C. beijerinckii and two-species communities of F. prausnitzii and B. adolescent., ACBM improved on predictions made by two previous models. Furthermore, when transcriptomic data were integrated with a metabolic model of E. coli to consider intracellular constraints in the metabolism, ACBM accurately predicted growth rate, half-rate constant, and concentration of biomass, glucose, and acidic products over time. The results also show that the framework was able to predict the metabolism changes in the early stationary compared to the log phase. Finally, ACBM was implemented to estimate starved cells under heterogeneous feeding and it was concluded that a percentage of cells are always subject to starvation in a bioreactor with high volume.The development of new methods capable of more realistic modeling of microbial communities necessitates that their results be quantitatively comparable with experimental findings. In this research, a new integrated agent and constraint based modeling framework abbreviated ACBM has been proposed that integrates agent-based and constraint-based modeling approaches. ACBM models the cell population in three-dimensional space to predict spatial and temporal dynamics and metabolic interactions. When used to simulate the batch growth of  The structured models consider the microbial cells as multi-component systems and they contain certain details of the intracellular processes. The kinetic models including detailed metabolic reaction kinetics are a well-known category of the structured models. However, kinetic modeling requires a large number of kinetic parameters which are mostly undetermined and they comprise non-linear equations that often require more complicated solution procedures1. Metabolic models are widely used structured models that can be constructed using reaction stoichiometry without considering enzyme kinetics. Assuming steady-state condition, the metabolite mass balances are applied to construct metabolic models including linear algebraic equations. Flux balance analysis (FBA) as a constraint-based metabolic modeling approach (CBM)2 calculates the fluxes of all reactions in a metabolic model while considering an objective function (e.g. maximization of growth rate). FBA does not generally apply any intracellular constraint and only extracellular constraints including uptake and secretion rates limit the predicted rates. Instead of incorporating the intracellular enzyme kinetics, an upper bound is determined for uptake rates of substrates commonly based on empirical data or if any, the substrate kinetics are used to calculate the extracellular rates using the substrate concentration. The limited understanding of intracellular constraints such as regulatory and signaling events and enzymatic kinetics does not allow for the accurate prediction using these models to expand model reliability over a wide range of environmental conditions. Over the past decade, the integration of omics data with metabolic models has been an important effort to incorporate the intracellular constraints within the metabolic models. In particular, several FBA-driven algorithms have been developed to integrate transcriptomics data into metabolic models3.A computer model is a simplified representation of a complex system (e.g. bio-populations) that provides a basis for testing and evaluation of hypotheses. Microbial cell models can be either structured or unstructured depending on whether they take into account the details of intracellular reactions and processes or not. The unstructured models such as Monod-type equations consider the cell as a black box and relate input changes to output responses using empirical data. However, they lack any information on the intracellular state and the narrow applicability range of these models makes it difficult to extrapolate the performance of biosystems, especially under perturbed conditions4. Subsequent approaches included temporal dynamics using dynamic FBA (dFBA) to simulate microbial growth5. Then, COMETS was introduced6 that incorporates spatial dynamics by integrating dFBA with diffusion on a lattice. Physical space in 2D was discretized into boxes that contained different microbial species and extracellular metabolites. The biomass and extracellular metabolite levels were updated in each time step using dFBA for each box based on the nutrients available in the environment and on the capacity of the metabolism. COMETS estimated the upper bounds of substrate uptake rates using a kinetic equation. This method is an equation-based model that describes biological processes by formulating interactions of individual biological components using a system of equations for variables in time and space. Indeed, by simulating colony growth as a two-dimensional diffusion, COMETS represents the space of the boxes continuously by assigning each box for a population of multiple cells. So it can not model each individual cell to investigate metabolic heterogeneity within a population of cells.The cell models can also be categorized to segregated or unsegregated, referring to whether they consider heterogeneity in the cell population or not. The metabolic models have mostly been applied within the unsegregated modeling framework, however, some approaches have been developed to model metabolic interactions within microbial communities. The first approach constructed a generalized metabolic model by combining the reconstructions of single microbes and considered community growth as the objective function of FBA, e.g.7 proposed a tool named MatNet for multiscale modeling of P. aeruginosa biofilm formation. The hybrid model was capable of modeling biofilm formation of a single species and qualitatively predicted the effect of oxygen limitation, nitrate addition, and gene knockout. Shashkova et al.8 used ABM and kinetic equations to model interactions between two bacterial species and between species of the gut. Their model was able to observe the emergent spatial structure and its alteration, depending on various feedback mechanisms. BacArena9 applied ABM and FBA to simulate multispecies communities and considered a two-dimensional grid to model a spatial environment. Temporal dynamics were modeled by including time steps, and the substrate uptake rate was constrained using the Michaelis-Menten kinetic equation. In comparison with COMETS as an equation-based and continuous method, BacArena models additional heterogeneity of cells by focusing on individuals using ABM, and this rule-based method improved the predicted doubling time for Clostridium beijerinckii. The predicted metabolite concentration ratio for acetate was comparable to experimental values for co-cultures of in vitro human intestinal microbiota while higher and lower ratios were calculated for butyrate and propionate, respectively.In recent years, individual-based models have been applied to consider heterogeneity in the cell population. They simulate populations and communities by following individuals and their properties, and agent-based models (ABMs) are a class of computational models for individual-based modeling. ABM models space as a heterogeneous environment in which individuals are represented as agents and move. Agents obey simple rules and ABMs consisting of dynamically interacting rule-based agents can result in different sorts of complex behavior. By incorporating ABM and CBM, Biggs and Papin10 of a cell, respectively. Thus, it can properly simulate the temporal and spatial dynamics of a cell population in different processes, such as batch and fed-batch growth. Compared to its predecessors, ACBM models microbial populations in three-dimensional space and makes predictions using mechanistic processes that more closely mimic the intra- and extracellular behaviors present in living microbes. Using substrate kinetics, ACBM was applied to simulate batch growth of C. beijerinckii and two-species communities of F. prausnitzii and B. adolescenti. Furthermore, transcriptomic data were integrated with a metabolic model of E. coli to consider intracellular constraints in the metabolism. Glucose concentration is a critical parameter for both productivity and quality in a fed-batch process of recombinant protein production. So, ACBM was used to estimate starved cells in a bioreactor with high cell density.The proposed methods were capable of identifying the microbial community structure by considering spatial and temporal multi-scale modeling approaches. Furthermore, BacArena and MatNet combined individual based modeling with FBA to consider the metabolic heterogeneity within a population of cells. Except for MatNet, the methods can model multi-species communities. However, it is still necessary to develop new methods that present results quantitatively comparable with experimental data of a bioprocess such as batch and fed-batch growth. In this research, a new integrated agent and constraint based modeling framework abbreviated ACBM Fig.  has beenC. beijerinckii in a batch culture including 10 g/l glucose and kinetic equation proposed by Bauer et al.9 was applied to calculate glucose uptake rate using glucose concentration. Figure ACBM was used to predict the growth of C. beijerinckii. Two previous approaches BacArena and COMETS predicted a doubling time of 1.1 and 0.5 h, respectively, for C. beijerinckii that is much smaller than the experimental value of 4.3 h11. So, ACBM improved the predicted growth rate while it used a metabolic model and kinetic equation for substrate uptake the same as BacArena and COMETS.The growth rate at the exponential phase equals 0.2 1/h, hence, ACBM predicts a doubling time of 3.47 h for 10. In the stationary phase, when a cell is under starvation and could not find any substrate, the extracellular constraint of lack of substrate controls the growth. So, ACBM does not apply the metabolic model and the cell moves randomly. When the cell finds substrate, it eats metabolites and ACBM applies the metabolic model to predict the growth and secretion rates. When the substrate concentration around the cell is high, overflow can occur and by-products can be produced. However, FBA does not generally apply any intracellular constraint and only extracellular constraints including uptake and secretion rates limit the predicted growth rate10. Hence, when ACBM applies FBA, the glucose uptake rate is determined using the Michaelis-Menten kinetic equation. This equation predicts the substrate uptake rate by using glucose concentration and considers a maximum glucose uptake, but FBA can not predict the overflow metabolism and the condition that glucose is abundant. So, it linearly increases the growth rate with an increase in glucose uptake rate and it can be the main reason for the overprediction of growth by ACBM when FBA is used.However, it overpredicted the growth rate that can be because of the lack of intracellular constraints. Cells are always faced with two intracellular and extracellular constraints for growth8. B. adolescentis produces acetate and F. prausnitzii metabolizes this acetate to butyrate. ACBM was implemented to simulate single- and two-species communities of F. prausnitzii and B. adolescentis  while the produced butyrate in the co-culture increased more than four times. It shows that in the co-culture, F. prausnitzii has been able to synthesize butyrate by consuming acetate. The experimental results of Rios-Covian et al.12 also show the enhanced formation of butyrate by F. prausnitzii (two to four times) in the presence of the bifidobacteria compared to the F. prausnitzii monocultures. Simulation results reveal that B. adolescentis produces about 4 g/l acetate in the monocultures, which it reduces to 1.1 g/l in the co-culture.Cross-feeding is an important metabolic interaction mechanism especially between bacteria inhabiting the human intestine such as Bifidobacterium and Faecalibacterium generatis Fig. . F. prauE. coli MG1655 were integrated with the metabolic model iJO1366 reconstructed for E. coli MG1655 using TRFBA to incorporate the intracellular constraints. Figure 13. Glucose is depleted at about 8 h that is experimentally confirmed. The predicted biomass is fully consistent with the experimental data for 6 h, but the higher concentration of biomass is observed at 8 h. The discrepancy at the end of growth can be attributed to a variety of issues such as ignorance of the toxic effect of organic acid accumulation and pH change by ACBM. The acetate concentration is negligible during 4 h of growth and then, it increases to 1.68 and 2 g/l at the end of the exponential phase based on the predicted and measured values, respectively. A 2D view of the environment during the batch cultivation is presented in supplementary file 4 as an MP4 format video file. ACBM truly predicts that a small amount of lactate is produced and succinate is not secreted during batch growth. Production of formate, a major fermentation product of E. coli14, is also predicted.Using the substrate kinetics or determining an upper bound for uptake rates of substrates does not implement the intracellular constraints and kinetic data of intracellular reactions are limited. So, transcriptomics data of aerobic growth of 13. Charbon et al.15 also reported a doubling time of 60 min for E. coli MG1655 when cells were grown in a minimal medium supplemented with glucose. At the late log phase, glucose is insufficient for all cells and exponential growth can not be sustained. Then, cells are subject to starvation, the average growth rate of the population decreases, and the variation of growth rate increases. Rahman et al.13 also mentioned that the end of the log phase is correlated with glucose depletion.Figure 10. Thus, using pathways with lower growth yield wasted glucose to the fermentation products.The proper prediction of fermentation products is because of TRFBA, which applies the intracellular constraints on the metabolism of the cell. When ACBM applies TRFBA and the transcriptomics data, the kinetic equation is not required and the extracellular constraint of the substrate concentration and the intracellular constraints applied by TRFBA predict glucose uptake rate and growth and product secretion rates. TRFBA limits the maximum rate of metabolic reactions based on the expression level of their corresponding genes so that an increase in substrate uptake rate can cause some reactions to reach their maximum rate and result in a compulsory change in metabolisms) of 2.72 µM. It demonstrates that glucose is the limiting substrate for growth. The Ks value of 3 and 6 µM were reported by Bavoil et al.16 and Nikaido and Rosenberg17, respectively, for wild-type E. coli growing on a glucose-minimal medium that is comparable with the predicted Ks.Figure E. coli central metabolic pathways at exponential (6 h) and early stationary (8 h) phases of growth were compared to specific activities of these enzymes measured by Rahman et al.13. The results show that the framework was able to predict the metabolism changes in the early stationary phase compared to the log phase. Especially, ACBM properly predicted flux reduction of glycolytic pathway and activation of the glyoxylate pathway enzymes Icl and MS at the early stationary phase. Both rates and activities of reactions catalyzed by acetate kinase and lactate dehydrogenase significantly reduced and cells declined excretion of organic acids lactate and acetate at the late log phase.Average reaction fluxes predicted by ACBM for 22 enzymes of Ratios of fluxes at the log and the early stationary were calculated and compared to the ratios for enzyme activities . As observed in Fig. Lack of control in substrate starvation is always risky for the production process and so ACBM was applied to estimate starved cells in a bioreactor. The fraction of starved cells overtime was determined under two homogeneous and heterogeneous feeding of 10 g/l glucose according to Fig. Figure In this research, a segregated and structured model was introduced to simulate microbial growth. The agent-based modeling approach was used to provide a segregated model at the multicellular level and the life cycle of cells was simulated. Glucose concentration spatially and temporally differentiates the population into separate phenotypes. In the log phase, glucose is sufficient for all cells and a homogeneous growth is observed. But at the end of this phase, the spatial concentration gradient and differential substrate availability lead to the distribution of phenotypes. Some of the microbial cells are metabolically active with different glucose uptake rates and some of them are metabolically inactive and under starvation. ACBM is also a structured model with incorporating the constraint-based modeling approach and the genome-scale metabolic models. Furthermore, transcriptomic data were integrated with a metabolic model to consider the intracellular metabolic constraints in addition to the extracellular glucose availability constraint.E. coli demonstrates that by combining an individual-based model with a metabolic model integrated with transcriptomic data, ACBM is capable of correlating the predicted fluxes with concentrations within a cell population.The improvement of predictions by the ACBM framework compared to the previous approaches can be attributed to the different formulation of ACBM. For example, the process of searching nutrients is analogous to a real biological system and using physical and morphological properties of cells for simulation improves the predictions. BacArena and COMETS model growth as a 2D diffusion while using ACBM, cells search for nutrients in a three-dimensional x, y, z environment. The appropriate prediction of concentrations for biomass, glucose and acidic products in batch culture of 18. The level of substrate limitation is crucial, especially for the fed-batch process of recombinant protein production, since it may cause undesired glucose starvation and leads to reduced cell growth and productivity and altered N-glycosylation quality19. Lack of control in substrate starvation is always risky for the production process and so ACBM was applied to estimate starved cells in a bioreactor. The results demonstrate that ACBM is a reliable tool for studying the starvation periods in sequential substrate injections of a fed-batch culture. Considering that a proper feeding strategy prevents glucose starvation, ACBM can be used to evaluate glucose concentration, periods of substrate injection, and stirring speed for different strategies. Starvation rates of high-volume bioreactor batch cultures have been neither computationally nor experimentally observed, so our predictions present an opportunity for future experimental validation.Starvation is one of the main sources of stress that induces cell death via apoptosis and necrosis in the cell20 was used for constraint-based modeling using GLPK as a solver for linear programming (LP) problems. MATLAB Control Java library 4.1.0 connects the two programming environments. To run the framework for each species, its genome-scale metabolic model was used and biomass formation was used as the objective function to be maximized by solving the LP problem using FBA or TRFBA2. A list of the used metabolic models is presented in Table The basis of framework, which was designed with the agent-based method, was constructed by object-oriented programming in Java 1.8. MATLAB 2015b and COBRA 2.05 ToolboxThe represented multi-scale model is agent-based in Java as the main platform for the implementation of ACBM, which calls MATLAB to apply a constraint-based metabolic model in each time step for predicting growth rate and uptake and secretion rates by each cell individual. Model agents are cells, metabolites and environment and each agent of the model is created as an object in Java. The framework can be applied for any environment and any kind and number of microorganisms and metabolites, and simulation of up to hundreds of species is possible by ACBM. Each agent in the model is equivalent to an object in Java and so, there is an object for each cell, metabolite, and environment. A graphical user interface (GUI) panel according to Fig. At start time (t = 0), one environment and a specific number of cells and metabolites according to their concentration in the environment are considered and then, in each time step, the number of each type of cells and metabolites are updated based on the rates predicted by the metabolic model.An environment object contains other objects (cells and metabolites) and is considered as a cube with basic properties length (x), width (y) and depth (z). The simulated environment can be part or all of an original environment. For example, it is not necessary to simulate the entire environment of a fully mixed bioreactor and simulation of a small cube indicates not only the changes inside the bioreactor but also reduces the CPU time. In this research, a small cube with a size of 1 × 0.4 × 0.4 mm was considered for simulation of batch growth in a stirred bioreactor that was completely mixed in the macro-scale. It should be mentioned that the system can be heterogeneous in millimeter-scale because of the stochastic movement of cells and metabolites.5) was considered as an object including a package of metabolites.Cells and metabolites move randomly in the environment. For implementing a random movement function, a random unit vector is first formed by generating two random angles  between 0 and 2π. Thus, the unit vector is d = . Then, this vector is multiplied by speed entered in the panel to provide velocity vector . When agitating is not used and water is stagnant, diffusion is important. But a stirred bioreactor was simulated in this research and mass transfer by convection was dominant. So, the same speed of 8000 µm/h was considered for both objects (cell and metabolites) and this speed was sufficiently enough for the objects to move quickly while experimental values of speed are much higher. Metabolites are produced or consumed by cells and their initial number is calculated based on their initial concentration. To reduce the number of metabolite objects as well as CPU time, a certain number of each metabolite . Substrate uptake rate (v) is calculated using Eq. i). In this research, a short time step (Δt = 1 min) was considered. To determine the biomass concentration, the average mass of one cell is multiplied to the number of cells and is divided by the eating volume. If the imported upper bound of uptake for each substrate in the GUI panel is less than the calculated rate by Eq. E. coli, the maximum uptake rate was determined using the glucose concentration (ΔC) and the Michaelis–Menten kinetic equation proposed by Bauer et al.9 and then, FBA was applied. For E. coli, transcriptomics data of Covert et al.21 were integrated with the metabolic model using TRFBA3 and hence, the glucose uptake rate was automatically limited by intracellular constraints. The transcriptomics data were obtained from the exponential phase of batch growth in a bioreactor and total RNA was isolated from exponentially growing cells.At the end of each time step, the number of produced cells and metabolites and consumed substrates is calculated by calling MATLAB and applying the metabolic model. To determine the number of produced cells and metabolites, the upper bound of the substrate uptake rate should first be calculated from the number of consumed metabolites as substrate. For this purpose, it is assumed that all found substrates can be consumed and the change in substrate concentration (ΔC) is specified from the number of found substrates (n) using Eq. entclass1pt{minimaentclass1pt{minimavp, vs are specific growth, product formation, and substrate uptake rates, respectively, predicted by FBA or TRFBA. Mass of produced biomass and products and consumed substrates by each cell is calculated and then, number of produced cells and metabolites and consumed substrates is determined and new objects are added to the environment and consumed objects are removed. When the total biomass of an individual reaches twice the average mass of a cell, a new cell object is born and placed at an empty space. The time steps continue until all cells die. If a cell can not find the substrate within the survive time, it dies. The flowchart of the cell process is presented in Fig. The calculated fluxes are sent from Java to MATLAB and the substrate uptake rate is bound in the metabolic model. Considering the maximization of growth rate as the objective function, the production rates of biomass and metabolites and uptake rates of substrates are calculated which are returned to Java. Then, the concentration of produced biomass and metabolites and consumed substrates is calculated in Java using Eqs. mentclass2pt{minimSupplementary file 1.Supplementary file 2.Supplementary file 3.Supplementary file 4.


E. coli, Shigella, Salmonella, and fungal genome-scale metabolic models (GSMMs). In contrast to the popular “congruence theory”, which explains the origin of genetic robustness as a byproduct of selection for environmental flexibility, we found no correlation between network robustness and the diversity of growth-supporting environments. On the contrary, our analysis indicates that amino acid synthesis rather than carbon metabolism dominates metabolic robustness.Cells show remarkable resilience against genetic and environmental perturbations. However, its evolutionary origin remains obscure. In order to leverage methods of systems biology for examining cellular robustness, a computationally accessible way of quantification is needed. Here, we present an unbiased metric of structural robustness in genome-scale metabolic models based on concepts prevalent in reliability engineering and fault analysis. The probability of failure (PoF) is defined as the (weighted) portion of all possible combinations of loss-of-function mutations that disable network functionality. It can be exactly determined if all essential reactions, synthetic lethal pairs of reactions, synthetic lethal triplets of reactions etc. are known. In theory, these minimal cut sets (MCSs) can be calculated for any network, but for large models the problem remains computationally intractable. Herein, we demonstrate that even at the genome scale only the lowest-cardinality MCSs are required to efficiently approximate the PoF with reasonable accuracy. Building on an improved theoretical understanding, we analysed the robustness of 489  Aside from biology, robustness and reliability are key design goals in many fields of engineering and particularly paramount in the development of safety-critical systems5. Thus, some of the theoretical groundwork relevant in these areas can be borrowed for a systems biology approach2.“Robustness” is a system’s intrinsic ability to maintain functionality under perturbation. Due to the generality of this definition, a consensus on an exact quantitative metric, especially in a biological context, has yet to emerge6 that provide a given function 9.Common basic reliability measures consider only the interaction of binary-state components, i.e. components that are either fully functional or fully dysfunctional. In such an analysis, a network is deemed functional if there exists at least one path from the input node(s) to the output node(s). Some early efforts to quantify structural robustness in metabolic networks follow the same principle. They correlate robustness with the number of unique, minimal pathways10, the same can be done for all possible ways of blocking these paths 11. Analogously, knowledge of these knockout combinations, termed minimal cut sets (MCSs)12, allows for computing the network’s PoF, which—in mathematical terms—is the complement of robustness13.Consistent with the characterisation of “functionality” as cell growth, “dysfunctionality” (i.e. the lack of growth) is caused by lethal combinations of reaction knockouts, which could arise via loss-of-function (LOF) mutations disabling vital enzymatic activity. Similarly to how all paths leading from input nodes to output nodes can be determined computationally13. As efficient algorithms for finding low-cardinality MCSs are available15, this allows for the examination of robustness in GSMMs.As we have shown previously, the great advantage in using the PoF as a surrogate for robustness lies in the fact that only the lowest cardinality-MCSs are sufficient to approximate it with negligible error13. Provided with a list of low-cardinality MCSs and running on a personal computer, the program is now capable of determining the PoF of a GSMM at reasonable accuracy in under a minute, whereas hours of high-performance computing time were required in the past. With the improved tool at hand we computed the PoF across a large panel of Enterobacteriaceae as well as 30 fungal species and show that their structural metabolic robustness does not correlate with their ability to thrive in nutritionally diverse environments.Here, we present fundamental improvements—both in theory and software implementation—of our PoF-calculating algorithmBox 1 List of symbolsm Number of minimal cut sets (MCSs) disabling growth in a metabolic networkmi Number of MCSs with cardinalities up to idm Cardinality up to which all MCSs have been calculated d0 Cardinality up to which all supersets of all known MCSs are considered by pof2.0fd Failure frequency at d random reaction deletions (i.e. the chance of a metabolic network not being able to grow given loss-of-function (LOF) mutations in d random reactions)d random reaction deletions computed with all MCSs up to cardinality dmF Probability of failure (PoF) dm and considering all possible unions of MCSs up to cardinality d0F, of a metabolic network with r reactions is defined as the probability that a given number of random LOF mutations disables growth . It can be expressed as the probability-weighted average of the failure frequencyd enzymes (reactions) being lethal. This givesp—describes the probability that d LOF mutations occur.The PoF, 13. In this context, an MCS is a minimal set of reaction deletions that suppresses growth12. Essential reactions, synthetic lethal pairs or synthetic lethal triplets are examples of MCSs with cardinalities one, two, or three, respectively. In the Supplementary Notes we expand on ref. 13 and show that, if all MCSs of a metabolic network are known, Eq. , but not on the number of reactions in the network. Thus, the PoF is independent of network size.Note that according to Eq. , F solelr6. Any combination of LOF mutations encompassing the essential reaction r6, one of the synthetic lethal pairs {r1, r2}, {r4, r5}, or one of the synthetic lethal triplets {r1, r3, r5}, {r2, r3, r4} is lethal. The failure frequency, fd (i.e. the probability that a given number of d LOF mutations results in cell death), is illustrated in Fig. d is dominated by single and double LOF mutations  is p + 2p2 − 7p4 + 7p5 − 2p6 = 0.11936 . For GSMMs both requirements cannot be met as the enumeration of all high-cardinality MCSs in a large network is computationally intractable and—even if it was not—the number of possible combinations would soon exceed the number of atoms in the universe. Thus, approximations are indispensable.Equation  determin15, which have the greatest impact on the PoF. Hence, F can still be reliably estimated, even when only a relatively small number of MCS are known13. This addresses the first issue. However, even if the number of included MCSs is reduced from m to m1 MCSs with dm (in this case dm = 1). The number of essential reactions, m1, times the mutation rate, p, is in fact the leading term in the sum of Eq. . For d ≤ dm = 3 all d ≥ 4. The resulting maximum error is represented by the hatched bars in the inset of Fig. iJO1366 in Fig. p = 3 × 10−3 and quickly approach zero for p < 0.5 × 10−3. Note that the sum in Eq.  PoF by computing d ≤ d0 = dm and formulated a parallelised algorithm to carry out the truncated sum. Here, we present pof2.0 that includes further algorithmic improvements and allows us to quickly evaluate d0. This has two implications: For a given number of MCSs F can be predicted more precisely and to achieve a certain accuracy the number of required MCSs can be reduced.In our previous work13. In short, we first sort the list of MCSs by cardinality. Then, for every element in the sorted list, we iterate over all MCSs that appear earlier in the list and form the respective unions with At the core of our method lies the fact that any lethal cut set must be a superset of at least one MCS. In order to estimate 16. This reduces the number of metabolites and reactions without losing information and is necessary for efficient utilisation of computational resources. Naturally, compressed networks also contain drastically fewer MCSs. pof2.0 is capable of handling linearly compressed networks, which entails a major leap in performance. The code is available at www.github.com/julibeg/PoF.Moreover, in metabolic pathway analysis, it is common practice to compress networks before analysisE. coli’s central carbon metabolism model (CCMM)17 and its GSMM iJO136618  gives an estimate of ~280 h for the previous implementation while pof2.0 took less than a second. Due to these advances, the bulk of the computational burden in estimating structural robustness now clearly lies at MCS enumeration.To assess the computational efficiency of pof2.0, we analysed its performance as a function of the number of processed MCSs for dm = 3, d0 = 10, and p = 10−4.The preceding sections established the theoretical foundation and computational feasibility of our approach to quantify structural robustness. Next, we capitalise on the reduced run-time of pof2.0 by analysing hundreds of GSMMs in order to showcase the utility of our approach and examine the nature of metabolic robustness. Unless stated otherwise, all PoF approximations reported below were calculated with E. coli we computed the PoF of iJO136618 growing on minimal medium under aerobic conditions for all its 181 single, growth-supporting carbon sources. As shown in Fig. r = −0.30, p = 3 × 10−5; Spearman: r = −0.48, p = 8 × 10−12).To explore the influence of varying carbon sources on the robustness of growth in r = −0.57, p = 5.4 × 10−16; Spearman r = −0.58, p = 1.3 × 10−16.Figure We further investigated the impact of the carbon source’s molecular composition on the PoF, which revealed a hierarchy based on chemical composition. On average, “pure” carbon sources  supported less robust growth than substrates containing either nitrogen or phosphate or both; see Supplementary Fig. F is linked to topological differences in metabolic networks.Growth on “elementally richer” substrates being more robust can be explained by higher redundancy. For instance, when growing on an amino acid, otherwise lethal mutations in ammonium transport and assimilation pathways would become irrelevant. As an example consider the 298 MCSs of cardinality 1 in the joint set of MCSs for aerobic growth on either glucose or glutamate, out of which 285 were identical for both. Only eight and five were specific to glucose and glutamate, respectively, which is reflected in a lower PoF for the latter. Three out of the eight essential reactions unique to growth on glucose are involved in ammonium transport. This illustrates how 19—remains strongly debated21. Approaches to explaining its emergence can be roughly split into three categories: congruent, adaptive and intrinsic21. Contrary to the adaptive hypothesis, which states that genetic robustness is selected for directly28, the congruent hypothesis postulates that it rather arises as a byproduct of selection for environmental resilience31. The intrinsic hypothesis, on the other hand, negates any evolutionary impact and argues that robustness is a fundamental property of complex systems and networks34. However, due to its multi-factorial nature, it is more likely that no single mechanism is responsible for the development of biological robustness. The actual origin may rather comprise a combination of the hypotheses introduced above.The evolutionary origin of genetic robustness—despite its ubiquityE. coli and Shigella35, 406 Salmonella36, as well as 30 fungal37 strains.To test the impact of the congruence mechanism , we speculated that organisms capable of growing in many different conditions  would exhibit low PoFs (robust towards LOF mutations). Accordingly, structural robustness in metabolic networks should correlate with the number of substrates enabling growth. To evaluate this idea, we calculated the PoF and counted the aerobic, growth-supporting carbon sources for GSMMs of 53 E. coli and Shigella models the PoF was calculated twice—once with regard to growth on glucose minimal medium and once for minimal medium with all growth-supporting carbon sources enabled. Being allowed to grow on all carbon sources the networks showed considerably higher robustness compared to growth on glucose alone .For the Shigella boydii Sb227. This strain showed the greatest robustness among all E. coli and Shigella models at glucose-optimal growth while ranking last when all carbon sources were enabled  to 2.95% (S. boydii CDC 3083-94) with an average of 2.87%. For Salmonella and the fungi, it was considerably lower with averages of 2.62% and 1.04%, respectively. Within the respective groups there was no correlation between F and the number of carbon sources. On the contrary, most E. coli models sat on a straight horizontal line from 167 to 186 different carbon sources with the PoF being practically identical at 2.8685%. Similarly, out of 406 Salmonella models, 213 had essentially the same Figure E. coli models with The observation that many strains have  identical PoF values, although differing substantially in carbon utilisation capability, suggests that additional carbon sources mostly only add extra uptake reactions to the network rather than increasing connectivity. For example, all E. coli’s “shared reactome”, i.e. the set of reactions present in all E. coli GSMMs. Under the investigated conditions , it was 1336/1774 = 75%. Considering only the E. coli strains with virtually equal PoF, it increased to 1447/1772 = 82%, indicating that the PoF is a good predictor for network overlap. Similarly, a pairwise comparison across all E. coli and Shigella models revealed that the difference in PoF correlates with the pairwise network dissimilarity, 1 − σi,j, of any two networks Mi and Mj , including additional vitamins and metal ions. Consequently, the growth medium was more complex for the bacterial models (containing 18 components) as opposed to the fungal models with only five components , we conclude that comparisons within groups are appropriate, but not across groups.In spite of decreased nutritional flexibility, all fungal species showed considerably larger robustness as opposed to the bacterial models discussed above. However, it appears that this observation is an artefact of the different model reconstruction procedures rather than a genuine biological effect. The fungal models’ biomass consisted of 44 components, while the bacterial biomass reactions were considerably more detailed  lie between 10−12 and 10−10 and are mostly determined by differences in the number of synthetic lethal triplets Δm3  upon random reaction deletionsE. coli, Shigella, as well as Salmonella strains) and 30 species of fungi growing on glucose minimal medium under aerobic conditions. Although the closely related E. coli and Salmonella strains, whose lineages separated 140 million years ago42, share a large fraction of their genetic material44, we found the Salmonella models to be considerably more robust. In fact, Salmonella serovars were shown to have fewer essential genes (relative to the genome size) than E. coli MG165547, which is also reflected in the corresponding metabolic models. This indicates higher redundancy and supports our in silico analysis of the respective GSMMs. However, in this work we have not undertaken any phylogenetic analyses and thus cannot discuss evolutionary trajectories that could explain these differences.Capitalising on reduced run-times for GSMMs, we were able to evaluate the PoF across 459 members of the family Enterobacteriaceae , our findings do not support a connection between nutritional flexibility and cellular robustness. In line with this result, the diversity of genetic capabilities observed in Salmonella was shown to not be indicative of strain-specific lifestyle36. Here we find that this is true not only for Enterobacteriaceae but also for fungi. Although the strain-specific portions of the pan-reactome are largely associated with altered carbon metabolism36, our analysis reveals that this does not lead to increased connectivity  upon genetic and environmental perturbations20. Due to the use of an optimisation principle, their analysis was inherently biased, while our approach is more general in the sense that it takes the complete network structure  into account52. It could be argued that robustness is most relevant in the fittest states. However, our results show that structural robustness impacts all levels of growth-optimality in a similar way  than a complete MCS of cardinality d. Hence, high-cardinality MCSs are not as relevant and can be neglected—provided d0 is sufficiently large and p is sufficiently small  can be confidently assumed to be very low.The probability of LOF mutations in a given number of reactions follows the binomial distribution, consequently depending on the total number of reactions in the model as well as the per-reaction mutation rate F, as fewer MCSs are required to give precise estimates in case of smaller mutation rates. For instance, in a network with 3000 reactions out of which 300 are essential the maximum relative error of the analytical PoF estimate from the essential reactions alone would be around 1% with p = 10−6 . However, we have demonstrated previously that PoF analyses at the level of genes and at the level of reactions yield qualitatively similar results13. Incidentally, recent advances in software for the enumeration of genetic MCSs63 allow for extending the scope of our method to the gene level. Additionally, we have shown here that the PoF is independent of the network’s size and mostly determined by the number of essential reactions . Thus, given knowledge of the essential genes64 , Eqs.  and 56 GSMMs of fungal species37 (accession IDs: MODEL16042800{00-55}) were retrieved from BioModels68. The minimal media can be found in Supplementary Table 69) was removed from the respective model. This reduced model sizes to ~1650 reactions for E. coli/ Shigella, ~1550 reactions for Salmonella, and ~1750 reactions for the fungi. Note that in terms of the PoF analysis, “consistent” and “native” models are equivalent as F is independent of the number of reactions and the set of MCSs is the same for both. However, the models were made consistent nonetheless as it is commonly considered good practice and also reduces the computational load on MCS enumeration. Additionally, the E. coli and Shigella batch was also made consistent with regard to optimal growth on glucose, removing every reaction not participating in flux patterns providing the highest possible growth rate. Thereby, model sizes were reduced to ~500 reactions. To avoid introducing any bias in the process of making the models consistent, glucose levels in the media were adjusted on a per-model basis beforehand so that all models would achieve the same growth rate. Moreover, for reasons stated below, the default upper and lower bounds on reaction fluxes were relaxed to ±10,000. The 54 E. coli and Shigella models contained ten auxotrophs, one of which was capable of growing on its supplementary medium component as sole carbon source. It was therefore removed from the dataset. Salmonella featured 27 auxotrophs, two of which were able to grow on their supplements alone and were subsequently excluded from the analysis. The supplements required by the other auxotrophs were added to their respective media and can be found in Supplementary Tables 70.Fifty-four GSMMs of 71 or JSON files and reformatted accordingly. The data was then subjected toLinear compression with an in-house Perl script. The target (i.e. biomass generation) reaction was exempt from compression.Transforming the MILP problem inferred from the compressed model into its dual form, again by an in-house Perl script.15.Solving the dual problem for MCSs with cardinalities up to To enumerate the models’ MCSs, the relevant information required was extracted from the respective SBMLp was set to 10−4 per reaction.The compressed MCSs were then used for PoF evaluation. For all models, the LOF mutation rate iJO1366 was added separately to the minimal medium . Therefore, these constraints were relaxed to ±10,000 in all models.Every carbon source available in E. coli’s CCMM17 and GSMM18, low-cardinality MCSs were enumerated up to m ≤ m compressed MCSs were extracted and evaluated for all d0 ≤ 15 (CCMM) and d0 ≤ 8 (GSMM). Additionally, the MCSs were decompressed and evaluated again in the uncompressed form with both pof2.0 and the old implementation available at https://github.com/mpgerstl/networkRobustnessToolbox. Computation was performed on an Intel® Xeon® CPU E5-2650 v3 @ 2.30 GHz, and run-times were recorded using Bash’s72 built-in time command.For 73. The implementation relies on Boost74 for calculating binomial coefficients and uses Luigi Pertoldi’s progress bar75. The code is available at www.github.com/julibeg/PoF.pof2.0 was written in C++11Further information on research design is available in the Supplementary materialReporting SummarySupplementary Data File 1Supplementary Data File 2


Meclofenamate is a nonsteroidal anti-inflammatory drug used in the treatment of mild-to-moderate pain yet poses a rare risk of hepatotoxicity through an unknown mechanism. Nonsteroidal anti-inflammatory drug (NSAID) bioactivation is a common molecular initiating event for hepatotoxicity. Thus, we hypothesized a similar mechanism for meclofenamate and leveraged computational and experimental approaches to identify and characterize its bioactivation. Analyses employing our XenoNet model indicated possible pathways to meclofenamate bioactivation into 19 reactive metabolites subsequently trapped into glutathione adducts. We describe the first reported bioactivation kinetics for meclofenamate and relative importance of those pathways using human liver microsomes. The findings validated only four of the many bioactivation pathways predicted by modeling. For experimental studies, dansyl glutathione was a critical trap for reactive quinone metabolites and provided a way to characterize adduct structures by mass spectrometry and quantitate yields during reactions. Of the four quinone adducts, we were able to characterize structures for three of them. Based on kinetics, the most efficient bioactivation pathway led to the monohydroxy para-quinone-imine followed by the dechloro-ortho-quinone-imine. Two very inefficient pathways led to the dihydroxy ortho-quinone and a likely multiply adducted quinone. When taken together, bioactivation pathways for meclofenamate accounted for approximately 13% of total metabolism. In sum, XenoNet facilitated prediction of reactive metabolite structures, whereas quantitative experimental studies provided a tractable approach to validate actual bioactivation pathways for meclofenamate. Our results provide a foundation for assessing reactive metabolite load more accurately for future comparative studies with other NSAIDs and drugs in general.Meclofenamate bioactivation may initiate hepatotoxicity, yet common risk assessment approaches are often cumbersome and inefficient and yield qualitative insights that do not scale relative bioactivation risks. We developed and applied innovative computational modeling and quantitative kinetics to identify and validate meclofenamate bioactivation pathways and relevance as a function of time and concentration. This strategy yielded novel insights on meclofenamate bioactivation and provides a tractable approach to more accurately and efficiently assess other drug bioactivations and correlate risks to toxicological outcomes.  Nonsteroidal anti-inflammatory drugs (NSAIDs) are effective in the treatment of rheumatoid arthritis and osteoarthritis, dysmenorrhea, menorrhagia, and fever , yet theTraditional bioactivation assessments for drugs involve reactions with human liver microsomes in the presence of reagents, such as cyanide or glutathione, which trap reactive metabolites . The resm), maximal metabolic rate (Vmax), and catalytic efficiency (Vmax/Km). Those kinetic constants then provide a basis for assessing the relative importance of individual and competing metabolic pathways for individual drugs and arrays of drugs. For bioactivation, we previously applied this kinetic approach to assess N-dealkylation of the antifungal drug terbinafine involving formation of a reactive allylic aldehyde trapped by dansyl hydrazine .All chemical solvents were purchased from Thermo Fisher Scientific . The following chemicals were purchased from Millipore-Sigma : substrate meclofenamic acid (meclofenamate); internal standard dansylamide; reducing agent Tris(2-carboxyethyl)phosphine hydrochloride; NADPH-regenerating system components NADP disodium salt, glucose-6-phosphate dehydrogenase, and glucose-6-phosphate, as well as dansyl cadaverine and dansyl amidoethylmercaptan. Magnesium chloride salt was purchased from Thermo Fisher Scientific. Trapping agent dansyl glutathione trifluoroacetic acid salt was purchased from Toronto Research Chemicals . Human liver microsomes pooled from 150 donors [human liver microsomes 150 (HLM150)] were purchased from Corning Gentest . Marvin 20.4 was used for drawing, displaying, and characterizing chemical structures, substructures, and reactions . Identical mixtures without addition of NADPH-regenerating system were incubated as negative controls. Aliquots were quenched by adding 2-fold volume of ice-cold methanol containing an internal standard (10 μM dansylamide) and reducing agent (5 mM Tris(2-carboxyethyl)phosphine) , the supernatant was transferred to a 96-well full-volume microplate and evaporated to dryness using an Organomation Microvap Nitrogen Evaporator System . Dried wells were then resuspended in mobile phase (20:80 water:acetonitrile + 0.1% formic acid) for high-pressure liquid chromatography coupled with UV-visible/fluorescence detection and analyzed as described in the following section. Each set of steady-state reactions was performed in triplicate and replicated three times. Initial rates were calculated and plotted against substrate concentration and then fit to the Michaelis-Menten equation, the summation of two Michaelis-Menten equations, or the Hill positive cooperativity model using GraphPad Prism 7.0 from GraphPad Software, Inc . The best-fit kinetics model and corresponding constants were determined using the extra sum-of-squares F test. In addition, we excluded kinetic mechanisms, which had open confidence intervals for best-fit values.The in vitro meclofenamate studies relied on reactions with HLM150 as a model for the average adult human liver. Microplate half-wells containing HLM150, 1 mM dansyl glutathione, and substrate in 100 mM potassium phosphate buffer, pH 7.4, with 0.1% DMSO as cosolvent were preincubated for 5 minutes at 37°C with shaking at 350 rpm using a BMG Labtech THERMOstar incubator . Control studies were initially carried out to identify suitable steady-state conditions for the final HLM150 protein concentrations and reaction times. Specific substrate concentrations were varied from 0 to 500 µM, biasing specific values to better reveal the relationship between initial rates and substrate concentration. Reactions were initiated upon addition of an NADPH-regenerating system  . The totosphine) . After 2Sample reactions were analyzed to quantitate reactive metabolite adducts by fluorescence, and then their structures were characterized by mass spectrometry. Reaction metabolites were separated by a 4.6 × 150 mm Waters XSelect HSS C18 3.5-µm column using a Shimadzu LC-20AB Prominence liquid chromatograph and detected by a Shimadzu RF-10AXL fluorescence detector or a Shimadzu SPD-10A VP UV-visible detector. Mobile phase consisted of solvents A (0.1% formic acid in 90:10 deionized water:acetonitrile) and B (0.1% formic acid in acetonitrile). The gradient method started with 89% solvent A and decreased to 67% over 3 minutes, then decreased to 56% A over 9 minutes, and then decreased again to 33% A over 5 minutes. Solvent A was increased back to 89% over 3 minutes and held for remainder of run. The total flow rate was 1 ml/min, and total run time per sample was 25 minutes. The fluorescence detector was set to emit an excitation energy of 340 nm and detect an emission energy of 525 nm to optimally detect dansyl fluorescence . The absAlthough quantitative, fluorescence response provides no structural information for adducts, and thus we analyzed dansyl glutathione–adducted metabolites by mass spectrometry to determine parent masses and fragmentation patterns for inferring purported adduct and reactive metabolite structures. Samples were injected onto an Agilent Technologic 1290 Infinity HPLC using the same chromatographic method and column as described previously. Analytes were characterized with the Agilent Technologic 6490 Triple Quad LC/MS. The electrospray ionization source was operated in negative and positive ion mode, and ion spectra were acquired in full-scan mode monitoring the mass-to-charge ratio range of 100–1200 amu. Subsequently, product ion spectra were generated from precursor ions with monitoring for fragmentation by collision-induced dissociation (30 eV) with a range of 45–1000 amu in negative ion mode.Supplemental information.Modeling of meclofenamate indicated a high likelihood for bioactivation into a reactive quinone-species metabolite from an overall model score of 0.93 . Shown in Supplemental Fig. 1).We assessed predicted bioactivations using mass-spectroscopic fragmentation approaches to characterize structures of quinone adducts trapped during meclofenamate microsomal reactions. Meclofenamate possesses an asymmetric diphenylamine motif that undergoes bioactivation into ortho- or para-quinones with a potential for dehalogenation. Parent and product ion scans were performed to identify putative adduct parent masses as well as characteristic dansyl glutathione fragments. Four fluorescent adducts were observed after meclofenamate metabolism. Several species of reactive quinone metabolites were characterized from mass-spectroscopic fragmentation: dihydroxy ortho-quinones, monohydroxy para-quinone-imines, and dechlorinated ortho-quinone-imines  and protein concentration . Higher-yield adducts formed linearly up to 60 minutes and 1 mg/ml protein concentration, whereas linearity was observed for lower-yield adducts only up to 0.25 mg/ml protein. From these results, we selected a 60-minute reaction time and 0.25 mg/ml protein for steady-state experiments. Second, the quantitation of adducted reactive metabolites depends on the independence of dansyl fluorescence from the remainder of the molecule structure. As a test, dansylamide, dansyl cadaverine, dansyl glutathione, and dansyl amidoethylmercaptan were shown to have similar fluorescence responses after normalization to dansylamide responses with slopes ranging from 0.96 for dansyl glutathione to 1.01 for dansyl cadaverine (variability < 5%) and with R2 values for quality of linear fits ranging from 0.99 for dansyl cadaverine to 1.0 for dansylamide as a function of concentration up to 25 µM  and a moderate Hill constant (Kh) for the midpoint of the curve. Kinetics for the monohydroxy para-quinone-imine conformed to the Michaelis-Menten mechanism with the second highest Vmax and the lowest Km. The similar dihydroxy ortho-quinone showed significant positive cooperativity with a moderate Vmax and weak meclofenamate binding based on its Kh. The likely multi-GSH adduct involved Michaelis-Menten kinetics for the least-efficient bioactivation pathway because of the lowest Vmax and a moderate Km. These data were then used to estimate fractional bioactivation contributions and estimate load burdens from the reactive metabolites.Characterization of adduct structures by mass spectrometry provided a strategy for correlating specific bioactivation pathways to quantify reaction kinetics using fluorescent responses from labeled, trapped meclofenamate quinones. A critical first step was the chromatographic resolution of these reactive metabolites as shown in the fluorescence chromatogram for meclofenamate metabolism . Quantitba) by calculating ratios of catalytic efficiencies for meclofenamate bioactivation and depletion for individual pathways and a combination of all possibilities  to more complex in vivo systems . This varied combination of data types may not accurately reflect what is experimentally possible with human liver microsomal reactions specifically resulting in overprediction or underprediction of putative metabolites. Knowledge of these possible shortcomings provides a path for continuing to improve model inference through larger, higher-quality data sets.Kinetic assessments are valuable in determining the mechanisms and efficiencies of reactive metabolite formations that often correlate with toxicological outcomes . AlthougMeclofenamate bioactivation involves at least two oxidative steps to generate a reactive quinone that undergoes subsequent trapping by glutathione. Despite that complexity, bioactivation kinetics may conform to a simple Michaelis-Menten mechanism when a single step dominates the kinetics for the pathway. The metabolism of meclofenamate to the monohydroxy para-quinone-imine or the suspected multiply glutathionylated metabolite reflected that outcome. Nevertheless, the kinetic profiles for the dechloro-ortho-quinone-imine and the dihydroxy ortho-quinone demonstrated positive cooperativity in which a low efficient bioactivation reaction transitions to a more efficient one. A possible explanation for these mechanisms could be reaction steps that are poorly coupled at low substrate concentrations yet improve at higher concentrations. Typically, this outcome occurs when the second reaction step is a low-affinity reaction so that intermediates accumulate until saturation of the second reaction step, resulting in coupled reactions. Alternatively, these kinetics could be indicative of multiple-substrate binding to a single enzyme, whereby binding at an initial site leads to more positive (cooperative) binding interactions for the second event. Although both mechanisms are possible, the latter cooperative one seems likely given the kinetics reported for the similarly structured NSAID diclofenac. CYP2C9 and CYP3A4 metabolism of diclofenac involves multiple-substrate binding during turnover . As a foSupplemental Fig. 5), the most efficient was that for the monohydroxy para-quinone-imine followed by the dechloro-ortho-quinone-imine. The pathways leading to the dihydroxy ortho-quinone and suspected multiply glutathionylated metabolite were very inefficient. These observations are chemically plausible given that formation of the monohydroxylated para-quinone-imine is more energetically favored than formation of either the dechloro-ortho-quinone-imine or dihydroxy ortho-quinone, as it requires one fewer metabolic step to form. The dechlorinated ortho-quinone-imine can only form after enzymatic removal of one chlorine atom, which requires an additional catalytic step. Finally, both the dihydroxylated ortho-quinone and the suspected multiply glutathionylated metabolite formed with low efficiencies because of the complex and numerous metabolic steps required to generate them. Consequently, the monohydroxy para-quinone-imine followed by the dechloro-ortho-quinone-imine are the dominant bioactivation pathways for meclofenamate, yet the relevance of those pathways will depend on variations in cytochrome P450 levels responsible for those reactions in the general population.Among all four bioactivation reactions (Knowledge of meclofenamate bioactivation provides insights on the possible cause for toxic risks. Meclofenamate is labeled as “ambiguous DILI concern” in the Food and Drug Administration DILIrank database, which is a comprehensive database of known hepatotoxicant drugs marketed or previously marketed in the United States. This classification indicates data are available on hepatotoxicity frequency, severity, and causality for meclofenamate, yet there is insufficient information for a definitive ranking on the severity of its DILI risk. Importantly, no prior reported studies exist on the mechanisms by which meclofenamate may induce hepatotoxicity. We have shown that meclofenamate is highly bioactivated into reactive quinone metabolites, which may deplete hepatocellular ATP and induce changes in the mitochondrial permeability transition, thereby causing hepatoxicity, as previously discussed by Herein, we demonstrated that computational models predicted many possible meclofenamate bioactivations and metabolites, but establishing relevant pathways required novel and quantitative kinetic experiments. Computational modeling rapidly yielded predictions for metabolism and bioactivation without limitations on the feasibility of experimental investigations. The reliability of model predictions may not be clear, yet outputs were useful in facilitating analysis of experimental data. Gaps in correlations indicated areas in which models can be improved to better realize the potential in improving the efficiency of these types of studies. Moreover, our experimental studies demonstrated the first practical application of dansyl glutathione to directly quantify adducts based off fluorescent response and assess bioactivation kinetics. Steady-state kinetics studies revealed which bioactivations occur, their fractional contributions to overall metabolism, and hence their potential to cause toxicity. The combined modeling strategy in this study facilitated the prediction of reactive metabolite structures, whereas data generated from this study provided a tractable strategy to assess reactive metabolite load more accurately for future comparative studies with other NSAIDs and drugs in general. In fact, several well used and structurally similar drugs are marketed on or withdrawn from the United States market that may reflect contributions from bioactivation pathways . Our cur


E. coli  and pentose phosphate-TCA) that each require different regulation schemes. It is shown quantitatively that hexokinase, glucose 6-phosphate dehydrogenase and glyceraldehyde phosphate dehydrogenase, all branch points of pathways, play the largest roles in regulating central metabolism.Experimental measurements or computational model predictions of the post-translational regulation of enzymes needed in a metabolic pathway is a difficult problem. Consequently, regulation is mostly known only for well-studied reactions of central metabolism in various model organisms. In this study, we use two approaches to predict enzyme regulation policies and investigate the hypothesis that regulation is driven by the need to maintain the solvent capacity in the cell. The first predictive method uses a statistical thermodynamics and metabolic control theory framework while the second method is performed using a hybrid optimization–reinforcement learning approach. Efficient regulation schemes were learned from experimental data that either agree with theoretical calculations or result in a higher cell fitness using maximum useful work as a metric. As previously hypothesized, regulation is herein shown to control the concentrations of both immediate and downstream product concentrations at physiological levels. Model predictions provide the following two novel general principles: (1) the regulation itself causes the reactions to be much further from equilibrium instead of the common assumption that highly non-equilibrium reactions are the targets for regulation; and (2) the minimal regulation needed to maintain metabolite levels at physiological concentrations maximizes the free energy dissipation rate instead of preserving a specific energy charge. The resulting energy dissipation rate is an emergent property of regulation which may be represented by a high value of the adenylate energy charge. In addition, the predictions demonstrate that the amount of regulation needed can be minimized if it is applied at the beginning or branch point of a pathway, in agreement with common notions. The approach is demonstrated for three pathways in the central metabolism of  It was proposed that the role of regulation of enzyme activities is to maintain values of the energy charge between 0.75 and 0.90. There are many known exceptions where the adenylate charge falls below 0.75 yet the cells remain viable ,47. Thisbet hedging strategies, cooperators, cheaters, non-cooperators, altruistic cells, etc., are commonly used in the literature. An unintended consequence of the application of these terms to cells has been that the anthropomorphic language frames and limits our thinking.There is a nuanced but very important distinction between the concepts of whether the purpose of regulation is to literally maintain an energy charge or whether the energy charge measurement is an emergent property. The former concept associates a free will to the cell in deciding its fate—if the cell finds that the energy charge is getting to low for demand, it cranks up the supply from energy generating pathways to alleviate this. The role of thermodynamics is replaced by choice. The consequence of assigning free will to individual cells has led to the application of social theory and game theory to cells. The terms On the other hand, viewing the energy charge as an emergent property assigns no such choice to the cell. Instead, the energy state of the cell is a function of the external nutrients and environment. If an isolated cell is in an energy-rich environment, the energy charge will be high. Otherwise, the energy charge drops and turning up the energy generating pathways has no beneficial effect . For tissues and other communities of cells, the energy state of the community is the important criterion, and specific individual cells may be programmed off or on despite favourable thermodynamics at the individual level.The increased application of physical concepts is transforming biology into a quantitative, physical science based less on pure observation and increasingly on fundamental principles. The model-based predictions of enzyme activities presented in this paper advance both the practice and theory of biology. The ability to predict from simulation or infer the free energy changes and control coefficients (in addition to fluxes) for each reaction allows the use of control theory and machine learning to analyse and explore the operations of the cell. In synthetic biology, the development of cell lines often requires additional circuits and can result in unforeseen consequences or lower cell growth rates. Simulation of cells with engineered or deleted circuits will allow prediction of the effects in place of difficult trial and error in experiments.Finally, it is important to understand the principles behind post-translational regulation because regulation of metabolism is precisely what controls a cell’s energetic behaviour. From bacterial growth and reproduction, to developing cells or even halting the growth of cancer cells, regulation plays the central role. Learning how cells regulate and control themselves is essential for designing new organisms that have an intended purpose (synthetic biology), developing new strategies to target and control microbial and metabolic diseases (medicine) and understanding design principles of biology . Currently, no other experimental or computational approach has been shown to identify points of regulation in metabolism in a rapid manner.4.4.1.A, B, C, D represents the molecular species, the concentrations are given by ni, i = {A, B, C, D}, and νi,j represent the unsigned stoichiometric coefficients for each molecular species i in the forward and reverse reactions j = {1, − 1}.For a reversible chemical reaction, the reaction is described by the chemical equationJnet,1, of the reaction where the forward and reverse rates are proportional to the respective reactantsk1 and k−1 represent the rate constants of the forward and the reverse reaction, respectively. On the other hand, the thermodynamic expression of the reaction uses the change in free energy, G, with respect to the extent of a reaction, ξ. The ratio of the respective reactants and products are combined to form the reaction affinity, A1 = −∂G/∂ξ1, such that,K1 = k1/k−1 is the equilibrium constant and Q1 is the reaction quotient. Also, the analogous equation for the reverse reaction is the reciprocal,K1 and K−1 are the equilibrium constants and Q1 and Q−1 are the reaction quotients for reaction 1 and −1, respectively. Equation  species such that MV ≤ Z. The vector of counts n can be split into subvectors SV is an MV by Z matrix and SB is MB by Z. The time dependence of each of the chemical species is given bynV satisfyingMB boundary conditions. The optimization is carried out with a nonlinear least-squares approach using the Levenberg–Marquardt method . In an n-step algorithm, the value function is meant to predict the discounted reward, rt:t+n, for n future steps. The n-step reward experienced by the agent is defined as rt : t+n = rt + γrt+1 + · · · + γn−1rt+n−1 + γnV(st+n), where γ ∈  is the discount factor. Each reward, rt = R, represents the feedback from moving into state st from st−1 after taking some action a. The first n steps represent the rewards experienced, while the term V(st+n) represents the future rewards. Once a terminal state is less than n steps away, the n-step reward is truncated to the appropriate length.Learning is conducted by iteratively updating the current policy function, lgorithm  to perfoε-greedy policy, which is defined as:ξ is a uniform random number between 0.0 and 1.0. As the value function is better estimated, the policy determines reactions to regulate that lead to the greatest cumulative reward. Exploration is imposed by randomly choosing reactions to regulate, allowing the policy to escape local minima. As the agent learns, ɛ is slowly annealed to reduce exploration and fluctuations in the value function. During each training episode, we begin at the state s = {1.0, …, 1.0}, such that all enzyme activities are unregulated. Trajectories through state space are stopped when the stopping criteria L = 0.0 is satisfied. This condition requires that all reactions have cost function values at or below zero before the RL ends and the predictions are in calibre with the experimental values.Learning the value function implicitly improves the policy. The relationship between the value of a state and the policy is given by an n-step reward, [V(st) − rt : t+n]2. The code implementing this framework is available in the electronic supplementary material.Finally, the state value function is estimated by using a neural network implemented in PyTorch  with a s4.4.lr ∈ {10−4, 10−5, 10−6}. Each algorithm learned and generated data using an ε-greedy policy with initial ε = 0.5 or 0.2 depending on the size of the pathway. ε was annealed by dividing by a factor of two every 25 learning episodes.Prediction of network regulation was performed using a trained neural network to estimate the value function. Network weights were adjusted using stochastic gradient descent with a learning rate, n ∈ {2, 4, …, 12} and each learning rate. The resulting average of 10 RL runs for the glycolysis–PPP–TCA pathway  show the mean reward for the 350 training episodes. Optimal regulation is prescribed by analysing the agent with the largest cumulative reward averaged over the last 50 terminal states.For each pathway, 10 agents are trained for each different value of 4.5.l-glutamine:2-oxoglutarate amidotransferase (GOGAT) reaction. The largest model consisted of 47 metabolites, of which 20 were fixed boundary species and 27 were allowed to vary. The number of variable metabolites (27) was less than the number of reactions (29) due to one cycle of eight reactions but only seven intermediate species, and also because the GOGAT reaction, which maintains a defined number of species in the TCA cycle, had two fixed species (glutamate and glutamine) and shared a variable species with the TCA cycle (2-oxoglutarate). Without the GOGAT reaction, the concentrations of metabolites in the TCA cycle could have a range of values as long as they maintain consistent values in forward and backward thermodynamic odds KQ−1 solutions of equation .The three metabolic models consisted of either the 10 reactions in gluconeogenesis or the 28 reactions of glycolysis, the PPP, the TCA cycle and the NADH-dependent equation . The fixi = 0.15.Standard free energies of formation of metabolites in aqueous solution as well as equilibrium constants were determined using the eQuilibrator software, version 0.1.8,  using pH4.6.E. coli studies by Bennett et al. [et al. [E. coli cells were grown in isotope-labelled media and then extracted in organic solvent containing unlabelled internal standards in known concentrations. Metabolites were extracted in cold solvent and analysed using chromatography-MS, and concentrations relative to the known standard concentrations were obtained using peak ratios of the labelled samples to unlabelled standards.The metabolomics data used in this study were from t et al.  and Park [et al. . BrieflyIf no experimental data are available, the analysis is carried out using estimates of metabolite concentrations . For this purpose, we use an estimate of 1.0 mM for each metabolite that is variable. For fixed metabolites that form the boundary conditions, specific values are required that induce appropriate non-equilibrium boundary conditions.Standard free energies of reaction were calculated using eQuilibrator and the eQuilibrator API . eQuilib


The accumulation of petroleum hydrocarbons in the environment substantially endangers terrestrial and aquatic ecosystems. Many microbial strains have been recognized to utilize aliphatic and aromatic hydrocarbons under aerobic conditions. Nevertheless, most of these pollutants are transferred by natural processes, including rain, into the underground anaerobic zones where their degradation is much more problematic. In oxic zones, anaerobic microenvironments can be formed as a consequence of the intensive respiratory activities of (facultative) aerobic microbes. Even though aerobic bioremediation has been well-characterized over the past few decades, ample research is yet to be done in the field of anaerobic hydrocarbon biodegradation. With the emergence of high-throughput techniques, known as omics , the individual biodegraders, hydrocarbon-degrading microbial communities and metabolic pathways, interactions can be described at a contaminated site. Omics approaches provide the opportunity to examine single microorganisms or microbial communities at the system level and elucidate the metabolic networks, interspecies interactions during hydrocarbon mineralization. Metatranscriptomics and metaproteomics, for example, can shed light on the active genes and proteins and functional importance of the less abundant species. Moreover, novel unculturable hydrocarbon-degrading strains and enzymes can be discovered and fit into the metabolic networks of the community. Our objective is to review the anaerobic hydrocarbon biodegradation processes, the most important hydrocarbon degraders and their diverse metabolic pathways, including the use of various terminal electron acceptors and various electron transfer processes. The review primarily focuses on the achievements obtained by the current high-throughput (multi-omics) techniques which opened new perspectives in understanding the processes at the system level including the metabolic routes of individual strains, metabolic/electric interaction of the members of microbial communities. Based on the multi-omics techniques, novel metabolic blocks can be designed and used for the construction of microbial strains/consortia for efficient removal of hydrocarbons in anaerobic zones. Various hydrocarbon (HC) compounds, derived from crude oil , are the most abundant hazardous organic wastes which are mostly released during the extraction processes, drilling of wells, transportation and unsuitable storage of oil, even in the immediate vicinity of filling stations . UsuallyIn an ecosystem, microbes have well-known roles in the conversion of hydrocarbons. Their extensive metabolic activity makes the inexpensive and efficient cleanup of contaminated sites possible. The organic pollutant is commonly utilized as an energy and nutrient source in metabolic processes. Bioconversion of contaminants can take place in either aerobic or anaerobic environments .By the end of the 20th century, in many remediation technologies, pure microbial cultures or simple consortia isolated by classical isolation methods have been applied for removal of contaminants, such as hydrocarbons . HoweverIt is well-known that many properties of conventionally isolated microorganisms in their original environment might be overlooked, which may be owing to the targeted isolation methods. On the other hand, an isolated microbe as monoculture might be inefficient degrader in the lab since its essential synergistic partners were removed during the isolation process . TherefoAdvanced molecular technologies allow us to disclose metabolic functions, routes, interactions and networks; therefore, their application in biodegradation might revolutionize the bioremediation technologies .Aerobic biodegradation of aliphatic and aromatic compounds (mono- and polycyclic) has been prominent and documented in several studies . The micIt is common knowledge that several microorganisms can utilize aromatic and aliphatic hydrocarbons for their growth under anoxic conditions. This topic was reviewed several times in the last decade . The ideWith the help of genomics, transcriptomics and proteomics, a deeper understanding of hydrocarbon biodegradation in pure cultures can be achieved. Additionally, metabolomics can elucidate the metabolites present during hydrocarbon biodegradation in pure cultures or consortia. However, culture-dependent methods have severe limitations when it comes to the investigation of microbial communities. Most of the microorganisms are difficult or even impossible to culture under laboratory conditions. Thus, their functions cannot be fully resolved by classical, standard approaches. The constant development of high throughput data generation and assessment has opened new frontiers in the research of hydrocarbon biodegradation. For examination of entire hydrocarbon-degrading communities, “meta-omics” approaches, including metagenomics, metatranscriptomics, metaproteomics, have been developed.In the next chapters, the current knowledge about anaerobic hydrocarbon-degrading microorganisms, metabolic pathways, microbial interactions in the multi-omics era is overviewed.The classical culture-based microbiological, molecular biological and biochemical methods have several limitations, including the problems regarding the unculturable microbes or studying a single microbe or a community at the system level. Powerful techniques of the multi-omics era overcome the problems of conventional biochemical and microbiological methods to provide a system-wide picture of the capabilities, molecular mechanisms and interactions of the cells and consortia during hydrocarbon mineralization. Most of the pollutants are composed of various hydrocarbons; their bioconversions require various metabolic pathways usually present in distinct microbes. Therefore, complex contaminations can only be eliminated by the concerted action of diverse microbial communities. Understanding such complicated systems needs high throughput approaches enabling to study the processes at the system level. In this chapter, we present a brief overview of the widespread branches of the omics. Geosporobacter ferrireducens IRF9 identified multiple anaerobic hydrocarbon activating genes  harbored by the strain . The assembled genomes provide a blueprint of the organism and all the biochemical pathways it possesses. Moreover, knowledge of the full genome sequence makes taxonomic identification easier and the databases built from the genomes serve as templates in the metagenomic databases, analysis. Many genomes of anaerobic hydrocarbon biodegraders have been published . Comparae strain .Aromatoleum aromaticum EbN1 during aromatics biodegradation applying more than 50 growth conditions. They identified 20 new proteins participating in the peripheral pathway of anaerobic aromatics mineralization and tested the effect of environmental conditions such as carbon limitation or solvent toxicity on the proteome of A. aromaticum EbN1  amplicon sequencing (or targeted metagenome sequencing) and (2) whole metagenome sequencing (mWGS) or shotgun metagenome sequencing. In the case of targeted metagenome sequencing, specific genes (targets) are amplified by PCR then sequenced on second- or third-generation sequencing platforms. The most common target is the V3–V4 hypervariable region of the 16S rRNA gene, but other regions, including V1–V2, V6–V8 or even the whole sequences , are alsmcrA for methanogenic archaea  and the 6-oxocyclohex-1-ene-1-carbonyl-coenzyme A hydrolases (bamA) of anaerobic hydrocarbon degraders  read-based analysis and (2) assembly based analysis.In the first case, the reads are utilized to obtain taxonomic and functional information. Reads are aligned with the NCBI RefSeq or the NCBI nr protein database. Diversity also can be calculated from the read count. In the second case, the reads are assembled into contigs with an appropriate assembler , and indSmithella sp. and members of the Anaerolineaceae family has been published   harbored glycyl-radical enzymes catalyzing the fumarate addition pathway  depending on the chain lengths of the alkanes . These iThe biodegradation of aromatics can be divided into two subsequent pathways . In the Aromatoleum sp. strain HxN1 (assA1 and assA2), coding for the catalytic subunit of Ass, were found in various loci in the genome of D. alkenivorans AK-01 , catalyses the reaction in the periplasm of cum EbN1 . The enzcum EbN1 . The enzcum EbN1  and has cum EbN1 . EBDH ancum EbN1 .Direct carboxylation of benzene has also been reported in a few studies . HoweverbcrABCD genes, which are organized into an operon in Thauera aromatica. The enzyme cleaves ATP into ADP + Pi during the reduction process and accepts ferredoxin as an electron donor. The presence of an ATP-dependent benzoyl-CoA reductase in the hyperthermophilic archaeon Ferroglobus placidus was recently demonstrated . The function of the Bam protein was first suggested by Laempe and colleagues . This enreducens . The enz pathway . A diffemembrane . The Bammembrane  and sulfmembrane . The strmembrane .Syntrophaceae in hydrocarbon biodegradation under methanogenic conditions . ir roots .Bioaugmentation of contaminated sites sometimes leads to unexpected modification in the rhizosphere. Recently published results justify that horizontal gene transfer occurred during rhizoremediation of organic compounds . In thesG. metallireducens/G. sulfurreducens co-cultures  is a critical element of syntrophic microbial communities. IET is a mechanism wherein the syntrophic partners share electrons through mediators (Mediated Interspecies Electron Transfer or MIET) or directly (Direct Interspecies Electron Transfer or DIET). Hydrogen functions as the dominant mediator in such communities, even though formate is energetically more favorable . Apart fcultures . Quinonecultures . In the cultures . In anotcultures . Recent partners . Based o species . The finDesulfobulbaceae family, however, can bridge the distance between the electron donor and acceptor with long-distance electron transfer (LDET)  . These sr (LDET) . They har (LDET) . Althougr (LDET) . Interacr (LDET) . By partr (LDET) . This prr (LDET) .G. metallireducens or Shewanella oneidensis, capable of extracellular electron transfer  systems, such as microbial fuel cells (MFC), microbial electrolysis cells (MEC) and their sediment variants (sMFC and sMEC) . In MFCstransfer . Neverthtransfer .G. metallireducens/G. sulfurreducens co-cultures. The authors also observed different gene expression patterns between DIET and hydrogen- coupled MIET  Decontamination of anoxic environments, anaerobic treatments of aquifers, oceanic water column, wastewater and sewage sludge. Anaerobic biomineralisation of aliphatic and aromatic compounds is a promising alternative to oxic biodegradation strategies . BecauseG. metallireducens GS-15 is a toluene-degrading strain under iron-reducing conditions that was proven to be also an “electricigen.” In other words, this strain may be utilized for low-power generation ((b) Bioenergy recovery. neration . Syntropneration . Anotherneration . MFCs ha(c) The remarkable diversity of biological catalysts involved in the anaerobic metabolism of hydrocarbons offers a broader range of applications by overcoming several limiting abiotic and biotic factors. The use of isolated enzymes mitigates microbial competitiveness, limiting nutrients, etc. However, the biocatalyst approach is still costly (low yield of enzyme production), and the enzyme integrity needs to be improved .Many new insights are needed to provide improvements to anaerobic biodegradation treatments. Physicochemical characterization of the polluted sites is a critical step for the application of the most efficacious approach. However, characterization of the natural local microflora is at least as necessary. Employing multi-omics techniques, the composition of the microbial community and the metabolic interactions of the community members, as well as other organisms, such as plants, can be discovered. So, cost-effective strategies can be planned for the remediation of hydrocarbon-contaminated sites. The recovery and the characterization of potential hydrocarbon degraders (in pure and mixed cultures) are important to deepen the understanding of their metabolic pathways, for the enhancement of the bioremediation efficiency and identification of interesting functional genes. In many cases, the microbes actively participating in biodegradation can not be isolated and cultured; however, the omics techniques enable us to characterize the metabolic activities of environmental samples which can be further used as inoculum in other remediation projects.Furthermore, omics techniques allow us to study the biodegradation processes at the system level, metabolic blocks, “metabolic bricks” can be generated and used in metabolic engineering processes for the construction of targeted or multipurpose strains/microbial consortia.The horizontal gene transfer events taking place in the environment might spread these metabolic bricks to the indigenous microbes and thus increasing the lifetime of a newly introduced metabolic route in the environment.The multi-omics era provides a multitude of opportunities for the examination of individual microbes, microbial communities, their metabolism and interactions. Genomics and metagenomics characterize the metabolic potential of the microorganisms; we can identify new microbes in a community and elucidate new pathways and genes which are responsible for hydrocarbon biodegradation. Transcriptomics and metatranscriptomics can further deepen our knowledge by highlighting active pathways in a genome or metagenome under given circumstances. It can even elucidate the role of less abundant members of a microbial community, and it highlights the importance of metabolic networks between community members. Similar results are provided by proteomic and metaproteomic studies, while metabolomics will confirm the chemical reactions occurring during hydrocarbon biodegradation and anaerobic respiration. The omics approaches, alone or in combination, are powerful tools to characterize microbial communities of hydrocarbon-contaminated sites and see the whole network as one big picture. Characterization of the microbiome at polluted sites is a crucial step for the application of the most efficacious remediation approaches. Based on the data provided by omics approaches, cost-effective strategies can be planned for the remediation of hydrocarbon-contaminated sites. The recovery and characterization of potential hydrocarbon-degraders (in pure and mixed cultures) are essential to broaden our understanding of their metabolic pathways, in order to enhance bioremediation efficiency and to identify interesting functional genes. Moreover, in combination with genetic/genomic/metabolic engineering, the stability, the catalytic potential and the enzyme production yield may be increased to promote successful bioremediation strategies. Most of the contaminants are mixtures of various hazardous materials; therefore, complex metabolic activities are required for the complete elimination of these pollutants. The revolution of the new high throughput technologies enables to study the molecular events at the system level and to design synthetic microbiome for targeted challenges, to combine remediation to energy recovery and to redirect the processes from simple elimination of pollutants to production of added-value materials .KL wrote the dominant part of the draft manuscript including the chapters on omics technologies. ÁEK and ÁS contributed to the section of “Introduction,” NB and GV were involved in the section of “Electron transfer between bacterial cells during hydrocarbon biodegradation.” TK wrote the draft version of the section “Applications and prospects,” AB and KP contributed to the part of “Metabolic aspects of hydrocarbon biodegradation, KP provided input to the sections “Introduction” and “Phytomicroremediation: plant-microbe, microbe-microbe interactions,” GR contributed to the part of “Syntrophy in hydrocarbon-degrading microbial communities,” “Phytomicroremediation: plant-microbe, microbe-microbe interactions and Conclusion.” KL, GR, and KP conceptualized the manuscript. GR and KP provided critical feedback and made the final improvement of the manuscript. All authors contributed to the figures, tables, and literature search and contributed to the article and approved the submitted version.TK was employed by the company Enviroinvest Zrt. The remaining 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.