Crohn’s disease (CD) is associated with an ecological imbalance of the intestinal microbiota, consisting of hundreds of species. The underlying complexity as well as individual differences between patients contributes to the difficulty to define a standardized treatment. Computational modeling can systematically investigate metabolic interactions between gut microbes to unravel mechanistic insights. In this study, we integrated metagenomic data of CD patients and healthy controls with genome-scale metabolic models into personalized in silico microbiotas. We predicted short chain fatty acid (SFCA) levels for patients and controls, which were overall congruent with experimental findings. As an emergent property, low concentrations of SCFA were predicted for CD patients and the SCFA signatures were unique to each patient. Consequently, we suggest personalized dietary treatments that could improve each patient’s SCFA levels. The underlying modeling approach could aid clinical practice to find dietary treatment and guide recovery by rationally proposing food aliments. in silico gut community models, with which the fermentation profile of CD patients could be improved. Taken together, these results can assist in the design of further experimental and clinical studies to aid CD patients with dietary supplementation.Modeling of the human gut microbiota metabolism predicts that fiber-containing diets can improve the microbe metabolism in Crohn’s disease (CD). By integrating metagenomic data from human gut samples into personalized metabolic models, the fermentation profile of gut microbes and the differences between CD patients and healthy controls were assessed. To revert the fermentation differences between healthy and CD individuals, predicted beneficial metabolites were added to the  Non-invasive treatments for CD include the intake of antibiotics5 and steroid therapies.6 In addition, defined diet formulas are used to ease the symptoms of the disease.7 However, the success of these treatments varies between patients.8 Additionally, after remission, patients have difficulties in finding an appropriate diet and often experience relapse. Considering the human gut metabolism, it has been suggested that the diet reshapes the microbiota.9 Overall, the microbial diversity is decreased in CD patients. A shortage of SCFAs10 coincides with a decrease of fermenting Firmicutes bacteria.11 Microbial SCFAs have been recognized as important modulators of the immune system and as a nutrition source.12 Butyrate, for example, is taken up as an additional energy source by the host,13 contributes to epithelial barrier integrity,14 and stimulates the immune system.15 CD patients suffer from a low butyrate concentration,16 but its dietary supplementation can revert many of the IBD symptoms,17 highlighting the relevance of this particular SCFA in CD.Various human diseases, including inflammatory bowel disease (IBD), are associated with a loss of functional and taxonomic diversity of the gut microbiota.18 it becomes difficult to track the ecological interactions differing between CD patients and healthy individuals. Meta-omics approaches are generally used to characterize the microbiota and its metabolic potential.19 However, these top-down approaches do not provide mechanistic insights on the resilience of the microbiota and how perturbations, such as diets, may affect the system as a whole.Given that the human gut microbiota is a complex microbial community with many different microbes that have varying metabolic potentials and substrate affinities,21 Briefly, genome-scale metabolic reconstructions are represented by the complete set of biochemical reactions derived from a genome annotation and organism-specific literature in a stoichiometric accurate manner.22 Such high-quality manually-curated metabolic reconstructions are available for organisms from all three domains of life, such as Escherichia coli,23 yeast,24 and human . Through the application of specific constraints , the metabolic reconstructions can be converted into condition-specific models, which predict the reaction flux rates and growth yield under a given objective that is optimized using flux balance analysis (FBA).20 In a recent publication,27 we combined FBA with agent based modeling to simulate the ecology of microbial communities through the BacArena framework. Metabolic interactions emerge from the exchange of metabolites between species and the environment. These interactions can influence the metabolite concentration and the microbial community by inducing cross-feeding or resource competition. Such COBRA-based approaches provide a powerful mean to investigate mechanistic links in complex biological systems, such as the human gut microbiota.28Bottom-up systems biology approaches can mechanistically describe biological systems and make relevant predictions. In particular, constraint-based reconstruction and analysis (COBRA) has been successfully applied to model the metabolism of different species and predict how perturbations affect the metabolic phenotype.29 In their study, the authors could distinguish two clusters of patients: A cluster of 57 patients, which had a microbiota composition similar to the healthy controls, and a cluster of 28 patients that had a distinguished dysbiotic microbiota. Compared to controls, these dysbiotic patients had a strongly differing functional and microbial abundance profile.A recent study on pediatric CD sequenced the metagenomes of a North American cohort consisting of 26 healthy controls and 85 patients newly diagnosed with CD.29 to simulate personalized in silico microbiotas with BacArena. We demonstrate that the simulated metabolic differences between patients and controls are congruent with experimental findings. We further show that predicted individual specific SCFA signatures are unique to each patient. Based on these results, we then predict personalized dietary treatments that would improve the SCFA concentrations of each patient. With this work, we demonstrate the added value of performing computational with integrating high-throughput data of individual microbiotas to predict mechanism-based personalized dietary intervention strategies for CD patients.Here, we retrieved the original metagenomic data of the 26 healthy controls and 28 dysbiotic patients29 using a hybrid computational modeling approach,27 in which we combined FBA with agent based modeling to simulate the ecology of microbial communities through the BacArena framework. The predicted interactions can be used to gain further insight into metabolic differences that may contribute to CD and to propose modeling-assisted dietary intervention strategies for CD patients  and significantly lower abundance of Bacteroidia and Clostridia  in CD patients  abundances. At the end of the simulation, the grid was populated by an average of 5902 +/− 1743 microbes (with an average grid occupation of 59 +/− 17%). Overall, the simulated abundances recapitulated the initial microbial differences, demonstrating that the in silico microbiotas were stable in BacArena Fig. . However29 Furthermore, the simulation results of the personalized in silico microbiota in BacArena illustrate that these microbes can co-exist as stable microbial communities in silico.Taken together, our workflow recapitulates the reported microbial differences between controls and CD patients.We investigated whether the difference in microbial abundance in the personalized in silico microbiotas also corresponded to differences in reaction content. In average, each personalized in silico microbiota consisted of 3,332,957 +/− 285,848 belonging to 3036 +/− 424 unique reactions. The presence and absence pattern of the unique reactions in the in silico microbiotas varied between individuals as well as between the two groups Fig. . Based o15 We analyzed the secretion of SCFAs after 24 h by each personalized in silico microbiota to establish whether known microbiota-level differences in SCFA production could be reproduced by our modeling approach. The SCFAs butyrate, propionate, isobutyrate, and acetate were significantly lower in CD patients  of L-lactate, and Gammaproteobacteria produced almost 50% of the total acetate Fig. . Notably29 reported the most distinct microbial differences between the healthy controls and the CD patients but also individual variability. Accordingly, the simulated relative microbial abundance also varied between the individuals .Paired-end Illumina raw reads of a study on early onset CD patients and healthy controls of a North American cohort54 the pre-processed reads were mapped with default parameters onto a reference set of 773 genomes, which were selected according to a previous study.30 Before mapping, the reference genomes of these organisms were combined into one file where each genome is represented as a chromosome. To filter out cross-mapped reads (reads mapped to multiple positions), samtools55 was used to discard mapped reads with a low-quality score. The coverage per genome  was calculated using samtools. To reduce the number of false positives, we set a threshold of at least 1% genome coverage for each microbe in each human individual. In accordance to another pipeline,56 the resulting coverages were normalized for each individual to obtain the relative microbe abundances.Using BWA,30 from http://vmh.life. These microbes have been chosen according to their prevalence in the human gut and the availability of a genome sequences, and they have been extensively curated based on available physiological and biochemical data.30We retrieved published gut microbial metabolic reconstruction57 The unique reaction set of personalized in silico microbiotas was determined by taking the union of all present microbe reactions retrieved from the corresponding metabolic model30 of each microbe. PCoA was performed on the metabolic distance between each individual’s reaction set similar to.30The mapped microbial abundances for each individual were compared by computing the Bray-Curtis similarity and subsequent visualization with principal coordinate analysis (PCoA) using the R package vegan.27 which represents bacteria as individuals in a grid environment that can exchange metabolites by secretion and uptake. Individual optimizations were carried out using the microbial biomass as an objective. Consequently, the observed concentrations of metabolites, in particular SCFA, are a product of the individual microbial energy metabolism. The dimensions of the two-dimensional quadratic environment were set 0.025 cm2 with 100 grid cells per side length. This resulted in 10,000 grid cells that could be potentially occupied by the microbes. To allow space for the in silico microbial community to grow, 500 microbes were initially added to the grid environment. The relative microbial abundances were used to scale the number of microbes to be added per species . In case the calculated number of microbes resulted in decimal places, we rounded the final number to the next highest integer. Hence, all microbes that were detected as present in the samples, were included and had an initial microbiota size ranging between 505 and 1109 microbe individuals. All possible metabolites (union of metabolites that can be taken up by each microbe) were added to the environment with a minimal concentration of 0.2 µM to provide a rich medium that is consistent between individuals. Therefore, metabolite concentrations that emerge from the simulations can be specifically attributed to the microbiota of each individual.The next step is to integrate the abundance information into a personalized in silico microbiota for each person. Therefore, we used a previously established R package for community modeling,Once the in silico microbiota for each CD patient and healthy control have been setup in BacArena, the growth of each microbial model in the microbiota was sequentially for each time step. A total of 24 time steps were simulated, one per hour, corresponding to an overall simulation time of 24 h. To reduce the complexity of the model, we simulated a well-mixed environment in which metabolite concentrations are uniformly distributed and microbes move randomly.58 was used for constraint-based modeling with ILOG CPLEX as a linear programming solver.The R package Sybil59 (26 controls and 28 CD patients) implemented in R.After the simulation, each personalized in silico microbiota was primarily analyzed in terms of the microbe abundance and metabolite concentrations. Since the simulations include temporal dynamics with different time points, we chose the last time point (24 h) for our analysis and comparison between individuals. This allowed the in silico microbial communities enough time to consume and produce metabolites, and to reach a steady state. The microbial abundances were determined by assessing the number of microbes in each personalized in silico microbiota. The vector of microbial abundances was then compared by computing the Bray-Curtis similarity with PCoA visualization. Abundances of specific taxa were calculated by summing up the relative abundances of each corresponding representative. The abundances of the most differing taxa were tested for significant differences between healthy controls and CD patients with the Wilcoxon rank-sum testt = 24 h). The concentration of the most relevant metabolites, butyrate, propionate, isobutyrate, L-lactate, and acetate, were assessed and tested for significant differences between the personalized in silico microbiota of healthy controls and of CD patients using the Wilcoxon rank-sum test. To investigate the influence of each microbial taxa on the metabolite concentrations, we further evaluated the metabolic fluxes of each microbe in the personalized in silico microbiota. For each taxa, the reaction fluxes in all corresponding microbes were summed up.Metabolite concentrations were determined by their molar concentration in the environment at the end of the simulation  were optimized separately. To enhance the growth of beneficial bacteria, we selected metabolites based on the ability of the CD low abundant microbes  to uptake these nutrients over the CD high abundant microbes . We then added the selected metabolites iteratively to the in silico medium with a maximal flux uptake constraint of 1000 mmol gDW−1 h−1 to investigate whether the SCFAs increased or decreased. Based on these simulations, the added metabolites which had a positive effect  were then collected and used as the personalized dietary treatment for each individual.According to their presence in each personalized in silico microbiota, the set of microbes was selectively analyzed for every individual. Each personalized in silico microbiota was then simulated in a rich medium containing all possible metabolite with flux uptake constraints of 1 mmol gDWWe tested the effect of the treatment on the personalized in silico microbiota of CD patients by adding a 100 times higher concentration of the predicted treatment metabolites to the in silico rich diet containing 0.2 µM for each metabolite. The personalized in silico microbiota simulations and analyses were then carried out as described above.https://github.com/ThieleLab/CodeBaseThe scripts to construct and simulate the individual specific microbiota models as well as the analysis scripts are available on GitHub: Table S1Table S2Supplemental figure legends


Although cellular metabolism has been widely studied, its fully comprehension is still a challenge. A main tool for this study is the analysis of meaningful pieces of knowledge called modes and, in particular, specially interesting classes of modes such as pathways and Elementary Flux Modes (EFMs). Its study often has to deal with issues such as the appearance of infeasibilities or the difficulty of finding representative enough sets of modes that are free of repetitions. Mode extraction methods usually incorporate strategies devoted to mitigate this phenomena but they still get a high ratio of repetitions in the set of solutions.This paper presents a proposal to improve the representativeness of the full set of metabolic reactions in the set of computed modes by penalizing the eventual high frequency of occurrence of some reactions during the extraction. This strategy can be applied to any linear programming based extraction existent method.Our strategy enhances the quality of a set of extracted EFMs favouring the presence of every reaction in it and improving the efficiency by mitigating the occurrence of repeated solutions. The new proposed strategy can complement other EFMs extraction methods based on linear programming. The obtained solutions are more likely to be diverse using less computing effort and improving the efficiency of the extraction. Constraint-based mathematical techniques are useful tools to analyse GSMN models. However, automatic characterisation of the biochemical reactions present in a particular metabolism constitutes a challenge [Stoichiometry can be used to construct a model of the biological system inside a cell. The resulting model is a genome-scale metabolic network (GSMN) and it explains how the chemical reactions occur and how the metabolites are produced and consumed during the metabolic process. Building high-quality GSMNs must follow some steps . The modhallenge .GSMN can also be seen as the addition of interrelated sub-networks. To support life, each sub-part of the metabolic network has to accomplish its specific biological function. Pathways are a special class of sub-networks. They are steady-state and thermodynamically feasible subsets of reactions, that means that mass balance remains unaltered while the reactions produce and consume metabolites. Elementary flux modes (EFMs)  are non-A very well-known optimization technique is Linear Programming (LP). There are very efficient implementations of linear program solvers available , 5. ThosThe length of the modes and the presence of every metabolic reaction in the set of solutions have been studied on . This paThere are two main ways of getting different solutions : find a method to generate seeds that produce different solutions or modify the objective function so that the optimization process tends to get solutions that are different from the ones previous obtained. In this paper, we are interested in studying the viability of this second approach.In order to drive the LP solver to different solutions on each run, in this paper it is proposed to dynamically modify the objective function to coerce the LP solver to consider less used reactions. As it seems obvious that proposing the most used reactions to be part of the seed once and again favours the occurrence of repeated solutions, a plausible method to try to avoid repetitions in the new solution is to penalize any reaction that has been included in previously obtained solutions. Our proposal can be viewed as a mechanism to help LP solvers not to fall insistently in local minimums.The paper is structured as follows. In the “Network metabolic models let a full or a context-specific analysis of the role that plays any reaction or metabolite inside the cell. It is particularly interesting the role that they play in particular disease research, where is needed to extract a specific piece of information from the full network. Pathways and Elementary Flux Modes (EFMs) are types of sub-network whose analysis have been remarked by plenty of works , 11. TheThere are two main groups of computational approaches to extract information from metabolic pathways: path-finding and stoichiometric . The firEach metabolic reaction inside a cell can be represented by its correspondent stoichiometric equation. All the equations are arranged in a stoichiometric matrix where columns represent metabolic reactions and rows represent metabolites. The matrix values represent the stoichiometric coefficients for the production or consumption of metabolites on each reaction.S a stoichiometric matrix . These coefficients represent the frequency at which reactions occur at the steady-state or, equivalently, the rate of metabolites production/consumption through the reactions. A feasible sequence of reactions occurring inside a cell can be comprised in a vector called flux rate that contains the reaction rates, that is, the values for the variables of the system of equations represented in the S matrix. If R is the full set of metabolic reactions, the flux vector Be mentclass2pt{minimEquation Once the above equations are solved at least two different solutions are obtained: the trivial one and other that represents the whole network. A pathway is just a solution of the solutions: a vector flux that is positive and verifies the steady-state condition. It can be viewed that any solution is associated to a subset of the full set of reactions formed by those that has non-zero rate. Starting from the whole network, and working in an iterative way, the goal is to find subsets of reactions, the ones associated with pathways, that correspond to solutions of the system. So, a pathway is a subset of the full set of reactions satisfying that we can find a flux-vector that is a solution of the previous equations and whose support  are exactly the values corresponding to reactions in the pathway. If the metabolic network is represented as a graph, a pathway can be seen as a sub-graph.minimality, is the condition that let transform the extraction method into an optimization problem instead of just a system of equations.It is said that The biological relevance of an EFM is inherited from the fact of the uniqueness of the set of EFMs and the canonical quality as a set of vectors that can generate any pathway, even those unobserved , 21.Linear programming (LP) is the most popular optimisation-based approach for EFMs extraction. LP is being widely used to reduce the complexity of combinational problems in systems biology introducing optimization objectives that lead the search and constraint the space of solutions to a subset within an specific focus –24.The existing literature describes how to formulate an EFMs extraction problem as a linear program considering the constraints defined in the previous Section  Eq. 3)..3). 3\dOnce a linear program is obtained, it can be solved using, for instance, the Simplex Algorithm implemented in plenty of LP solvers.A trivial solution for the linear program posed in Eq. Additional constraints can be seen as set of reactions forced to have positive fluxes (positive constraints) or, contrarily, as set of reactions forced to be inactive, which means that their associated fluxes are equal to zero (negative constraints).seed as a constraint of this kind in reference to the fact that a seed is the precursor of one solution. Seeds are needed to coerce the solvers to find non trivial, thermodynamically feasible solutions and can also be used to try to find solutions that are different from the previous ones. There are existing heuristics that, searching for good seeds, introduce jumps as a strategy to escape of the attraction of local minimums. The attraction of those local minimums is one of the causes of the repetitions in the solutions found by the LP solver.We define a λi).Observe that the objective function N).A fairly approach for the extraction of EFMs is to use a computer program based on linear programming. This program essentially consists of a number of iterations of the Simplex method. Algorithm 1 shows the typical composition the program used. The main loop is iterated at least as many times as solutions needed . So, it is not enough to produce a large set of different seeds to obtain a large set of different pathways. It is not easy to choose seeds to get new pathways, and the difficulty increases as more solutions are computed.r1 produces a metabolite m and it can only be eliminated by another reaction r2. If the reaction r1 is imposed to be part of the solution but not the reaction r2, it is impossible to get a solution satisfying the steady-state condition (m will be produced and cannot be eliminated). A seed is called infeasible if its associated linear-program problem has no solution.On the other hand, the chosen seed can led to a problem that has no solution at all. That is, when a certain set of reactions are imposed to be in the solution and another set cannot appear, sometimes contradictory conditions are being imposed. Suppose, for example, that a reaction In order to avoid infeasibilities, the set of seeds have to be restricted to a positive ones, that is, seeds that only determine what reactions are required to be part of the solution but not what are forbidden to be.Another frequent problem of a set of solutions after run an long extraction experiment is the under or over-representation of some part of the metabolic networks. This phenomenon comes associated to some kind of affinity of the seed generator or a lack of dispersion or randomness of its conception.Each iteration requires its own seed that is incorporated as a part of the final computed solution. The process of building a seed consists of choosing what reactions are included in the constraint and, therefore, in the particular solution of a constrained LP using that seed. Defining different constraints from previous ones does not guarantee different solutions. As the Simplex algorithm is deterministic, the method to compose the seeds is critical to get a significant set of solutions.Due to the fact that the seed induces the final solution, the correspondent seed generator is also responsible of the quality of the final set of solutions. It seems clear that the generation of a new seed should be influenced by the previous ones, and in that way, avoid to obtain the same EFM twice. For example, graph-affinity based approaches use the graph adjacency of reactions to build seeds, so in some way assures some kind of minimality by forcing the connectivity of the solution. The counterpart is that the adjacency can cause over-representation of a determined subgraph in detriment of the global meaning. It is also worth to say that sometimes the same problems are due to the exhaustion of the method to generateb different seeds.A completely random seed generator can be considered as the simplest and fair seed generator. It could be a module of an invented extraction method that produces constraints for a linear program on every iteration. This is a neutral way to generate seeds that frees us to record previously produced seeds to avoid repeated seeds. Algorithm 2 shows how it works.N the number of iterations performed in one optimization problem and Oi the number of occurrences of the reaction ri in the experiment. The frequency of occurrence for each ri is Pathways and EFMs extraction methods incorporate strategies to avoid repeated solutions as much as possible. The frequency distribution of the reactions present in the solution is a characteristic of each extraction method. Be mentclass2pt{minimThe frequency distribution is somehow conditioned by the extraction method, but there are other characteristics that can influence on it. For example, the intrinsic properties of the biological network (its size or its coupling relations), or even the amount of runs done for an experiment can influence the outcome.It is reasonable to expect similarity between two sets of frequencies obtained in two separated experiments. So, if the frequencies are almost the same, we can expect that they express properties of the network and not of the chosen extraction method. This can open a new path to understand why some reactions appear more often in the set of solutions than others.Depending on structural properties of the network or magnitude factor of the stoichiometric coefficients, solvers could tend to include the same reactions in the final solution in almost any case, and this can lead to obtain repeated solutions independently of the chosen seed.penalization scheme that modifies previous results is proposed in order to increase the number of different solutions, and/or to get them faster. Our aim is to force the solver to avoid (when possible) reactions that are present in solutions computed previously in order to get new ones.In this work, a weights {wi} to formulate it as The proposed strategy consists of modifying the objective function with sets of positive Observe that this strategy is not equivalent to the use of negative seeds. The latter one can lead us to infeasibilities while the use of weights only discourages the use of reactions that has appeared before but does not ban them. Therefore, different sets of weights may provide different solutions even when using the same seed.It is interesting to study the influence of a set of weights over the solutions. To that, the first step is to analyse if the use of weights has a real impact on the set of solutions obtained. Once we are sure that our approach modifies the set of solutions, a second question is how to choose the weights in order to obtain sets of solutions with the desired properties: the number of repeated solutions should be as small as possible and the set should be representative (as many different solutions as possible).chi-square.To answer these questions we have to compare the outcomes of different experiments by applying different statistical tools to compare the results. In this work, we have used the Wilcoxon signed-rank test  and a teInitially, all the objective function weights equal 1 . We propose to use as weight for a reaction Fi the higher wi becomes and, over a threshold, the optimizer is induced to consider other less penalized reactions . The proposed modification of the objective function weights should result in differences between the frequencies of a non-penalized experiment (Fi) and the penalized one (F′i). Algorithm 3 extends the more general Algorithm 1 by adding the modification of the objective function and the computation of occurrences and frequencies for each reaction in the set of obtained solutions.As it can be deduced, the higher is the frequency F between penalized and non-penalized experiments would involve that the penalization approach has an impact in the obtained solutions.Being able to compare different pathway extraction experiments is required in order to measure the effectiveness of our penalization strategy. Differences in the sets of obtained frequencies F and F′ the resulting frequencies in two different experiments, the question is how to measure the possible differences between them. In other words, our objective is to determine whether two samples were selected from populations with the same distribution or not. Observe that we cannot compare these two samples performing a standard chi-square test because the values Fi are not independent in general. As we have mentioned before, there are often structural dependencies between reactions and metabolites that can force two related frequencies to be the same. Thus, we have chosen another statistical test, the Wilcoxon signed rank test [Be ank test .F and F′ we can use the well-known statistic  almost equal. This is important because we can assure that if we find differences between frequencies they are not caused by random oscillations produced by the seed generator.It is well-known that high Wilcoxon By observing the first three rows we can assure that the results of experiments with and without penalizations are clearly different and that this difference seems to grow with the value of the penalization. The last row shows that experiments with different penalizations have also a different behaviour. It was clear from rows two and three that there were differences and now we can see that this difference is clearly significant.Table Therefore, we conclude that the introduction of weights in the objective function has an influence in the results, and that there is also a clear difference between different weights. The above tables also suggest that bigger values of the penalization have more impact in this behaviour.chi-square based statistic. It shows how the penalization has an influence over the chi-square value considering the same number of iterations.We are also interested in the possible influence of the penalization over the set of frequencies in experiments with a different number of iterations. Table Table However, the main part of this difference seems to be achieved with relatively low values of the penalization. If we compare two sets of frequencies obtained with different penalizations the difference between them seems to be less significant .It also seems that there is some kind of connection between the length of the experiments and the influence of the penalizations. Experiments with a higher number of iterations should be performed in order to get accurate conclusions.Once we have checked that using penalizations changes the set of frequencies obtained in one experiment, we try to evaluate these changes among different runs. Figure p =0 and p =2). Negative bars reflect how some reactions are persuaded to be so frequent, and the positive ones represent that those reactions are being included in the set of solutions more often. The expected result was that the greater is the previous frequency, the most negative is the difference between both experiments. Figure Moreover, Fig. In this paper, a new EFM extraction strategy is proposed. It can be used together with other LP-based methods. A penalization associated to the previous occurrence of each reaction during an experiment provides information that the LP solver uses to avoid the recurrent appearance of the same reactions in the full set of solutions. As main effect, the solutions are more likely to be diverse. Additionally, rarely included reactions are better represented in the set of solutions. Other factors can affect the effectiveness like the size of the GSMN and the number of iterations of the experiments.The biological relevance of the extracted EFMs is at least the same that it is supposed to the full set of EFMs. Recently, context-specific approaches are focused on extract a subset of EMFs where a set of reactions are present , 23. OurRegarding future work, it could be relevant to study what results are obtained by doing longer experiments. Besides, frequency distribution and the apparent convergence of the set of solutions using a combination of the proposed factors induces us to think in a measure of “knowledge that holds a extracted subset of pathways from the total remaining”. Furthermore, it seems relevant to us the analysis of the shape of the distribution of solutions and the over and under representation of reactions on them.


The switch from quiescence (G0) into G1 and cell cycle progression critically depends on specific nutrients and metabolic capabilities. Conversely, metabolic networks are regulated by enzyme–metabolite interaction and transcriptional regulation that lead to flux modifications to support cell growth. How cells process and integrate environmental information into coordinated responses is challenging to analyse and not yet described quantitatively.Saccharomyces cerevisiae.To quantitatively monitor the central carbon metabolism during G0 exit and the first 2 h after reentering the cell cycle from synchronized 13C metabolic flux analysis was used to observe the intracellular metabolite flux changes, and the metabolome and proteome were observed to identify regulatory mechanisms.Dynamic tailored G0 cells responded immediately to an extracellular increase of glucose. The intracellular metabolic flux changed in time and specific events were observed. High fluxes into trehalose and glycogen synthesis were observed during the G0 exit. Both fluxes then decreased, reaching a minimum at t = 65 min. Here, storage degradation contributed significantly (i.e. 21%) to the glycolytic flux. In contrast to these changes, the glucose uptake rate remained constant after the G0 exit. The flux into the oxidative pentose phosphate pathway was highest  at t = 65 min, while it was very low at other time points. The maximum flux seems to correlate with a late G1 state preparing for the S phase transition. In the G1/S phase (t = 87 min), anaplerotic reactions such as glyoxylate shunt increased. Protein results show that during this transition, proteins belonging to clusters related with ribosome biogenesis and assembly, and initiation transcription factors clusters were continuously synthetised.The intracellular flux distribution changes dynamically and these major rearrangements highlight the coordinate reorganization of metabolic flux to meet requirements for growth during different cell state.The online version of this article (10.1007/s11306-019-1584-4) contains supplementary material, which is available to authorized users. All living cells adjust metabolism and cell growth to the nutrient availability in the environment. When conditions are unfavorable, cells enter quiescence (or G0), which is the most common cell state in natural environments  now enable an accurate estimate of intracellular fluxes without assumptions about the activity or inactivity of parallel metabolic pathways  while no other chemicals are used allowing for a natural synchronization for about 10 h. The major metabolites and flux profiles  were studied during G0 exit, the G1 phase and the initiation of S phase.Most of these studies relied on shake flask or chemostat culture . A seed culture was performed using a shake flask culture aerobically at 200 rpm and 30 °C using 100 mL synthetic medium containing 20 g/L glucose  using 13C uniformly labeled [U-13C6] glucose  in the continuous media for 13C tracing, 13C and 12C glucose medium were switched every 30 min to enable flux identification for 120 min. The biomass dry weight concentration was measured as described  were spun down in Eppendorf tubes for 5 s at 14,000 ×g. Cells were resuspended in 1 mL deionized water and spun down. The fluid was poured off, and cells were resuspended in the remaining traces of water by vortexing (this prevents excessive clumping during the following fixation). The cells were fixed in 70% ethanol. Samples were stored at 4 °C overnight. Stored samples were washed three times with 0.5 M sodium citrate, pH 7. 0. 25 mL RNase solution (10 mg/mL) was added and samples were incubated for 1 h at 37 °C. Cells were centrifuged for 2 min at 14,000 ×g and resuspended in staining buffer . Samples were incubated for at least 2 h at 4 °C. Finally, cells were pelleted and resuspended in 1.5 mL EDTA solution , sonicated for 15 s and analysed by flow cytometry, measuring and recording 25,000 or 50,000 events.Flow cytometric analysis was used for determining DNA content (FL2-A histogram), size by forward-scattered light height (FSC-H) and internal complexity side-scattered light height (SSC-H) respectively, to determine G0 population and cell cycle stage of the cells as previous reported . FL2-A versus FSC-H plots were analysed using Flowjow software to reveal the percentage of cells in G0, G1, and S . FACSCalibur parameters: the fluorescence emission maximum for DNA-bound PI is about 615–620 nm. When excited by a 488 nm laser, PI can therefore be detected in both, the red/orange emission channel (FL2) tandem dye detection as well as the red emission channel (L3). Data acquisition and analysis were done by using CellQuest software R and Flojow . Also the 10 min samples had a different side-scattered fluorescence (SSC) distribution as compared to the 10 h sample . Distribution of forward-scattered light (FSC) fluorescence which is proportional to the cell-surface area, showed no differences in the plot area for all samples. These results together indicate that 10 h starvation (G0) samples had smaller nuclei as compared to the samples of different sample points but showed no difference in cell size. These results agree with the report of Laporte et al. that G0 phase leads to chromatin condensation , and the volume was brought to 100 mL with glycerol. From a 1 mg/mL stock solution in water, 4′,6-diamidino-2-phenylindole (DAPI) was added to 50 ng/mL. After mixing, the solution was stored at − 20 °C. Solutions that have turned brown were discarded. Calcofluor white stain was prepared according to provider instructions , mixing it in equal volume with KOH 10%. Cells fixed in ethanol were washed three times with deionized water and finally suspended in 1 mL, from this cell solution 10 µL was left in a slide and incubated at 37 °C to dry. The slides were analysed by adding one drop of mounting solution and one drop of calcofluor and analysed in microscope Olympus 100R.Microscopy was used to determine budding index (BI) and nuclei localization Fig. c. This i13C and 12C glucose  flux approximations was applied  classification system . The biomass concentration was nearly constant. Some decrease (5%) was observed between 40 and 80 min. Then an increase was observed after 80 min . There was no detectable secretion of metabolic byproducts, like ethanol or glycerol. Therefore, the biomass constituents were fixed in the biomass reaction.A  −1 Fig. . The \do13C-MFA using PWA flux approximations was applied to determine intracellular fluxes based on measured metabolite concentrations, enrichments, and the metabolic network model specified in Table S1. The experiment was designed to enable a sensitive monitoring of the glucose uptake rate, i.e. no significant accumulation of substrate in the broth (feeding at D = 0.1 h−1). Furthermore, a feed switching between 13C6 and unlabeled glucose every 30 min was used to generate labeling transients during 120 min and allow for a longer experiment compared to a classical wash-in experiment . This could be explained by exchange fluxes of these amino acids with the respective precursors in central carbon metabolism, which were in the range of 1–2% of the glucose uptake rate (Table S2).The enrichment patterns were quite different among the amino acids Fig. b. For maTherefore, the response in fluxes and metabolites are discussed below based on the time-intervals between break points and the observed cell state 0–10 min (G0/G1 entry), 10–87 min (G1), and 87–120 min (late G1 and S phase transition).−1) , i.e. the ATP concentration (10.5 vs. 12.6 µmol/g DW) and also the energy charge (0.91 vs. 0.87) . Furthermore, the energy metabolites were nearly constant during the transitions. Thus, although the extracellular glucose uptake rate changed significantly there is homeostasis in the energy metabolites.The energy charge is considered an important physiological parameter for the cellular state. Here we observe that nucleotide levels of G0 cells were comparable to the reference steady-state condition (D = 0.1 h−1). 50% of the metabolites were lower (1.2- to 100-fold change) . Especially: (1) upper glycolysis had significantly reduced concentrations while TCA cycle intermediates remained comparable to growing cells, (2) some amino acids  were increased more than 8-fold. The pathway specific increases or decreases suggest a coordinated regulation of these metabolites. Especially, the increase in specific amino acids like Trp or Phe that require ATP during synthesis supports a coordinated behavior.In G0 cells, 28% of the 54 measured intracellular metabolites showed a higher (1.2- to 62-fold) concentration compared to the reference condition : (1) concentration low in G0, increased to a maximum around 90–120 min (later G1/S phase), (2) an increase till a maximum around 50 min (middle G1 phase) was reached, after that a decrease, (3) the highest concentration was observed in G0 and then decreased till 120 min.The glycogen pool was almost depleted (~ 0 µmol/g DW) after 10 h of starvation while trehalose was one of the largest intracellular pools   which was higher compared to the later steady-state concentration. The glucose uptake rate increased from 0 to ~ 1.4 mmol/g/h within 10 min, consuming nearly all glucose fed to the bioreactor . While the glucose uptake rate was nearly constant after 10 min, the extracellular glucose concentration still increased until about 20 min. This effect is more visible in Fig. S5c, showing the uptake rate as a function of the extracellular concentration. First, the glucose uptake rate increased proportionally with the glucose concentration. Later the uptake was constant while the glucose concentration decreased. This suggests that there are adjustments in the glucose transport capabilities, possibly due to the synthesis of transporters with different affinity and uptake capacity over the fermentation time course.Looking at the intracellular space, it can be observed that the metabolic flux during the first 2.5 min was directed towards glycogen synthesis , trehalose synthesis  and glycolysis . Only 3% (20 μmol/g DW/h) was directed to oxPPP , and much less to trehalose , glycogen  and oxPPP  . The glycolytic and TCA fluxes reached the maximum  as well as trehalose . Significantly decreased is the flux into the oxPPP  and glycogen was again degraded, generating additional flux into G6P  , PFK1 (115%), PFK2 (109%), FBA (84%), TPI (100%), PGK (90%), PGM (98%), GPM (94%), HXK2 (106%) with an average standard deviation of 20%. Most of those reactions are supposed to be equilibrium reactions :Almost all those unique proteins (that were found in one condition but were too low to be detected in other samples) or significantly changed proteins in our conditions agreed with the reported proteomics of stationary/G0 phase cells . In general, the protein levels of the TCA cycle, de novo purine biosynthesis and chorismate pathways were higher than at steady-state, and the enzymes of glycolysis, storage, and PP pathways were lower.Glucose metabolism, amino sugar metabolism, fructose and mannose metabolism, N-glycan biosynthesis: HXK1, UGP1, GPH1 and VAN1. Glycerophospholipid-glycerolipid metabolism: GUT1, especially GPP1, GPT2 and ALD4 increased its concentration.Amino acids pathways: proteins that belong to glutamate metabolism, arginine biosynthesis and degradation and proline biosynthesis were highly produced. Arginine and proline and metabolism were highly induced during the transition, which agrees with the doubling of the flux from α-ketoglutarate (aKG) at t = 10 min.RNA polymerase biogenesis, ribosome biogenesis, ribosome exportation and spliceosome: RNA polymerase subunits, corresponding to the RNA polymerase activity (RNA polymerase I and II) for transcription of ribosomes and mRNA and snRNA, increased their production from 0 to 30 min. Ribosome subunits synthesis RPL12A, RPS31, RPL37A, RPL38 and RPL29 were also induced during transition. Transcription factors HCR1 and TIF5 involved with termination/recycling phases of translation were also peaked in this period. PRP43, spliceosome, a subunit involved in the release of mature mRNA was beginning its transcription during this phase. All these processes coincide with the G1 entrance and cell growth development.The proteins with more important changes in concentration were derived from protein measurement at t = 30 min. These proteins belong to nucleotide phosphate metabolic process, nucleotide metabolic process, cellular amino acid metabolic process, polysaccharide metabolic process, cellular polysaccharide metabolic process, and carbohydrate metabolic process.Several rearrangements of fluxes at the level of PPP occurred at 65 min (G1 phase). The change at the level of PPP proteins coincides with a drop in concentration in most of the rest of the proteins. The drop in concentration could be related to an enhanced volume of the cells due to growth. GND1 concentration enhanced at this phase, which agrees with the turn off of the production of Rib5P. This high rearrangement at the level of PPP is for enhancing the level of nucleotides and NADPH necessary for RNA transcription that is enhancing demand during late G1. It has been reported that an increase in NADPH demand to 22 times the anabolic requirement for NADPH was accompanied by the intracellular accumulation of PPP metabolites consistent with an increase in flux through this pathway. NADPH demand agreed with NCP1 concentration peak. NADPH–cytochrome P540 reductase is a protein that catalyzes the transfer of electrons from NADPH to the cytochrome P450 protein, which is required to activate oxygen for the oxidation reactions. In addition GND1, UGA1, MAE1 and HAS1 belong to the oxidative stress pathway. Reactive oxygen species (ROS) can be generated as a result of an enhanced respiration which could signal the initiation of S phase in a later stage. It has been reported that increase in the ROS steady-state level is required for entry into S phase, i.e. an increase in endogenous ROS levels in fibroblasts is necessary for cell cycle progression through the G1 phase of the cell cycle  be metabolized by the glyoxylate cycle. PRP43 (spliceosome), GDH1 (NADPH generation) and NDE (NADH) peaked at this time point, and NADH and NADPH pathways were also highly active. At 120 min, a peak in concentration in UGP1 could be related with a high influx to glycogen build up and burn. In addition, GND1, an isoenzyme of the oxidative pentose phosphate reached a peak at 120 min which doubles the flux at 87 min. HXK1 peaked at this stage probably to phosphorylate income glucose or free glucose. Interestingly, one subunit of the fatty acid oxidation FAA1 also peaked at this stage, in addition ALD4 peaked at this point probably to avoid the production of by-products and reroute AcCoA towards TCA. Glutamate synthesis and degradation (UGA1 and CAR2) can be highly active during S phase. Interestingly a multifactor translation initiation factor (TIF5) peaked at this phase. In addition, RPL38, one subunit of the ribosome peaked at this stage.S. cerevisiae during G0 exiting, re-entering G1 and the initiation of the S phase was monitored. Additionally, protein levels were measured during the transition. The used experimental setup consisted of two independent bioreactor cultivations, operated under the same conditions. Based on this biological redundancy, together with the applied dense time series measurements, we are convinced that the obtained results are highly reliable and reproducible.Using current fluxomics and metabolomics approaches, the metabolite and flux pattern in G0 cells responded very quickly to increased extracellular glucose availability and rapidly entered G1 (88% of the population) in 25 min. The glucose uptake rate increased from 0 to 1452 μmol/g DW/h within 10 min. The short time span of the first transition suggests that the G0 exit was mainly triggered by the changed extracellular conditions (glucose) and metabolic activity. In later phases the contrary was observed, i.e. intracellular fluxes did change while the extracellular environment (glucose concentration) was constant. This suggests that after 10 min, intracellular mechanisms like cell cycle dependent regulation rather than extracellular stimuli influenced the metabolic fluxes.Storage metabolism was highly dynamic: the fluxes to trehalose and glycogen were highest during G0 exit.Both trehalose and glycogen then decreased to the minimum at t = 65 min, and degradation of storage compounds contributed significantly to the glycolytic flux (21%).A major rearrangement occurs at the level of PPP at t = 65 min, and oxPPP/glycolysis split ratio reached a maximum of 36.4%. In all other phases the oxPPP flux was much lower (< 10%). This rearrangement occurred in late G1 in which G1/S transition seems to occur.Anaplerotic reactions such as glyoxylate shunt increased at t = 87 min (initiation of S phase).The flux distribution changed dynamically and specific events were observed during the transition. Especially,13C model does not balance cofactors, there is no impact of TCA cycle flux values on glycolysis or other pathways.The model used in this work did not consider different compartments. This simplification might bias the results obtained for the TCA cycle fluxes, i.e. when there would be significantly different metabolism in the mitochondria and in the cytosol Below is the link to the electronic supplementary material.


Production of biofuels and bioenergy precursors by phototrophic microorganisms, such as microalgae and cyanobacteria, is a promising alternative to conventional fuels obtained from non-renewable resources. Several species of microalgae have been investigated as potential candidates for the production of biofuels, for the most part due to their exceptional metabolic capability to accumulate large quantities of lipids. Constraint-based modeling, a systems biology approach that accurately predicts the metabolic phenotype of phototrophs, has been deployed to identify suitable culture conditions as well as to explore genetic enhancement strategies for bioproduction. Core metabolic models were employed to gain insight into the central carbon metabolism in photosynthetic microorganisms. More recently, comprehensive genome-scale models, including organelle-specific information at high resolution, have been developed to gain new insight into the metabolism of phototrophic cell factories. Here, we review the current state of the art of constraint-based modeling and computational method development and discuss how advanced models led to increased prediction accuracy and thus improved lipid production in microalgae. Chlamydomonas sp., Synechocystis sp., and Chlorella sp., have attracted significant attention from the biotechnology industry because of their ability to efficiently transform renewable resources  into biomass and fuel precursors [Photosynthetic microorganisms have been recognized as one of the oldest life forms on Earth . These oecursors .2 levels from 280 ppm before the industrial revolution to today’s 407 ppm [2 emissions have been attributed to the burning of fossil fuels [The world’s ever-expanding requirement for cheap energy and fuel requires constant improvement of production platforms to meet the demand. The increased fuel consumption has led to an increase in global greenhouse gas emissions , exempli 407 ppm , 6. Overil fuels .13C metabolic flux analysis (13C MFA), and elementary modes (EM) analysis. We focus in particular on the latest insights into central carbon metabolism  of oleaginous microalgae obtained by computational modeling as it is most relevant for production of biofuels and fuel precursors. Furthermore, we discuss the impact of time course modeling as well as the importance of incorporating compartmentalization into genome-scale models for microalgae and highlight the complexity of modeling lipid metabolism to increase biofuel productivity.Biofuels are categorized into first-, second-, and third-generation biofuels depending on the type of raw material that is used for their production . First-gyanophyta) and eukaryotic microalgae, the latter including green algae (Chlorophyta), red algae (Rhodophyta), and diatoms (Bacillariophyta). Characteristic for all microalgae is their ability to grow photoautotrophically with CO2 and light as only carbon and energy sources. Several microalgae are also able to grow heterotrophically in the absence of light using various organic substrates, or grow mixotrophically, which refers to the uptake of organic carbon, e.g., glucose, sucrose, or acetate during growth in the light [−1 year−1 [−1 year−1) [Chlamydomonas [Chlorella [Nannochloropsis [Synechocystis [Tetraselmis [Monoraphidium [Ostreococcus [Tisochrysis [Phaeodactylum [Chlamydomonas, Synechocystis, Phaeodactylum) [Microalgae have historically been classified into two classes: bacterial microalgae  , 18. Mic year−1) . Severalydomonas –30, Chlohlorella –35, Nannloropsis –38, Synehocystis –46, Tetrraselmis , Monorapaphidium , Ostreoceococcus , Tisochrochrysis , and Phadactylum –54. The actylum)  also renVarious modeling approaches have been deployed to improve the applicability of microorganisms for industrial applications. Modeling efforts can be categorized into isotope labeling-based, kinetic-based, and constraint-based approaches . IsotopeGenome-scale metabolic models (GSMs) are a mathematical representation of all the available biochemical and genomic information about a specific organism. GSMs have extensively been used to guide strain engineering designs by optimizing biochemical processes within an organism . The recChlamydomonas reinhardtii [Synechocystis sp. [The first GSMs for oleaginous microalgae were reconstructed for nhardtii  and Synestis sp. . Reconststis sp. –60. Manustis sp.  and PATRstis sp. , have bestis sp. . Howeverstis sp. , 64. AutAll GSM models can be expressed as a general mass balance, which includes every metabolite being produced or consumed within the network in its respective reaction. This mass balance takes the form shown in Eq. :1\documeC represents the instantaneous concentration of metabolites inside the cell, the vector contains all reaction rates and the matrix represents the stoichiometric information about reactions and participant metabolites. The stoichiometric matrix is a shared requirement among all constraint-based flux analysis approaches. Each column of this matrix contains the stoichiometric coefficients of a compound for all included reactions. In a similar fashion, each row represents the coefficients of all metabolites that take part in a single reaction [m number of metabolites would render the S matrix of m × n dimensions, with n always greater than m.The vector reaction . An m num number of metabolites, there are m change rates inside vector C, m transport rates, and p intracellular rates that are unknown. The system of equations then comprises only m mass balances and as many as n = 2m + p variables [m − n variables would be required. Large metabolic networks contain degrees of freedom that can amount to several hundreds. Therefore, the so-called core models, focusing on central metabolism, have been developed. These core models are used in metabolic flux analysis, such as the 13C-MFA, i.e., fluxomics. However, it is currently computationally infeasible to use large and compartmentalized metabolic networks for fluxomics analysis. Due to this, metabolic engineers have simplified the problem by transforming Eq.  is a broadly used modeling reaction, which drives the supplemented resources across the metabolic network to produce all known cellular components in the model . Maximizing the BOF allows simulating growth rate and the yield of carbon source to biomass (henceforth referred to as biomass yield). The BOF can be determined from the genome sequence  or throuP. tricornutum [C. reinhardtii, and maximization of hydrogen production rate for both C. reinhardtii [Synechocystis sp. [There are several levels of refinement of the BOF , but it cornutum , 54, maxcornutum , and mincornutum  for C. rnhardtii  and Synestis sp. .C. vulgaris and other phototrophs, it has been shown that the biomass composition is also dependent on nitrogen availability  by parameterizing the differential equations through the method of orthogonal collocation on finite elements, described by Cuthrell and Biegler . The BOFChlorella vulgaris. The time series flux distributions accurately simulate 75% of expression and proteomics data collected over the course of growth, including allosteric reactions and multi-subunit enzymes. This approach also enabled the determination of the net content of nitrogen pools at each condition [Experiment-based BOF constraints are an alternative method to simulate dynamic metabolic behavior . Changesondition . When anondition , but uFBThe aim of uFBA is to calculate internal flux distributions from existing time-course data, e.g., target metabolomics data. These datasets typically contain information about several (five to ten) metabolites such as glycerol, ethanol, and acetate. It is necessary to determine the rate of change of these metabolites from the experimental data and to include these rates in the system of equations . IdeallyMFA is an alternative to FBA which also assumes a steady-state mass balance . When wo13C labeling [The larger the metabolic network, the more the fluxes are necessary to measure for system determination. Therefore, metabolic networks of several hundred reactions require measurements of internal fluxes for most of the fluxes, e.g. by labeling , 31, 42.EM is based on the calculation of all the solutions of the system in Eq.  in the aChlamydomonas [C. protothecoides [C. reinhardtii [Synechocystis sp. [Advances in modeling of microalgae are in part due to the availability of extensive omic datasets. Having full genome sequences available was crucial for generating the initial genome-scale metabolic models for the microalgae ydomonas , 26 and ydomonas . Fluxomihecoides , C. reinnhardtii , and Synstis sp. ). This tstis sp. . In addistis sp. . In thisiCZ843 [iCZ946 [iRJ1321 [iRC1080 [iNS934 [iLB1027 [Nannochloropsis sp. [Several microalgae are able to grow as autotrophs, heterotrophs, or mixotrophs. Some metabolic pathways are only active under certain growth modes, including the oxidative/reductive pentose phosphate pathway , 39, 40,iCZ843 , iCZ946  [iCZ946 , iRJ1321[iRJ1321 , iRC1080[iRC1080 , AlgaGEM[iRC1080 , iNS934  [iNS934 , iLB1027[iLB1027 , and a mpsis sp. .P. tricornutum [Synechocystis sp. [C. reinhardtii [Chlorella sp. [Synechocystis sp. The constraints regarding growth conditions directly affect the way carbon is distributed across the metabolic network, and thus the biomass yield and production rate. So, it is crucial to determine and adjust these constraints if needed for each growth condition. For example, under autotrophic growth the biomass yields have been reported to be close to 100%, since no carbon is lost in the process [2 in oleaginous microalgae has been reported to vary between 37% [Synechocystis sp. [C. reinhardtii [Chlorella sp. [2 due to energy production through the TCA cycle and the oxidative pentose phosphate pathway (PPP) [2 is fixed once again [Synechocystis sp.), 100% (C. reinhardtii) and 80% (Chlorella sp.) assuming a closed system.Experimentally, highest biomass yields have been reported for autotrophic conditions, while lowest were obtained under heterotrophic growth in cornutum , Synechostis sp. , C. reinnhardtii , and Chlella sp. . Mixotroella sp. , in whic process , 53, 79,ween 37%  to 40% fnhardtii  and 50.5ay (PPP) , 53, 79.ce again . ReporteSince light directly impacts microalgae growth and behavior, efforts have been made to define the quality and quantity of light constraints in metabolic models , 37. ModChlorella and determine the pool size of nitrogen [P. tricornutum [Although metabolic modeling has focused on simulating the intracellular environment of a cell under steady state, allowing the accumulation of certain metabolites in pools has proven necessary for the correct prediction of phenotypic states , 87. Metnitrogen . The detcornutum .Eukaryotic microalgae contain different organelles . The exact compartmentalization is species dependent. Accurate annotation of proteins and compartmentalization in the model is necessary for maximizing information content and gaining detailed knowledge about microalgae metabolism. Flux distributions highly depend on the model’s capability for metabolic exchange prediction between organelles. Careful manual curation of these models and delimitation of capabilities while adding reactions and reconstructing eukaryotic models in an automatic matter is thus crucial to achieve maximal predictability .C. pyrenoidosa [The example of nicotinamide adenine dinucleotide phosphate (NADPH) production in eukaryotic microalgae highlights the importance of compartmentalization. The PPP plays the role of producing NADPH in the cytosol, while the electron transport chain (ETC) is in charge of producing it in the chloroplast. Non-compartmentalized models can predict that the entire NADPH demand is supplied by the ETC, rather than PPP supplying NADPH demand outside the chloroplast. This issue was encountered in the first metabolic model of an oleaginous microalgae enoidosa . While tEarly metabolic models were focused on the reconstruction of core algae models, which were later expanded to include genome-scale information Table  19, 20,, 49, 50.C. vulgaris [2 and low light [Nannochloropsis gaditana reported increased lipid productivity under mixotrophic growth conditions [Phototrophs produce several different kinds of lipids, including tri- and diglycerides, phospho- and glycolipids and hydrocarbons . More spvulgaris . Modelinvulgaris , 48, 54,nditions .C. protothecoides was reported to redirect 81% of the input carbon flux toward fatty acid synthesis, but as a consequence decreased its growth rate by 30% [C. reinhardtii was found to accumulate TAG when faced with nutrient limitation, but its growth halted after 8 h of cultivation [Tetraselmis sp. after 24 h, though TAG accumulation continued after this time point. The authors claimed this to be a result of decreased lipid degradation rather than lipid production.When microalgae are subjected to nitrogen depletion conditions, carbon flux is drawn away from photosynthetic pathways as cells shift into the stationary phase and begin to store carbon as starch and lipids. This phenomenon and its effect on biomass composition are displayed in Fig. e by 30% . In a sitivation . Interestivation  reportedC. reinhardtii, are only capable of assimilating two-carbon organic compounds, like acetate [2) and the energy source is light. In the thylakoid lumen of eukaryotic microalgae, the ETC takes advantage of protons from light to store its energy in the form of ATP and NADPH, which are subsequently used to reduce CO2 molecules into triose phosphates (G3P) in the Calvin cycle. G3P can then be converted into glucose 6-phosphate (G6P), sucrose, starch and other sugars in the chloroplast.Most studies on oleaginous microalgae have focused on the central carbon metabolism and revealed new findings about glycolysis, PPP, TCA cycle, and the Calvin cycle. Figure  acetate . When gl acetate . In micr acetate . Under aC. reinhardtii grown with acetate [C. protothecoides grown with glucose. However, under autotrophic and mixotrophic conditions, only half of the activity has been reported [C. reinhardtii was operating as two branches with production of 2-oxoglutarate on one end, and malate on the other, with an input through oxaloacetate via the anaplerotic activity of the phosphoenolpyruvate carboxylase  dehydrogenase and succinyl CoA synthetase [The TCA accounts for the highest carbon fluxes and number of active reactions under heterotrophic growth conditions , 35. Und acetate  and 18.7reported , with onreported . The rolreported  reportedase Fig. . Zero flnthetase , 78. Knonthetase  have claP. tricornutum a low flux through the whole PPP pathway was determined. The reduced flux is explained with this organisms’ ability to obtain 5-carbon carbohydrates via phosphopentose epimerase [The oxidative and reductive phases of the PPP serve different purposes. While the oxidative phase serves as a catabolic pathway for NADPH production from the oxidation of G6P, the reductive phase represents an anabolic pathway of biosynthesis of 5-carbon carbohydrates for synthesis of nucleic acid, coenzyme A, ATP, and other biomass and lipids biosynthetic precursors . High flpimerase .C. reinhardtii under autotrophic conditions. In the latter study, cells were found to prefer indirect energy transport by taking G3P from the chloroplast to the mitochondria and degrading it to 3-phosphoglycerate (3PG), releasing both ATP and NADH [C. reinhardtii uses acetate as a carbon source instead of glucose greatly affects its phenotypic behavior and flux distribution under heterotrophy. Since the input to the PPP is G6P, incoming acetate would have to be transformed through several reactions in the glyoxylate shunt to oxaloacetate and then to G6P  subsequently [C. reinhardtii the majority of carbon flux was found to be directed toward the Calvin cycle, rather than glycolysis and TCA under mixotrophic growth [Synechocystis sp. however, was found to be dominated completely by the organic carbon uptake before a specific threshold of light intensity was surpassed. After this verge of irradiance, rubisco-dependent carboxylation and oxygenation were increased immediately and all Calvin cycle reactions were activated [Reducing equivalents and ATP formed in the ETC under autotrophic conditions are used later in the Calvin cycle to produce triose phosphates (G3P) for further synthesis of carbohydrates, which can be assimilated or turned into backbone structures of lipids. During autotrophic growth conditions, the entire anabolic activity relies on the Calvin cycle. G3P is transformed into higher carbohydrate molecules, such as pentoses and hexoses, through the PPP and gluconeogenesis, respectively. Moreover, lipid and amino acid anabolism is dependent on pyruvate produced from the G3P . It has equently . Naturalc growth . The cyactivated .Great advances have been made in constraint-based modeling of photosynthetic microorganisms over the last two decades. Metabolic modeling has been proven critical for our understanding of complex metabolism in microalgae. Model-driven approaches have helped to identify boundaries for light and nutrient conditions as well as suitable genetic targets to increase lipid productivity. Metabolic models have progressed from core models to genome-scale metabolic models, which now include detailed compartmentalization and light uptake. Furthermore, the dynamic behavior and rapidly changing phenotypes due to changing environmental parameters are important traits of these organisms and have now been included in model simulations. Those recent extensions and improvements allow elucidating phenotypic behavior under different growth and culture conditions over time. In addition, these new models provide a high-quality standard for the improvements of existing metabolic models as well as for future reconstructions. Despite extensive efforts on refinement and manual curation of metabolic models, there are still open questions regarding the central metabolism and dynamic biomass composition in microalgae. Coupling metabolic modeling with fluxomic experiments can improve our knowledge of the activity of the glyoxylate shunt and ornithine shunt. Furthermore, time course-dependent expression datasets are needed to constrain and validate the models and to gain insight into the dynamics of metabolism. These datasets will enable to broaden the scope of the models and to elucidate missing transport reactions. Multi-omics dataset can also increase the predictability of carbon exchange and storage within the cell and guide improved production of desirable compounds in microalgae.


Cell wall antibiotics are crucial for combatting the emerging wave of resistant bacteria. Yet, our understanding of antibiotic action is limited, as many strains devoid of all resistance determinants display far higher antibiotic tolerance in vivo than suggested by the antibiotic-target binding affinity in vitro. To resolve this conflict, here we develop a comprehensive theory for the bacterial cell wall biosynthetic pathway and study its perturbation by antibiotics. We find that the closed-loop architecture of the lipid II cycle of wall biosynthesis features a highly asymmetric distribution of pathway intermediates, and show that antibiotic tolerance scales inversely with the abundance of the targeted pathway intermediate. We formalize this principle of minimal target exposure as intrinsic resistance mechanism and predict how cooperative drug-target interactions can mitigate resistance. The theory accurately predicts the in vivo efficacy for various cell wall antibiotics in different Gram-positive bacteria and contributes to a systems-level understanding of antibiotic action. Antibiotics targeting cell wall synthesis display an unexplained gap between in vivo efficacy and in vitro binding affinity for their target. Here, Piepenbreier et al. develop a model for bacterial cell wall biosynthesis, show how it is affected by antibiotics, and use it to predict in vivo efficacy of antibiotics. Escherichia coli mathematical modelling accurately predicted non-trivial susceptibility patterns against ribosome-targeting antibiotics at different growth rates1, showed that a positive feedback on resistance gene regulation can lead to growth bistability of an E. coli population under chloramphenicol treatment2, and revealed how non-optimal responses to DNA stress under ciprofloxacin treatment can lead to suppressive drug interactions when combined with ribosome-targeting antibiotics3. Jointly, these studies demonstrate that intricate interactions between well-characterised biological parts elicit emergent and sometimes counterintuitive physiological responses, which can hardly be understood without theoretical frameworks. However, to date most of the predictive models for drug-target interactions focussed on translation-inhibiting antibiotics, which is facilitated by a well-established theoretical framework describing ribosome partitioning within bacterial cells6. Thus, to gain a better understanding of antibiotics targeting other essential processes, such DNA synthesis, transcription, and cell envelope biogenesis, theoretical models for these essential processes are urgently needed.Theoretical modelling of key biological processes has advanced our understanding of how cells respond towards environmental perturbations, such as antibiotic treatment. For instance, in 8. Despite decades of experimental studies of the cell wall biosynthetic pathway in various organisms, to date there remain significant gaps in our understanding of cell wall antibiotic action. Most strikingly, for many cell wall antibiotics there are vast differences between their in vivo efficacy compared to the in vitro binding affinity for their molecular target—even in strains deleted for resistance determinants that could reduce antibiotic potency in vivo. For instance, in mutants of Bacillus subtilis, Staphylococcus aureus and Enterococcus faecalis lacking all known resistance determinants against nisin, ramoplanin or vancomycin, the minimal inhibitory concentrations (MICs) against these antibiotics are 20–200-fold higher14 than the dissociation constants (KD) for the respective drug-target interaction17, highlighting that these antibiotics are significantly less active in vivo than in vitro. This apparent in vivo efficacy gap led to the notion that either all of these organisms might carry additional, yet undiscovered resistance determinants, or that the antibiotics might be inactivated in vivo, e.g., via sequestration to auxiliary cellular structures, effectively reducing the concentration of active antibiotics18. The variety of compounds, as well as the diversity of species displaying an in vivo efficacy gap, raises doubts about these hypotheses and suggests that there might be another, more universal origin of this phenomenon.Antibiotics targeting the cell wall biosynthetic pathway are amongst the most important, clinically relevant last-resort antibiotics, such as ramoplanin, vancomycin and other glycopeptides20). At the core of this pathway is the lipid II cycle, which encompasses all membrane-associated reactions of cell wall biosynthesis and is responsible for shuttling peptidoglycan (PG) subunits across the cytoplasmic membrane , i.e. bacitracin, friulimicin, ramoplanin, vancomycin and nisin  and N-acetylmuramic acid (MurNAc), cross-linked by a MurNAc-attached pentapeptide  or cross-linking properties (e.g. in Corynebacteria)26, the central lipid II cycle of cell wall biosynthesis is highly conserved throughout the bacterial world , we will adapt the model to Gram-positive-specific cell wall synthesis in a second stage. This will allow us to make testable predictions for cell wall antibiotic action in B. subtilis and other Gram-positive bacteria.The bacterial cell wall consists of an alternating polymer of ide Fig. 24,25. Evrld Fig. . Accordi28. Accordingly, given that the sacculus of E. coli contains N = 3.5 × 106 PG monomers (at a doubling time TD = 36 min)29 and that ~δ = 50% of the produced PG is degraded by hydrolases31, balanced growth requires that the total rate of PG monomer translocation across the membrane, jPG, has to equal 5 lipid carrier molecules33. At the required synthesis rate, this implies that each lipid carrier transitions within 90 seconds through all states of the cycle (UPP > UP > lipid I > lipid I> UPP >…) 33 over lipid I and lipid II 32  and Michaelis–Menten constants (KM) to the values obtained from literature . Taken together, this initial mathematical model for the lipid II cycle provides a first holistic view on this essential metabolic pathway in the Gram-negative model organism E. coli, integrating key biochemical properties, enzyme concentrations and pool levels of cycle intermediates.When the flux across all reactions of the lipid II cycle is balanced, the model predicts an asymmetric distribution of cycle intermediates across the two leaflets of the cytoplasmic membrane. Especially, UPP and lipid II are predominantly found in the external leaflet, while UP displays an even distribution Fig. . Within E. coli features a PG thickness of 1.5 glycan layers on average40, B. subtilis and many other Gram-positive bacteria have a much thicker wall of about 20 layers8. Thus, when comparing Gram-negative and Gram-positive cells of equal sizes and at similar doubling times, the lipid II cycle has to transport PG precursors at a ~13-fold higher rate in the latter (see Supplementary Note E. coli and B. subtilis). Theoretically, increases of the PG synthesis rate can be achieved by tuning three factors: (i) increasing the abundance of enzymes in the lipid II cycle, (ii) increasing the concentrations of lipid carriers, or (iii) increasing the catalytic rates of all associated enzymes. Interestingly, although proteomic studies in B. subtilis and E. coli revealed differences in the absolute enzyme abundances41, their surface concentration is almost invariant between organisms—with typically between 50 and 100 molecules per μm2 for each enzyme species  compared to E. coli (KM = 20 μM43). However, if the goal is to speed up PG synthesis—why does the Gram-positive PG synthetic machinery feature lower substrate affinity while increasing substrate abundance, ultimately leading to comparable levels of enzyme saturation as in Gram-negatives? A potential origin could lie in the speed/affinity trade-off known in enzyme kinetics45, according to which speeding up the kcat value of an enzyme can lead to a sacrifice in substrate affinity and a concomitant increase of the KM value  and speed, i.e., Even though for Gram-positive bacteria a comprehensive biochemical understanding of the PG synthetic machinery, and in particular of the PBPs, has not been laid out, we next integrated all existing quantitative knowledge from diverse species to consolidate them in a modified mathematical model for the Gram-positive cell wall synthesis. First of all, while ies Fig. —showing lue Fig. . For higKM value of MraY. This model is also consistent with the experimentally observed 10–20-fold higher lipid carrier substrate pools, which would then be required to achieve similar levels of enzyme saturation as in Gram-negatives, such that enzymes can operate close to their maximal speeds. Accordingly, to establish a self-consistent generic model for the Gram-positive cell wall biosynthesis, we scaled all parameters for the lipid II cycle in E. coli, i.e., the kcat and KM values, as well as the rate of UPP de novo biosynthesis, by a factor of 13  is met by faster enzymes with 10–20-fold higher catalytic rates. The speed-affinity trade-off then dictates that all substrate affinities will be 10–20-fold lower in Gram-positive enzymes, as observed for the oli Fig. . AlthougKD) for the antibiotic/target interaction have been characterised in vitro  we predict a hyperbolic decrease of the total PG synthesis rate with increasing antibiotic concentration, reaching 50% of the maximal PG synthesis rate at 1.8 μM bacitracin (IC50BAC) , which effectively sequesters lipid carriers from the cycle and thereby triggers a concerted decrease of all free cycle intermediates  Fig. . To undeons Fig. . Here ittes Fig. . Thus, f50 value (IC50NIS = 10 μM) about 700-fold higher than the in vitro dissociation constant entering the model simulation (KDNIS = 0.015 μM48)  of the total number of lipid carriers in the cycle  rises to ~50% of the total abundance of cycle intermediates  Fig. —qualitat II Fig. . Howevercle Fig. , therebytes Fig. , therebytes Fig. . Thus, wlue Fig. . In summ50 values with experimentally determined MICs for the given antibiotics  was ~100-fold higher than the predicted IC50 value (IC50BAC = 1.8 μM). However, the model did not factor in the action of the BceAB resistance pump, which confers high levels of bacitracin resistance to wildtype B. subtilis cells49. The MIC of a strain deleted for bceAB ; instead closely matches the model-predicted IC50, confirming that the in vivo efficacy gap is only ~two-fold for the UPP-binding antibiotic bacitracin  is only a factor of two higher than the experimental MIC of a strain deleted for the primary nisin resistance determinant , revealing a 330-fold higher in vivo MIC compared to the in vitro KD  lipid carrier intermediates of the cycle are summarised as a bactoprenol reservoir, Sreservoir, which can be interconverted into the unbound lipid carrier with first order rate constants k1 and k−1, leading to PG synthesis at a rate A] according to50 in vivo is not only governed by the biochemical properties of antibiotic binding, but strongly influenced by two factors governing the lipid II cycling reactions: First, the dissociation constant for the antibiotic-target interaction is substituted by the in vivo dissociation constant, γ, as well as the kinetics of antibiotic binding and unbinding from its target (see Supplementary Note B. subtilis (15 μM) is expected to be much smaller than the sum of all other carrier intermediates (2700 μM), the model predicts a buffering factor for the lipid II binding nisin of Next, we wanted to derive an intuitive mathematical formula describing how antibiotic susceptibility depends on the pool size of the targeted lipid carrier, thereby rationalizing the origin of the in vivo efficacy gap. To obtain a closed analytical expression for the PG synthesis rate as a function of the antibiotic concentration, we considered a simplified model of the lipid II cycle  the model predicts an in vivo efficacy gap similar to nisin n = 2), for which the model predicts a 20-fold lower efficacy gap B. subtilis (MICVAN = 0.35 μM9) is remarkably similar to the value predicted for the cooperatively binding variant (IC50VAN = 0.65 μM) , which we find in excellent quantitative agreement with experimental data (MICRAM = 0.49 μM10) , a similar level of target binding is achieved at a 22-fold lower antibiotic concentration compared to hyperbolic binding kinetics (n = 1)  is drastically more active than nisin (n = 1), although both antibiotics have almost identical in vitro dissociation constants to lipid II. Thus, cooperativity in drug-target interactions can greatly boost the vivo efficacy of the drug by more efficiently sequestering the target as soon as the KD value is exceeded.Following a similar rationale as before, the half-maximal rate of PG synthesis is now reached at an antibiotic concentration of 180 Fig. . Intuiti.6% Fig. . Clearly 1) Fig. . This exn = 1) to dimeric target binding (n=2) will increase antibiotic potency by a factor 57, our model predictions for monomeric binding (IC50FRI = 1.46 μM) are in excellent agreement with the experimental susceptibility in B. subtilis (MICFRI = 1.15 μM58) , Amycolatopsis orientalis (vancomycin) or Actinomycetes species (ramoplanin)65.Over the last decade quantitative experimentation and theoretical modelling has fostered significant progress in our understanding of antibiotic action against bacteria22. Although molecular studies have revealed how cooperativity can emerge from glycopeptide–lipid II interactions66, it remained enigmatic why it has such a drastic effect on antibiotic efficacy in vivo. Our work reveals that cooperativity alleviates the buffering effect within the lipid II cycle, such that much less antibiotic is required to achieve a similar level of target-inhibition compared to a non-cooperatively binding drug  and for vancomycin (MICVAN/KDVAN = 24 12), and also the MIC of E. faecalis against vancomycin exceeds the in vitro dissociation constant 47-fold14—all very similar to the values in B. subtilis  binding low-abundant cycle intermediates in a highly cooperative manner or by (ii) targeting the high-abundant intermediate pools. In addition, our model of the lipid II cycle provides the basis for broader analyses of various further classes of cell wall antibiotics, such as drugs inhibiting the enzymes in the lipid II cycle (e.g. beta-lactams inhibiting PBPs) or drugs targeting the substrates of PG precursor production (e.g. fosfomycin). To this end, the model will need to be expanded, e.g., to explicitly incorporate the biochemical characteristics and copy numbers of all redundant PBPs , highlighting the importance of further biochemical studies of PBPs and other lipid II cycle-associated enzymes for developing a complete systems-level description of this essential cellular pathway. Likewise, the seamless biochemical characterization of enzymes involved in PG precursor synthesis and cell wall recycling will enable quantitative modelling of drugs interfering with these important aspects of cell wall synthesis. Hence, the presented model serves as an excellent starting point to develop a whole-cell model of antibiotic action. One important aspect will be the development of theoretical models describing the regulation and action of known resistance mechanisms (which are deleted in the strains considered in this work), to provide a systems-level description of antibiotic action in wildtype cells. First steps in developing such models have been made, e.g., for the bacitracin resistance determinant BceAB in (i)IN = internal pool of undecaprenyl pyrophosphate (UPP)UPPOUT = external pool of undecaprenyl pyrophosphateUPPIN = internal pool of undecaprenyl phosphate (UP)UPOUT = external pool of undecaprenyl phosphateUPLI = pool of lipid IIN = internal pool of lipid IILIIOUT = external pool of lipid IILIIThe individual states of lipid carrier are included as time-dependent variables in the model, distinguishing between lipid carriers localised in the inner (IN) and outer (OUT) leaflet of the cytoplasmic membrane:(ii)35 at sufficiently high levels to saturate the enzymes of the corresponding reactions (Supplementary Table The cytoplasmic production of soluble PG precursors (UDP-MurNAc-pentapeptide and UDP-GlcNAc) is not described in detail in the model. Since the precursor pool levels are homeostatically controlled(iii)TD. Likewise, the growth-dependent dilution of all individual lipid intermediate pools occurs at a rate The de novo synthesis of UPP in the cytoplasm has to balance the overall growth-driven dilution of all lipid II cycle intermediates. To this end, we assume a constant UPP production rate (iv)Si), enzyme levels (E), catalytic constants of the enzymes (kcat) as well as the Michaelis–Menten constants (KM) parameterise the reaction dynamics.The individual enzymatic reactions are modelled by Michaelis-Menten kinetics, for which substrate levels ((v)IN to LIIOUT) are largely unknown, and the flipping of UPP (UPPIN to UPPOUT) and UP (UPOUT to UPIN) was only hypothesised, for parsimony reasons we assumed first order kinetics for these reactions, as quantified by an effective rate constant ki .Since the biochemical properties of the enzymes catalysing the flipping reaction of lipid II  and its target (T) (where T can be any of the dynamic variables in Eqs. (AT),kass = 0.75 μM−1 × min−1 (as measured for the binding of bacitracin to its target UPP 72) and calculated the dissociation rates from experimentally determined in vitro dissociation constants 50).In order to accommodate cell wall antibiotic treatment in the theoretical model of the lipid II cycle, we considered ligand-binding between the antibiotic ( in Eqs. –9)\docum in Eqs. –10 was eKD values) as well as the cooperativity of antibiotic-target-interactions (defined by the Hill coefficient n)  can bind to its free target (Sunbound) within the lipid II cycle with in vitro dissociation constant Sbound), but now the sum of all other, non-target lipid II cycle intermediates are represented as ‘bactoprenol reservoir’ (Sreservoir). For simplifying reasons, the inter-conversion of one species into the other follows first order kinetics, determined by the equilibrium constant α balances the overall growth-driven dilution of all reaction species with rate γ:Sreservoir), and later consider the scenario in which new lipid carriers feed the free target pool (Sunbound), the latter of which is the case for UPP-binding antibiotics. In flux-balance STOT = Sreservoir + Sunbound + Sbound) is given byk−1, k1 ≫ γ (see Supplementary Note E. coli), both solutions can be approximated byA]) compared to the unperturbed synthesis rate isTo arrive at an analytical expression for the PG synthesis rate in dependence on the antibiotic concentration, we developed a reduced model of the lipid II cycle Fig. . Similarmentclass2pt{minimjPG is reached at an antibiotic concentration 50 clearly scales with the n-th root of the ratio between bactoprenol reservoir and target pool in the absence of antibiotic (Starget).When incorporating cooperative drug-target binding as in Eq. , we analKM values of the respective enzymes . To constrain the model to a physiological parameter regime we followed the rationale detailed in the Supplementary Note lsqnonlin imbedded in the MATLABTM software, solving nonlinear least-squares curve fitting problems of the formχ2 of the residual at χ2) was defined as the final parameter set (Supplementary Table The numerical solution of the differential equations and all simulations were performed with custom scripts developed in MATLABFurther information on research design is available in the Supplementary InformationReporting SummaryPeer Review File