Genome-scale metabolic models (GEMs) are powerful tools for understanding metabolism from a systems-level perspective. However, GEMs in their most basic form fail to account for cellular regulation. A diverse set of mechanisms regulate cellular metabolism, enabling organisms to respond to a wide range of conditions. This limitation of GEMs has prompted the development of new methods to integrate regulatory mechanisms, thereby enhancing the predictive capabilities and broadening the scope of GEMs. Here, we cover integrative models encompassing six types of regulatory mechanisms: transcriptional regulatory networks (TRNs), post-translational modifications (PTMs), epigenetics, protein–protein interactions and protein stability (PPIs/PS), allostery, and signaling networks. We discuss 22 integrative GEM modeling methods and how these have been used to simulate metabolic regulation during normal and pathological conditions. While these advances have been remarkable, there remains a need for comprehensive and widespread integration of regulatory constraints into GEMs. We conclude by discussing challenges in constructing GEMs with regulation and highlight areas that need to be addressed for the successful modeling of metabolic regulation. Next-generation integrative GEMs that incorporate multiple regulatory mechanisms and their crosstalk will be invaluable for discovering cell-type and disease-specific metabolic control mechanisms. Cellular metabolism is a fundamental biological process used by all living organisms to generate and expend energy for growth . AlthougMost of our understanding of metabolism comes from cumulative data from biochemical experiments carried out over the past century. Although experimental evidence has been insightful, this type of investigation is often restricted to studying an isolated metabolic pathway in a limited number of conditions. To overcome this limitation, modern approaches seek to study metabolism from a systems biology perspective ,7,8. In While GEMs in their most basic form can model cellular metabolism reasonably well ,14,15, tWhile this enumeration of regulatory mechanisms is not exhaustive, these six mechanisms represent major ways through which cellular regulation affects metabolism. Of note, various methods have focused on integrating omics data directly into GEMs to improve model accuracy. Several excellent reviews have already covered this topic in greater detail ,21,22,23Before discussing how regulatory mechanisms have been integrated into GEMs, we begin with a brief overview on mathematical methods relevant to the algorithms discussed throughout this review .S, where rows signify metabolites and columns represent reactions. For each reaction (column), the stoichiometric coefficients of all metabolites involved in the reaction are set to a non-zero value. Specifically, positive coefficients indicate the production of a metabolite, while negative coefficients indicate the consumption of a metabolite. A key assumption of FBA is steady-state metabolism in which each metabolite’s production and consumption is balanced equally [S represents the stoichiometric matrix, v is the vector of reaction fluxes, and b, representative of changes in metabolite concentrations, is set to a zero vector to mathematically reflect steady-state metabolism. Since the number of reactions exceeds the number of metabolites, the system is underdetermined, and a large solution space exists; however, this can be narrowed by imposing additional constraints and narrowing the flux bounds. In FBA, linear optimization techniques are applied to solve for a flux distribution that optimizes an objective function (objZ). To reflect evolutionary pressure, growth is typically maximized by defining a biomass objective function that consists of biomass precursors [objZ is the objective function, biomassv is the flux through a user-defined biomass reaction, v is the vector of all reaction fluxes, lb is a vector of the lower bound flux limit, and ub is a vector of the upper bound flux limit. Constraint-based modeling (CBM) is the standard framework for reconstructing and analyzing GEMs, primarily through the addition of model constraints . The mos equally . Mathemaecursors . Other oecursors . These civ represents the flux through reaction i, n is equivalent to the total number of reactions, ilb is the lower flux bound for reaction i, and iub is the upper flux bound for reaction i. In FVA, the objective function (objZ) serves as a reference to find the possible lower and upper flux limits for Equation (3a) and Equation (3b), respectively. A different method, called parsimonious FBA (pFBA), also improves GEM simulation accuracy by determining the feasible flux ranges based on the assumption that cells maximize efficient enzyme usage to promote their growth [iv is the flux through reaction i, n is the total number of reactions, biomassv is the flux through the biomass reaction, biomass,lbv is the lower limit of the flux through the biomass reaction, ilb is the lower flux bound for reaction i, and iub is the upper flux bound for reaction i. Of note, the flux solutions achieved using pFBA tend to emphasize a small number of high-flux reactions due to the underlying assumptions of pFBA.Although FBA can generate flux solutions that match experimental data ,49, thisr growth . This asTranscriptional regulation describes the diverse ways in which gene transcription into messenger RNA (mRNA) is regulated by the cell. mRNA transcripts carry gene-encoded instructions for protein production to the ribosome, where translation occurs. Since gene transcription is required to express the proteins that participate in metabolic reactions, the association between genes, proteins, and reactions is strongly dependent on transcriptional regulation. Transcriptional regulation is often represented through transcriptional regulatory networks (TRNs), which describe how the transcription of target genes is influenced by regulatory genes and environmental perturbations ,52. In tregulatory flux balance analysis (rFBA). This algorithm is an expansion of FBA in which metabolic models with Boolean TRNs are used to predict steady-state flux distributions over a series of time intervals [E. coli growth predictions from GEMs across numerous metabolic environments.The simplest TRN is a Boolean network in which genes assume one of two states: active or inactive. This status is based on multiple factors including the activity of regulating genes and environmental conditions . Booleanntervals . To modesteady-state rFBA (SR-FBA), which simulates steady-state metabolism more comprehensively by incorporating both metabolic and regulatory constraints into a single optimization problem [integrated FBA (iFBA), which incorporates kinetic models and ordinary differential equations (ODEs) [While rFBA marked an important step forward in modeling the transcriptional regulation of metabolism, it is limited by its selection of only one valid metabolic state for each interval when multiple could occur. This limitation was addressed by  problem . Insteads (ODEs) ; howevertoolbox for integrating genome-scale metabolism, expression, and regulation (TIGER) was developed [FlexFlux is a similar platform but improves upon TIGER in terms of usability as TRNs and GEMs can be inputted in a standardized file format [FlexFlux also enables the integration of multi-state regulatory networks and allows the conversion of discrete regulatory states into continuous intervals. In order to facilitate the combination of Boolean TRNs and GEMs, a platform called eveloped . TIGER ae format . FlexFluProbabilistic regulation of metabolism (PROM) is a method that more comprehensively addressed these limitations by shifting the discrete paradigm to a continuous model of transcriptional regulation [Mycobacterium tuberculosis (M. tb), leading to enhanced simulation accuracy using the M. tb GEM [While Boolean TRNs have been shown to improve flux simulations, there are several limitations endemic to this framework. These include an overly simplistic model of metabolism, a theory-driven approach, and the need for extensive literature searching to define regulatory rules . This wagulation . Using T. tb GEM .Transcriptional regulated FBA (TRFBA) is a method that represents TRNs continuously and improves upon PROM by reducing the amount of transcriptomics data required to build continuous TRNs [E. coli, only TRFBA is more accurate than pFBA when applied to S. cerevisiae [CoRegFlux was developed to address this limitation [learning cooperative regulation networks (hLICORN), CoRegFlux determines TF–target gene relationships from transcriptomics data in the absence of a pre-existing TRN before predicting fluxes.Advancing the continuous TRN paradigm, several other algorithms have been developed. ous TRNs . Of noterevisiae . Howevermitation . Using lIntegrated deduced and metabolism (IDREAM) is a method that functions similarly to continuous TRN methods such as PROM but alternatively integrates an environment and gene regulatory influence network (EGRIN) [optimization of regulatory and metabolic networks (OptRAM) is an in silico strain design algorithm that optimizes the production of desired metabolites and has successfully been applied to S. cerevisiae [ (EGRIN) ,55. EGRI (EGRIN) . Buildinrevisiae .While TRN modeling and integration into GEMs has advanced considerably, these integration methods fail to account for additional regulatory mechanisms such as signaling or allostery. This limits the extent to which they accurately model cellular metabolism, as significant numbers of metabolic fluxes are unable to be explained by transcriptional regulation alone , necessiPost-translational modifications (PTMs) induce chemical changes onto proteins that alter their function, interaction, and localization ,58. GiveRegulated metabolic branch analysis (RuMBA) introduced one way to study PTMs in bacterial cells [Flux space shift (FSS) analysis was developed to address this specific issue by focusing on differential enzyme regulation for optimal growth in certain nutrient conditions [al cells . This menditions .comparative analysis of regulators of metabolism (CAROM) is a data-driven method that integrates omics data to decipher how both microbes and mammalian cells allocate different types of regulation, including PTMs [In contrast to RuMBA and FSS, ing PTMs . CAROM aprotein-specific information matrix (PSIM) is a genome-scale model that focuses on the protein secretory system [The methods discussed above were specifically designed to study how PTMs influence metabolic activity by introducing new CBM constraints. In contrast, some other studies have investigated the role of PTM regulation in metabolism indirectly. For instance, y system . Given ty system , the mody system . This woEpigenetics refer to biochemical changes that are transiently passed down to successive generations without modifying the DNA sequence. This enables eukaryotic cells to have identical genomes yet different phenotypes. While DNA cytosine methylation, non-coding RNAs, and histone modifications all play crucial roles in the mechanisms of epigenetics ,69,70, hepigenome-scale metabolic network model (EGEM) was developed [GEMs potentially offer a framework for measuring how metabolism interacts with epigenetics ,78. Howeeveloped . This moeveloped .fast reconstruction of compact context-specific metabolic networks for the integration of transcriptomics data (FASTCORMICS) method incorporates microarray data to existing GEMs [While EGEM mechanistically accounts for epigenetic regulation, recent studies have tried to model the resulting transcriptional impact of epigenetic regulation on metabolism. The ing GEMs . Althouging GEMs .dynamic flux activity (DFA) approach constrains GEMs with time-course metabolomics [As mentioned above, histone PTMs and metabolic states are naturally intertwined because of the small molecules required for covalent modifications. However, the process of epigenetic modification occurs in a highly dynamic fashion. Therefore, the changes in metabolite concentrations over time are important data that can provide better understanding of this interplay. The bolomics ,82. Chanbolomics . AlthougEnzyme activity is also influenced by the structural stability of the protein and its interactions with other proteins. Protein–protein interactions (PPIs), which entail physicochemical contacts between proteins, govern a wide range of cellular processes including but not limited to signal transduction , moleculIn the context of metabolism, PPIs play a major role in regulating reduction–oxidation  reactions  and induE. coli growth and metabolism in extreme temperatures by integrating protein structure information [E. coli GEM with protein structural information, Chang et al. not only simulated growth rate patterns resembling what was observed experimentally, but they also revealed metabolic mechanisms that may confer thermotolerance for heat-adapted E. coli strains. These findings were supported by follow-up experiments that showed increased growth for E. coli cultured in conditions supplemented with metabolites normally impacted by heat stress. Other than direct PPI integration into GEMs, several groups have integrated protein stability data to more accurately model metabolism using GEMs. Protein structural integrity is critical for proper functionality. One of the earliest studies by Chang et al. investigated ormation . This inE. coli and Thermotoga maritima to investigate how growth is limited by protein instability due to heat stress. The authors further showcased how GEM-PRO models can be used for applications at the intersection between systems and structural biology. However, GEM-PRO has not yet been widely applied since its introduction as it requires an abundance of protein structure information, which is not readily available nor attainable for most organisms. Although structural information may be derived from homology modeling, this method can often compromise the overall quality of the model.A successive study by the same group formally introduced the computational process of integrating protein structure information into GEMs . The appAllosteric regulation describes the modulation of enzyme activity via effectors, which are ligands or metabolites that bind to an enzyme at a location other than the active site. Upon binding to an enzyme, effectors can either enhance  or attenuate  activity through the associated reaction. This form of regulation is often depicted as “feedback” or “feedforward loops’’ depending on whether the effector metabolite is produced downstream or upstream of the reaction catalyzed by the regulated enzyme, respectively. Allosteric regulation enables biochemical adaptation to rapid changes in the cellular environment, particularly metabolite concentrations. Similar to PPIs/PS, allosteric regulation plays a key role in cell signaling, biomolecular transport, and metabolism ,95.allosteric regulation FBA (arFBA), which was designed to incorporate allosteric regulation when solving for flux predictions. This method introduces a regulation (R) matrix  that characterizes effector–reaction relationships. A value of 1 indicates reaction activation via effector binding, while a value of −1 indicates reaction inhibition (systematic identification of meaningful metabolic enzyme regulation (SIMMER), contextualizes experimental data via Michaelis–Menten rate law equations. The authors also used an extended S. cerevisiae GEM to infer fluxomics-constrained genome-scale metabolic fluxes via FVA. Both studies revealed distinct ways that metabolism is regulated depending on the environmental conditions. However, they both investigated allosteric regulation of metabolism at a small scale (≈100–300 reactions).Although allosteric regulation plays a major role in regulating metabolism, this regulatory aspect has not been widely considered in genome-scale metabolic modeling studies. In fact, Machado et al. was the first group to integrate genome-scale allosteric regulation with metabolic models . Specifihibition . In a tab vector in CBM). More importantly, signaling systems such as phosphorylation of the G-protein coupled receptor can respond to environmental perturbations quickly, but the reset of the system via receptor internalization can be slow [The signaling pathways enable cells to quickly respond to fast-changing environmental and extracellular signals for a wide range of behaviors, from chemotaxis to developmental processes. Generally, a cascade of proteins participates in the process. For example, the Wnt signaling pathway plays an important role in embryonic development by controlling body axis formation . This pa be slow . In othe be slow ,104.To address this issue of timescales, metabolic modeling with ODEs enables the computation of metabolite concentrations as a function of time. However, this approach is limited by high computational costs, difficulty in finding unknown kinetic parameters, and the inability to connect to phenotypic properties. As with TRN mechanisms, dynamic kinetic modeling with ODEs can capture signaling mechanisms in ways that traditional modeling methods fail to achieve. To leverage the advantages of both GEMs and ODEs, two integrated models, iFBA   is the first approach for addressing this challenge of curating GEMs integrated with regulation [S. cerevisiae and greatly improve the model’s accuracy. Nevertheless, unlike the curation of traditional metabolic network GEMs, for which a comprehensive suite of tools exists, the curation of integrated GEMs has not been automated yet, and GEMINI has been applied only to TRNs.Integrated GEM model development involves an iterative process of incorporating regulatory information and conducting regular quality checks until a high-quality model is achieved. Once a draft model is reconstructed, the curation of these models poses additional challenges . Errors gulation . GEMINI GEM with enzymatic constraints using kinetic and omics, is one method that could be leveraged to integrate enzyme kinetic information into GEMs [S. cerevisiae GEM, yielding an updated model with kinetic constraints that generated more accurate simulations compared to previous models. Although GECKO demonstrated the value of incorporating kinetic constraints into GEMs, these parameters are not widely available for most enzymes. However, this limitation could be remedied by methods such as DeepEC (Deep learning of Enzyme Commission numbers) [Modeling regulatory mechanisms characterized by dynamic enzymatic activity, such as allostery and PTMs, will further require the inclusion of kinetic parameters that relate enzyme concentrations to metabolic flux changes. GECKO, or nto GEMs . This menumbers) , which acomputation of microbial ecosystems in time and space (COMETS) [3-dimensional dynamic flux balance analysis (3DdFBA) [dynamic FBA (dFBA) [Another major area for improvement involves the ability to computationally model metabolism at the spatiotemporal level. This is because regulatory events often occur at different timescales (milliseconds vs. hours), and the degree of regulation can be distributed unevenly depending on the cellular objective . For exa(COMETS)  and 3-di(3DdFBA) , which sA (dFBA) . It is iOver the past three decades, GEMs have become integral for modeling metabolism at a systems-level perspective. GEMs have enabled the study of metabolic rewiring in response to environmental factors and paved the way for metabolic engineering in agricultural, industrial, and medical applications ,116,117.Within this review, we covered six regulatory mechanisms relevant to metabolism: TRNs, PTMs, epigenetics, PPIs/PS, allostery, and signaling. We discussed how various methods have integrated these regulatory mechanisms into GEMs, thereby improving the accuracy in model simulations. We also highlighted areas for improving the integration of regulatory information into GEMs. These include the continued incorporation of highly curated experimental data on regulatory mechanisms, iterative curation of integrated GEMs, addition of dynamic constraints to capture spatiotemporal metabolic changes, and supplementation with AI methods that can provide missing information on protein structure , biomoleLooking to the future of metabolic modeling, the successful construction of next-generation GEMs and ultimately whole cell models for complex organisms  relies o


Crypthecodinium cohnii, a marine heterotrophic dinoflagellate, is successfully used for the industrial production of DHA because it can accumulate DHA at high concentrations within the cells. Glycerol is an interesting renewable substrate for DHA production since it is a by-product of biodiesel production and other industries, and is globally generated in large quantities. The DHA production potential from glycerol, ethanol and glucose is compared by combining fermentation experiments with the pathway-scale kinetic modeling and constraint-based stoichiometric modeling of C. cohnii metabolism. Glycerol has the slowest biomass growth rate among the tested substrates. This is partially compensated by the highest PUFAs fraction, where DHA is dominant. Mathematical modeling reveals that glycerol has the best experimentally observed carbon transformation rate into biomass, reaching the closest values to the theoretical upper limit. In addition to our observations, the published experimental evidence indicates that crude glycerol is readily consumed by C. cohnii, making glycerol an attractive substrate for DHA production.Docosahexaenoic acid (DHA) is one of the most important long-chain polyunsaturated fatty acids (LC-PUFAs), with numerous health benefits.  Knowledge-based bioeconomy implies the conversion of cheap renewable resources into biotechnological products with added value.Docosahexaenoic acid (DHA) is one of the most important long-chain polyunsaturated fatty acids (LC-PUFAs), with numerous health benefits such as reducing the risk of cardiovascular diseases, cancer, and rheumatoid arthritis; alleviating depression symptoms and post-natal depression; and contributing to immune-modulatory effects . DHA alsCrypthecodinium cohnii, a marine heterotrophic dinoflagellate, is successfully used for the industrial production of DHA because it can accumulate DHA at high concentrations within the cells [C. cohnii, do not require light; hence, a high biomass density can be reached in conventional bioreactors.Efforts to explore alternative sources of DHA have been made in the last decade, including the generation of transgenic oilseed plants  and larghe cells . In contC. cohnii are glucose, ethanol, and acetate. Ethanol and acetate are found to be superior to glucose for the production of DHA, likely because of their short conversion pathway to acetyl-CoA, the key precursor of fatty acid synthesis [C. cohnii growth and abundant DHA synthesis in glycerol. Glycerol is an interesting renewable substrate since it is a by-product of biodiesel production and other industries, and is generated globally in large quantities. The contradictory information in the literature about the consumption of glycerol by C. cohnii, and DHA production from glycerol, calls for a closer look at this substrate. Notably, glycerol consumption requires just two additional reactions (glycerol kinase and glycerol-3-phosphate dehydrogenase) until it enters the metabolic “highway” of glycolysis.The established carbon substrates for the growth of ynthesis . No or mynthesis ,8,9. Howynthesis ,11,12 deThe systems biology approach is used to gain a mechanistic understanding of the functioning of metabolic pathways and the theoretical limitations of different biotechnologically used but insufficiently explored organisms by combining laboratory experiments and mathematical modeling ,14,15,16C. cohnii-central metabolic fluxes with three substrates: (i) glucose, as the most widely used carbon substrate for laboratory cultivation of this dinoflagellate [C. cohnii [In the present work, the authors focused on the experimental work and mathematical modeling of agellate ; (ii) etagellate ; and . The DHA content in these cultivations was in the range of 3.0–3.5% of the biomass dry weight. Here, this value would correspond to the black lines at the top panel of The strongest absorbance at 3014 cmre PUFAs . PreviouC. cohnii, including metabolic reactions that connect glucose, ethanol and glycerol uptake and the Krebs cycle with the production of Acetyl-CoA, the precursor of DHA, was developed. The model is organized into three compartments . The model contains 35 reactions and 36 metabolites -based model of abolites . 13C metabolic flux analysis [Brenda [SABIO-RK [UniProt [Equilibrator [https://randr.nist.gov/enzyme/, accessed on 3 January 2022). The unit used for the reaction fluxes in the model is mmol·L−1·min−1.The model structure was developed based on research by Zhang’s group on transcriptomics  and the analysis  of DHA panalysis ; however [Brenda , SABIO-RSABIO-RK  and UniP[UniProt . The tri[UniProt . The equlibrator  and the 13C metabolic flux analysis [−1·L−1 and reaction rates, including the Krebs cycle and Acetyl-CoA production. For modeling purposes, a single, concentration-independent substrate uptake rate for glycerol and ethanol was derived from the cultivation experiments described in Three experimental parameter sets have been developed for the kinetic model to account for different substrate uptakes: glucose, glycerol and ethanol. The most detailed published dataset available corresponds to the consumption of glucose based on analysis  with a gDuring the parameter estimation, it became clear that a single set of model parameters could not describe all three examined substrates. The same parameter set of kinetic models could be used for glucose and glycerol experiments. This could be expected because of the common pathway of glucose and glycerol from Gra3P to pyruvate, which then enters the mitochondria, serving as the precursor for both mitochondrial oxaloacetate (reaction PYC) and mitochondrial Acetyl-CoA (reaction PDH). It turned out that, in the case of ethanol that enters the Krebs cycle via Acetyl-CoA, the PDH reaction rate had to be close to zero to facilitate all of the mitochondrial pyruvate flux towards mitochondrial oxaloacetate.−1·L−1  at the experimentally observed uptake rate is glucose (21.46 mmoL·min−1·L−1) followed by ethanol (15.52 mmoL·min−1·L−1) and glycerol (7.27 mmoL·min−1·L−1).The simulations of the glucose/glycerol model confirm the experimentally determined production flux of cellular Acetyl-CoA at 3.87 mmoL·minin−1·L−1 . The samC. cohnii has been developed. The model is organized in three compartments  and has 398 reactions and 468 metabolites. Out of these 398 reactions, 35 are transport reactions . The model simulates the uptake of the substrates, as well as H2O, O2, H+ and ammonia, which is available to the C. cohnii for uptake in a bioreactor. The model is available in COBRA format and MS Excel format , while glucose is the least efficient (76.5 mmoL mmoLC1·gDW−1). The optimization of the stoichiometric model, without taking into account the fluxes simulated by the kinetic model, reveals that any substrate of interest can be transformed into biomass with a ratio of about 42 mmoLC1·gDW−1. This means that the experimentally observed transformation rate of glycerol is the closest to the theoretical value using 35% more carbon than predicted by the model in an optimal case. In the case of glucose and ethanol, that is 80% and 45%, respectively.The effectivity of carbon conversion into biomass can be analyzed in several ways. We looked at the biomass production rate and the efficiency of substrate carbon transformation into biomass . The expmax) was determined by maximizing biomass function, assuming that all substrates will be targeted at biomass production with DHA as a part of the biomass. Knowing that the DHA fraction in the experimentally produced biomass was variable  increases from 39% to 81%, respectively. These calculations are based on the assumption that all metabolic resources that do not form biomass are directed by the available metabolic reactions towards the production of DHA.C. cohnii-central metabolism that are validated by 13C fluxomic data [In the present study, we created kinetic and stoichiometric models of mic data . The knoKinetic models usually cover a pathway-scale number of reactions . KineticIn contrast to kinetic models, stoichiometric models require fewer details for individual reactions and, as a consequence, can be applied at the genome-scale ,43. The The combination of both models enabled the feasibility of internal fluxes, which were calculated by the kinetic models of ethanol and glycerol, to be tested; they have never been measured experimentally. The test resulted in a rejection of some steady-state fluxes that were suggested by the kinetic model in the case of glycerol and ethanol, showing the usefulness of the iterative application of both model types. Steady-state fluxes that were kinetically feasible in the ODE-based model became unfeasible in the constraint-based stoichiometric model, where all biomass compounds had to be produced in a specific proportion. Thus, the stoichiometric model demonstrated that some fluxes simulated by the kinetic model disabled the production of all necessary metabolites in parallel with the production of biomass at the experimentally observed specific growth rate, suggesting the necessity for additional experiments to determine feasible flux distributions. C. cohnii. We used both model types to establish (1) if the enzymatic capacity ensured the sufficient supply kinetics of Acetyl-CoA, the key central metabolite needed for DHA production, and (2) if there was the required number of metabolic precursors available for the building blocks of DHA. So far, this kind of approach has not been applied in the analysis of C. cohnii or any other dinoflagellates.Our aim here was to employ the model simulation of central metabolism for a better understanding of the conversion of several substrates into the target product: DHA. In particular, we were interested in glycerol as a potential renewable for the synthesis of PUFAs, still poorly studied as a substrate for growth and DHA production in Both kinetic and stoichiometric models were used to simulate the observed kinetics for the uptake of glucose, ethanol and glycerol, with a particular focus on the early stages of culture growth. Kinetic and stoichiometric models were able to simulate the experimental observations . max of PDH is close to zero). The necessity to block the reaction in the case of ethanol is determined by the fact that, in contrast to the glucose and glycerol pathways, the ethanol catabolic pathway produces mitochondrial Acetyl-CoA, and all pyruvate pools should be redirected for the regeneration of mitochondrial oxaloacetate to provide the acceptor for the CS reaction. There are several possible mechanisms for the heavy reduction in PDH flux: (1) the allosteric inhibition of PDH by Acetyl-CoA [−3 mmoL·L−1) than when consuming glucose (4.5 × 10−4 mmoL·L−1) or glycerol (1.8 × 10−3 mmoL·L−1).At the level of the pathway-scale kinetic model, it was found that the functioning of the model with ethanol as the substrate was only possible if the PDH reaction did not operate  theetyl-CoA , and (3)C. cohnii is incorporated in triacylglycerols [We found that with glycerol, the cells grew slower than with glucose yet tended to accumulate more PUFAs, than with both other substrates . This islycerols . TherefoCrude glycerol, derived from biodiesel production, contains inhibitory substances, and its utilization for food-grade DHA production poses problems, as previously analyzed by Sijtsma et al. . HoweverC. cohnii has been published.The fact that the stoichiometric model could find ways to produce DHA equally well from carbon supplied by any of the analyzed substrates indicates that some details of metabolism (inhibition due to substrate concentration or enzyme capacity limitations and other factors), which are not included in the stoichiometric model, would make the substrate conversion rate closer to the experimentally observed conversion rates. Unfortunately, a genome-scale, constraint-based stoichiometric model cannot be developed at this moment as no genome sequence of The assumption that all free metabolic resources are targeted towards DHA production is introduced for the estimation of the production potential of DHA. Metabolic engineering  is neede13C data enables a more detailed insight into the flux distribution within the organism. The combined application of different types of models enables the rejection of many unfeasible hypotheses that may arise due to the limited predictivity of each separate modeling type. Both models and their combinations can be used to explore a wider range of problems in metabolism and its optimization.The combination of ODE-based, pathway-scale kinetic modeling and constraint-based stoichiometric modeling with 13C data on the DHA production from glucose [To explore the potential of DHA production from glycerol, glucose and ethanol, the authors combined literature data, their own experimental results, the pathway-scale kinetic model and medium-scale stoichiometric model . The 13C glucose  were useCrypthecodinium cohnii CCMP 316 was obtained from the National Center for Marine Algae and Microbiota, USA. It was cultivated on a complex medium containing 2 g L−1 yeast extract, 25 g L−1 sea salt (Sigma-Aldrich) and various concentrations of glycerol, glucose and/or ethanol, as specified in the Results section. Cultivations were carried out aerobically at 25 °C in 0.5 L or 1 L Erlenmeyer shaken flasks with 200 mL of culture on a rotary shaker at 140–180 r.p.m. The concentrations of glucose, ethanol and glycerol in culture media were monitored by HPLC, as described previously [Culture maintenance and cultivations were performed on a medium with sea salts and yeast extract, as described previously . In brieeviously ,48.−1, with a spectral resolution of 4 cm−1, and 64 scans were coadded. Only spectra with absorbance within the absorption limits between 0.25 and 0.80  were used for data analysis. The FTIR spectra were vector normalized and deconvoluted (second derivative) for more precise evaluation of weak-intensity spectral bands and to resolve the overlapping components, if any [FTIR spectra of algal biomass were recorded using Vertex 70 coupled with the microplate reader HTS-XT . Spectra were recorded in the frequency range of 3800–600 cm, if any . Data weCOPASI (COmplex PAthway SImulator) simulation software [COPASI was tested using ConvAn software [COPASI wrapper SpaceScanner [The model was developed in software ,51 versisoftware . During eScanner  to seleceScanner . The totmV was added to the reactions used from [Vmax of these reactions without changing the Vf to Vr ratios. Kinetic equations of all enzymatic reactions had overexpression coefficients k that could be used for optimizing enzyme concentrations to increase Acetyl-CoA or other molecule production. Currently, all coefficients k = 1 so that the model corresponds to wild-type concentrations of enzymes.Model parameters were either obtained from the literature or inferred from experimental data. An additional parameter sed from  to changCOPASI. From Park et al. [Species concentration constraints were applied in the parameter estimation task in k et al. , it was −1·L−1 since it is frequently used in kinetic models, while in the stoichiometric model, the metabolic flux unit is mmoL·gDW−1·h−1. To transition from dry-weight-related measurements to absolute weight, it was assumed that dry weight made up 33% of the absolute weight and the cell density was 1 g·mL−1. Mitochondrial volume was made to be 1% of the cytosol volume [The metabolic flux unit in the kinetic model is mmoL·minl volume .13C metabolic flux analysis for growth on glucose. The second and third sets included experimentally measured glycerol and ethanol consumption rates  productglycerol  increaseThe iterative application of the pathway-scale kinetic model and constraint-based stoichiometric model combines the accuracy of the kinetic model of the main product-forming pathways with the large-scale stoichiometric model’s ability to determine if the pathways addressed by the kinetic model could be supplied with all of the necessary molecular components. Simultaneously, biomass could be produced by the metabolic network of the organism of interest. This approach is important for improving the understanding of metabolic network functionality and increasing the predictability and efficiency of metabolic engineering efforts.C. cohnii for the production of DHA. Despite a lower consumption rate and lower specific growth rate, the PUFA content and efficiency of carbon transformation into biomass are better with glycerol than with glucose. Therefore, the sustainability parameters [Our experiments, in combination with modeling, supported the potential of glycerol as another renewable substrate of rameters  of DHA p


Arabidopsis thaliana culture collection, we could significantly reduce the gap-filling solution in comparison to filling gaps in individual reconstructions without affecting the genomic support. Inspection of the metabolic interactions in the soil communities allows us to identify microbes with community roles of helpers and beneficiaries. Therefore, COMMIT offers a versatile fully automated solution for large-scale modelling of microbial communities for diverse biotechnological applications.Composition and functions of microbial communities affect important traits in diverse hosts, from crops to humans. Yet, mechanistic understanding of how metabolism of individual microbes is affected by the community composition and metabolite leakage is lacking. Here, we first show that the consensus of automatically generated metabolic reconstructions improves the quality of the draft reconstructions, measured by comparison to reference models. We then devise an approach for gap filling, termed COMMIT, that considers metabolites for secretion based on their permeability and the composition of the community. By applying COMMIT with two soil communities from the  Arabidopsis thaliana culture collection, providing only genome sequences. Finally, we show that the obtained models have 90% genomic support and demonstrate that the derived interactions are corroborated by independent computational predictions.Microbial communities are important in ecology, human health, and crop productivity. However, detailed information on the interactions within natural microbial communities is hampered by the community size, lack of detailed information on the biochemistry of single organisms, and the complexity of interactions between community members. Metabolic models are comprised of biochemical reaction networks based on the genome annotation, and can provide mechanistic insights into community functions. Previous analyses of microbial community models have been performed with high-quality reference models or models generated using a single reconstruction pipeline. However, these models do not contain information on the composition of the community that determines the metabolites exchanged between the community members. In addition, the quality of metabolic models is affected by the reconstruction approach used, with direct consequences on the inferred interactions between community members. Here, we use fully automated consensus reconstructions from four approaches to arrive at functional models with improved genomic support while considering the community composition. We applied our pipeline to two soil communities from the  Microbial communities have been extensively studied due to their importance in ecology ,2, humanConstraint-based modelling of genome-scale metabolic networks provides the means to in silico analyse microbial community interactions –12. The However, a consensus reconstruction is not guaranteed to be functional (i.e. to simulate growth), as knowledge gaps may occur in all of the underlying (draft) reconstructions. To address this issue, several algorithms for gap filling, applicable to single and community reconstructions , have beThe problem of finding metabolic interactions within microbial communities using constraint-based methods has been addressed by multiple studies, focussing on pairwise or higher-level interactions ,10,30–34Arabidopsis thaliana microbial culture collections, At-SPHERE, for two different soil community compositions  A letter containing a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. 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Please don't hesitate to contact us if you have any questions or comments.Sincerely,Vassily HatzimanikatisAssociate EditorPLOS Computational BiologyKiran PatilDeputy EditorPLOS Computational Biology***********************Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: The authors present a tool that gap-fills individual microbial metabolic reconstructions based on the metabolic reconstructions of organisms found in the same community. The COMMIT algorithm starts with gap-filling a single random metabolic model from the community on minimal media. COMMIT takes into account the permeability of metabolites when deciding on the set of gap-filled reactions. After finding the optimal gap-filling reaction set, it simulates the maximum biomass flux of the model and adds the list of secreted metabolites to the media for gap-filling the next randomly chosen model, and so on, until all models have been gap-filled. COMMIT metabolic reconstructions contain fewer gap-filled reactions than their individually gap-filled counterparts from other sources. COMMIT is a novel gap-filling algorithm that considers both metabolite permeability and other members of the microbial community, which are important factors to consider when modeling microbial metabolism. While I see many uses for this method, I also have a few concerns and questions about the general applicability of the metabolic reconstructions that are produced by the algorithm.Major pointsIf you have an organism that is found in multiple different communities, how different is the resulting metabolic reconstruction? With COMMIT, the gap-filling reactions are dependent on the community, so supposedly the end-result would differ. With that in mind, can a COMMIT reconstruction of an organism be used in different applications or only within the context of that particular community?It is not clear how much (if any) of this work is manual. The authors talk about selecting the optimal set of secreted metabolites based on summed growth rate and number of gap-filled reactions, but it is not clear if this is automatically done by the algorithm or if this step is manual.Some general terminology needs reworking regarding the use of the phrases metabolic model vs. reconstruction. The authors frequently use “model” where “reconstruction” would be more appropriate. In short, a reconstruction is the set of reactions, genes, and metabolites, whereas a model is a reconstruction with applied constraints and is used for simulations.The authors associate reconstruction quality by the number of gaps, but I disagree with that assessment. Depending on what you want to learn from the reconstruction or its models, it’s good to have gaps as they tell you where there is a lack of knowledge of the microbe’s metabolism.L112-114: How come KBase, CarveMe and RAVEN 2.0 were more similar to each other? Do they build on the similar annotations, databases, or algorithms? Looking at the lower triangle in Fig. 1A, how come AuReMe is so completely different from the others? They look about 90% different, what is the reason the gene differences are so big? How come RAVEN is so similar to the consensus but the others seem quite distant?Figure 1B and 1C: I don’t understand these figures; they need clearer explanations. What is the orange Sum boxplot showing? It is not clear from the figure or caption.How does a consensus model from just the species-specific reconstructions compare to the genus-specific reconstructions ? Is a consensus model from all isolates useful?What is the unscaled sensitivity of the reconstructions in Fig. 1D and S1 and how does the sequence similarity compare among all the genomes? I would expect that the genus-specific genomes are less similar than the species-specific ones, so how does that affect the scaling? Is the sensitivity similar among all and it’s the sequence similarity that is dragging the genus-specific reconstructions down in the plots, or a combination of lower sequence similarities and lower sensitivity?L336-337: The manuscript states a “strong reduction” here, whereas in Fig. 6 the corresponding field is yellow, which according to the caption indicates “a smaller reduction of biomass”. Also, I would expect that the R. thiooxydans model dependency on sulphur was already present in the draft model, is this not the case? I don’t see how gap-filling the reconstruction  could introduce a dependency; for that, reactions must be removed from the network or directionality changed from reversible to irreversible .L340-342: I feel that this sentence is overstated in the current version of the manuscript. High-confidence models are compared with experimental data of multiple metabolites, both in terms of uptake and secretion, but this kind of benchmarking has not been done in this study. These models are potentially high confidence, but without some sort of validation for all models for multiple metabolites, I feel that the authors cannot make this statement.Minor pointsL130-133: Model quality assessed with number of gaps. Why is Memote not used for assessing model quality here? It’s used later in the manuscript.L145-147: Why does RAVEN have larger networks and AuReMe smaller? Are they higher/lower in gap-filled reactions? Was the periplasm compartment accounted for in the comparisons like it was in the consensus models?L160-161: What does “low translation efficiency” refer to? Reaction/metabolite/gene translation into MXNref? Also, what is the reference point for “low” here? 30%? 50%? 70%?L161-163: keep in mind that both reference models were built using a draft reconstruction combined from KEGG (used by RAVEN) and Model SEED (uses RAST like KBase), and in the case of B. megaterium, a pre-existing network that I cannot access, and the paper is only available in a foreign language, so I cannot check its origin.L193: The use of exported and exchanged metabolites is confusing. Perhaps rephrasing “exported” metabolites to “secreted” might make the text clearer?L198: The new definition of “exchangeable metabolite” is unfortunate here given the traditional phrase for a metabolic reconstruction boundary reaction is “exchange reaction”. Is there any other phrase that could make the distinction between the two clearer?L237-239: I find Fig. 3 generally difficult to understand. It is not clear how the scaling has been done. Which value is being scaled against which value in the optimal solutions?L240-241: Here comes one example of my confusion with “exchanged metabolites”. In Fig. 3, is the number of exchanged metabolites referring to the number of metabolites secreted by each gap-filled model, or is it the total number of metabolites added to the minimal medium?L252-253: “suggesting a dependence between these two criteria”. I am not sure I understand this correctly; the results suggest a dependence of the sum of biomass reaction fluxes and the number of exchanged metabolites added to the medium? I would have expected that to be the case, unless maybe if all models were already growing at their maximum capacity.L260-262: What were the scores of the two reference models? Scores are only  listed for B. metaterium in the text. For an audience not familiar with memote, what are good scores?L277: Fig. 4B, the line types indicate the average similarity based on what? Reactions?L525-527: There’s a maximum biomass flux, is there a minimum? Maybe the other end of the range; 2.8 1/h being very fast-growing bacteria, perhaps the other end could be constrained to very slow growing bacteria?Reviewer #2: In this work, Wendering and Nikoloski develop a community gap-filling algorithm that aims to identify a minimal solution set, while exploring 100 random gap-filling orderings, according to the following criteria: number of added reactions, dependence of the first member on exported metabolites of subsequent models, number of exchanged metabolites, and sum of biomass fluxes of all community members. The authors observed that the solution set obtained by COMMIT was significantly smaller than that obtained by gap-filling each model individually. This is a contribution that adds to a large body of literature that addresses similar challenges for individual models and microbial community ones. There is a number of key issues that remain unclear.Major comments:1) It is not surprising that the number of added reactions is lower as it is mathematically provable that allowing for cross-feeding between models will lead to reduction of the need of added reactions for connectivity. What is needed is to quantify whether the reduction reaches a particular threshold that would not have happened by chance. Possibly an F-test would be a solution.2) The optimization formulation minimizes sum of molar fluxes. This de-emphasizes flows involving metabolites with large molecular weights possibly causing systematic discrepancies.3) Gap filling algorithms including COMMIT are not unsupervised algorithms for fixing gaps. Each gap resolution strategy in the model needs to be scrutinized for biochemical evidence. In our experience, gap-filling without any follow up leads to bloated models that propagate misannotated reactions in follow up investigations. The authors need to specify specific instances where the cross-feeding and/or strategy suggested by COMMIT was experimentally verified. Also, they need to caution for cases where COMMIT tends to make systematically erroneous suggestions. Absent of this, this effort is simply a computational exercise devoid of any potential for new insight.4) Gap filling almost always leads to the formation of thermodynamically infeasible cycles especially for community models. It is unclear whether there is a safeguard against this. Are there any unbounded fluxes?5) The authors need to make the case why we need yet another algorithm for gap filling. What is new in the approach that is beyond a simple modification of existing approaches.6) L76-78: potentially misleading, as SteadyCom solves a set of linear problems iteratively, where the number of iterations is independent of the number of organisms in the community7) L423: since CarveMe is stated to generate a GSM model using a supplied medium, not clear how using a static medium is justified in this work as nutrients available to an organism will be a function of metabolites excreted by others in the community and the plant root exudates as well8) L439-443: why were different genome annotation tools (such as RAST and DFAST) used for different GSM reconstruction tools? How do the results differ if a single tool is used?9) The authors state that the models generated using automated tools are of high confidence but provide no comparison between simulated growth and experimental data. Have those models been validated? Can the models display growth individually? Or the only growth simulations performed were as a community? Did the predicted results quantitatively match experimental observations?10) The biomass equation acts as a sink in metabolic models, and thus a primary determinant of network fluxes and capabilities. Since GSM models of two community members is available, how do the results change if the biomass reactions from these models are used instead of the universal biomass reaction from CarveMe reconstructions?11) The motivation behind determining highly-permeable metabolites and treating them differently during gap-filling is clear, but how would the authors account for possible confoundments that differentiate a permeable metabolite from being available for consumption by other members in a community, such as intracellular concentrations, and role as a metabolic substrate?12) L379-381: If the ordering of the gap-filling is what assigns a community member to be a ‘provider’ (by providing specific compounds to the community that cannot be produced by other members), can the authors comment on the inferences made about that organism’s role in the microbial community being biased by the gap-filling process?Minor comments:1) L54: Suggest replacing ‘analyse’ for ‘analyses’2) L525: Suggest explaining in further detail what ‘satisfying results’ entail3) L256: Suggest specifying whether the biomass flux upper bound pertains to the entire community or to each of the individual consensus models4) L567: It would benefit the readers if the definition of sink reactions was provided somewhere in the text.Reviewer #3: In this paper, the authors present a new gapfilling tool COMMIT for automated large-scale modeling of microbial communities. This approach allows for gapfilling of consensus models at the community level. The authors then apply the approach to analyze microbial communities associated with Arabidopsis. They construct models for over 400 arabidopsis rhizosphere isolates using multiple model reconstruction approaches. They merge these models into consensus models. The commit approach then gapfills individual models one by one, expanding the gapfilling media based on the capabilities of each previous model gapfilling. This is an interesting and valuable approach as it will scale better than the community-level gapfilling employed by tools like KBase. COMMIT could thus support generation of much larger and more complex community models.Overall, there is clear merit in the proposed interative gapfilling approach, as it does offer a means of gapfilling larger communities. The consensus approach to model building is more questionable. There is some question as to whether a larger model is necessarily better, and incompatibility and conflicts between different modeling approaches may introduce more problems than it solves.All this said, many questions arise from the studies, methods, and data presented in the paper:1.) Note, KBase already has tools for constructing and gapfilling community models, which can be constrained to specific abundances. This could perhaps be mentioned in the introduction. Again, as mentioned above, this approach gapfills the entire community at the same time and thus won’t scale to large numbers of species.2.) Merging and reconciling models, particularly models constructed from different biochemistry databases like KEGG, ModelSEED, BIGG and MetaCyc can be extremely challenging because of differences in the representation of biochemistry among these sources. Many metabolites don’t have structures and thus aren’t matched well in resources like MNXref. In other cases, reactions differ by the level of lumping performed, the number of monomers in a polymeric compound, or compartmentalization of metabolites in the reaction. Did the authors encounter these challenges? How was this overcome?3.) Note, in building KBase models, the authors could have retained the AuReMe gene calls and identifiers and just had RAST reannotate the existing genes. KBase permits upload of existing gene calls in GFF and genbank format. This would probably be a preferable workflow for what the authors wanted to do.4.) Was a single universal biomass used? Why not vary the biomass based on species ? Would the method be sensitive to this? Can the decision to use a single universal biomass be justified?5.) Did charge (at pH 7) come into play on the permeability prediction? Highly charged compounds would generally not be permeable.6.) With consensus modeling, there’s a major concern of adding many false positive reactions. Do the authors have some way to testing for this (e.g. comparing with Biolog data)? The comparison to published models performed is good, but data performance would be helpful as well.7.) The reaction counts from Raven are generally surprisingly high (significantly larger than many published models). This doesn’t necessarily imply improved quality (but it might be). Can the authors perhaps explain what kinds of reactions Raven is annotating that other methods are missing? Are the reactions active? What kind of metabolism is represented?8.) How much did the annotations of the models agree? Did they generally assign the same genes to the same reactions? Merging conflicting annotations in consensus models could cause problems. How did the authors handle this case?9.) How did the authors relate 16s data to their isolate genomes for which they built models? By species taxonomy matches? By blasting 16s sequences against isolate genomes?10.) Were any metrics used to determine if 100 iterations of the COMMIT algorithm was sufficient? Were solutions significantly different based on the order in which the gapfilling was performed?**********Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.The Reviewer #1: YesReviewer #2: YesReviewer #3: Yes**********what does this mean?). If published, this will include your full peer review and any attached files.PLOS authors have the option to publish the peer review history of their article  digital diagnostic tool, Data Requirements:http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. 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Read more information on sharing protocols at  22 Dec 2021AttachmentReview_response.pdfSubmitted filename: Click here for additional data file. 9 Feb 2022Dear Dr. Nikoloski,We are pleased to inform you that your manuscript 'COMMIT: Consideration of metabolite leakage and community composition improves microbial community reconstructions' has been provisionally accepted for publication in PLOS Computational Biology.Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.Should you, your institution's press office or the journal office choose to press release your paper, you will automatically be opted out of early publication. We ask that you notify us now if you or your institution is planning to press release the article. All press must be co-ordinated with PLOS.Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology. Best regards,Vassily HatzimanikatisAssociate EditorPLOS Computational BiologyKiran PatilDeputy EditorPLOS Computational Biology***********************************************************Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: I would like to thank the authors for answering my questions and concerns in detail and incorporating changes where applicable. Microbial community metabolic modeling is challenging and I think the COMMIT tool will be good resource for community-level modeling efforts. I have no further comments on the manuscript.Reviewer #2: The authors addressed most of our comments. They may want to caution the reader in regard to the possibility/likelihood of the formation of thermodynamically infeasible cycles and ways to remedy this.Reviewer #3: The authors have generally adapted the manuscript well to my comments. However, the issue of using a single universal biomass for all species seems like an important one. I would argue that it is the distinctiveness of the biomass, specifically the organism-specific cofactor requirements and thus cofactor availability, that account of alot of the reason for various species to exist in the community (some species can simply do chemistry that others cannot). This is somewhat neglected when using a universal biomass. None of those cofactor biosynthesis pathways or transports will be activated. I understand that correcting for this falls outside the scope of the current study, but some discussion in the revised manuscript of this limitation and the need to improve methods to compensate for it seems important to include. Otherwise, it's likely readers won't even realize a universal biomass is being used as this detail is somewhat buried in the methods.**********Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.The Reviewer #1: YesReviewer #2: YesReviewer #3: Yes**********what does this mean?). If published, this will include your full peer review and any attached files.PLOS authors have the option to publish the peer review history of their article  1223-442824 | ploscompbiol.org | @PLOSCompBiolPLOS Computational Biology | Carlyle House, Carlyle Road, Cambridge CB4 3DN | United Kingdom


E. coli. To adapt this model for Saccharomyces cerevisiae, we developed yETFL, in which we augmented the original formulation with additional considerations for biomass composition, the compartmentalized cellular expression system, and the energetic costs of biological processes. We demonstrated the ability of yETFL to predict maximum growth rate, essential genes, and the phenotype of overflow metabolism. We envision that the presented formulation can be extended to a wide range of eukaryotic organisms to the benefit of academic and industrial research.Eukaryotic organisms play an important role in industrial biotechnology, from the production of fuels and commodity chemicals to therapeutic proteins. To optimize these industrial systems, a mathematical approach can be used to integrate the description of multiple biological networks into a single model for cell analysis and engineering. One of the most accurate models of biological systems include Expression and Thermodynamics FLux (ETFL), which efficiently integrates RNA and protein synthesis with traditional genome-scale metabolic models. However, ETFL is so far only applicable for  Formulating metabolic networks mathematically can help researchers study metabolic diseases and optimize the production of industrially important molecules. Here, the authors propose a framework that allows to model eukaryotic metabolism considering gene expression and thermodynamic constraints. Saccharomyces cerevisiae1 and Yarrowia lypolytica2) and are host organisms for the production of fuels and specialty and commodity chemicals. Also eukaryotic, mammalian systems such as Chinese hamster ovary cells are the main platform organism used for therapeutic protein production3. In contrast to bacterial cells, the eukaryotes have compartmentalized cell structure to localize macromolecules with different biological tasks. This fundamental difference renders the engineering of the eukaryotes more complex and challenging. To help optimize and plan for industrial applications, complex biological systems such as these can be represented in silico by specific networks designed to capture key processes.Eukaryotic organisms are extremely important in industrial biotechnology , which is a constraint-based optimization technique, where the metabolic flux of individual reactions is computed in a metabolic network by formulating a linear optimization problem6. However, FBA can predict biologically irrelevant solutions, including cycles with unrealistically high fluxes7 or thermodynamically infeasible solutions9. Despite its wide applicability, FBA cannot predict some important features of metabolic networks, such as those that account for limited catalytic capacity of enzymes or limitations in cellular expression systems.Metabolic networks are the most widely studied and modeled type of biological networks, with over 6000 genome-scale metabolic models (GEMs) reconstructed for archaea, bacteria, and eukaryotes9 enforces the coupling between the directionality of each reaction with its corresponding Gibbs free energy to eliminate thermodynamically infeasible predictions. More importantly, TFA also directly integrates variables for the concentrations of metabolites, which enables the integration of metabolomics data. Genome-scale models with Enzymatic Constraints using Kinetic and Omics data (GECKO) are another FBA-based method that accounts for the limited catalytic activity of enzymes by inclusion of enzyme concentrations as variables10. Previous studies have shown that GECKO can capture a realistic maximum specific growth rate and the occurrence of overflow metabolism in Saccharomyces cerevisiae10. However, GECKO does not explicitly consider the cost of protein synthesis. Instead, it assumes that the fractions of peptides within a protein pool are inversely proportional to their molecular weight. The molecular weight represents the cost of the enzyme within the context of proteome allocation. However, the actual cost of enzyme synthesis is absent from the formulation. Therefore, GECKO fails to account for the competition for amino acids required for enzyme synthesis, which is an important part of the expression system.To overcome some of the issues with FBA and eliminate unrealistic solutions, additional constraints that represent empirical or mechanistic evidence have been introduced. For example, thermodynamic-based flux balance analysis (TFA)13. ME-models include individual mRNA and enzyme concentrations as well as their cost of synthesis and cellular expression capacity. A new approach to construct ME-models, called Expression and Thermodynamics-enabled Flux (ETFL)13, was recently proposed to address the significant drawback of needing to solve the nonlinear programming (NLP) problem. The approach approximates bilinear terms with a zeroth-order piecewise-linear function by discretizing growth and solving locally linearized mixed-integer problems instead of an NLP problem. Similar to published ME-models14, the first ETFL model was developed for Escherichia coli. However, the ETFL formulation can readily be extended to the study of eukaryotic organisms.Metabolic and Expression Models (ME-models) are another class of constraint-based models that include the cellular expression system in addition to metabolic and catalytic constraintsS. cerevisiae is an industrially relevant organism15 that is widely used for biological and medical research studies16. Several GEMs of this organism have been published over the years due to its ubiquity in metabolic engineering22. However, likely due to additional requisite considerations in modeling the compartmentalized cellular expression systems of eukaryotes, no ME-model of S. cerevisiae has been developed. The previous ME-models were constructed for bacteria13, with one ribosome and one RNA polymerase being sufficient to represent the cellular expression machinery. In contrast, S. cerevisiae as a eukaryotic organism additionally has mitochondrial ribosomes and RNA polymerases. In this work, we extended the ETFL formulation and code for applicability to eukaryotic systems. In this new formulation, we account for the additional ribosomes and RNA polymerases within the eukaryotic mitochondrial expression system. We also included an allocation constraint for the fraction of proteins that are allocated to metabolism and cellular expression. Herein, we propose an ETFL model for S. cerevisiae, named yETFL, which is based on the extended ETFL formulation. The methodological advancements in ETFL provide avenues toward development of such models for the study of other eukaryotes.S. cerevisiae based on the ETFL formulation , 3991 reactions, 1149 genes, and 14 compartments (including the extracellular space). There are 2614 reactions associated to genes.We present here yETFL, a ME-model of on Table . yETFL iInformation about the thermodynamic properties of reactions allows us to (i) integrate the available metabolomics and fluxomics data into the models, (ii) compute thermodynamically consistent values of metabolic fluxes and metabolite concentrations, and (iii) determine thermodynamically feasible directionalities. Using the group-contribution method (GCM), we estimated the Gibbs free energies of formation for 1092 of 1326 total unique metabolites. We then estimated the Gibbs free energies for 1880 reactions in the Yeast8 GEM, which only includes reactions in an aqueous environment (see “Methods”). Yeast8 has 1304 reactions in the membrane compartments (nonaqueous environment). We did not apply thermodynamic constraints for these 1304 reactions as thermodynamic relations for membrane-associated metabolites require correction based on information about the nonaqueous environments, which is not always available.S. cerevisiae (see “Methods”). Of these enzymes, 77 were transporters associated to 167 transport reactions, there are 107 complexes among the enzymes, and the remainder are monomeric enzymes composed of a single peptide. A complexation reaction is considered for each enzyme to account for its synthesis from the constituent peptides. Operon structures were considered in the previous formulation of ME-models for the bacterial cells14. Similar to the original ETFL formulation, yETFL does not account for these structures since such mechanistic details were not necessary for the studies here. However, the details about the operon structures can be included in the ETFL formulation by expanding around the corresponding existing transcription steps, as it was done in the previous ME-models.In yETFL, we modeled the synthesis of 1059 enzymes coupled to 2588 of 2614 reactions with associated genes. The catalytic constraints are specified by coupling the reactions and the enzymes, which requires information on S. cerevisiae, there are different RNA polymerases and ribosomes. Notably, the mitochondria have their own RNA polymerase and ribosome. The extended ETFL formulation, presented here, enables implementing multiple ribosomes and RNA polymerases, the latter of which includes: (i) the RNA polymerase II, which transcribes nuclear genes and (ii) the mitochondrial RNA polymerase, which transcribes the mitochondrial genes. The model also includes three ribosomes, where one ribosome is associated with mitochondrial genes and the other two ribosomes are associated with nuclear genes, but differ in their composition (see “Methods”). Altogether, yETFL includes 1149 metabolic genes from Yeast8 and an additional 244 genes that encode the composition of the aforementioned ribosomes and RNA polymerases.While one RNA polymerase and one ribosome can sufficiently represent bacterial expression system, in a eukaryotic cell such as S. cerevisiae as observed in rich growth medium as a conservative upper bound on growth rate. Here, we assumed that the highest growth rate S. cerevisiae can achieve in a normal condition is when it grows on the rich medium . It is worth mentioning that To study the inclusion or exclusion of thermodynamic constraints and a variable or constant type of resource allocation (“Methods”), we developed four different types of models Table . The incS. cerevisiae are GECKO models, ecYeast710 and ecYeast822, and WM_S288C23, a whole-cell model. The Gecko models contain phenomenological constraints for proteome limitations. In contrast, yETFL is a fine-grained framework that accounts for proteome limitations mechanistically by integrating additional processes, such as transcription and translation. As a result, yETFL can predict parameters such as growth-condition-dependent biomass composition as well as transcription and translation machinery content, which cannot be done by the GECKO models. Moreover, the mechanistic representation of the expression system provides additional capabilities to yETFL to simulate the perturbations on the expression machinery, RNA transcripts, and gene copy numbers. Finally, in addition to proteomics data, which can also be integrated into the GECKO models, yETFL enables the integration of transcriptomics data.Similar models to yETFL developed for S. cerevisiae, WM_S288C, decomposes cell functionality into 26 cellular processes23. yETFL includes three of those cellular processes, i.e., metabolism, RNA transcription, and protein translation, which makes WM_S288C broader in scope. A comparison of the common parts between both models shows that both approaches use a constraint-based framework to model metabolism, but they differ in the form they model expression. While WM_S288C uses ordinary differential equations, yETFL uses a constraint-based optimization framework. The simplified approach used in yETFL allows for an efficient analysis of cellular behavior for different physiological conditions and different strains overcoming the requirement of the vast number of biophysical parameters present in WM_S288C and which are highly dependent on the strain and the environmental conditions24. Furthermore, yETFL is able to simulate cellular processes under the macroscopic steady-state assumption and study the cell behavior in time intervals spanning a few hours25, with a reasonable computational effort.The recently developed whole-cell model of 26. However, standard FBA models predict that the growth rate increases linearly with increased carbon uptake. Since ETFL accounts for expression limitations, it is expected to predict this shift in the cellular growth rate.The cellular growth rate should plateau when high values of substrate uptake are attained, as limitations in the expression system and catalytic activity of enzymes cause shift the growth rate from a glucose-dependent limitation to an enzyme-dependent one. This phenomenon is described by established empirical models of microbial growth, where the growth shifts from nutrient limitation to proteome limitation13). In both constant and variable biomass composition, and in contrast to FBA, the growth rate plateaued at higher values of glucose uptake rate, which is in accordance with the experimental results27. That is, we observed a shift from glucose-limited growth to proteome-limited growth. The maximum predicted growth rate was 0.44 and 0.41 h−1 for E(T)FL.cb and E(T)FL.vb, respectively. Both agree with experimentally measured maximum growth rates reported in the literature, which are in the range of 0.4–0.45 h−1 for different strains30. The accuracy of our predictions with experimental observations is important, as the maximum growth rate was highly overestimated in previously reported ME-models13 that were developed for the other organisms, likely due to the lack of an allocation constraint on the total amount of metabolic enzymes (see Eq. (We investigated the variations in growth rate with constant (E[T]FL.cb) and variable (E[T]FL.vb) biomass composition by examining the predicted maximum growth rate versus the glucose uptake Fig. . With a −1 h−1  presented an earlier onset of the Crabtree effect relative to the E[T]FL.cb models Fig. . We can ely Fig. . A poten10, an additional parameter was introduced to further constrain the availability of enzymes. Since the saturation rate of individual enzymes is not known, this parameter was introduced as the saturation rate of the total enzymatic pool and it was calculated by fitting the model predictions to the experimental data. Here, we captured the Crabtree effect without additional parameters, as yETFL explicitly accounts for the saturation rates of individual enzymes. Moreover, yETFL also allows for integration of experimentally observed saturation rates of individual enzymes by the addition of saturation parameters to the catalytic constraint of each enzyme. These parameters can then be found by fitting the model predictions to the experimental data, as has been reported37. Following a similar procedure, we can also integrate different experimental transcriptional and translational efficiencies into the model.It is of note that yETFL was able to capture the Crabtree effect solely by integration of experimentally measured data and without ad hoc modifications in the model or the formulation. In an earlier studyS. cerevisiae, by extension of the recently published formulation of ETFL to consider compartmentalized expression systems with separate ribosomes and RNA polymerases. This is the first model for yeast that includes RNA and enzyme concentration data, and this explicit simulation of expression broadens the applications of yETFL to the simulation of the impacts of different perturbations on cellular mechanisms. To test the accuracy of yETFL, we validated the predictions of the model against experimental data. Moreover, we reproduced the emergence of the Crabtree effect, and observed the secretion of ethanol in aerobic conditions without needing to integrate experimental data as with previous descriptions of the Crabtree effect10.In this work, we developed a model for a eukaryotic organism, E. coli overflow metabolism25, will yield valuable insights on the optimality of the regulatory mechanisms in S. cerevisiae. We envision that this information can be applied to design industrially valuable strains. Also, yETFL can be used as a scaffold to integrate other biological networks, such as regulatory or signaling networks5, as a vital step toward constructing a whole-cell model38. Finally, the extension of the ETFL formulation presented here is readily adaptable to any eukaryotic organism for which a well-curated GEM is available. The quality of the information about enzymes  will affect the quantitative predictions of the model, though new data are easily inputted into ETFL such that the predictions will always be as good as the available data. We envision that the availability of eukaryotic ME-models will improve the understanding and engineering of industrial hosts for the refinement and creation of better eukaryotic systems in biotechnology, for applications ranging from the production of fuels and commodity chemicals to therapeutic proteins.Overall, a key advantage of the ETFL formulation is its direct extension to other types of analyses, such as the study of the Crabtree effect at the steady state as we have presented in this work. Future work in understanding the emergence of this effect in a dynamic setting, as previously shown for the 13 .The most recent GEM of 13).Pseudometabolites defined for RNAs and proteins as well as pseudoreactions defined for their synthesis were replaced by the explicit expressions for RNA and protein synthesis  unique metabolites from Yeast8 , we used the macromolecular fractions from the Yeast8 biomass reaction. The mass fractions for different macromolecules were calculated using the below equation:45, i.e.,For each type of macromolecule, In this equation, BBBreactants is the set of reactants in biomass reaction and byproducts is the set of all products except biomass.When generating an ETFL model, it is important to remove protein and RNA metabolites from the biomass equation to prevent double counting of the metabolic requirements, since the explicit mRNA and peptide synthesis reactions already account for their respective participation in cell growth.−1, and j and RNA l in mmol gDW−1. In ETFL, we model the participation of macromolecules in the cellular biomass composition as follows:entclass1pt{minimaS. cerevisiae by reviewing the literature 47. Since the data are usually reported for a few particular growth rates, we resampled it using piecewise-linear interpolation.To create an E[T]FL.vb model, it is necessary to know the fraction of each biomass component at different growth rates. We gathered this information for 13, such as structural proteins, signaling proteins, or chaperones. However, since the dummy protein is not associated with a cellular function, the optimization procedure will apportion the whole protein content to the proteins that are associated with a cellular task . Consequently, the concentration of the latter proteins is overestimated, which results in overestimating the maximum growth rate, and the Crabtree effect emerges at higher growth rates. To realistically account for enzyme participation in the proteome, we can define Since ME-models do not consider all the cellular tasks of proteins, ETFL defines a generic, so-called dummy protein to represent the fraction of the proteome not accounted for in the modelS. cerevisiae available in PaxDB48 to compute this fraction as This way, the constraints in Eqs.  and 5)  5) enfor13.The growth dependence of the DNA abundance in the cell was modeled as proposed in the original ETFL formulationi in the pooling and biomass reactions, respectively. When it is desired to model a growth-dependent stoichiometric coefficient in the biomass reaction, the said stoichiometric coefficient can be redefined as a function of To consider the growth dependence of the biomass composition, we introduced the variation of the other biomass components in the ETFL formulation. The growth dependence of carbohydrates, lipids, and ions is implemented in a similar way to the one of DNAs, RNAs, and proteins in the original ETFL formulation. Specifically, we first discretize the growth into bins and then we use a MILP optimization to determine the discretized growth value (bin) that corresponds to the studied physiology. Then, we defined a metabolite pool for each of these macromolecules. In Yeast8, each biomass component is attached to a pooling reaction that transforms the sum of specific metabolites  into a single metabolite pool . The mass balance equation for these modeling metabolites is the following:i in the discretized growth bin u, following notations from Salvy and Hatzimanikatis13. i in a reference model .In this equation, S. cerevisiae, we defined multiple RNA polymerases and ribosomes in yETFL  molecules encoded by four different genes. In addition to these four rRNAs, the cytosolic ribosomes contain 78 peptides encoded by 137 genes50. Out of 78 peptides, 19 are encoded by a single gene and 59 peptides are encoded by either of two alternative genes. To account for alternative ribosomal peptides, we defined two sets of genes: set A containing 59 genes encoding for the 59 peptides , and set B containing the alternative genes of set A . Then, we constructed two cytosolic ribosomes, one where we constructed the 59 peptides using the set A and the other where we used the set B. We assumed a similar elongation rate for both cytosolic ribosomes. The two modeled ribosomes represent only two out of many possible combinations of the peptides from sets A and B. Implementing these 259 possibilities is currently computationally intractable. Here, as a first approximation, we decided to keep the two ribosomal compositions because we wanted to be inclusive of all ribosomal genes while having a realistic production cost. The other possible combinations can be readily integrated into the model by adding similar constraints to what we have already included for the two modeled ribosomes. A mitochondrial ribosome was also defined to translate mitochondrial genes. This ribosome is composed of two rRNAs and 78 peptides52.Ribosome: the structure of the cytosolic ribosomes in To model the ribosomes and the RNA polymerases, information about their constituting peptides, ribosomal RNA, and catalytic rate constants is required. To consider the eukaryotic complexity of FL Table RNA polymFurther details about the expansion of the ETFL formulation to implement multiple expression systems are provided in 53, is quantified in genome-scale models using the GAM. In ETFL, we consider the energetic cost of protein synthesis explicitly, and this cost should be removed from the GAM to avoid the overestimation of energetic requirements in the polymerization of peptides .8\documSince 2 moles of GTP are needed to attach 1 mole of amino acid to the peptide (Eq. ), and fr1 mole of ATP is required to produce 1 mole of GTP. Therefore, we can deduce that peptide polymerization requires 2 moles of ATP per 1 mole of amino acid.−1 of each amino acid are required to produce 1 g of biomass. From there, it is straightforward to compute the total amount of amino acids (~4.1 mmol) required for the production of 1 g of biomass. Combined, we can calculate that to produce 1 g of biomass, the energetic cost is −1 of ATP for peptide synthesis, which we removed from the GAM.We also know that the stoichiometric coefficients of amino acids in the biomass reaction of Yeast8 give information on how many mmol gDWWe assumed similar composition for isoenzymes if composition information was only available for one of them. For example, if one of the isoenzymes is a dimer, the other is also assumed to be a dimer.We assumed that monomeric enzymes catalyze reactions (i) that depend on a single gene, and (ii) for which information about their enzyme composition was not available.S. cerevisiae10.If an enzyme peptide composition is identified, either from databases or by approximation, but its 10. We set −1), which ensures that these reactions are not catalytically constrained and only the gene–protein–reaction relationship is preserved. We also checked the impact of constraining the transport reactions. To this end, these reactions were constrained by the median While the reactions that transport a metabolite from one compartment to another one are associated with genes, their Coupling the reactions in metabolic networks with their enzymes is the most important step in the process of creating an ETFL model. Ideally, assigning enzymes to reactions requires information about: (i) gene–protein–reaction rules, (ii) catalytic rate constants (ons Fig. :We assum54 to assess the quality of yETFL. The ETFL formulation enables single-gene knockouts by blocking the flux through transcription reaction for each gene. The predicted essential genes were compared against experimental data for S. cerevisiae obtained from http://www-sequence.stanford.edu/group/yeast_deletion_project/downloads.html. Before deleting the genes, the culture medium was modified according to Lu et al.22. Briefly, the minimal medium supplemented with amino acids and nucleotides was used for the simulations, and the model was allowed to uptake glucose as the sole carbon source. The MCC was used as a metric to evaluate the quality of predictions for FBA and ETFL because of its robustness to the imbalance in the number of essential and nonessential genes. MCC can take values from −1 to 1, where values of MCC close to −1 indicate predictions opposed to the ground truth, 0 random predictions, and 1 perfect predictions.We used gene essentiality analysis10.The results of this paper were obtained by simulating the cell growth as a function of different carbon uptake rates. This allows the exhibition of proteome-limited behavior and overflow metabolism in the presence of excess glucose. For all simulations, the model was allowed to uptake glucose as a carbon source, some essential inorganic compounds, and oxygen. To prepare the model for the simulations, it was modified as described previously in Sánchez et al.55 and then the total enzyme concentrations10, consecutively, to account for the parsimonious enzyme usage. Finally, the Chebyshev center of the enzyme space was used as a representative solution25.To capture the Crabtree effect, the substrate uptake rate was minimized for different values of the growth rate. Then, we fixed the values of the substrate uptake rates at the computed minima and minimized the total fluxesFurther information on research design is available in the Supplementary InformationPeer Review FileReporting Summary