metabolome characterization occurring in cattle depend on the different breeds, traits, tissues, times, etc. To generate a better understanding of the underlying metabolic mechanisms in cattle, candidate metabolic biomarkers for various tissues and their enriched metabolic pathways are summarized in this review for important economic traits, such as feed efficiency and disease.Based on previous studies, we found that researchers investigated the metabolomics of plasma, serum, milk, rumen fluid for feed efficiency, body performance, disease, etc., traits in cattle . Feed efMetabolic disease is another important trait that affects efficient cattle production, where metabolomic applications are helping to understand the mechanisms and define the predictive metabolic biomarkers for incident diseases . Many meMetaboAnalyst software (version 5.0) [Bos taurus library were also realized to show the relative betweenness centrality against pathway impact value. The results showed that nine significantly metabolic pathways (FDR < 0.05) were revealed  [For the feed efficiency trait, the enrichment of the retinol metabolic pathway was revealed in beef cattle, where two metabolites in the pathway  were found in the low feed efficient animals . Howeverion 5.0) , and metrevealed , where trevealed . Six metrevealed  and the ion 5.0) .https://www.genome.jp/kegg/, accessed on 20 September 2021) of Bos taurus species. It is suggested that the aminoacyl-tRNA biosynthesis pathway is mainly related to the other nine pathways. They are the alanine, aspartate and glutamate metabolism (bta00250), the glycine, serine and threonine metabolism (bta00260), the cysteine and methionine metabolism (bta00270), the valine, leucine and isoleucine biosynthesis (bta00290), the lysine biosynthesis (bta00300), the arginine and proline metabolism (bta00330), the histidine metabolism (bta00340), the phenylalanine, tyrosine and tryptophan biosynthesis (bta00400), and the tryptophan metabolism (bta00380) (The aminoacyl-tRNA biosynthesis pathway is an amino acid metabolism and biosynthesis related pathway that has been identified as associated with RFI in dairy cows  and pigsta00380) . It was is bta0020, the lyMetabolomics has been applied in metabolic biomarker identification, genetic mechanism revelation, genomic prediction, understanding nutritional physiology, etc., for different economic traits of different species, which promotes the applications of metabolomics in cattle.The application of metabolomics and the other integrated omics data analysis lead to the clear cognition of the complex metabolic mechanisms ; for exaMetabolomic-based genomic prediction has been conducted in plant species, such as wheat and barley, to display the potentiality of metabolite application as the predictor variables when no genotype is available ,48,49,50Diet-based rumen metabolomic analysis can help reveal the nutritional biochemical physiology after feeding different diets ,54. For Metabolomic analysis integrated with other omics data could contribute to the better understanding of the metabolomic complexity based on systems biology, but multiple layer integration would cause the challenge of statistics under the appropriate hypothesis ,58. The Metabolomics is the joint to connect genotypes with phenotypes , so theiiJL463 and iDZ470 were constructed for Riemerella anatipestifer wild type strain CH-1  and Riemerella anatipestifer wild type strain CH-2 , respectively [The genome-metabolite network has been constructed in bacterial species ,60; for ectively . In beefectively  detectedectively . System ectively  found thEMMAX (efficient mixed-model association eXpedited), FaST-LMM , GCTA , GEMMA (genome-wide efficient mixed-model association) [The mGWAS is the direct association model between genomics and metabolomics to test the candidate SNPs or QTLs related to metabolites. It can be analyzed in the tools that are applied for GWAS, such as ciation) ,65,66,67 control ,69), a iMetaboAnalyst [HACL1)) associated with two metabolites (α-ketoglutarate and succinic acid) was identified in high-low feed efficient dairy cattle [IMPaLA, Metabox (R based), XCMS, etc., [The gene-metabolite interplay network can be constructed for transcriptomic-metabolomic analysis based on the Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways using oAnalyst ,71; for y cattle . LikewisS, etc., ,73,74,75S, etc., ,73. BaseS, etc., , KEGG [7S, etc.,  and UnipS, etc.,  databaseIntLIM [IntLIM [p-value indicates the gene-metabolite association is different from the cases to the controls [R package IntLIM  was usedIntLIM , where tIntLIM . The lin [IntLIM  used is controls ,81.For the two-layer omics data integration, epigenomic−metabolomic interactions could discover novel molecular targets via epigenetic mechanisms regulating the expression levels of metabolic genes and thereby altering the metabolome ,83. WongAMON [MIMOSA [So far, the analysis between microbiome and metabolome could predict which compounds have been produced by a community of bacteria or the host in an R package AMON . However [MIMOSA  is a rel [MIMOSA  developeLipidome is one subset of the metabolome as same to amino acids, sugars and nucleic acids, but lipidomics has emerged as an independent field due to the functionally structural diversity and high endogenous abundance of lipids resulting in the complexities of the organismal lipidomes ,88. The CARM-1, Ube2g2, Cactin and Ndufaf6) during macrophage differentiation and osteoclastogenesis and the metabolic profile of cells to potentially influence the apoptotic and proliferative states [In the previous study, transcriptomic, proteomic and metabolomic integrated analysis was used to investigate the overexpression and inhibition of miR-223 affecting gene regulation in the cytoplasm of the monocyte−macrophage cell line . They che states . Jamil ee states  also proe states  firstly The current metabolomics analysis methods and tools are widely applied for metabolic biomarker detection, cluster classification, pathway and network identification, two-layer data integration, etc., which is usually limited in the metabolomics category . StatistMetabR, glmnet, IntLIM, etc., [Generally, a linear regression model is considered to analyze metabolomics data for significant metabolite identification by fitting phenotypes  as covariates ,80. SomeM, etc., ,93,94.MetaboAnalyst, VOCCluster [MetaboClust) [hcapca) [In order to cluster the metabolites, principal component analysis (PCA), linear discriminant analysis (LDA) and partial least squares discriminant analysis (PLS-DA) are normally used in the R packages or other tools, such as CCluster ,95. ToolboClust) , automat[hcapca)  are also[hcapca) . The pre[hcapca) .Notably, metabolomics data is complex and nonlinear, so machine-learning methods are applied for the nonlinear data interpretation based on random forest, support vector machine, artificial neural network algorithms, etc., ,103,104.limma and WGCNA [WGCNA  can construct a similarity matrix by Pearson correlation coefficients to measure the profiles’ similarity for the further network construction, and then identify the metabolically relevant key modules [Some transcriptomic expression and co-expression analysis approaches are also available for metabolic data by considering the metabolite values as the expression levels to perform the metabolite analysis and the interacted networks, such as using R package nd WGCNA ,109,110. modules .Metabolomic and integrated other omics data analysis are available for the measurement of dynamically metabolic responses, identification of biologically metabolic markers, revelation of potentially genetic architecture, understanding of systematic networks. In cattle, the classified metabolome clusters, detected relevant candidate metabolites, identified metabolic pathways, potential systematic networks have been studied to achieve promising and meaningful results. We summarized the previous results of one-layer metabolomic analysis and potential two-layer integration analysis that can be presented in Multiple integrated omics analysis would become critical and favorable in a further study, especially for the integration of genomics, epigenomics, transcriptomics, proteomics, microbiomics and lipidomics to reveal the metabolic-related mechanisms, identify multiple-layer biomarkers and improve genomic predictions, etc. Theoretically, metabolite QTLs, DNA methylation QTLs, expression QTLs (eQTLs), protein QTLs (pQTLs), microbe QTLs could be integrated on the genome level by constructing a multiple-omics network using those QTLs as the joint. In the meantime, the annotated genes/proteins to QTLs affecting metabolite concentrations that are regulated by the genetic/epigenetic variants could be connected together based on the biological pathways . Thus, tIn summary, this review concludes the useful metabolic information from the previous research results including the characterizations of metabolomics profiles, metabolomics applications, integrated metabolomics analysis with other omics, methods and tools in metabolomics analysis, and the further potentialities and implications in cattle, which may contribute to the production improvement, disease reduction, efficient farming for the cattle economically important traits.


Mycobacterium tuberculosis (Mtb) is one of the most formidablepathogens causing tuberculosis (TB), a devastating infectious diseaseresponsible for the highest human mortality and morbidity. The emergence ofdrug-resistant strains of the pathogen has increased the burden of TBtremendously and new therapeutics to overcome the problem of drug resistance areurgently needed. Metabolism of Mtb and its interactions with the host isimportant for its survival and virulence; this is an important topic of researchwhere there is growing interest in developing new therapies and drugs thattarget these interactions and metabolism of the pathogen during infection. Mtbadapts its metabolism in its intracellular niche and acquires multiple nutrientsources from the host cell. Carbon metabolic pathways and fluxes of Mtb has beenextensively researched for over a decade and is well-defined. Recently, therehas been investigations and efforts to measure metabolism of nitrogen, which isanother important nutrient for Mtb during infection. This review discusses ourcurrent understanding of the central carbon and nitrogen metabolism, andmetabolic fluxes that are important for the survival of the TB pathogen. Mycobacterium tuberculosis (Mtb) becomes resistant to thefirst-line drugs isoniazid or rifampicin causing multidrug-resistant (MDR)-TB.Extensively drug-resistant (XDR)-TB cases are the ones where the MDR-TB strains areresistant to any fluoroquinolone and second-line drugs. There were 470000 globalincidents, and 180000 deaths from MDR-TB in 2020 [Despite decades of research and development in vaccination and therapeutics,tuberculosis (TB) still remains one of the world’s deadliest infectiousdiseases . TB causMetabolism of a biological system is key to sustaining growth, survival, andfunction. Metabolism comprises complex sets of biological processes with hundreds ofbiochemical reactions that can be broadly classified into one that producesmetabolic products, energy, and biomass (anabolism) and the other involved inbreakdown of substrates (catabolism). Cellular carbon metabolism is at the heart ofsustaining the metabolic network function. Dysfunction or adaptations in carbonmetabolism is implicated in many human diseases including cancer, cardiovascular andmetabolic disorders . In cancMtb are transmitted through aerosols and are engulfed by alveolar macrophages in thelungs of infected individuals. Inside macrophages, Mtb pathogen resides inphagosomes where it is challenged with harsh host cell defence responses includinghypoxia, acidification, nutrient starvation, and oxidative stress . Howeverb reductase, cytochrome c oxidase) andthrough anaerobic phosphorylation  are present in Mtb [in vitro, and during early replication in the host [in vitro and compared the Mtbprofile with its related pathogen Mycobacterium bovis, thecausative agent of TB in cattle. Mtb utilized carbohydrates including glucose,mannose, trehalose, and two- and three-carbon substrates including glycerol andpyruvate through glycolytic oxidation [M. bovis was unable to utilise glucose, pyruvate, andalanine due to the mutations in pyruvate kinase pykA and alaninedehydrogenase ald confirming metabolic heterogeneity between thetwo mycobacterial pathogens [ppgk andglka) to perform glucose phosphorylation, the first step inglycolysis that incorporates carbon atoms from carbohydrates into the CCM [in vitro growth of Mtb onglucose as the carbon source. They are dispensable for Mtb’s intracellulargrowth but essential for Mtb’s persistence in mice lungs [pfkA catalyses the phosphorylation of fructose 6-phosphate, akey step in glycolysis [pfkA was non-essential for Mtb’s survival in mice butwas essential to sustain the survivability of non-replicating Mtb under hypoxia[Mycobacterium leprae, the relatedpathogen uses host glucose-derived carbon for synthesising amino acids during growthin Schwann cells, but Mtb replicating in human THP-1 macrophages do not [in vitro growth of Mtb and precursor for the three-carbon (C3)glycolytic substrates utilized by Mtb inside macrophages [M. bovis BCG, quantifying thecarbon fluxes on glycerol and Tween-80 using Metabolic Flux Analysis (MFA), asystems-based experimental (13C-labelling in chemostat system) andcomputational modelling analyses. Both Mtb and BCG had relatively higherglycolytic/gluconeogenic fluxes at slow and fast growth rates tested. Applying MFA,Beste et al. identified a ‘GAS’ pathway for pyruvate dissimilationinvolving the oxidative TCA cycle, glyoxylate shunt, and anaplerotic CO2fixation. Isocitrate lyase (icl), is an important enzyme for lipidmetabolism, for the persistence of Mtb at slow growth rates and for the operation ofGAS pathway [in vitro [The genome sequence analysis of Mtb by Cole et al.  confirmet in Mtb ,19. Sevethe host . Lofthouthe host  conductexidation .In contathogens . Mtb has the CCM ,26.Thesycolysis . Deletio hypoxia. Glucose hypoxia,26,28,29rophages ,25. Bestrophages  provided pathway ,30–32. Gin vitro ,34. Duriin vitro .pykA) is the rate-limiting step of glycolysis andis important for catabolism of glucose, and co-catabolism of carbon sources andfatty acids [pykA did not affect thein vivo replication of Mtb in mice models but attenuatedin vitro utilisation of glycolytic and gluconeogenic substratesthrough the accumulation of phosphoenolpyruvate (PEP), citrate, aconite, andconsequent allosteric inhibition of isocitrate dehydrogenase(icdh), a key enzyme of the TCA cycle [13C-isotopomer analysis and MFArevealed metabolic adaptations of Mtb on bedaquiline (BDQ), an anti-TB drug whichinhibits oxidative phosphorylation [pykA was a key node inthis adaptation [pykA Mtb mutant illuminating an effective synergisticdrug therapeutic combination of BDQ and inhibitors of pykA.Although pykA is an attractive target because of its regulatoryrole on metabolism, the presence of pykA human orthologue meansthat drug development against this Mtb enzyme is not straightforward.Pyruvate kinase , an enzyme that catalyses conversion ofα-ketoglutarate (or 2-oxoglutarate) into succinyl-CoA with production of NADHwas lacking in Mtb [in vitro culturesconfirming the operation of an alternative route as proposed by Tian et al. [icl1 andicl2 which are essential for Mtb to grow on fatty acidsubstrates and to survive in mice models [icl1mutant lacked activity of the glyoxylate shunt and methylcitrate cycle and exhibitedslow growth on steric acid [The TCA cycle is at the epicentre of CCM that it generates substrates for oxidativephosphorylation and energy production, and biosynthetic precursors for amino acidsand lipids. The annotated Mtb’s genome encodes a full TCA cycle , but recg in Mtb . Tian etg in Mtb  posed a g in Mtb . KDG catn et al. ,25,41. Gn et al. . Isocitrn et al. ,32,38,46e models ,47. Mtb ric acid . In addiric acid .pta) and acetatekinase (ackA). Acetate can also be converted into acetyl-CoA viaacetyl-CoA synthetase (acs). Acetate enters the metabolic networkvia the TCA cycle which is oxidised to generate substrates for ATP production. Theuse of oxidative or the reductive TCA cycle by Mtb was dependent on the carbonsubstrate. For example, growth on acetate used the glyoxylate shunt and oxidativeTCA cycle, but growth on glycerol used a reductive TCA cycle [l-lactate dehydrogenase ildD2; utilisation of lactate andpyruvate required the TCA cycle, glyoxylate and GABA shunt, valine degradation andmethylcitrate cycle [2fixation [Both the TCA cycle and glyoxylate shunt are primary routes for metabolism of fattyacid-derived substrates. Mtb degrades fatty acids via β-oxidation andgenerates acetyl-coenzyme A (CoA) which is converted into acetate through theenzymatic activities of phosphotransacetylase  and six putative cell wallproteins  [prpC,prpD, and icl genes , and compared these fluxes with that measured duringgrowth on glycerol and oleic acid [Mtb utilizes host immune cell-derived lipids (fatty acids and cholesterol) as primarynutrient sources for survival in the hypoxic and nutrient-limited macrophageintracellular environment ,52. Mtb  in vivo ,53.The 4/Mce4F) . Microar4/Mce4F) identifi4/Mce4F) . Propion4/Mce4F) ,52. Propcl genes . It is ieic acid . Mtbhadeic acid ,59–62. Teic acid ,45.In vitro growth comparisons on dextrose, acetate, and glycerol andon combinations of substrates (cholesterol-acetate and glycerol-oleic acid)demonstrated Mtb to selectively produce highest biomass on glycerol [Mycobacterium smegmatis, where carotenoid production was higheron glucose than that on acetate and glycerol [13C-substrates to track the incorporation ofcarbons into the CCM metabolic intermediates of Mtb batch cultures, and demonstratedthe use of glycolysis/gluconeogenesis, PPP, and TCA cycle by Mtb during aerobicgrowth on dextrose, acetate, and glycerol and posed substrate-specific fates andcompartmentalised metabolism in Mtb [13C-labelled substrates (glycerol-Tween 80 or cholesterol-acetate)exhibited no compartmentalised assimilation of different carbon substrates [glycerol ,45.Suchglycerol . de Carvglycerol  usedisom in Mtb ;howeverbstrates ,45. Mtb bstrates ,42,45.amtB-glnK-glnD operon encoding for AmtBtransporter protein, GlnK PII signalling protein and GlnD uridylyl transferase areinduced under conditions of nitrogen limitations [In addition to carbon, nitrogen is another essential building block for biomassincluding nucleic acids, amino acids, proteins, lipids, and cofactors. Nitrogenmetabolism is important for Mtb’s nutrition and survival in the human host.Like other bacterial species, the regulation of nitrogen metabolism in Mtb isdependent on the nitrogen status, i.e., the ratio of the metabolic intermediateα-ketoglutarate or 2-oxoglutarate to glutamine . The regitations . GlnE reitations ,68. The In vitro, Mtb can utilize a range of nitrogen sources includingammonium chloride and various amino acids [narGHJI locus [in vitro. This study also demonstrated that like carbonco-catabolism, Mtb can co-assimilate two amino acids as nitrogen sources invitro. Our own work investigated nitrogen metabolism of Mtb in humanmacrophages and identified multiple amino acids including aspartate, glutamate,glutamine, valine, leucine, alanine, and glycine that are available to Mtb duringintracellular growth [in vitro growth andfor virulence in mice and macrophages [ansA is essential to assimilate nitrogen fromasparagine and to resist acid stress in the phagosomes [de novo synthesizedprimarily via amination of 2-oxoglutarate catalysed by gltBDoperon, which encodes large and small subunits of GOGAT; glutamate can also besynthesized by glutamate dehydrogenase gdh. Deletion of GOGAT andgdh causes glutamate auxotrophy in Mtb and significantreduction in growth in presence of glutamate as sole nitrogen source respectively[de novo biosynthesis of these aminoacids is essential in intracellular Mtb, and that the enzymes for theirbiosynthesis, LeuD and SerC are potential drug targets [in vivo growth remain largely unknown. Mutagenesis and geneknockout analysis studies are useful in identifying those genes that are requiredfor nitrogen uptake or metabolism during intracellular growth, but they cannotprovide the nitrogen metabolic flux measurements. To this end, systems-basedtechnology such as MFA and metabolic modelling can aid in quantification ofintracellular nitrogen fluxes. However, nitrogen metabolic modelling, isotopiclabelling, and flux analysis needs to be further developed. Currently, theincomplete knowledge about the transaminases and lack of nitrogen atomic backbonerearrangement in the metabolic network limits direct application of carbon-based MFAto measure nitrogen fluxes.no acids ,69,70. Tno acids . Nitrogeno acids . Mtb canJI locus ,72. Agapr growth . Nitrogerophages .Asparagagosomes . Glutamaectively. Glutamiectively. Leucine targets . Alaninein vivo and thevalidation of the proposed drug targets in clinical trials remain underinvestigated. Whilst carbon metabolism of Mtb is well-researched, nitrogenmetabolism, remains underexplored. Till date, only a few studies exist thatidentified nitrogen sources such as amino acids to be important for the nutritionand survival of the TB pathogen. The intracellular nitrogen fluxes that supportMtb’s growth in vitro or in the human host cells has neverbeen attempted. Also, the intersecting nodes between carbon and nitrogen metabolicpathways, and those that are important for TB infection have not been elucidated.Measuring nitrogen fluxes alone can be technically challenging due to the lack ofbiochemical information for enzymes such as transaminases/transamidases and the verylimited nitrogen atomic backbone rearrangement which is insufficient for robustsystems-based analysis such as mathematical modelling and MFA. An alternativeapproach such as to measure carbon and nitrogen co-metabolic fluxes to overcome thelimited atomic measurements for nitrogen and to deduce nitrogen metabolic fluxesfrom the carbon–nitrogen co-metabolic profiles. An illustration ofcarbon–nitrogen co-metabolism in amino acids is depicted in in vitro and in ex vivo Mtbreplicating in macrophages. Also, the metabolic flux measurement techniques used byprevious studies are not consistent across in vitro and exvivo models, which makes it difficult to compare the phenotypes derivedfrom the two models. The metabolic flux studies in in vitro Mtbprimarily uses steady state cultivation and isotopic labelling of the bacteria suchas in chemostat setup [ex vivo Mtb because growth ofMtb-infected human macrophages or cells cannot be cultivated in the invitro chemostat setup. This will require a sophisticated bioreactorsetup for cultivation of human cells to provide an appropriate environment for humancell proliferation. Future research to measure metabolic fluxes of Mtb in animalmodels, and in human tissues such as the lungs will provide new information on theclinically relevant metabolism of Mtb, which in turn will facilitate the developmentof new and effective therapeutics.Recent decades of research have advanced our understanding of Mtb’s metabolicphysiology and identified cellular processes and components that are essential forits virulence and survival in the host. Mtb adapts its nutritional behaviour andmetabolic fluxes during infection and growth on different carbon sources. Theseadaptations have been measured by several studies and attempts to identify metabolicdrug targets have been successful. A summary of the enzymes identified as drugtargets and their involvement in carbon and nitrogen metabolism is provided in at setup . However


We developed a detailed mathematical model of carbon fixation, which accounts for various environmental parameters and for energy and nitrogen partitioning across photosynthetic components. This allows us to assess environment-dependent plant physiology and performance as a function of resource allocation patterns. Models of C4 plants optimized for conditions experienced by evolutionary ancestors perform better than models accounting for experimental growth conditions, indicating low phenotypic plasticity. Supporting this interpretation, the model predicts that C4 species need to re-allocate more nitrogen between photosynthetic components than C3 species to adapt to new environments. We thus hypothesize that observed resource distribution patterns in C4 plants still reflect optimality in ancestral environments, allowing the quantitative inference of these environments from today’s plants. Our work allows us to quantify environmental effects on photosynthetic resource allocation and performance in the light of evolutionary history.The regulation of resource allocation in biological systems observed today is the cumulative result of natural selection in ancestral and recent environments. To what extent are observed resource allocation patterns in different photosynthetic types optimally adapted to current conditions, and to what extent do they reflect ancestral environments? Here, we explore these questions for C Major constraints on metabolic fluxes can arise from scarcity of chemical compounds, e.g., nitrogen necessary to produce enzymes3, or from the limited solvent capacity of cellular compartments5. To ensure optimal metabolic efficiency, gene regulation has to balance available resources appropriately. Modern methods of modeling metabolism rely strongly on the assumption of metabolic optimality under physicochemical constraints8. Accordingly, resource allocation and its constraints are under intense investigation, although these studies are mostly restricted to unicellular organisms. However, the metabolic efficiency of a given metabolic system is not static, but depends on the environment. Thus, uncertainties about the environmental properties that an organism has adapted to remain a major obstacle in the application of these methods. Autotrophic systems, such as plant leaves, are ideal to study the interaction of the environment and resource allocation, as the diversity of nutrient sources is much lower than for heterotrophs, which results in a reduced complexity of the space of possible environments. Furthermore, the effect of environmental factors on plant performance, e.g., the rate of CO2 assimilation, have been studied intensively9. In particular, C3 and C4 photosynthesis represent complementary gene expression and resource allocation patterns that result in high fitness in specific ecological niches.Metabolic efficiency is an important determinant of organismal fitness2 is catalyzed by the enzyme ribulose-1,5-bisphosphate carboxylase/oxygenase (Rubisco) as part of the Calvin-Benson cycle. Rubisco also shows an affinity for O2, resulting in a toxic by-product, which needs to be recycled by the photorespiratory pathway and causes a significant loss of carbon and energy10. Rubisco is an important resource sink in the leaf proteome of plants: it utilizes up to 30% of leaf nitrogen and up to 65% of total soluble protein12. While C3 plants operate the Calvin-Benson cycle in their mesophyll cells to fix carbon, C4 plants express it in the bundle sheath cells and use phosphoenolpyruvate (PEP) carboxylase (PEPC) in their mesophyll cells for the initial fixation of carbon. The resulting C4 acids are eventually decarboxylated in the bundle sheath cells, creating a local high-CO2 environment around Rubisco that suppresses photorespiration. While the exact biochemical implementation of the C4 cycle varies between species, the C4 cycle is completed by the regeneration of PEP by pyruvate, phosphate dikinase (PPDK).In all plants, the fixation of carbon from CO3 photosynthesis, C4 metabolism requires additional nitrogen to produce the C4 enzymes; this additional investment is counteracted by reduced Rubisco requirements due to the concentration of CO2 around Rubisco13. The energy requirements of C4 metabolism also differ from those of the C3 pathway14, as further ATP is needed for the regeneration of PEP, while ATP and NADPH requirements of the photorespiratory pathway are reduced. The metabolic efficiencies of the C3 and C4 system depend strongly on the environment. To achieve optimal metabolic efficiency, plants have to coordinate gene expression of the Calvin-Benson cycle, photorespiration, light reactions, and, in the case of C4 plants, the C4 cycle; this coordination occurs in a complex response to the availability of light energy and nitrogen and of factors that influence the rate of photorespiration. The diversity of photosynthetic resource allocation patterns is emphasized by the existence of C3–C4 intermediate photosynthesis in some plants, where features of the archetypical C4 syndrome are only partially expressed. The genus Flaveria contains closely related species that employ the C3, C3–C4 intermediate, and C4 versions of photosynthetic metabolism, making it an ideal system to study the interaction between resource allocation and environment in photosynthesis.Compared to C3 and C4 plants, Sage and McKown15 argued that C4 plants show limited regulation of Rubisco content in response to environmental factors like sunflecks and low temperatures. Although the extent of phenotypic plasticity in plants is intensively studied e.g.18, the plasticity in terms of resource allocation is not fully understood. In particular, it is not clear whether the phenotypic plasticity of different plant lineages is sufficient to acclimate optimally to the current environment; instead, many plants might still allocate at least parts of their resources in patterns that were optimal in the environments that dominated their recent evolutionary history.The selection pressures caused by environmental factors over evolutionary time scales are expected to lead to corresponding adaptations of gene regulation. In contrast, environmental variation on the time scale of individual generations may select for regulatory programs that adjust plant metabolism to the environment they currently face, a process called phenotypic plasticity. Reviewing the occurrence of phenotypic plasticity in C4 dicotyledonous plants are assumed to have evolved are regions of low latitude showing combinations of heat, drought, and salinity13. For Flaveria, analyses that combine phylogenetic context and environmental information point toward an evolutionary origin in open habitats with high temperatures20. The last common C3 ancestor of the current Flaveria species lived 2–3 million years ago21, when CO2 levels were significantly lower than the current, postindustrial level23. In summary, Flaveria species likely faced high light intensities, high temperatures, and low atmospheric CO2 levels during their recent evolutionary history.The areas where C2 assimilation rate of C3, C4, and C3–C4 intermediate plants is based on the mechanistic biochemical models of Berry and Farquhar24, Farquhar et al.25, and von Caemmerer26. These models predict the light- and enzyme-limited CO2 assimilation rate with great success, and take into consideration enzymatic activities and various environmental parameters, including mesophyll CO2 level and light intensities. In many ecosystems, the most limiting resource for plant growth is nitrogen28, and a high proportion of nitrogen is used in photosynthesis29. The increased nitrogen-use efficiency of C4 species compared to C3 relatives indicates that nitrogen availability may have played a major role in C4 evolution30. Models of optimal nitrogen allocation were successfully used to understand the response to environmental factors like elevated CO232, light34, and temperature35, but these approaches were limited to C3 plants. In order to understand how optimal resource allocation patterns shifted during C4 evolution, a new modeling framework is required.The standard method to model the CO2 assimilation occurring in C3, C4, and C3–C4 intermediate species. To achieve this goal, we developed a mathematical model for these photosynthetic types that integrates knowledge of resource costs and relevant environmental factors. Using this model, we seek to understand (1) to what extent resource allocation is phenotypically plastic and to what extent it appears adapted to an environment the plants were facing during their evolutionary history; and (2) if resource allocation patterns can be used to identify unique environments to which allocation is optimally adapted.Here, we aim for a detailed understanding of the interplay between resource allocation and current and past evolutionary environments in relation to CO2 assimilation rate, which—depending on its parameterization—can describe C3, C3–C4 intermediate, and C4 photosynthetic types. Figure 4 cycle, and thylakoids). The definitions of the corresponding model parameters are listed in Table 4 cycle. In this study, we parameterize the model to describe species from the genus Flaveria; parameter values are listed in Supplementary Table Here, we present a nitrogen-dependent light- and enzyme-limited model for the steady-state CO3–C4 models originally developed by von Caemmerer9 and modified by Heckmann, et al.2. We added a fixed budget of nitrogen constraining the total abundance of photosynthetic proteins using previous knowledge about the major nitrogen requirements of photosynthetic components, e.g., Rubisco36. Furthermore, we extended the existing models by explicitly modeling the ATP and NADPH production of the linear and cyclic electron transport . Thus, an environment-dependent photosynthetic nitrogen budget is distributed across the enzymes of the Calvin-Benson cycle in the mesophyll and bundle sheath cell, the C4 cycle, and the proteins of the LET and CET in the thylakoid membranes. Combining this model with the temperature dependency of the photosynthetic apparatus37 results in a detailed model of photosynthesis that incorporates leaf nitrogen level, light intensity, mesophyll CO2 and O2 levels, and the effects of temperature.We extended the light- and enzyme-limited C2 assimilation rate 39. We developed a robust optimization pipeline that reliably finds optimal resource allocation dependent on environments and photosynthetic types. In previous work, optimality assumptions were successfully used in a variety of photosynthetic systems; examples are the explanation of the coordination of ribulose-1,5-bisphosphate carboxylation and regeneration during C3 photosynthesis41, optimal nitrogen allocation in C3 plants in different environments42, the exploration of evolutionary trajectories from C3 to C4 photosynthesis2, the exploration of alternative inter-cellular transport pathways in C2 plants43, and the prediction of proteome allocation in cyanobacteria44.In order to understand physiological data in the context of environmental adaptation, we aim to find optimal resource allocation in a given environment. To this end, we assume that resource allocation has been optimized by natural selection to maximize the CO2 fixation rate to determine (1) the optimal relative investment of nitrogen into Rubisco, the C4 cycle enzymes, and the proteins of the light-dependent reactions, (2) the optimal partitioning of NADPH between the Calvin-Benson cycle and the photorespiratory pathway, (3) the optimal partitioning of ATP across the Calvin-Benson cycle, photorespiratory pathway, and C4 cycle (if relevant), and (4) the optimal proportion of LET and CET.We use optimality of the modeled CO2 and O2 mesophyll partial pressures. The photosynthetic type is defined by six parameters: the Rubisco distribution between mesophyll and bundle sheath cells (β); the Rubisco kinetics, ; the maximal C4 cycle activity ; the fraction of glycine decarboxylated by the glycine decarboxylase complex in the bundle sheath cell that is derived from oxygenation by Rubisco in the mesophyll cell (ξ); the Michaelis constant of PEPC for bicarbonate , and the bundle sheath cell conductance for CO2  . The values for the parameters are taken from the literature . In our model, Nps can be allocated across the following major pools of leaf photosynthetic nitrogen: the main enzyme of the Calvin-Benson cycle (nEtot), Rubisco; the main enzymes of the C4 cycle (nC4), PEPC and PPDK (we decided to focus on PEPC and PPDK as the major nitrogen pools of the C4 cycle based on the enzyme molecular weights and turnover numbers46); and the thylakoids (nJmax), which include the photosynthetic electron transport chains. The CO2 assimilation rate and other model parameters can be predicted for a freely chosen nitrogen allocation. Note that we are interested in determining the optimal nitrogen allocation  based on phenomenological observations (see Supplementary Methods S1 for details).To calculate the CO47. The amount of catalytic sites of Rubisco  is calculated from the invested nitrogen by Eq.  and turn-over rates  are used to calculate the maximal rate of C4 cycle activity48. Equation Vpmax, and nitrogen investment into the C4 enzymes (nC4 Nps),11; indices indicate the considered enzyme.We calculated the nitrogen cost of CNthy, [µmol (µmol Chl)−1]) is related to the maximal electron transport rate  via the amount of cytochrome f per chlorophyl −1]) and by considering photosystems I and II −1]) as well as the light harvesting complexes −1]). In the following, we describe these relationships in quantitative detail [Eqs. (Nitrogen invested into the thylakoids (il [Eqs. –15)]; i]; iNthy,49 for abundances of PSI and PSII to include phenomenological stoichiometry rules between LHC and the components of the electron transport chain ; pI]; pI49 fHC . WJmax is related to Nthy as described in Eqs. −1 across various C3 species. We are not aware of a comparable data set for C4 plants. Assuming 95% of LET in C3 plants, this leads to a capacity of 172 mmol e- (mmol cyt s)−1 for cytJmax.For the LET,  in Eqs. –11). \d. \dJmax ids [Eq. ], accounids [Eq. ]. The amids ) is calculated based on an empirical factor39 that relates the amount of nitrogen invested into thylakoids to the amount of chlorophyll in C3 plants .Chlorophyll content (yt [Eqs. –10)]; c]; cChl, JmaxCL, which describes the scaling of Jmax with cyt for the CET. This factor is assumed to be 3, as PSII is more expensive in terms of nitrogen compared to PSI49.The derivation for the CET is analogous to the case of the LET:p and nJmax, affect Jmax in LET and CET via the cytochrome f content.In summary, the free optimization parameters related to nitrogen allocation to the light reactions, 2 assimilation rate. To find the maximal CO2 assimilation rate under the given environmental, physiological, and biochemical constraints, we optimize the allocation of photosynthetic nitrogen  into Rubisco (nEtot), C4 cycle (nC4), LET, and CET (the latter two represented by p and nJmax) through an augmented Lagrangian approach using the auglag-function of the package ‘nloptr’51. The optimization is constrained to make sure that the results are biologically realistic with respect to the modeled photosynthetic type, e.g., C3 species were not able to invest nitrogen into the C4 cycle  and the absorbed light of a certain irradiance  is presented in Eqs.  Jmax, the maximum electron transport rate; (2) Θ, the convexity of the transition between the initial slope and the plateau of the hyperbola; (3) α, the leaf absorptance; (4) f, a correction factor accounting for the spectral quality of the light; and (5) p, the fraction of absorbed quanta that reaches PSI and PSII of LET (with (1 − p) reaching the CET). Iabso is set to either ILET or ICET depending on the considered path of electron transport. The fraction of irradiance that is absorbed by the LET is shared equally between PSI and PSII , 9,53 t5 in Eq. ], while 2 fixation9. As NADPH production results from LET, the amount of electrons is calculated using Eqs. 2 fixatio4 pathway. This means that the available energy is calculated in total and then partitioned54 into Jmp, Jmc, and Js, the fractions of Jmax invested into the C4 cycle, the Calvin-Benson cycle and the photorespiratory pathway in the mesophyll, and the Calvin-Benson cycle and the photorespiratory pathway in the bundle sheath cell, respectively. During optimization, the activity of each process is constrained by its allocated energy pool, i.e., the energy allocation equals the relative energy allocation of the processes (see Supplementary Methods S3 for details). In summary, the optimal energy allocation is a function of the nitrogen pools.The available energy needs to be partitioned between five pools: (1) the Calvin-Benson cycle in the mesophyll; (2) the Calvin-Benson cycle in the bundle sheath; (3) the photorespiratory pathway in the mesophyll; (4) the photorespiratory pathway in the bundle sheath cell; and (5) the C9. The ATP-limited . The light-limited CO2 assimilation rate is:A limitation in the production of both ATP and NADPH arises under light-limited conditions2 assimilation rate when the electron transport rate is not limiting (Ac) is taken from Heckmann et al.2 and extended by a parameter representing the fraction of PSII activity in the bundle sheath cells, which affects O2 generation. This parameter is set to p. In the whole model, each limitation is considered independently; the plant’s CO2 assimilation rate is determined by the lower of the two limitations:The model for the CO2 assimilation rate by changing the maximal activity of the C4 cycle, the carboxylation rate of Rubisco, and the electron transport rate. Temperature also affects the specificity of Rubisco and the Michaelis constants of Rubisco and PEPC. We model the temperature response by an extended Arrhenius function that describes two counteracting effects: rate increases with increasing temperature and enzyme inactivation through thermal instability37. We use parameters taken from literature or fitted to available data.Temperature affects the CO37:The extended Arrhenius function is given by Massad et al.k25); (2) the activation energy (E); (3) the deactivation energy (H); (4) an entropy factor (S); (5) the universal gas constant (R); and (6) the temperature considered (T). (see Supplementary Methods The parameters of the extended Arrhenius function are: (1) the value of the considered enzyme at temperatures 25 °C . The measured data include curves of the CO2 assimilation rate as a function of intercellular CO2 concentration (Ci) and the ratio of atmospheric CO2 concentration (Ca) and Ci. We derive the CO2 concentration in the mesophyll cell (Cm) for a given Ca by considering this Ca/Ci-ratio and assuming that the ratio of Cm to Ci is 0.85 . As can be seen from our sensitivity analysis  is defined as the total fraction of nitrogen that needs to be re-allocated between photosynthetic pools to optimally adjust photosynthesis from the evolutionary scenario  used in the respective studies (‘growth scenario’) or to the environments in which they likely evolved (‘evolutionary scenario’); with respect to our model, these environments differ in terms of atmospheric CO2 concentration, temperature, and light intensity  Vogan and Sage30, and (3) Dwyer et al.56. Vogan and Sage39 measured the net CO2 assimilation rate as a function of intercellular CO2 concentration (A-Ci curve) and as a function of temperatures between 15 °C and 45 °C for C3, C3–C4 intermediate, and C4Flaveria species. In this experiment, plants were grown at light intensities of 560 µmol quanta m−2 s−1, 37 °C at daytime, current atmospheric O2 concentration, and 380 µbar or 180 µbar atmospheric CO2 concentrations  differ from both the EGC and the evolutionary condition. Typically, the EMC shows higher light intensities than the EGC. In contrast, the major difference between the evolutionary environment and the EMC is the atmospheric CO3Flaveria species (F. pringlei or F. robusta), the model results assuming an optimal allocation under the evolutionary scenario agree qualitatively with the measured data of Vogan and Sage39, and visually, they appear to fit the data better than results assuming optimality under the EGC30 . Thus, it is possible that the somewhat better fit for the evolutionary scenario is caused by random fluctuations or experimental errors rather than by a superiority of one scenario over the other.For C30 Figs. –S5. To a3-C4 intermediates, F. ramosissima and F. floridana. Again, the predictions assuming an optimal allocation under the evolutionary scenario agree qualitatively with the measured data of Vogan and Sage39, and seem to fit the data better than predictions under the EGC . In Fig. 59. When in vitro PEPC activity is corrected using independent data on in vitro-in vivo differences . Thus, we assume that plants require multiple hours to days in order to adjust their protein levels to a new environmental condition. Accordingly, we assume that plants cannot adapt their resource allocation patterns on the timescale of a measurement, which lasts on the order of minutes to hours. This is our rationale for simulating plants optimally adapted to the EGC, even when analyzing data collected at rather different EMCs. However, it is conceivable that at least the energy allocation, including the proportion of LET, can adjust to the EMC on the timescale of the experiment. We thus performed simulations under an alternative model, where nitrogen allocation is optimized for the EGC, but energy allocation is subsequently optimized for the EMC. The results are qualitatively similar to the above results from simulations where both nitrogen and energy allocation are optimized for the EGC .Compared to a parameterization optimized for the growth scenario, the model optimally adapted to the evolutionary scenario leads to superior predictions of plant performance and resource allocation in C−2 s−1 light intensity, 30 °C, a mesophyll CO2 level of 100 µbar, and an O2 level of 200 mbar. This environment corresponds to an atmospheric CO2 concentration of about 280 µbar  tend to favor an increased nitrogen investment into the dark reactions, which goes along with a reduced investment into the electron transport chain. The effect of temperature is of special importance for plants using the C4 cycle, as temperature increases PEPC activity drastically37 and therefore reduces the necessary nitrogen investment into the C4 cycle. This allows an increased investment into Rubisco and the electron transport chain, both of which show reduced activity at elevated temperatures due to thermal instabilities. Lower mesophyll CO2 levels tend to increase the investment into the C4 cycle while decreasing the investment into the electron transport chain and  into Rubisco.Optimal resource allocation patterns are determined by an interplay between the different environmental factors. For C4Flaveria species show a lower degree of photosynthetic phenotypic plasticity than closely related C3 species . We then summed these fractions to quantify the total fraction of nitrogen that needs to be re-allocated between photosynthetic pools to adjust photosynthesis between the two optimal nitrogen allocation patterns . Our results thus indicate a link between required nitrogen re-allocation and limited photosynthetic phenotypic plasticity, suggesting a possible causal relationship.Our results indicate that C δn, see . Table 2Flaveria  potentially show short-term trade-offs64, these might lead to a discrepancy between modeled and real evolutionary scenarios. In particular, the natural ancestral habitat must have exhibited periodically as well as randomly fluctuating conditions, compared to the stable EGCs in audited growth chambers and the statically modeled evolutionary scenario.Although the predictions for total nitrogen investment into the thylakoids based on the evolutionary scenario are highly consistent with the measurements performed by Dwyer et al.4 evolution remains unclear, further research is needed to assess the effect of nitrogen availability on plants under the ancestral, current, and transitional environments. Furthermore, while our approach of maximizing the assimilation rate per available CO2 concentration will account for water-use efficiency implicitly, a promising avenue for future evolutionary studies will be the explicit inclusion of stomatal responses .Given the complexity of our physiological model, we needed to make a number of assumptions. We addressed uncertainties in model parameters through sensitivity analyses, showing that our conclusions are robust against variation in these parameters  across a wide range of environmental conditions provides a solid basis for the presented results. The complexity of the analysis is reduced by considering the model genus Flaveria that allows us to focus on the effect of different photosynthetic types rather than differences across genera.There are only a limited number of data sets available that include the information for each considered environmental factor. In the three available data sets that included all necessary information, plants were not grown under the same conditions under which experiments were performed . The EGC and EMC show their biggest difference in the light intensities, but other factors differ also, e.g., temperature (Supplementary Tables 4 and C4-like plants, the predictive performance of the evolutionary and the growth scenario models is similar for C3 and C3–C4 intermediate Flaveria species (Supplementary Table 3 and C3–C4 plants, which make it difficult to quantify model performance on noisy data (Figs. 3 and C3–C4 intermediate plants compared to C4 and C4-like plants. Thus, in contrast to the latter photosynthetic types, it may not be possible to estimate ancestral evolutionary environments for C3 plants based on our approach.In contrast to the findings in Cta Figs. –S5. OverOur model provides a powerful tool to analyze the resource allocation of photosynthetic organisms and its dependence on environmental factors, allowing estimates for the maximal electron transport rate for LET and CET, the proportion of LET and CET as well as the nitrogen and energy allocation for which measurements are currently infeasible or impractical. This may prove to be of particular utility for systematically assessing the likely performance of crops in environments distinct from their natural habitats and for suggesting engineering targets in cases of limited phenotypic plasticity.Supplementary Information.


Azotobacter vinelandii, which uses a complex respiratory protection mechanism to consume oxygen at a high rate to keep intracellular conditions microaerobic. Our model accurately predicts growth rate under high oxygen and substrate concentrations, consistent with a large electron flux directed to the respiratory protection mechanism. While a partially decoupled electron transport chain compensates for some of the energy imbalance under high-oxygen conditions, it does not account for all substrate intake, leading to increased maintenance rates. Interestingly, the respiratory protection mechanism is required for accurate predictions even when ammonia is supplemented during growth, suggesting that the respiratory protection mechanism might be a core principle of metabolism and not just used for nitrogenase protection. We have also shown that rearrangement of flux through the electron transport system allows A. vinelandii to adapt to different oxygen concentrations, metal availability, and genetic disruption, which cause an ammonia excretion phenotype. Accurately determining the energy balance in an aerobic nitrogen-fixing metabolic model is required for future engineering approaches.There is considerable interest in promoting biological nitrogen fixation (BNF) as a mechanism to reduce the inputs of nitrogenous fertilizers in agriculture, but considerable fundamental knowledge gaps still need to be addressed. BNF is catalyzed by nitrogenase, which requires a large input of energy in the form of ATP and low potential electrons. Diazotrophs that respire aerobically have an advantage in meeting the ATP demands of BNF but face challenges in protecting nitrogenase from inactivation by oxygen. Here, we constructed a genome-scale metabolic model of the nitrogen-fixing bacterium  Howeverrylation . Other dreaction , and uptone pool , 24.A. vinelandii branches into two paths from the quinone pool, the fully coupled branch, including the bc1 complex, cytochrome c4/c5, and o-type or cbb3 terminal oxidases, and the partially coupled branch, with cytochrome bd . Cytochrome bd accumulates under high-aeration conditions, and knockout mutants lacking bd oxidase cannot grow diazotrophically at any aeration rate  was published that encompasses much of the eriments . This frn source  , as the electron-bifurcating enzyme complex is not yet in databases. V-nitrogenase does have a KEGG annotation, but the stoichiometry is inaccurate. Fe-only nitrogenase has no annotation in any database. Download Copyright © 2021 Alleman et al.2021Alleman et al.https://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the Pseudomonadaceae, A. vinelandii contains phosphofructose kinase and has a complete Embden-Meyerhoff pathway (A. vinelandii utilizes the Entner-Doudoroff (ED) pathway . Microbiologists since the 1950s have observed that the genus irements , 69. Theotection .2 concentrations. Kuhla and Oelze  of A. vinelandii growing in continuous diazotrophic cultures in different O2 concentrations and carbon sources, using the Pirt method  requires an ATP/substrate ratio term. An issue arises with converting the maintenance coefficient to ATPM when considering the ATP produced per O2 consumed (P/O ratio) of the different branches of the ETS. The fully coupled branch uses 1 mol of glucose to produce 32 mol of ATP, but the partially coupled respiratory protection branch produces only 9 mol of ATP per mol of glucose. Experimentally during high substrate and high O2 conditions, A. vinelandii requires decoupling of the ETS through the partially coupled branch to maintain growth  rate under different Ond Oelze  measuredt method   and the second assuming all flux to O2 through NDHII and cytochrome bd   . In bothntration . This upntration .2 concentrations. Each model was given an experimental substrate uptake rate and the predicted ATPM flux for each O2 concentration. Growth rates were then predicted and tested for error against experimental data. Using the fully coupled branch results in growth overestimates for all O2 concentrations  increase linearly with O2 concentration. However, partitioning of the ATP differentiates the 12 μM condition from the high O2 concentrations. The percentage of ATP consumed in ATPM reaction plateaus at around 60% of total ATP consumed for 48, 108, 144, and 192 μM O2 but only at ∼30% for 12 μM O2. This differentiation allows more ATP to be utilized in biomass production, creating higher growth yields for the 12 μM O2 concentration.The overall growth efficiencies can be further investigated with detailed maintenance estimates. The growth yield was predicted using the experimental sucrose uptake rate and plotted versus the experimentally determined growth yield . Similarotection . However plotted . The flu2 damage  was used to show similar growth rates of 0.202 h−1 for 108 and 0.222 h−1 for 12 μM O2. Flux samples were taken and normalized to sucrose uptake rate to compare electron allocation in the model. NADH production in the TCA cycle increased in 108 μM O2 compared to 12 μM O2, but flux is decreased in NADH-consuming reactions such as those involving glutamate synthase, relative to carbon uptake , so an increase in flux in other conditions is above this line or a decrease is below. Download Copyright © 2021 Alleman et al.2021Alleman et al.https://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the A. vinelandii’s nitrogen fixation regulatory system by deleting the nifL gene allows nitrogenase to be constitutively expressed even in the presence of high ammonia concentrations in the medium  were set to excrete ammonia at a rate of 3 mmolammonia · h−1 · g CDW−1 as estimated from the work of Plunkett et al.  and the terminal oxidase cytochrome bd with high Vmax (maximum reaction velocity) and low affinity for O2  base metabolic reactions not accounted for in the model and (ii) reactions that respond to O2 and dissipate energy. For the first category, more accurate physiological data and biomass composition would help predict energetic needs. The current model predicts growth yields for 12, 44, and 108 μM O2 concentrations, so a significant change in the biomass equation is not expected  under high O2 and continuous culture . Metabolic models are saved in json and smbl format. All analysis and figure creation were documented in Jupyter notebooks. See the supplemental methods  for furt10.1128/mBio.02593-21.3TABLE S3A. vinelandii model (iDT1278)  and the previous iDT1278)  Table S3Copyright © 2021 Alleman et al.2021Alleman et al.https://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International license.This content is distributed under the terms of the