Technical advances at the interface of biology and computation, such as single-cell RNA-sequencing (scRNA-seq), reveal new layers of complexity in cellular systems. An emerging area of investigation using the systems biology approach is the study of the metabolism of immune cells. The diverse spectra of immune cell phenotypes, sparsity of immune cell numbers in vivo, limitations in the number of metabolites identified, dynamic nature of cellular metabolism and metabolic fluxes, tissue specificity, and high dependence on the local milieu make investigations in immunometabolism challenging, especially at the single-cell level. In this review, we define the systemic nature of immunometabolism, summarize cell- and system-based approaches, and introduce mathematical modeling approaches for systems interrogation of metabolic changes in immune cells. We close the review by discussing the applications and shortcomings of metabolic modeling techniques. With systems-oriented studies of metabolism expected to become a mainstay of immunological research, an understanding of current approaches toward systems immunometabolism will help investigators make the best use of current resources and push the boundaries of the discipline. IIl y a des systèmes vivants; il nʼy a pas de matière vivante.There are living systems; there is no living matter.These words of Nobel laureate Dr. Jacques Monod  are incr+ ILC3s, CD62L+ ILC3s, and HLA-DR+ ILC3s -paradigm . Extraceparadigm .+ PD1+ T cells are spatially restricted to the tumor-immune boundary, implicating a broader, noncheckpoint-dependent mechanism of immune exclusion in human colorectal cancers. Similarly, Levine et al. implemented mass cytometry to determine metabolic regulators of CD8+ T cell activation after Listeria monocytogenes infection in vivo . F. F125]. Box 2 Compass: an FBA tool to study immunometabolismCompass is an FBA algorithm that uses single-cell transcriptomic profiles to produce a quantitative profile for the metabolic state of single cells. Even though the mRNA expression of enzymes is not an accurate proxy for their metabolic activity, a global analysis of the metabolic network (as enabled by RNA-seq) in the context of a large sample set (as offered by single-cell genomics) coupled with strict criteria for hypothesis testing provides an effective framework for predicting cellular metabolic states.r, the maximal flux r and every cell, Compass finds a flux distribution  that minimizes the overall penalty incurred while maintaining a flux of at least ω = 0.95) through r. The additive inverse of this penalty term is the reaction score.The first step of Compass is agnostic to gene expression and computes, for every metabolic reaction k-nearest neighbors graph, similar to other scRNA-Seq algorithms [The use of genome-scale metabolic networks allows the entire metabolic transcriptome to impact the computed score for any particular reaction, rather than just the mRNA coding for the enzymes that catalyze it. This reduces the effect of instances where mRNA expression does not correlate with metabolic activity and of scRNA-Seq dropouts . Compassgorithms ,130–133.gorithms  or microgorithms ) or baseThe resulting quantitative profile of the metabolic state of a cell, represented by a reaction score matrix, is subjected to further analyses, which can be (a) hierarchical clustering of metabolic reactions as metareactions, (b) computing differential expression of reactions, (c) the correlation of reactions with phenotype under interrogation, and (d) the analysis of data-driven pathways .Genome-scale models can be useful tools to gain a better understanding of the metabolic requirements of rare immune cells, especially in vivo, and consequently are an important tool to study immune cells both under homeostasis and in disease. With the increasing availability of high-throughput data, metabolic models can have several potential applications in both preclinical and clinical settings Fig. , a few o+ T cells within an inflammatory microenvironment, such as an arthritic joint, express lactate transporters to support their survival [+ biosynthesis activity in seven mouse tissues [Caenorhabditis elegans as a model, Yilmaz et al. implemented their new computational pipeline MERGE to identify tissue-specific metabolism in the nematode. Applying tissue-specific constraints on scRNA-seq data from various tissues of C. elegans, the authors found that the metabolic properties of a nematode tissue depend on the established functions of the tissue and that metabolic similarities with analogous human tissues could be identified [Immune cells moving from blood or lymphoid tissue to the tissue of residence face a shift in microenvironment-derived metabolic input as well as oxygen concentrations. Angelin and colleagues demonstrated that Tregs maintain OXPHOS only under nutrient- and oxygen-replete conditions . Under gsurvival . Simulatsurvival , 93. In  tissues . Similarentified . These sDistinct T cell subsets are associated with autoimmunity and inflammation. In EAE, an animal model of multiple sclerosis, the balance between Th17p and Th17n/Treg cells regulates the outcome and severity of disease. Using the FBA algorithm Compass, we studied the metabolic underpinnings of T cell pathogenicity in simplified in vitro settings . Leverag13C metabolomics data. Applying this pipeline, the authors identified UDP-GlcNac and glutamine metabolism as characteristic features of M2 macrophage polarization. Furthermore, an inflammation-induced aspartate-argininosuccinate shunt was identified as a link between the metabolic rewiring of the TCA cycle and the production of nitric oxide [Arabidopsis, yeast, mice, and humans [DLD (dihydrolipoamide dehydrogenase) and BCKDHA (branched-chain keto acid dehydrogenase E1) in the brain and liver [The basis of genome-scale networks is the integration of omics data to generate draft reconstructions upon which GSMMs are built. Integration approaches that can incorporate multiple omics data can enhance the depth of network-based approaches. Jha et al. developed such a network-based approach concordant with metabolomics integrated with transcription (“CoMBI-T”) that allows the integration of transcriptional and ic oxide . The autd humans . Of noted humans . This apnd liver . Such inSLC2A5 in B cells, aldehyde dehydrogenase 1 family member A1 (ALDH1A1) in monocytes, superoxide dismutase 2 (SOD2) in neutrophils, equilibrative nucleoside transporter 1 (ENT1 or SLC29A1) and catalase (CAT) in eosinophils, and mitochondrially encoded NADH:ubiquinone oxidoreductase core subunit 2 (MT-ND2) in basophils [This increasing understanding of the human metabolic network provides an opportunity for the clinical application of GSMMs to characterize and predict the outcome of a disease. A recent attempt to increase the patient-specific understanding of diseases is the Human Pathology Atlas developed in 2017. Based on data from ~8000 patients in 17 cancer types and datasets from local and open-source data repositories such as the Cancer Genome Atlas and the Human Protein Atlas, the authors identified genes associated with survival in various cancer types . By applasophils . The recasophils  integratasophils , Recon 3asophils  and iHSAasophils , and theasophils  databaseGSMMs and FBA make simplifying assumptions due to incomplete information. For example, computational predictions by gap-filling algorithms –107 are Saccharomyces cerevisiae [supermodules to which the metabolic network is segmented. scFEA uses a neural network to allow rich modeling of non-linear dependencies of flux on gene expression but ignores reaction stoichiometry. scFEA also segments the metabolic network and prunes non-carbon molecules, resulting in less granular mechanistic predictions [The steady-state assumption in static FBA, namely that net influx through each metabolic reaction is equal to the net outflux, hinders analysis of temporal dynamics of cellular metabolism. Some insight into the system behavior if the assumption is relaxed is offered by the dual variables of the FBA constraints, sometimes called “shadow prices” , 110. Anrevisiae . Based orevisiae . uFBA inrevisiae  relaxes dictions .GSMMs also lack widely accepted standardized protocols for workflow and the validation of model outputs. Genome-scale networks require manual and laborious curation, a process that can introduce significant variability in predictions , 112. ToIn the domain of single-cell studies, future research will also address the lack of specificity in GSMMs. For example, different subsets of the metabolic network may be available to different cell types. The molecular composition of a cell’s environment, which is modeled in FBA and affects the outcomes of the computation, is uncertain even in synthetic and highly controlled growth environments. Better modeling of cellular environments will increase the predictive capability of FBA-based algorithms. The diverse protocols for single-cell sequencing also pose both challenges and promise. For example, we mainly tested the Compass algorithm on Smart-Seq single-cell data , 33. WhiThe ultimate quest of all approaches for interrogating immunometabolism is finding the link between genotype and metabolic phenotype to predict patient- and disease-specific fates of immune cells and to provide novel targets to check the progression of immunological diseases. With the increased availability of large datasets, including the Human Cell Atlas , and the


Stable isotope labelling experiments provide many opportunities for probing metabolic pathways. One goal of such experiments is to define the metabolic phenotype of an organism in terms of the fluxes supported by the entire metabolic network. Metabolic flux analysis (MFA) is used routinely in prokaryotes, but its application to plants is more challenging. Here we examine the status of MFA in plants, highlighting difficulties that hinder wider exploitation of the technique. We conclude that simulation of network fluxes using constraints-based modelling offers a more versatile approach for exploring the capabilities of a network, and that MFA might be best used to probe the interesting features that simulation reveals.13C-MFA has made significant contributions to the analysis of network-wide metabolic responses, and the provision of energy and reducing power, in heterotrophic systems such as plant cell cultures and developing embryos  In autotrophic networks involving the assimilation of a single carbon atom substrate, all metabolites become uniformly labelled at isotopic steady state, and analysis of such systems requires a transient 13C labelling experiment followed by non-stationary (INST) MFA. In principle, INST-MFA can also be used to interrogate heterotrophic networks, and this would be the appropriate strategy for investigating systems in which a metabolic steady state cannot be maintained for long enough to achieve an isotopic steady state after supply of a labelled substrate. (C) Both steady-state MFA and, to a lesser extent, INST-MFA are employed routinely for the analysis of non-compartmented metabolic networks in microbes. (D) The extension of MFA to distinguish between fluxes through equivalent reactions in different subcellular compartments of eukaryotic plant cells relies on the analysis of products that are synthesized in specific cellular locations. These products report on the labelling patterns of defined subcellular pools of network intermediates, and their usefulness depends on the extent to which the labelled intermediates exchange between different organelles. (E) Resolving the distribution of fluxes in different cell types in a complex tissue or organ similarly relies on measurement of labelling patterns of compounds that reflect the isotopomer profiles of network intermediates in individual cell types, and the ability to achieve this may be compromised by the nature and extent of exchange of metabolites between the different cell types.(A) Metabolic flux analysis (MFA) is based on a set of mass balance relationships describing flux through the network at metabolic steady state. The relationships are constrained by measurements of isotopomer abundances of metabolic intermediates and/or products at isotopic steady state following supply of a substrate labelled with a stable isotope. Least-squares regression analysis of this overdetermined problem is used to infer the combination of flux values in the network that best explains the observed redistribution of label. Heterotrophic networks are commonly analysed by steady-state MFA involving the supply of a partially 13C-MFA is that the provision of energy and reducing power can only be addressed indirectly because the interconversion of pairs of coenzymes does not involve a carbon transfer. This means that 13C-MFA cannot distinguish between the activity of NAD- and NADP-dependent enzymes, and this leads to uncertainty in deducing coenzyme budgets for the network. In principle, this problem might be solved using a deuterium labelling strategy developed in mammalian cells . The stoichiometric matrix provides a mathematical description of the network in which the rows represent metabolites and the columns represent reactions. Here, column 3 indicates that reaction 3 consumes equimolar quantities of A and B to produce intermediate C. (B) If the metabolic system is in a steady state, the concentration of every intermediate will be constant, and the product of the stoichiometric matrix and the flux vector will be zero. There may be many flux distributions that correspond to a metabolic steady state, and an optimal solution for a particular set of conditions can be found by using an optimization technique such as linear programming. Operationally it is necessary to apply a set of constraints to the network, such as substrate consumption rate, biomass composition. and known limits on specific fluxes, or more generally metabolomic, transcriptomic. or proteomic data, and to assume that the network operates to achieve a specific objective. The latter would typically be an efficiency objective, such as minimization of the sum of fluxes or maximization of growth. Note that in contrast to MFA, the computational problem is underdetermined, so the optimal solution is not unique. The extent to which the specified objective function can be satisfied by alternative flux distributions can be assessed using flux variability analysis. (C) The applications of flux balance analysis to plants can be greatly extended by setting up sets of models that provide a description of the system under different conditions and solving them as a single optimization problem. In this example, the system is described by five phases that are linked by transfers of cytosolic, mitochondrial, plastidic, and vacuolar metabolites. More generally, the different models might represent different tissues in a whole plant, or different cell types in a tissue, or different time points across a developmental time scale. In the simplest application, the impact of the diel cycle on leaf metabolism can be modelled by setting up light and dark models, with linking metabolite fluxes, and solving the two models simultaneously.(A) A metabolic network interconverts a set of intermediates  and thereby converts inputs  to outputs (E) at rates characterized by fluxes (The selection of the constraints is very important in determining the validity and usefulness of the flux distributions predicted by FBA, but there has been more than a decade of experience in using this technique in plants, and the technique is now well established as a method for exploring the metabolic capacity of the plant metabolic network. Recent applications of the technique have included an analysis of leaf energy balance in the light (13C-MFA in plants.Given the difficulties that have arisen in the application of empirical MFA to plants, there is a strong case for exploiting the power of stoichiometric modelling to identify situations in which the investment in time and effort for MFA would be justified. For example, FBA models can be used routinely to predict the consequences of metabolic engineering (


Staphylococcus epidermidis is a common commensal of collagen-rich regions of the body, such as the skin, but also represents a threat to patients with medical implants (joints and heart), and to preterm babies. Far less studied than Staphylococcus aureus, the mechanisms behind this increasingly recognised pathogenicity are yet to be fully understood. Improving our knowledge of the metabolic processes that allow S. epidermidis to colonise different body sites is key to defining its pathogenic potential. Thus, we have constructed a fully curated, genome-scale metabolic model for S. epidermidis RP62A, and investigated its metabolic properties with a focus on substrate auxotrophies and its utilisation for energy and biomass production. Our results show that, although glucose is available in the medium, only a small portion of it enters the glycolytic pathways, whils most is utilised for the production of biofilm, storage and the structural components of biomass. Amino acids, proline, valine, alanine, glutamate and arginine, are preferred sources of energy and biomass production. In contrast to previous studies, we have shown that this strain has no real substrate auxotrophies, although removal of proline from the media has the highest impact on the model and the experimental growth characteristics. Further study is needed to determine the significance of proline, an abundant amino acid in collagen, in S. epidermidis colonisation. Staphylococci are non-motile Gram-positive cocci, and ubiquitous commensals of the skin and mucous membranes. They are opportunistic pathogens and the most frequent cause of nosocomial infections associated with implanted medical devices.Staphylococcus aureus is probably the best-known and studied member of the genus, a number of non-aureus Staphylococci (NAS) are increasingly recognised as clinically significant pathogens [Staphylococcus epidermidis, which can colonise numerous sites throughout the body and is now the most common NAS species associated with infections of indwelling medical devices, endocarditis and neonatal infections [Although athogens ,2,3. Of fections ,5.S. epidermidis is a facultative anaerobe and possesses complete Embden–Meyerhof–Parnas (glycolytic) and pentose phosphate pathways, as well as the tricarboxylic acid (TCA) cycle (which lacks the glyoxylate shunt) [e shunt) . They mae shunt) ,7,8.S. epidermidis can survive in or on sites as diverse as skin, synovial fluid and the pericardium, suggests a great deal of flexibility in the utilisation of nutrient sources and this, in turn, implies considerable metabolic flexibility. Identifying the minimal nutrient requirements for growth and amino acid auxotrophies is a necessary first step in characterising this flexibility, although for staphylococci this has proven difficult [S. epidermidis.The fact that ifficult ,10,11 anWe propose that a better understanding of this flexibility would, in addition to the inherent contribution to basic science, have potential clinical applications, for example, in the development of prophylactic treatment against the colonisation of indwelling medical devices, in tailoring treatments to specific sites of infection, and in designing improved media for laboratory research .Genome-scale metabolic models (GSMs) describe the network of reactions that are assumed to be present in a given organism, typically derived from an annotated genome, and may be used in a variety of endeavours, including the identification of novel pathways , metabolS. epidermidis and used it to investigate substrate preferences, and understand the growth requirements and potential routes of energy production in an aerobic environment. We have combined modelling and an experimental approach to investigate the metabolic abilities of S. epidermidis to utilise amino acids, its substrate auxotrophies and the impact of amino acid removal on growth and metabolism.In this work, we have constructed the first curated genome-scale metabolic model for S. epidermidis RP62A, version 20.1, using the ScrumPy metabolic modelling package [The model was constructed on the basis of the BioCyc Pathway/Genome Database (PGDB) ,20 for S package  and in a package , Ahmad e package , and wasThe top levelmodule, which serves to import the modules listed below.Automatically generatedreactions extracted from the PGDB, automatically corrected where necessary, as described in Transport reactionsto account for the import of the various media components and export of metabolic by-products .Biomass generationS. aureus [consisting of “pseudo-transporters” to allow for the export of biomass precursors. Biomass composition, comprised of biofilm and planktonic cell composition, was defined as a modification of that described for . aureus   with minimisation of total flux as the objective function. Additional constraints of cell maintenance cost, biomass production and substrate availability in the media were included to define the linear program as:lzhütter , Holzhütlzhütter , Singh elzhütter , vi..j=b−1)- and non-growth (8 mmol ATP gDW−1 h−1)-associated maintenance cost, respectively [ectively ,34. μ vaThe effect of removing individual amino acids from the medium was identified by setting a constraint of 0 to the associated transporter and setting quations  and 2)  μ in Eququations  when groquations .Medium based on that described by Hussain et al.   and inocula were prepared as follows: a 25% glycerol stock was streaked out on BHI agar and incubated at 37 °C. After 24 h, 10 mL of fresh BHI broth were inoculated with 3 individual colonies and incubated for 18 h at 37 °C, shaking (180 rpm). Cells were recovered by centrifugation at 3000 rcf for 5 min. Finally, bacterial pellets were washed twice with sterile PBS, to minimise the potential carry over of nutrients, and re-suspended with PBS up to the original sample volume. An approximate concentration of 1.5 × 108 CFU/ml for the bacterial inoculum was estimated by serial dilution and cell counting.The Amino acids were removed from the MHHW medium one at a time to determine the effect on growth characteristics. The reduction in total available C, N and S as a result of removing the amino acid was assumed to be negligible and no other adjustments were made to the composition of the medium. Original HHW medium and BHI were used as a positive control for growth.6 CFU/mL. 150 μL of each sample was then added to three independent wells in a 96-well plate and incubated at 37 °C and shaking (180 rpm) for 48 h. Each experiment was performed in triplicate and cell growth was monitored by measuring absorbance spectrophotometrically at 600 nm (OD600) at 0, 4, 6, 8, 18, 24, 25, 26 and 48 h. No bacterial growth was observed when inoculated in an MHHW medium without any amino acids , indicating no potential nutrient carry-over. Non-inoculated MHHW medium broth and BHI broth were used as sterility controls and their OD measurements were used as background values, being subtracted from the absorbance measurements of the test samples at each timepoint.Aliquots of inoculum were added in a 1/100 proportion to each test medium (20 μL to 2 mL), to give an approximate final concentration of 1.5 × 10−1). This was achieved by multiplying the OD value by a constant factor of 0.11, which was derived from preliminary experiments measuring OD and dry weight at the same timepoints.In order to make quantitative comparisons between experimental OD observations and model flux calculations, OD must first be converted into units of biomass  and t the subject, we may also determineAs all inocula had reached stationary phase by 48 h, growth parameters were obtained by fitting the logistic (Verhulst’s) equation:S. epidermidis RP62A consists of 895 reactions and 864 internal metabolites, with an additional 95 transport reactions and 74 external metabolites  associations, 55 are spontaneous reactions, and the remaining reactions (169 reactions) have no gene–protein-reaction (GPR) associations and are inferred through the pathway prediction algorithm in the PGDB.The optimal solution to Equation , assumin2, and NH4 respectively.The import fluxes in isoleucine, leucine, phenylalanine, tryptophan, tyrosine, asparagine, histidine and methionine were equal to their respective biomass export fluxes, which is consistent with their direct incorporation into the biomass protein component and glycine, although its availability was not used. The uptake of amino acids relative to their biomass contribution is presented in Examination of the LP solution  showed that approximately 90% glucose consumption was used to satisfy the demand for biofilm, storage and structural components, with only 10% entering glycolysis.4, CO2, acetate and succinate as by-products. It is noteworthy that, although glucose was available, it was not utilised in this solution (see discussion).One explanation for the excess amino acid uptake is that these compounds are catabolised for energy generation; in order to investigate this further, Equation  was solvAs described above, Equation  was repe−1), and these were then used to determine the parameters K and Optical density measurements were first converted to biomass concentration . The time taken to reach half-maximum density , it is notable that they were not simply taken up in the proportions defined by the biomass composition, but varied considerably, between 0% in the case of glycine and 2590% in the case of proline, as shown in Figure 22, and that in an experimental setting such an observation would be taken as evidence for the operation of a conventional glycolysis/TCA/OP scheme, the model analysis suggests quite a different metabolic arrangement. This highlights the fact that a combination of modelling and experimental approaches makes it possible to identify potential modes of metabolism that could not be predicted on the basis of observation of input/output data alone.It is interesting to note that, although the overall model solution utilised glucose and oxygen while excreting CO2 as the terminal electron acceptor.In the absence of a demand for biomass, a fixed demand for ATP was satisfied utilising alanine, proline and glutamate as precursors, despite the presence of complete glycolytic and TCA cycle pathways and the availability of glucose. In the scheme described in Similar schemes for the oxidation of amino acids to pyruvate and ultimately to acetate for ATP synthesis in staphylococci were previously described by a number of authors  [trophies ,48,49,50trophies ,11,51. Germidis) . In thisA more detailed characterisation of the impact that these absences have upon flux distribution in the model, while both interesting and technically straightforward, is beyond the scope of the present investigation. The experimental observation that growth increased in the absence of certain amino acids is something that could not be explained from the model results. We propose, as a working hypothesis, that this effect results from changes in the concentration of signalling molecules in the environment and, as no simple LP method contains information about concentrations, this represents a fundamental limitation of the approach  in collagen, needs to be experimentally studied.We have shown the potential for a complex interaction between amino acid and energy metabolism, whereby amino acids are catabolised with some substrate-level phosphorylation, generating pyruvate, which then feeds the electron transport chain and oxidative phosphorylation. Further experimental investigations are now needed in clinically relevant conditions to shed light on the factors that promote the colonisation of


However, the development of comprehensive metabolism predictors is hampered by the lack of highly accurate metabolic resources. Hence, we recently proposed a manually curated metabolic database (MetaQSAR), the level of accuracy of which is well suited to the development of predictive models. (2) Methods: MetaQSAR was used to extract datasets to predict the metabolic reactions subdivided into major classes, classes and subclasses. The collected datasets comprised a total of 3788 first-generation metabolic reactions. Predictive models were developed by using standard random forest algorithms and sets of physicochemical, stereo-electronic and constitutional descriptors. (3) Results: The developed models showed satisfactory performance, especially for hydrolyses and conjugations, while redox reactions were predicted with greater difficulty, which was reasonable as they depend on many complex features that are not properly encoded by the included descriptors. (4) Conclusions: The generated models allowed a precise comparison of the propensity of each metabolic reaction to be predicted and the factors affecting their predictability were discussed in detail. Overall, the study led to the development of a freely downloadable global predictor, MetaClass, which correctly predicts 80% of the reported reactions, as assessed by an explorative validation analysis on an external dataset, with an overall MCC = 0.44. From their advent in pharmaceutical research, machine learning (ML) algorithms have found many successful applications, ranging from hit identification to drug delivery optimization ,2,3. ThiIn general, artificial intelligence (AI) methods can find at least three major applications focused on drug metabolism  since thNotwithstanding the above, most of the reported predictive studies are still focused on redox metabolism, with particular attention paid to CYP-450 catalyzed reactions . In contThe discrepancy between the studies focused on redox metabolic reactions and those dealing with the other metabolic reactions might be justified by considering the marked relevance of the former, which represent by far the most common biotransformations . NeverthA more pertinent cause that might explain the scarcity of comprehensive predictors is the lack of extended and truly accurate metabolic databases. Most available datasets are focused on the metabolic reactions catalyzed by CYP-450 isozymes  and ofteOn these grounds, we recently reported a novel metabolic database (MetaQSAR), which was generated by manual and critical meta-analyses of the specialized literature published during the 2005–2015 period . The colBased on these encouraging results, the MetaQSAR database is here exploited to perform an exhaustive predictive analysis of all the sets of metabolic reactions for which the database includes sufficient instances . In these predictive studies, we follow the same classification system adopted by MetaQSAR, which subdivides the metabolic reactions into three main classes , 21 classes and 101 subclasses. In detail, the reported analyses involve the 3 main classes, 18 classes and 23 populated subclasses. Details concerning the subdivision into main classes, classes and subclasses can be found elsewhere . The modBesides developing comprehensive models able to predict the occurrence of the major metabolic reactions, the study aims to offer a comparative analysis of the propensity of each metabolic reaction to be predicted. Such a propensity might depend on the chemical space covered by the extracted datasets and on the informative richness of the computed descriptors, but also on the intrinsic features that govern the predicted reactions. These comparisons should reveal which reactions are unpredictable (at least by using the available data), which can be predicted even by applying standard methods, as reported here, and which reactions require targeted approaches to enhance the resulting performance. The predictive models generated for the classes of reactions are also utilized to develop a global tool, called MetaClass, and implemented within the VEGA environment , which pThe reported comparative analysis is based on the metabolic reactions collected within the MetaQSAR database and focuses on the first-generation reactions. Overall, the study involved 3788 metabolic reactions, which could be subdivided into 3 major classes, 21 classes and 101 subclasses. Predictive models were generated for the three major classes  and for As described in the Methods, the initial predictive analyses of the three major classes were utilized in the validation phase to tune the developed models by selecting the best-performing algorithm and by optimizing the corresponding hyperparameters. Moreover, they also had a calibrating role for the following class- and subclass-specific studies since these initial analyses were carried out for evaluating (1) the performance achieved by various sets of descriptors, (2) the relevance of using balanced datasets and (3) the role of the substrate’s ionization state. The following predictive studies were then carried out by applying the derived best-performing conditions.The comparison of the results reached by the three major classes reveals that hydrolyses afford, on average, the best performance regardless of the utilized descriptors and datasets, while conjugations yield the worst results. These findings can be explained by considering that the hydrolytic reactions, while involving different enzymes, comprise a rather homogeneous set of metabolic reactions. Hence, a single predictive model can account for all the collected reactions. In contrast, the redox reactions and especially the conjugations comprise a wide variety of metabolic reactions, which involve different enzymes, different catalytic mechanisms and different substrate preferences. Thus, their occurrence cannot be properly predicted by unique models.Concerning the set of descriptors, While the overall metrics show limited differences, the comparison of the class-specific performance reached by balanced and unbalanced datasets emphasizes the beneficial effects exerted by balancing the datasets. The beneficial effect of the balanced datasets can be appreciated by considering that the capacity to recognize the instances of the minority classes  is around 0.5 in all the analyses involving the unbalanced datasets. This means that the thus obtained predictions are comparable to the random results. In contrast, the performance of the minority class increases by using the balanced datasets, reaching rather satisfactory values at least for redox reactions and hydrolyses.With regard to the role of the ionization state, The Kier–Hall indices afford also here the best models, and the performance of both sets of descriptors is similarly affected by the ionization. The effect on Kier–Hall topological indices suggests that they properly capture the structural differences between neutral and ionized molecules. The effects on stereo-electronic parameters are expected and predictable, while the impact on physicochemical descriptors can be mostly ascribed to lipophilicity-related features. Since the ionization plays a negative  role in most comparisons (4 out of 6) and considering the possible inaccuracies introduced by automatic generation of the most plausible ionized forms, the following class-specific models were developed by considering the substrates in their neutral form.Overall, The analysis of the reported average performance reveals a trend in substantial disagreement with that evidenced by The analysis of the performance reached by each specific class allows for some considerations. Concerning the redox reactions, Concerning the hydrolyses, When focusing on conjugations, With regard to the sets of descriptors, Along with the discussed heterogeneity of the involved metabolic reactions, a factor that can explain the differences in performance reached by the analyzed classes is the efficiency of the considered metabolic reaction. Stated differently, a metabolic class can be conveniently predicted if almost all the substrates that contain a given reactive group undergo the corresponding metabolic reaction. By contrast, when the presence of a given reactive moiety is a necessary but not sufficient condition and many substrates that include such a reactive center do not undergo the metabolic reaction, its occurrence can be predicted with greater difficulty. Regardless of the heterogeneity of the involved reactive moieties, In detail, the achieved performance for redox reactions confirms the difficulty in predicting the biotransformations on the carbon atoms. This is partly ascribable to the richness of substrates within these subclasses, but is especially due to the variety of factors that govern these redox reactions, which cannot be described by the simple occurrence of reactive fragments. Only the subclasses of reactions involving double bonds and carbonyls can be conveniently predicted (MCC > 0.6). In addition, O-glucoronidations on the resulting performance, while the further classification of the reactions with GSH has a negligible role on the developed predictive models.The subclasses for the hydrolyses reach remarkable performance, especially for esters, the subdivision of which into neutral and ionizable substrates enhances the resulting performance. The overall effect of the clustering into subclasses can be appreciated by analyzing the charts reported in With regard to the utilized sets of descriptors, As discussed above, the performance of the Kier–Hall indices depends on the efficacy of the considered reactions. The performance achieved by the analyzed subclasses confirms the greater efficacy of hydrolyses and conjugations compared to redox reactions. Stated differently, the performance values compiled in To explore the relevance of each descriptor included in the utilized sets, the analysis of the feature relevance was performed by Weka. Attention was here focused on the predictive analyses involving the 18 analyzed classes since they represent a comprehensive analysis of all metabolic reactions. The feature relevance was analyzed by considering together all the utilized descriptors. The results were assessed by cross-validation repeated 10 times. Only the descriptors included by at least five validation runs were considered as relevant features.O-glucuronidations to 15 for redox reactions of >NH, >NOH, and –N=O. Although there is no correlation between the number of relevant descriptors and the performance of each class, one may observe that the average number of descriptors for the three main classes is in line with the average performance , thus confirming that the best-performing models are, on average, characterized by a limited number of variables.As detailed in the Methods, the predictive models generated for the classes were deployed by a tool that was developed to predict the occurrence of the corresponding biotransformations for a given input molecule. The tool, called MetaClass, was generated by the Tree2C approach  and implTo provide a preliminary validation of its predictive performance, the MetaClass predictor was tested to predict the metabolic reactions for a set of 10 molecules not included in the database used to develop the models since their metabolic studies were published after 2015. The study involved 2787 substrates that undergo 3788 first-generation metabolic reactions, as classified into 3 main classes, 21 classes and 101 subclasses. The MetaQSAR database contains the 3D structure of the collected substrates in their neutral state . For thehttp://www.ra.cs.uni-tuebingen.de/software/bluedesc/ (accessed on 23 September 2021). In detail, the code was encapsulated into a front-end VEGA script that supports the analysis of molecular databases as well as the generation of the CSV output files.The study involved the calculation of three sets of descriptors. The first set comprised 168 various variables, including constitutional, topological and physicochemical descriptors as computed by BlueDesc. These descriptors were computed by using the Java code available at The second set comprised 25 constitutional, geometrical and physicochemical descriptors as computed by VEGA plus 12 stereo-electronic parameters as calculated by PM7 semi-empirical calculations (see above). The last set comprised 44 Kier–Hall topological indices, which are categorical values that encode for the occurrence of specific functional groups . They wehttps://cdk.github.io/cdk/1.5/docs/api/org/openscience/cdk/qsar/descriptors/molecular/KierHallSmartsDescriptor.html (accessed on 23 September 2021). A description of the included constitutional, geometrical, physicochemical and stereo-electronic descriptors is provided in The complete list of the Kier–Hall topological indices with the corresponding SMARTS strings can be found at As mentioned above, the presented predictive studies involved the three major classes and the classes and subclasses including at least 50 metabolic reactions. The initial predictive studies on the three major classes were exploited to select the optimal classification algorithm and to optimize the corresponding parameters. The tuning of the RF hyperparameters was performed by means of the “Experimenter” module in Weka. In detail, the following parameters were considered: (1) the batch size; (2) the number of threads; (3) the number of iterations; (4) the attribute importance. Overall, 14 runs were carried out based on 10-fold cross validation, by which each test was repeated on the dataset 10 times with different random number seeds.Based on these tests, all the reported classification models were developed by the random forest machine learning algorithm as implemented in the Weka program with the following parameters: (1) the batch size = 100; (2) the number of threads = 1; (3) number of iterations = 100; (4) the attribute importance was not evaluated.The most significant features were selected by using the Weka program according to both the BestFirst search algorithm  and the WrapperSubsetEval attribute evaluator . As described in the Results, the predictive models were developed by considering the substrates in their neutral form for the three main classes of metabolic reactions and for all the classes and the subclasses with at least 50 occurrences. All the reported predictive models were developed by using balanced datasets as obtained by random undersampling using an ad hoc script implemented in the VEGA program. In contrast, the protonated forms of the substrates and the unbalanced datasets were utilized only to predict the occurrence of the three main classes.The models generated for the classes of metabolic reactions see  were utiTo develop the MetaClass predictor, the Tree2C approach was applied to the predictive models for the metabolic classes by generating the corresponding C code for each model. The generated codes were then merged into a unique script that predicts the occurrence of all the classes for the molecule loaded in the VEGA workspace. To speed up the MetaClass predictor and to support its release, the resulting codes were assembled into a precompiled binary library, which was optimized for use within the VEGA environment.To simplify the generation of the MetaClass predictor and to support its constant updating, a script to automatize the model generation (MetaClass builder) was also developed. Based on a database of metabolic reactions structured as implemented by MetaQSAR, the script performs the following tasks: (1) extracting the datasets for the classes of metabolic reactions; (2) balancing them by random undersampling of the majority class; (3) calculating the selected descriptors for the collected substrates, which can be calculated directly by the VEGA program or can be provided externally; (4) generating the predictive models by interfacing the script with the Weka program; (5) transforming the models into the corresponding C codes by using Tree2C and (6) assembling the final precompiled library.MetaClass builder can have two major applications. First, we use this to automatically generate updated releases of the MetaClass predictor, which parallels our continuous efforts to update the MetaQSAR database. Second, any research group can use this tool to develop its own predictor system by exploiting their internal metabolic data, which should be structured as requested by the MetaQSAR database features.The study describes a set of tree-based models to predict the occurrence of specific metabolic reactions. They were developed by using a standard random forest procedure and exploiting rather limited sets of representative descriptors. It should be noted that better models might be generated by using extended sets of descriptors through an optimization procedure specifically tailored to each analyzed dataset of metabolic reactions. Nevertheless, the primary objective of the study was focused on an extensive comparison of the achieved performance when predicting the occurrence of the various metabolic reactions as classified by the MetaQSAR database. Thus, the applied procedures were similarly performed for all datasets, and the possible resulting loss of performance similarly affected all the developed models, thus enabling a reasonably unbiased comparison of all the achieved performance results.Even when considering the corresponding subclasses, the redox reactions revealed the poorest performance. These negative results underline the complexity of the factors governing these metabolic reactions and suggest that predicting these reactions requires tailored approaches involving optimized algorithms and/or specifically designed descriptors.The hydrolyses provided almost always the best models and benefited from a detailed clustering of their reactions.When subdivided into classes and subclasses, the conjugations yielded, on average, satisfactory predictive models; this suggests that these reactions can be conveniently predicted by recognizing the involved reactive groups.When considering the performance achieved by each predicted class, the obtained results can be summarized as follows:While considering the comparative aim of the study, the developed models for the considered metabolic classes provided satisfactory performance  in 10 out of 18 classes. Therefore, a global classification system, called MetaClass, was developed within the VEGA environment to predict the occurrence of the various metabolic reactions. Clearly, these predictions should be cautiously taken by considering the here described performance. Nevertheless, they can provide a reasonable picture of the overall stability of the tested molecules as well as of the most probable reactions that they can undergo. Finally, a script (MetaClass builder) was developed to automatize the development of the predictive models and of the resulting classification system. Besides allowing the constant updating of the MetaClass predictor, this can be used by any researcher to develop similar predictive tools by exploiting its own metabolic data.


Mathematical modeling is a promising tool for better understanding of cellular processes. In recent years, the development of coarse-grained models has gained attraction since these simple models are able to capture and describe a broad range of growth conditions. Coarse-grained models often comprise only two cellular components, a low molecular component as representative for central metabolism and energy generation and a macromolecular component, representing the entire proteome. A framework is presented that presents a strict mass conservative model for bacterial growth during a biotechnological production process. After providing interesting properties for the steady-state solution, applications are presented 1) for a production process of an amino acid and 2) production of a metabolite from central metabolism. To gain a full understanding of cellular processes, the usage of mathematical modeling and the analysis of those have become a standard in metabolic engineering, systems biology, and process engineering. Predictive models which can describe relevant cellular processes can be used as a basis for process observation and process design with the intention to optimize the properties and behavior of the cells. Even though bacteria are very diverse, the basic principles of their metabolism are quite similar. In general, every bacterial population has to cope with its environment, scavenge for nutrients, and then coordinate its central metabolism accordingly for growth and survival. The underlying regulatory networks are very densely intertwined, large, complex, and not fully known or incompletely understood, thus providing a big challenge to understand the processes in its entirety. Mathematical models trying to describe all these processes in detail are challenging and nearly impossible because of the huge number of variables and uncertain parameters.Coarse-grained models have been used in the recent years and are now frequently used to get a better understanding on cellular control strategies, gene expression, and resource allocation Typically, coarse-grained models are written down as a set of differential equations for the components of the model, whose unit, for example, is the number of molecules per cell or mol/g dry cell weight. However, mass balance equations must fulfill the conservation of mass as dictated by the first fundamental theorem of thermodynamics, and often, a consistent transfer from mass balance equations to differential equations for the concentrations of the model components is faulty or inadequate. Therefore, we start by a brief recapitulation of the structure of the ordinary differential equations for coarse-grained models that are combined with models for the environment, for example, in a bioreactor process system. Here, a new relationship for the specific growth rate in dependence on the exchange reactions of the entire network is given. This equation is fundamental since it guarantees strict mass conservation for the complete system. Conventionally, the growth rate is an empirical function and, therefore, strict mass conservation is not ensured. In a second step, we analyze the model and show interesting properties of the steady-state behavior. We provide a general steady-state solution for biochemical networks and compare outcomes of a traditional flux balance analysis with our new approach. Finally, various applications and extensions for a broad spectrum of problem formulations in biotechnology are provided: 1) an L-phenylalanine production process and 2) the production of a metabolite from central metabolism. Hereby, problems of resource allocation as well as problems of parameter estimation are addressed.mi of a component i, the mass balance reads asFrom thermodynamic principles, mass conversion is crucial and plays the major role of determining the time course of selected quantities of interest  which are called state variables. From a static view on the biochemical reaction equations alone, however, it is not possible to infer on the time course of the state variables. A mass balance equation that describes the change of a compound over time and sums up the material flow in and out of the system comes into play here. It is a differential equation. Since we are interested in the mass J describes the mass flow into the system while P describes conversion inside the system, for example, by biochemical reactions. Both summands depend on other state variables in the system. In the current form, the equation cannot be applied. The reason is as follows: for biochemical reaction networks, P describes mass conversion by reactions, and the reaction velocity strongly depends on the concentration of a compound given by ci = mi/V of the reaction partners and not on the mass mi of the reaction partners alone. For applications in systems biology, synthetic biology, and biotechnology, a different convention is used for the definition of the concentration of the cellular components . Since it is much easier to determine the entire biomass mX than the cellular volume, the following definition is used, instead, for the concentration of an intracellular metabolite: ci = mi/mX.In this general equation, N and a rate vector μ is an integral parameter that—in a strict sense—is determined by the mass exchange of the population with its environment. Therefore, it is defined asTo avoid inconsistencies, it is recommended to always start from the mass balance and reformulate the mass balance into an equation for the concentration . For a cellular network, the basic differential equation then readsτ of the population in the relationship τ =  ln 2/μ. For the biomass itself, also, a mass balance is set up that takes into account the changes of biomass concentration due to removal from the bioreactor and biomass formation due to growth. However, a different approach can be used as shown in the Supporting Information that describes the changes of biomass based on the changes of all compounds representing the biomass. Therefore, from a formal point of view, the specific growth rate μ only depends on the rate vector The specific growth rate is related to the doubling time W representing the mass matrix. Together with the equations for the concentration for a substrate S and biomass X in a bioreactor system with feeding rate qin, feed concentration Sin, and stoichiometric vector Plugging N. Solutions for rate vector N, providing possible fluxes through the cellular network W has to be taken into account as well, and the steady-state solution for the intracellular network is obtained from the relationshipIn classic flux balance analysis, the equation for a cellular network only consists of the stoichiometric matrix N as in the classic flux balance analysis but also by the kernel of matrix W, which is determined by the molecular composition of the cell. The determinant of W is given bywhich is obtained from i, and given the strict mass conservation, the sum over all mass fractions equals one. Therefore, the determinant of W is always zero, and W is nonsingular. Additionally, one can show that the kernel of W is in fact one-dimensional (the proof can be found in Supplementary Information). The complete solution N, denoted by N, denoted by N+, and the kernel of W, denoted by The addends of the second term are the mass fractions of cellular component s and an arbitrary vector The two summands in the solution are not given in a unique way and can be written with scalar factor This principle holds true for all types of cellular networks independently of its size and form, which can range from whole-cell models to, in this case, coarse-grained models as shown in A typical minimal reaction system as shown in M, proteins P, and reactions ri that connect the pools with each other and the environment. Rate rT describes the transport of the substrate into the cell, while rate rO describes overflow metabolism. Proteins P are synthesized with rate rPIt is to be noted that an extension to two or more anabolic reactions can be performed easily since, in general, the mass fractions of the macromolecules are well-known. The reaction systems, therefore, consist of a pool of metabolites Thus, the intracellular network for this minimal model can be written asM and proteins P, respectively. With the observation from rP, is only defined by the second term. Thus, for the assumption of the known specific growth rate μ and molecular composition of the cell, this rate is fixed, while the remaining rates, meaning the substrate uptake rate rT and the overflow metabolism rate rO, are coupled through one degree of freedom a. If one of these rates is known, the degree of freedom a can be determined and, therefore, the last remaining rate.For the basic structure, with To illustrate the different outcomes when applying the new approach with strict mass conservation as seen in S is taken up and four metabolites are generated which in the conventional approach are consumed in reaction r5 to produce biomass. To make it realistic, we assume that the stoichiometric coefficient for biomass is 100, that is, 100 small molecules are used to get 1 mol protein/ biomass. The reaction system is given as follows:Substrate N1 for the internal network has four rows and five columns:In the case of constraint-based models that are used, for example, for flux balance analysis or by N1 is one-dimensional, and the only possible solution, when providing 1 unit flux of substrate uptake, results in 0.01 unit of biomass . The situation becomes different when strict mass conservation is taken into account. Here, we consider the formation of protein/biomass. Therefore, the overall biomass composition dictates the flux distribution in this case. From the depicted scheme, we infer the molecular weight for the components as follows  N2  and the vector of molecular weights, the specific growth μ can be calculated as mentioned before with Hence, the null space of r1 and r4) appear. In the case at hand, the stoichiometric matrix N2, taking into account the protein/ biomass fraction as additional component, has five rows and five columns and has full rank. However, the null space of W ⋅ N2 with W given in W strongly depends on the cellular composition; the composition itself is the steady-state solution, if the system is given in the standard form . This flux vector is very different from the solution not considering strict mass conservation.It is to be noted that here only reactions that exchange with the environment  is not possible since μ itself depends on R and T. Therefore, we proceed as follows: for the case at hand, an algebraic system could be set up for the steady-state solution of the differential equation system. The system readsS, relationships of the form T = g1, and R = g2 are determined. In this way, also the dynamical system could be simulated. In addition, in this format, the system for the intracellular network consists only of two independent variables M and P. T and R from the specific growth rate as measured experimentally .The program is simplified to only one design variable T fraction is always higher than that for the R fraction which is not the case in A comparison of the growth rate indicates that only a slightly higher growth rate could be achieved in the optimal case. This is based on the observation that the protein fraction that is allocated to the Escherichia coli strain with glycerol as the substrate and decoupled biomass and product formation due to L-tyrosine auxotrophism, meaning biomass is only formed if L-tyrosine is available . As reasons for this behavior have not been investigated at this point, the mechanistics to depict this are not incorporated in the model. Using t = 71 h was performed using MATLAB R2020a with ode15s as ordinary differential equation solver and was compared to experimental results  that is excreted into the medium via reaction r3  as a function of time and a fixed-end time tend = 20 h. With the feed, the substrate concentration can be adjusted in such a way that the metabolite is excreted at best. In contrast to a batch process, the substrate is fed into the medium and, therefore, high sugar concentrations in the beginning (as for the batch process) are avoided. Since a continuous process requires much more time, a steady state is reached normally first after five times the respective time constant (in our case approx. 20 h); this type of process design is also not considered here.• A fed-batch process in a bioreactor is considered with a flexible input profile for the incoming substrate feed rate • The initial conditions are set fix for all model state variables.• The bioreactor has a maximum working volume of 5 l, while in the beginning, the experiment starts with 1 l.tend: MexV.• The objective function is the amount of product expressed in mole at The second example considers the optimal production of a metabolite  A standard procedure, often applied in bioprocess engineering tries to feed the substrate in an exponential way to keep the specific growth rate r1 is estimated given the biomass yield coefficient Y during the batch phase and since the current substrate concentration is low , we finally obtainTypically, The feeding profile is applied after the end of the batch phase.ai to optimize.2) The second profile uses a polynomial function of time for the feeding rate:tk:3) The last profile is a piecewise linear profile with six fixed switching points R fraction is high  and, therefore, due to the coupling to the T fraction, the rate of byproduct formation is low. After starting the feeding, the intracellular system switches to high values for the T fraction Next, a comparison of the feeding profiles and the final value of the objective function is shown in First, a typical outcome for the standard case is shown in rmax for all reactions. To consider these uncertainties, an ensemble of 20 models is generated during each iteration step of the optimization. This results also in an ensemble for the values of the objective function Φ, following the approach proposed by α, expectation E, and variance Var. With this formulation, stronger variations in the values of the objective function, expressed in the variance of Φ, are penalized. Since the feeding profile is geared to the growth rate, a much more conservative output is expected; if the substrate uptake, for example, would be higher than expected, more biomass would be produced, and few byproducts will be released. As can be seen in left of The simulation studies are based on a fixed set of kinetic parameters and, so far, did not consider any uncertainties with respect to the quality of these. Typically, kinetic parameters are obtained by parameter identification and subsequent parameter estimation and analysis. For our example at hand, in the next step, the uncertainty of the kinetic parameters is taken into account during the optimization procedure. Important parameters of the model are the maximal reaction velocities tend, also the cost of substrate is of interest. In a fed-batch process, the total amount of substrate Stot fed, considering the substrate concentration at the beginning S0, can be calculated byBesides the optimization of the product at tend, and minimization of the substrate cost for the entire process can be presented with a Pareto front that is shown in The outcome of having two objective functions, maximization of product at W that requires information on the mass fraction of the components of the model. With a simple example, we could show that depending on the mass composition of the cell, larger differences in the flux distribution in comparison to the standard approach could appear. With the condition of strict mass conservation, we are also able to provide a general solution for a cellular network independently of its internal structure.In bioprocess engineering, the design of experiments often is based on a mathematical description. While simple growth models taking into account only biomass, substrate, and product often are insufficient to describe the observed dynamics, whole-cell models are cumbersome and are difficult to calibrate. A good model comprises coarse-grained models because they are simple in the model structure but take into account the most important cellular processes. In this study, we propose an approach to use coarse-grained models based on a strict mass conservation to model bacterial growth as a basis for metabolic engineering applications. In this way, classical flux analysis could be extended to take into account fluxes into macromolecules such as the proteome. Additional solutions are provided by the null space of the mass matrix R fraction representing the transcription and translation apparatus and a T fraction, taking into account metabolic and transport enzymes. The outcome of these simulation studies is compared with that of a model where the R fraction is an adjustable quantity in an optimization program (the sum of the R fraction and T fraction is taken as constant). The results of the optimization program show that an optimal allocation of proteins led to a slightly higher growth rate with a comparable course of the R fraction as a function of the specific growth rate, and we conclude that the measured data are in good agreement with the expectation of an efficient and optimal acting organism.As the focus of this research is coarse-grained models, we provided a formulation for a minimal model whose structure is in accordance with that in previous studies Many studies have dealt with the derivation of growth laws under various conditions Escherichia coli FUS4 (pF81kan) strain was used as described by aroF, pheA, and tyrA  along the aromatic biosynthesis pathway. Simultaneously, it harbors the pF81kan plasmid decoding for the genes aroF, pheA, aroB (3-dehydroquinate synthase), and aroL (shikimate kinase 2) under the control of an inducable tac promoter. Furthermore, kanamycin resistance is integrated as the selection marker For the L-phenylalanine production process, in a stirred-tank bioreactor of 3.6 l working volume, a recombinant The cells were cultivated in a defined minimal medium with glycerol as the sole carbon source. All the components with their corresponding concentrations as well as its production protocol were adapted from the study by 600) of 0.01. After incubation at 37°C and 250 rpm for at least 24 h, the cells were centrifuged  and resuspended in fresh minimal medium. These cell suspensions were used for inoculation of cultivations in the stirred-tank bioreactor with a starting OD600 of 0.1.Provision of cell biomass for the inoculation for the cultivation in a stirred-tank bioreactor was realized by a two-step preliminary cultivation in shake flasks. First, a single colony of cells grown on minimal medium agar plates (E. coli FUS4 (pF81kan) for L-phenylalanine production, a 3.6 glass stirred-tank bioreactor was used . The bioreactor was equipped with two six-bladed flat-blade turbines and three equidistant baffles. The minimal medium for cultivation was prepared ex situ and pumped into the bioreactor under sterile conditions to a starting volume of 1 l. The temperature was kept at 37 °C. 42% phosphoric acid and 25% ammonia were used as titration solutions to keep the pH at 7 ± 0.1. Dissolved oxygen levels above 30% were provided by step-wise increase of either stirrer speed or aeration rate up to 1,500 rpm and 5 l/min, respectively. Furthermore, an antifoam probe was used for controlled titration of antifoam solution, if necessary . The cultivation started with an initial batch phase. After depletion of glycerol, an exponential feeding was set for the biomass production phase with a defined growth rate of μset = 0.1 1/h. Two fed-batch media were used with either 120 g/l glycerol, 2.5 g/l L-phenylalanine, 3.6 g/l L-tyrosine, 60 g/l ammonium sulfate, and 0.1 g/l kanamycin (fed-batch medium 1) or 400 g/l glycerol, 1.11 g/l L-phenylalanine, 3.8 g/l L-tyrosine, 25 g/l ammonium sulfate, and 0.1 g/l kanamycin (fed-batch medium 2). The former and the latter were titrated with 25% ammonia or 5 M potassium hydroxide to allow complete dissolution of L-tyrosine. After a sufficiently high biomass concentration of at least 20 g/l was provided, the cells were induced with 0.3 mM IPTG. Fed-batch medium 3 with the components 800 g/l, 8 g/l ammonium sulfate, 8 g/l ammonium phosphate, and 0.1 g/l kanamycin was then constantly provided with a rate of 0.18 gglycerol/gBiomassh. At the start of each fed-batch media supply, the concentrated media components calcium chloride dihydroxide (15 g/l) and iron(II) sulfate heptahydrate with sodium citrate dihydrate (22.5 g/l and 200 g/l), magnesium sulfate heptahydrate (300 g/l), and thiamine hydrochloride (7.5 g/l) were mixed in a 1:5:1:1 ratio and injected to the fermentation broth via a septum. For the start of fed-batch phase 1, 2, or 3, a mixture of 4.8, 9.6, and 8.8 ml were injected, respectively For laboratory-scale cultivation of recombinant μm filter and were stored at 4°C upon measurement. The quantification method for both amino acids is already described by μl of samples was injected to an isocratic flow of 0.6 ml/min and 5 mM sulfuric acid as mobile phase with a constant temperature of 60°C. The quantification of each component was realized by measurement of external standards.Cell dry weights were measured gravimetrically. Pre-weighted dried 2-ml microcentrifuge tubes (80 °C for at least 24 h) were used for centrifugation of 2 ml of the cell suspension . The supernatant was further used for sample preparation for high-performance liquid chromatographies (HPLCs) or discarded. The cell pellet was dried again at 80°C for at least 24 h. The biomass concentration was calculated by the difference of weight between the microcentrifuge tube with dried cell pellets and the empty microcentrifuge tube. For the quantification of the amino acid concentrations of L-phenylalanine and L-tyrosine as well as for the organic compounds glycerol, acetate, lactate, succinate, pyruvate, malate, and ethanol, two different HPLCs were used. The samples for HPLC analysis were prepared by filtration of the supernatant of each sample through a 0.2-


Computational and statistical analysis of shotgun metagenomes can predict gene abundance and is helpful for elucidating the functional and taxonomic compositions of environmental samples. Gene products are compared against physicochemical conditions or perturbations to shed light on the functions performed by the microbial community of an environmental sample; however, this information is not always available. The present study proposes a method for inferring the metabolic potential of metagenome samples by constructing a reference based on determining the probability distribution of the counts of each enzyme annotated. To test the methodology, we used marine water samples distributed worldwide as references. Then, the references were utilized to compare the annotated enzymes of two different water samples extracted from the Gulf of Mexico (GoM) to distinguish those enzymes with atypical behavior. The enzymes whose annotation counts presented frequencies significantly different from those of the reference were used to perform metabolic reconstruction, which naturally identified pathways. We found that several of the enzymes were involved in the biodegradation of petroleum, which is consistent with the impact of human hydrocarbon extraction activity and its ubiquitous presence in the GoM. The examination of other reconstructed pathways revealed significant enzymes indicating the presence of microbial communities characterizing each ocean depth and ocean cycle, providing a fingerprint of each sampled site. The Gulf of Mexico (GoM) is an area with important oil industry activity that is constantly affected by the extraction and transportation of hydrocarbons, sometimes causing large-scale spills, which have repeatedly disturbed the area . The intShotgun metagenomics has become an essential tool for inspecting the metabolic potential and taxonomic composition of environmental DNA . SequencSeveral studies outlining the functional potential of ocean water columns and sediments are based on metagenomic studies. The metabolic potential of the microbial communities revealed in metagenomic studies is expected to correlate with the characteristics of the physical and chemical parameters of each sample. Examples of these measurable parameters are dissolved organic matter (DOM), inorganic matter, temperature, pH, and depth. Other parameters that are difficult to assess are the direct and indirect interactions between microorganisms distributed in water layers and sediments. The inference of pathways based only on the above information may make some functions challenging to appraise since these parameters are not always available.In recent years, publicly available metagenomic databases have grown to house thousands of studies, providing the unique opportunity to compare experiments to identify the differences between gene products and taxa in distinct biomes . HoweverWe evaluated two metagenomes of water samples from the GoM collected in March 2016 . Sample We downloaded the assembled sequences of 19 water samples from the Sequence Read Archive (SRA) database collected on GEOTRACES cruises  coveringe-value ≤ 1E−04 were classified based on their functions according to the Enzymatic Commission (EC) number (The GoM and reference samples and the annotated gene products of enzymes showing 45% sequence identity and an ) number . A minor) number .1 with default parameters to trim adaptors and clean reads. Trimmed paired-end reads were then merged into a single fasta file for later assembly with IDBA-UD , where θgl represents certain parameters to be determined. Thus, for a given metagenome, k, not belonging to the reference, we can tell if the observed frequencies, ygk, are within the reference values or constitute a statistically unexpected event.We extend this idea further and consider a collection of metagenomes processed according to the same workflow but under slightly different environmental conditions. In this case, we expect greater variability in the observed fitdistr function from the R package MASS2. Since the data to be fitted were frequencies, we try to fit a normal distribution only when s are the sample means and standard deviation. When this condition was not fulfilled, the theoretical distributions with which we attempted to fit the data were gamma, log-normal, Weibull. In this case, the goodness of fit for each distribution was verified through the Anderson–Darling test in the R package goftest.3 To choose the optimal fit, we used the Akaike information criterion.Once the parameters of each enzyme were assigned to each metagenome in the reference, we obtained an empirical distribution for the enzymes in the reference . We fittNext, for the two metagenomes under study, we calculated quantities in a manner analogous to Eq. 1:k = 1, 2, and using the set fg of fitted distributions, we calculated the probability:with Zgk score determined with the following equation:To ease interpretation, rather than to work directly with the values in Eq. 2, we choose to express these probabilities in terms of an equivalent N(x) is the PDF of a normal distribution with a zero mean and a unitary standard deviation. The set {Zgk} is the basic information that we use to derive our results. An example of the results of these procedures is provided in where z-scores lower than −1. The networks were displayed using Cytoscape software  using MCL software  with an The selection of genes encoding enzymes representing the metabolic potential of metagenomic samples is mainly based on the search of key (marker) enzymes of expected metabolic pathways of the microbial communities. The resolution of the reconstructed pathways is usually improved by searching for other enzymes using software and data bases as for example KEGG Mapper  or by maIn contrast, our approach aims to highlight enzymes, in a sample under study, with values of the rates in Eq. 1 that are significantly different from those of the reference group of metagenomes under similar environmental conditions. We then take this set of enzymes with atypical rates as a seed with which to reconstruct a metabolic network, which gives a hint of the metabolic potential of the sample.P directly, as described in “Materials and Methods,” it is convenient to transform it into a z-score using Eq. 3. These calculations can be easily performed with the appropriate software. We provide an example of the code used in R in z-score can be calculated by hand with the usual formula. As is well known, the z-score in the center of the curve is zero, meaning that enzymes with values close to zero behave the same as in the reference. The z-scores to the right of the mean are positive, and the z-scores to the left of the mean are negative. Additionally, an important property of the z-score is that it can be used to calculate the percentage of the population below a given value. For this study, enzymes of the GoM presenting an EZS ≥ 2.0 have a rate higher than 97.72 of the reference observations. The equivalent z-score (EZS) above this region should be considered to have an atypical behavior; i.e., the enzymes with an EZS ≥ 2 are involved in metabolic functions overrepresented in the GoM communities. However, the enzymes located in the negative part of the curve, with an EZS ≤ −1, are also atypical but may be more relevant in the reference’s metagenomes. Finally, those enzymes in the interval between −1 > EZS ≤ 2 should be relevant for the communities represented in both the reference and the GoM metagenomes.The reference, as described in “Materials and Methods,” comprises a set of PDFs for those enzymes present in all 19 selected metagenomes. To obtain a random sampling and maximized variability of the metagenomes, we gathered samples located at different longitudes, latitudes, and depths. As described in the methodology section, we calculated the PDF for each enzyme appearing in all 19 analyzed reference metagenomes. After the procedure was performed, 1,127 enzymes with a full EC description available were retained for posterior analysis. The statistical analysis showed that 49 (4%) enzymes had a gamma distribution, 257 (23%) had a Weibull distribution, 356 (32%) presented a log-normal distribution, and 465 (41%) showed a normal distribution . We thenWe then analyzed the behavior of enzymes essential for the maintenance of cellular integrity that should be present in every metagenome. Examples of such proteins include RNA polymerase subunits, aminoacyl-RNAt synthetase (aaRS), ribosomal proteins, and some metabolic enzymes that have been identified in representative organisms . The KEGIn the next step, we explored whether the enzymes were equally distributed in the pathways, which was not the case, as shown in n = 2); environmental adaptation, endocrine system (n = 1); and drug resistance: antimicrobial (n = 1).The 879 enzymes that were associated with a metabolic pathway and had an EZS were organized into the B functional classes stored in the KEGG BRITE database , yieldinAmong the boxplots shown in To evaluate the pathways defining the metabolic potential of both metagenomes, we took as a starting point the BRITE classes showing the highest proportion of enzymes with a significant EZS in q3 and beyond in the distribution.As shown in The results presented in From the network, it was evident that the pathways of drug metabolism (other enzymes) in A04_AAIW showed several connected reactions in which the enzymes presented a significant EZS . Among tphoA gene  was annotated in our metagenome but not in the reference samples, and cyclohexane-1-ene-1-carbonyl-CoA dehydrogenase (EC: 1.3.8.10) was annotated in the reference but not in our metagenomes. Finally, the enzyme (EC: 1.3.62.80) pimeloyl-CoA dehydrogenase was not detected in the reference or in A04_AAIW. We will later discuss the preprocessing and postprocessing methodologies that may affect enzyme identification in metagenomic samples.The following steps in the conversion of benzoyl-CoA to acetyl or succinyl-CoA can proceed eductase . The red species . After tortho- or meta-cleavage pathways   involved in the elimination of phenolic compounds was significantly represented in A04_AAIW . In phenpathways . These palt Lake . In our  (1–48%) . From thParvibaculum lavamentivorans, which is usually detected in habitats contaminated with oil, diesel, and other compounds  and Sulfitobacter sp. DFL_14 (D18_MAX), both reported as oil degraders as previously commented.Lipids are hydrocarbons that are soluble in non-polar solvents . They arA04_AAIW , we founn waters , and in r column . Moreover column . A set or column , we founThe examples presented in the previous section showed pathway reconstructions considering the BRITE classes with wider enrichment to be those related to xenobiotic and lipid metabolism. However, as shown in The network was grouped into 35 clusters in A04_AAIW and 51 in D18_MAX, from which we extracted those clusters included more than 4 enzymes. These clusters were regrouped to evaluate the interactions within the network . The cluHalomonas salina strain AS11, which produces high levels of aldehyde dehydrogenase   catalyzes reactions of the fatty acid degradation pathway, valine, leucine, and isoleucine degradation, tryptophan metabolism, lysine degradation, β-alanine metabolism, pantothenate and CoA biosynthesis, limonene and pinene degradation, ascorbate and aldarate metabolism, and glycolysis/gluconeogenesis, among others. This enzyme has been characterized in marine bacteria such as rogenase  that mayrogenase .D-amino acid lyase that, similar to other D-amino acid lyases, is a key enzyme involved in the use of D-amino acids as a nitrogen source integrating DOM in marine environments , which is shared by the reference and this metagenome. Cystathionine gamma-synthase catalyzes reactions involved in cysteine and methionine metabolism, seleno compound metabolism, and sulfur metabolism. Cluster 23 also shares with cluster 3 threonine ammonia-lyase , which was significantly detected in our metagenome. This enzyme is a ronments .Major cluster MC2_8_a1 contains 12 groups, five of which are interconnected  by purine nucleosidase , with EZSs equally represented in the reference and the metagenome. This enzyme is involved in purine metabolism and nicotinate and nicotinamide metabolism. Clusters 10, 11, 14, 22, 25, 26, 29, and 10 share a 5′-nucleotidase  and purine nucleoside phosphorylase , both of which have significant EZSs and catalyze reactions involved in purine metabolism, pyrimidine metabolism, nicotinate and nicotinamide metabolism, and the biosynthesis of secondary metabolites. In a previous section, we discussed the relevance of 5′-nucleotidase in the phosphate cycle. Clusters 11 and 14 share thymidine phosphorylase (EC: 2.4.2.4) and thymidine kinase (EC: 2.7.1.21), both of which were identified at significant levels and catalyze reactions involved in pyrimidine metabolism and drug metabolism. Clusters 10, 14, 22, and 29 contain enzymes related to drug metabolism – other enzymes, such as hypoxanthine-guanine phosphoribosyltransferase (PRTase) , whose activity is also associated with the purine salvage pathway that generates adenine and guanine ribonucleotides and deoxynucleotides from hypoxanthine. This enzyme shows broad specificity and is universally distributed in the three cellular domains .Other pathways involved in arginine metabolism and the one-carbon pool associated with folate were identified in MC2_8_a2, which included some enzymes related to nucleotide metabolism. In particular, the one-carbon pool involved in folate metabolism was associated with a cluster of five enzymes, three of which were detected at significant levels: dihydrofolate reductase (DHFR) , formyltetrahydrofolate deformylase , and methionyl-tRNA formyltransferase . DHFR catalyzes the reduction of dihydrofolate (DHF) to tetrahydrofolate (THF); this is an indispensable enzyme for all organisms because of its role in the biosynthesis of purine nucleotides and some amino acids . This enThe clusters in L-glutamine  and further into L-glutamate . An alternative pathway with the significant role of directly transforming ammonia into L-glutamate, mediated by glutamate dehydrogenase [NAD(P)+] , was also identified. The end product of this reaction enters D-glutamine and D-glutamate metabolism, in which glutamate is reversibly transformed into two oxoglutarate by glutamate dehydrogenase [NAD(P)+]. In turn, two oxoglutarate is taken up by the citrate cycle or is transformed into D-glutamate by glutamate racemase . D-Glutamate is subsequently transformed into UDP-N-acetylmuramoyl-L-alanyl-D-glutamate by UDP-N-acetylmuramoylalanine-D-glutamate ligase , and the next product enters peptidoglycan biosynthesis. All of the enzymes of this pathway have significant EZSs. The abovementioned findings are important since although D-amino acids are minor components of living organisms, they occur in a wide range of natural environments, such as soils  , which is then transformed into as soils , rivers,as soils , among oN-carbamoyl-β-alanine, catalyzed by dihydropyrimidinase . The last reaction is the conversion to β-alanine by the enzyme beta-ureidopropionase . Similar results have shown that the non-protein amino acids β-alanine and γ-aminobutyric acid can be found as dissolved free amino acids in marine water (n = 12), all of which participated in reactions involved in purine metabolism.MC1_9_a1 includes four populated pathways: β-alanine metabolism; valine, leucine, and isoleucine degradation; glyoxylate and dicarboxylate metabolism; and cysteine and methionine metabolism. Clusters 11, 19, and 24 contain aldehyde dehydrogenase, which participates in alkane degradation as previously mentioned. This versatile enzyme in this cluster also participates in the production of β-alanine. From this pathway, we identified all of the steps in the bidirectional conversion of uracil into β-alanine. The enzymes participating in this pathway are dihydropyrimidine dehydrogenase (NAD+) subunit PreT  and dihydropyrimidine dehydrogenase (NADP+) , which catalyzes the transformation of uracil into 5,6-dihydrouracil, followed by the reaction converting this compound into ne water . The seqExtracting meaningful biological information from metagenomes is a serious bioinformatics challenge. A considerable number of tools have been employed to identify useful information that can help to understand the taxonomic and genomic composition of several biomes . ConsequHowever, as shown in the results, some enzymes, such as some of the aaRSs, are non-normally distributed. Moreover, the log-normal and Weibull observed distributions have long tails, which are characteristic of these kinds of distributions. The meaning of this behavior is difficult to explain; however, we know that these enzymes are not well preserved in known species, and several of them have been tested only in representative organisms. It is possible that the organisms with these aaRSs are not heavily represented in the selected samples. This lack of preservation of certain aaRSs has been shown for some archaeal, bacterial, and organellar genomes that instead employ indirect aminoacylation pathways , which mAs previously mentioned, identifying valuable information in metagenome samples is challenging since the methodological decisions made concerning trimming, assembly, and annotation can impact the results and affect the tested distributions, especially for those genes that are less widely distributed in the samples. However, in the analysis performed herein, we attempted to consider methodological and biological variation by evaluating the distribution of each enzyme.Another factor affecting the PDFs of enzymes is the kind of metagenome selected to construct the reference dataset. The approach applied herein first considered samples collected worldwide, representing distinct depths and conditions, which were compared with the GoM samples under the assumption that they should differ, at least concerning the presence of hydrocarbons. However, the environmental conditions were poorly described in several metagenomic studies, even when physicochemical parameters were included. Therefore, the selection of reference samples could be challenging. In these cases, the analysis encountered reference conditions presenting small variations compared with our metagenomes. As a result, we found similarities between the samples, leading to poor enzyme identification, but we hope to identify some enzymes defining the tested conditions. Additionally, the databases used for annotation will introduce bias. In this work, we employed MG-RAST, which uses several databases to perform this task. Nonetheless, the annotations are incomplete.It may be possible to improve our statistical method by modifying the selection of the reference samples. This can be done by performing sampling at several points at the same depth, longitude, and latitude and probably in the same season, considering the impact of this last parameter on the biophysiochemical composition of ocean samples, which we think will highlight the uniqueness of certain enzymes in the tested metagenomes. Moreover, by selecting the reference in this way, we expect to increase the detection of enzymes in the reference since we expect all of them to be preserved in the metagenomes; however, this is also a disadvantage since not all enzymes are represented in all metagenomes. Nevertheless, we wanted to be strict concerning this point. We also expect the enzymes to be more normally distributed in these new references, considering that the samples may be more similar.The boxplots showing the distribution of EZS in The approach also naturally highlighted other enzymes related to petroleum biodegradation and those involved in lipid and amino acid metabolism in both metagenomes, in accord with previous studies that have demonstrated that “crude oil pollution constitutes a temporary condition of carbon excess coupled to limited availability of nitrogen that prompts marine oil-degrading bacteria to accumulate storage compounds”  such as Notably, the results related to the presence of enzymes involved in oil degradation are consistent with previous works of our own and other groups that investigated the Mexican exclusive economic zone and identified oil-degrading microorganisms derived from 16S amplicon analysis ; isolateIn this study, the inspection of BRITE classes provided a general view of the global metabolism represented in the GoM metagenomes. Nevertheless, for the definition of a more detailed metabolic profile, network reconstruction is necessary. The reconstructed network revealed the interconnection of compounds whose production was catalyzed by the identified enzymes. This reconstruction considered not only the enzymes with a significant EZS ≥ 2 but also the enzymes in the interval between −1 and 2. As explained above, the EZSs located in the interval corresponded to enzymes that were equally represented in the reference and in the GoM metagenomes.Phakellia fusca in another study  . This enhoA gene  that hashoA gene . MoreovehoA gene . The samhoA gene . HoweverhoA gene .Among these enzymes, we identified key enzymes of the benzoyl-CoA pathway and some deep-sea enzyme markers. Furthermore, the identification of the β-alanine pathway in D18_MAX was also consistent with reports showing that in the marine water column, these non-protein amino acids comprise a small fraction (<4%) of the total amino acid pool, which may be released during phytoplankton decomposition  and thenA general reconstruction of metabolic pathways that could be occurring within the marine samples analyzed in this study is depicted in The identification of enzymes with bioremediation potential in ocean samples as other molecules important for medical treatments and biotechnological uses is desirable because these enzymes are more tolerant to high pressure, salinity, and temperature than enzymes identified under other environmental conditions. We proved that our approach produced promising results in this regard. In this report, we describe some examples of the more significant cases to illustrate the scope of our method, leaving some enzymes and pathways less well explained. Moreover, metagenomic bins  encode aThe amount of available biological data is continuously increasing; hence, the bioinformatics community has the golden opportunity to solve or retrieve hidden information from genomic and metagenomic data and gather information about microorganisms and gene functions that have been unexplored thus far. In this paper, we present a method for identifying the metabolic potential within metagenomic samples. Our proposed strategy explores the statistical properties of the enzymes collected from the samples, converting them into a baseline and allowing us to explore the overrepresentation of the enzymes catalyzing the reactions describing the metabolic potential of tested metagenomes. As a case study, we used two metagenomes collected in the GoM and sequences annotated by our group that were compared to reference metagenomes of the GEOTRACES project. This statistical analysis provided detailed examples of how our strategy generated clues about the metabolic network-defining pathways. Furthermore, the network reconstruction showed congruence between the identified pathways and the features of the sampled sites. Our results are promising, and we are aware that several steps in the sample treatment, sequencing, and bioinformatics pipelines employed for assembly and annotation may improve metabolic profile prediction. However, this strategy provided consistent results and a new approach for exploring the metabolic network of biomes.The original contributions presented in the study are included in the article/AL and R-MG-R conceived and designed the methodology and analysis and wrote the manuscript. FG-G performed the network reconstruction and clustering analysis. AE-Z and LS performed the MG-RAST annotation. MS-O curated the essential enzymes to aid in the bioinformatics analysis, she assembled, binned, and annotated the genomes from the metagenomes, and prepared the The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.