Arabidopsis thaliana plant leaves. In combination with experimental measurements, we show how the regulated interplay between diurnal starch and organic acid accumulation defines the plant acclimation process. We confirm fumarate accumulation as a requirement for cold acclimation and further predict γ–aminobutyric acid to have a key role in metabolic signaling under cold conditions. These results demonstrate how flux sampling can be used to analyze the feasible flux solutions across changing environmental conditions, whereas eliminating the need to make assumptions which introduce observer bias.The development of high-throughput ‘omic techniques has sparked a rising interest in genome-scale metabolic models, with applications ranging from disease diagnostics to crop adaptation. Efficient and accurate methods are required to analyze large metabolic networks. Flux sampling can be used to explore the feasible flux solutions in metabolic networks by generating probability distributions of steady-state reaction fluxes. Unlike other methods, flux sampling can be used without assuming a particular cellular objective. We have undertaken a rigorous comparison of several sampling algorithms and concluded that the coordinate hit-and-run with rounding (CHRR) algorithm is the most efficient based on both run-time and multiple convergence diagnostics. We demonstrate the power of CHRR by using it to study the metabolic changes that underlie photosynthetic acclimation to cold of  Flux sampling minimizes observer bias and is therefore a powerful tool for studying metabolic acclimation. Unlike other methods, flux sampling can be used without assuming that metabolism is optimized towards a single objective. This is particularly useful when studying metabolism in changing environments. A team lead by Jean-Marc Schwartz compared three different flux sampling algorithms in order to identify the most appropriate method to analyze changes in metabolic phenotypes. They applied flux sampling to several large-scale networks of plant metabolism to predict metabolic properties across changing temperatures. In order to breed plants for global climate changes, the limits on photosynthesis and metabolism across different environmental conditions need to be understood. Here, they used flux sampling methods to understand changes in photosynthesis and carbon accumulation in cold temperatures. They showed how an intricate balance between carbon and nitrogen metabolism is crucial for acclimation to cold. Metabolism describes a cellular phenotype under given conditions, and changes in metabolite concentrations and reaction fluxes can be used to assess a cellular response to changing environmental conditions.High-throughput technologies have resulted in a rapid increase in available ‘omic data sets.3 CBM imposes stoichiometric constraints on the metabolic reactions and analyzes the possible flux solutions at steady state. Because the system is assumed to be at steady state, even genome-scale models can be solved at little computational expense.With the existence of large-scale metabolic networks comes the need to have appropriate modeling techniques available for their analysis. The majority of techniques for analyzing large-scale metabolic networks fall within the paradigm of constraint-based modeling (CBM).4 The key feature of FBA and FVA is that they compute the steady state of a model using an objective function. The objective function defines a reaction that is to be maximized or minimized when solving the system under the set constraints. A typical objective is “maximum biomass production”, whereby essential macromolecules such as proteins and lipids are defined at known ratios or quantities in an outgoing reaction of the metabolic system.6 FBA computes single steady-state solutions, which satisfy the objective. However, often multiple solutions exist and their range can be computed using FVA.7 FVA provides no indication as to whether all single-point solutions within the range are feasible and which solutions are the most likely. In order to reduce the number of feasible solutions of FBA and to further constrain the feasible flux ranges returned by FVA, it is common practice to introduce multiple objective functions.8Two of the most widely used forms of CBM are flux balance analysis (FBA) and flux variability analysis (FVA).9 Although biomass production as estimated by FBA was seen to match experimental data in Escherichia coli,10 this may not be an appropriate objective when studying short-term environmental changes. In the green algae Chlamydomonas reinhardtii, a 13C-metabolic flux analysis was shown to contradict the assumptions of a prior FBA analysis by demonstrating that maximum biomass and maximum ATP production cannot stand alone as cellular objectives.11 Optimal growth conditions, to which most objective functions are tailored, are an exception in natural environments.5 Evolutionarily, metabolism is most likely optimized for overall robustness across many conditions, rather than a single condition-specific objective. Bacillus subtilis mutants, which outperform the wild-type in terms of biomass production in control conditions have been found experimentally; the wild-type, however, is more robust to both environmental and genetic perturbations and therefore holds an evolutionary advantage.12However, defining one or multiple objective function(s) intrinsically introduces an observer bias as to what the main “goal” of the cell is, in the context of the analysis.14 in crop sciences, optimization for increased yield in control conditions rather than in changing environments is a likely explanation for discrepancies between laboratory and in field results.16Understanding the optimization process that allows an organism to tolerate changing environmental conditions is of particular interest in crop sciences, where increasing yields will need to be achieved, despite rapidly changing environmental conditions. Owing to their sessile nature, plants are exposed to frequent and sometimes extreme environmental fluctuations. Plant metabolism can therefore be presumed to hold an inherent robustness to changing environmental conditions. Furthermore, plant metabolism is highly intricate as it includes multi-cellular autotrophic and heterotrophic tissues with complex cellular compartmentalization. Analyses of plant metabolism and of plant metabolic strategies can therefore be considered a comprehensive case study of metabolism in general. Genetic modifications do not always produce a desired effect owing to network robustness:17 however, owing to their computational intensiveness, these methods are only efficient when applied to small, simple networks18 or genome-scale models with one or more objective function.19 When wanting to analyze genome-scale metabolic networks without the use of an objective function, such approaches cannot practically be applied. Sampling of feasible flux solutions provides a realistic alternative.If we wish to use CBM techniques to assess network robustness and phenotypic plasticity, we must be able to capture all alternative solutions and the probability with which they occur (the solutions space) of a metabolic network across different conditions. To calculate the exact properties of the solution space, we can use mathematical techniques such as convex analysis and vertex enumeration;18 A chain of samples is said to have converged once it contains enough samples to give an accurate representation of the solution space.20 Flux sampling provides information both on the range of feasible flux solutions (similar to FVA) but also on their probability. Importantly, unlike FBA, flux sampling does not require  an objective function to be specified. Therefore, flux sampling methods hold great potential for analyzing optimization strategies that are not defined by clear objectives such as a simple biomass reactions.Flux sampling generates a sequence of feasible solutions  that satisfy the network constraints, until the entire solution space is analyzed. Enough samples need to be generated for the samples to provide an accurate representation of the feasible solution space.25 Starch, malate, and fumarate are the three major carbon storage compounds which accumulate during the day in leaves of the model plant Arabidopsis thaliana.27 Increased cytosolic fumarate accumulation is a known cold response of A. thaliana leaves and has been linked to an increased photosynthetic capacity that sustains metabolism in cooler temperatures.24 Evidently, tight regulation of carbon partitioning is required for successful cold acclimation. Given the large number of reactions and pathways involved in linking primary carbon assimilation to its downstream storage products starch, malate, and fumarate, CBM seems appropriate. Of the CBM methods available, flux sampling allows us to gain a detailed understanding of the solution space and the interdependence of the different carbon stores under different temperature conditions, without imposing the constraint of an objective function.When plants are exposed to a change in environmental conditions, such as temperature, which last only for a few days, optimizing biomass production during this period is arguably of secondary importance; sustaining metabolic function with minimal cost may be a higher priority to plants. For example, the allocation of carbon into different transient storage compounds accumulated to maintain cellular processes, has been shown to change when plants are exposed to environmental stresses.A. thaliana have been constructed.32 Here, we used three of them to formally assess for the efficiency of existing and easily accessible flux sampling algorithms: the coordinate hit-and-run with rounding (CHRR),33 the artificially centered hit-and-run (ACHR)34 and the optimized general parallel (OPTGP)35 algorithms. We identified the most efficient sampling method based on run-time and convergence, and applied it to study plant acclimation to cold. We experimentally measured diurnal CO2 uptake and organic carbon accumulation of A. thaliana in control and cold conditions. By constraining a leaf metabolic model to the two conditions and using an appropriate flux sampling algorithm, we were able to explore inherent metabolic robustness to temperature and predict the metabolic changes required to support a photosynthetic acclimation response to cold.Multiple large-scale metabolic networks of the model plant 37 this will, to our knowledge, be the first time that the available algorithms are formally compared with one another in the context of metabolic modeling, and that flux sampling is applied to study network robustness across changing environmental conditions.Although flux sampling has previously been applied as a technique for studying the solution space of metabolic networks,A. thaliana. We tested the run-times of 500,000, 5,000,000, and 50,000,000 samples (S), of which 5000 were stored and the rest were discarded with constant measures of thinning. For S = 50,000,000, the CHRR algorithm was 2.5 times faster than the OPTGP and 5.3 times faster than the ACHR for the Arnold model .40 Notably, different convergence diagnostics test different features and may not always be in good agreement. Therefore, more than one diagnostic should be used to confirm that the sampling chain is likely to have reached convergence.41 The ACHR and OPTGP algorithms have been compared using five genome-scale metabolic models and three different convergence diagnostics, including the PSRF.35 However, the PSRF assumes a normal distribution of solutions,42 which is questionable given that sampling is most needed when the distribution of flux estimates is non-normal,41 as is often the case in metabolic modeling.Previous comparisons between the ACHR and CHRR algorithmsA. thaliana are transferred from 20 °C to 4 °C, photosynthesis is inhibited.24 Metabolism slows down in cooler temperatures and, in order to sustain normal metabolic functions, plants need to acclimate their CO2 uptake, altering the concentrations of metabolic enzymes to achieve a new steady state.44 After 7 days of cold, we observe that the A. thaliana wild-type Col-0 is able to achieve the same level of photosynthesis as measured in control conditions , we were able to compute converged flux sampling distributions for all reactions. We did so for both control and cold conditions, which allowed us to overlay the sampling distributions of reaction fluxes and to assess changes required in plant metabolic behavior for acclimation  over the flux sampling distributions Fig. . This fuBoth sucrose export to other tissues and cytosolic pyruvate production as a precursor for the tricarboxylic acid (TCA) cycle are predicted to be unchanged. The model suggests that, given equal carbon assimilation in control and cold conditions, cellular maintenance and export functions are supported equally in both conditions on the time scale considered. Although sucrose export is difficult to measure experimentally, we observed the rate of respiration in the cold to be the same as in control conditions Fig. . Given t45 a reshuffling of metabolites across cellular compartments has therefore previously been proposed as an important temperature acclimation response.46For fumarate (and other metabolites not shown) the model predicts a shift in cellular compartmentalization with temperature. Model results show an increase in fumarate export from the mitochondrion into the cytosol in the cold. The reverse is shown for fumarate export from the chloroplast, where it is produced via the breakdown of arginosuccinate Fig. . Leaves fum2.2 mutant of Col-0 is unable to acclimate to cold.24 This reaction is thus essential for photosynthetic acclimation to cold.Model results suggest an increase in flux from cytosolic malate to fumarate via cytosolic fumarase (FUM2) Fig. . This isγ-aminobutyric acid (GABA), however, is predicted to increase in the cold. GABA has previously been reported to accumulate in response to environmental stresses, including cold treatment.47 GABA has been suggested as a signaling molecule of the carbon to nitrogen status in plant leaves and evidence for its role in regulating nitrate uptake exists for both rapeseed and A. thaliana.50A. thaliana plants in the cold show increased nitrogen assimilation compared with those in control conditions.51The sampling distributions suggest a trade off between increased carbon compound accumulation and decreased amino-acid production Fig. , linking48 it may be counteracted by the increased accumulation of malate. Increased levels of malate have previously been shown to suppress nitrate reductase expression and activity in tobacco leaves.52 Malate levels in Col-0 may be kept below a certain threshold, by redirecting carbon to fumarate, thereby supporting adequate nitrogen assimilation and an increased photosynthetic capacity. This hypothesis is supported by the observation that A. thaliana mutants, which show increased levels of malate and decreased levels of fumarate, grow significantly less well in high-nitrogen conditions than Col-0.22 Fumarate has few known metabolic functions in A. thaliana leaves,26 and may thus serve the purpose of a carbon storage buffer in changing environmental conditions.If GABA is indeed involved in carbon:nitrogen signaling,Based on run-time and platform, CHRR is faster than OPTGP, which is itself faster than ACHR. CHRR also converges faster than both OPTGP and ACHR. Users with unrestricted access to MATLAB are therefore recommended to use CHRR. For those who wish to work using an open-source platform, OPTGP is recommended over ACHR; in general, OPTGP converges faster than ACHR, has a shorter run-time and allows for parallel processes.20 and that results should confirmed via manual inspections of trace and autocorrelation plots.When running sampling algorithms, sets of flux samples are produced for each reaction in the model. Here, we have tested convergence for all reactions of the models using three different sample chains. We have highlighted the importance of checking for convergence using different diagnostics when analyzing an irregular solution space of large networks. If only a subset of reaction fluxes are of interest, only those distributions will have to be checked for convergence. Flux sampling provides a powerful tool for exploratory analyses assessing metabolic differences across different environmental conditions. Our results further confirm the notion that it is not possible to fully automate convergence analyses using a single diagnosticA. thaliana, we demonstrate how flux sampling can be used effectively to analyze alternative feasible solutions across multiple conditions whilst eliminating the need to make assumptions that introduce observer bias. Given short-term environmental changes, adequately sustaining basic metabolic functions with minimal resource investment may be a more-likely cellular objective on that time scale than, for example, maximizing growth. We therefore did not set an objective function for flux sampling but used four experimentally measured flux values  to constrain a leaf metabolic model.28 We further demonstrated how these flux sampling results can lead to different conclusion than traditional FBA analyses.Flux sampling is currently an under-utilized technique in the metabolic modeling of large-scale networks. Using cold acclimation of the model plant 24 The model further demonstrates the properties of the flux distributions of GABA to differ in cold and control conditions, highlighting GABA as a plausible signaling molecule for supporting a shift in the nitrogen and carbon balance, required to sustain photosynthesis in the cold. Thus, through flux sampling, we were able to generate novel hypotheses about the roles of GABA, fumarate and malate in cold acclimation, which would have been unfeasible to detect using FBA and FVA methods.By constraining the model to both cold and control conditions we were able to select reactions that show different flux distributions across the two conditions. Our model highlights reactions that are essential to change with temperature  such as the production of cytosolic fumarate via malate.By overlaying different FBA solutions onto flux sampling distributions obtained under condition-specific model constraints, FBA in combination with flux sampling, could, in future work, be used to determine plausible objective functions and help generate predictions about how cellular objectives might be changing in response to environmental changes.54 for the MATLAB programming language and the COBRApy package55 for the open-source Python programming language. Three algorithms for flux sampling exist across the two platforms: CHRR (MATLAB), ACHR (MATLAB and Python), and OPTGP (Python). Further flux-sampling algorithms exist;58 however, as they are not currently available in the COBRA packages, they are here not considered for comparison.60The artificially centered hit-and-run (ACHR) sampler estimates the center of the solution space in a “warm-up” phase. This estimate is then continuously revised with further sampling. The center estimate is used to inform the direction of further sampling such that the full solution space is covered in fewer steps than in traditional hit-and-run sampling (where the direction of the next sample is chosen at random).34 Although the Markovian nature of hit-and-run  is lost in the ACHR, it overcomes the edge-trapping limitation of the standard hit-and-run algorithm .The optimized general parallel sampler (OPTGP) is argued to be an improvement on the ACHR, because from the warm-up point it generates multiple short chains from the estimated center and only considers the last point in the chain as a sample.35 It thereby increases the randomness and efficiency with which the total solution space is explored. Furthermore, it allows for parallel sampling. Larger samples can thus be generated in shorter run-times.The coordinate hit-and-run with rounding (CHRR) algorithm starts with a pre-processing step that rounds the solution space to a more regular, convex shape, and therefore a Markov chain can be used to explore the rounded solution space without the limitation of edge-trapping. After sampling, the solutions are back-transformed to match the original solution space in order to obtain the true value of the sampled points.61Constraint-based reconstruction and analysis (COBRA) methods for genome-scale metabolic networks are integrated in the COBRA toolbox62 In flux sampling, an algorithm’s efficiency is defined by the run-time and the number of samples required for apparent convergence to the true flux distribution. Here, we apply three different diagnostics in order to test for convergence:Raftery & Lewis diagnostic: this diagnostic estimates the total number of samples, Nmax, required for a set of samples to achieve convergence, based on a given subset of samples (pilot chain).63 We estimated Nmax required for convergence using the CODA package in R.64 The diagnostic further returns a dependence factor, I, which is indicative of autocorrelation (the degree of dependence between consecutive samples). Chains with I > 5 are here considered to be problematic as this value suggests high dependence between samples or influential starting values .Interval-based potential scale reduction factor (IPSRF): adapted from the original Gelman-Rubin diagnostic, PSRF,40 the IPSRF is based on comparing the differences between consecutive samples  with the total differences observed between all samples . Because interval length, rather than variance of the samples , is considered, a normal distribution of the samples is no longer a requirement.42 As with PSRF, the IPSRF approaches 1 with chain convergence. Here, we consider chains to have failed this convergence diagnostic if IPSRF < 0.9 or IPSRF > 1.1 as calculated using the MCMC Diagnostics toolbox in MATLAB.Gweke diagnostic: this diagnostic, as implemented in the R CODA package,64 tests whether the mean of the first samples of the chain (10%) is significantly different from the mean of the last set of samples (50%) of the chain.65 Assuming that the last set of samples has converged to the stationary distribution, if the two subsets are not significantly different, the entire chain can be considered to have converged. Here we consider chains to have failed this convergence diagnostic if z > 1.28.The aim of flux sampling is to generate enough consecutive samples (a long enough chain) in order to get an accurate depiction of the solution space. A sample chain is considered to have converged once it can be assumed that the sampled subset of solutions represent the properties of the true solutions obtained from an infinite amount of samples .Because each of the convergence diagnostics tests for different criteria, we use all of the above in order to assure sample convergence. Here, we consider the flux sampling distribution of a reaction to have converged if it passes all of the above criteria.55 The linear programming solver used was Gurobi, version 8.0.0. The samplers were used in accordance with COBRA documentation using default parameter settings unless otherwise specified. Although an ACHR implementation is available both in the COBRA toolbox and in COBRApy, the comparisons made here are based on the Python implementation of the ACHR sampler because it is open-source and because the OPTGP, which is available only in Python, directly builds on the general parallel sampler (GP) of the ACHR. We did collect preliminary convergence and run-time data of the ACHR algorithm in MATLAB; however, because its convergence was evidently slower than CHRR, we have chosen to omit its MATLAB implementation from further analyses. OPTGP and CHRR algorithms were run using two parallel processes; there is currently no option to run ACHR as multiple processes.COBRA Toolbox version 3.0.0 and COBRApy version 0.10.1 were installed on MATLAB R2017a and Python version 3.5.2, respectively.A. thaliana metabolic models were obtained in SBML format and are from here on referred to by their first author: the Poolman,32 Arnold,28 and Dal’Molin2 models. The Poolman model is based on the Aracyc database66 and describes a non-compartmentalized heterotrophic culture using 1406 reactions. The Arnold model describes a compartmentalized, photoautotrophic system and is based on 549 manually curated A. thaliana specific reactions. The Dal’Molin model is a compartmentalized network reconstruction of 1601 reactions, applicable to both photosynthetic and non-photosynthetic tissues of plant metabolism.2 The original model constraints32 were used when comparing sampler performance across these models, such that the Arnold, Poolman, and Dal’Molin model had 270, 645, and 330 degrees of freedom respectively.To compare the performance of the samplers, three published genome-scale 67 Sample chains that are thinned store only every kth sample in the chain, where T = k is called the thinning constant. In order to compare autocorrelation of the three algorithms, we applied three different thinning constants  storing 5000 samples for each chain. Three replicate chains were run for each value of T. Convergence diagnostics were calculated for sample chains produced for each of the model reactions. Run-times were obtained on a personal laptop .Samples that are close together within a sample chain can be autocorrelated . In order to avoid the effects of autocorrelation and to ensure convergence, a large number of samples should be run and a technique called thinning can be applied.2 influx and outflux) by the A. thaliana wild-type Columbia-0 (Col-0) was measured using infrared gas analysis at 100 μmol m−2 s−1 light under control conditions (20 °C) and after 1 week of cold treatment (4 °C) as described previously.24 Fumarate, malate and starch concentrations at the onset and at the end of the photoperiod were measured for both control and cold conditions using enzyme assays.24 Averages of 3–4 replicated were calculated. Measurements taken across the different conditions were tested for significant differences using an unpaired t test (p < 0.05) assuming unequal variances, as implemented in R.Carbon assimilation and respiration −1 Day−1. The resulting values were applied as model constraints. Upper and lower bounds were applied according to the calculated standard errors of three to four replicates as shown in Fig. 68Given that the Arnold model is leaf specific and manually curated, it suits the purpose of studying photosynthetic plant acclimation. In order to do so we constrained the model with our experimental diurnal flux data for malate, fumarate, and starch accumulation as well as COage Fig. . DiurnalFurther information on research design is available in the reporting summary


Phytophthora infestans as a first step towards an integrative model with its host. We predict the biochemical reactions in different cellular compartments and investigate the gene–protein–reaction associations in this model to obtain an impression of the biochemical capabilities of P. infestans. Furthermore, we generate life stage‐specific models to place the transcriptomic changes of the genes encoding metabolic enzymes into a functional context. In sporangia and zoospores, there is an overall down‐regulation, most strikingly reflected in the fatty acid biosynthesis pathway. To investigate the robustness of the GEM, we simulate gene deletions to predict which enzymes are essential for in vitro growth. This model is an essential first step towards an understanding of P. infestans and its interactions with plants as a system, which will help to formulate new hypotheses on infection mechanisms and disease prevention.Genome‐scale metabolic models (GEMs) provide a functional view of the complex network of biochemical reactions in the living cell. Initially mainly applied to reconstruct the metabolism of model organisms, the availability of increasingly sophisticated reconstruction methods and more extensive biochemical databases now make it possible to reconstruct GEMs for less well‐characterized organisms, and have the potential to unravel the metabolism in pathogen–host systems. Here, we present a GEM for the oomycete plant pathogen  It is eet al., et al., The foundation of a GEM is the set of biochemical reactions that may occur in a cell, often catalysed by enzymes. Hence, the identification of enzyme encoding genes in the genome of an organism can help to reconstruct an overview of its biochemical capabilities  We identified all putative enzymes encoded in the Phytophthora infestans is able to assimilate a range of nitrogen compounds, preferably amino acids, but also inorganic forms, such as nitrate  and the cofactors Coenzyme‐A, NADH, NADPH and FADH2, which are generally essential for a eukaryotic cell . It has been reported that many eukaryotes have a highly conserved, independent mitochondrial FAB pathway that is crucial for development  cycle typically occurs in the mitochondria . P. infestans was initially unable to simulate growth  because of missing reactions or invalid reaction directionality constraints. This can be the result of an incomplete genome sequence or misannotations. We therefore performed a model gap‐filling optimization to find the minimal set of reactions in KEGG that must be added to the model to correct this . This method proposed 16 additional reactions, and highlighted three reactions that must be reversed to allow for the production of all biomass precursors. Next, eight extra drain reactions were added to the model to satisfy the steady‐state constraint. Notably, no gap‐filling solutions were found for the production of the fatty acids EPA and behenic acid (a.k.a docosanoate), both of which are produced by P. infestans  and 107 associated genes were removed from the model. The reconstructed metabolic model of P. infestans have been studied . However, a more precise examination of the genome sequence revealed an unannotated open reading frame  that probably encodes this enzyme.After all correction steps, 928 of the 2394 (39%) reactions in the model were able to carry flux based on the defined growth medium, 377 of which carried a non‐zero flux when we calculated the optimal fluxes for maximal biomass production . Of the 2685 metabolites in the model, 809 could not be produced based on our defined growth medium, and may require additional nutrient uptake. By iteratively adding uptake reactions to the model for each of these metabolites, we can simulate whether the import of a specific metabolite would allow the production of additional metabolites (Table S2). This reveals unresolved gaps in the model that could have a technical cause, but may also hint at biological properties. For example, episterol is proposed as a compound that would enable the production of four other metabolites. This is striking as P. infestans GEM  with GEMs of other eukaryotic microbes . Although these numbers might be smaller because of the genome annotation quality and the level of model curation, they might also be a result of the loss of primary metabolic pathways, for which these parasites rely on nutrient import from their hosts . The diatom model is presumably of higher quality, as most reactions are manually curated. However, it might also hint at less redundancy of metabolic enzymes.The relation of a gene to an enzyme and its associated reactions is called the gene–protein–reaction (GPR) association , and deployed the iMAT algorithm . For instance, the mycelium model contains two unique reactions of the ‘Vitamin B6 metabolism’ pathway (KEGG R00173 and R00174), which represent the interconversion of pyridoxal (vitamin B6) to pyridoxal phosphate, an important cofactor for a large number of reactions, especially for the synthesis of amino acids  a straightforward procedure. However, gene silencing is feasible and has been applied to study the function of several genes involved in pathogenesis or signal transduction. The first functional study dealing with genes involved in primary metabolism was published only recently. Abrahamian et al. . By building this model, we can identify genes that have an essential role when converting simple nutrients to the building blocks of life. The metabolic model reconstructed here provides a scaffold for future genome‐wide systems biology approaches to characterize the metabolism of P. infestans, and is an essential first step towards an integrative model of P. infestans–host interactions.Life stage‐specific models provide a direct functional context for transcriptome data by predicting the behaviour of getKEGGModelForOrganism method from the RAVEN Toolbox , currently hosted at the National Center for Biotechnology Information . Default parameters were maintained for hmmbuild and hmmsearch, and an E‐value threshold of 10−20 was applied for hmmsearch. Similar to the getKEGGModelForOrganism function of the RAVEN Toolbox log(EbestKO)<0.9, where E represents the E‐value of the respective protein to a KO group, and EbestKO represents the E‐value of the best‐matching KO group for that protein. In other words, protein hits are often removed if they have a better match to another KO group. Second, any protein match to a KO group was removed if log(E)log(EbestProt)<0.5, where E again represents the E‐value of the respective protein match to a KO group, and EbestProt represents the lowest E‐value of any protein to this KO group. This reduces the number of matches per KO group to reduce the number of false positives, as there is clearly a better matching protein. Subsequently, we retrieved all KO annotations of P. infestans from KEGG (organism ID ‘pif’). The combined set of matched KO groups was used to retrieve all associated reactions and metabolites from KEGG. Consequently, each reaction in the model was associated with a number of P. infestans genes. We hypothesized that each of the genes associated with a reaction is able to catalyse it. We did not consider enzyme complexes, which together would fulfil a single enzymatic task. Reactions were removed automatically if their stoichiometry was undefined  + UDP‐D‐glucose <=> 1,3‐beta‐D‐glucan(n + 1) + UDP’), and if the same metabolite ID occurred at both sides of the reaction arrow, which implies a polymer reaction (e.g. ‘UTP + RNA <=> diphosphate + RNA’). In addition, reactions that were associated with metabolites containing the substrings ‘acceptor’, ‘donor’, ‘tRNA’, ‘enzyme’, ‘aglycon’ and ‘fatty acid’ were removed.We re‐implemented the 1b Eddy,  to trainP. infestans proteins using LocTree 3  to solve the (mixed‐integer) linear programs.The initially reconstructed model was exported to SBML and Microsoft Excel format using CobraPy v0.4.1  from the model, and then iteratively adds uptake reactions for these metabolites, to see whether the uptake of these metabolites unblocks metabolites elsewhere in the model.After these correction steps, we used the function et al., unpublished data) to quantify gene expression in four in vitro life stages of P. infestans, i.e. mycelium, sporangia, zoospores and germinating cysts. Gene expression of P. infestans strain T30‐4  incorporated in the COBRA Toolbox , mitochondrion (mito), extracellular space (extr), endoplasmic reticulum (ER), peroxisome (pero), Golgi complex (golg) and vacuole (vacu). The bars at the bottom left show the total numbers of reactions in each subcellular compartment. The connected bullets indicate the compartments that are compared, and the bars in the graph represent the number of reactions  that overlap between the compartments.Click here for additional data file.Fig. S2 Frequencies of gene numbers per reaction (a) and reaction numbers per gene (b) in the Phytophthora infestans model.Click here for additional data file.Fig. S3 Transcriptome data of Phytophthora infestans in relation to stage‐specific metabolic models. (a) Distributions of transcripts per million (TPM) expression values of all P. infestans genes (background) and the genes in the model, combined from four life stages. The red line indicates the TPM threshold set to distinguish expressed/non‐expressed genes in the model. (b) The percentages of all P. infestans genes (background) and the genes in the model for which gene expression in each life stage exceeds the TPM threshold. MY, mycelium; SP, sporangia; ZO, zoospores; GC, germinating cysts.Click here for additional data file.Fig. S4 Numbers of reactions per KEGG pathway that are shared between the Phytophthora infestans life stage‐specific models of mycelium (MY), sporangia (SP), zoospores (ZO) and germinating cysts (GC). The colours of the tiles scale to the relative frequencies of all non‐core reactions (i.e. the reactions that are absent in at least one stage‐specific model). The numbers in the two right‐most columns represent the core set of reactions  and the total set of reactions for the respective pathway (core + non‐core).Click here for additional data file.Table S1 Properties of all reactions in the Phytophthora infestans model.Click here for additional data file.Table S2 Gap‐filling solutions, drain reactions, candidate metabolites and essential reactions in the Phytophthora infestans model.Click here for additional data file.File S1 The Phytophthora infestans model in SBML format.Click here for additional data file.


Constraint-based metabolic flux analysis of knockout strategies is an efficient method to simulate the production of useful metabolites in microbes. Owing to the recent development of technologies for artificial DNA synthesis, it may become important in the near future to mathematically design minimum metabolic networks to simulate metabolite production.We have developed a computational method where parsimonious metabolic flux distribution is computed for designated constraints on growth and production rates which are represented by grids. When the growth rate of this obtained parsimonious metabolic network is maximized, higher production rates compared to those noted using existing methods are observed for many target metabolites. The set of reactions used in this parsimonious flux distribution consists of reactions included in the original genome scale model iAF1260. The computational experiments show that the grid size affects the obtained production rates. Under the conditions that the growth rate is maximized and the minimum cases of flux variability analysis are considered, the developed method produced more than 90% of metabolites, while the existing methods produced less than 50%. Mathematical explanations using examples are provided to demonstrate potential reasons for the ability of the proposed algorithm to identify design strategies that the existing methods could not identify.We developed an efficient method for computing the design of minimum metabolic networks by using constraint-based flux balance analysis to simulate the production of useful metabolites. The source code is freely available, and is implemented in MATLAB and COBRA toolbox.The online version of this article (10.1186/s12859-018-2352-6) contains supplementary material, which is available to authorized users. Finding knockout strategies with minimum sets of genes for the production of valuable metabolites is an important problem in computational biology. Because a significant amount of time and effort is required for knocking out several genes, a smaller number of knockouts is preferred in knockout strategies.However, the technologies for DNA synthesis are being improved . AlthougFBA) is a widely used method for estimating metabolic flux. In FBA, a pseudo-steady sate is assumed where the sum of incoming fluxes is equal to the sum of outgoing fluxes for each internal metabolite  indicates that a and b are the lower and upper bounds of the flux for the corresponding reaction. Suppose that the necessary minimum GR is 1 in this example.The core idea of GridProd is explained using the following examples. Suppose that a toy model of the metabolic network as shown in Fig. In the original state, if GR is maximized, GR becomes 10 by  = . However, PR becomes 0 since the sum of upper bounds of R1 and R2 is 10, and all flow from R1 and R2 goes to R7. If PR is maximized, R6 becomes 8 since R4 =5 and R5 =3 are the bottle necks. Therefore, TMGR and TMPR are 10 and 8, respectively. If PR is maximized for a fixed GR as in IdealKnock, PR becomes max.The optimal design strategy in this network to obtain the maximum PR under the condition that GR is maximized is to knockout R3 where R5 is optional. In this case,  = is obtained. Note that the minimum necessary GR is set to 1 in this example. If R3 is not knocked out,  = is always obtained.GR≤1 is fixed and PR is maximized. Note that setting GR<1 is possible for the first LP, although the necessary minimum GR is 1 for the second LP. Then,  = is obtained, and PR is 8. Since R3 is not knocked out in this case,  = is obtained when GR is maximized. Thus, the ideal flow-based approach that maximizes PR for the fixed values of GR cannot identify the strategy of knocking out R3 and does not obtain PR =4.Suppose we adopt the strategy where a set of reactions not included in the initially obtained flux is knocked out. If GR > 1 is fixed and PR is maximized, R3 must be used since the upper bound of R8 is 1. Therefore, R3 is not knocked out, and then  = is obtained when GR is maximized. Next, suppose that To address this, GridProd applies P to both GR and PR. However, there may be multiple flows that satisfy the given constraints for GR and PR. For example, if  = is given as the constraints, there are multiple flows satisfying these constraints. However, R4 must be used in any flow since the upper bound of R5 is 3. If R4 is 5, then R8 is 1 and R3 =R5 =0 holds. If R3 and R5 are knocked out,  = is achieved. However, if R4 < 5 holds, then R3 and R8 must be used and R5 is optional. Then  = is obtained. Since GridProd minimizes the total sum of absolute values of fluxes,  = is obtained by knocking out R3.R1+R2=6 must hold. R5 and R8 are optional. In every case, the consequent reaction knockout results in  =. Note that the necessary minimum growth is assumed as 1 in this example, however, GR is allowed to be less than 1 if GR ≥ 1 is satisfied in the consequent strategies. When = is given, R4 must be used since the upper bound of R5 is 3. R3 is optional. If R3 is used, then R5 must be used, and R8 is optional. If {R3,R5,R8} is knocked out, then GR becomes 0 and minGrowth cannot be satisfied. If only R8 is knocked out, then  = is obtained. When  = is given, there are multiple flows. If R4 is not used, then R3 and R5 must be 5 and 3, respectively. Consequently, R4 and R8 are knocked out, and then  = is obtained. If R4 is used, R3 must be used since the upper bound of R8 is 1. R5 and R8 are optional. Then,  = is obtained. When  = is given, R4 must be used since the upper bound of R5 is 3. Since the upper bound of R8 is 1, R3 must be used. R5 and R8 are optional. Then,  = is obtained. If  is , , or , then there is no flux satisfying the condition since the lower bound of R2 is 5.To discuss the effects of the size of each grid, we analyze each case where GR ∈{0,1,2} and PR ∈{3,4,5} are given in the following. Suppose that  = or  = is given. Then, R4 must be used since the upper bound of R5 is 3. In addition to R4, R3 also must be used since GR≤2 and 3≤PR≤5. Then, one of the possible obtained flow by the first LP is  = since the sum of absolute values of fluxes are minimized in the first LP of GridProd. Consequently, R3, R5, and R8 are knockedout. Then the second LP is not feasible. However, if the size of each grid is small and the corresponding constraints are 1−ε≤GR≤1+ε and 4−ε≤PR≤4+ε where ε is a small positive constant, then  = is achieved in the second LP. Therefore, the size of each grid affects the resulting PR of the target metabolites. Table P−1 becomes larger, the production ability improves when P−1≤25. However, when P−1>25 holds, the production ability does not improve as P−1 becomes larger. This indicates that the necessary minimum size of ε in the above example is related to the necessary minimum size of P−1.Therefore, when GR ∈{0,1,2} and PR ∈{3,4,5} are given for the first LP, the consequent  obtained by the second LP is represented in Table Table Since finding an optimal subnetwork that achieves the maximum PR is NP-hard problem, it is almost impossible to find it for genome-scale models in realistic time. Threfore, GridProd does not ensure to find the optimal subnetwork. However, it succeeds to find a better subnetwork than other methods for many target metabolites.GridProd computes the design of chemical reaction networks by choosing reactions used in the first LP. Because many reactions in iAF1260 are not associated with genes, it is not directly possible to extend the idea of GridProd for the selection of a set of genes.P−2 small grids, and conducts LP twice for each grid. The area size of each grid is (P×TMGR)×(P×TMPR). TMPR stands for theoretical maximum production rate. The first LP obtains reactions included in the designed DNA, and the second LP calculates the PR of the target metabolite under the condition that the GR is maximized for each grid. The design strategy of the grid whose PR is the best is then adopted as the GridProd solution.In this study, we introduce a novel method of calculating parsimonious metabolic networks for producing metabolites (GridProd) by extending the idea of IdealKnock and pFBA. In contrast to IdealKnock, in the calculation of the ideal points, GridProd applies “P” to PR as well as GR. Furthermore, GridProd divides the solution space of FBA into P−1=25.Computational experiments were conducted to inspect the efficiency of GridProd using a genome-scale model, iAF1260. The production ability of GridProd strategies was compared to those of IdealKnock and FastPros strategies. GridProd achieves higher PR than IdealKnock for many target metabolites. The average computation time for GridProd is within a few minutes for each target metabolite. The effects of the grid sizes were also inspected. When the solution space was divided into 625 small grids, the obtained PRs were the optimal in the computational experiments, which corresponds to The pseudo-code of GridProd is as follows.Si,j is the stoichiometric matrix. LBj and UBj are the lower and upper bounds of vj, respectively, that represents the flux of the jth reaction.In the above pseudo-code, the TMGR and TMPR are calculated first. biomassLB” and “biomassUB” represent the lower and upper bounds of GR, respectively. Similarly, “targetLB” and “targetUB” represent the lower and upper bounds of PR, respectively, which are used as the constraints in the first LP. Each grid is represented by the two constraints, “ biomassLB≤vgrowth≤biomassUB” and “ targetLB≤vtarget≤targetUB”. TMPR×P and TMGR×P represent the horizontal and vertical lengths of the grids, respectively.In each grid, LP is conducted twice. “−5) are represented as biomassLB”, “biomassUB‘”, “targetLB”, and “targetUB” are used, but the fluxes of the reactions included in PR. Otherwise 0 is stored. Finally, the  that yields the maximum value in PR is searched, and the corresponding PR are obtained. The minimum and maximum PRs from FVA for In the solution of the first LP, a set of reactions whose fluxes are almost 0


Kluyveromyces marxianus is a thermotolerant yeast with multiple biotechnological potentials for industrial applications, which can metabolize a broad range of carbon sources, including less conventional sugars like lactose, xylose, arabinose and inulin. These phenotypic traits are sustained even up to 45 °C, what makes it a relevant candidate for industrial biotechnology applications, such as ethanol production. It is therefore of much interest to get more insight into the metabolism of this yeast. Recent studies suggested, that thermotolerance is achieved by reducing the number of growth-determining proteins or suppressing oxidative phosphorylation. Here we aimed to find related factors contributing to the thermotolerance of K. marxianus.Kluyveromyces marxianus, iSM996, using a publicly available Kluyveromyces lactis model as template. The model was manually curated and refined to include the missing species-specific metabolic capabilities. The iSM996 model includes 1913 reactions, associated with 996 genes and 1531 metabolites. It performed well to predict the carbon source utilization and growth rates under different growth conditions. Moreover, the model was coupled with transcriptomics data and used to perform simulations at various growth temperatures.Here, we reported the first genome-scale metabolic model of K. marxianus iSM996 represents a well-annotated metabolic model of thermotolerant yeast, which provides a new insight into theoretical metabolic profiles at different temperatures of K. marxianus. This could accelerate the integrative analysis of multi-omics data, leading to model-driven strain design and improvement. Kluyveromyces marxianus is a prospective microbial host for industrial biotechnology. It is known as a fast growing, Crabtree negative organism, capable of utilizing a broad selection of sugars and having a high secretion capacity for proteins [K. marxianus has been successfully applied in numerous studies for the endogenous enzymes production including inulinase [Kluyveromyces lactis contains 94% of K. marxianus genes [K. marxianus is thermotolerant, growing up to 45–50 °C. Since it has been isolated mainly from dairy products for years, it has GRAS  and QPS  status, therefore making it suitable for applications in the food and pharma industry.The ascomycetous yeast proteins , 2. For nulinase , β-galacnulinase , β-gluconulinase  and β-xynulinase . Even thus genes , only K.K. marxianus intracellular metabolite levels at high temperatures. Such knowledge may be useful for minimal media design and for identifying high temperature metabolic capabilities, in particular for evaluation of the production potential of various compounds.Thermotolerant hosts may positively impact the high temperature industrial bioprocesses in several ways. Firstly, thermotolerance is favourable once the simultaneous saccharification and fermentation (SSF) is considered as many amylases and cellulases are more efficient at high temperatures . SecondlGenome-scale metabolic models (GEMs) are valuable systems biology tools as they combine genome annotation, cultivation and other experimental data for a given organism into a whole-cell metabolic network. Complementary to the general omics analysis, GEMs give an ability to integrate omics data into metabolic networks and predict the condition specific metabolic capabilities. GEMs have been successfully used to design strains and evaluate the cell capabilities upon different conditions , 14.K. marxianus, we reconstructed iSM996, the first genome-scale metabolic model (GEM) for this species. This model was used to predict the growth on various carbon sources and we found a good consistency between the model predictions and the experimental data reported in the literature. We used transcriptomics data to obtain the context specific models at different chemostat conditions, i.e. 30 °C YPD shaking, 30 °C YPD non-shaking and 45 °C YPD shaking. The models revealed the main metabolic bottlenecks associated with growth at high temperatures. To our knowledge, this approach is one of the first attempts to use GEMs to evaluate metabolic profiles at different temperatures.To evaluate the metabolic capabilities of K. marxianus DMKU3–1042 was based on the published genome annotation (NCBI accession PRJDA65233) and other databases including KEGG [Kluyveromyces lactis [getModelFromHomology, which utilises BLASTP [getKEGGModelForOrganism. This function uses HMMER (http://hmmer.org/) in homology search, where the query proteome is queried against KEGG Orthology (KO) specific hidden Markov model (HMM) sets. The default e-value threshold was used, i.e. 1E-50. It was then compartmentalised with the RAVEN function predictLocalization, which uses WoLF PSORT [The genome-scale metabolic network reconstruction for ing KEGG , MetaCycing KEGG , Transpoing KEGG  and BRENing KEGG . Two draing KEGG . The firs lactis . This was BLASTP  for the LF PSORT  protein LF PSORT  as referK. marxianus bibliographic data wherever possible. The cell dry weight composition (g/gDW) for protein, carbohydrate, lipid, RNA and DNA content was incorporated from cultivation study [K. marxianus.The biomass composition was adapted from iOD907 and adjusted with on study . The stoon study  was usedon study . The detfillGaps was used to identify the candidate reactions for the gap filling, which were kept in the model upon no contradictions in the literature. Such pre-processed draft model was then greatly improved with K. marxianus literature knowledge. For instance, we added the missing uptake pathways for several carbon [The semi-automatic gap filling was performed to ensure that the draft model could produce all biomass components in Verduyn medium . This mel carbon  sources l carbon , metaboll carbon , BRENDA l carbon  and Metal carbon , Transpol carbon  as referThe iSM996 model  under the accession ID GSE66600. Three conditions were considered from the downloaded dataset: 30 °C YPD shaking (30D), 30 °C YPD non-shaking (30DS) and 45 °C YPD shaking (45D). TSS-seq dataset also contained the data for D-xylose medium (YPX) in 30 °C (30X). However, it was decided not to include this condition in the analysis, since KmXKS1 gene, responsible for D-xylulose phosphorylation, was inactive therefore preventing D-xylose assimilation. However, all four conditions were utilised to identify the genes which were turned off in at least one condition. Thereafter, three condition specific models were obtained, each having inactivated reactions once their associated genes were inactive. No threshold values for expression abundance were considered, the gene was called as inactive if it had zero expression values in all three replicates per condition.The quantitative transcription start site sequencing (TSS-seq)  data wasoptimizeCbModel function from The COBRA Toolbox for MATLAB [The values for reduced cost were calculated using the r MATLAB .K. marxianus included four steps: i) obtain and curate the draft reconstruction based on template model iOD907; ii) fetch and curate the second draft model from KEGG; iii) merge both draft models; iv) perform the thorough manual curation. The first draft model after curation had 875 genes including 20 manually identified homologs and 29 non-gene-associated spontaneous reactions. Meanwhile, the compartmentalised and curated second draft model had 524 genes. These two models were merged into a new draft model with 987 genes, 1934 reactions and 1678 metabolites. We then added exchange, biomass and ATP maintenance reactions from iOD907 and performed the growth simulation in a minimal medium. As the model could predict growth, we used the draft model as a basis for further model modifications.The model reconstruction of The manual curation started by fixing two inconsistencies inferred from the template GEM. Firstly, in iOD907 all the cytosolic metabolites could be transported to extracellular space and had exchange reactions. Since the cell ability to import or secrete all cytosolic metabolites seemed unspecific, we commenced the manual check by using Yeast 7.6 as reference. Overall, the number of transportable cytosolic metabolites was decreased from 313 to 182 in iSM996. Another iOD907 problem was that the cell could import or secrete several fatty acid-acyl carrier protein (ACP) complexes even though the cell membrane should be impermeable for such large complexes. These complexes were therefore replaced by the corresponding free fatty acids. Correspondingly, the biosynthetic pathways were added for the known products like 2-phenylethanol, phenethyl acetate or ethyl acetate.K. marxianus specific 110 genes, 455 reactions and 298 metabolites. The most represented metabolic pathways are related to transport, exchange reactions and amino acid, lipid, carbohydrate metabolism , 30 °C static (30DS) and 45 °C shaking (45D). The analysis would greatly benefit from additionally considering the metabolomics data, however we reckon that the comparative analysis of condition-specific models based on only transcriptomics data is still relevant to identify the key differences for biomass precursor synthesis between the conditions.The TSS-seq data was used to turn off the gene-associated reactions without transcriptional evidence while leaving the constraints for other reactions intact. These models were also used to predict the maximal production capacity for the main biomass components Fig. . We calcK. marxianus retains the ability to allocate the amino acids necessary for roughly the same protein mass. Amino acid auxotrophies to L-arginine and L-histidine were identified in 30D and 45D. High temperature-specific auxotrophies included the previously reported L-lysine, L-isoleucine [The simulations indicate that across the conditions, oleucine  and prevKmRIB3, which catalyses the final reactions of GTP and D-ribul 5-P (D-ribulose 5-phosphate) linear pathways (r_0939 and r_0940 correspondingly) is inactivated. However, the interconversion ability is possibly retained between riboflavin and the downstream metabolites FMN and FAD. At the 45D condition, the expression of KmRIB4 and KmFMN1 genes are inactivated. The former gene is responsible for 67dm81Drl lumazine) production (r_0938), while the latter gene is involved in FMN conversion from riboflavin (r_0937). Thus, under the high temperature condition, K. marxianus can only interconvert FMN and FAD or hydrolyse it back to riboflavin. These findings suggest that the organism has to find an optimal balance between ATP synthesis (riboflavin) and other important metabolic functions linked with FMN and FAD. While at the 30DS condition, the cell can freely allocate these three compounds. Under the 45D condition, K. marxianus features an irreversible riboflavin production from FMN and FAD, suggesting that ATP shortage is likely the main limitation for the cell at high temperatures, probably further affected by the limited ferroheme availability. The additional supplementation of riboflavin is known to increase the tolerance to high temperatures upon low ATP/ADP ratio [The auxotrophy to riboflavin, found in 30DS and 45D conditions, has the other potential benefits in addition to just conserving the building blocks. Two condition-specific strategies are considered to inactivate de novo riboflavin synthesis. As shown in Fig. DP ratio . Since tKmDGK1 gene, which is a known contributor to the increased heat sensitivity when overexpressed [The lipid pool size remains the same at all three conditions. However, this assumption is based on the arbitrary abundance value for myo-inositol (0.001 mmol/gDW/h), so one may find the different lipid pool sizes once the experimental values for myo-inositol are used. The excessive availability for the other lipid components is suppressed by an inactivation of the xpressed .KmISN1 and KmSDT1 genes, dAMP shortage cannot be compensated by salvaging other purine nucleotides. This suggest that the cell aims to conserve these building blocks. This coincides with the upregulation of the genes responsible for DNA repair [The significant decrease of flux found in deoxynucleotides was the shortage of dAMP. Due to the inactivation of the A repair .K. marxianus. This model is capable of predicting the growth on the majority of the reported carbon and nitrogen sources. The growth simulations hereby indicate the close correspondence between in vivo an in silico growth rates for the numerous carbon sources. In addition, the model contains several unique biosynthetic pathways for aroma compounds like 2-phenylethanol, phenethyl acetate and ethyl acetate. The iSM996 was used to construct three condition specific models in YPD medium while considering the low oxygen and high temperature conditions. The results suggested that at the high temperature the cell turns off more genes thereby introducing new auxotrophies and hereby utilizing as many resources as possible from the medium. These findings may be used to the growth medium design upon the low oxygen availability and high temperature. Finally, the iSM996 model is a solid tool to evaluate K. marxianus metabolic features, allowing the experimental data integration and the model-driven strain design.We hereby present iSM996, the first genome scale-metabolic model for the thermotolerant yeast Additional file 1. Model file in SBML format.Additional file 2. Model file in Excel format.Additional file 3. The full iSM996 report from memote – the genome-scale metabolic model test suite.Additional file 4. Biomass composition details for overall components (Sheet 1), deoxyribonucleotides (Sheet 2), ribonucleotides (Sheet 3), amino acids (Sheet 4). Also included the model performance upon chemostat conditions for the growth rate (Sheet 5), oxygen consumption (Sheet 6) and carbon dioxide production (Sheet 7). The model performance upon different carbon sources in respect of the growth rate is also included (Sheet 8). References are included in the file.Additional file 5. List of inactive genes (Sheet 1) and corresponding reactions (Sheet 2) between 30D, 30DS, 30X and 45D conditions.Additional file 6: Figure S1. A radar chart showing the predicted potential for biomass precursors excessive production in 30D, 30DS and 45D conditions. As the magnitude is different for each metabolite, the relative production values are shown, where 100% indicates the largest production capacity between conditions. The data for the 30D condition is shown as the green polygon bordered with the dashed border while the corresponding data for the 30DS condition is in purple (dotted border) and the data for the 45D condition is in red (dot dash border) color. (a) Abbreviations: G6P , F6P (beta-D-fructose 6-phosphate), E4P (D-erythrose 4-phosphate), R5P (D-ribose 5-phosphate), GAP , 3PG (3-phosphoglycerate), PEP (phosphoenolpyruvate), PYR (pyruvate), OXA , ACA (acetyl-CoA), 2OG (2-oxoglutarate), SCA (succinyl-CoA). (b) Abbreviations: AMP (adenosine monophosphate), CMP (cytidine monophosphate), GMP (guanosine monophosphate), UMP (uridine monophosphate), dAMP (deoxyadenosine monophosphate), dCMP (deoxycytidine monophosphate), dGMP (deoxyguanosine monophosphate), dTMP (thymidine monophosphate).


Fine-tuning the aeration for cultivations when oxygen-limited conditions are demanded  is still a challenge in the area of bioreactor automation and advanced control. In this work, an innovative control strategy based on metabolic fluxes was implemented and evaluated in a case study: micro-aerated ethanol fermentation.Saccharomyces cerevisiae, defined medium, and glucose as carbon source. Simulations of a genome-scale metabolic model for Saccharomyces cerevisiae were used to identify the range of oxygen and substrate fluxes that would maximize ethanol fluxes. Oxygen supply and feed flow rate were manipulated to control oxygen and substrate fluxes, as well as the respiratory quotient (RQ). The performance of the controlled cultivation was compared to two other fermentation strategies: a conventional “Brazilian fuel-ethanol plant” fermentation and a strictly anaerobic fermentation (with ultra-pure nitrogen used as the inlet gas). The cultivation carried out under the proposed control strategy showed the best average volumetric ethanol productivity (7.0 g L−1 h−1), with a final ethanol concentration of 87 g L−1 and yield of 0.46 gethanol gsubstrate−1. The other fermentation strategies showed lower yields (close to 0.40 gethanol gsubstrate−1) and ethanol productivity around 4.0 g L−1 h−1.The experiments were carried out in fed-batch mode, using commercial The control system based on fluxes was successfully implemented. The proposed approach could also be adapted to control several bioprocesses that require restrict aeration. The performance of bioreactors depends on the control of several cultivation conditions , in order to direct cell metabolism towards the improvement in yield, selectivity, and productivity of the target product. For example, the control of the oxygen supply to facultative microorganisms plays a key role in driving metabolic routes towards the production of biomass (favored under aerobic conditions) or the synthesis of some fermentative products (favored by low or zero oxygen availability) .Conventional strategies in aerobic processes are essentially based on measurements of the dissolved oxygen concentration (DOC), which is then controlled by adjusting the stirrer speed and, occasionally, the composition of the gas supplied to the reactor  or the total gas flow rate , 3. SomeH. influenzae, S. pnemoniae, and N. meningitidis [S. cerevisiae [E. coli [P. stipitis [n-butanol [However, the application of these strategies may be not effective under microaerobic conditions, because ordinary probes are not accurate at low dissolved oxygen tension . Under ongitidis –9, and brevisiae , by E. c[E. coli , and by stipitis . The pro-butanol , 2,3-but-butanol  and acet-butanol , importa-butanol  and bioe-butanol , servingS. cerevisiae, the catabolism of sugars is a key factor affecting process performance and is strongly influenced by oxygen availability. If the oxygen supplied is below a threshold value, glycerol will be produced, decreasing the ethanol yield [In the context of bioethanol production using ol yield . On the ol yield , also leol yield  and to mol yield , 21. Furol yield , 22.S. cerevisiae under oxygen limitation was reported in a couple of works [S. cerevisiae cultures [S. cerevisiae and consisted in the manipulation of the inlet gas stream composition to maintain RQ at the desired level and enforce microaerobic conditions [S. cerevisiae respiratory activity [Despite the importance of the control of micro-aerobic conditions in fermentations, there are not many studies addressing this topic in the literature. The use of a constant (sparged or headspace) air flow, without any control, to cultivate of works , 22, 23.cultures , 25, wasnditions . Easily activity , 25. FurSaccharomyces cerevisiae, in particular, has been extensively studied, with at least 12 GSMs published ever since 2003 [S. cerevisiae GSMs have been employed with satisfactory results to improve the understanding of yeast physiology, as well as to predict targets for metabolic engineering in order to overproduce chemicals such as succinic acid [l-tyrosine [In this context, genome-scale metabolic models (GSMs) can also be employed for bioreactor control. They are a source of in silico data reproducing the cell metabolism. With these models, it is possible to estimate intracellular and extracellular fluxes of metabolites at steady-state for different environmental conditions, considering the inlet fluxes of substrate and oxygen—which in fact drive the metabolic reactions occurring within the cell. nce 2003 . S. cerenic acid , fumaricnic acid , bioethanic acid , 2,3-butnic acid  and l-tytyrosine . Still, GSMs are stoichiometric models, which assume steady-state behavior. Usually, this is not the case in real fermentations, especially in industrial scale, but the information concerning metabolic fluxes may delimit regions of operation for the reactor. Following this concept, the GSMs output can be understood as a pseudo-stationary response to the environmental conditions observed during the process. These estimates of substrate/product fluxes may provide useful information for the control system, even though the bioreactor does not operate at steady-state.An innovative bioreactor control system is herein reported, based on metabolic fluxes estimated using a GSM. This new approach is evaluated using the production of bioethanol under microaerobic conditions as a case study. Indeed, an important problem in industrial fermentations is to increase bioethanol production at the expense of biomass and glycerol, and this was the focus of this work. A novel supervisory system is also presented, which combines advanced strategies for bioprocess control, on-line data acquisition, and a flux-oriented control model.S. cerevisiae fermentation operated in fed-batch mode was chosen as a case study to test the flux-based micro-aeration control (FMC).The development of the metabolic flux-oriented control involves several steps including GSM simulations, selection of suitable simulated data, and their integration with model equations to configure the control system. Additionally, it is important to assess the control performance by applying it to a real process. In the present work, ethanol production in S. cerevisiae iND750 [iMM) for different species  were collected and used to generate mathematical correlations (MC), which in turn provided estimations of substrate MM, as well as the mathematical correlations to predict JMC, are presented in the following section.Initially, simulations using the genome-scale metabolic model of e iND750  and the e iND750  were runmentclass2pt{minim2 flow rate, cell mass, temperature, pressure and outlet gas composition), combined with equations derived from mass balances, the selected outputs, inlet O2 mol fraction (air) whereas In the next step, the controller was set up. In brief, from a set of on-line (or at-line) inputs  was compared to other fermentation strategies: a conventional fermentation strategy, used in Brazilian Bioethanol Plants (BBP), and another cultivation carried out under strictly anaerobic conditions (SAC).S. cerevisiae iND750 [2, and glycerol were generated for each simulated condition  of e iND750  were rune iND750 . Differeentclass1pt{minimaDW−1 h−1). A first shift occurs at a minimum critical value of Figure entclass1pt{minimaentclass1pt{minimaS. cerevisiae metabolism that were expected under the influence of different fluxes of oxygen: biomass formation was favored at higher oxygen fluxes, while glycerol production was intensified at low oxygen fluxes, as already reported [The responses of the metabolic model were consistent with the changes in reported . From thmentclass2pt{minimIn order to implement the information mapped through GSM simulations Figs. a, 2a in mentclass2pt{minimmentclass2pt{minimMM and AIR) was updated using Eqs. Equation mentclass2pt{minimmentclass2pt{minimAIR) and fresh medium feed rate (F), respectively  framework, experiments were carried out in fed-batch mode, using defined medium containing glucose as the sole carbon source. Glucose, biomass, ethanol and glycerol profiles for the reactor operating under FMC can be seen in Figure SM3 ; (iii) a final batch phase (from 10.6 to 12.6 h), started when glucose feeding was stopped (at 10.6 h), still carried out under micro-aeration conditions implemented by the proposed control strategy for O2 supply.Using the control logic previously summarized . The micro-aeration control remained active until all glucose was consumed at the end of the 3rd stage of the FMC experiment in order to get a full picture of its performance.After 2.6 h the dissolved oxygen was set to zero   Fig. a followeX) and, consequently, the oxygen uptake flux A reduction of the cell fermentative capability, probably caused by ethanol inhibition or viability loss, as discussed later, may have contributed to decreasing the specific growth rate  values obtained at-line, and the on-line calculated volume (V) . This production is higher than the values predicted by the metabolic model, which would vary from 0 to 0.12 mmol gDW−1 h−1 (data not shown) for the values of Regarding glycerol production, there was an accumulation of 9 g LIn the previous topics, the flux-based micro-aeration control (FMC) was detailed and its implementation was described. However, the embracement of the FMC strategy in real life cultivations will depend on its ethanol productivity and yield, when compared to other fermentation strategies. So, two additional reference cultivations were performed. The first reference fed-batch cultivation represented the conventional fermentation process in a Brazilian Bioethanol Plant (BBP), which is carried out without aeration. The second reference cultivation was conducted under strictly anaerobic conditions (SAC). The same experimental conditions employed in FMC fermentation, including FMC’s fresh medium feeding profile, were reproduced for both BBP and SAC. Thus, after BBP and SAC experiments were carried out, the results from the three cultivations strategies can be compared to further evaluate the performance of the micro-aeration control based on the metabolic fluxes.The experimental data showing the changes in the concentrations of glucose, biomass, ethanol, and glycerol obtained in the FMC, BBP and SAC experiments  and converted mainly to ethanol, with overall yields ranging from 0.46 to 0.40 gDW−1 h−1 throughout the fed-batch phase  in chemostat cultures under anaerobic/micro-aerated conditions using S. cerevisiae CBS 8066 [S. cerevisiae lab strain (maximum specific growth rate of 0.45 h−1 at 30 °C) shows high glucose uptake fluxes (up 20 mmol gDW−1 h−1) under anaerobic conditions [S. cerevisiae strains would certainly lead to larger experimental ethanol fluxes.Regarding ethanol production, the highest experimental ethanol flux achieved was 17 mmol gFMC Fig. a, applyiCBS 8066 . This fanditions . Thus, tIn this case, the control action proved to be sufficiently robust in managing with the limited capability of the commercial baker’s yeast used for ethanol production. Higher inlet fluxes of oxygen led to increased biomass fluxes, resulting in an RQ decrease, which was satisfactorily corrected by the implemented control loop Fig. .−1, most certainly due to product inhibition and viability loss. This increase in glucose concentration was a consequence of misleading biomass information provided by the at-line optical density measurements, which reflected the concentrations of viable and non-viable cells. High ethanol concentrations can trigger viability loss, but the OD600 readings ), ethanol can act as an inhibitor of yeast growth, while high ethanol concentrations (10% (v/v)) greatly reduce cell viability . One of In addition, other assumptions, such as the pseudo-stationary state for substrate balance and the constant value for biomass yield, could also influence the feed flow rate calculated by the expression F Box . NeverthTable ethanol L−1 h−1, respectively) than those obtained in any other reported study, while the product yield (0.46 gethanol gsubstrate−1) was similar to the values achieved in four [The cultivations performed according to the metabolic flux-based control logic showed higher productivity  and others following heterofermentative patterns.Overall, the integration of on-line/at-line data acquisition with the trajectory predicted for the metabolic fluxes from GSM simulations within the control logic provided suitable oxygen fluxes for running a micro-aerated fermentation. The structure of the proposed control system is more flexible and comprehensive than micro-aeration tuning schemes based just on RQ measurements. The control algorithm and the mathematical model can be easily modified to handle different inputs (JS. cerevisiae was successfully implemented. A new supervisory system (SuperSys_Ferm) was developed and was evaluated under real fermentation conditions, with biomass concentrations ranging from 4 to 16 gDW L−1, ethanol concentrations over 70 g L−1, and fed-batch/batch bioreactor operation mode. The efficacy of the control strategy was confirmed by the high ethanol yield  and productivity  that were achieved relative to controls.The proposed control system based on fluxes estimated from a genome-scale metabolic model (GSM) for This work has applied GSM simulations for controlling a bioprocess, manipulating both feeding and inlet gas flow rates to meet cell requirements for the desired product. As already mentioned, tuning of the control action and estimation of experimental fluxes by the supervisory system would greatly benefit from the use of an in-line biomass sensor able to determine the actual active cell concentration, which was not employed in this study. The proposed control approach is rather general and can be adapted to control several bioprocesses that require restricted aeration.Saccharomyces cerevisiae  and minimal medium , with glucose as carbon source (30 g L−1 for batch cultivations and 300 g L−1 for the feeding medium) [Fed-batch cultures were carried out using fresh commercial  medium) .Three cultivation strategies were evaluated: (i) Metabolic Flux oriented based micro-aeration Control (FMC); (ii) “Brazilian Bioethanol Plant” type fermentation (BBP); (iii) Strictly Anaerobic Condition (SAC).The BBP strategy reproduced the current combined fed-batch/batch cultivations used for ethanol production in most of the Brazilian sugarcane mills. Briefly, in the usual Brazilian bioethanol production process, also known as Melle-Boinot  a stream4OH (7%) and H3PO4 (20%). Ammonium solution added during all cultures, doubling as a nitrogen source [2 and an additional Mettler Toledo Inpro 6800 probe for O2. The feed supply was provided by an Ismatec BVP pump. In all the experiments, data acquisition and monitoring/control of the instruments were achieved using SuperSys_Ferm, an in-house computational tool for flux-based control of micro-aerated fermentation processes. SuperSys_Ferm was implemented in LabView, via a Compact FieldPoint , and was based on SuperSys_HCDC, which was developed to assist fed-batch bioreactor operation during high cell density cultivations [The experiments were conducted in a 5-L stirred tank bioreactor (fabricated in-house) with a working volume of 3.5 L. The pH was automatically controlled  at 4.5 by the addition of NHn source , 51. Theivations , 53.−1. After inoculation, the cultivations were split into three stages, as described in the following.For all experiments, 41 g  of fresh commercial baker’s yeast was suspended in 0.6 L of defined medium. This inoculum was transferred to the bioreactor leading to an initial biomass concentration of about 3.5 g LDW L−1). In this stage, the oxygen saturation was kept at 30% by means of a PID controller that adjusted the stirrer speed between 200 and 1000 rpm. The air was supplied to the bioreactor at flow rates ranging from 0.5 to 5 L min−1, adjusted using a mass flow controller . For all experiments, as soon as the biomass concentration reached the desired range, air supply was shut down and industrial nitrogen started to be flushed to the bioreactor to reduce DOC.The first stage was a batch phase used for activation of the yeast cells and increase of the biomass concentration up to the desired range (8–12 g2 (v/v)), supplied by two mass flow controllers at the rates automatically defined by the FMC control strategy. For BBP, no gas stream was supplied, whereas for SAC ultrapure nitrogen (99.999% N2 (v/v)) was provided at a constant flow rate of 1 L min−1.For all experiments, the second and third stages mimic the current combined fed-batch/batch cultivations used for ethanol production in Brazil. The second stage started after the DOC was below 3% and was conducted in fed-batch mode. For FMC, the flow rate of the feeding medium was defined by the control strategy (further detailed in Methods Control Algorithm Design). For both BBP and SAC cultivations, the feeding profiles reproduced the one automatically implemented in the FMC culture by the control action. Since all experiments were performed using the same feeding pattern and the same overall mass of supplied substrate, this approach enabled a direct comparison of the three competing strategies. Concerning the gas supply in this cultivation stage, for FMC the inlet gas stream was a mixture of air and industrial nitrogen  at λ = 600 nm and dry cell weight method [600 measurements into cell mass concentration, CX (gDW L−1), to be used as input to the control action (better detailed in Methods Control Algorithm Design).During the experiments, samples were withdrawn and biomass formation was measured by at-line optical density readings  , using ti component was based on Eq. i is the volumetric production or consumption rate , in mmol of “i” L−1 h−1, and Cx is the biomass concentration, in gDW L−1.Determination of the experimental flux (Box mentclass2pt{minimmentclass2pt{minimmentclass2pt{minimIndex) was defined as the ratio between the concentrations of ethanol and glycerol at the end of the cultivation, as stated in Eq. An additional index, denominated Overall Selectivity Index (Si/s)  Eq.  and volu p,i Eq.  were obtAIR), nitrogen (QN2), and fresh medium feed (F). The nomenclature included at the beginning of the article provides a detailed description of all fluxes used in this work and their symbols.Besides experimental fluxes  were collected for each The simulations focused on mapping the metabolism, given inlet fluxes of oxygen and glucose ranging from 15 (fully aerobic) to 0.001 (severely oxygen-limited) mmol Oectively . SeveralMM, In Fig. mentclass2pt{minim2 and CO2 molar fractions in the exhaust gas as input variables (Box The flux-based micro-aerated control fermentation (FMC) was implemented as an on-line closed-loop type control policy , with RQmentclass2pt{minimmentclass2pt{minim2 equation was based on the combination of the metabolic flux definition and mass balance  during the experiment’s second and third stages (as described in Methods Cultivation Strategies). The respiratory quotient  and the volume (V) were estimated at-line by the supervisory system. The value of CSF was set to the actual glucose concentration in the feeding medium (~ 300 g L−1) measured before the experiment was started.Cell masses min), outlet temperature (Tout), outlet oxygen fraction . The influence of RQCA on Figure S3. FMC cultivation profile: biomass (black square), ethanol (red circle), glycerol (brown inverted triangle), glucose (blue triangle), dissolved oxygen (green line). (a) Beginning of control action; (b) end of fresh medium feeding. Figure S4. BBP cultivation profile: biomass (black square), ethanol (red circle), glycerol (brown inverted triangle), glucose (blue triangle), dissolved oxygen (green line). (a) Beginning of fresh medium feeding (F profile reproduced from FMC); (b) end of fresh medium feeding. Figure S5. SAC cultivation profile: biomass (black square), ethanol (red circle), glycerol (brown inverted triangle), glucose (blue triangle), dissolved oxygen (green line). (a) Beginning of fresh medium feeding (F profile reproduced from FMC); (b) end of fresh medium feeding. Table S1. Results of in silico studies (Step 1) using the IND750 metabolic model . Influence of the oxygen inlet fluxes on the biomass, CO2, and ethanol production fluxes (for an inlet glucose flux of 3 mmol gDW−1 h−1). *Conditions for the maximum ethanol flux production. Table S2. Ethanol fluxes for different oxygen inlet fluxes (Step 2) (considering an inlet glucose flux of 3 mmol gDW−1 h−1). *Inlet O2 flux that led to 90% of the maximum ethanol production flux observed. + Maximum ethanol flux production