The reconstruction and analysis of genome-scale metabolic models constitutes a powerful systems biology approach, with applications ranging from basic understanding of genotype-phenotype mapping to solving biomedical and environmental problems. However, the biological insight obtained from these models is limited by multiple heterogeneous sources of uncertainty, which are often difficult to quantify. Here we review the major sources of uncertainty and survey existing approaches developed for representing and addressing them. A unified formal characterization of these uncertainties through probabilistic approaches and ensemble modeling will facilitate convergence towards consistent reconstruction pipelines, improved data integration algorithms, and more accurate assessment of predictive capacity.The online version contains supplementary material available at 10.1186/s13059-021-02289-z. Genome-scale metabolic models (GEMs) aim to capture a systems-level representation of the entirety of metabolic functions of a cell. They represent complex cellular metabolic networks using a stoichiometric matrix, which enables sophisticated mathematical analysis of metabolism at the whole-cell level . Not onlOver 100 well-curated GEMs exist for a range of prokaryotes and eukaryotes, offering an organized and mathematically tractable representation of these organisms’ metabolic networks , 13. A dDespite the numerous reconstructions and wide range of applications, GEMs have important limitations . In thisOur ability to assess and communicate the sources of uncertainty associated with a model can have great impact on the relevance of predictions and on the degree to which these predictions can be constructively used for follow-up studies, as has been noted for the field of systems biology in general . This reThe first step towards a GEM reconstruction is the identification and functional annotation of the genes encoding metabolic enzymes present in the genome Table . These aA few reconstruction pipelines try to circumvent the problem of incorrect or missing functional annotation by using previously curated GEMs as annotation templates. Using several different reconstruction pipelines—RAVEN , 39, AuRAnother approach is to directly incorporate uncertainty in functional annotation by assigning several likely annotations to each gene rather than picking the single most likely. In one likelihood-based approach, metabolic reactions are annotated probabilistically by taking into account the overall homology score, BLAST e-value, and keeping track of suboptimal annotations . In thisOther concepts that have been used to generally improve gene functional annotation could be further incorporated into GEM annotation pipelines. For example, functional annotation of enzymes could be improved by the incorporation of enzyme active/catalytic site information from databases such as M-CSA . AdditioTo use a GEM for the prediction of expected phenotypes, or for the simulation of dynamic processes, one must define the chemical composition of the environment Table . EstabliEscherichia coli GEM, that the overall distribution of metabolic fluxes is robust to the environmental composition; however, specific fluxes vary, with most discrete variations occurring in a connected “high-flux backbone” of reactions [GEMs provide an opportunity to address the uncertainty associated with complex environments. GEM analysis algorithms, such as FBA, are computationally efficient and can thus be run across a large ensemble of environments to quantify the sensitivity of simulated fluxes to nutrient composition. Several studies have quantified this sensitivity by identifying aspects of GEM predictions that are either strongly affected by or robust to variation in the environmental composition –77. Desceactions . Subsequeactions . Reed aneactions . These seactions  and thateactions . VariablA more recent approach, inspired by the statistical physics concept of network percolation, utilizes random sampling of nutrient compositions to quantify which metabolites can be consistently produced by a given metabolic network across many environments . This apThe specification of the environment for GEM analysis could be further improved using “reverse ecology” methods that aim to infer the native environment from the metabolic network structure either through constraint-based optimization –83 or byThe cell biomass used in GEMs is an inventory list of all compounds essential for growth of a given organism, weighted to represent the amount of each component present in 1 g of dry-weight biomass. The reaction that transforms all biomass components into a unit of biomass is used to represent growth in GEMs and is necessary to perform popular analyses such as FBA. Since several aspects of the biomass reaction and its use have been reviewed before , we willE. coli for Gram-negative or Bacillus subtilis for Gram-positive bacteria) is often used as template, despite the significant uncharacterized variation in biomass composition likely to exist across different organisms. This trend has been verified by hierarchical clustering of biomass compositions from 71 curated GEMs: rather than taxonomic relations, the clusters were defined by the template biomass functions used in the model reconstruction [The main source of uncertainty in the formulation of biomass composition is the lack of direct experimental measurements for most organisms. In the absence of specific data, the biomass composition from a model organism  of metabolic reactions that they utilize , 118. Thcorrect solution in this solution space , choices and uncertainty in some of the above aspects of the computation necessarily lead to uncertainty in the prediction of the fluxes themselves. In this section, we will review prior work addressing this uncertainty, with an emphasis on methods geared towards embracing and reporting it  . Any poiit Table .Table 513C flux experiments in E. coli. It was early on demonstrated that FBA with maximization of growth rate could predict the phenotype of E. coli wild-type strains, supporting the assumption that unicellular organisms have evolved towards maximal growth [E. coli strains evolved through 50,000 generations [E. coli strains also provided nuance to our understanding of evolutionary pressures by confirming that E. coli evolves towards maximization of growth rate primarily by increasing substrate usage, but only if the ancestral strain is initially far from the optimum [The flagship method for simulating metabolic fluxes in GEMs, FBA, uses linear programming to identify a point (or a subspace) in the solution space that optimizes a predefined cellular objective , 126–129l growth . Indeed,l growth . Taking erations . Althougerations . A diffe optimum .13C-measurements of 9 different bacteria, which found  that metabolism operates close to a Pareto surface that balances the trade-off between maximization of growth and ability to adapt to changing conditions [In a number of instances, the phenotypes of knock-out mutants are actually more accurately predicted when taking into account suboptimal solutions (near but not exactly on the FBA predicted optimum). For example, the increased accuracy of the MOMA and related methods stems from the assumption that a knock-out strain is still steered towards the wild-type optimum by the cellular regulatory network and may not necessarily approach the knock-out optimum . The PSEnditions . In summnditions , 140.To avoid biased assumptions of the metabolic goal of a microorganism, one can characterize the complete solution space to describe all possible phenotypes satisfying the steady-state and flux constraints. It is important to note that, even at the optimum predicted by FBA, the solution is rarely unique. The predicted flux vector must therefore be analyzed with caution. Flux variability analysis (FVA) can be used to estimate the range of possible fluxes at the optimum , but sin13C - flux data, can be elegantly incorporated in calculations of posterior flux distributions in a generic Bayesian framework that provides insight into the uncertainty associated with individual fluxes and flux couplings.Random sampling provides a scalable approach to describe possible phenotypes in the solution space. Monte-Carlo-based algorithms –153 haveThe uncertainty in model predictions can be reduced by introduction of additional constraints which reduce the size of the solution space , 125. ThS. cerevisiae and E. coli across three different conditions [Another branch of methods uses either transcriptome  or protenditions . An addinditions  which tanditions , and thenditions . In any The steady-state assumption forms the basis of constraint-based analysis by requiring mass-balance of all intracellular metabolites and defines the solution space discussed throughout this section. This assumption is justified because transient changes in metabolite concentrations occur rapidly compared to environmental and regulatory perturbations, leading to rapid convergence to a quasi-steady-state where metabolite concentrations are constant , 187. HoIn this review, we highlighted methods that use probabilistic approaches and ensemble modeling to represent the uncertainty associated with constraint-based reconstruction and analysis of GEMs. Formalizing the representation of uncertainty in GEMs would improve confidence in modeling results. Although we concede that this is a difficult task, we hope that this review will serve as a roadmap for how this issue can be further addressed. We maintain that ensemble approaches (which are in essence discrete representations of probability distributions) provide a strong framework that naturally captures the uncertainty arising from the many possible outcomes in each step of the reconstruction and flux analysis process Fig. . A practMultiomics data integration is an increasingly important application of GEMS as biological studies are now collecting and analyzing multiple sources of high-throughput data. GEMs can facilitate the integration of this data in a knowledge-based format that provides mechanistic insight , 196. ApWhile this review has been entirely focused on uncertainty in GEM approaches, it is also important to remember that future efforts will need to creatively address major open questions on how to integrate metabolic models with other layers of biological complexity and their associated uncertainties. Several methods have been proposed to extend the basis of GEMs to include some other layers, such as metabolism and expression (ME) models that incorporate the processes of gene transcription and translation  or dynamAdditional file 1. Review history.


Hence, a compromise modeling solution has been developed between the non-generalizable accuracy of the first principles models (FPMs) and the oversimplification of the empirical models (EMs). The work presents a novel model of moderate complexity that is simplified enough to be generalizable and computationally affordable, while retaining physical meaning. The methodology is based on a general degradation mechanism that can be algorithmically generated from the carbon number of the target compound, as well as from the knowledge of two kinetic parameters, one for the faster initial rate and the other one for the subsequent degradation steps. The contaminant degradation mechanism has been combined with an appropriately simplified implementation of the well-known Fenton and photo-Fenton kinetics. This model describes the degradation not only of the target compound and of the oxidant, but also of total organic carbon (TOC), which is used to define the overall quality of the water. Experimental design techniques were used along with a non-conventional modeling methodology of programmable process structures (PPS). This novel modeling approach was applied and validated on the degradation of three model compounds. A successful prediction of the evolution of the contaminants H A notable experimental effort has been spent in the last 20 years in investigating the advanced oxidation processes (AOPs), being an effective alternative to conventional biological processes for the treatment of toxic and recalcitrant wastewaters, and for the removal of contaminants of emerging concern (CECs)  radicals, advanced electrochemical oxidation technologies (such as electro-Fenton and electro-photo-Fenton), nanocatalytic heterogeneous Fenton technology, and semiconductor photocatalysis (TiO2/UV), as well as the combination of processes involving at least one AOP.A recent review by Mazivila et al.  presentsIn particular, among the classical AOPs, the photo-Fenton process has attracted special attention of the scientific community with an actual number of scientific papers related to photo-Fenton process of about 2700, as recently highlighted by Cabrera Reina et al. . ScientiNevertheless, the transition from a pure experimental approach to a model-based approach is mandatory to allow process design, monitoring, control, and eventually process automation on which industrial applications are generally based on.The literature review reveals that the proposed models can be enclosed in two main categories: first principles models (FPMs) and empirical models (EMs).Some FPMs rely on the detailed kinetic modeling of Fenton and photo-Fenton processes and follow the scheme proposed by Kang et al.  based onThe FPMs are accurate models that aim at a full understanding of the chemical process. However, two main weak points arise, limiting their applicability in the real world. On one hand, the resulting computational effort might be unaffordable. On the other hand, the high complexity of Fenton and photo-Fenton systems, involving many reaction mechanisms that are still under investigation, makes it difficult to develop a comprehensive FPM that can include all the involved reaction mechanisms for more general cases of various and multiple targets.Regarding the empirical models, in literature, it is possible to find preliminary works proposing the use of response surface platform for regression models  is the first selected target compound, being the most widely used antipyretic and analgesic. As the second model compound, sulfaquinoxaline sodium salt  is selected because it is a potential food contaminant in animal products. Finally, formic acid  is studied as the third target compound since it is a by-product of the degradation of many hazardous organic compounds and belongs to the group of carboxylic acids that are hardly degradable even by chemical oxidation  technique was used to select the proper set of Fenton and photo-Fenton experiments to be performed in order to properly describe the system behavior for the different selected targets. The DOE was then combined with a non-conventional methodology named direct computer mapping (DCM)  (33% w/v) from Panreac Química SLU  and iron sulfate (FeSO4·7H2O) from Merck , adopted as the ferrous ion (Fe2+) source, were used as Fenton reagents. HPLC gradient-grade methanol (MeOH) purchased from J.T. Baker Inc.  and filtered milliQ-grade water were used as HPLC mobile phases. High-purity (> 99%) ascorbic acid from Riedel de Haën , 0.2% 1,10-phenanthroline from Scharlab SL , sodium acetate anhydrous, and 95–98% sulfuric acid, both from Panreac Química SLU , were used to perform measurements of iron species. Hydrogen chloride HCl 37% from J.T. Baker Inc.  was used to adjust the initial pH. Deionized water with a conductivity lower than 1.25 μs was provided by Adesco S.A.  and was used as water matrix in all experiments.Paracetamol and sulfaquinoxaline sodium salt of 98% and 95% purity, respectively, purchased from Sigma-Aldrich , and formic acid (98%) purchased from Honeywell Fluka  were used as target compounds. Reagent-grade hydrogen peroxide  concentrations were performed with a Shimadzu VCHS/CSN TOC analyzer  and samples were taken every 15.0 min (the measuring time of the equipment being 15.0 min). The samples were maintained refrigerated after extraction by submerging the flask in ice during the whole sampling time, with the aim of slowing down the degradation of the organic matter since the cooling of the samples to 2–5 °C is a preservation technique in case of measuring organic content  in order to stop further degradation of PCT, being a well-known HO• scavenger . In particular, paracetamol concentration ([PCT]) was determined using an Akady 5 μm C-18150 × 4.6 mm column, maintained at 25.0 °C as stationary phase, and a mixture of methanol:water (25:75) flowing at 0.4 mL min−1. In this case, the diode array detector was set at 250 nm. Under these conditions, retention time was 2.0 min. In this case, samples were taken at 0.0, 2.0, 5.0, 10.0, 15.0, 20.0, 25.0, 30.0, 45.0, 60.0, 75.0, 90.0, and 120.0 min, and were previously treated with methanol (in proportion 50:50) in order to stop the oxidation reactions.For the determination of SQX concentration ([SQX]), the same Akady 5 μm C-18150 × 4.6 mm column, kept at 25.0 °C, was used as stationary phase, while methanol and 0.1% (v/v) formic acid  were used as the mobile phase flowing at 1.5 mL minIn the case of formic acid (FA), only the TOC concentration was followed during the treatment span.2O2 and iron species concentrations were performed with a Hitachi U-2001 UV-VIS spectrophotometer . Hydrogen peroxide concentration ([H2O2]) was determined following the spectrophotometric technique described by Nogueira et al.  were analyzed using the 1,10-phenantranoline method following ISO 6332:2+-phenantroline complex at 510 nm. To measure total iron concentration, ascorbic acid must be used so as to convert all the ferric ions (Fe3+) to ferrous ions (Fe2+). Then, through the difference, ferric ion concentration could be determined. In this case, samples were taken every 5.0 min until a reaction time of 30.0 min, and then every 15.0 min until the end of the assay.The iron species (FeVIRR) of 1.5 L and connected to a glass jacketed reservoir tank, both provided by Thermo Fisher Scientific, Barcelona, Spain.The pilot plant that was used to perform Fenton and photo-Fenton assays is a 15.0-L system composed of an annular photo-reactor with an irradiated volume (E = 3.36 × 10−4 Einstein min−1 (300 and 420 nm). The pilot plant is also equipped with sensors  connected to a programmable logic controller (PLC) that allows data acquisition and process control and to a SCADA system that allows data management.The annular photo-reactor is equipped with an Actinic BL TL-DK 36 W/10 1SL lamp (UVA-UVB) provided by Barcelona LED , and the incident photon flux, measured by Yamal-Turbay et al.  using poFinally, a flowmeter is available for the control of the recirculation flow rate.A schematic view of the pilot plant is shown in Fig. 2+]0, [Fe3+]0, [FeTOT]0). Finally, in the case of performing photo-Fenton experiments, the light was switched on 10.0 min before starting the experiment in order to allow the lamp to stabilize. The final step is the addition of hydrogen peroxide that makes the experiments start and that was added manually and all the once.Regarding the experimental protocol, the glass reservoir was first filled with 10.0 L of deionized water, and then after 10.0 min of recirculation, 4.9 L of deionized water in which the model contaminant was previously dissolved was added and recirculated for 15.0 min with the aim of ensuring a good homogenization of the matrix. After that, a sample was taken to measure the initial concentrations of TOC and the target compound. Then, after the pH was adjusted to 2.8 ± 0.2, the remaining 0.1 L of deionized water, in which iron sulfate was previously dissolved, was filled. After 10.0 min more of recirculation, another sample was taken with the aim of checking the initial concentration of the iron species ([Fe2+]0 was set to 10.0 mg L−1 (corresponding to 0.18 mmol L−1), or rather to the maximum legal value in wastewaters in Spain (DOGC 2O2]0) was set to 378.0 mg L−1, corresponding to 11.12 mmol L−1. The latter was chosen being the highest value of the oxidant concentration among the ones used to perform the experiments with the target compounds that will be detailed in the following sections.As the first instance, a set of blank assays without any target compound (BLANK 1–4 in Table ain DOGC . The ini8H9NO2) as the target compound was carried out. A subset of these experiments was used to fit the proposed model to the specific degradation mechanism. Another subset of the experiments in Table Then, a set of experiments using paracetamol  and photo-Fenton  experiments were performed fixing the initial concentration of PCT ([PCT]0 = 40.00 mg L−1) corresponding to 0.26 mmol L−1 and to an initial TOC concentration ([TOC]0 = 25.92 mg L−1), and changing the initial concentrations of ferrous ion [Fe2+]0 and hydrogen peroxide [H2O2]0.In particular, Fenton .In this case, a 2−1 as the maximum value of the factorial design (+ 1), and half such value, 0.09 mmol L−1, as the minimum value of the factorial design (− 1), and one and a half times less, 0.13 mmol L−1, as the central value of the factorial design (0).The initial ferrous ion concentration was varied between 0.18 mmol L−1) the stoichiometric dose as maximum and minimum values of the factorial design . The stoichiometric dose (5.56 mmol L−1) corresponds to the central value of the factorial design (0).The initial hydrogen peroxide ion concentration was varied between half and twice  of the experiments that were performed. Especially, the experiments from EXP1_PCT to EXP9_PCT are the experiments performed under dark conditions while those from EXP10_PCT to EXP_18_PCT are the ones performed under irradiated conditions.The resulting design of experiment in the case of PCT is presented in Table Moreover, a set of preliminary standard blank assays, but with the presence of the target compound, was also performed and it is presented in Table Next, a new target compound, the sulfaquinoxaline sodium salt , was used for validating the novel modeling approach that was proposed for PCT.In this case, the aim was proving that the proposed methodological approach allows obtaining a generalizable solution that can be used to describe the photo-Fenton degradation of any kind of target compound.Hence, in this case, to estimate the kinetic parameters of the relative degradation mechanism, a set of six experiments, three Fenton (dark conditions) and three photo-Fenton (irradiated conditions), was performed.−1 corresponding to 0.08 mmol L−1 and to an initial concentration of TOC ([TOC]0 = 13.72 mg L−1). The initial concentration of ferrous ion was also fixed and set to 0.18 mmol L−1. Conversely, the initial concentration of hydrogen peroxide was varied.The initial concentration of SQX was fixed to 25.00 mg L2 factorial design was applied. The initial concentration of hydrogen peroxide was varied between the stoichiometric value  to achieve total mineralization of 0.08 mmol L−1 of SQX  and twice  such value.Again, a 2T, λ, and VIRR) of the experiments that were performed, is reported. Especially, the experiments from EXP1_SQX to EXP3_SQX are the experiments performed under dark conditions while those from EXP4_SQX to EXP6_SQX are the ones performed under irradiated conditions.The resulting design of experiment in the case of SQX is shown in Table In addition, as for PCT, a set of five preliminary standard blank assays was performed in order to check the possible direct photolysis of SQX (BLANK ASSAY 14 in Table 2O2).Finally, the modeling approach was validated for the degradation of a third compound, formic acid  and two photo-Fenton (irradiated conditions), was performed.−1 corresponding to 0.87 mmol L−1 and to an initial concentration of TOC, ([TOC]0 = 10.43 mg L−1). The initial concentration of ferrous ion was also fixed and set to 0.09 mmol L−1. Conversely, the initial concentration of hydrogen peroxide was changed between the stoichiometric value (0.88 mmol L−1) to achieve total mineralization of 0.87 mmol L−1 of FA (according to the stoichiometric reaction shown in Eq. (−1) such value.The initial concentrations of FA were fixed to 40.00 mg L−1 and 4.41 mmol L−1, respectively, so to test the effect of higher concentrations of the Fenton reagents.Additionally, another photo-Fenton experiment was performed by increasing the initial concentrations of ferrous ion and hydrogen peroxide to 0.18 mmol LT, λ, and VIRR) of the experiments that were performed. Especially, the experiments from EXP1_FA to EXP2_FA are the experiments performed under dark conditions while those from EXP3_FA to EXP5_FA are the ones performed under irradiated conditions.The resulting design of experiment in the case of FA is shown in Table −1.All the experiments were performed for 120.0 min in batch mode with recirculation and ensuring perfect mixing conditions by setting the recirculation flow rate to 12.0 L min3+ to Fe2+ (Fenton-like reaction) at an appreciable rate. Temperature was also continuously monitored and it was checked that it was inside the range T = 28.0 ± 2.0 °C.In particular, pH was continuously monitored in order to ensure that it was inside the range (2.5 < pH < 3.0–4.0) that, according to Pignatello , Pignate(i)To develop a model that can be exploited for future industrialization of Fenton and photo-Fenton processes. In particular, a model that can be simplified enough to be computationally affordable but without losing its physical meaning. Or, in other words, a compromise modeling solution between the unaffordable accuracy of the first principle models (FPMs) and the oversimplification of the empirical models (EMs).(ii)To develop a rationally simplified but easily configurable and generally usable approach that can be applied for different wastewater systems containing single or multiple targets by also modeling a lumped parameter that can be used to define the overall quality of the water such as the TOC.The modeling effort had to face two main challenges:In the present work, starting from well-known FPMs, a set of hypotheses, rationally selected and based on empirical observations of the Fenton and photo-Fenton system behavior, have been proposed and are listed below:2O, H2O2, and Fe2+ and described by a set of kinetic reactions involving these compounds, as well as Fe3+, free radicals (at least HO• and + and OH−), was assumed as the core mechanism of the proposed model. The target invariant free radical production of Fenton process was described by the H2O2-driven Fe reaction cycle:The existence of a general target independent model of Fenton system, initiated by mixing H• in the lighted photo-Fenton system. The target invariant light initialized free radical production of the photo-Fenton process proposed by Cabrera Reina et al. :k0 of the photo-Fenton reaction was determined in line with data by Cabrera Reina et al.  is to be identified and validated.Kinetic parameter  and of their fragments (FR) may be interpreted as the series of consecutive breakage steps (B), comprising second-order binary reaction of the target and its fragments with free radicals. The number of these steps was assumed to be formally  determined by the number of carbon atoms (NC) in the molecule to be decomposed. It was assumed that in the decomposition steps the targeted compounds and their fragments interact basically with free radical HO• (main oxidant species) as also proposed by other authors, e.g., by Conte et al.  for the first breakage step of the targeted compound, andkfragment = kb  for all the following fragmentation steps.As the first preliminary hypothesis, it was also supposed a faster initial rate of the degradation mechanism based on the hypothesis that the by-products are more hardly degradable than the parent compound. Hence, it was assumed that the breakage steps can be characterized by two target-specific parameters, as follows:ktarget and kfragment have to be estimated and validated for the various targets, individually.The target-specific temperature-dependent parameters b) in the fragments originating from the parent compound (FRb). The number of fragments depends on the number of carbon atoms in the starting molecule, as follows:It was assumed that the concentration of the TOC can be calculated from the fictitious number of carbon atoms  also participates in this competition.In order to avoid infeasible stiffness that can be generated by the competitive reactions  with HOHence, the developed model presents two main steps: a core mechanism , as , as 8), The non-conventional methodology of PPS ;GraphML-based model data files ;MS Excel user interface with VBA for initial data and parameters, as well as for visualization of simulated results.Recent experimental implementation consists of:2O2 reactant is fed and mixed with the previously mixed solution of the target compound and Fe2+;Compartment [1] the tank reactor of 9.00 L, where the HCompartment [2] of 2.25 L, connecting compartments [1] and [3];Compartment [3] of 1.50 L, representing the irradiated volume of the annular reactor;Compartment [4] of 2.25 L, connecting compartments [3] and [4].In particular, in the present work, in order to follow the real hydro-dynamical conditions as well as to support possible future scaling up of the process, we compartmentalized the pilot plant into a circular set of four parts:2O2 that followed the fast but realistically finite time because it was observed that this short-term dosage better fits the experimented behavior of the system than starting from a calculated initial condition;Compartment [1] is associated with the feeding of HThe reaction in Eq.  was takeAll the other reactions were taken into account in the whole set of compartments ([1]–[4]).Accordingly, it must be noted that:Two-state prototypes: one for the general Fenton components (core mechanism) and another one for the target-related components ;2O2 feeding, and one for recirculation of the water ensured by a recycle pumping between the compartments.Six transition prototypes: one for the Fenton system (Eqs.  and 5)))5)), oneIn the actual model implementation, the following state and transition prototypes were defined:Figure All the abovementioned state elements and transition elements are summarized in Table Figure Once the model was formulated and the experimental designs were proposed for the selected model compounds, it was possible to proceed to the model training and validation step.First, the estimation of the kinetic parameters of the core mechanism was carried out by using the data of the blank assays, performed without target compounds Table .Then, the model was trained and validated by using PCT as the target compound  by using the respective experimental dataset  were used.Next, in the knowledge of the previously fixed general parameters, the identification and validation were limited to the 2 additional parameters, considering model hypotheses H4, H5, and H6, while 3 evaluation measures  and for each of the three selected targets. The comparison is evaluated by the RMSE, calculated by the following expression:ith variable, where:yik, value of the kth measurement of the ith variablei = 1, 2, …I, the ith element of the set of measured variablesroot mean square error of the 2O2 (I = 3).The measured data, involved in the RMSE calculations, were the normalized concentrations of the target compound, TOC, and Hk0, k1, k2, and kelimination of reactions in Eqs. , .From the experimental results in Fig. 3+ and oxidation of Fe2+, both reacting with H2O2  were assumed equal to those estimated in the previous step and presented in Table The kinetic parameters of the core mechanisms  obtained in the case of using [PCT]0 = 0.26 mmol L−1; [Fe2+]0 = 0.09 mmol L−1; [H2O2]0 = 5.56 mmol L−1 under dark and irradiated conditions, respectively, is reported.An illustrative case of the model training for the case of EXP4_PCT and EXP_13_PCT  obtained in the case of using [PCT]0 = 0.26 mmol L−1; [Fe2+]0 = 0.18 mmol L−1; [H2O2]0 = 5.56 mmol L−1 under dark and irradiated conditions, respectively, is reported.Finally, an illustrative case of the model validation for the cases of EXP6_PCT and EXP15_PCT  performed using PCT as the model compound. RMSE resulted in 30% for PCT, 7% for TOC, and 11% for HIn addition, a comparative study illustrating the differences between the proposed model and a FPM developed by Audino et al. , for twoAs can be observed, the proposed PPS model, compared with the more accurate FPM by Audino et al. , slightlIn this step, the experimental data derived by the assays performed using SQX as the model compound were used to validate the proposed methodology, previously fitted to the degradation of PCT.k0, k1, k2, and kelimination, were not estimated and were assumed equal to those summarized in Table −1] for the first degradation step of the target compound;−1] for the following degradation steps of the fragments.Also, in this case, the kinetic parameters of the core mechanism, or rather Hence, as can be observed, the estimation strategy of the kinetic parameters describing the degradation mechanism of SQX is based on the same methodology followed for PCT. However, having the SQX a different number of carbon atoms and consequently a different number of breakage steps, compared with PCT, it was necessary to proceed to the estimation of the specific kinetic parameters of its degradation mechanism.2O2 rather than the target and the specific SQX degradation mechanism. The estimated values of the relative kinetic parameters are summarized in Table As for PCT, also in this case, parameter estimation strategy was tuned in order to give priority to a best fitting of TOC and HIn this case, the rate of the first degradation step resulted to be similar to the rate of the subsequent degradation steps.The degradability of SQX resulted to be obviously less than the one observed for PCT because of the greater carbon number, as well as a direct consequence of its structure.2O2 are presented to discuss the SQX case because the main aim was to validate the proposed methodology as a general approach that can be applied for single or multiple targets in different wastewaters, whose quality can be described by a lumped parameter (as it is the TOC). Hence, Fig. 2O2 obtained in the case of EXP2_SQX and EXP5_SQX  performed using SQX as the model compound, resulting in 17% for SQX, 26% for TOC, and 19% for H2O2). However, it must be taken into account that a smaller number of experiments (6 against 18) was employed.The RMSE values slightly increased compared with the previous results obtained with PCT  than to train it (with PCT), since a smaller number of kinetic parameters needed to be estimated. This shows a clear advantage of the proposed simplified but generalizable methodology.In this step, the experimental data derived by the assays performed with FA were used to validate the proposed methodology with a third model compound.This model compound was selected in order to test the response of the model for the degradation of a very simple molecule.k0, k1, k2, and kelimination, were not estimated and were assumed equal to those summarized in Table As for PCT and SQX, also in this case, the kinetic parameters of the core mechanism, or rather Moreover, even though the starting molecule of FA is composed of only one carbon atom, for coherence with the methodological approach defined for the first two targets, it was decided to take into account the attack to the parent compound and the attack to the intermediates originating from it.−1] for the first degradation step of the target compound;−1] for the following degradation steps of the intermediates.Consequently, to validate the methodology using FA, the two kinetic parameters describing the first degradation step and the following ones needed to be estimated:In this case, it must be noticed that it was decided to only follow the TOC evolution due to the simplicity of the starting molecule of FA composed of only one carbon atom.The specific FA degradation mechanism and the estimated values of the related kinetic parameters are summarized in the following Table As can be observed, the first step (attack to the parent compound) is characterized by a kinetic parameter of one order magnitude higher than the one describing the subsequent attack to the intermediates originating from the first degradation step. In this case, the parameter estimation suggests that the second degradation step could probably be avoided. However, this hypothesis needs to be experimentally confirmed by the evolution of formic acid during the treatment span .2O2 and particularly the comparison between experimental and simulated data obtained in the case of EXP2_FA and EXP4_FA . Hence, only detection via HPLC of the target molecule and of the produced intermediates can help describe the system behavior during the first minutes of the Fenton and photo-Fenton treatments of formic acid.The model in this case overestimates the enhancement of the process performance due to the use of irradiation, describing the photo-Fenton process as the faster one. This result is probably due, as already observed, to the lack of experimental measurements during the first minutes of the reaction. Moreover, it must be noted that a very low number of experiments (five) was performed to validate the proposed methodology with this third compound.2O2 is completely consumed under both dark and irradiated conditions in about 45.0 and 60.0 min, respectively.Finally, also in this case, H2O2, and highlighted the acceptable prediction of the model.The root main square error (RMSE) average value (averaged as in the previous cases between the RMSEs obtained for each experiment (dark and irradiated conditions) performed using FA as model compound) resulted in 16% for TOC and 18% for H2O2 remained constant , so showing an improvement of the estimation capability of the proposed methodology.As can be observed, after the third validation, the RMSE value for TOC decreased while the one related to HTo conclude and summarize the results of the model fitting, Table 2O2 slightly increased.Despite the fewer number of experiments used to validate the proposed methodology with SQX rather than with PCT, it was possible to improve the prediction of the target compound. However, the RMSE associated with the predictions of TOC and HThe acceptable fit of the model was finally illustrated by plotting the predicted values versus the actual measured values for each of the selected targets  and the related TOC  it supports fast model discovery by the automatized generation and configuration of various models from the description of the process network and from two general meta-prototypes; (ii) it supports the easy modification of the locally implementable declarative programs, associated with the state and transition prototypes; and (iii) the transition-based model representation helps the availability controlled normalized description of competitive fast processes.The generalization capability of the methodology was successfully confirmed by the experimental validation of the developed model first for the degradation of paracetamol and next for the degradation of sulfaquinoxaline sodium salt and formic acid. Once the model is systematically created and validated to the first compound, the partial fitting of the model to further compounds was shown to require the adjustment of significantly fewer number of model parameters, which in turn needs less experimental data to produce the validation of the model at acceptable levels (RMSE).The proposed model proved to be a causally interpretable and generalized candidate solution for the simulation-based analysis and design of Fenton and photo-Fenton reaction mediated degradation of various wastewaters that contain one or multiple target compounds.2O2 is to be studied to improve the decontamination ability of the process.Further research should include applying and validating the proposed methodology for multiple target compounds or mixtures of organic contaminants. Also, the simulation supported design of controlled multi-step or fed-batch dosage of H


Escherichia coli, to evaluate the production performance of the strain as a case study. The experimental data of glucose consumption and cell growth were used as FBA constraints. Bi-level FBA optimization with maximized growth and shikimic acid production were the objective functions. Results suggest that the shikimic acid concentration in the high-shikimic-acid-producing strain constructed in the experiment reached up to 84% of the maximum value by simulation. Thus, this method can be used to evaluate the performance of strains and estimate the milestones of strain improvement.Flux balance analysis (FBA) is used to improve the microbial production of useful compounds. However, a large gap often exists between the FBA solution and the experimental yield, because of growth and byproducts. FBA has been extended to dynamic FBA (dFBA), which is applicable to time-varying processes, such as batch or fed-batch cultures, and has significantly contributed to metabolic and cultural engineering applications. On the other hand, the performance of the experimental strains has not been fully evaluated. In this study, we applied dFBA to the production of shikimic acid from glucose in  The microbial production of various useful compounds has been actively studied. With the recent development of synthetic biotechnology, the production of useful compounds that microorganisms do not naturally produce can be made possible by introducing biosynthetic pathways (synthetic metabolic pathways), designed by combining heterologous and modified (mutant) enzymes. In addition, active research on the use of metabolic models has contributed to an effective improvement in the yield of useful compounds ,2,3,4. IFBA is a method that assumes a steady state in which the concentration of a metabolite does not change with time. An FBA solution (the distribution of metabolic fluxes) that maximizes or minimizes the objective function is searched, using a stoichiometric matrix composed of stoichiometric coefficients of reactions that constitute the metabolic model . In the In addition, the theoretical maximum yield under given constraints (conditions) can be obtained with FBA, although this is usually different from the actual yield in a dynamic production process with growth. From this point of view, dynamic FBA (dFBA) has been developed, which is an extension of FBA applicable to dynamic production processes, such as batch and fed-batch cultures with growth . The dFBSaccharomyces cerevisiae and Scheffersomyces stipitis . On the other hand, the units of the data extracted from the experimental data and their approximated values are mM or g/L. Therefore, it is necessary to perform unit conversions so that the values can be used as constrains in dFBA. The equations of glucose and cell concentrations were polynomially approximated as a function of time t. These equations were differentiated with respect to t, and then divided by the equation of cell concentrations, to obtain the equations of specific glucose uptake and growth rate. The approximated time course of the obtained specific glucose uptake rate and specific growth rate is shown in In the dFBA of this study, the FBA is sequentially performed at an arbitrary time. Therefore, it is necessary to prepare a time course of the specific uptake rate of the substrate (glucose), and the specific growth rate of the bacterial cell (biomass) as constrains (lower and upper boundaries) in dFBA. The constraints to dFBA are the values of the flux at any time The approximated specific glucose uptake rate −1) =The approximated specifics growth rate E. coli used for FBA was iJO1366 [th FBA repetition. Thus, the time course of each flux was obtained. Among the obtained fluxes, glucose uptake, cell growth (biomass synthesis), and shikimic acid production (discharge) fluxes were numerically integrated, and time-course data of each concentration were obtained  model, FBA assuming a steady state is used for the intracellular simulation. Therefore, it is impossible to express the limitation of metabolic flux or the accumulation of intermediate metabolites, due to some factors such as imbalance of enzyme amounts and cofactor supply, feedback regulations.Therefore, in this study, the dFBA can more easily acquire the time courses of the metabolic fluxes in the metabolic model using time-course data approximation. Additionally, in compound production, by using the fluxes of specific substrate uptake and growth obtained by approximation as FBA constraints, it is possible to estimate the difference between the current strain and the theoretical maximum values, and to estimate the room of improvement.In a more detailed analysis, such as pathway optimization, dFBA does not reach simulation and analysis using a dynamic (kinetic) model. In the construction of a dynamic model, parameter estimation is a very costly operation, which is a barrier to the construction of a large-scale dynamic model. It has been suggested that combining flux time-course data with metabolome-based intracellular metabolite concentration time-course data facilitates parameter estimation ,35,36,37The workflow of the method is summarized in https://automeris.io/WebPlotDigitizer/) [Using the online version of WebPlotDigitizer 4.2 (itizer/) , the ploitizer/) .E. coli is 0.33 g DCW/OD600 [The cell concentration obtained from the literature is either DCW or OD values. In this study, the conversion factor of DCW per OD in CW/OD600 . If the t by the following polynomial equations (Equations (7) and (8)).The extracted time-course numerical data was divided into arbitrary sections as needed, and a polynomial approximation using the least squares method was performed. The approximated concentrations glucose and cells were expressed as a function of time −1) used for the dFBA constraints were calculated by dividing the derivatives of the approximation equations of the substrate and cell concentration with respect to the time t by the cell concentration (g/L) at that time.The specific rate of glucose uptake (mmol/g/h) and the specific rate of growth (ht (h).In the dFBA method, instead of formulating a differential equation and estimating the kinetic parameter values in the equations, the obtained values by approximation equations are used in the FBA at any time t. Depending on the approximation result, the specific glucose uptake rate and the specific growth rate may show negative values. In such cases, 0 was compulsorily set. In addition, as mentioned in The specific substrate uptake rate and the specific growth rate given as input constraints to the FBA part were calculated by differentiating the approximate equation of the substrate concentration and the bacterial cell concentration divided by the approximate expression of the bacterial cell concentration at time t (h) was sequentially performed to obtain time-course data of the flux. Using this method, the time-course data of metabolic fluxes were collected.As mentioned above, the FBA part is divided into two steps. In the first step, the objective function was to maximize the specific growth rate while relaxing constraints as needed. In the second step, the specific growth rate was fixed at the value obtained in the first step, and the production flux of the target compound was maximized as an objective function. The step size of the calculation was 0.01 (h), and FBA at any time The time course of extracellular metabolites and the cell concentration were calculated by numerically integrating the time courses of the fluxes obtained by dFBA using Simpson’s rule. In addition, the final concentration of the target compound obtained by numerical integration was regarded as the maximum production concentration of the target compound under experimental substrate consumption and growth constraints. The obtained maximum production concentration of the target compound was compared to the actual experimental data, and the production performance of the strain used in the experiment under defined constraints and its theoretical maximum value were estimated.https://github.com/opencobra/cobratoolbox.git) were used for the dFBA simulation, and Gurobi 8.1  was used for the FBA solver. The home-made MATLAB script (computer code) used for the calculation of time-course of metabolic fluxes are available on GitHub .The MATLAB© 2018b  and COBRA Toolbox (E. coli. Time-course data on shikimate production by E. coli was selected from previous publication [https://automeris.io/WebPlotDigitizer/) [600 value from the literature for the conversion. In this case, the unit of cell concentration was (g/L) for DCW in the time course data, which was used as is.The above dFBA was applied to the example of shikimic acid production from glucose in lication . The numitizer/) . The ext−1) by dividing the derivatives of the approximation equations for glucose and cell concentration with respect to time t by the corresponding cell concentration (g/L).The values for FBA constraints in dFBA were converted to specific glucose uptake rate (mmol/g DCW/h) and specific growth rate , shikimic acid, and cells were calculated by numerical integration using the Simpson’s rule, based on the output values sequentially obtained FBA. From these results, data at the time of maximum production of the target compound under the constraints of experimental substrate consumption and cell growth were estimated.By comparing with the actual experimental data, the theoretical yield using the current strain was estimated under the same constraints on substrate consumption and bacterial growth as in the experiment. The actual yield of the strains compared to the theoretical yield under the experimental constraints will inform whether the yield will be increased by optimizing the culture process, or by metabolic engineering in the future. These results will also be used for strain evaluation and planning of engineering strategies.


Synechococcus elongatus with heterotrophic Escherichia coli K-12, Escherichia coli W, Yarrowia lipolytica, or Bacillus subtilis. Model simulations reveae metabolic exchanges that sustain the heterotrophs in minimal media devoid of any organic carbon source, pointing to S. elongatus-E. coli K-12 as the most active community. Experimental validation of flux predictions for this pair confirms metabolic interactions and potential production capabilities. Synthetic communities bypass member-specific metabolic bottlenecks (e.g. histidine- and transport-related reactions) and compensate for lethal genetic traits, achieving up to 27% recovery from lethal knockouts. The study provides a robust modelling framework for the rational design of synthetic communities with optimized growth sustainability using phototrophic partners.Microbial communities comprised of phototrophs and heterotrophs hold great promise for sustainable biotechnology. Successful application of these communities relies on the selection of appropriate partners. Here we construct four community metabolic models to guide strain selection, pairing phototrophic, sucrose-secreting  Successful application of microbial community for bioproduction relies on the selection of appropriate heterotroph and phototroph partners. Here, the authors construct community metabolic models to guide strain selection and experimentally validate metabolic exchanges that sustain the heterotrophs in minimal media. This type of association dominates many biofilms, microbial mats, and lichens3, thriving in desiccation, nutrient starvation, and salinity or temperature extremes4. This ability to survive extreme conditions is due, in part, to division of labor and subsequent interactions between members of the community. Photoautotrophic members, classically either cyanobacteria or eukaryotic algae, convert CO2 into organic carbon for growth and maintenance of the heterotrophic partner(s). Exchange of these metabolites can sustain the heterotrophs under conditions devoid of any organic carbon source. In turn, the heterotrophs provide additional CO2, protection from environmental factors and predation, and often, a diverse array of metabolites produced by secondary metabolism5.Phototrophic microbial communities exhibit symbiosis between photoautotrophic and heterotrophic organisms supported primarily by solar energy and the fixation of carbon dioxide  have been utilized for the production of biofuels7, α-amylase, and polyhydroxyalkanoates among other compounds12. Complex communities consisting of algae and bacteria also have potential applications in waste-water treatment15, bioremediation16, and as a bloom control method for phytoplankton17. Traditionally, microbial communities have been selected in long term adaptation and optimization experiments to define optimal culture conditions18. The critical challenge in synthetic community design is to maintain syntrophic interactions between members to avoid culture collapse19. Development of SPCs for bioproduction involves four critical steps: (a) strain selection, (b) screening of cultivation conditions, (c) efficient extraction of added-value products, and (d) process control and biomass recycling. The first three steps (a–c) are important drivers for implementation of successful bioproduction processes that can be optimized and guided using metabolic modeling.To date, understanding, engineering, and determining viable cultivation conditions for natural phototrophic communities remains challenging21 and microbial communities (community-metabolic models henceforth referd to as CM-models)25. These models account for biochemical and genomic information for an individual or community at the genome-scale. Resulting models are solved using flux balance analysis and can accurately predict thousands of functional states26. Simulations performed with CM-models describe key metabolic functions of microbial communities, defining all possible interactions among partners based on genetic and/or metabolic fitness. CM-models also enable prediction of effective culture conditions for production in robust biotechnological processes22.Constraint-based metabolic modeling is a systems biology tool that provides a comprehensive metabolic understanding about individual microorganisms (metabolic models henceforth referred to as M-models)Synechococcus elongatus PCC7942, with its high growth rate and robust metabolism, is able to synthesize hydrogen, ethanol, 2,3-butanediol, sucrose, squalene, and fatty acids among other organic chemicals from light and CO227. For heterotrophic partners, we focus on established microbial cell factories, i.e., Escherichia coli, Bacillus subtilis, and the fungus Yarrowia lipolytica. CM-models for four synthetic communities based on the sucrose-secreting S. elongatus in pairwise combination with E. coli (strains K-12 and W), B. subtilis str. 168, and Y. lipolytica Po1g are deployed. Predictions about biomass and metabolites  production yields as well as flux distributions through the metabolic networks are experimentally validated using physiological and gene expression data. We explore metabolic fitness and genetic stability by evaluating compensatory mechanisms in resistance to knockouts of genes with lethal phenotypic traits mimicking enzymatic damage. We test predictions experimentally for ten knockout strains and explore potential production capabilities of organic chemicals, such as methanol, formaldehyde, ethanol, butanal, and succinate for all microbial communities.Here, we reconstruct CM-models encompassing bacteria and fungi that are important contributors to biofuel production. The cyanobacterium 23. These models can be used to elucidate, understand, and generate hypotheses about biological mechanisms shaping interactions between community members22. CM-models and M-models predict biological functions based on key substrate uptake capabilities referred to as constraints. Using the M-models of E. coli K-12 iML1515, E. coli W iJO1366W29, B. subtilis str. 168, iYO84430, and Y. lipolytica Po1g, iYali431  was added into the SMP of all models. Metabolites in the SMP of all CM-models are listed in Supplementary Data CM-models are a mathematical representation of genomic and metabolic knowledge of microorganisms within a community431 Fig. , we reco−1 h−1 by an engineered S. elongatus strain (S. elongatus cscB+)33. When this constraint was added into the M-model of S. elongatus (iJB792) the growth rate dropped about 16% from 0.0539 h−1 to 0.044 h−1, similar to experimental observations (0.045 ± 0.07 h−1). Growth rate simulations and experimental results are shown in Fig. Y. lipolytica. Since, Y. lipolytica cannot use sucrose as its sole carbon source we used an engineered strain (Y. lipolytica suc+) with sucrose uptake capabilities in all the experiments shown here34.We simulated CM-models based on experimental constraints, such as the sucrose secretion rate of 0.182 mmol gDWS. elongatus (cscB+ or WT) should be able to grow at similar growth rates with E. coli or B. subtilis as in monoculture (0.039 ± 0.01 h−1 averaged across cocultures), but should grow faster when it is cultivated with Y. lipolytica (0.062 h−1). These expectations were validated by experiments with the exception of S. elongates-Y. lipolytica communities in which S. elongatus did not see a boost in growth but instead exhibited diminished growth, despite our simulations showing active exchange of isoleucine and other amino acids.Experimental validation of the CM-models yielded interesting and varied results. Predictions using the CM-models showed that S. elongatus cscB+ with each heterotrophic partner supported growth of both community members over 72–96 h . Growth curves for all SPCs are shown in Supplementary Fig. Synthetic phototrophic communities (SPC) of 6 h Fig. . Surprish−1 Fig. . For theE. coli K-12 was capable of producing the most metabolites (111 metabolites), followed by E. coli W (106 metabolites), Y. lipolytica (60 metabolites), and B. subtilis (39 metabolites).CM-models offer a remarkably higher topological potential, achieving feasible solutions while optimizing for the synthesis of target metabolites by shifting the resources across members. CM-models contain the most comprehensive collection of metabolites that are intermediates in the synthesis of biomass or are part of the biomass compositions  of the community members. Here, we simulated production capabilities of every metabolite in the models , or succinate (0.066 ± 0.004 g gDW−1), but only SPCs containing E. coli strains were able to synthesize formaldehyde (average yield 0.017 g gDW−1) and butanal (average yield 0.012 ± 0.002 g gDW−1) , that are declared as primary feedstock for chemical synthesis by the Environmental Protection Agency of the United States of America. Currently these metabolites are manufactured primarily through either chemical synthesis or single-strain biorefineriesals Fig. , we pred−1) Fig. . MetabolE. coli K-12, the model predicted that S. elongatus cscB+ would increase the flux exchange of serine and threonine over two-fold, resulting in higher secretion of these metabolites. In turn, E. coli K-12 would provide adenine, phenylalanine, and isoleucine at higher fluxes . We predicted that the SPC containing E. coli K-12 was the most efficient in exchanging amino acids based on its total metabolite exchange flux, e.g., isoleucine, valine, glutamate, serine, and phenylalanine  were pyruvate, methanol, formate, acetate, and high concentrations (13.7 mM) of ethanol, suggesting that these are also available for metabolite exchange. These metabolites were often lower in coculture than in monocultures, providing further support of this exchange.Metabolic interactions were experimentally characterized using Nuclear Magnetic Resonance (NMR) and Gas Chromatography-Mass Spectrometry (GC-MS). Metabolic profiles for 34 metabolites were measured from biomass samples and culture medium supernatants under mono- and coculture conditions. Experimentally determined metabolic profiles validated the exchange of predicted metabolites. NMR and GC-MS analysis of intracellular Table  and extrS. elongatus cscB+ and E. coli K-12 using GC-MS. Some intracellular metabolites, including the amino acids glutamate and aspartate and the dipeptide glycylproline (precursor of serine and threonine synthesis) accumulated to higher relative levels in S. elongatus compared to E. coli. Other metabolites, such as malonate, were detected intracellularly as well. GC-MS analysis  .CM-Models not only unravel metabolic exchange but can also decipher alterations in the activity of complete pathways. Shifting from mono- to coculture conditions triggered changes across fluxes in multiple pathways of the entire network. Our predictions suggested that these metabolic changes occur in all SPCs studied here. The predicted fold-change (coculture/monoculture) of subsystem fluxes in all SPCs were remarkably correlated  Fig. . SimilarS. elongatus and E. coli W showed significantly differential expression  of genes associated with alanine, aspartate, and glutamate metabolism, arginine and proline metabolism, the pentose phosphate pathway, phototroph-specific metabolism, purine and pyrimidine metabolism, and transport reactions as predicted  across the entire metabolic network. Histidine metabolism is linked with the pentose phosphate pathway and alanine, aspartate, and glutamate metabolism, encompassing the synthesis of several glutamate precursors. Even though we could not quantify/detect intracellular accumulation of histidine experimentally, glutamine, a histidine precursor, was accumulated in both S. elongatus (9.9 mM) and E. coli K-12 (2.1 mM). This metabolite was not found in the supernatant of any mono- or cocultures. Overall, CM-models are a reliable tool to identify functional states in association with growth phenotypes, offering details of cellular communication and potential network bottlenecks limiting microbial interactions.We quantified and compared expression and fluxes by pathway, identifying potential bottlenecks that if relieved could improve biomass yields. For example, predicted flux and observed expression data associated with transporters located in the thylakoid as well as histidine metabolism in the cytoplasm were highly activated, making up around 50% of the total expression (RNA-seq reads) and flux .Tolerance to inhibitors is one of the main challenges for strain engineering of monocultures. Often growth rates and productivities are limited by the accumulation of toxic intermediates  that can harm productivity or lead to culture collapseS. elongatus cscB+, 350 genes are essential, meaning if they are knocked out S. elongatus cscB+ cannot grow in minimal media. This is in contrast to S. elongatus cscB + grown in communities where the number of lethal deletions falls to 327 or 326, depending on the cocultivation partner  mutants with variable growth phenotypes in monoculture versus coculture conditions to test experimentally. Six of those mutants were predicted to not grow in monoculture and were associated with amino acid metabolism , cofactor and prosthetic group biosynthesis (cysG and thrC), and inner membrane transport (phoE). Of these, most strains died in monoculture in minimal media as expected and only the strain lacking ilvE grew in monoculture under our cultivation conditions , oxidative phosphorylation (atpC), the pentose phosphate pathway , and inner membrane transport (cycA)  Fig. , 9. All E. coli strains missing ilvC, cysG, pheA, and thrC was rescued by S. elongatus cscB+ as predicted for the strains ilvC and pheA . The model demonstrated good accuracy for growth/no-growth prediction of the ten assayed KOs. Matthews correlation coefficient (MCC) values were estimated for each condition, by comparing experimental and predicted outcomes (Supplementary Data E. coli K-12 monoculture (0.90), followed by S. elongatus cscB+ coculture (0.7) and E. coli K-12 coculture (0.7); the positive predicted values ranged from 0.83 to 1 for all conditions. Selected strains were also cultured in rich medium (80% Luria-Bertani (LB) + 20% BG-11). We observed that all KOs were rescued in monoculture. Interestingly, the phototrophic communities maintained syntrophic interactions despite the capability of E. coli to thrive in rich medium. Overall, the growth rates of community and monoculture increased up to 41% while cultured in rich medium  has resulted in a promising approach to overcome current limitations11. Furthermore, the use of both synthetic and natural phototrophic communities allows for the utilization of renewable resources for sustainable production39, maintaining diverse and robust microbial interactions, reducing overall cost of feedstocks and minimizing transport logistics35. We explored the potential of photosynthesis-based processes as sustainable growth. Simulations predicted different growth phenotypes depending on the heterotrophic partner . The SPCs containing E. coli improved community growth effectively by exchanging metabolites , as well as into the interactions among stages for each microbial community. The broader potential of CM-model simulations enables quantitative insights into metabolic exchange and pathway fitness. Other approaches, e.g., one developed for the diatom Phaeodactylum tricornutum and the bacterium Pseudoalteromonas haloplanktis48, using a combination of kinetic and constraint-based models, require determination of specific exchange rates  for simulation. Experimental quantification of these parameters can be challenging even for monocultures23, limiting the simulation capabilities of these multiscale models. The shared metabolite pool provides strong versatility to CM-models to determine production capabilities of each microbial community as well as to track quantitative biochemical fluxes and therefore specific resources used to produce metabolites of interest.Mathematical models of heterotrophic-autotrophic communities have been previously published, encompassing a limited number of parameters, such as inorganic carbon, nitrogen, phosphorous, and light uptake rates50, but our modeling predictions for all SPCs indicated that cocultivation can help circumvent potential inhibitory effects by redirecting flux and metabolic exchanges between members 52. Additionally, experimental results using transposon sequencing (TN-seq) applied to microbial communities have shown differences in gene essentiality between mono- and coculture conditions55. This effect, described as community dependent essentiality, resulted in similar phenotypic outcomes as generated by our metabolic modeling approach. For example, TN-seq data of E. coli collected during cocultivation with Hafnia alvei, Geotrichum candidum, and Penicillium camembertii54 showed similar gene essentiality  as our SPC of S. elongates and E. coli. Interestingly, gene essentially of the ATP synthase/thiamin triphosphate synthase complex (atpC in our SPC) was also observed in a different coculture composed of Staphylococcus aureus and Pseudomonas aeruginosa (atpD)53 hinting at commonalities in the evolution of diverse microbial communities that could be independent of the members. This intriguing hypothesis requires additional experimental confirmation.Usually, inhibitory effects can diminish the growth of microorganisms in their natural environment and in many industrial applicationsers Fig. . An expe56. However, the development of innovative modeling tools that enable quantitative identification of potential metabolic drivers among a myriad of physiological stages  results in solid advances toward a more comprehensive understanding of microbial community structure and function. Additionally, combinations of these model-driven hypotheses with omic studies will help guide the design and execution of synthetic phototrophic microbial communities.To date, a lack of detailed knowledge about microbial communities has limited our ability to predict their responses and redirect their activity for improved bioproductionS. elongatus PCC7942, iJB79232, B. subtilis, iYO84430, Y. lipolytica, iYali431, E. coli W and K-12, iECW137228 and iML151429. Additional information about the models is shown in Table 20. The COBRA Toolbox is a MATLAB  software suite for quantitative prediction of cellular and multicellular biochemical networks, implementing the most comprehensive collection modelling methods and algorithms to perform high-throughput model-driven analysis20.CM-models were reconstructed using M-models of 22. This compartment streamlines the connectivity of individual models and the extracellular space based on each microorganism’s capabilities. Metabolites suitable for sharing were manually curated based on experimental data of community members in isolation. We performed a high-throughput growth assay  using S. elongatus, testing over 180 different carbon sources  as described by Zuniga et al.20 for MATLAB. We simulated the maximal growth rate of the community members using the Flux Balance Analysis (FBA)-associated algorithm OptCom20. This algorithm maximizes for the biomass objective functions or biomass reactions, which contain all metabolites that comprise organism biomass . The growth rate of the population results from the sum of fluxes through both biomass reactions of individual models. Constraints about CO2 and light consumption rates were imported from the iJB792 model. The sucrose secretion rate of S. elongatus was constrained to 0.182 mmol gDW−1 h−1. Benchmarking of experimental and predicted results was performed by calculating modeling statistics for the community members under mono- and coculture: true positive (TP), true negative (TN), false positive (FP), false negative (FN), and the confusion matrix and various measures of quality, such as accuracy, specificity, sensitivity, positive predicted, negative predicted, and Matthews correlation coefficient (TP + TN/(TP + TN + FP + FN))60. Metabolites productivity calculations were generated by constraining each metabolite production rate (0–2 mmol gDW−1 h−1) and maximizing for the biomass growth of both community members at the same time. We considered metabolite production feasible if both community members grew; these metabolites were selected and are shown in Fig. 61. Examples of the calculations are given in Supplementary Data CM-models benchmarking was performed using the Gurobi Optimizer Version 5.6.3 solver  in the COBRA Toolbox20. Exchange rates of these metabolites were iteratively varied to zero flux or double flux. Simulations deployed growth rate sensitivity of each member in the community. Core sets of vital metabolic exchanges were defined and compared for all CM-models  of individual microorganisms when using M-models and predicted growth rate of the community member when using CM-models, Eq.  for the community member (j), Eq.  for all subsystems, conditions, and community members. The culture condition  exits at m. Predicted fluxes and gene expression data were normalized to values from −1 to 1 and compared using two sided t-test of The Statistics and Machine Learning Toolbox for MATLAB. The flux variability was determined using FVA64.We developed a method to compare expression data of individual microorganisms and communities with predicted flux distributions. Transcriptomic data for the pair els, Eq. , where iy k, Eq. . For exa(j), Eq. . SupplemSnk,j from mono- to coculture conditions defines pathway usage as syntrophically active , neutrally active , and deactivated . Syntrophically active pathways were assumed to uptake or secrete mass from and to the partner as a result of metabolic exchange. Thus, Snk,j,m1 represents each pathway and can take values from −1 to 1 depending on the total carried flux under mono- (m1) and coculture (m2) conditions, Eq.  simulations of over 12,800 genes in the metabolic networks (monoculture and community) were performed in turn, determining growth phenotypes under monoculture and community conditions. Genes predicted to be essential and non-essential were compared across conditions and growth patterns stabilizing, improving or decreasing the growth of the community members were determined.S. elongatus PCC7942 (ATCC #33912) was engineered to secrete sucrose through the expression of the sucrose/proton symporter cscB+ 33. Inoculum culture of sucrose-secreting cyanobacterium was prepared using BG-11 (Sigma–Aldrich) medium supplemented with 1 g L−1 HEPES (pH 8.9) and 100 mM NaCl at 35 °C. BG-11 medium is composed of (in 1 L): 1.5 g NaNO3, 0.04 g K2HPO4, 0.075 g MgSO4·7H2O, 0.036 g CaCl2·2H2O, 0.006 g Citric Acid·H2O, 0.006 g Ferric Ammonium Citrate, 0.001 g Na2EDTA·2H2O, 0.02 g Na2CO3, 1 mL BG-11 trace metals solution. The BG-11 trace metals solution (in 1 L) consists of: 2.86 g H3BO3, 1.81 g MnCl2·4H2O, 0.22 g ZnSO4·7H2O, 0.39 g Na2MoO4·2H2O, 0.079 g CuSO4·5H2O, 49.4 mg Co(NO3)2·6H2O. Cultures were illuminated 24 h a day while shaking at 150 rounds per minute8. All experiments were performed with six to eight replicates. Flask cocultures were completed in 25 mL volumes in baffled flasks. Cultures were plated on rich media to check for contamination. Once cyanobacteria were exposed to coculture media (CoBBG-11 or CoYBG-11) no subsequent subcultures were made to avoid evolution away from sucrose secretion. To prepare precultures for S. elongatus, S. elongatus cultures at exponentially growing phase were centrifuged and washed twice with BG-11 and suspended in a proper volume of coculture medium. To prepare precultures for heterotrophic strains , single colonies were picked into LB-Miller media and grown until turbid at 37 °C. Cells were diluted into the appropriate coculture media containing 2% sucrose to acclimate the cells to coculture media, and maintained within log-phase growth (OD600 < 0.70) before use in cocultures. The log-phase cultures were centrifuged and washed twice with BG-11 and suspended in a proper volume of coculture medium. Coculture inoculum was prepared from cultures growing in exponential phase (OD750 0.5) using ~2.5 × 107 of S. elongatus (0.1 OD750) and ~7.5 × 106 of heterotrophs (0.01 OD600). Experiments were carried out in batch cultures. Samples were obtained in exponential phase assuming pseudo steady state. The Synechococcus elongatus biomass concentration was analyzed by FACSCalibur flow cytometer  after adding BD Liquid Counting Beads . The absolute cell numbers in samples were determined by comparing cellular events to the counting beads events measured by the flow cytometer using the equation provided in the kit’s total dissolved solids document. For the heterotrophic strains, serial dilutions were plated on LB plates to determine cell numbers. Colony-forming units (CFU) were counted after overnight incubation at 37 °C. All heterotrophs were propagated in BG-11 (Sigma–Aldrich) using the same methods of Hays et al.8, while E. coli and B. subtilis 168 strains were maintained in LB-Miller at 37 °C and Y. lipolytica Po1g was maintained in YNB media at 25 °C as recommended by Yeastern Biotech Co. . Strains were streaked from frozen stocks on LB plates before growth in liquid media. Seven E. coli knockout strains  were obtained from the Keio collection65 in Pamela Silver’s Lab at Harvard University. Knockout experiments in rich media were performed in 24-well plates using 0.8 mL of LB + 0.2 mL of BG-11 + 0.4% glucose. Inoculums were prepared as in growth experiments and we kept same culture conditions. Cell numbers were determined using LB agar plates. Samples were collected at 0, 8, 24, 32, and 48 h. The experiment was performed in triplicates.S. elongatus were determined experimentally by performing growth assays on 180 carbon sources. Biolog plates PM1 and PM2 were obtained from BIOLOG Inc. and the manufacturer’s protocol was followed66. Starting culture density was OD750 = 0.3, culture media was standard BG11, incubated 25–27 °C. Biolog plates were run in duplicate. The plates were incubated in a light room and examined at 490 nm for dye absorbance alterations and at 750 nm to assess optical density. Intracellular metabolites of E. coli and S. elongatus were extracted by the methanol-chloroform-water extraction method. This yielded 8.39 mg and 7.46 mg of dry metabolite extract, respectively. One milligram of each extract was used for NMR (Varian Direct Drive (VNMRS) 600 MHz spectrometer, Agilent Technologies, Santa Clara, CA, USA) and GC-MS 67. Medium samples were dried and derivatized as well. 1D 1H NMR analysis was done with normal setting values for global metabolomics68. The remaining 7.39 mg and 6.46 mg were dissolved in 180 µL D2O with 0.5 mM NMR standard for NMR data acquisition.Exchange capabilities of 69. The reads were aligned to the S. elongatus genome in the NCBI database (Assembly No. GCF_000012525.1). Subread package-featureCounts (version 1.5.0-p1)70 was used to determine reads per each coding region. The aligned sequencing reads were used to determine RNA expression as reads per kilobase per million. The aligned reads were also used to determine differential gene expression using DESeq271.RNA extraction, library generation and sequencing were performed by harvesting and snap-freezing cells in liquid nitrogen in biological triplicates for each condition. Cell lysates were prepared by grinding the frozen cell pellets in liquid nitrogen with 400 µl of RLT buffer (Qiagen RNeasy kit). RNA was stabilized by the addition of 2 ml Trizol reagent (Thermo Fisher Scientific) to each 1 ml of lysate. Total RNA was extracted using the RNeasy kit (Qiagen). mRNA was enriched using the Dynabeads mRNA purification kit (Invitrogen). Sequencing libraries were generated using the KAPA RNA HyperPrep kit (Roche) and following the recommended protocol. The libraries were paired-end sequenced on an Illumina HiSeq TM 4000, using 100 bp cycle kits. The sequencing adaptors were trimmed using the trim_galore programFurther information on research design is available in the Supplementary InformationPeer Review FileReporting SummaryDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5Supplementary Data 6Supplementary Data 7Supplementary Data 8Supplementary Data 9


Manufacturing artificial living cells would open endless research possibilities in basic and applied sciences. With this motivation, many research groups are developing methodologies to construct a stable minimal cell that is capable of achieving metabolic homeostasis, reproducing, and evolving in a controlled environment. Using as a template the gene set for a minimal cell proposed previously by Gil and coworkers, we have put together a network depicting its inferred minimal metabolism needed for life. This network has been further compressed as a metabolic Directed Acyclic Graph (m-DAG) in order to better visualize its topology and to find its essential reactions . We have also compared this minimal m-DAG to those of the smallest natural genome known until now and a synthetic minimal cell created in the laboratory. The modeling of m-DAGs based on minimal metabolisms can be a first approach for the synthesis and manipulation of minimal cells.Mycoplasma mycoides JCVI-syn1.0, and of “Candidatus Nasuia deltocephalinicola”, the bacteria with the smallest natural genome known to date. The comparison of the m-DAGs derived from a theoretical, an artificial, and a natural genome denote slightly different lifestyles, with a consistent core metabolism. The MetaDAG methodology we employ uses homogeneous descriptors and identifiers from the KEGG database, so that comparisons between bacterial strains are not only easy but also suitable for many research fields. The modeling of m-DAGs based on minimal metabolisms can be the first step for the synthesis and manipulation of minimal cells.Defining the essential gene components for a system to be considered alive is a crucial step toward the synthesis of artificial life. Fifteen years ago, Gil and coworkers proposed the core of a putative minimal bacterial genome, which would provide the capability to achieve metabolic homeostasis, reproduce, and evolve to a bacterium in an ideally controlled environment. They also proposed a simplified metabolic chart capable of providing energy and basic components for a minimal living cell. For this work, we have identified the components of the minimal metabolic network based on the aforementioned studies, associated them to the KEGG database and, by applying the MetaDAG methodology, determined its Metabolic Building Blocks (MBB) and reconstructed its metabolic Directed Acyclic Graph (m-DAG). The reaction graph of this metabolic network consists of 80 compounds and 98 reactions, while its m-DAG has 36 MBBs. Additionally, we identified 12 essential reactions in the m-DAG that are critical for maintaining the connectivity of this network. In a similar manner, we reconstructed the m-DAG of JCVI-syn3.0, which is an artificially designed and manufactured viable cell whose genome arose by minimizing the one from  One of the most ambitious aspirations of modern biology is to synthesize artificial living cells. Manufacturing a cell opens endless research possibilities, both in basic and advanced sciences, and it would be critical and a turning point in fields from medicine to evolutionary biology. To reduce the levels of difficulty on this task, most efforts are focused on the synthesis of minimal cells. On the one hand, they will help by increasing our understanding of living systems; on the other hand, they can be used as capsules for the introduction of genetic material to customize cells for applied purposes . SeveralThe bottom–up approach consists of the assembly, piece by piece, of each non-living biological component  in ordehttp://www.essentialgene.org/ [The top–down approach consists of deconstructing living cells ,9. Takinene.org/ ). Comparene.org/ . In addiene.org/ ,14. The ene.org/ .There is a third approach for the construction of a minimal genome that searches for the biochemical and modular description of well-defined pathways needed to perform all essential functions . DespiteA cohesive metabolic network proposal can lead the path to the synthesis of minimal cells. A minimal cell would depend on a minimal set of anabolic pathways to convert and assemble its biomolecule building blocks with the use of the energy and nutrients available in the environment, to reach metabolic homeostasis, and to achieve cellular growth and reproduction. Nevertheless, there is scientific consensus regarding the existence of a variety of minimal metabolic schemes that are ecologically dependent and able to sustain a universal genetic machinery . The simMetabolic networks determine the physiology and biochemistry of a cell. They are made of three components: the metabolic pathways, the chemical reactions involved in the metabolism, and the regulatory interactions of these reactions. Metabolic networks tend to be highly complex, even for simple organisms. For example, if we consider the metabolism of porphyrin and chlorophyll which is present in some animals, plants, fungi, bacteria, and archaea, we get a metabolic pathway map of 135 nodes and 181 edges in the reference pathway in the KEGG database (pathway: map00860). A pathway map with so many components is very difficult to visualize, especially when we are interested in the pathway topology. To this extent, it is highly advantageous to suitably reduce the number of nodes in order to visualize the network more precisely. Alberich and coworkers (2017) designed a methodology called MetaDAG , which cFor the current work, we constructed the minimal metabolic network from the theoretical minimal gene set machinery revised in Gabaldón and coworkers (2007) , and comCa. Nasuia deltocephalinicola” str. NAS-ALF [The metabolic networks for this study were inferred from the reviewed version of the theoretical minimal genome described by Gabaldón et al. (2007) , the gen NAS-ALF  (which i NAS-ALF ), and th NAS-ALF . We firsRG = , is a directed graph with a set of nodes R that are reactions and whose edges are defined as follows: there is an edge pointing from reaction iR to reaction jR if, and only if, a metabolite produced by reaction iR is a substrate in reaction jR. The fact that it is a directed graph establishes a natural production/consumption order between two reactions—that is, what is produced by iR is then consumed by jR. Before generating the directed graph, we manually curated it to remove redundancies (enzymes encoded by orthologous genes).Using the above obtained information, which is a set of reactions for each metabolic network, we generated the corresponding reaction graph that models the relationship between reactions in terms of shared metabolites. A reaction graph, denoted by iR, jR are said to be biconnected if there is a path in each direction between them. A strongly connected component of a reaction graph is a subgraph such that every pair of reactions in it are biconnected. These strongly connected components are contracted in a single node. The reactions that are not biconnected to any other reaction become a node by themselves. Each node is called a Metabolic Building Block (MBB for short), and the MetaDAG software automatically assigns an ID to each MBB. When each MMB is contracted to a single vertex, the resulting quotient graph is a metabolic Directed Acyclic Graph (m-DAG for short). Thus, the m-DAG is defined as follows: its nodes are the MBBs obtained from the reaction graph, and there is an edge between two MBBs, MBB1 and MBB2, if there is an edge in the reaction graph from a reaction in MBB1 to a reaction in MBB2. We denote by Gm the m-DAG, thus Gm =  where N is the set of MBBs and E is the edges between them such thatIn order to analyze the reaction graph in a visually friendly manner, we used the MetaDAG methodology . In a reMBBs contracting only one reaction and whose removal disconnects the reaction graph are considered essential reactions because they are crucial to maintain the network’s connectivity.The first step toward the creation of the minimal metabolic network was to extrapolate the list of genes and enzymes belonging to the set presented by Gabaldón and coworkers (2007)  Figure  to obtaiThis methodology gave us a resulting reaction graph with some redundancies , so we manually curated this graph to include only one copy of each reaction and their corresponding metabolites needed for a functional cell. The reaction graph obtained is composed of 98 reactions and 80 metabolites . The facDespite the fact that the reaction graph of the theoretical minimal organism constructed in this work has only 98 reactions and 80 metabolites, it is difficult to visualize the detailed relationships between the reactions that make up the network’s connectivity . To solvThe m-DAG we obtained from the minimal metabolic reaction graph  has a toIn addition, essential reactions  can be easily identified using this approach , the resulting essential reactions are trustworthy in a sense that researchers might overlook an enzyme doing the same job as the one highlighted and, if they find it, it would be a new discovery not previously described for a specific metabolic pathway.In the case of a minimal metabolic network, each item included in the list of reactions and compounds is hypothetically essential for survival. When we extrapolate these results to living organisms possessing natural minimized genomes, such as pathogens or mutualist endosymbiotic bacteria, we should consider that their metabolism is a patchwork dependent on the host and, in many cases, also dependent on other bacteria with which they live in consortia. Therefore, the study of their networks’ connectivity has the potential of pointing out genes encoding critical steps that connect the different partners in a given pathway. Subsequently, the genes that encode those reactions can become targets for genetic engineering, and/or for mechanisms intended to regulate the cell metabolism; additionally, they might also have the potential to destroy the stability of the relationship, even killing the undesired organism in a parasitic relationship.Ca. Nasuia deltocephalinicola” str. NAS-ALF , while others participate closely in the same pathways , which may be useful information for genetic engineering purposes. Once again, the essential reactions are involved in the metabolism of nucleotides, phospholipids, and coenzymes, even though there are significant differences between the list of reactions included in the reconstruction of JCVI-syn3.0 and the metabolic minimal network . JCVI-syIn order to contrast the MBBs of the three m-DAGs constructed in this study, The construction of the minimal metabolic reaction graph and its consequent m-DAG presented in this work can be of great use in the field of synthetic biology. The composition of compounds and reactions that we present can easily be extrapolated to any phylogenetically diverse bacteria of interest considering that we did not focus specifically on genes. Chemistry and molecular biology technologies are also thriving. Thus, the in silico design of bacteria with the small number of metabolic genes described in this paper may be more feasible than previously thought.