Genome-scale metabolic models are frequently used in computational biology. They offer an integrative view on the metabolic network of an organism without the need to know kinetic information in detail. However, the huge solution space which comes with the analysis of genome-scale models by using, e.g., Flux Balance Analysis (FBA) poses a problem, since it is hard to thoroughly investigate and often only an arbitrarily selected individual flux distribution is discussed as an outcome of FBA. Here, we introduce a new approach to inspect the solution space and we compare it with other approaches, namely Flux Variability Analysis (FVA) and CoPE-FBA, using several different genome-scale models of lactic acid bacteria. We examine the extent to which different types of experimental data limit the solution space and how the robustness of the system increases as a result. We find that our new approach to inspect the solution space is a good complementary method that offers additional insights into the variance of biological phenotypes and can help to prevent wrong conclusions in the analysis of FBA results. Computational modelling has become a standard approach to achieve a comprehensive understanding of metabolic networks. In the absence of detailed kinetic data and in order to represent metabolism as a whole, genome-scale models based on the stoichiometric wiring of the system are a suitable way to, e.g., determine permissible and optimal flux distributions . For thiHowever, even with all of the above described types of constraints, the solution space of an FBA problem remains large and FBA solutions are still not unique. There are various attempts to study properties of this solution space. In general, the solution space of a constraint-based model is convex , consistIn the past, different methods have been developed to go beyond FVA when inspecting the solution space. Kelk and colleagues developed a method named CoPE-FBA, which decomposes the alternative flux distributions into three topological features, namely vertices, rays and linealities  . They shOther common methods rely on sampling the solution space for the investigation of its properties. Monte-Carlo sampling of the steady-state flux distribution has been used to calculate the probability distribution of the flux values as well as the correlated reactions, revealing those sets of reactions which display a highly correlated flux . It has An inevitable consequence of having a large solution space is that many solutions denote biologically unrealistic phenotypes. For instance, the generation of internal loops in the network might result in the interconnectivity of two electron pools, or the production of energy resources such as ATP . As a reEnterococcus faecalis [glnA) of Enterococcus faecalis applying different constrains, e.g., metabolic and proteomic data [Streptococcus pyogenes [Lactococcus lactis [In this study, we investigated the solution space of different genome-scale models particularly focusing on inconsistencies between simulation and experimental results using a new strategy. With this strategy, we fix individual fluxes randomly to different values within the permissible interval given by FVA and recalculate FBA. In this way, we get a multitude of different optimal flux distributions in a computationally relatively cheap, but not exhaustive way. We used this approach to examine the effect of different experimental constraints on the solution space, to study the capabilities of the models to fit the experimental data. While Monte-Carlo methods have majorly focused on the analysis of individual/subsets of reactions , our method is designed to obtain a whole-system overview by showing the degree of sensitivity of reactions, the extent of the sensitivity/variability of such reactions, and the model behaviour at phenotype decisive branching points, by using a relatively small sample size. We also compared our findings to the results obtained using the CoPE-FBA method. The comparison was aimed at finding to what extent the results of our method are mirrored by the modules generated by CoPE-FBA. For this purpose, we used models of faecalis  and a knmic data  to tracepyogenes  and Lacts lactis  in orderE. faecalis , as welpyogenes  and L. l. lactis  were useglnA mutant, in which the flux of glutamine synthetase (R_GLNA) was set to zero. For both models, experimental data on the medium composition, as well as on uptake and release of different metabolites, namely carbohydrates, organic acids (fermentation products) and amino acids, as well as dry mass measurements were available and integrated into the models step-wise. The feasible flux interval of each reaction was determined by FVA [Initially, we used a published genome-scale metabolic model of E. faecalis  in its wd by FVA . Thus, w−6 are considered to be “variable”. All other reaction fluxes are seen as “stable”. It is also interesting to note that the majority of reactions in all models, except for wt + med + met + pro, had an interval size larger than 10−3. For each reaction showing a flux interval determined by FVA, the respective flux value was fixed to 10 different randomly selected values within the given FVA interval. We will refer to this as a “perturbation”. Then, for each of the 10 randomly fixed flux values, FVA and FBA were recalculated and the effect on the flux distribution in terms of taking an alternative optimal distribution was investigated. In addition, we were interested in the extent to which reactions show a variable flux and therefore, we will refer to reactions that change their flux value in response to a perturbation by at least 5 percent as “sensitive”, and reactions that change their flux by less than that and therefore always carry approximately the same flux value irrespective of any perturbation as “robust”. It has to be pointed out that the value of ±5% resulted in an acceptable distinction between different characteristics among models within our set-up, but this can be adjusted to a higher/lower value if necessary. Please note that the concept of “stable” and “robust” are not the same, as “stable” refers to reactions for which FVA denotes no flux variability, while “robust” refers to variable reactions with a very small flux interval. We found the width of the permissible flux to be an important indicator of the size of the solution space.Knowing the number of variable reactions and the extent of this variability is certainly important information. However, it does not easily allow insight into how variable biological phenotypes in the solution space are. To gain a comprehensive picture, we wanted to investigate how robust the steady-state flux distribution and especially the resulting conclusions are with respect to different alternate optimal flux distributions. Thus, we developed a new approach based on the FVA results: Here, fluxes which according to default parameters in FVA display a variability of flux beyond a change of 10E. faecalis, with and without the given experimental constraints. Accordingly, we first counted how many reactions in the models (wildtype and mutant) were sensitive (exhibited flux changes of more than 5 percent) after a perturbation in comparison to the original flux distribution . For FVA, we also used PySCeS-CBMPy   as determined by FVA were divided into 20 bins and the frequency of fluxes occurring in each bin was calculated A–C. MoreThe result suggests that although FVA is fundamental in the analysis of the solution space, it only captures one aspect of the solution space, which is the mere existence of alternative optimal flux values. However, it is also important to analyse the width of the permissible interval in a direct way, e.g., by the definition of sensitive reactions, which seems to be one crucial aspect when analysing the solution space.In order to study biologically relevant phenotypes and their appearance in the solution space of FBA, three different metabolic branching points were analysed using the perturbation approach. Branching points are interesting in this respect, since they represent points where alternative biological phenotypes can differ significantly. Looking only at FVA results it is possible to analyse feasible flux ranges for single reactions, but impossible to extract permissible ratios between several fluxes.First, we investigated the branching of fluxes at the level of pyruvate. In lactic acid bacteria, pyruvate can be converted to either lactate which corresponds to homolactic fermentation or to mixed acids, comprising ethanol, formate and acetate, referred to as mixed acid fermentation. This particular branching point is highly relevant for biotechnological applications .The branching point also plays an important role in determining the state of energy production in anaerobic organisms in general. As can be seen, the step-wise addition of constraints results in narrowing down the range of flux distributions. The non-constrained model (both for the wildtype and the mutant) predicts a highly variable flux distribution, ranging from absolutely homolactic to lactate-free fermentation. This finding is not surprising, since both types of fermentation can exist in lactic acid bacteria. Defining the medium helped to rule out a lactate-free fermentation from the solution space for both models. However, fully homolactic fermentation is still very frequently predicted, whereas a mix of homolactic and mixed-acid fermentation is observed experimentally. This is noteworthy, since FBA is frequently performed based on only data of the medium composition, which in this case, is clearly not sufficient for a reasonable model prediction. Only the integration of metabolic flux data, e.g., in form of uptake and production rates, as expected, fixes the amount of fermentation products so that the flux distribution profile can more accurately reflect the experimental data.However, in the model of the mutant, even the integration of the metabolic flux data still allows qualitative differences in the flux distributions . In thisThe fact that the addition of the constraints in the wildtype model resulted in the elimination of non-physiological behaviour suggested that the solution space of the constrained wildtype model is more highly limited than the one of the mutant. This is consistent with the result of the above perturbation/sensitivity analysis, revealing that less reactions in the wildtype model are sensitive to perturbations in the network , suggestIn a second example, the flux distribution at a branching point in serine metabolism is evaluated . This brFinally, we investigated a branching point in glutamine metabolism, where nitrogen groups are distributed throughout metabolism via the amino acid L-glutamine. Thus, the distribution of glutamine among different pathways was studied . Here agThe results of our perturbation approach suggest that the solution space of the wildtype model is indeed considerably smaller than that of the mutant. Thus, the wildtype model was more robust with respect to perturbations. The number of sensitive reactions in the wildtype model was less than half of that of the mutant model in the most constrained cases. This finding can be considered to be an informative indicator of the solution space. Moreover, analysing the flux distribution profiles at metabolic branching points revealed that there is no variation in response to perturbation among different FBA runs (in the three examples shown here) in the wildtype model, whereas in the mutant model, especially in the case of the pyruvate branching point, the variation resulted in qualitatively incorrect predictions, contradictory to experimental data.To validate that the wildtype model better fits the data , the production rate of the fermentation products, ethanol, formate and acetate, resulting from the perturbation analysis were compared to the experimental data for the two different models. The result showed that in the mutant model, only 2.8% of the ethanol production values, 50% of the acetate and 7.9% of the formate production values were within a ±10% interval of the measured experimental data. In the case of the wildtype, no flux distribution profile was beyond the ±10% interval of the experimental data. This was expected, as it was described above that there was no observed variation at the pyruvate branching point in the wildtype model.To find out whether the constraints on the fermentation products are the main contributor to the smaller solution space in the wildtype, the exchange reaction constraints of the four fermentation products of the mutant, namely lactate, formate, ethanol and acetate were integrated into the wildtype model. The model was then again subjected to the perturbation approach, and the result revealed that the sensitivity of the model increased to a level comparable to that of the mutant model. This suggests that the smaller solution space in the wildtype is mainly a result of the specific constraints of these four reactions. Not surprisingly, the four reactions are involved in energy metabolism and the flux ratio of these reactions determines the amount of energy that the system produces.The result indicates that the functional analysis of the solution space can be very informative when studying biologically relevant phenotypes, as the functional consequences of having large or small solution spaces can be determined.Using the above described perturbation approach seems to offer a relatively cheap  and fast way to investigate the solution space of whole-genome scale models. In the following, we compare its results to another widely used approach—CoPE-FBA. This method is a freely available open source software that guarantees access to the sources. We want to see whether the modules generated by CoPE-FBA can reflect the extent to which each model is constrained and whether they can relate to the ability of the models to reproduce biologically meaningful results.For this purpose, we analysed the quantitative impact that the constraints have on the size of the solution space by using CoPE-FBA developed by Kelk et al. This software analyses the solution space by defining modules consisting of sets of reactions with variable flux that are linearly independent. The combination of variable fluxes within these modules results in the expansion of the solution space.E. faecalis, for which we have the above described range of experimental data . We calculated the solution space of the non-constrained models and compared these to the models constrained with medium composition, metabolite flux data and/or proteome data. Here, a higher number of modules with a lower number of reactions in each would imply a smaller solution space. As can be seen in We again used the wildtype and mutant model of Comparing the result of the solution space analysis from CoPE-FBA to the perturbation procedure, it is apparent that although CoPE-FBA successfully captures the quality of reducing the solution space by applying more constraints to the system, it comes short in reflecting the extent of reduction. The perturbation analysis, as discussed above, showed that the integration of metabolic flux data results in a considerable reduction in the sensitivity both in the general term and the functional aspects of the solution space . It also revealed that the fully constrained wildtype model has a considerably more limited solution space compared to the fully constrained mutant model. Neither of the two qualities were detected by the CoPE-FBA method. It has to be mentioned that the CoPE-FBA could not be performed fully, as enumerating the number of solutions was computationally infeasible due to the large solution space of the models. We suggest that in addition to being faster, even for large models, the perturbation procedure reflects more aspects of the solution space that can be helpful to also functionally analyse the solution space.Traditionally, maximal growth is the objective function of choice when computing FBA on microbial genome-scale metabolic models. Under conditions of limiting resources/balanced growth, commonly applied for such studies, maximizing growth intrinsically implies the maximization of growth associated ATP production, and consequently, minimizing non-growth associated ATP consumption. The latter processes are included in genome-scale models in the form of a generic ATPm reaction which refers to all processes that require ATP, but do not yield biomass. Consequently, the reaction boundaries of both reactions can directly contribute to shape the solution space, as the main criteria in FBA is maximizing the growth-associated ATP production (assuming that the objective function is the biomass reaction). As a parameter, ATPm has been shown to be important for the result of FBA and has a pronounced impact on the consistency of biomass production .Due to its central importance, in several studies the ATPm has been experimentally assessed with the aim to constrain the model in a biologically relevant way ,28. The The result of the scan revealed no significant change in the size of the solution space until the ATPm value was right on the edge of the feasible state. While CoPE-FBA reported a significantly smaller solution space at this point, a closer look at the optimization process revealed that FVA failed to determine the flux interval for several reactions at this point. To make sure this is not a model-specific problem, the same procedure was performed on the mutant model, which resulted in the same kind of artefact. This suggests that when a parameter is tied to the edge of the feasible state , the optimisation process might fail to calculate the entire feasible interval, resulting in an artefact, which in this case appeared as a smaller solution space.To test whether this problem relates exclusively to ATP/energetically-involved reactions or not, the procedure was performed on lactate dehydrogenase , as well as on ribulose 5-phosphate 3-epimerase . The result revealed that the same artefact appeared in the case of both examples, although to different extents (data not shown). Consequently, we suggest that this is a universal characteristic of reactions in a constraint-based model and has to be considered when integrating experimental data into models. This is particularly important for the constraints whose values are obtained from an optimisation process such as ATPm.E. faecalis wt model [The problem of creating a numerical artefact by working at the edge of feasible solutions was discovered in the originally published version of the data integrated wt model  when usiOf course, the question is how such an adjustment that avoids the problem of working at the edge of feasibility or having an artificially small solution space influences biologically relevant results in this study or in any other computational study. Therefore, we compared the results of the originally published parametrisation of the model with an optimality tolerance of FVA set to 100%  with the one where the tolerance is set to 99.9%, as well as with the results of the slightly adjusted model version, also analysed with a tolerance of 100%, as well as 99.9%. We repeated this analysis with our new perturbation approach. The number of sensitive reactions showed a similar, but less dramatic trend  Supplem. FinallyE. faecalis or rather general to genome-scale metabolic models, the genome-scale models of S. pyogenes [L. lactis [E. faecalis. For the model of S. pyogenes, a previously published genome-scale model together with experimental data [E. faecalis, constraints were step-wise integrated into the model, comprising medium composition and metabolite uptake and production rates. Due to the absence of proteome data, two artificial sets of proteome data were generated for S. pyogenes  to observe the effect of the deactivation of model reactions on the solution space. The two artificial sets of proteome data contain 11 “absent” reactions and are integrated into the model separately. Between the two sets, one set contained the absence of 5 variable reaction and 6 stable reactions (according to the above definition), while the other contained the absence of 10 stable and only 1 variable reaction . Here again, the integration of experimental data at each step (medium composition and metabolite uptake and production rates) resulted not only in a lower number of variable but also sensitive reactions  decreased the number of sensitive reactions only by 3, the integration of the second set resulted in a decrease of 44 reactions (To further test whether the inactivation of variable reactions (which increases the proportion of stable reactions in the model) has a reproducible effect (decrease) on the number of sensitive reactions, again, artificial proteome data sets, now for the eactions . Hence, Genome-scale metabolic models are mathematically underdetermined systems with large solution spaces. The solution space comprises all the possible flux distributions that result in the optimum value of the objective function. Flux distribution profiles in any given model are highly variable, mainly due to branches and nonlinearities of the metabolic networks on the one hand, and the lack of sufficient constraints on the other hand. Thus, while satisfying the optimum value of the objective function, two possible flux distributions might be enormously different. To find out about the extent of variation at different levels, genome-scale metabolic models were subjected to perturbations, and the response of the FBA was observed accordingly. In that way, different specific optimal flux distributions became visible and were sampled. It became apparent that there are not only quantitative differences in the respective flux distributions, but also qualitative ones that impact the biological interpretation of the results.During the analysis, we were, however, also interested in the quantitative differences of sensitivity. We therefore defined a significantly changed flux value to vary more than ±5% compared to the original values. We defined fluxes that only changed to a smaller degree as “robust”. This allowed us in a straightforward manner to analyse the influence of constraints and differences in models w.r.t. the size of the permissive flux intervals. We found that the number of “sensitive” reactions—those that display values beyond ±5% deviation of their original value—is a good indicator of the size of the solution space in genome-scale models. We show that the models with lower numbers of sensitive reactions are able to fit the experimental data better and have  better predictive characteristics.The substantial variation in flux distributions obtained by FBA underlines the fact that a reported optimal flux distribution is just one out of many other optimal distributions and therefore the distribution profile that is a result of one run of FBA is arbitrary. It is therefore important that the result of a FBA flux distribution is referred to as ‘an optimal’ instead of ‘the optimal’ flux distribution.To decrease the number of biologically inconsistent results, it is vital to integrate biological constraints. In our analysis, generally the integration of proteome data was the most effective in reducing the solution space. However, metabolic flux data on exchange reactions (metabolic uptake and production rates) can also already significantly reduce the solution space (decrease in sensitivity), e.g., at branching points. The fact that the degree of reduction is really case-specific underlines the second point .The analysis of the solution space should be taken into account in any study using FBA. As the above cases demonstrate, constraints like metabolite exchange rates, which are arguably one of the more commonly used constraints, can effectively reduce the solution space such that biologically relevant results for certain questions  are achieved, but this is not the case for every model/data-set. There are different ways to investigate the solution space. In our study, sampling by perturbation was an easy and informative way to investigate the different optimal flux distributions. We suggest that the functional analysis of the solution space using our perturbation method gives an explicit account for the robustness as well as reliability of genome-scale models. This also enables us to understand which data sets and which biological phenotypes can effectively shrink the solution space and increase the predictability of models.E. faecalis mutant). Therefore, the analysis of the solution space using the perturbation procedure helped to yield more information regarding the behaviour of the network as a whole. Another difference between the method presented in this article and Monte-Carlo sampling is a far smaller sample size needed to capture the network response to different metabolic states. While Monte-Carlo sampling needs a large sample size to reveal a comprehensive overview  using the CHRR method (the most efficient Monte-Carlo method available right now ) on an intel Core i7 at 2.5 GHz as reported by Fallahi and colleagues [E. faecalis model on an Intel Core i5 2.3 GHz, 16 MB memory and HDD hard drive, when the flux distribution profiles were obtained using FBA (on MATLAB). Our method also allows the acquisition of flux distributions using FVA, which takes more time—in this case between 31 to 51 min for the same models on the same hardware setup. Comprehensive information regarding the run time of different models used in the above-mentioned study using CHRR and the perturbation process in this study, as well as the number of metabolites and reactions of each model used can be found in the However, there are alternative methods for the analysis of the solution space not investigated here, e.g., Monte-Carlo sampling. This approach is mostly used to calculate the probability distribution of individual fluxes as well as to determine correlated reaction sets which can be further used for experimental design ,14. Whiloints in ), our melleagues . In thislleagues . The perThree further aspects result from our analysis:3.Caution has to be taken if outcomes of FBA are close to the edge of the feasible solution space w.r.t. some parameter, e.g., ATP maintenance. This is at least true when applying methods that are based on FVA, as shown in Finally, it is important to note that none of the employed methods allows to distinguish very clearly between the absolute solution space of the FBA as such and the practically determined solution space as reported by the numerical methods or software. In our study, there was no qualitative difference between various optimization algorithms with respect to major trends such as the decrease in the number of sensitive reactions following the integration of constraints. However, different numerical solvers/algorithms and/or software surprisingly resulted in minor quantitative differences, e.g., in the number of sensitive reactions, or even major differences, e.g., the average number of reactions reacting to one perturbation. Therefore, in addition to reliable qualitative outcome (the trend of change), the best quantitative indicator for the size of the solution space is the number of sensitive reactions, which only shows slight differences between different algorithms/software.E. faecalis (wildtype) [glnA) of Enterococcus faecalis [S. pyogenes [L. lactis [E. faecalis model contains 709 reactions , 644 metabolites and 688 genes. The model of S. pyogenes contains 576 reactions, 558 metabolites and 481 genes. The model of L. lactis contains 754 reactions, 650 metabolites and 516 genes.The genome-scale metabolic models of ildtype)  and of afaecalis  were usefaecalis  for the faecalis  for the pyogenes  and L. l. lactis  together. lactis . To inte. lactis . The comS represents the stoichiometric matrix and v is the vector of flux distribution. Here, the maximum and minimum values of individual reactions can be obtained using FVA [f is the objective function vector and maxv and minv are the vectors of maximum and minimum allowable flux values, respectively, for each reaction. Using this characteristic of constraint-based models, the perturbation procedure we proposed is based on the idea that a change in the flux value of a reaction would result in a different combination of fluxes in the network, as shown in the The perturbation procedure was used to determine the effect of alternative optimal values taken by each reaction on the flux distribution profile of the network. Given the fact that parameters within the permissible flux interval calculated by FVA can result in the optimal value of the objective function, we wanted to find out how each point in the permissible interval affects the quantitative and qualitative flux distribution in the network. The steady-state flux distribution of a constraint-based model can be obtained by:sing FVA  by maximConsequently, the robustness of model predictions, whether they are qualitative biological phenotypes, or flux values/range for a several reactions can be examined and the overall predictability of the model can be determined.Apple.com (accessed on 14 February 2020)). To perform the perturbations, the biomass reaction was set as constraint and fixed at the intended value . Afterwards, the flux boundaries of variable reactions were determined by FVA (using CPLEX 12.8.0 [ibm.com (accessed on 27 February 2020)) as the solver) with an optimality percentage of 100% or 99% as indicated in the text. The permissible interval size for the flux of each reaction as calculated by FVA was determined and a threshold of 10−6 was applied to consider a reaction as variable. Next, for each variable reaction, 10 random values within the determined permissible interval were selected using the ‘rand’ function in MATLAB. The rand function yields a single uniformly distributed number within the given interval. The respective reaction was fixed at the given random value  and the flux distribution profile was recalculated each time using FVA. For validation purposes, the analysis was repeated and the flux distribution was obtained with FBA  in COBRLPK 4.65  on PythoLPK 4.65  and the −6 as a threshold. Afterwards, flux modules, which are the sets of variable reactions that are linearly independent, were determined. The modules were then used to analyse the solution space.A standard analysis of the solution space was performed using CoPE-FBA with CPLEX as solver . For thi


Enterococcus spp., exhibit remarkable anti-neoplastic and probiotic properties, which can aid in silver nanoparticle (AgNPs) induced reactive oxygen species (ROS)-based CRC treatment. However, the effects of AgNPs on gut microbial metabolism have not been reported thus far. In this study, a detailed systems-level understanding of ROS metabolism in Enterococcus durans (E. durans), a representative gut microbe, was gained using constraint-based modeling, wherein, the critical association between ROS and folate metabolism was established. Experimental studies involving low AgNP concentration treatment of E. durans cultures confirmed these modeling predictions . Besides, the computational studies established various metabolic pathways involving amino acids, energy metabolites, nucleotides, and SCFAs as the key players in elevating folate levels on ROS exposure. The anti-cancer potential of E. durans was also studied through MTT analysis of HCT 116 cells treated with microbial culture (AgNP treated) supernatant. A decrease in cell viability by 19% implicated the role of microbial metabolites (primarily folate) in causing cell death. The genome-scale modeling approach was then extended to extensively model CRC metabolism, as well as CRC–E. durans interactions in the context of CRC treatment, using tissue-specific metabolic models of CRC and healthy colon. These findings on further validation can facilitate the development of robust and effective cancer therapy.The onset of colorectal cancer (CRC) is often attributed to gut bacterial dysbiosis, and thus gut microbiota are highly relevant in devising treatment strategies. Certain gut microbes, like  In the state of homeostasis, the gut bacteria-derived metabolites synthesize essential nutrients and compounds7, some of which have demonstrated remarkable anti-neoplastic properties8. For instance, Enterococcal peptides obtained from clinical strains of Enterococcus genus (a representative gut microbe) exhibit anti-proliferative effects against colorectal adenocarcinoma and other cancer types9. Furthermore, Enterococcus durans was shown to produce butyrate, which is anti-inflammatory in nature and is required to maintain the integrity of intestinal epithelium10. Such studies have highlighted the relevance of gut microbes in devising effective, novel cancer treatment therapies, as in the case of nanoparticle-based CRC treatment  has been associated with various extrinsic factors such as infection, unhealthy diet, and lifestyle12, that have been captured through various in vitro and in vivo experiments. Moreover, with the advent of constraint-based modeling (CBM), genome-scale metabolic models (GSMMs) too have aimed at investigating the re-programmed metabolism for devising novel therapeutic strategies14. To illustrate, context-specific metabolic models of colon and CRC cell types have been developed to understand the aberrant metabolism in CRC, as well as deciphering drug targets and biomarkers for cancer diagnostics. For instance, one such experimental and computational study discovered the FUT9 gene as a crucial promoter of advanced stage colon cancer15. Despite these computational advances, there have been limited computational studies to understand the contribution of reactive species generation (known to exert cytotoxic effects in cancer cells) and gut microbiome secreted metabolites towards CRC metabolism and treatment. Therefore, it would be interesting to investigate and model the role of gut bacteria secreted metabolites in cancer cell killing.The transformation of a healthy colon cell into a cancerous cell type is a complex event, which disrupts cell characteristics at metabolic, signaling, and regulatory levelsE. durans. These computational findings were supported through experiments. Furthermore, the complexity and systems-level understanding of the integral metabolic interactions between gut microbe and host  was gained using tissue-specific metabolic models. These models were developed from proteomics and literature-based data sources, representing healthy colon and CRC conditions. In addition, we have reported the differences between the CRC vs. healthy colon models in terms of their biomass values and attempted at elucidating the metabolic alterations behind aberrant CRC metabolism using genome-scale metabolic modeling.Here we present a computational and experimental study that reveals the effects of AgNP-mediated reactive species generation on gut bacterial metabolism. The effects of reactive oxygen species (ROS) were extensively modeled using the GSMM of E. durans, the bacterial cultures were exposed to different AgNP concentrations  reduced µ to 0.08 ± 0.016 h−1, thereby indicating the deleterious effects of nanoparticles at higher concentrations. Thus, the lowest concentration of AgNPs (25 ppm) exhibited no major detrimental effects on microbial viability. Further, the effects of AgNPs at such low concentrations were quantified experimentally on ROS generation   Fig. . At 6th 16, as experimental studies cannot capture all the metabolic complexities simultaneously. The metabolic effects of ROS (oxidative stress) on E. durans were computationally captured for the first time in this study, wherein CBM of E. durans was used to identify metabolic consequences associated with increased generation of reactive species (ROS/RNS) within the microbial system. Genome-scale metabolic model (GSMM) of E. durans (E. durans ATCC 6056) was downloaded from virtual human metabolic (VMH)17, and an extensive manual curation of the model was performed using scientific literature to incorporate relevant reactive species reactions to generate expanded E. durans model with ROS reactions  for the original and ROS expanded models (detail in the Methods section), seven reactions- most of them associated with folate metabolism, showed heightened fluxes in the expanded ROS model. These reactions were catalyzed by: dihydrofolate reductase (EC:1.5.1.3), methenyltetrahydrofolate cyclohydrolase (EC:3.5.4.9), formate-tetrahydrofolate ligase (EC:6.3.4.3). In addition, minNorm analysis indicated that these seven reactions, in turn, influenced major metabolic pathways, i.e., amino acid/peptide metabolism, nucleotide metabolism, carbohydrate metabolism , and energy metabolism, as elucidated in Fig. Flux variability analysis (FVA)e EC:3.5..9, formaBased on the modeling predictions, the effects of ROS on folate levels were examined experimentally. Interestingly, the findings showed AgNP-induced oxidative stress also elevated both intracellular  on HCT 116 cells  treated bacterial culture supernatant exerted cytotoxic effects on cancer cells. The viability of the cancer cells treated with 9th h supernatant from nanoparticle treated cultures was reduced by 19% as compared to control  in detail.Previous studies have reported that many microbe-secreted metabolites exhibit anticancer propertiesrol Fig. . Interesrol Fig. . As micr22. The generic human metabolic network was constrained using proteomic data obtained from the Human Protein Atlas 23, as well as gene regulation data  from the literature24. The multi-omics data was then integrated using iMAT algorithm25. The data-constrained models were further conditioned to grow on a defined nutrient medium for mammalian cells, i.e., DMEM growth medium as per the experimental studies , Enoyl Coenzyme A Hydratase , and Enoyl Coenzyme A Reductase (EC:1.3.1.38) showed increased fluxes, indicating beta-oxidation of fatty acids was a metabolically pronounced phenomenon in both the CRC and CRC- ii.Fatty acid synthesis: The pathways involving reactions catalyzed by Very-Long-Chain 3-Oxoacyl Coenzyme A Synthase (EC:2.3.1.199) and Very-Long-Chain 3-Oxoacyl Coenzyme A Reductase (EC:1.1.1.330) also had increased flux values, indicative of fulfilling the metabolic requirements of cancer cells.iii.Amino acid metabolism: Tyrosine metabolic pathway displayed enhanced flux through the reaction catalyzed by 3, 4-Dihydroxymandelaldehyde:NADP + Oxidoreductase (EC:1.2.1.5).iv.Squalene and cholesterol metabolic pathways were also affected in these metabolic networks. For instance, Isopentenyl-Diphosphate D-Isomerase  which is important in squalene synthesis showed increased flux value in both models.v.The reaction catalyzed by the enzyme Deoxyuridine Phosphorylase  in nucleotide interconversion also showed increased flux.The first step in investigating the metabolic attributes differentiating healthy colon and CRC was to model the growth of the models, which is a function of the flux obtained through their biomass reactions, respectively using flux balance analysis (FBA). The flux through the biomass reaction of the CRC model was found to be higher (0.0223 mmol/g-DW/h), compared to that of the healthy colon model (0.0003 mmol/g-DW/h), thus, indicating that transformed cells grow and proliferate at relatively higher rates. This defining characteristic of CRC cells is attributed to their ability to cater to the increasing biosynthetic demands for increased proliferation, which was further explored by computing variation in fluxes of the entire metabolic network. To do so, FVA and subsequently, flux distribution ratio  analysis of colon and CRC metabolic models, as well as colon-microbe and CRC–microbe models was performed. A surge in biochemical flux was observed through different major metabolic pathways in CRC compared to the colon Fig.  and CRC-The relevance of these enzymes and related pathways in cancer cells have been discussed at great length in the E. durans (ROS exposed) model when compared to colon–E. durans:i.E. durans integrated metabolic model, steryl sulfatase  and Hydroxysteroid (17-Beta) Dehydrogenase 4  showed increased flux values.Steroid metabolism: In the CRC–ii.E. durans integration.Oxidative phosphorylation (OXPHOS): One of the crucial highlights of the CRC–microbe integrated metabolic model was increased flux through Sn-Glycerol-3-Phosphate: (Acceptor) 2-Oxidoreductase (EC:1.1.5.3) catalyzed reaction of the OXPHOS pathway. This established the importance of OXPHOS in rewired CRC metabolism when exposed to iii.Arachidonic acid metabolism: Arachidonate 5-Lipoxygenase (EC:1.13.11.34) catalyzed reaction showed increased flux value in the CRC–microbe model.The FSr analysis between the host (CRC and colon)–microbe model sets emphasized changes brought about in the fluxes of the following CRC biochemical reactions in presence of E. durans. These included the following:i.Phosphatidylinositol (PI) and inositol phosphate metabolism: The flux through various enzyme-catalyzed reactions involved in the PI pathway exhibited increased fluxes in the CRC-microbe integrated model compared to the CRC model alone. These enzymes included 1-Phosphatidylinositol-4-Phosphate 5-Kinase  and Phosphatidylinositol N-acetylglucosaminyltransferase (EC:2.4.1.198).ii.E. durans integrated model. These reactions are catalyzed by phospholipase A2 (EC:3.1.1.4).Glycerophospholipid metabolism: The reaction catalyzing the generation of 1-Palmitoylglycerophosphoinositol and 1-Arachidonoylglycerophosphoinositol showed increased fluxes in the CRC-iii.E. durans integrated model.Propanoate metabolism: 2-Hydroxybutyrate dehydrogenase , catalyzed reaction showed increased flux in the CRC–Moreover, we also compared fluxes between CRC and CRC–microbe models to identify metabolic changes specifically driven by E. durans and colon–E. durans, was to identify any affected reactions/enzymes that behaved differentially in CRC (or CRC–E. durans) models and could serve as promising new drug targets. These included:Sn-Glycerol-3-Phosphate: (Acceptor) 2-Oxidoreductase (E.C.1.1.3.21) catalyzed reaction of the OXPHOS pathway which displayed increased flux in CRC-microbe integrated model (16.67% increment) indicating that the CRC cells favor oxidative phosphorylation (OXPHOS) over glycolysis.3, 4-Dihydroxymandelaldehyde Dehydrogenase (E.C.1.2.1.5) catalyzed reactions carried increased flux in CRC and CRC–microbe metabolic models (increase by 62.5%).Catechol O-Methyltransferase  catalyzed reaction from phenylalanine metabolism in CRC–microbe model showed increased flux by 41.67%.Another important aspect of our computational studies involving FSr analysis for different sets of metabolic models, viz. CRC and colon; CRC–These novel predictions have been summarized in Table E. durans secreted metabolites can also affect CRC metabolism. In this study, gut bacteria secreted thymidine (intercellular exchange) showed increased flux in CRC–microbe model, thus acting as the point of interaction between the two models. The secretome analysis of cancer cells and its relevance in promoting/controlling the disorder has been discussed in the next section.The secreted metabolite profiles (secretome) of the host and host-microbe models were also analyzed to better understand the metabolic changes associated with CRC metabolism (in the presence and absence of gut microbe). Based upon the FSr analysis of the colon v/s CRC and colon–microbe vs. CRC–microbe models, the exchanges with FSr values falling in the defined range (0.8 > FSr > 2) were further analyzed to establish the secretome of the CRC model. The maximum fluxes for these exchanges were subsequently observed to identify the metabolites with increased secretion in cancer cells Fig. . In caseE. durans to nanoparticle exposure was examined, as AgNPs have been reported to generate intracellular oxidative stress28. in biological systems. Despite the notable antioxidant properties displayed by E. durans29, a lower concentration (25 ppm) of AgNPs resulted in an increased generation of intracellular reactive species 31. Based on these findings, it was hypothesized that increased ROS levels may impact the gut microbial metabolism and secretion profiles of metabolites, such as folate, while the latter being of major relevance in key metabolic pathways.The primary aim of this study was to uncover the role of gut microbes in nanoparticle-aided CRC management using guided computational and experimental approaches. Specifically, genome-scale metabolic modeling was utilized to substantiate the metabolic interactions between gut microbe and CRC metabolisms, which were identified through experimental analysis. Firstly, the response of ies Fig. . Further32 to analyze the systems-level effects of ROS on the metabolism of E. durans. The modeling framework assisted in establishing the critical link between folic acid metabolism and other important intermediary metabolic pathways  in the gut microbe exposed to ROS  to form 5, 10-methylene THF (MLTHF). A positive flux was generated in this reaction, implying an increased release of folate derivatives, thereby affecting folate metabolism. Similarly, an increased flux was observed in methylenetetrahydrofolate dehydrogenase (EC:1.5.1.5) catalyzed reaction that synthesizes METHF (methenyl THF) from MLTHF (derived from serine metabolism), thus associating energy (NADPH) and nucleic acid metabolism with folate metabolism34.To test this hypothesis, we used the systems biology modeling approach (COBRA toolbox)Interestingly, the novel link between folic acid derivatives and SCFA (propionate) metabolism was predicted by the model Fig. . The twoE. durans and CRC were extensively modeled to assess the role of gut microbes in disease etiology. To do so, multi-omics (proteomics and transcriptomics) data-driven metabolic models of CRC and colon were generated (refer methods section). These models were used to analyze distinct metabolic features of CRC cells often represented through rapid growth and division in tumor cells when compared to their healthy counterparts (colonocytes)35. A higher rate of cell proliferation was observed in the CRC model in terms of increased biomass flux , as compared to the healthy colon model, thus corroborating the existing literature reports36. Moreover, these tissue-specific models were also able to capture various metabolic pathways  to the transformed cell for sustaining its growth and proliferation.Moreover, the interactions between ays Fig. , responsFurther, to understand the effect of gut microbes on CRC metabolism, the host–microbe interactions were simulated by constraining the host-microbe integrated model as per the experimental conditions. These metabolic interactions can aid in deciphering the interplay between gut microbes and tumor cells, and hence be advantageous in devising novel therapeutic targets in the context of AgNP-based CRC treatment. The metabolites secreted by gut microbes also affected CRC cell viability, as a significant reduction in viability was observed in HCT 116 cells treated with supernatants obtained at the 9th h of bacterial culture growth—both control and AgNP treated cultures Fig. . Moreove37. However, owing to the limitations of GSMs, these models were unable to capture other significant cellular aspects  associated with metabolism. Nonetheless, the tissue-specific models (CRC and CRC–E. durans) effectively captured various metabolic pathways that contribute to aberrant CRC metabolism , as no decrease in flux was observed in the flux through the CRC-biomass reaction. Typically, an oncogenic transformation operates at multiple levels of signaling, metabolic, and regulatory variations, all culminating in the re-wiring of cellular metabolic pathwaysism Fig. .38. In such cases, the cells prefer to metabolize carbohydrates through glycolysis, despite having completely functional mitochondria, thus not resorting to a more efficient oxidative phosphorylation (OXPHOS) pathway. However, recent studies have shown that certain cancers (prostate and ovarian) exhibited a switch from glycolysis to OXPHOS for energy generation39. This change in energy metabolism is another prominent characteristic feature of cancer metabolism, which makes the OXPHOS pathway an effective target for cancer therapeutics. This phenomenon has not been reported in CRC-related experimental studies this far. In addition to linking carbohydrate and lipid metabolism, this enzyme also catalyzes the generation of hydrogen peroxide (H2O2), the latter resulting in increased intracellular oxidative stress40. This chronic oxidative stress in turn is conducive to the pro-inflammatory micro-environment of CRC tissues. Thus, given its significance in the OXPHOS pathway, this enzyme can serve as a novel chemotherapeutic drug target.One of the major outcomes of this study was the agreement observed between the computational predictions and literature findings for the affected pathways in CRC and CRC–microbe models. A detailed review of the same has been discussed in the Supplementary Information  facilitates the conversion of 3,4-dihydroxymandelaldehyde to 3,4-dihydroxymandelic acid (DHMA) in tyrosine metabolism. DHMA, a catechol, is a norepinephrine metabolite known to possess strong antioxidative potential43. Furthermore, this tumor-inhibiting attribute of SAM is well established in gastric and colon cancers44. In CRC–microbe model, an increase in flux through this reaction was observed (41.67%). On the other hand, high SAH serum levels inhibit SAM-dependent methyltransferases . Elevated serum concentrations of SAH have been reported in chronic diseases like cardiovascular and chronic kidney diseases45. However, the role of SAH has not been established in colon cancer yet. The reduced levels of SAM  can result in increased cancer cell proliferation and growth making COMT a promising drug target, an aspect that can motivate future experimental studies.Catechol O-methyltransferase  catalyzes the synthesis of S-Adenosyl-homocysteine (SAH) from S-Adenosyl-methionine (SAM), the latter being a major methyl donor in transmethylation reactions that can downregulate the expression of oncogenic promoters by reversing DNA hypomethylation, thereby inhibiting tumor growth46. Other metabolites partaking in fatty acid metabolism, glycolysis, sphingolipid, and amino acid metabolism also showed increased exchange fluxes in the CRC model, compared to the colon  which has a prominent role in promoting tumor growth and can act as a potential target for anticancer therapy47 also showed increased secretion in the CRC model.To better understand the anomalous behavior of CRC, the secretome profiles obtained from medium constrained models focused on the metabolites accountable for deviant cellular characteristics observed in CRC by altering the tumor micro-environment. The models were constrained as per the DMEM composition, wherein various macro- and micro-nutrients were provided as substrate inputs. Several metabolite secretions were affected in diseased conditions compared to a healthy colon. For instance, increased secretion of alpha-ketoglutarate (EX_akg), an intermediate of the tricarboxylic acid cycle, reinstated its relevance in the oxidation of fatty acids, amino acids, and glucoselon Fig. . An esse48. Pregnenolone (EX_prgnlone[e]b) and sulfites (EX_so3[e]b) which promote prostate cancer49 and ulcerative colitis, potentially leading to colon cancer50 respectively, also showed increased secretion in the integrated model. In addition to the tumor-promoting metabolite secretions, dehydroepiandrosterone sulfate (EX_dheas[e]b) a key adrenal steroid that is known to have some protective role in CRC51 also showed elevated levels in the host–microbe integrated model. Moreover, it was thymidine secreted by E. durans that acted as an important metabolite connecting the microbe metabolism with that of the host. Increased extracellular transport of thymidine from microbe to CRC could have possibly boosted the latter’s pyrimidine metabolism compared to the healthy colon, as captured and supported by the FSr analysis. Thus, all the computational predictions cumulatively emphasized the applicability of GSMMs in comprehending CRC metabolism and potential drug targets.Similarly, CRC-microbe secretome analysis also featured elevated fluxes in various metabolites secretions Fig.  like oroTo summarize, CBM effectively predicted the association between ROS and folate metabolism, which was also verified through experiments. Moreover, context-specific models of CRC and colon could accurately capture the fundamental biochemical differences between a healthy colon- and CRC-cell, further demonstrating the metabolic adaptations essential for CRC survival. The integration of CRC and gut microbe metabolic models to simulate host-microbe interactions was beneficial in understanding CRC metabolism in presence of a gut microbe. These metabolic interactions can help mimic the interplay between gut microbes and tumor cells under in vivo conditions and can be advantageous while devising novel therapeutic targets in the context of AgNP-based CRC treatment.Silver nanoparticles (AgNPs) were obtained from Sigma Aldrich . Size distribution analysis was carried out using dynamic light scattering and zeta potential was measured using Horiba Scientific Nanopartica nanoparticle analyzer (SZ-100). A scanning electron microscope was used to study NP–bacteria interaction.E. durans, a facultative aerobe, procured from MTCC (MTCC No. 3031) was used as the model organism. The bacterial culture was grown in shake flasks containing MRS broth at 37 °C, 180 rpm, in a shaker (Scigenics Orbitek). The total cell concentrations at different time points were measured through optical density (cell scatter) at 600 nm (JASCO V-630 Spectrophotometer), and a comparison with a standard plot of OD vs. cell concentration was done.The AgNPs (25–250 ppm) were dispersed in the medium using a water bath sonicator. The medium was then inoculated with the appropriate volume of the subculture (inoculum), such that the OD value at the 0th h was 0.1.52. 3′-(p-amino-phenyl) fluorescein, APF  and dihydroethidium, DHE  were used to detect hydroxyl and superoxide radicals, respectively. The samples  were incubated with the dyes (2 mM DHE at 37 °C and 5 mM APF at room temperature) for 30 min. Upon detection through a fluorescent spectrophotometer, the hydroxyl and superoxide radical concentrations were evaluated using the standards plots of hydrogen peroxide and potassium superoxide, respectively. The concentration of superoxide and hydroxyl radicals was reported in nmol/(g-cell).Intracellular ROS were measured by following the procedures from literature53. Carbinol in 0.05 M KH2PO4 which was used as the mobile phase was filtered through 0.46-micron filters before use and then sonicated in a bath sonicator for 10 min for degassing the solution. The flow rate was maintained at 0.4 mL/min.The bacterial culture was harvested every 3 h and culture volume corresponding to 10 OD was used for sample extraction. The extracted culture volume was centrifuged, and the bacterial pellet obtained was suspended in 1 ml of milli Q water. It was then sonicated (Q Sonica sonicator), at an amplitude of 70%, for a processing time of 4 min (pulse on and off time being 2 s). The sonicated sample was then placed in a water bath at 100 °C and subjected to heat for 5 min to release any folate bound to the folate binding proteins. The cell-free extract was obtained by centrifuging the sample. The supernatant was collected, filtered, and used further for folate estimation. For quantifying extracellular folate, released by the bacterial cells into the growth medium, 1 ml of culture was collected every 3 h and the filtered supernatant was used for HPLC using UFLC Shimadzu HPLC setup. C18 Hypersil column Folic acid  was used as standard (0–125 μM) in the estimation of folate in samples .54.HCT 116 (colon cancer cell line) was obtained from Dr. Bert Vogelstein, John Hopkins University, Baltimore, USA. The tumor cells were grown in Dulbecco’s Modified Eagle Media (DMEM), with 5% serum. The cells were seeded and grown in a 96-wells plate and were treated with bacterial supernatant (control and 25 ppm AgNPs), and different concentrations of synthetic folic acid. MTT cell proliferation assay was then performed to quantify cell viability on exposure to the drug after 48 h of treatmentE. durans GSMM was downloaded from the VMH database (https://vmh.uni.lu/) and expanded using ROS reactions curated from the literature.In our study, the unconstrained 55. A total of eight ROS reactions and 11 metabolites were added to the model. These ROS reactions focused on the biochemical interactions between reactive species , and amino acids56, and nucleic acids57. The resulting reconstruction (with ROS reactions) was then merged with the downloaded metabolic model, thus, formulating the ROS expanded model  to the model. rBioNet enables the user to add these reactions in a quality-controlled manner, by exempting sources of manual errorE. durans) to absolute flux values of reactions for disease model (ROS-expanded E. durans) was calculated. The range for FSr is user-defined. The reactions with FSr values in the range 0.8 > FSr > 2 were identified. These were the reactions that were considered as affected due to the addition of ROS reactions to the model. minNorm analysis was then carried out on these reactions. minNorm function in MATLAB is a tool for frequency estimation of the data vector, for a given function.FVA was then performed that provided the flux values (minimum and maximum) FSr, which is the ratio between absolute flux values of reactions for healthy model . A data matrix is constructed, wherein the primary reaction set represents reactions with a high and medium confidence level to be present in the cell type, and this data matrix is fed in the iMAT algorithm. The gap-filling was then done using MILP (mixed-integer linear programming) approach, maintaining the defined stoichiometric and thermodynamic constraints. The preliminary models once generated are further curated to satisfy the sanity checks as per COBRA toolbox standards. Further, to the healthy colon model, transport reactions were added as reported in literature58, and the biomass reaction was modified to exclude replicating precursors and include dependency on cellular folate59. However, the CRC model was retained with the biomass reaction as in Recon 3D. Additionally, both the healthy and CRC colon models were expanded to include exchange reactions for all the metabolites appearing in the extracellular compartment.Recon 3D, a human metabolic reconstruction, consisting of metabolic reactions and their corresponding enzymes/genes was used to generate the colon and CRC condition-specific tissue models. The ‘omics’ data (obtained from HPA)26 provided by the COBRA toolbox was used to integrate host and microbe models. This toolbox is primarily used for modeling microbe-microbe/host-microbe interactions, as well as personalized microbial communities.The Microbiome Modeling Toolboxα = 0.05) and Tuckey’s multiple comparison tests were carried out.All cultures and measurements were carried out in triplicates . Values have been reported as mean ± SD . One-way ANOVA (level of significance, Further information on research design is available in the Supplementary InformationSupplementary Data 1Supplementary Data 2Supplementary Data 3Reporting Summary


Experimental evidences have shown that random encounters and short-range potentials might not be sufficient to explain the high efficiency of biochemical reactions in living cells. However, while the latest in vitro studies are limited by present-day technology, agent-based simulations provide an in silico support to the outcomes hitherto obtained and shed light on behaviours not yet well understood. Our results grasp properties hard to uncover through other computational methods, such as the effect of electromagnetic potentials on glycolytic oscillations.Agent-based modelling and simulation have been effectively applied to the study of complex biological systems, especially when composed of many interacting entities. Representing biomolecules as autonomous agents allows this approach to bring out the global behaviour of biochemical processes as resulting from local molecular interactions. In this paper, we leverage the capabilities of the agent paradigm to construct an  However, interactions beyond the Debye screening length (3), carried out by the molecular cognate partners of a biochemical reaction, are not well investigated. Nonetheless, experimental evidences for the existence of collective excitations of biological macromolecules are available in the Raman and Far-infrared spectroscopic domains5. Although long-distance electrostatic interactions have been considered unlikely, electrodynamic interactions, occurring between oscillating electric dipoles, might have a long-range nature; deterministic selective forces can thus be activated at a distance when the molecules undergo coherent collective oscillations6. The existence of forces of this kind might justify the efficiency of biochemical reactions more than the sole effect of stochastic short-range interactions, which rely just on Brownian diffusion and chemical affinity. Numerical studies proved that the overall interaction potential 7.Long-distance electrodynamic interactions between two small molecules have been largely studied within the framework of quantum electrodynamics, since long-range forces can be detected among excited atoms with similar transition frequencies8. However, detecting long-range molecular recruitments in biosystems is still held back by the current technology; even these recent results, gained through Fluorescence Correlation Spectroscopy, are limited to systems where long-range interactions are built-in (by setting up a solution in which electrostatic interactions are non-screened).These phenomena have been lately analysed, theoretically and experimentally, in the interactions among lysozyme molecules and oppositely charged dyesin silico the existing theoretical models. Indeed, numerical simulations, such as those performed through Molecular Dynamics, have been already successfully carried out8, taking into account an a priori knowledge of numerous physical parameters characterising the molecular interactions under study. On the one hand, a model that considers the largest amount of empirical information allows generating a faithful representation of the biological system and provides a reliable in silico support for theoretical and experimental analyses; on the other hand, the lack of empirical data may limit the complexity of the system simulated.Computational approaches might be able to overcome some of these hurdles, allowing to test in silico the behaviour of the entities interacting in a real biological system. ABMs require instructing the agents representing the simulated molecules with minimal empirical information, letting the global behaviour of the process result from local interactions, which are generated dynamically at each step of the simulation. The system evolves due to the ability of every agent to perceive and respond to the states of its environment, which is unpredictable and populated by other agents; the agent’s perception results in performing an appropriate action (if any) able to modify the environment9. The agent-based approach allows both the environment and the molecules to be three-dimensional  of a well-studied process, the glycolysis of yeasts, to simulate the effect of the long-distance electrodynamic interactions among the biomolecules involved in the pathway. Agent-based simulations make use of autonomous systems (agents) able to interact with one another in a concurrent and asynchronous fashion; they can thus fairly faithfully replicate in silico supporting experimental studies12. With the present work, we leverage the flexibility of the agent-based modelling to construct in silico biochemical systems; this approach is intended to simulate the glycolytic process by taking into account different types of forces driving molecular interactions. We aim to abstract the core features of biochemical systems characterised by purely random molecular encounters and compare them to those where cognate partners interactions are mainly driven by deterministic long-range forces. ABMs allow us to reproduce these phenomena in a network of mutually conditioning reactions without knowing a priori all the parameters needed in a numerical simulation, which might be missing or difficult to assay experimentally.ABMs have been already successfully applied in the analysis of several biological systems and used to develop tools for in vivo and highlight possible discrepancies with the values obtained in vitro. These results would provide the basis for setting up further experimental studies.By analysing the concentration changes of the molecular species during each step of the agent-based simulation, we are able to hypothesise how long-distance interactions may quantitatively and qualitatively affect the glycolysis process. This way, we can also hint at what might be the physical phenomena underlying the related kinetic parameters if they would be assayed The construction of an ABM able to represent the molecular interactions of a metabolic pathway requires some information on the pathway itself and on the environment where it takes place. In particular, we need to know the sequence of reactions to simulate, or a subset of those relevant for our analysis, and some quantitative data, such as the initial concentrations of the species involved (as it will be better explained later in this section). In this perspective, a kinetic model can serve as a source of such data and as a reference against which to compare our results.in vitro, to directly describe the global properties of the system through a set of differential equations. Conversely, we aim to understand if kinetic data actually underlie processes related to the ability of molecules to perceive each other, even from a long distance. An ABM of molecular interactions allows not considering a priori some of these parameters and thus provides a better baseline over which carrying out our in silico study. ABMs describe molecular interactions at a local level, but they also possess compositionality, that is, the capability of recursively applying the rules characterising agents interactions to define progressively higher abstraction levels. In this way, we can hide the unnecessary details of a specific level and, at the same time, observe its global behaviour14. Considering the case of a metabolic pathway, a kinetic model treats enzymatic reactions as mathematical functions that relate the concentrations of reactants to those of products, assuming that they incorporate the role carried out by each molecular interaction. In our ABM, instead, each enzyme is represented by a dedicated agent able to perceive the environment and its cognate partners; the interactions among the molecules are thus explicit in the definition of the model. The compositionality of ABMs also makes it possible to conduct the study at an abstraction level that can be represented with a small amount of empirical data, without losing accuracy in reproducing macromolecular behaviours.We cannot completely base our study on a kinetic model, since it uses experimental parameters, often assayed Nonetheless, not all the kinetic parameters can be overlooked: in order for a modelled saturated enzyme to generate the products of the reaction, faithfully to its biological counterpart, it must wait for a time interval corresponding to the reciprocal of its 15. However, by considering the enzymatic reactions as just mathematical functions from reactants to products, they mostly focus on changes in metabolite concentrations and do not provide the actual number of enzyme molecules in the simulated environment. In contrast, for the reasons explained above, this information is fundamental for constructing our ABM. Based on this requirement, we identified in the “Smallbone2013 - Iteration 18”16 a model particularly suitable to serve as a source for the ABM, since it contains a complete set of experimental data on the isoenzymes involved in a well-studied metabolic process, the glycolysis of Saccharomyces cerevisiae. The Smallbone2013 model provides a detailed description of the chain of reactions that generates energy from glucose by breaking it into two molecules of pyruvate. In addition to the main branch of glycolysis, it includes the glycerol, glycogen and trehalose branches and also considers the alcoholic fermentation steps, which lead to the formation of ethanol  file filled with experimental data18. Therefore, its main function is to translate the kinetic representation of the metabolic reactions into our agent-based model. To do this, for every reaction in the SBML model, it gets the reactants and products, and generates XML code for each of its interactions. It also associates, to each modelled molecule and reaction, the physical and kinetic parameters needed to set up the simulation; for the study proposed in this paper, they are limited to the molecular weights  and the turnover numbers. Our agent-based simulator can also deal with a higher level of detail, obtained by forcing an enzyme to form a complex with an encountered cognate metabolite on the basis of a priority list constructed over the A dedicated module of the simulator converts the SBML model to an XML (Extensible Markup Language) file specifically formatted to be interpreted by the simulator itself but also to be human-readableadenylate kinase, ATPase, and UDP to UTP reactions and glucose transport (between the extracellular environment and the cytosol). The most significant of these reactions is the adenylate kinase, since it controls the ratio of ATP, ADP and AMP , which in turn affects the allosteric regulation of important enzymes, such as phosphofructokinase and hexokinase21. However, the length of the simulated process . The simulator’s module mentioned above converts these values into the initial particle numbers, needed to instantiate the agents at the beginning of the simulation. In this regard, we point out that, although agent-based simulations have a fairly light computational load, reproducing a metabolic pathway involves thousands of molecules, and therefore as many agents running concurrently. The resulting resources demand conditioned the molecular concentrations we were able to simulate. More precisely, we scaled the concentrations provided by the Smallbone2013 model to values less than 1 mmol/l. Indeed, the Smallbone2013 model provides a wide range of species concentrations ; scaling them just proportionally to the simulated volume  would have caused the species with lower concentrations to disappear from the system. Adapting the concentrations provided by the Smallbone2013 model to values less than 1 mmol/l is a first approximation to meet the limits in the computational power. Future development of the simulator will implement distributed computing to deal with concentrations more faithful to experimental data. In Supplementary Table Our agent-based model is intended to study the glycolytic pathway from the general perspective of the oxidation of one molecule of glucose to two molecules of pyruvate; for this reason, we consider the pyruvate as the end product of the process and excluded the fermentation-related reactions, catalysed by the pyruvate decarboxylase isoenzymes  and by the two alcohol dehydrogenase isoenzymes (ADH1 and ADH5). Therefore, the branches acting on pyruvate, that is, the succinate and acetate branches of glycolysis, are not taken into account in our model.26, since they function as control points of the whole glycolysis process, despite the Smallbone2013 model considers irreversible only the reaction performed by phosphofructokinase.To complete the list of changes we made to the original kinetic model, we report that, according to most of the literature, we modelled the reactions catalysed by hexokinase (and glucokinase), phosphofructokinase, and pyruvate kinase as irreversibleThe subset of reactions characterising the model at the basis of our simulations, as resulting from the above-described adaptations, can be found in Fig. 28. In what follows, we introduce the basic principles over which the simulator has been designed; this information can help the reader to better understand the results of our work. Further details on modelling and implementation choices are provided in Sect. The study proposed in this manuscript has been carried out with the aid of Orion, a spatial simulator for metabolic pathways. It has been developed in Java starting from a prototype projectE is the set of all states for the environmentPer is a partition of EAc is a set of actionssee: action: do: Per represents the perception of the environment from the agent’s point of view. An agent observes the environment (see), selects the appropriate action (action), and acts (do) on the environment itself9.Orion is a agent-based simulator, this means that the molecules involved in the pathway are represented by agents, autonomous systems able to perceive changes in their environment and react to them. Formally, a reactive agent is defined by a 6-tuple 31. These modelling choices produce a fairly realistic molecular crowding in the simulated portion of the cytoplasm. Moreover, by making every molecule spherical, we can correlate its shape to its diffusion coefficient through the Stokes-Einstein equation for the Brownian motion of a spherical particle:T the temperature, r the radius of the molecule. For our simulations, we set The simulations are performed in the three-dimensional space, representing a portion of the cytoplasm, that is, the environment perceived by the agents. Each molecule is modelled as a sphere, whose radius is estimated from its molecular weight and the average value of the molar specific volume of a protein in solutionD, obtained via Equation x in a time t:Each molecule can freely move, inside the simulation volume, according to a vector applied to the centre of its sphere: its direction is generated randomly, based on polar coordinates, while its module is calculated from the ambient diffusion coefficient The simulator enables to set the space unit and the time scale as per requirement; in this study, we consider the angstrom 8.To simulate the effects of the molecular interactions operating at different distances, we endowed agents with specifically designed perception capabilities. Their core property lies in the definition of a perception distance at which we want the enzyme to be able to find a cognate metabolite; the perception distance extends beyond the surface of the sphere representing the enzyme. As the distance of the metabolite from the enzyme increases, the intensity of the forces acting on it diminishes; for this reason, each perception sphere is characterised by different interaction probabilities, depending on its size . We modelled this system allowing enzymes and complexes to identify a cognate metabolite within a 10 Å perception distance models the effects of electromagnetic potentials limited by the Debye screening3; it restricts the interactions to just those allowed by stochastic short-range forces.A system where a perception distances of300 Å, chosen as the average length to simulate the existence of long-range electrodynamic forces among biomolecules (considering that the size of the simulation volume of our study is 1000 cubic angstroms). As mentioned in the Introduction, these are deterministic attractive forces activated by a long-range potential between two dipolar molecules A and B, if they vibrate at frequencies 7.A system characterised by In Fig. 5 and 10 Åperception distances), while a r2+d2 type radius models the effects of the long-distance electrodynamic interactions. We point out that the figure arranges side by side two different types of radii just for comparative purposes; in the ABMs defined for glycolysis, only one type of radius is allowed per modelled system.We simulated three different systems, in which the interactions characterising the glycolytic process are driven by the specific kinds of forces whose effects on the pathway we aim to compare. Going into details, the agent-based modelling approach makes us able to define:Imposing fixed perception distances for each simulated system may be considered a limitation, since a molecule involved in multiple interactions can be affected by different kinds of electrodynamic forces. However, to define the glycolysis ABM, we need to balance the accounted systems’ details with the availability and reliability of experimental data; nonetheless, we have to consider the computational cost of the simulations. Modelling different radii for each agent (in the same simulation) would imply taking into account, a priori, a high number of physical parameters that are currently unknown . We experienced a similar problem with Molecular Dynamics simulations; the aim of our agent-based approach is, indeed, to assess the possible presence of long-range molecular interactions in a metabolic pathway by relying on few empirically known parameters.By setting the local rules that determine movements and interactions of the molecules involved in our model of yeast glycolysis ; it turned out to be sufficiently long for us to observe and compare the specific features of each of the three modelled systems.In Fig. perception distances of300 Å, which represents a system where we hypothesise the existence of selective long-range molecular recruitments, has the highest reactivity and efficiency  and “captures” the formation of complexes, even when they are partly-saturated enzymes.The outcomes of the agent-based simulations detailed above suggest that the two systems reproducing an off-resonance situation, where molecular interactions rely only on van der Waals-like potentials or, at least, on electromagnetic forces shorter than the Debye length, are not able to oxidise glucose at a high rate. This property is particularly true when we limit the 35, making our one-second interval of simulation just a testbed to validate the capability of ABMs to support the study of the above-described forces in biological systems. However, if confirmed by further analyses, this result might suggest the non-feasibility of the lock-and-key model for enzymes in metabolic processes.Such a possibility allowed us to observe, in the system limited by short-range electrostatic interactions, a condition that might be detrimental for the cell anaerobic metabolism, which commits the production of energy (in the form of ATP) only to a fast-paced glycolytic process. At the current stage of our work, this consideration represents just a hypothesis: in real cells, glycolysis’ processes take place in times ranging from few seconds to hours36. Considering the high level of abstraction of the current glycolysis ABM, this result might be considered another clue that, by not limiting molecular interactions to just shape complementarities and chemical affinities, we generated processes more faithful to those occurring in cellular glycolysis.Interestingly, even though enzymes regulation has not been modelled, the systems driven by electromagnetic forces (including those below the Debye screening length) produce oscillatory-like fluctuations in the concentrations of fructose 1,6-bisphosphtate, the main product of phosphofructokinase. Moreover, as shown in Fig. 10, such divergences might also be attributed to the possible inaccuracy through which kinetic parameters are essayed in vitro. Indeed, already in the early 2000s, Teusink et al. questioned that in vitro kinetics could be able to faithfully describe an in vivo behaviour37.We could not reach such a conclusion if we based our analysis on a standard kinetic model, which derives the changes over time of the concentrations  through rate and balance equations. As it lacks the capability to represent the granularity of a molecular system, this approach hardly grasps the fluctuations in the species amounts, generating several discrepancies with the results we gained through our agent-based simulations. Although differential equations best suit modelling the continuum or macroscale level38. Other modelling approaches in Systems Biology  also struggled to deal with this problem due to the complexity of representing molecules 3D shape and diffusion at different scales39.Furthermore, the standard kinetic modelling is based on the Michaelis-Menten formalism, which assumes diffusion-limited enzymatic reactions and a homogeneous environment, not considering the effects of molecular crowding on diffusion processes8. In this case, simulating just one type of protein (the white egg Lysozyme) and one oppositely charged dye (the Alexa Fluor 488) required an a priori knowledge of several data  consumption of glucose through glycolysis, even in presence of a high oxygen concentration32, may provide the current model with a many-body perspective. Shape calculus and hierarchical structures can be applied to represent molecular conformations and increase the accuracy of the interactions between cognate partners; these approaches would allow modelling the geometry of molecules shapes and collisions with a higher precision45. Moreover, we may better capture the collective synchronisation properties of a population of molecules behaving as coupled oscillators by using BOSL, the biological oscillators synchronisation logic46. Putting efforts in these directions might provide a new standpoint in our comprehension of molecular interactions and disclose aspects of biological systems that are still unexplored.Similar results might also be reached by empowering the capabilities of the agent-based approach with methods from other disciplines. Among them, the topological data analysis, already used to better understand enzymatic reactions through ABMsSupplementary Information.Supplementary Information.


Glucose, glutamine, and a four-carbon input to the malate shuttle were important carbon sources in the baseline human umbilical vein endothelial cell (HUVEC) 13C MFA model. We observed two to three times higher glutamine uptake in fidarestat and azaserine-treated cells. Fidarestat and DHEA-treated HUVEC showed decreased 13C enrichment of glycolytic and TCA metabolites and amino acids. Azaserine-treated HUVEC primarily showed 13C enrichment differences in UDP-GlcNAc. 13C MFA estimated decreased pentose phosphate pathway flux and increased TCA activity with reversed malate shuttle direction in fidarestat and DHEA-treated HUVEC. In contrast, 13C MFA estimated increases in both pentose phosphate pathway and TCA activity in azaserine-treated cells. These data show the potential importance of endothelial malate shuttle activity and suggest that inhibiting glycolytic side branch pathways can change the metabolic network, highlighting the need to study systemic metabolic therapeutic effects.Disrupted endothelial metabolism is linked to endothelial dysfunction and cardiovascular disease. Targeted metabolic inhibitors are potential therapeutics; however, their systemic impact on endothelial metabolism remains unknown. In this study, we combined stable isotope labeling with  Endothelial cells play an important role in pathologies ranging from atherosclerosis to cancer to Alzheimer’s disease. Endothelial glucose metabolism is disrupted in many of these diseases. Recent efforts demonstrate that manipulating endothelial metabolism can alter cell signaling pathways and thereby cell function ,2,3. Man+ in the reaction. Sorbitol, a hydrophilic alcohol, cannot readily diffuse through the cell membrane, and its accumulation inside the cell potentially causes osmotic stress . Al. Al10]. c stress . Sorbitots (AGE) . IncreasPH ratio . The polPH ratio ,14,15. HPH ratio ,17.+. Thus, the PPP oxidative branch produces NADPH, an essential reducing agent for fatty acid, sterol, nucleotide, and non-essential amino acid synthesis. The bidirectional non-oxidative branch converts ribulose 5-phosphate to ribose 5-phosphate, a nucleic acid building block, and xylulose 5-phosphate. These metabolites can then be converted into fructose 6-phosphate or glyceraldehyde 3-phosphate, re-entering glycolysis . Th. Th18]. ycolysis . Oxidatiycolysis ,21. Non-ycolysis .Increased endothelial glucose flux also affects the hexosamine biosynthetic pathway (HBP), which is important in the post-translational protein modification O-GlcNAcylation  23,24].,24.23,24The goal of this work was to study how inhibiting glycolytic side branch pathways using established chemical inhibitors would affect other parts of the metabolic network. Fidarestat, an aldose reductase inhibitor that has shown some promise in clinical trials of diabetic neuropathy, was used to inhibit the polyol pathway . Dehydro13C metabolic flux analysis (13C MFA) model to enhance our analytic capabilities  and outputs  for endothelial cells that were either untreated (vehicle control) or treated with each glycolytic side branch pathway inhibitor . GlucoseWe next used partial least squares discriminant analysis (PLS-DA) to reduce the dimensionality of the mass spectrometry dataset  and sele13C MFA. While fidarestat has been widely shown to inhibit the polyol pathway, we could not detect polyol pathway inhibition directly since our mass spectrometry data did not include sorbitol and we were unable to detect sorbitol using a colorimetric assay. Fidarestat treatment decreased the total 13C enrichment of glycolytic and TCA metabolites, the amino acids serine, glycine, aspartate, and alanine, as well as UDP-D-glucose and UDP-GlcNAc (13C enrichment of pyruvate decreased by about 10% with fidarestat treatment (p < 0.001) while 13C enrichment of lactate decreased by about 8%  with fidarestat treatment. The 13C enrichment of fumarate and malate was around half that of the other TCA metabolites  and glycine by 34% (p < 0.01). Glutamate enrichment decreased by 7%, alanine by 22%, and aspartate by 16% , as well as a slight decrease in pyruvate  and 13C enrichment of glycine, glutamate, alanine, and aspartate also decreased in DHEA-treated cells  did not change, other PPP fluxes were estimated to decrease by 32%; however, they remained within the confidence interval of the untreated group. TCA cycle activity increased in endothelial cells treated with DHEA, although the lower bound of 95% confidence intervals for many of these fluxes slightly overlapped with the untreated group .Azaserine-treated endothelial cells, which should have decreased HBP flux, showed decreased UDP-GlcNAc in the total pool data  and 30% istently . When 13ed cells d. The ised cells e. The la13C MFA predicted no change in glycolytic flux with azaserine. However, in contrast to the other groups, MFA predicted that PPP flux would increase by 1.4–1.7 over fluxes in untreated cells, although the confidence intervals for these fluxes overlapped. 13C MFA further predicted increased flux throughout the TCA cycle, driven by a combination of increased pyruvate shuttling into the mitochondria, glutamine influx, and malate influx  source flux was required to fit the 13C MFA model for all four treatment groups. We propose several possible explanations for the unlabeled C4 source (4 compound could come from media proteins or amino acids. Glutamine (2 mmol/L) is the most concentrated media amino acid. When we simulated glutamine entry and cytosolic conversion to oxaloacetate in our model, we obtained a satisfactory fit (data not shown). However, these reactions typically occur in mitochondria and to our knowledge, there is limited evidence of that they occur in cytosol. Furthermore, this model predicted increased PPP flux in fidarestat-treated cells, which contradicts isotope labeling data.Several unique metabolic characteristics of endothelial cells became evident in the baseline FA model . An unla4 source . First, 4 source may be malate drawn from preexisting intracellular carbon pools such as cytoplasmic succinate or succinyl-CoA. Succinate accumulates in mitochondria when succinate dehydrogenase is inhibited . However, additional unlabeled carbons were needed to fit m + 0 and m + 2 malate, alpha ketoglutarate, and glutamate as well as the absence of m + 1 and m + 2 pyruvate and lactate in the experimental data. We therefore added an unlabeled three-carbon source to dilute pyruvate and a four-carbon source to dilute malate. Incorporating the three-carbon dilution to pyruvate slightly decreased the SSR value to 166, while the four-carbon dilution to malate reduced the SSR to 42, which was considered an acceptable fit .13C MFA HUVEC model consisted of 79 reactions, 105 fluxes, 39 metabolites, and 45 degrees of freedom (−6) in the untreated group and were associated with large uncertainty in all groups, likely due to the number of unbounded dilution reactions tied into this pathway. For this reason, HBP fluxes were excluded from our flux ratio analysis. The metabolic model, confidence intervals, and MFA results can be found in The final  freedom . Labeled13C MFA, 95% confidence intervals were calculated using parameter continuation, which varies all parameters upward and downward one at a time until the chi-square distributions are reached.Supervised partial least-square discriminant analysis, principal component analysis, and variable importance projection (VIP) scores were obtained using MetaboAnalyst . Statist