Microbial communities affect many facets of human health and well-being. Naturally occurring bacteria, whether in nature or the human body, rarely exist in isolation. A deeper understanding of the metabolic functions of these communities is now possible with emerging computational models. In this review, we summarize frameworks for constructing mechanistic models of microbial community metabolism and discuss available algorithms for model analysis. We highlight essential decision points that greatly influence algorithm selection, as well as model analysis. Polymicrobial metabolic models can be utilized to gain insights into host-pathogen interactions, bacterial engineering, and many more translational applications. Microbial communities affect many facets of human health and well-being. Naturally occurring bacteria, whether in nature or the human body, rarely exist in isolation. Bacteria also play a key role in a variety of industries. Engineered Escherichia coli are used to produce commercial quantities of insulin and microbial inoculants are used in soil to sequester carbon from the atmosphere.3,4 Knowledge of the bacterial metabolic shifts that result in product synthesis has been utilized to create effective metabolic systems in these industries. In the future, a better understanding of bacterial community metabolism will inform decisions to address questions in industry, health care, and basic science.Bacterial communities have an ever-expanding impact on both the global ecosystem, through nutrient cycling, and society, through the health benefits and burdens they cause. In the human gut microbiota, bacteria type and abundance have direct implications for nutrient absorption, age-associated diseases such as Alzheimer's, and susceptibility to gastrointestinal infection. Without the microbiome, up to 30% of ingested energy would be lost in silico. Additionally, the high throughput capability of modeling is conducive to exploring community systems that would be impossible to systematically explore experimentally, allowing for the beginning of mechanistic understanding of bacterial metabolism in community settings.There is little known regarding microbial metabolism at the community level. Bacteria behave differently when in natural environments inhabited by multiple species compared to in isolation, which is typical in most laboratory experiments. Polymicrobial community interactions are governed by a set of poorly understood rules that encapsulate the tension between competition, genetic parsimony, and energy conservation. Experimental studies of these interactions often involve isolating the bacteria of interest and then co-culturing with other bacterial species to evaluate the community effects. This strategy presents a significant barrier for the field, as many bacteria are difficult or impossible to culture in a laboratory setting. Computational modeling can help to overcome this hurdle, enabling the study of these interactions Genome-scale network reconstructions (GENREs) and genome-scale models (GEMs) are powerful tools for studying bacterial community metabolism. GENREs function primarily as a repository for the biochemical reactions an organism is capable of executing. GEMs are derived from GENREs that have undergone both gap-filling and manual curation in order to achieve a high level of predicted metabolic output accuracy. GEMs can be utilized for computational simulations to further biological investigations and discoveries. By integrating multiple GEMs of various bacteria into one simulated community, the metabolic interactions of the polymicrobial community can be analyzed using Flux Balance Analysis (FBA) and related modeling methods. FBA-based simulations can provide information on what genes, metabolic pathways, and metabolites are utilized by community members in simulated environments. Integrating omic data into the model provides a layer of physiological insight in relation to gene transcription, metabolite usage, and protein synthesis, depending on the data used. Through understanding community metabolism we can better predict bacterial evolution, host–pathogen interactions, and improve bacterial engineering.in silico simulation of polymicrobial communities and the metabolic interactions that occur between community members. Through an understanding of GEM construction and curation we gain insight into how additional omic data integration can add context to these metabolic models. After a single bacterial GEM has been constructed we can tackle the question of what kind of bacterial community we want to model, as well as what kind of analysis we want to perform, and the algorithms that can aid in this process. Polymicrobial metabolic models allow for a deeper understanding of both the individuals within a community and the function of a community as a whole. With this knowledge we gain the ability to better modulate these behaviors in order to produce desirable outcomes.In this review we discuss FBA-based algorithms that allow for the 5,6 GENREs can capture diverse information including stoichiometric mappings of substrates to products and the enzymes that catalyze these chemical transformations. With the use of many analytical methods that have emerged, these complex networks can enable the investigation of numerous metabolic states.7,8GENREs are high quality repositories of information that synthesize biochemical knowledge into a convenient, computationally interpretable format.9,10Network construction begins with the annotated genome . The gen11,12 While these automated curation algorithms circumvent the labor of manual curation, they can reduce model quality by adding reactions without strong biological evidence.Initially constructed models often contain key inconsistencies when compared to physiological data, and those inconsistencies require curation to resolve. Curation refers to a broad range of activities aimed at improving the overall quality of the model. Models are curated to ensure that they are able to carry flux through the biomass synthesis OF. Gap filling algorithms can be used to ensure model growth by adding reactions from established databases.13 Unresolved loops can have effects that permeate through the model, leading to issues such as inflated growth yield predictions. These cycles can be caused by imbalanced reactions, reaction reversibility issues, or a multitude of other model errors. Loops are typically investigated with the aid of algorithms, but ultimately resolved through manual curation.13,14Another common target of curation is the resolution of energy generating cycles. These cycles are thermodynamically infeasible loops that are capable of charging electron carriers (such as ATP) without metabolite consumption.Escherichia coli and human metabolic models have been released following multiple rounds of curation.15,16 Manual curation is often an arduous task due to the wide variety of curation points traversing carbon source utilization predictions, reaction validity, and annotation consistency. However, the curation process results in a deeper understanding of organismal metabolism, often a reconciliation of conflicting literature, as well as a higher quality model.While recently there have been significant gains in the automation of the curation process, the best models in the field are often the result of extensive manual curation. New versions of the widely utilized Frequently, with known constraints on reaction fluxes, there remains a large set of potential metabolic states of the network. Experimental data can be used to contextualize the model, trimming possible states to only those that are most biologically accurate in a given environment or experimental condition.17–20 These methods typically convert gene expression or protein abundance levels to reaction weights that represent the likelihood that individual reactions are being utilized by the organism. By applying these weights to the model, the predicted metabolic state can be guided towards what is observed experimentally.Transcriptomic and proteomic data provide evidence for what metabolic pathways are utilized by an organism at a given point in time or in a particular environmental condition. Transcriptomic data indicates which genes are expressed and methods often use that expression state as a surrogate for which reactions are available to the network. Protein abundance data offers more direct evidence for reactions available to the network based on what proteins are present. However, transcriptomic data is often more comprehensive and more commonly used for contextualization since it is more readily available. Several algorithms have been developed to integrate transcriptomic and proteomic data with metabolic models.21Metabolomic profiles of supernatants from growth culture experiments provide evidence for the metabolites an organism consumes and produces as it grows. This data can be integrated as bounds on the exchange reactions that force the model to mimic the uptake and secretion of metabolites that were observed experimentally. It can also be analyzed as evidence for what metabolic pathways are being utilized and therefore integrated into the model as reaction weights.22,23 For example, exchange reaction values of particular solutions can be used to predict metabolites that are consumed/produced by the organism which can be compared to available metabolomic data.24When assessing the quality of a metabolic model there are two main types of tests that are performed; those that measure accuracy of predictions about the corresponding biology and others that evaluate model standardization. Efforts to assess accuracy of the biological predictions involve the comparison of model predictions to experimental data. The growth of an organism in a defined media is both relatively simple to measure experimentally and a prediction that such metabolic network models can readily generate, offering a direct comparison to evaluate accuracy. This comparison allows for the absence (or erroneous presence) of metabolic pathways to be identified as points for curation. However, while this assessment of growth is a convenient test for easily cultured bacteria, it cannot be utilized for others that are difficult to grow in isolation in a laboratory setting. There are several other types of biological predictions frequently used to assess model quality as described elsewhere.9,25 The degree to which objects in the model correspond to these databases is used to assess model standardization. MEMOTE was developed by the metabolic modeling community in an effort to create a holistic quality assessment.26 MEMOTE conducts a uniform set of tests to assess both biological accuracy and model standardization then provides a detailed report with score insights and specific points of potential improvement. While benchmarking approaches are used to measure model quality, they also identify gaps in the model that serve as points for curation. Therefore, quality assessments are not the end point for the model development process, but rather a feedback mechanism to inform further curation.27Model standardization is commonly assessed through identifiers and annotations associated with model objects. Databases such as BiGG and ModelSEED set forth standardized identifiers for metabolites and reactions that allow for direct comparisons across models.in silico a few key decisions must be made  the “bag-of-genes” approach or (2) the discrete approach.et al. to simulate the metabolic relationships that emerge when pairs of microbes are grown in co-culture.30 The models allowed for the identification of key cross-fed metabolites and how those metabolites impact the growth capability of each microbe. Spatially, this approach assumes that all bacteria have equal access to the communal metabolites. However, physiologically this equal access is often not the case. To simulate the uneven access to communal metabolites, Klitgord and Segrè incorporated another layer of compartmentalization via a shared environmental space.31 The shared environmental space allows for inter-species metabolite exchange via shuttle reactions, while individual extracellular compartments allow for bacteria-specific media conditions. Bacterial compartmentalization sets the stage for how an individual bacterial species will interact with other community members, as well as the surrounding environment. Thus, defining the spatial limitations of metabolite exchanges and metabolic machinery is a critical decision in any multi-species modeling effort.In the discrete approach, each bacterial model exists in a separate cytosolic compartment. Individual bacteria then interact metabolically through a shared extracellular space, where species-specific transport reactions are able to move communal metabolites into and out of the bacterial cytoplasm. This approach was used by Pacheco 32 The argument is that bacteria have not necessarily evolved for optimization of a community biomass objective, even if participation in a community structure may be beneficial with respect to specific evolutionary objectives. Conversely, there are examples of bacteria participating metabolically in “social good” via individual sacrifice; however such cooperation and its associated mechanisms are only beginning to be understood.32–34Choosing an objective function (OF) is the next defining feature for community metabolism modeling. There are three broad categories that encompass approaches for defining potential OFs: individual level, community level, or multi-scale. The goal of an individual-focused OF is to maximize an objective like biomass synthesis at the individual level, agnostic to the overall polymicrobial community biomass production. Community level OFs often optimize biomass production across all species, at the expense of the biomass production of some individual species. This assumption of “sacrifice” is counter to some observations, where bacterial guilds are selfish and prioritize individual biomass over community biomass.35 The inner problem is defined as individual-level biomass synthesis maximization, while the outer problem is community biomass synthesis maximization. The inner problem is optimized first in order to identify the maximum biomass production of each bacterial species. The outer problem is then optimized, but individual bacteria are allowed to grow at a proportion of their optimal biomass in order to simulate sacrifice of an individual species’ growth for community biomass synthesis maximization. The multi-scale tool MICOM offers the additional flexibility of manually adjusting the trade-off values assigned to individual bacteria, while also being able to integrate metagenomic community data.36Multi-scale OFs often seek to optimize biomass production at both the individual and community level. Multi-scale OFs allow for the investigation of the trade-offs of bacteria sacrificing individual-level growth in exchange for greater community growth. These OFs strike a balance between the evolutionary concept that bacterial species focus on individual growth while also considering the evolutionary benefits of community-level metabolic interdependence. OptCom is a method that breaks down these two optimization equations into inner and outer problems.The definition of OFs for the simulation of a microbial community requires assumptions on global and local network optimization. Furthermore, how the objective function is defined influences what type of metabolic interactions a final model is best suited to investigate.37 The initial application of dFBA did not involve community modeling, and instead focused on the metabolic dynamics of an individual species. Dynamic multi-species metabolic modeling (DMMM) extends FBA to microbial communities by maximizing biomass synthesis of an individual bacterial species while continuing to account for community dynamics by tracking bacterial population sizes and metabolite concentrations.38 If an individual species is unable to produce maintenance levels of ATP, a death rate is calculated and applied to that species. The interplay of growth and death rates results in fluctuating population size, which directly affects the proportion of metabolites an individual species is producing and consuming, thus changing community metabolite composition. However, DMMM does not account for the metabolic changes that occur as a bacteria dies and its resources become available to the community. Additionally, DMMM lacks a clear option for integrating experimental data into the model.FBA solutions offer insight into the instantaneous metabolic state of a given metabolic network. However, bacterial communities are in a continuous state of metabolic evolution. In order to simulate these dynamic events it is critical to account for temporal changes. Dynamic FBA (dFBA) is a dynamic modeling algorithm that incorporates time by iteratively calculating flux values and metabolite levels and using those values to update the physiological context of the model for the next simulated time point.35,39 With all dynamic models a primary drawback is the computational burden of running the analysis. DMMM circumvents this computational burden by solving FBA problems at a time point for each microbe. Brunner et al. reduced the number of optimization problems that have to be solved when running dFBA by using the solution from a previous time-step in dynamic analysis to inform the solution at the current time step, resulting in less computational power and time requirements.40Similarly, an extension of OptCom, dynamic-OptCom (d-OptCom) incorporates time by iteratively using the rates of community metabolism uptake and output, as the metabolic parameters for an individual bacteria's growth rate.41 COMETS presents a unique opportunity to investigate how spatial considerations impact both community and individual level metabolism. Agent-based models (ABMs) allow for the integration of spatial considerations to investigate how an organism physically interacts with the surrounding environment. MatNet creates an intersection between GEMs and ABMs that allows for spatial considerations to be accounted for in metabolic network models.42 This approach was used to construct a multiscale model of Pseudomonas aeruginosa that was able to recapitulate decreased oxygen accessibility in relation to surface location in the context of biofilm formation. Similar to MatNet, BacArena is able to take into consideration the metabolic heterogeneity within a bacterial community due to its larger focus on an individual-centric ABM.43 BacArena was able to more accurately predict Clostridium beijerinckii doubling time when compared to COMETS. The number of tools available to study metabolic modeling with a spatio-temporal aspect is growing rapidly.44,45Another key consideration for modeling polymicrobial communities is to incorporate a spatial component, which takes into account the constraints that physical location puts on a bacterial community. Accounting for the spatial aspect offers the ability to incorporate metabolic gradients that determine what metabolites individual bacteria can access. This metabolic gradient is dictated by bacterial production of metabolic byproducts and the spatial arrangement of all members in the community. COMETS is a tool developed to account for the spatial component of microbial communities, by integrating metabolite diffusion with FBA in order to evaluate how polymicrobial communities metabolically equilibrate.46As for models of individual species, the quality of microbial community models can be enriched with the integration of experimental data. Since obligate commensal species are often difficult or impossible to culture in a laboratory setting, the ability of metagenomic, metatranscriptomic, metaproteomic, and metabolomic techniques to be used on naturally occurring communities makes these approaches exceedingly valuable. The collected data can be used to characterize the complex metabolic interactions occurring in microbial communities and can inform the construction, contextualization, and validation of community models.47,48 While whole-metagenome sequencing (WMS), a type of amplicon-based sequencing, provides higher resolution data, revealing strain-level variation among community members, it is more expensive than lower resolution amplicon-based sequencing.49 These methods can be used in the investigation of communities that occur naturally or are difficult to culture. Metagenomic data can inform the decision of which individual models to include in a community simulation.50Once a microbial community is defined, the first step in a simulation is to characterize the members of that community. Metagenomic approaches such as amplicon-based sequencing are culture-independent methods that quantify species abundance in a community.51 In Descriptive OptCom, experimental growth rate data informs the biomass constraints for both individual bacterial species and the community.35 While this analysis provides useful insights into the metabolic activity of a community, it only offers a static snapshot. Metagenomics can also be performed across time points to provide dynamic abundance data to assess the growth of individual members of the community. Dynamic OptCom is capable of integrating this temporal data to investigate how the structure of a community evolves over time as individual members flourish or diminish.39 BOFdat integrates experimental growth data into the biomass objective function formulation of individual organisms, allowing for more accurate recapitulation of physiological metabolism.52 These individually curated GEMs can then be combined to simulate community interaction.After the initial model has been constructed, more data can be integrated in order to better fit the model to a physiologically relevant context. Metagenomic profiling can be used to provide growth rate data for members of the community.53 Metatranscriptomic and metaproteomic data characterize the RNA and proteins that mold community metabolism. Both of these data sets provide evidence for what metabolic pathways are being utilized by the community and therefore can be integrated as reaction weights.54 RIPTiDe and TIMBR are both integration algorithms that utilize transcriptomic data to create reaction weights, which then impact predicted model metabolic outputs.17,55 RIPTiDe additionally allows for this transcriptomic data to be used to “prune” reactions and metabolites from a model that do not have strong transcriptional support and are not necessary for an OF to carry flux. However, due to the varying residence time of RNA (∼3 minutes) and proteins (0.5–35 hours), these data offer different temporal snapshots of what is occurring in the organisms.56While metagenomics provides information about the microbes present in a community, communities of similar composition can still differ greatly in which functions are active.39 Exchange reaction constraints can be tailored to this data to reproduce metabolite availability, production, and consumption. Additionally, measured secreted metabolites can provide evidence about what pathways are active and can therefore be integrated as reaction weights.21Metabolomics can provide useful information about the shared metabolite pool and exchanges that occur in a microbial community.in silico predictions with experimental data. Exchange reaction values from model simulations can be converted to metabolite abundances that can be compared to metabolomic data.24In silico growth of community members can be compared to abundance data from metagenomic profiling to evaluate accuracy of associated predictions. For example, Zuñiga et al. validated a community model by comparing simulated growth data to experimental bacterial community growth data.57 Additionally, Stolyar et al. built a metabolic model of methane production using a simple bacterial community composed of the sulfate-reducing bacteria Desulfovibrio vulgaris and the methanogen Methanococcus maripaludis.58 Their model was able to recapitulate experimental community growth data, while also differentiating between potential essential and nonessential interspecies electron shuttles for syntrophic growth. A validated model can then be used to explore bacterial relationships in different simulated contexts.The analysis of community models often begins with validating 29 Knowledge of identified essential genes can be utilized to design a single species that has the metabolic functionality of a larger community. Essential genes can also function as potential targets for novel drug development.59 Gene essentiality analysis allows us to identify how essential genes change after a selective pressure is applied to a community, resulting in the loss or mutation of previously essential genes over time.60 Cornerstone species in a community can be identified by finding the bacteria that provide the highest proportion of essential genes.61The contexts a model is best suited to investigate are inextricably linked to bacterial community construction . A model31 SEM (search for exchanged metabolites) is a method to identify the minimal number of essential metabolites exchanged between bacteria for mutual growth in co-culture. SMM  is an approach to create a minimal media for co-culture based on the essential metabolite exchanges. SIM (search for interaction inducing media) is a method to generate different media conditions based on which metabolites the respective bacteria are able to produce or consume. Predicted biomass synthesis from FBA simulations defines each media condition as having induced either neutral, mutual, or commensal interactions. In parallel with Klitgord's work regarding induced metabolic relationships, OptAux takes a genetic approach as opposed to a minimal media based approach.62 OptAux integrates time-course sequencing of co-cultured bacteria grown under forced cooperation conditions. OptAux utilizes this genetic data to make predictions regarding protein availability, and its impact on community composition.Metabolic relationships between bacteria can evolve naturally or be induced. Klitgord and Segrè developed three algorithms that allow for the identification of naturally occurring metabolic relationships, as well as the investigation of induced metabolic relationships .31 SEM  can be used to identify metabolically limiting factors that block increased community growth and therefore hinder the production of desirable products.et al. modeled bacterial competition in order to explore how bacteria in a community system evolve to “cheat” the system.64 They discovered that for bacteria in the studied community it is more energetically favorable to “steal” thiamine from a neighbor than it is to produce thiamine itself. Nutrient cycling creates an environment that is conducive to the evolution of “lazy” bacteria, which over time will cut genetic “fat” in favor of scavenging the metabolic byproducts of its neighboring community members.69 However, if shared resources are in high demand, competitive selective pressures are likely to prevent a wide outcropping of “free-loading” bacterial populations. Thommes et al. explored how to intentionally design metabolically parsimonious bacterial communities through multi-strain E. coli computational models.70Conversely, Hibbing 71 By simulating different single-carbon source utilization and implementing experimentally determined growth parameters, alternative metabolic pathways can be discovered and later experimentally validated. This approach can be extended to explore engineered polymicrobial systems. In some cases, potentially harmful metabolic byproducts are reduced or eliminated through co-culture consumption. One example is engineered E. coli to assist in carbon sequestration via an altered metabolism which allows for carbon dioxide to be converted to formic acid.72 Alternatively, polymicrobial modeling allows for the identification of critical metabolic interactions found in “harmful” bacterial interactions. If these keystone interactions are identified, they can subsequently be circumvented via antibiotic therapeutics that target specific bacterial metabolism. This type of exploration is especially relevant to human pathogenesis rooted in multi-bacterial infection. By excising the initial experimental step in favor of modeling, time and resources are saved, while a wide array of possibilities are explored.An additional benefit of polymicrobial modeling is the relative ease with which alternative hypotheses can be explored.73 Polymicrobial community modeling can quickly iterate through multiple potential growing conditions, and the subsequent output can be used to optimize desired metabolite production. Additionally, these simulations can be applied to systems that may be hard to isolate metabolically in vivo, such as host–pathogen interactions. Through simulating host–tissue metabolism in conjunction with a pathogen of interest, one can potentially observe how the infecting bacteria is metabolically altering the host for its own benefit.74 Such modeling efforts have the potential to drive much drug target discovery and the development of novel therapeutic strategies.Much like the bacteria they emulate, polymicrobial metabolic models are continuously evolving in regard to useful data integration approaches and relevant applications. These models offer inherent versatility that experimental methods do not possess. For example, models allow for the flexibility to simulate numerous conditions in which a polymicrobial community could be found. This ability is conducive to studying bacterial communities that may be hard to access, such as microbial communities in the human gut or anaerobes in inaccessible environmental niches like those found in deep sea vents, as well as bacterial communities that could be engineered and do not yet exist.Prevotella melaninogenica, are known to degrade this mucus.75 Polymicrobial models can be used to simulate the metabolic interactions that occur as bacteria infect the lung epithelium. These models can offer a deeper understanding of how these infections occur, which can be used to improve therapies. Mucin catabolism in the context of CF is just one of many examples of how polymicrobial modeling can be applied to investigate novel therapeutic strategies. Polymicrobial models can also be used to identify metabolic links between primary and secondary infections, to elucidate how bacteria can work in chorus with one another.The interface of tissue and bacterial models can also be used to explore how metabolism functions in bacterial infections. For example, in the case of cystic fibrosis (CF), mucus hypersecretion creates a hospitable niche for bacterial growth, resulting in inflammation and hospitalization. Some species of bacteria, such as The avenues of exploration that polymicrobial modeling present are limited by the number and quality of available models, as well as validated methods for identifying key genes, metabolites, and pathways important in specific clinical applications. However, with the continued development of more sophisticated methods and the improved quality of metabolic models, these constraints are rapidly dissolving.There are no conflicts of interest to declare.


Escherichia coli strains deleted for y-genes. Since the products of these y-genes potentially play a role in a variety of metabolic processes, the experiments were designed to be agnostic as to their potential metabolic impact. The obtained data highlight the robustness of E. coli’s central metabolism to y-gene deletion. For two y-genes, deletion resulted in significant changes in carbon and energy fluxes, demonstrating the involvement of the corresponding y-gene products in metabolic function or regulation. This work also introduces novel metrics to measure the actual scope and quality of high-throughput fluxomics investigations. We have developed a robust workflow to measure high-resolution fluxotypes (metabolic flux phenotypes) for large strain libraries under fully controlled growth conditions. This was achieved by optimizing and automating the whole high-throughput fluxomics process and integrating all relevant software tools. This workflow allowed us to obtain highly detailed maps of carbon fluxes in the central carbon metabolism in a fully automated manner. It was applied to investigate the glucose fluxotypes of 180  E. coli, 35–40% of genes (the ‘y-ome’) are of unknown function -D-glucose + 20% [U-13C6]-D-glucose. To minimize sources of unlabeled carbon atoms from the first cultivation steps in subsequent experiments, the cells were inoculated at a starting OD between 0.08 and 0.12.To perform the experiments, the glycerol stocks of relevant strains were used to inoculate liquid LB medium in microplates. The LB cultures were used to inoculate precultures in minimal synthetic medium containing 17.4 g·L13C-labelling experiments, sampling of labeled metabolites, and sample preparation for NMR and MS analyses. The first system allowed 48 13C-labelling experiments to be performed automatically in parallel in 15 mL bioreactors under controlled growth conditions, with automated collection of labelled samples (of biomass or culture medium) at defined culture times or optical densities. The robot and its operation are described in detail by Heux et al. -D-glucose and 20% [U-13C6]-D-glucose. All cultures were performed in 15 mL reaction vessels, at 37 °C, pH = 7, a stirring speed of 2300 rpm and with 5 L·min−1 of compressed air fed into the culture module. Four to eight supernatant samples were collected in each reactor throughout the culture to analyze the exometabolome and to calculate the rates of substrate consumption and end-product production. The biomass was automatically sampled once the OD600nm had reached 1.2, indicating that the metabolic and isotopic steady-state had been achieved: 4 mL samples of culture were pelleted by automated centrifugation (5 min/4410 g), manually hydrolyzed with 250 µL 6 N HCl for 15 h at 110 °C and washed twice in 1 mL D2O by rotary evaporation  between each washing step. Aliquots (10 µL) of biomass hydrolysate supernatant were then collected and transferred into 96 well plates, diluted with 990 µL pure H2O and transferred to vials for LC-MS analysis. Samples of biomass hydrolysate supernatant (150 µL) were also mixed with 50 µL of TSP d4 (4 mM in D2O) and 150 µL of each mixture was then transferred into 3 mm NMR tubes. The  (1.2.1) , and con13C-label into proteinogenic amino acids (listed in m/z), using the following source parameters: Capillary temperature, 275 °C; source heater temperature, 250 °C; sheath gas flow rate, 45 a.u. (arbitrary unit); auxiliary gas flow rate, 20 a.u.; S-Lens RF level, 40%; source voltage, 5 kV. Metabolites were identified by extracting the exact mass with a tolerance of 5 ppm. The raw MS isotopic profiles of proteinogenic amino acids were then quantified using Tracefinder . The isotopic profiles (Carbon Isotopologue Distributions) were obtained after correcting for natural isotopic abundances using IsoCor 1.2 [https://github.com/MetaSys-LISBP/IsoCor (accessed on 20 May 2020)). The raw MS data are available from Metabolights (accession number MTBLS2188).The incorporation of oCor 1.2   page equipped with a 5 mm CQPI cryoprobe at 280 K. To precisely quantify the extracellular compounds, the 1D-1H NMR data were recorded after a 30° presaturation pulse (zgpr30), with a relaxation delay of 7 s. NMR spectra were processed using Topspin 3.5pl6 . The raw NMR data are available from Metabolights (accession number MTBLS2188).Culture supernatants were analyzed by 1D-13C labeling profiles of acetate and lactate, including positional information on label incorporation, were also measured for the flux calculations.The rate of glucose consumption and the rates of acetate and lactate production were quantified by analyzing the four-to-eight samples collected during the cell culture period. The The growth parameters calculated from the experimental datasets for each culture were the growth rate, glucose uptake rate, acetate and lactate production rates and biomass yield. The growth rate was calculated from OD values measured during the culture period. The rates of glucose consumption and of acetate and lactate production were calculated from the exometabolome data. All calculations were performed using Physiofit (v0.9) , a softwExtracellular fluxes were determined from the rates of disappearance (or appearance) of substrates and products, in the culture supernatants, as measured by NMR.https://metasys.insa-toulouse.fr/software/influx/ (accessed on 20 May 2020)), including the mass balances and carbon atom transitions of the biochemical reaction network. The metabolic network contained the main pathways of E. coli’s central metabolism: glycolysis (EMP), the pentose phosphate pathway (PPP), the Entner-Doudoroff (ED) pathway, the tricarboxylic acid cycle (TCA), and anaplerotic reactions, the glyoxylate shunt, and the reactions for amino acid biosynthesis [13C-labelling patterns of metabolites using appropriate mathematical models of glucose metabolism in E. coli [1H NMR, as detailed above. The fluxes were normalized to the rate of substrate uptake, which was arbitrarily set at 100.Fluxes were calculated using the software influx_si 4.1   was written in a specific FTBL file , which whttp://metexplore.toulouse.inra.fr (accessed on 20 May 2020)). Metexplore was used to visualize flux maps for strains of interest [The FTBL model was converted by an influx_si module (ftbl2metxml.py) into Systems Biology Markup Language , readable by the online application Metexplore  . The resThe data and meta-data, generated throughout the workflow, were stored, managed, and processed as described below. E. coli strains with 13C-labelled compounds and to the collection of samples: Settings and data from the robotic culture platform (Tecan Evo 200) were automatically and separately recorded for each of the 48 bioreactors: pH values, O2 values, OD600nm values, volumes, sampling times, and tube locations and associated barcodes. The data were linked and stored in an SQL database, making them traceable to each robotic run. The most important elements of this database are listed in Culture and sampling data are related to the parallel cultures of Sample preparation data: All the steps performed on the sample preparation platform (Tecan Evo 200) were automatically recorded in an SQL database: Volumes, tube locations on the worktable, associated barcodes and sampling times. The data were visualized and previous runs re-examined using the robot’s traceability software, and a log file was automatically generated for each run with errors and software information. Analytical data: All mass spectrometry and NMR data were saved on a server to guarantee sample traceability. This included the raw MS data, the MS data processed with Tracefinder, the MS data processed with Isocor, the raw NMR data, the NMR data processed with TopSpin, and the NMR data processed with Physiofit. Corrected CID values, extracellular fluxes and the positional enrichment of extracellular metabolites are listed in Flux calculations: All flux calculation files were stored on a server. This included the input (FTBL) files for influx_si, and the output (KVH) files. The most important elements are included in Statistical analysis and flux mapping: All the data used and generated for statistical analysis and flux mapping were stored on a server.−1·h−1) of NADPH, NADH/FADH2, and ATP in the central carbon metabolism were calculated as the sum of the estimated fluxes of the reactions that are expected to produce  or consume  the cofactors. Values were averaged over the biological replicates. NADPH production: Pentose-Phosphate Pathway (PPP) = glucose 6-phosphate dehydrogenase (zwf) + phosphogluconate dehydrogenase (gnd); TCA cycle = isocitrate dehydrogenase (idh); malic enzyme (mae). NADH production: glycolysis = glyceraldehyde-3-phosphate dehydrogenase ; Oxidative metabolism = pyruvate dehydrogenase (pdh) + TCA cycle enzymes, including alpha-ketoglutarate dehydrogenase (akgdh) + malate dehydrogenase ; malic enzyme (mae) and biomass formation. NADH consumption: lactate dehydrogenase (out_Lac). FADH2 production: TCA cycle = succinate dehydrogenase . ATP production: glycolysis = phosphoglycerate kinase (pgk) + pyruvate kinase (pyk); TCA cycle = succinyl-CoA synthetase (assimilated to akgdh); acetate metabolism = acetate kinase . ATP consumption: glycolysis = glucose PTS system (Glucupt_U + Glucupt_1)  + 6-phosphofructokinase (pfk); ppc  and pep carboxykinase (reverse flux).The production rates (mmol.gDW


Thus, fluxomics reveals the functioning of multi-molecular metabolic pathways and is increasingly applied in biotechnology and pharmacology. Here, we describe the main fluxomics approaches and experimental platforms. Moreover, we summarize recent fluxomic results in different biological systems.Fluxomics is an innovative -omics research field that measures the rates of all intracellular fluxes in the central metabolism of biological systems. Fluxomics gathers data from multiple different -omics fields, portraying the whole picture of molecular interactions. Recently, fluxomics has become one of the most relevant approaches to investigate metabolic phenotypes. Metabolic flux using  Throughout recent decades discoveries explaining the complex nature of the cell have provided the scientific community with an immense amount of data. As more information has been revealed, the need for classification and quantification of this data has resulted in the creation of various–omics fields. This approach recognizes whole systems, rather than groups of separated processes . Many tyVibrio alginolyticus, which is resistant to cephalosporin antibiotics, and the role of bacterial metabolism in drug and multidrug resistance. This was achieved by detecting the metabolic differences of acetyl-CoA fluxes into and through the P-cycle and fatty acid biosynthesis , both resistant and responders, and by using a 13C traceability experiment  is commonly used in fluxomics analyses but is only applicable for volatile metabolites or ones that can be treated to become volatile compounds through derivatization processes. Liquid chromatography-mass spectrometry (LC-MS) provides potent approaches that offer combined sensitivity and selectivity. MS approaches such as different ionization modes (positive or negative) or mass analyzer technology can be used to increase the number of detected metabolites. Nevertheless, chromatographic experiments require specific sample pre-treatment, have limited experimental time scales, and do not depict the 3D structure or interactions of the molecule.Beside its exceptionally high sensitivity, mass spectrometry is usually combined with other powerful analytical platforms, mainly gas chromatography (GC) or liquid chromatography (LC), bringing powerful advantages that can overcome both peak overlaps and the low sensitivities of NMR approaches .NMR is a non-destructive, non-selective and fast method that has been widely used for molecular identification and structural elucidation used with minimal sample preparation requirements . While t1H-NMR spectroscopy) can be inherently quantitative, providing a potent analytical tool for metabolomics studies  of metabolic pathways cannot be measured directly due to the intrinsic properties of metabolism such as dynamics, the fluxes can be measured indirectly by the shifts in metabolite levels . What dii) will differ, depending on the cell and its function in a multicellular organism. As for kinetic regulation, it is a function of kinetic parameters of enzymes catalyzing the reaction (k) , concentration of substrate (S) and product (P) and effector/signaling molecules (I). (i) (Capacity-based regulation is a function related strictly to gene regulatory processes of the cell. Those processes such as enzyme production and stability within the cell (Eles (I). . Those v(I). (i)  and quan(I). (i) .in vivo (2 evolution rate), and metabolite production. The final result is a metabolic flux map with an estimate of the flux of each reaction  identifies the whole set of fluxes in a part of the metabolic network of a microorganism in vivo . Informain vivo . Those rreaction .For mathematical explanation of the flux calculation, the reader is referred to . A variaAnother approach to describe a metabolic network is called flux balance analysis (FBA). When compared to MFA, FBA works on a broader scale, and it enables reconstruction of a metabolic network on the genome-scale level. These reconstructions utilize all information about metabolic reactions in an organism and the genes that encode each enzyme. However, this approach does not count for regulatory interactions and detailed kinetics, giving only partial biological information of the situation of systems at steady state. To obtain fluxes from FBA, first a reconstructed metabolic network must be converted to a mathematical matrix. Within this matrix, a set of constraints is imposed by mass balance equations and reaction bounds. Then, based on the biological objective , linear programming is used to determine the sought fluxes by either maximizing or minimizing objective function while considering given constrains . The dif13C-isotope substrate followed by NMR monitoring of 13C-labeled metabolite propagation through the metabolic intermediates in certain metabolic pathways. 13C-labeled fluxomics is an extension of FBA in which all the precursors (substrates) used by the cells are 13C-enriched. Consumed substrates are later incorporated into the metabolic pathways connected to the used substrate. The level of incorporation will depend on intracellular fluxes that could be measured using NMR and/or MS. The information obtained from those experiments can be utilized to discriminate metabolic variants (isotopic profiling), measure specific fluxes  and investigate the whole fluxome   cycle mostly through pyruvate carboxylase (81%)  . For exase (81%) . Anotherse (81%) . Isotopiergetics .13C-labeled glucose followed by tissue resection. NMR analysis of patient cancerous tissues showed enhancement of pyruvate carboxylase (PC) activity. Furthermore, results from patient cancer tissues cultured in 13C6-glucose or 13C5,15N2-glutamine tracers provided clear evidence of selective activation of PC over glutaminase (GLS) in NSCLC (Isotope labelling was recently used to determine whether pyruvate or glutamine are anaplerotic sources requiring pyruvate carboxylase (PC) and glutaminase 1 (GLS1) activity. Sellers et al.  utilizedin NSCLC .et. al. . Alex line embryos (which accumulate more oil when compared to LH59) increased the amount of Glucose 6-phosphate (G6P) entering into the plastid, the aldolase in the plastid, the export of TPs  to the cytosol, the glycolytic flux in the cytosol, Phosphoenolpyruvate carboxylase (PEPC), and plastidic malic enzyme. It was concluded that increasing the levels of plastidic malic enzyme should enhance the fatty acid content of seeds  biosynthesis. This then enhances the production of the antimalarial drug artemisinin. This shift in pathways relies on the flux rate and metabolites concentration  sets and FBA. The results showed growth rates comparable to experimental observations in different media, and by considering HCR sets in the context of known drug targets for tuberculosis treatment they proposed new alternative, but equivalent drug targets  (https://www.ebi.ac.uk/pride/) (www.hmdb.ca) (https://metlin.scripps.edu/)  has resulted in an increased number of recent studies. The massive amount of data produced from these studies must be properly managed to increase its accessibility. This has given rise to various -omics databases such as PeptideAtlas (as.org/) , PRIDE (/pride/)  (proteomhmdb.ca)  and METLps.edu/)   is a novel database published in 2014 that focus on central carbon metabolic systems of microbes and animal cells. The database contains 581 cases of quantitative flux results among 36 organisms including: Homo sapiens, Escherichia coli, Saccharomyces cerevisiae and Pichia pastoris. Based on user input it can utilize four modules  for comparison and alignment of different flux distributions. Additionally, this database provides the opportunity to perform similarity calculations by utilizing deposited data and altering genetic and environmental factors  is an integrated multisource database that contains quantitative molecular data of several types including metabolite concentrations, RNA modifications and half-lives, protein abundances and modifications, and reaction rate parameters. Developed in 2020, Datanator includes various data for 1,030 organisms integrated from over 8,000 articles. Although it does not contain flux related data yet, the authors are planning to include it in the near future, as well as information on RNA/protein localizations and protein half-lives. In such case, Datanator would be a valuable source for comparative analyses of relationships between variable networks and systems (Datanator ( systems .http://bigg.ucsd.edu) is a large-scale database containing genome-scale metabolic network reconstructions. It contains more than 100 genome-scale metabolic models. Those models contain information about biochemical reactions, metabolites and genes related to the metabolism of specific organisms. The information provided in BIGG Models is standardized across different models, which allows users to browse, share and visualize the networks in a structured manner , dynamic metabolic flux analysis (DMFA), flux balance analysis (FBA) or


Escherichia coli, we show that our approach results in a substantial reduction of 99% of metabolites. Applications to genome-scale metabolic models across kingdoms of life result in up to 55% and 85% reduction in the number of metabolites when arbitrary and mass-action kinetics is assumed, respectively. We also show that predictions of the specific growth rate from the reduced models match those based on the original models. Since steady-state flux phenotypes from the original model are preserved in the reduced, the approach paves the way for analysing other metabolic phenotypes in large-scale biochemical networks.Large-scale biochemical models are of increasing sizes due to the consideration of interacting organisms and tissues. Model reduction approaches that preserve the flux phenotypes can simplify the analysis and predictions of steady-state metabolic phenotypes. However, existing approaches either restrict functionality of reduced models or do not lead to significant decreases in the number of modelled metabolites. Here, we introduce an approach for model reduction based on the structural property of balancing of complexes that preserves the steady-state fluxes supported by the network and can be efficiently determined at genome scale. Using two large-scale mass-action kinetic models of  Generation of large-scale stoichiometric models, capturing the metabolism of individual cell types and their interactions in an organism or communities1, has propelled the development of computational approaches for prediction and analysis of metabolic phenotypes4. The sheer size of genome-scale metabolic networks indisputably leads to computational and numerical challenges when employing them to predict and analyse metabolic phenotypes, particularly when these networks are endowed with enzyme kinetics7. Against this background we ask: Can large-scale biochemical models be reduced in an unbiased, i.e. fully automated fashion, while still guaranteeing that the steady-state flux phenotypes are preserved in the resulting models of smaller size?Advances in phenotyping, quantitative genetics methods, and systems biology have helped characterize function of genes embedded in different types of biochemical networks9. These approaches can be categorized based on different criteria: (i) whether they only employ the structure of the network 13 or also consider the kinetics of reaction fluxes23, (ii) whether they approximate or provide one-to-one correspondence of the steady-state properties between the original and reduced network25, and (iii) whether the reduction process is fully automated, i.e. unbiased, or semi-automated (i.e. requires user input)9.There already exist several frameworks and theories to reduce biochemical modelssteady-state flux properties of large-scale metabolic networks. One group comprises approaches based on user-specified input, consisting of pre-selected metabolites, reactions, and functions (e.g. biomass production) that must be present or supported by the reduced model and, thus, result in reduced models biased by the user’s input26. Other approaches in this group start with user-defined subsystems that are subsequently connected (and further refined) to obtain a minimal model that can fulfil a pre-specified function27. In contrast, using ideas from reaction coupling28, a recent unbiased approach provides an efficient reduction of stoichiometric models by reaction removal, while ensuring one-to-one correspondence between the elementary flux modes of the original and reduced model10. Since these approaches do not consider kinetics of reaction flux, they remain silent about the effects that the reduction has on the concentrations of the remaining metabolites.Reduction approaches rooted in the constraint-based modelling framework have been successfully employed to arrive at reduced models that approximate 29. They usually invoke the quasi-steady state assumption (QSSA), whereby the modelled components can be grouped into those with small concentrations, referred to as intermediates, and those with large concentrations (i.e. substrates and products), such that the network displays two (or more) timescales. Invoking QSSA implies that the intermediates, that change on the fast time scale, are expressed as functions of the slow components16. Therefore, these intermediates are eliminated from the original network and, then, the reduced network, capturing the slow dynamics, is further analysed. Application of QSSA is not straightforward since it requires data on kinetic parameters that are challenging to obtain at a genome-scale level30. Therefore, such approaches cannot be analytically carried out29, and often involve approximations that lead to inaccuracies of estimations.Approaches for reduction of models with mass action kinetics are particularly important to solve or approximate different reaction mechanisms 23. Assuming steady state, the concentration of such a component can be readily expressed as a function of the concentrations of the remaining components. This approach guarantees correspondence between the conservation laws of the original and reduced network and the respective numbers of positive steady states23. This idea has been generalized to allow linear removal of some subsets of components that appear only with stoichiometry at most one in any reaction of a given network endowed with mass action kinetics14. Yet, structural conditions ensuring that the steady-state flux spaces of the reduced network are subset of the reduced network by removal of components of any stoichiometry in networks endowed with arbitrary kinetics remain elusive.One unbiased technique to eliminate a component in mass action networks requires that the component appears only as a sole substrate or product in the reactions in which it participatesHere we identify such a structural property for model reduction and show that it can be efficiently computed and applied in genome-scale metabolic networks from organisms across the kingdoms of life. The condition allows consideration of biochemical constraints and can, therefore, be invoked with or without assumptions on optimized biological function. The key advantage of the structural condition is that it can be applied to large-scale biochemical networks endowed with mass action kinetics, and under some restrictions, to networks endowed with arbitrary kinetics, while guaranteeing that the steady-state flux phenotypes of the original model are preserved in the reduced.32. In addition, the reactions are weighted by non-negative numbers which correspond to fluxes of a steady-state flux distribution, balanced, whereby the production and consumption rates are the same.To illustrate the condition, we first introduce some key concepts from stoichiometric modelling of biochemical networks. A biochemical network is composed of irreversible reactions through which biochemical species acting as substrates are transformed into products. The biochemical network on Fig. d graph “31,32. Intrivially balanced if it includes a species that appears in no other complex in the network. This result is a consequence of the balancing of species due to the steady state assumption. A balanced complex that includes species all of which appear in other complexes are termed non-trivially balanced. For instance, complex C cannot be balanced as it is a sink, while D, A + E, and F are trivially balanced since species D, E, and F appear only in these complexes that have both incoming and outgoing reactions. Note that our definition of trivially balanced complexes extends the notion of an intermediate species in other reduction approaches23. Finally, 2A is a non-trivially balanced complex, since A appears in two complexes of which one, A + E, is trivially balanced. In fact, by considering only the steady-state conditions, it is the interlinking of species into complexes that contributes to the formation of balanced complexes.An analogous condition on balancing can be defined for a single complex: Given a biochemical network, a complex is balanced in a set of steady-state flux distributions For a set delling “”. The apetworks “”. The id34. Seminal theoretical results pinpoint that complex balanced networks do not exhibit exotic properties, like multistationarity and oscillations. However, it has not yet been addressed how one can identify individual balanced complexes and what the implications of their presence in the network are with respect to the capacity to exhibit particular phenotypic properties.Networks in which all complexes are balanced are termed complex balanced, and they can be identified by calculating the structural property of deficiency10, however, based on the coupling of reactions around balanced species and without the rewiring of reactions.We next ask if balanced complexes are relevant for reduction of networks which are not complex balanced. To answer this question, we first consider the scenario with a network endowed with arbitrary kinetics. If a balanced complex has only one outgoing reaction, then the flux of this reaction can be expressed as a sum of the fluxes of incoming reactions. The balanced complex can then be safely removed since the flux of the outgoing reaction can be substituted with the respective sum of fluxes of the incoming reactions for the balanced complex. This is concomitant to introducing a bipartite directed clique, connecting each complex in the incoming neighbourhood with the complex in the outgoing neighbourhood Fig. b,d. NoteAttempting to remove a balanced complex with more than one outgoing reaction fails in general; however, under the constraint that all outgoing reactions are fully coupled (i.e. their flux ratio in every steady state is a unique constant) all outgoing reaction fluxes collapse into one and the balanced complex can be removed. Interestingly, this condition is trivially met for networks endowed with mass action kinetics, since the ratio of fluxes of reactions outgoing from any complex is given by the ratio of the respective rate constants. Importantly, this removal can be carried out even if values for the rate constants are not specified, since the ratio is ensured to be constant. Therefore, under mass action, a balanced complex can be removed by introducing a bipartite directed clique of reactions with rescaled kinetic constants see “c,e. For 23. However, the proposed approach allows removal of species that participate in any number of complexes with any stoichiometry, provided they appear only in balanced complexes. It also provides a sound extension of a reduction approach in which complexes are–arbitrarily–assumed to be balanced18—and leads to biases in the model reduction since the complexes are not demonstrated to be balanced. In our approach, the conservation laws in the original network hold in the reduced, but not necessarily vice versa  and the complex ‘3-phospho-glycerate + PGK-3-phospho-glycerate-complex' is trivially balanced. From the 484 and 1639 balanced complexes 23% and 26% had only one outgoing reaction; for instance, ‘l-aspartate + PRASCS-ATP-complex’, ‘ATP + PRASCS’, and ‘glucose-6-phosphate + FBP’ are balanced complexes with such properties  and succinate dehydrogenase (SUCDi) together with the related substrate-enzyme complexes  all reactions are assumed to be reversible in contrast to the case when irreversibility constraints, included in the original models, are used, (ii) all reactions follow arbitrary kinetics or their fluxes are described by mass action kinetics, (iii) balanced complexes are determined with respect to the set of steady-state flux distributions compatible with reversibility in comparison to steady-state flux distributions at optimal specific growth rate. Note that reversible reactions are split into two irreversible reactions before applying the approach.Motivated by the findings from the reduction of the core and genome-scale kinetic models of M. barkeri is an exception to this finding, with 30% increase in species reduction when considering reaction irreversibility. In addition, imposing constraints on biomass had negligible additional effect on the balanced complexes in majority of the networks, except in the models of P. putida and N. pharaonis, for which there was an increase by 26 and 30% in the number of removed species, respectively  in the number of removed species across all organisms Fig. . The modConsideration of mass action kinetics led to an increase in model reduction of, on average, 26% in comparison to the case of arbitrary kinetics when all reactions are considered reversible Fig. a,b. In cArabidopsis thaliana core, M. musculus, N. paharaonis and P. putida model and reached up to 55.1% reduction in the model of M. barkeri. On average we observed 18% of species being removed across all considered networks. Instead, when mass action kinetics was considered, we found a reduction between 24.3% for E. coli to 85.7% in T. maritima, with an average of 44% across the considered models. These results demonstrated that substantial reduction in the number of removed species is possible, while ensuring that the key network properties at steady state are matched between the original and reduced network. In addition, the reduction eliminated up to 17 (12%) species which enter complexes with stoichiometry larger than one  in the specific scenarios considered. In comparison to the reduction of the large-scale mass action model of N. pharaonis to 100% in T. maritima  participating in the biomass reactions from the original model (with specified irreversibility). This allows us to compare the simulated specific growth rate between the original and reduced models. The resulting reduced models included 4% fewer metabolites in the model of 36. To this end, we calculated the ranges of reactions that are present in the reduced and original model following standard procedure  approach for reduction of models with arbitrary or mass action kinetics at steady state. The approach is based on identifying balanced complexes which contain either a single outgoing reaction, in the case of arbitrary kinetics, or more than one outgoing reaction, for mass action kinetics. We also show that the structural condition can be efficiently identified in large-scale networks, assuming they operate at steady state. Moreover, such balanced complexes can be safely removed from the network as their removal translates into identification of substitution of variables which preserves the steady-state flux distributions of the original model. In addition, the variable substitution can be graphically represented by rewriting the network, leading to a reduced network, and can be carried out without knowledge of kinetic parameters (in the case of mass action kinetics). Most importantly, if a species appears only in balanced complexes, it can be removed from the network and, under the assumption of mass action kinetic, its steady-state concentration can be represented as functions of the steady-state concentrations of the metabolites that remain in the reduced network.Our extensive analysis of genome-scale kinetic models endowed with mass action show that more than 99% of the metabolites can be removed following the proposed reduction. In addition, since the approach is constraint-based, it also allows us to examine if reaction reversibility or assumption on cellular tasks (e.g. growth) that are optimized have an effect on the size of the reduced model, in terms of number of species. The analysis of genome-scale metabolic models across kingdoms of life show that reaction reversibility and assumption of kinetics have the largest effect on the size of the reduced models, leading to up to 85% reduction in the number of species. Nevertheless, we show that if the reduction is performed such that no metabolite participating in the biomass reaction is removed, the reduced model is not affected with respect to predicted growth phenotypes.We would like to emphasize that once the balanced complexes are identified, it is a choice of the modeller which balanced complexes should be removed in the specific analysis case. For instance, we showed that the removal of the balanced complexes, that do not include species that participate in a biomass reactions, does not affect the prediction of specific growth rates. In this scenario, we also showed that the results from flux variability analysis and predictions of essential reactions in reduced and original models are in very good agreement.Since the proposed approach is based on a property that can be efficiently determined even in large-scale networks, it provides the means for reduction of multi-tissue and microbial community models. Moreover, it opens the possibility to study the relationship of key properties, such as robustness and multistationarity, between the original and reduced models. However, these applications will have to ensure imposing additional constraints on the removal of the balanced complexes that do not affect the conservation laws in the network. Finally, our approach opens the possibility for unbiased model reduction by seeking to identify other types of structural motifs in large-scale metabolic networks.48. The blocked reactions, reactions with absolute flux values less than 10–9 mmol/gDW/h, in the metabolic network were determined by Flux Variability Analysis36 and were removed from the original models. Each reversible reaction was split into two irreversible reactions. Two cases for the irreversible reactions originally declared in the model were considered: (1) all were treated as reversible  or (2) were maintained as irreversible. The lower bounds for the irreversible reactions were set to zero, while the upper bounds were fixed to the maximum of the upper bounds in the original model. Optimum biomass was determined per Flux Balance Analysis49 with the assumed reaction reversibility.The genome-scale metabolic models of twelve organisms  in models with considered irreversibility and compare the predictions before and after removal of balanced complexes. Blocked reactions are removed from the original network and each reversible reaction is split into two irreversible reactions. To avoid cases where no biomass production is ensured in the original model after removal of blocked reactions due to numerical issues, we set the lower bound of the biomass reaction to 5% of the optimal biomass obtained from the model including blocked reactions. In addition, we ensure that the biomass reaction, whose flux is optimized during FBA, is still included in the reduced model. Therefore, we only remove balanced complexes that do not include metabolites (i.e. species) participating in the biomass reactions from the original model.36 at 99% of optimal biomass for all reactions that appear in both the original and reduced models considering any kinetic. We then classified the reactions into those that do and do not show differences in the flux ranges between each original and corresponding reduced model. Similar analysis was conducted with respect to reaction essentiality: A reaction that appears in both an original and corresponding reduced model was knocked out and the effect on growth was examined. The reactions were classified as those that are essential or not in each model.We conducted flux variability analysisSupplementary Information 1.Supplementary Table S1.Supplementary Table S2.Supplementary Table S3.


Simulation results were compared with experimental data obtained from different sources and proved the model is able to successfully describe microbial kinetics  and reactor performance . The capacity of the model to simulate different system configurations is also shown. Model results suggest CO2 dissolved concentration might be limiting existing MES systems, and highlight the importance of the delivery method utilized to supply it. Simulation results also indicate that for biofilm-driven reactors, continuous mode significantly enhances microbial growth and might allow denser biofilms to be formed and higher current densities to be achieved.Up to now, computational modeling of microbial electrosynthesis (MES) has been underexplored, but is necessary to achieve breakthrough understanding of the process-limiting steps. Here, a general framework for modeling microbial kinetics in a MES reactor is presented. A thermodynamic approach is used to link microbial metabolism to the electrochemical reduction of an intracellular mediator, allowing to predict cellular growth and current consumption. The model accounts for CO MES is lectrode . Until naterial) . Even thaterial) . In thataterial) , but proMES is a complex system that combines both electrochemistry and biotechnology. When trying to improve reactor performance, all physical, chemical, and biological processes occurring simultaneously have to be properly regulated. A major breakthrough would require a deeper understanding of this inherent complexity. To that end, computational models are a systematic approach that can be used for testing hypotheses and obtain knowledge on the described system, as pointed out by Escherichia coli, and showed that trade-offs between improving growth rates and yields could exist. When looking at the biocatalyst itself, metabolic modeling allows for an in-depth analysis of the molecular and biochemical mechanisms occurring within a particular microorganism. These complex mathematical expressions encompass all major metabolic pathways, and simulate them in perspective of the entire metabolic network. 2 concentrations and applied cathodic potentials. Their model showed that high CO2 concentrations decreased coulombic efficiency, while a higher cathodic potential increased the coulombic efficiency. 2 into formate electrochemically, which is then used aerobically by planktonic cells to grow. They were able to study the dynamics between CO2, O2, and biomass growth as well as the influence of some operational parameters on the general performance of the reactor. O2 and CO2 mass transfer were found to be limiting the formate-mediated reactor. Their study also indicates that gas recycling to increase overall CO2 utilization will be necessary when scaling-up these systems. To date, few modeling studies have been published on microbial electrosynthesis and the dynamics between microorganisms and operating conditions. 2 supply. To achieve this, a dynamic black-box model of a MES reactor for the reduction of CO2 including microbial kinetics with product inhibition and integrated chain elongation, was implemented and solved with the MATLAB software package (MATLAB 2019b).The use of computational modeling of MES at reactor scale for process understanding and system optimization has clearly been underexplored. Previous modeling papers mainly focused on studying the effects of operational parameters on the general performance of specific MES processes. Moreover, one of the main knowledge gaps in MES is that microbial growth rates and microbial kinetics have not been experimentally elucidated and are thus unknown to date. To achieve a higher process performance, a deeper understanding on the microbial metabolism and production kinetics is necessary. In addition, the study of how microorganisms adapt to changing operational parameters and to different reactor environments  is of crucial importance when elucidating what is limiting MES performance. A general black-box mathematical model allowing for the dynamic description of attached microbial cells, and their interactions with the cathode can help to study such complex environments and potentially elucidate current process bottlenecks. To this end, the objective of this work was to develop a reactor-scale mathematical modeling framework for the study of biofilm-driven microbial electrosynthesis processes with multiple product spectrum and different operational conditions, i.e., batch or continuous mode, continuous or discontinuous COSince microbial kinetics in MES are not yet available, the biofilm-driven reactor from The model consists of a bioelectrochemical reactor with multiple domains encompassing all subsequent mass balance equations, as well as all electrochemical and biological kinetic reactions. The four domains of the system modeled to simulate reactors from Jourdin et al. are shown in •The biofilm is a continuous phase, thus different microbial species and their distribution are neglected.•All reactions occur in the biofilm only. Reactions occurring in the bulk liquid are neglected, as the prevalence of the biofilm over suspended cells was demonstrated on their investigation.•Electrical resistances of the catholyte and the biofilm matrix can be neglected.•Volumes of all compartments are constant.•All liquid compartments are well mixed.•The biofilm domain is also well-mixed .•Microorganisms accumulate in the biofilm domain and do not flow out (detachment from the biofilm is neglected).•pH, electrical potential, and temperature are strictly controlled.2 (in detail in Lak). It is possible to simulate reactors with different geometries, cathode properties or cell cultures modifying the obtained mass balance equations.Simulations were performed with a set of mass balances including the exchange rate (flow in and out) from the continuous operation, the net rate of reactions in the biofilm, and the gas/liquid transfer of COA general scheme of the microbial catalyst, with all the relevant biological and electrochemical reactions is depicted in via multiple transmembrane redox centers  (+):In microbial electrosynthesis, electrons must be transferred from the surface of the cathode to the intracellular space of the microorganism likely chromes) . This rechromes) . For simThe electrochemical rate rocesses .The electrochemical rate coefficients, which account for the electrical potential of the electrode and the mediator, To date, the exact mechanism for extracellular electron transfer (EET) is largely unknown. A wide range of different mechanisms has been investigated, from direct electron transfer , 2011 toVfc) domain is included.The transfer of electrons from cathode to microorganism results in the observed electric current. This current is determined by a balance between the electrochemical reaction rate 2, but the pathways for butyrate and caproate production in MES systems are largely unknown. Acetate elongation can occur via multiple pathways, including or not carbon dioxide utilization . A part of that energy is used for butyrate (△GBut) and caproate (△GCap) production, as well as for biomass growth and cell maintenance reactions (△GAn), whereas the rest is dissipated as heat (△GDiss). The biomass formula is assumed to be CH1.8O0.5N0.2  and butyrate (Eq. 9) elongation reactions are described as:+ is the only redox mediator species that limit the rate of the redox reactions of the modeled microorganism. The Gibbs energy of formation for this pair was estimated from the standard redox potential and adapted to reactor conditions, as described by + was chosen (in detail in the The Gibbs energies of reaction Cat) is a factor representing how many times the catabolic reaction must occur to supply enough energy for the anabolic, elongation, and dissipation reactions. Using a dissipation energy for chemoautotrophic CO2 reducing processes of The catabolic rate  can then be described as a function of the carbon dioxide uptake and maintenance rates (Eq. 14).The maintenance coefficient on CO(Eq. 13) . The speThe specific elongation rates for butyrate and caproate production are then described using double and triple hyperbolic uptake equations, respectively. iw and iZ are empirical sigmoidal functions used to ensure the rates have a smooth increase when the concentration reaches the threshold value Where iA and iT incorporated into the substrate uptake expressions have no biological meaning and are The additional tuning parameters al paper .2) is achieved by using a Herbert-Pirt relation (Eq. 19) and the general metabolic stoichiometry (Eq. 11).The overall coupling between substrate uptake, biomass growth, maintenance, and elongation reactions for all the remaining metabolites  are known for their toxicity, which can be attributed to their acid form. The acid form is able to diffuse across the cell membrane and deprotonate in the cytoplasm, generating a pH gradient. In order to maintain homeostasis, cells typically have to use membrane-bound ATPases to expel the excess of protons to the outside. As more ATP is redirected to keep this gradient under control, growth and production yields are substantially decreased , 2007. Mmol m−3) refers to the critical concentration at which the whole metabolism is halted due to the toxicity of the produced compound. Acetate, butyrate, and caproate inhibition terms are then added to the carbon dioxide uptake rate Eq. 12 and to the elongation rates Eq. 15 and Eq. 16 as follows:When modeling microorganisms in MES systems, it is important to account for CAs inhibition. However, product inhibition kinetics in MES remains unknown to date, hence a generalized inhibition model is preferred here. In this study, a linear model is adopted . ProductThe kinetic maximum specific rates 2 sparging. Since the gas-liquid mass transfer coefficient Lak for CO2 was not reported in the original work, its value was approximated from the reported inorganic carbon concentrations and found to be of the same order of magnitude as those reported on similar sparging mechanisms, i.e., 2.5 h–1 (CO2 /(molx h), 2.12 × 10–2 molBut /(molx h), 4.64 × 10–3 molCap /(molx h), 123 mmolAc/L and 43 mmolBut/L, respectively. There is a lack of reported values in MES for these kinetic parameters, hence it is difficult to assess the values obtained here. 2 specific uptake rate on the same order of magnitude as the one obtained in this study, of −0.2 molCO2 /(molx h), when characterizing acetogenic metabolism by using a genome-scale metabolic reconstruction approach; however, they failed to confirm the value experimentally   .2 is still far from being depleted. A combination of poor gas-liquid mass transfer and a low gas inlet CO2 partial pressure were the limiting steps during this first period. The effect of changing these input parameters is depicted in Lak results on a higher biomass production rate, as CO2 is dissolved faster into the liquid  of the feed gas determines the saturation concentration at which carbon dioxide can be dissolved into the liquid  was continuously sparged with pure CO2. The model properly predicts the acetate concentration profile obtained experimentally , as can be seen when comparing The biomass concentration obtained after 50 days (25 mmol/L) is five times lower than the amount produced in a continuous reactor with constant CO2 by Marshall helped to mitigate the effect on the microbial kinetics. The amount of carbon dioxide that can be dissolved in the system increases linearly with the CO2 partial pressure used in the gas (2 liquid concentration was obtained by the use of 100% CO2 as feeding gas when compared with the 30% used by 2 uptake and avoided a more severe rate inhibition by the carbon source. Since the limiting effect of CO2 and other chemical species in microbial kinetics is low, it is likely that the reactor was limited by the absolute amount of biomass in the system.The kinetic parameters are presented in  the gas . A 3.3 t2 reduction (The current in periods II and III is correctly described by the model, as can be seen in eduction . Hence, eduction .S in The model assumes no concentration gradients in the individual domains. Hence, concentration steps occur only between the domains or at the inflow. To support the assumption that gradients are negligible, the magnitude of the concentration steps will be discussed. Experimental measurements were performed at the sampling port S in , thus co2 concentration gradients over the entire duration of 2 reaction time is estimated to be 4 min, while the residence time of the convective flow is 0.13 min (2 concentration gradients in the reactor domains can be neglected (First, we focus on carbon dioxide. It is consumed by the microorganisms in the biofilm domain and transfers from the gas phase to the bulk liquid in the bubble column. Results obtained for CO0.13 min . The rateglected .2 and all products accounted for in the current model behave as acid. In addition, the presence of a buffer must also be taken into consideration. It is therefore the balance between these production and consumption processes, that determines local pH gradients. In the present study, pH was assumed to be constant but since it has a great influence on both electrochemical and biological reactions, this assumption needs to be further investigated.The pH of a biologically active cathodic chamber is highly dependent on the acid-base reaction equilibria. CO2, H+, and the buffer compound was used to determine if large pH gradients would be present in the biofilm. These calculations and respective explanations can be found in the + ions are not able to diffuse into the biofilm quick enough, the presence of a buffer allows to compensate for the consumed H+ in the biofilm by a buffering reaction with a reaction time in the same order of magnitude as for CO2. According to the calculated diffusion and reaction times, CO2 diffusion slowed down the biological reaction, which at the same time limited the proton consumption rate by the microorganism. The protonated buffer compound diffusion through the biofilm and buffering reaction would then have to keep up to effectively control pH. By analogy to the case treated by Bulk pH is strictly monitored and controlled by acid and base addition, therefore gradients due to protons diffusing from anode to biofilm can be neglected. However, reactions are happening within the biofilm and not in the liquid bulk, therefore a gradient might still be present at the vicinity of the electrode. An estimation of both characteristic reaction and diffusion times for CO2 into longer chain products such as caproate.Only one bacterial population has been included in this model, even though the simulated reactors were systems working with mixed cultures. Therefore, the model could be expanded to include multiple microorganisms with differentiated metabolisms . As an eAs previously described, pH gradients and other chemicals’ gradients should be further investigated for biofilm-driven systems. The addition of acid-base equilibria, hydrogen evolution, and electromigration would allow to better understand gradients at the biofilm level, potentially giving additional insights on rate limiting processes. These gradients could also help to understand biofilm development and biofilm/planktonic cells dynamics. Moreover, mass and ion transport can be expected to become of paramount importance as MES current density and microbial productivity continue to increase . In thisThe use of a product inhibition model is necessary to account for the inherent toxicity of the produced carboxylates. Even though the model used in this paper gave good results, it should be expanded and validated with experiments in which products have been added to the inflow. This would give a better and more tailored description of product toxicity within these systems, and subsequently a better understanding of chain elongation metabolism and kinetics.2 can limit the rate of microbial electrosynthesis. Carbon dioxide is the main substrate and the only carbon source in most MES reactors, hence its concentration has a great impact on cell kinetics. Its relatively high half-saturation constant and low solubility make microorganisms very susceptible to small changes in its dissolved concentration. The model indicates that the use of pure CO2 as feeding gas can mitigate this effect, as shown experimentally in 2 diffusion might become the limiting step at some point. Results also indicate not to underestimate the critical effect of the CO2 delivery strategy on reactor performance (2 delivery systems are one of the reasons why obtained production rates are still low across the field (2 to sustain a highly active microbial population, a better understanding can be achieved of which steps are intrinsically limiting steps in said MES processes.Simulations done in this work suggest that COformance . In MES he field . Regardl2 (To date, most MES studies have been performed under batch conditions and not many researchers used a continuous reactor for reducing CO2 . The mod2 . In that2 dissolved concentration. This implies that a more careful assessment of the inorganic carbon supply method is needed to increase production rates. Furthermore, simulations show that operating in continuous mode leads to higher cell densities. Since most current studies are done in batch mode, this might be one of the reasons why cell titers are far below their theoretical maximum (The mathematical model presented in this work is able to accurately describe the behavior of different biofilm-driven MES reactors operating in batch, fed-batch, and continuous mode. It was found that under previously reported operational conditions biomass growth was partially limited by the CO maximum . These rThe original contributions presented in the study are included in the article/OC-P developed the model and drafted the manuscript. AS and LJ contributed to the modeling effort and data interpretation. All authors contributed to manuscript revision, conception, design of the study, read and approved the submitted version.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.