Lignin is a natural polymer that is interwoven with cellulose and hemicellulose within plant cell walls. Due to this molecular arrangement, lignin is a major contributor to the recalcitrance of plant materials with respect to the extraction of sugars and their fermentation into ethanol, butanol, and other potential bioenergy crops. The lignin biosynthetic pathway is similar, but not identical in different plant species. It is in each case comprised of a moderate number of enzymatic steps, but its responses to manipulations, such as gene knock-downs, are complicated by the fact that several of the key enzymes are involved in several reaction steps. This feature poses a challenge to bioenergy production, as it renders it difficult to select the most promising combinations of genetic manipulations for the optimization of lignin composition and amount.Populus trichocarpa), alfalfa (Medicago truncatula), switchgrass (Panicum virgatum) and the grass Brachypodium distachyon.Here, we present several computational models than can aid in the analysis of data characterizing lignin biosynthesis. While minimizing technical details, we focus on the questions of what types of data are particularly useful for modeling and what genuine benefits the biofuel researcher may gain from the resulting models. We demonstrate our analysis with mathematical models for black cottonwood (Despite commonality in pathway structure, different plant species show different regulatory features and distinct spatial and topological characteristics. The putative lignin biosynthes pathway is not able to explain the plant specific laboratory data, and the necessity of plant specific modeling should be heeded. At its core is the phenolic polymer lignin, which is interwoven with cellulose and hemicellulose, and thereby impedes access of cellulolytic enzymes, necessitating costly physico-chemical pretreatments before effective microbial fermentation can take place. With the exception of cellulose, lignin is the most abundant terrestrial biopolymer and accounts for roughly 30% of all organic carbon in the biosphere . It giveBoth the amount and composition of lignin are thought to be correlated with the hardness as well as the recalcitrance of structural plant materials. It is therefore important to the production and manipulation of bioenergy crops to understand the details of lignin synthesis and the deposition and polymerization of monolignols in the plant cell wall. In particular, the question arises whether it is possible and feasible to intervene in the phenylpropanoid pathway of lignin biosynthesis in a targeted and effective manner, for instance through gene knock-downs. The answer to this question is evidently preconditioned on detailed knowledge of this pathway and its control in situ. This knowledge in turn requires different types of biological data and, in cases where these are difficult to understand, the use of computational models that are capable of integrating small or large datasets of the same or different types and explaining observations that are sometimes unexpected.In this article, we discuss computational models that are beneficial for explaining counterintuitive aspects of lignin biosynthesis and for making predictions regarding rational alterations in the molecular make-up of the pathway. We decided to present this material not in the form of a typical modeling paper, which would inform fellow modelers regarding all steps and technical details of model design, parameter estimation, methods of diagnostics and analysis, and interpretation of results. Instead, this paper is intended to address the practicing bioenergy scientist or engineer. It focuses on two overarching questions. First, what kinds and quantities of biological information are needed, or particularly beneficial, for setting up models of lignin synthesis and recalcitrance that have explanatory or predictive power? And second, if we succeed in constructing and implementing an effective model, what genuinely new insights might this model be able to offer? Guided by these questions, we will brush over most of the typical mathematical modeling steps and refer the reader to details in pertinent articles and reviews in the published literature.It may surprise newcomers to the field of computational modeling that even within the limited scope of metabolic pathway modeling, the choices of mathematical formats and methods are all but unlimited. There is not “one” model that is somehow optimal, but there are many distinct options and numerous nuances. Even the representation of an enzyme catalyzed reaction can take a variety of mathematical formats, which are the result of different assumptions and focus either on molecular mechanisms or on the systemic behavior of a pathway system . StudyinPopulus trichocarpa (black cottonwood poplar), Medicago sativa , Panicum virgatum (switchgrass), and the model grass Brachypodium distachyon, as far as they are known or suspected today. A commonality among these species is that the pathway of lignin biosynthesis uses phenylalanine as its starting substrate; however, monocot grasses, including B. distachyon, and possibly P. virgatum as well, also use tyrosine, in addition to phenylalanine. It is presumably a biochemical necessity that most intermediates between these initial substrates and the final monolignols are by and large preserved, but the pathway systems in the species are connected in a slightly different manner through enzymatic reactions. These differences are not only of academic interest to the evolutionary biologist, but also of great significance to the biofuel researcher, because targeted interventions are almost always based on specific changes in gene expression, with concomitant alterations in fluxes through enzymatic reaction steps, such that a precise understanding of the details of the metabolic system is a prerequisite for targeted manipulations.Although the structure of the lignin polymer is rather similar among different plant species, targeted experiments have revealed that the pathway of lignin biosynthesis exhibits variations among these same plant species. These variations are primarily manifest in the presence or absence of some of the involved enzymes, secondarily in different enzyme activities and substrate affinities, and third in possibly different regulatory control structures. As an illustration, Fig. Predicting global effects of such manipulations on the ultimate lignin output and composition is not trivial, because the pathway utilizes the same enzymes for different reaction steps, but presumably with different substrate affinities Fig. . FurtherIn an ideal modeling world, experimental teams would be able to measure every piece of information needed to create a comprehensive model. The data would be of high quality, obtained in situ, from the same species and from multiple organisms. Obviously, this high bar cannot often be reached, and one must ask instead what compromises are still sufficient for modeling. We discuss this issue in the following.Vmax, KM, Kcat, or Ki, which correspond to rates and affinities in conceptual frameworks like the Michaelis–Menten mechanism.To design and explore a model with computational methods, one needs to choose proper functional forms for the fluxes and determine their parameters. In a true mechanistic model, the mathematical format of a flux corresponds directly to the alleged biophysical or chemical mechanism, and typical parameters may be pH and temperature, and more specifically for metabolic models, may include quantities such as In an idealized modeling situation, two scenarios can lead to a full model. First, knowledge of all metabolite concentrations and of all mechanisms, including input to the system, along with a complete set of physical and kinetic parameters, measured in vivo, can quite easily be converted into a comprehensive model. However, even in this quite unrealistic case, the model would ignore the spatial distribution of processes and stochastic events, which could, for instance, be due to environmental randomness or to very low numbers of enzyme or substrate molecules. Second, knowledge of all fluxes of the system and a complete set of measured physical parameters would allow the design of the model, again with the same limitation as before. At present, neither scenario is realistic, and missing information must be obtained from other sources, such as in vitro measurements, or inferred through computational means.At this point, many modeling approaches and methods are readily available that could create functioning models out of such data, if they were available. However, they are not, and the more important point therefore is to realign the existing modeling techniques with the realities of data acquisition in a field where some of the key metabolic intermediates are below the level of solid quantification.As a premier example, flux balance analysis (FBA)  and its Chlamydomonas reinhardtii under different CO2 conditions, and Chang et al. tyrosine experiment, 35% of tyrosine is labeled and phenylalanine is unlabeled . The labeled fluxes in Fig. Simulations of the scheme in Fig. ata Fig. . PhenylaV24 shows a higher labeled portion than V28 when phenylalanine contains the feeding label;Each model in the ensemble captures the experimental data with respect to the label distribution in steady-state fluxes. For instance, The lignin compositions and S/G ratios in all scenarios are compatible with experimental data;13C9-phenylalanine and 13C9-tyrosine experimental data; andThe labeled lignin composition is compatible with p-coumaric acid match with experimental data.The labeled ferulic acid and Because the system is mathematically underdetermined, its steady-state solution is not unique see  section.Further details are presented in Table V8 admits small values in comparison to its parallel reactions in cytosol compartment, i.e., V22 and V23. This result demonstrates that, while the main pathway for the reactions catalyzed by CCR and CAD resides in the cytosol, a relatively small and undisturbed flux through CCR/CAD at the ER is sufficient to establish the metabolic channel necessary for preferential incorporation. In fact, considering the wrinkled environment of the ER surface, it is not hard to imagine that localized pools would keep a small fraction of the pathway undisturbed from exchanges of metabolites with the cytosol.The boxplots in Figs. In a kinetic systems model, the dynamics of the pathway is represented by a system of ordinary differential equations (ODEs) in which the metabolites are the states. The rate of change in each metabolite is determined by sums and differences of all fluxes that directly affect this metabolite. Each flux is a mathematical function of the metabolites and other variables of the system that needs to be selected. Although the fluxes are usually nonlinear functions, the collection of fluxes itself forms a linear system, which can be represented as a matrix equation of the typeX is the vector of metabolites, S is the stoichiometric matrix, and V is the vector of fluxes. The stoichiometric matrix S defines the pathway structure. An element Si,j of this matrix equals 1 if flux Vj is directed toward metabolite Xi. It is − 1, if flux Vj removes material from metabolite Xi, and it is equal to 0, if flux Vj has no direct effect on metabolite Xi. In long form, the matrix equation can be rewritten for each equation asn is the total number of fluxes.Here, The steady state of a system is important for two reasons. First, many biological systems tend to operate close to such a state, where the overall concentrations of metabolites do not change, even though flux is running through the system. Second, from a mathematical point of view, many analyses at a steady state are much simpler than for the differential equations themselves, because now one has, by definition, Brachypodium study, we chose an alternative to FBA and MOMA. Namely, we intended to obtain the most likely solution without specifying an objective function for the FBA optimization. Because the degrees of freedom of a solution to our system are directly associated with diverging branch points, we focused on the flux split ratios (FSRs) at these points. In cases where these FSRs were known, we used their values; otherwise, we performed large-scale Monte-Carlo simulations with thousands of combinations of FSRs and retained only those solutions where all fluxes were positive at all time points of an experiment. This strategy led to the most likely flux profiles. Details of this method are discussed in . Each pair, entered into the model, yields steady-state values of the fluxes V1,…, V5 and D. These are filtered to retain only desired fluxes. For instance, in the actual case study of Brachypodium, only those flux profiles are retained that satisfy the following criteria:Fluxes take only non-negative values at all time points;The lignin composition and S/G ratio are compatible with experimental data.Now, thousands of pairs   Df from L1 and L3 are known from inputs of the pathway, Vin, we can compute L4 from the computed steady-state fluxes in the previous step and an estimated L2. Therefore, L2 is the only unknown to be estimated, and L4, Df and Dr can consequently be computed. In fact, we only need to estimate the label level of one of the parallel metabolite pools in the cytosol and ER compartments.Assuming that L is generated randomly by Monte-Carlo sampling, and the labeled fluxes can then be computed. The labeled fluxes corresponding to Fig. Similar to the use of split ratios, vector D as L2D, which is equal to L2(Df − Dr), whereas Eq. , that a “new math” is needed that allows us to combine different data and heterogeneous information in a more efficacious manner than is possible today. Ultimately, a deeper understanding of such responses would allow us to answer questions like “how does ‘a’ plant react to natural or artificial changes?” or “why does plant (or plant species) A respond differently to a perturbation than plant (or plant species) B?”Mathematical modeling in biology is still in its infancy. Especially within the realm of plant and crop science, the number of modeling articles is negligible in comparison to experimental papers. As a consequence, the collective experience with plant and crop modeling approaches is still limited, and much more practice and many more case studies will be needed to gain a glimpse into the systemic responses of plants to interventions and manipulations. It may even be, as some experts claim  or from quantitative transcriptomics, where one would expect to find similarities between gene expression and changes in enzyme activities, which however do not always materialize in reality, due to post-transcriptional alterations. It would also benefit both sides to obtain and computationally analyze data describing the same process in different species, as we demonstrated here with the different models for lignin biosynthesis. At first, these comparative analyses could shed light on questions such as: whether apparent differences between species are experimental or modeling errors; whether different designs have evolved in line with the general phylogeny of these species or whether they are due to other factors; and whether different natural designs are dictated by different environmental needs or demands. Together, these combined analyses would have the potential of revealing design principles that govern these processes and could provide deep explanations for why certain species solve a task in the observed fashion and not in a different fashion.As a tangible target, experimentalists and modelers should explore together to what degree metabolic responses can be predicted  from the existence of genes and enzymes  could bOthers studies have attempted to connect several scales of the biological hierarchy of processes, both in time and size e.g., –41). Not. Not41])Crops in silico [The epitome of such models is whole-plant-plus-environment models that have been developed in recent years and capture governing processes and responses quite well. For instance, SOYSIM  is a comn silico –51. To bn silico , and it


Plasmodium spanning the blood, transmission, and mosquito stages. The stage-specific models of Plasmodium falciparum uncovered stage-dependent changes in central carbon metabolism and predicted potential targets that could affect several life cycle stages. The species-specific models further highlight differences between experimental animal models and the human-infecting species. Comparisons between human- and rodent-infecting species revealed differences in thiamine (vitamin B1), choline, and pantothenate (vitamin B5) metabolism. Thus, we show that genome-scale analysis of multiple stages and species of Plasmodium can prioritize potential drug targets that could be both anti-malarials and transmission blocking agents, in addition to guiding translation from non-human experimental disease models.Several antimalarial drugs exist, but differences between life cycle stages among malaria species pose challenges for developing more effective therapies. To understand the diversity among stages and species, we reconstructed genome-scale metabolic models (GeMMs) of metabolism for five life cycle stages and five species of  In silico gene-knock out simulations across species and stages uncovered functional metabolic differences between human- and rodent-infecting species as well as across the parasite’s life-cycle stages. These findings may help identify drug regimens that are more effective in targeting human-infecting species across multiple stages of the organism.Malaria kills nearly one-half million people a year and over 1 billion people are at risk of becoming infected by the parasite. Plasmodial infections are difficult to treat for a myriad of reasons, but the ability of the organism to remain latent in hosts and the complex life cycles greatly contributed to the difficulty in treat malaria. Genome-scale metabolic models (GeMMs) enable hierarchical integration of disparate data types into a framework amenable to computational simulations enabling deeper mechanistic insights from high-throughput data measurements. In this study, GeMMs of multiple Plasmodium species are used to study metabolic similarities and differences across the Plasmodium genus.  Malaria is a worldwide problem of clinical significance causing an estimated 483,000 deaths, with a disproportionate percentage occurring in children less than 5 years of age, according to the World Health Organization. AdditioPlasmodium falciparum . We used these stage-specific genome scale metabolic models GeMMs to characterize functional metabolic features of each stage as well as to predict essential targets whose inhibition would interfere with malaria growth across asexual, sexual (transmission) and mosquito stages. Moreover, we reconstructed GeMMs for four additional Plasmodium species that infect rodents, non-human and human primates . We used these Plasmodium GeMMs to investigate cross-species similarities and differences with particular focus on characterizing functional metabolic differences between rodent- and human-infecting species. Results provide a means to rank order and stratify established and new malaria treatment targets in addition to providing key insights into differences between rodent versus primate specific infections and implications for the interpretation of experimental animal models.Among potential drug targets, metabolic genes are of particular interest, since many anabolic and catabolic processes are critical for cellular growth and survival. Furthermore, methods have been developed to identify vulnerabilities in human pathogens by accurately predicting essential metabolic genes in genome-scale metabolic network reconstructions –14. HereP. falciparum , the Malaria Parasite Metabolic Pathway (MPMP) Database (http://mpmp.huji.ac.il/), and specific biochemical and genetic characterization studies from 332 primary and review literature reference articles  associations could be defined for 480 genes and 68% of all enzymatic reactions  versus apicoplast pyruvate dehydrogenase knockout (PDHapi-KO) P. falciparum parasites[parasites. Glucoseparasites,22 were parasites , schizont, early gametocyte (GII), late gametocyte (GV) and ookinete (ook)   , i.e., correlated reaction sets (co-sets), that in turn can yield insight into metabolic capabilities,29 and aAcross the different stages, there were considerable changes in central carbon metabolism, based on the co-sets . The metP. falciparum , Plasmodium vivax (Pviv) Sal-1 (iAM-Pv461), Plasmodium berghei (Pber) ANKA (iAM-Pb448), Plasmodium cynomolgi (Pcyn) strain B (iAM-Pc455), and Plasmodium knowlesi (Pkno) strain H (iAM-Pk459). The core metabolic content reflects the intersection of the genes, reactions, and metabolites of all five reconstructions, whereas the pan metabolic content is the union of these entities. The core Plasmodial metabolic content is comprised of 1064 reactions and 422 orthologous genes  of the orthologs differed in their essentiality across the 5 Plasmodium species. Reactions with the most striking differences in essentiality across malaria species were between the rodent and non-rodent species, namely: thiamine pyrophosphokinase (TPK), and choline kinase (Table H in in vitro) and rodents (in vivo); however, it is not clear from these studies whether an equally potent antimalarial effect is observed in both species. Our multi-species reconstructions revealed three key thiamine (Vitamin B1) biosynthesis enzymes: phosphomethylpyrimidine kinase (PMPK), hydroxyphosphomethylpyrimidine kinase (HMPK1), and thiamine-phosphate pyrophosphorylase (TMPPP) that are absent in rodent malaria, but present in non-rodent malarial species , the first enzyme in the Kennedy pathway (CDP-choline pathway) for synthesis of phosphatidylcholine (PC)  , inhibitnolamine . Thus, ein silico single gene deletion experiments, showed that pantothenate metabolism was not essential for growth in any of the life cycle stages of P. berghei. In contrast, pantothenate metabolism was essential for growth during the asexual and early gametocyte stages of P. falciparum . A list of P. falciparum metabolic pathways was built based on current genome annotation of P. falciparum (Plasmodb.org), the Malaria Parasite Metabolic Pathway (MPMP) Database (http://mpmp.huji.ac.il/), and malaria-specific biochemical characterization studies (Table A in The genome sequence and genome annotations for iAM-Pf480-predicted flux rates against kinetic flux data (rapid stable-isotope labeling) of glycolysis in wild-type (WT) and pyruvate dehydrogenase (PDH) deficient P. falciparum parasites cultured in vitro[iAM-Pf480 model was allowed to uptake metabolites available in standard in vitro growth conditions  . For the gametocyte stages, we developed two models. The first model (GII) simulated early gametocyte stage II which is metabolically active and hence, the objective function was set to maximize the production of biomass precursors. The constraint on the lower bound of the biomass function was relaxed to 0 mmol/gDW/h since it’s expected that the early gametocyte stages will exhibit a lower growth rate compared to the asexual stages. Lactate secretion was set to a minimum of 80% of glucose uptake rate[An experimentally measured growth rate [http://broadinstitute.github.io/picard/) and samtools[RP009370). SRA filRP009370). Tophat2RP009370) was used samtools were use samtools was usedP. falciparum ) were later used for evaluation of stage—specific models’ predictions. The network flux states were sampled and significantly different reactions (FDR < 0.05 and (> 75th or < 25th percentile of the log2 fold change in reaction fluxes)) were identified following removal of loop reactions. The corresponding genes were selected using gene-protein-reaction relationships and were compared against the list of significantly differentially expressed genes.Stage-specific model predictions were compared against differential gene expression (DEG) following a previously published workflow, outlineper se. Sampled reaction fluxes in the pentose phosphate pathway were compared across the different stages and differential flux activity was acknowledged if the flux distributions were significantly different following multiple hypothesis correction, as previously described[Correlated reaction sets (co-sets) were calculated using the sampled steady state solution points for the iAM-Pf480 stage-specific models . The details of the procedure for building Plasmodium multi-species genome-scale metabolic models are outlined in  analysis results.Co-Sets predict a stage-dependent fate of glucose-6-phosphate in P. falciparumSpecies-specific model building procedureReconstruction of species-specific models.Curation notes for specific enzymes that differed across the species.Host-specific hemoglobin compositionValidation of the species-specific reconstruction workflowMetabolic Similarities across Plasmodium speciesVariations in metabolic capacities between rodent- and human-infecting malaria speciesPhylogenetic analysis using TPK and CK vs. DHODH.Life cycle stage-specific models of P. bergheiReferences (Supporting Information)(PDF)Click here for additional data file.S1 TablesTable_SA iAM-Pf480 content descriptionTable_SB Single gene deletion list and performance evaluation of iAM-Pf480 and iTH366Tables_SC Druggable targets compiled list and performance evaluation of iAM-Pf480 and iTH366Tables_SD Validation of iAM-Pf480 predicted flux rates: uptake rates used to constrain and validate model predictions as published in PMID:24163372Tables_SE Validation of iAM-Pf480 predicted flux rates: correlation between predicted and experimentally measured flux rates for wild-type and pyruvate dehydrogenase (PDH) deficient P. falciparum parasitesTable_SF Doubling time (h) times and glucose uptake rates of P. falciparum stage-specific modelsTable_SG Correlated reaction sets (CoSets) across the life cycle stage-specific models of P. falciparumTable_SH Gene essentiality predictions across the 5 plasmodium species studied in this work. Representative genes belonging to the same OG group are shown in the table. Pfal: P. falciparum, Pber: P. berghei, Pkno: P. knowlesi, Pcyn: P. cynomolgi, Pviv: P. vivax, grRed: growth reductionTable_SI Variation in metabolic reactions between 5 plasmodium species: 14 enzymatic and transport reactions coded for by 9 genes that differe between species-modelsTable_SJ Performance evaluation of iAM-Pb448Table_SK Pantothenate CoSet and differential essentiality across P. falciparum and P.berghei stage specific models.(XLSX)Click here for additional data file.S1 Fig(TIF)Click here for additional data file.S2 Fig(TIF)Click here for additional data file.S3 Fig(TIF)Click here for additional data file.S1 Model(ZIP)Click here for additional data file.


For industrial-scale operations, practical considerations limit production to ca. 6000 L ha−1 year−1. According to published economic models and life cycle analyses, such production rates cannot support long-term viable commercialisation of solar-powered cultivation of natural microalgae strains exclusively as feedstock for biofuels. The commercial viability of microalgal biofuels depends critically upon limitations in microalgal physiology (primarily in rates of C-fixation); we discuss the scope for addressing this bottleneck concluding that even deployment of genetically modified microalgae with radically enhanced characteristics would leave a very significant logistical if not financial burden.Algal biofuels have been offered as an alternative to fossil fuels, based on claims that microalgae can provide a highly productive source of compounds as feedstocks for sustainable transport fuels. Life cycle analyses identify algal productivity as a critical factor affecting commercial and environmental viability. Here, we use mechanistic modelling of the biological processes driving microalgal growth to explore optimal production scenarios in an industrial setting, enabling us to quantify limits to algal biofuels potential. We demonstrate how physiological and operational trade-offs combine to restrict the potential for solar-powered algal-biodiesel production in open ponds to a ceiling of ca. 8000 L haThe online version of this article (doi:10.1007/s10811-017-1214-3) contains supplementary material, which is available to authorized users. The transport sector is expected to remain largely reliant on carbon-based energy systems for the foreseeable future  and a need for CO2 as the substrate (thus requiring a carbon concentrating mechanism to optimise C-fixation). The analysis of Flynn and Raven (Um) of the order of a few divisions per day. Such growth rate potentials contrast greatly with assumed maximum rates used in some models of microalgal productivity . RuBisCO has a rather low specific catalytic rate, a competing affinity for the by-product of photosynthesis −1; Williams and Laurens −2 day−1  attempting to quantify environmental impacts and commercial potential  and high, yet N-stressed, productivity; the latter is required to stimulate high lipid content. Importantly, a failure to take into account dynamic effects of photoacclimation within a growing algal population (that collectively self-shades community photosynthesis), and nutrient uptake regulation, leads to an over-estimation of productivity. That likelihood is greater again if implausible growth rates are assumed in models .Our model describes the physiological interactions at the heart of this complex process. The basis of the microalgal model is a well-established Flynn  acclimatThe Electronic Supplemental Material contains full details of the model equations , along w2-stat that would simultaneously maintain non-limiting CO2 for photosynthesis and also flush out RuBisCO-inhibitory O2), and that temperature is also optimal. Temperature optimality is especially problematic in reality as evaporation from ponds lowers temperatures, while elevated temperatures (enhanced in dense cultures by light absorbance) stimulates significant elevated metabolism in the short term , the quotient describing the relevant growth rate, XiCu, has the general form:The carbon-specific growth rate is designated as XiC denoting the C-quota for each nutrient while XiC0 and XiCm are the quotas necessary to sustain minimum and maximum growth, respectively. KQXi acts like a half-saturation constant affects the curve shape. At each timestep, this quotient is used to test (through Boolean logic terms) which, if any, of the nutrients are limiting. The form of the expression describing the rate of change of XiC forces uptake of any non-limiting nutrients to be moderated:with XiC approaches its absolute maximum value XiCabs at which point transport of the non-limiting nutrient ceases. The rate at which XiC approaches XiCabs is regulated by the parameter θβ. The explicit expressions for each stoichiometric variable modelled in this investigation are presented in The first term on the right hand side (the nutrient uptake rate) contains logic expressions within the brackets that are governed by the outcome of Eq. . This exCu balances photosynthesis against losses through respiration. Total (depth integrated) photosynthetic activity, PS, in the water column is calculated by integrating the Smith equation (Smith τ (assuming a homogeneous cell suspension) to obtain  and k is the attenuation factor of the culture and a function of ChlC and total algal C-biomass. Parameter τ is system depth. Variables are updated at each timestep to capture photoacclimation effects. The dynamics of photoacclimation (i.e. changes in the Chl/C quota with light and nutrient-status of the cells) are described so:Here, whereNPSCu is whichever is the lower of the N-, P- or (for diatom) Si-limited forms of Eq. basres is basal respiration; redco is the cost for reducing nitrate to ammonium; 1.5 is the anabolic respiration cost in terms of gC per gN assimilated into biomass; ChlCm is the maximum Chl/C (ChlC); NCm is the maximum cellular N/C; Um is the maximum growth rate (Flynn te Flynn .αChl) to raise C-fixation, a low value of respiration to minimise production losses  and simulations run within the Powersim Constructor v2.51 platform as we have used in our previous studies  at the prevailing temperature regime; this could well involve the usage of different strains of microalgae during different seasons, especially for exploitation at higher latitudes. The parameter values explored are presented in Table To take additional factors into account which had not been considered previously using a multi-nutrient mechanistic modelling approach ; these are values that are consistent with cellular activities of RuBisCO . Discontinuous harvesting was configured to coincide with local dusk, to take advantage of a whole daylight’s worth of photosynthetic activity, before partial loss of algal-C through net cellular respiration during the dark phase (night). Harvesting other than using a continuous chemostat-like approach results in short periods of oscillation in nutrient status of the microalgae as the sudden input of significant volumes of fresh medium relieves nutrient stress. In such instances, the nutrient status of the microalgae typically re-entered quasi-steady state within the following light phase of growth. However, if the harvesting proportion was greater than ca. 50% on any one occasion, then (depending on the maximum growth rate and the time averaged dilution rate) re-establishment of quasi-steady state could take longer than one light–dark period.The harvesting methods explored were continuous culture (akin to a chemostat), discontinuous culture with a prescribed daily harvesting/dilution frequency, and semi-automated harvesting triggered when growth plateaus (here set by parameter −1 and 1.11 mg P L−1 (holding the N/P ratio constant throughout) work well in this regard (Kenny and Flynn −2) are inevitably obtained using higher nutrient concentrations, for commercial viability the areal rate of productivity (i.e. g biomass-C m−2 day−1) is the critically important factor. To ensure the required N-depletion develops to maximise biofuel production (g biofuel-C m−2 day−1), half-concentration nutrient levels (i.e. f/4) were found to be sufficient. For depths of 5 cm and less, f/2 levels proved more effective; the shallow depth permits higher nutrient levels to be used, giving higher biomass densities while still permitting N-source exhaustion and the consequential accumulation of surplus C for exploitation as biofuels. However, such conditions can only be achieved using specialised photobioreactors; open ponds require depths of ca. 20 cm to ensure adequate mixing  and also to minimise the potential for eutrophication of local waterways in the event of spillage. Our previous studies have indicated that for maximum biomass productivity, N and P concentrations set to f/2 , considering such an idealised system allows us to bypass technological bottlenecks that may hamper the commercialisation of algae biofuel production and concentrate purely on physiological constraints. Our projections should thus be considered as representing the upper end of the productivity spectrum when operated over a whole year.Throughout, we assume that the culture system operates optimally from a logistic and engineering standpoint. Thus, we assume no mechanical breakdowns, all media transfers and harvesting attained extremely rapidly  and without wastage, no biomass loss through disease or cell disruption during culture, homogenous culture mixing with constant pH attained by COThe model operates, as does biochemistry, with reference to carbon; results are thus given in terms of gC, not as dry weight. Transforms to dry weight units are considered in Um = 1.386 day−1) optimised areal production of biomass and biofuel feedstocks  for each combination of geographic location and bioreactor operational depth . Figures −2 day−1 at high latitudes and 2.7 g biomass-C m−2 day−1 at tropical latitudes . Setting these conditions, the maximum specific growth rate, Um Fig.  and resuUm Fig. ; the ratUm = 2.7 day−1 gave an average AXP over the year of 1.6 g biofuel-C m−2 day−1 for a depth of 7.5 cm, falling to 1.3 g biofuel-C m−2 day−1 with the more realistic open pond depth of 20 cm  cultivation systems will result in the evolution of slower growing populations Droop , and the2 is considered to represent a major restraint on location and operation of massive open systems , though these are less suited to conversion to biofuels  over the period, as computed in our simulations and accounting for factors such as cloud cover and variations in solar elevation, is approximately 400 Wm−2. From the results of our analysis, the maximum solar to chemical energy conversion efficiency from algae is thus 0.25%, a value comparable with estimates of photosynthetic efficiency for lipid production of 0.31% ; this equates to just under 10 t biomass-C ha−1 year−1. This value obtained from our simulations falls in the mid to upper range of rates achieved in real pond systems  is essentially dormant. In consequence, productivity levels at medum-to-high latitudes during summer may be quite respectable , a biomass production rate of 2.7 g biomass-C mUm at 2.7 day−1 . Assuming a carbon density of 720 gC L−1 . Repeating this analysis assuming a potential microalgal autotrophic growth rate at the upper extreme of plausibility  considered as leading to a positive outcome. We now use our results to re-appraise the LCAs conducted by Sun et al.  exploring the commercial viability of microalgal biofuels considered a range of productivity scenarios, with only the highest values  with maximum lipid content (60%)  biomass production capacity would have to be forfeited for a <10% gain in low-value biofuels production −1. For optimised AXP (Table −1 and 9 gP (L biodiesel)−1; however, using the more realistic 20-cm-deep raceways, inputs of 144 gN (L biodiesel)−1 and 13 gP (L biodiesel)−1 are required. These consumption figures are of the same order as those estimated using (fixed) stoichiometric arguments for biomass production  mode −1 and 13 gP (L biodiesel)−1. For algal biofuels to replace 10% of the 350 billion litres of transport fuel consumed in the EU each year (European Commission 2O5) used to fertilise Europe’s terrestrial crops each year  and/or that the percentage of cellular protein as RuBisCO is increased . Very significant enhancements to microalgal productivity (i.e. approaching 5-fold) through GM techniques are needed to overcome these constraints. However, from the forgoing, even this enhancement does not guarantee commercial or sustainable success, and that is before considering the potential environmental risks posed by the inevitable escape to the wild of such organisms grown in vast open ponds . As Williams and Laurens , such that the hectarage required in the above mentioned example of European biofuels production was decreased by ca. 5-fold (to 2 million ha), the flux of N and P fertiliser around the system would remain at many hundreds of thousands of tonnes annually. Even deploying some form of coupled photovoltaic solar farm with LED-lit PBR installations, allowing continuous irradiance and a relatively bio-secure platform for GM microalgae, would require that fertiliser flow. And then there is the irony that to achieve this productivity the input of a commensurate quantity of CO Laurens  allude, ESM 1(DOC 300 kb)ESM 2(XLS 48 kb)ESM 3(XLS 48 kb)ESM 4(XLS 44 kb)


Assuming a steady-state condition within a cell, metabolic fluxes satisfy an underdetermined linear system of stoichiometric equations. Characterizing the space of fluxes that satisfy such equations along with given bounds  is considered of utmost importance for the understanding of cellular metabolism. Extreme values for each individual flux can be computed with linear programming , and their marginal distributions can be approximately computed with Monte Carlo sampling. Here we present an approximate analytic method for the latter task based on expectation propagation equations that does not involve sampling and can achieve much better predictions than other existing analytic methods. The method is iterative, and its computation time is dominated by one matrix inversion per iteration. With respect to sampling, we show through extensive simulation that it has some advantages including computation time, and the ability to efficiently fix empirically estimated distributions of fluxes. Large-scale metabolic models of organisms from microbes to mammals can provide great insight into cellular function, but their analysis remains challenging. Here, the authors provide an approximate analytic method to estimate the feasible solution space for the flux vectors of metabolic networks, enabling more accurate analysis under a wide range of conditions of interest. M metabolites and N reactions. In mathematical terms, we can define a M × N stoichiometric matrix S in which rows correspond to the stoichiometric coefficients of the corresponding metabolites in all reactions. A positive (resp. negative) Sij term indicates that metabolite i is created (resp. consumed) by reaction j. Assuming mass-balance and limited interval of variation for the different reactions, we can cast the problem in terms of finding the set of fluxes ν∈The metabolism of a cell entails a complex network of chemical reactions performed by thousands of enzymes that continuously process intake nutrients to allow for growth, replication, defence and other cellular tasksb∈νinf, νsup represent the extremes of variability for the variables of our problem. Only in few cases, the extremes are experimentally accessible, in the remaining ones they are fixed to arbitrarily large values. It turns out that N≥M, and the system is typically underdetermined. As an example, the RECON1 model of Homo sapiens has N=2,469 fluxes  and M=1,587 metabolites . The mass-balance constraints and the flux inequalities encoded in where The most widely used technique to analyse fluxes in large-scale metabolic reconstruction is flux balance analysis (FBA)367As long as no prior knowledge is considered, each point of the polytope is an equally viable metabolic phenotype of the biological system under investigation. Therefore, being able to sample high-dimensional polytopes becomes a theoretical problem with concrete practical applications. From a theoretical standpoint, the problem is known to be #P-hard6817S should be statistically uncorrelated. Unfortunately, neither assumption is really fulfilled by large-scale metabolic reconstructions. To give an example, consider the rows of the stoichiometric matrix for E. colicore modelRecently, alternative statistical methods based on message passing (MP) techniques 7202122Escherichia coli.In this work, we propose a new Bayesian inference strategy to analyse with unprecedented efficiency large dimensional polytopes. The use of a Bayesian framework allows us to map the original problem of sampling the feasible space of solutions of ν compatible with E(ν) whose minimum(s) lies on the assignment of variables ν satisfying the stoichiometric constraints in We are going to formulate an iterative strategy to solve the problem of finding a multivariate probability measure over the set of fluxes b given a set of fluxes ν as a Boltzmann distribution:We define the likelihood of observing β is a positive parameter, the ‘inverse temperature' in statistical physics jargon, that governs the penalty of whose configurations of fluxes that are far from the minimum of the energy. In a Bayesian perspective, one can consider the posterior probability of observing where where the priorνn∈[enforces the bounds over the allowed range of fluxes. The function β→∞ limit. Neglecting terms that do not depend on ν, the posterior takes the form ofand eventually we will investigate the n∈{1, …, N}. However, performing this computation naively would require the calculation of a multiple integral that is in principle computationally very expensive and cannot be performed analytically in an efficient way.where we have not explicitly reported the normalization constant. By marginalization of A standard way of approximately computing ψn(νn) with a single Gaussian distribution ψn(νn). That isAs a first approximation, one can think of replacing each exact prior We estimate the marginal posteriors from the distributiona and the variances d in Notice that in this approximation fluxes result unbounded. Marginals obtained by this strategy against the HR Monte Carlo estimate are shown in EP27nth flux and its corresponding approximate prior φn. We define a tilted distribution Qn) is to require that the multivariate Gaussian distribution One way of determining the unknown parameters an, dn that is explicitly reported in section 3.from which we get a relation for the parameters n∈{1, …, N}, from marginalization of the tilted distribution Qn), we encountered convergence problems and thus we decreased it to 109. Numerical convergence of EP depends on the refinement of parameters a and d or, more precisely, on the estimate of the marginal distributions of fluxes. At each iteration t, we compute an error ɛ, which measures how the approximate marginal distributions change in two consecutive iterations. Formally, we define the error as the maximum value of the sum of the differences  of the mean and second moment of the marginal distribution, that isAfter the preprocessing, we run HR and EP, both implemented on Matlab or as Matlab libraries, to the reduced model. Let us explain how the two methods work. Starting from a point lying on the polytope, HR iteratively chooses a random direction and collects new samples in that direction such that they also reside in the solution space. In this work, we use an optimized implementation of HR, called ɛt is smaller than a predetermined target precision (we used 10−5), the algorithm stops.If To quantitatively compare the two techniques, we report here the scatter plots of variances and means of the approximate marginals computed via HR and EP. Moreover, we estimate the degree of correlation among the two sets of parameters computing the Pearson product-moment correlation coefficient.Notice that we cannot have access to the exact marginals and that we assume that the results obtained by HR are exact only asymptotically. Thus, our performances, both for the direct comparison of the means and variances and for the Pearson's coefficient, should be considered accurate if they are approached by the Monte Carlo ones for an increasing number of explored points.E. coli, C. neuron and Homo sapiens, respectively. For each organism, we report on the top-left panel the time spent by EP (straight line) and by HR (cyan points) and on the bottom-left panel the Pearson correlation coefficients. Both measures of time and correlation are plotted as functions of the number of configuration T obtained from the HR algorithm. As shown in these plots, we can notice that to reach a high correlation regime a very large number of explored configurations, employing a computing time that is always several orders of magnitude larger than the EP running time. This is particularly strinking in the case of the RECON1 model, for which we needed to run HR for about 20 days in order to reach results similar to the outcomes of EP, that converges in less than 1 h on the same machine.The three large subplots in y axis, we plot the EP means (variances) against the HR means (variances) for an increasing number of explored configurations, as indicated in x axis. Results clearly show that as T grows, the points (both means and variances) are more and more aligned to the identity line: not only these measures are highly correlated for large T, but they assume very similar values. This is remarkably appreciable in the results for CHOLnorm model: for T=4 × 104 the means of the scatter plots are quite unaligned but as T reaches 4 × 107, they almost lie on the identity line. In fact, means are poorly correlated for T=4 × 104 while the Pearson correlation coefficient is close to 1 for T=4 × 107.To underline how EP seems to approach HR results in the asymptotic limit, we report in the rest of the sub-figures the scatter plots of the means (top) and the variances (bottom) of the marginals. On the The EP formalism can efficiently deal with a slightly modified version of problem of sampling metabolic networks. Suppose to have access to experimental measurements of the distribution of some fluxes under specific environmental conditions. We would like to embed this empirical knowledge in our algorithm, by matching the posterior distribution of the measured fluxes with the empirical measurements. Within the EP scheme, this task corresponds to matching the first two moments (mean and variance) of the posteriors with the one defined by the empirical measurements. With the inclusion of empirically established prior knowledge, we want to investigate how the experimental evidence is related to the metabolism at the level of reactions or, in other words, we want to determine how fluxes modify in order to reproduce the experiments. In this perspective, the EP scheme can easily accommodate additional constraints on the posteriors by modifying the EP update equations as outlined in Methods section.iJR904 model of E. coli for a constrained growth rate. In fact, one of the few fluxes that are experimentally accessible is the biomass flux, often measured in terms of doubling per hour. As a matter of example, we decide to extract one of the growth rates reported in Glc (P5-ori) can be well fitted by a Gaussian probability density of mean 0.92 h−1 and variance 0.0324, h−2. This curve represent single-cell measures of a population of bacteria living in the so-called minimal substrate whose main characteristics are in principle well caught by the iJR904 model. We fixed the bound on the glucose exchange flux EX_glc(e) such that the maximum allowed growth rate (about 2 h−1) contained all experimental values in the profile labelled as Glc (P5-ori) of −1 h−1.We have tested this variant of EP algorithm on the iJR904 model in two different conditions. First, we do not impose any additional constraint and we run the original EP algorithm as described in the previous section. Then, as described in Methods section, we fix the marginal posterior of the biomass. We can now compare the means and the variances of all the other fluxes in the two cases and single out those fluxes that have been more affected by the empirical constraints on the growth rate. We report in We then apply EP algorithm to the modified iJR904 model when the lower bound and the upper bound of the biomass is fixed to the average value of the experimental profile. The comparison (not shown) between the two approaches suggests that the most relevant change concerns the EX_asp_L(e) flux as both the average value and the variance estimated in the second case are about two times the ones predicted by constrained EP. The distributions of most other fluxes remain do not considerably change. We underline that the different behaviour of the marginals in the two cases, even if not significant for most of the fluxes, was in principle unpredictable without the use of constrained EP; and we do not exclude that fixing other empirical profiles can lead to very different results. Likewise, it seems unlikely that the results computed with constrained EP could be obtained using unbiased samples as provided by standard HR implementations  of EP is three order of magnitude smaller than HR. We underline that exact marginals are generally inaccessible and we cannot compare our results against a ground-truth; our measures well approximate ‘true' distributions as long as the exactness of HR in the asymptotic limit is correct.In this work, we have shown how to study the space of feasible configurations of metabolic fluxes within a cell via an analytic description of the marginal probability distribution characterizing each flux. Such marginals are described as truncated Gaussian densities whose parameters are determined through an iterative and extremely efficient algorithm, the EP algorithm. We have compared our predictions against the estimates provided by HR sampling technique and results shown in Subsection 1 suggest a very good agreement between EP and HR for a large number of explored configurations, iJR904 model of E. coli affect non-trivially all other fluxes. This is a remarkable advantage of the EP algorithm with respect to other methods.We have shown how to include empirical knowledge on distribution of fluxes on the EP algorithm without compromising the computing time. More precisely, we have investigated how fixing an experimental profile of the growth rate into the EP provides an analytic estimate of each single flux marginal, which relies on the optimization of two parameters, the mean and the variance of a Gaussian distribution. The formalism allows in principle more complicated parametrizations of posteriors to include other biological insights.N3), rendering EP extremely convenient in terms of computation time with respect to existing alternatives.EP equations are extremely easy to derive and to implement, as the main loop can be written in few lines of Matlab code. The method is iterative, and the number of operations in each iteration scales as Θ, to include as many distributions as possible without compromising the convergence of the algorithm. Moreover, the Gaussian profile itself is surely a limitation of the approximation as true marginals can have in principle arbitrary profiles.An shown in β and equations become numerically unstable for too large β . On the other hand, β can be seen as the inverse-variance of a Gaussian noise affecting the conservation laws. The nature of this noise could depend on localization properties on the cell and real thermal noise. In this case, an optimization of the free energy with respect to β can in principle lead to better predictions.EP performances are sensitive to the parameter Qn) are iteratively tuned in a way that the first and second moments of the two distributions match. The update rule for the parameters an and dn of the Gaussian prior will be derived in details in the following section.The algorithm described in the EP section relies on local moves in which, at each step, we refine only the parameters of one single prior, minimizing the dissimilarity between the auxiliary tilted distribution Qn). The covariance matrix where D, Σ, n. EquivalentlyNote that we are omitting for notational simplicity the dependence of Q and Qn) operations per iteration. We propose in N3) operations per iteration.Notice that the sequential update scheme described in the EP section requires the inversion of the matrix f(νi) for flux i. We aim at determining how the posteriors of other fluxes would modify to fit with the experimental results compared, for instance, to the unconstrained case. The so-called maximum entropy principleSν=b, is simplyLet us assume to have access to experimental measures of the  posterior β→∞ and g(νi) is the  function of unknown Lagrange multipliers that has to be determined in order for the constraint ai, di can be achieved by slightly modifying the EP update for flux i. Assuming as before that the prior of each flux n≠i can be approximated as a Gaussian profile φn of parameters an and dn, also to be determined, we must impose thatwhere ai and di can be easily computed and take the formwhere the distribution This expression is exactly the same in The computations were performed on a Dell Poweredge server with 128 Gb of memory and 48 AMD Opteron CPUs clocked at 1.9 Ghz. No constraint have been placed on the number of CPU threads, allowing both EP and HR to parallelize their processes. We observed that EP used 2–3 cores, exclusively in the matrix inversion phase (which was time-dominant), while HR employed a variable number of cores (around six or seven at some times). For this reason only, the order of magnitude of computing times of HR and EP are fairly comparable but they are sufficient to underline the differences between the two algorithms.https://github.com/anna-pa-m/Metabolic-EP.An implementation of the algorithm presented in this work is publicly available at All data generated or analysed during this study are included in the manuscript and its How to cite this article: Braunstein, A. et al. An analytic approximation of the feasible space of metabolic networks. Nat. Commun.8, 14915 doi: 10.1038/ncomms14915 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Supplementary figures, supplementary notes and supplementary references.


In this sense, abnormal metabolic states have been found in different neuropathological diseases. Determination of metabolic states of astrocytes is difficult to model using current experimental approaches given the high number of reactions and metabolites present. Thus, genome-scale metabolic networks derived from transcriptomic data can be used as a framework to elucidate how astrocytes modulate human brain metabolic states during normal conditions and in neurodegenerative diseases. We performed a Genome-Scale Reconstruction of the Human Astrocyte Metabolic Network with the purpose of elucidating a significant portion of the metabolic map of the astrocyte. This is the first global high-quality, manually curated metabolic reconstruction network of a human astrocyte. It includes 5,007 metabolites and 5,659 reactions distributed among 8 cell compartments, . Using the reconstructed network, the metabolic capabilities of human astrocytes were calculated and compared both in normal and ischemic conditions. We identified reactions activated in these two states, which can be useful for understanding the astrocytic pathways that are affected during brain disease. Additionally, we also showed that the obtained flux distributions in the model, are in accordance with literature-based findings. Up to date, this is the most complete representation of the human astrocyte in terms of inclusion of genes, proteins, reactions and metabolic pathways, being a useful guide for  Astrocytes are the most numerous glial cells found in the vertebrate brain . The reconstruction covers a large number of metabolic reactions that belong in most part to the energetic metabolism including carbohydrate metabolism, amino acid metabolism, xenobiotics biodegradation, nucleotide metabolism and metabolism of cofactors and vitamins. Furthermore, the model was validated using a flux Balance Analysis (FBA), for prediction of fluxes in the simulation. Additionally, network evaluation was performed to examine if the model was capable to generate the common astrocytic metabolites reported by the literature  using MATLAB 2012bAll network reactions of the model were mathematically described and assembled in a stoichiometric matrix (S), where the mass balance equation system for all metabolites is represented as follows:m size times n. m represents the number of metabolites  and n the number of reactions including exchange reactions ; v is the reaction flux vector to be identified. Restrictions for every reaction have the form:Where S is a stoichiometric matrix of Vi and Va are represented by inferior and superior limits, respectively, which define maximum and minimum allowable flux limits for every reaction, limited between -1,000 and 1,000  was used to adjust and evaluate restrictions imposed on the model under normal physiological conditions  were defined. These reactions allowed to establish the astrocytic metabolism under an physiological excitatory stimulus. Two objective functions were considered because according to literature, astrocyte metabolism its highly dependent on (1) ATP derived from energetic pathways and 2) the glutamate and glutamine exchange between astrocytes and extracellular space  with a standard deviation equal to the standard deviation of the flux (denominator) divided by the square root of the number of samples. Therefore, Z itself follows a normal distribution with a standard deviation equal to the inverted square root of the number of samples. To keep the error lower than 0.15, five thousand simulations were performed, which reduced error probability to 0.999%. Results obtained at different biological states were validated by comparing metabolic changes with literature reports making an extended bibliographic search in databases such as OMIN (Online Mendelian Inheritance in Man) , non-associated to gene transport reactions (9%) and non-associated to gene intracellular reactions (3%); Figure .Regarding subcellular location, cytosolic and mitochondrial reaction contributed with 59% of the total reactions in the model. 23% of reactions belonged to peroxisome, lysosome, endoplasmic reticulum, golgi apparatus and nucleus. Transport reactions among the different organelles and extracellular space represented 18% of total reactions Figure .Reactions were gathered around different metabolic routes Figure , being 3Due to the high coverage of gene-associated reactions, is possible to use this model for the integrated computational analysis of astrocyte metabolism and genomic data , main modulator of phosphorylation reaction of glucose to glucose-6-phosphate, was calculated in 0.49 μmol/g/min. This value is similar to previous experimental results obtained by nuclear magnetic resonance spectroscopic approach, which reported 0.41 ± 0.03 miccromol. g(−1). min(−1) , it was observed an initial metabolic flux activation by citrate synthase (EC:2.3.3.1). This enzyme catalyzes the first reaction of the acetate condensation coming from acetyl-CoA and oxaloacetate. During the aldol condensation reaction between acetyl-CoA and oxaloacetate, a thioester group (CoA) is hydrolyzed, forming citrate . In this aspect, respiration is inhibited but glycolysis continues in astrocytes causing an accumulation in lactate and protons and a rapid intracellular acidification , which would enable systematic studies of human astrocyte metabolism. This model includes the central routes of carbohydrate metabolism, energetic metabolism, purine metabolism, aminoacids metabolism, vitamin and cofactor metabolism, glutamate-glutamine cycle, lipid metabolism and glutathione metabolism.We studied the flux distribution in these pathways. For this goal, two simulations were generated from this reconstruction, representing the astrocyte in normal physiological state and ischemic conditions. Through these simulations, we tried to gain some insight into the metabolic pathways and metabolites that were present in these metabolic states. In this aspect, the model was capable of yielding results, which were in correspondence to the experimentally proved phenomena.By setting the objective function, the model was demanded to generate the maximum energy production. Therefore, increased fluxes in energetic pathways were observed. Specifically, a higher activation in the TCA cycle pathway was observed, followed by glycolysis, pentose phosphate and oxidative phosphorylation, showing direct relations among these different cycles. Our results shown glycolytic flux activation in response to an abrupt energetic demand   and glyceraldehyde 3-phosphate dehydrogenase (EC:1.2.1.12). The latter not only catalyzes the sixth step of glycolysis, but also has been involved in non-metabolic processes including transcription, apoptosis and axonal transport , identification of active therapeutic targets, discovering of key proteins in response to an insult , future drug evaluations and determination of biomarkers in different neurologic diseases such as Alzheimer, Parkinson, Huntington, Amyotrophic Lateral Sclerosis, Multiple Sclerosis, Schizophrenia, among others. The study of the metabolic behavior of these diseases during aging will help to understand characteristics of receptors, transporters and pumps that are vital in the development of these processes (De Lores Arnaiz and Ordieres, In conclusion, we generated the most complete metabolic reconstruction of an astrocytic to the date. In this aspect, the simulation of different conditions in or astrocytic model were positively correlated with previous studies Danbolt, ; showingCM and JG designed the methods and simulations; CM and DS performed the simulations; CM, DS, GB, and JG analyzed the data; CM, JG, and DS wrote the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Clostridium acetobutylicum and Wolinella succinogenes that interact via interspecies hydrogen transfer and applied different environmental conditions for which we expected the metabolic-exchange rates to change. We used stoichiometric models of the metabolism of the two microorganisms that represents our current physiological understanding and found that this understanding - the model - is sufficient to infer the identity and magnitude of the metabolic-exchange fluxes and it suggested unexpected interactions. Where the model could not fit all experimental data, it indicates specific requirement for further physiological studies. We show that the nitrogen source influences the rate of interspecies hydrogen transfer in the co-culture. Additionally, the model can predict the intracellular fluxes and optimal metabolic exchange rates, which can point to engineering strategies. This study therefore offers a realistic illustration of the strengths and weaknesses of model-based integration of heterogenous data that makes inference of metabolic-exchange fluxes possible from community-level experimental data.An important challenge in microbial ecology is to infer metabolic-exchange fluxes between growing microbial species from community-level data, concerning species abundances and metabolite concentrations. Here we apply a model-based approach to integrate such experimental data and thereby infer metabolic-exchange fluxes. We designed a synthetic anaerobic co-culture of  Microbial communities carry out important processes for the planet’s ecosystem, animal health and industrial purposes. Engineering such communities is not straightforward; they are generally composed of many interacting microorganisms, and they are highly dynamic. Developing methods that relate the systemic properties of communities to the underlying metabolic processes and interactions of the community members is a major challenge in microbial ecology. Those interactions drive community behaviour, including its (in-)stability upon environmental perturbations . MetabolCurrent approaches focus mostly on correlation and co-occurrence of species members for inference of community-interaction partners , 6. ThesUnfortunately, quantifying metabolic exchange fluxes—metabolic interactions—directly from experimental data is rarely possible. Generally, only net fluxes are inferred from dynamic metabolite levels measured at the community level that result from contributions of many species. To determine the individual contributions of those species, we suggested that their metabolic capacities, expressed in terms of quantitative models, should be integrated with experimental data . Here weet al. on a methanogenic co-culture  the substrate concentration and Km the substrate affinity. At each time step in dFBA the biomass production rate for each organism is independently optimised based on the specific substrate uptake rate. Implementing such dynamic uptake reaction enables the model to respond to changes in external concentrations.We used stoichiometric metabolic models of s (dFBA) , which eC. acetobutylicum and for W. succinogenes a coarse-grained model, which lumps metabolic segments into single reactions. We used a coarse-grained model as we expected that we could model our results without the need for full genome-scale reconstruction. We did do the reconstruction to verify that this was indeed the case . Having a coarse-grained model facilitates computation and interpretation, especially if these methods are applied to larger and more complex microbial ecosystems.For the simulations we use a genome-scale metabolic model for the metabolism of C. acetobutylicum has the advantage that it captures changes in its metabolism, as we observed that final acetate and butyrate concentrations, produced by C. acetobutylicum changes when the growth medium was varied. Another advantage is that it describes the metabolic flexibility associated with H2 production by C. acetobutylicum and leads to oxidization of ferredoxin. Ferredoxin is a conserved moiety whose total concentration does not change (only its redox state), and when it is oxidized by another reaction, it will result in decreased H2 production. Since C. acetobutylicum contains several reactions that can oxidize or reduce ferredoxin, the H2 production flux is flexible, influencing the community interactions that we aim to quantify. For instance, NO2- uptake decreases the amount of H2 production, because both reactions require ferredoxin, which results in potential interesting dynamics between the two species, because W. succinogenes provides NO2-, but requires H2 which is produced by C. acetobutylicum. Several genome-scale metabolic models of C. acetobutylicum are available [Conversely, the detailed model of vailable , 33. We vailable , becauseW. succinogenes, containing eight reactions  (https://sourceforge.net/projects/cbmpy/files/publications/data/2017_Hanemaaijer/). Those 41 reactions are involved in either malate cycling, proline and nucleotide biosynthesis, and carry very small fluxes relative to the fluxes in C. acetobutylicum’s core-metabolism. Two reactions that did carry a high flux are involved in ferredoxin cycling, but had no impact on the H2 production flux. There was also no variability identified in other uptake or production fluxes. These results suggest that in our system, the calculated flux distribution within C. acetobutylicum can be robustly predicted from community-level experimental data alone.We therefore performed a Flux Variability Analysis (FVA) , to checBesides providing a method for inferring experimental fluxes from experimental data, the metabolic model can also be used to predict the optimal behaviour of the community when not constrained with experimental data. Optimisation informs us about optimal metabolic coupling between the microorganisms when growth of both species are optimised.4+ + NO3-’ and ‘NO3-’ condition when we released the constraints on the butyrate/acetate production ratio and the NH4+/NO2- consumption ratio of C. acetobutylicum , growth rate and biomass abundances corresponding to the optimal state in the ‘NHutylicum .C. acetobutylicum would have a changed metabolism relative to the experimental data. For instance, acetate rather than butyrate should be produced when C. acetobutylicum grows optimally. This behaviour was seen both in the ‘NH4+ + NO3-’ and the ‘NO3-’ condition. The explanation is that more ATP can be generated from acetate production than from butyrate production. An optimal C. acetobutylicum would not consume NO2- when growing at the ‘NH4+ + NO3-’ condition, because NO2- reduction by nitrite reductase decreases growth of C. acetobutylicum according to the metabolic model. As explained, the amount of H2 produced is inversely related with the amount of NO2- taken up. As a consequence, 159% more H2 was produced in the optimal scenario relative to the experiments in the ‘NH4+ + NO3-’ condition. A smaller increase in H2 production (+23%) was shown in the ‘NO3-’ condition, suggesting that the interactions between the two species were not optimal in the experiments at those two conditions. However, the experimental growth-rate of C. acetobutylicum was close to its maximal, computed value. For the ‘NH4+ + NO3-’ the experimental growth rate was 87% of the optimal value, whereas for the ‘NO3-’ this was 94%. These results suggest that the experimental behaviour of the community with imposed bidirectional interactions is closer to the optimal metabolic behaviour than a community with unidirectional interactions.The model predicted that an optimal In this study we showed that the combination of a stoichiometric metabolic model with measured community-level concentrations and biomass abundances allows for the inference of metabolic interactions in a microbial community. This approach is complementary with current approaches that are based on correlation or co-occurrence networks, which predicts the community-interaction structure for large complex ecosystems , 41, 42.Stoichiometric models of metabolism make inference of metabolic exchange fluxes possible because they relate the uptake and production of environmental metabolites, to intracellular metabolic fluxes, organism abundance and growth rate. Such models are therefore integrating heterogeneous data types from which we make inferences about community behaviour. In addition to experimental data of species abundances and metabolite concentrations, molecular data can be used in the construction of stoichiometric metabolic models –45. It i2 exchange in our co-culture. Recently, Embree et al. [Metabolic models have been used to predict the behaviour of industrially relevant co-cultures and the type of interactions required to predict this behaviour , 14. We e et al.  also infW. succinogenes sufficed for the inference of metabolic interactions, as we recently suggested [We have shown that our approach works for a co-culture and a next step would be the inference of metabolic interactions in a complex ecosystem. A complex community will have more interactions between the members of the community. In addition to beneficial relationships, competition can also play an important role in microbial communities . The advuggested . More deEven though metabolic interactions can be inferred from experimental data, not all data and systems are equally amenable to a modeling approach. Firstly, a community with growing micro-organisms is advantageous. Growing cells have an active metabolism and increase their biomass in time, while interacting with other species. While non-growing species may also have an active metabolism, they do not increase in biomass, causing them to have lower fluxes, which makes it difficult to assign flux-values to such organisms. Secondly, controlled environments allow for more targeted perturbations of the community. Manipulation of the environment results in different dominating processes in the ecosystem . In addiTo conclude, in our eyes metabolic models are an indispensable tool for the inference of the metabolic interactions, as illustrated with our co-culture study. We have shown that the nitrogen-source quantitatively influences the interspecies hydrogen transfer, which was not feasible with experimental data alone. Moreover, the metabolic models can be used for more purposes than inference of metabolic interactions. They can also be used to infer the intracellular fluxes of species, which informs us about the metabolic adaptations of microorganisms, during different conditions. The models can also be used to investigate whether species in a community grow optimally or whether they are limited by external factors. This is particularly interesting for communities used for industrial processes, such as the anaerobic digestion process, where high biogas yields are desired. Finally, metabolic models could indicate strategies to steer the community in a desired direction, guiding community engineering approaches. Thus metabolic models have great potential –are simply required– to study complex, microbial ecosystems.S1 Material and Methods(PDF)Click here for additional data file.S1 Table+ and H2O, are element-balanced in the metabolic model.All metabolites, except for H(PDF)Click here for additional data file.S2 Table(PDF)Click here for additional data file.S1 FigThe metabolite profile plots contain error bars, but the other subplots not. The biomass ratios are based on the gene-copy data and the carbon balance consisted of the measured metabolites that contained carbon. The remaining missing carbon is assumed to be incorporated into biomass.(EPS)Click here for additional data file.S2 Figμ (h-1). All lines are lineair what suggests that the specific uptake and production rates of both species are scaled with the growth. The N2 condition is not plotted, because the simulated growth rate was constant over the whole simulation.The extracted specific uptake and production rates (mmol/(gDW⋅h)) are plotted against the simulated growth rate (EPS)Click here for additional data file.S3 FigA the calculated flux-values for C. acetobutylicum are normalized for the glucose uptake. B shows the calculated flux-values for W. succinogenes and are normalized for the H2 uptake. Note that H2 production by C. acetobutylicum is not equal to the specific H2 uptake rate of W. succinogenes as the biomass abundances should be taken into account, which were not equal during the experiment.In (EPS)Click here for additional data file.S1 FileThe reactions and the corresponding reversibility and bounds are listed in ‘reactions’. The metabolites-id and the corresponding names are listed in ‘metabolites’. All reactions and their corresponding substrates and products are listed in ‘network_react’, where in ‘network_metab’ all reactions per metabolite is listed. All metabolites and their corresponding MIRIAM information is listed in ‘miriam.’(XLS)Click here for additional data file.


One commonly accepted theory is that a species with a high substrate affinity and low growth rate (k-strategist) will win the competition against a second species with a lower substrate affinity and higher growth rate (r-strategist) if both species are subjected to low substrate concentrations. In this study two nitrite oxidizing bacteria (NOB), Nitrospira defluvii (k-strategist) and Nitrobacter vulgaris (r-strategist), were cultivated in a continuous reactor systems. The minimal hydraulic retention time (HRT) required for maintaining the slower growing Nitrospira was first determined. A reactor containing Nitrobacter was set to the same HRT and Nitrospira was injected to evaluate the effect of the dilution rate on the competition between both species. By following the microbial population dynamics with qPCR analysis, it was shown that not only the substrate affinity drives the competition between k- and r-strategists but also the dilution rate. Experimental data and numerical simulations both revealed that the washout of Nitrobacter was significantly delayed at dilution rates close to the μmax of Nitrospira. The competition could be even reverted towards Nitrobacter (r-strategist) despite of low nitrite concentrations and dilution rates lower than the μmax of Nitrospira.The conditions present in both  Nitrospira (k-strategist) and Nitrobacter (r-strategist). Nitrospira possess a low maximum specific growth rate, but is well-adapted to low nitrite concentrations, whereas Nitrobacter is known to be a relatively fast-growing NOB with low affinities to nitrite [Nitrospira spp. and Nitrobacter spp. both use nitrite as substrate for growth, only the most adapted species will win the competition for nitrite and will hence outcompete the other one [Nitrobacter spp., since it was found in wwtp all over the world [Nitrobacter spp. were present in wwtps, while the dominant bacterium was Nitrospira spp. [Nitrospira and not Nitrobacter is the major NOB. However, in natural environments such as in soils or biofilms k and r strategists are found both at the same time despite of low bulk substrate concentrations [Nitrobacter and Nitrospira, the washout of Nitrobacter was delayed [a priori that the winner would always be the species with the highest affinity for the limiting substrate. Nevertheless, in 1980, Hansen and Hubell established a theory, in which the competition of two species was described at a known limiting substrate concentration and at a certain dilution rate. Their study suggested that the dilution rate can revert the competition towards the r-strategist even at low substrate concentrations [In microbiology the competition of two species for one substrate is driven by their substrate affinity and their doubling time , 2. An e nitrite , 4. Sincther one , 6. NOB ther one  and playhe world . Nonetheira spp. , 9, 10. trations . Their otrations . While ttrations , 14. A s delayed . In theitrations .Nitrobacter and Nitrospira was evaluated at low substrate concentrations by means of dedicated experiments and numerical simulations. The aim was to show that not only the substrate concentration and hence the nitrite affinity constant will drive the competition between two species, but also the dilution rate, leading to a delayed washout of Nitrobacter and in some cases even to the unexpected dominance of Nitrobacter at low nitrite concentrations.In this study, the effect of the dilution rate (retention time) on the competition of Nitrobacter vulgaris AB1 and Nitrospira defluvii A17 and the strains were provided from Hamburg University, Germany. Both bacteria were cultivated in batch flasks in a mineral salt freshwater medium for oligotrophic growth [2-N l-1 day-1, the pH was kept at pH 7, the temperature was controlled at 28°C a temperature controlled water jacket and DO at 7 mgO2 l-1. Baffles were used to assure good liquid gas transfer. Contamination was tested on a regular basis using Tryptone Soy agar CM0131 (Thermo Scientific). Nitrate and nitrite were measured with a spectrophotometer.The strains used in this experiment were Nitrospira defluvii in the system was evaluated in the highly enriched Nitrospira defluvii reactor. The dilution rate was increased in a step-wise manner from 0.55 to 0.7 day-1 and the nitrite concentration was determined on a daily basis to follow nitrite accumulation over time. An increase of nitrite concentrations to values equal to the influent nitrite concentrations was evaluated as washout; the corresponding dilution rate was identified as the growth rate of Nitrospira defluvii.In order to determine the effect of the washout rate on interspecies competition, the minimal retention time needed to keep Nitrobacter reactor was set to 0.58 days-1, corresponding with a value just below the minimal HRT needed to avoid the washout of Nitrospira as determined in a separate test  and a light microscope (BX41—Olympus).The dilution rate of the ate test . Both re-1) and were kept in a warm water bath at 95°C for 15 minutes, followed by a cooling step on crushed ice for 10 minutes. The samples were centrifuged for 30 seconds at 13000 rpm and the pellet re-suspended in 180 μL deionized water.Samples were obtained from the effluent (600ml) and spun down at 4000 rpm for 20 minutes (Thermo Scientific Megafuge), the supernatant was discarded and the gained cell pellet was stored at -80°C until further usage. DNA extraction was based on the method of Niemann . The sam® Green Supermix . A “StepOne—Real Time PCR System” by Applied Biosystems was used to run the qPCR assays. All primers were optimized with a gradient qPCR. The resulting conditions, primer concentrations are listed in ref)T before the inoculation of the second culture (Ctarget)T in order to have a zero value and to check if the reactors were contaminated. In order to compare the ΔCT values between samples the following equation ΔCT = CT(ref) − CT(target) was used [Nitrobacter culture) and 0 (no Nitrobacter present).In addition to the alkaline lysis, a phenol extraction and ethanol precipitation was completed to remove possible contaminants from the extracted DNA . A phenowas used . For theSi) on the limiting substrate (S), at the given intrinsic rate of increase (ri), as quantified by the smallest value for J, k will win the competition against the other species. The intrinsic rate of increase (ri) of strain i is defined as the difference between the growth rate (μi) of the strain and the given dilution rate (D) [ri = (μi − D) with Nitrobacter and Nitrospira. The critical parameter J corresponding with the experimental conditions, was calculated and a sensitivity analysis was conducted to assess the effect of the dilution rate. For the nitrite affinity constant values of 1.5 and 0.21 mgNO2-N l-1 as well as maximum specific growth rates of 1.6 and 1 day-1 were used for Nitrobacter, whereas the values for Nitrospira were kept constant (0.12 mgNO2-N l-1 and 0.67 day-1), respectively  : ri = (μ2KO2+SO2 . Dilutioectively .Nitrobacter and Nitrospira was implemented in the Aquasim software [Nitrospira (Nsp) is represented as k-strategist, with a low growth rate but a high affinity for nitrite, whereas Nitrobacter (Nb) is represented as r-strategist, with a high growth rate and low affinity for nitrite. The affinity constants and growth rates were set according to reported literature values  and an r-strategist (Nitrobacter). Since the knowledge of maximum growth rate of Nitrospira defluvii was highly important for this experiment, its value was estimated by determining the minimal hydraulic retention time before washout occurred, by gradually increasing the flow rate  than that of Nitrospira (2*109 cells mL-1) due to a higher yield coefficient of the latter one [Nitrobacter was inoculated with Nitrospira based on cell concentration with a ratio 0.75:0.25 and this ratio was also used as starting condition in the model. In order to compare the simulation results with molecular data from the qPCR assay, both results were expressed in a ratio of Nb: (Nsp+Nb). A ratio of 1 meant that a pure culture of Nitrobacter was present and a ratio of 0 that Nitrospira dominated the system. Accordingly, at a ratio of 0.5 both bacteria were present in equal amounts.Two separate reactors were run and as expected the number of cells of tter one , 31. The-1) applied in the experiment perfectly corresponded with the simulations conducted at a similar dilution rate  could be explained by inaccuracies in the pump frequency. The validated model was subsequently applied to study the effect of the dilution rate on the competition at given nitrite affinity constants and growth rates  small changes had a big impact on the time needed for complete washout of Nitrobacter. The time needed for washout of Nitrobacter increased from 100 hours to over 1000 hours for dilution rates from 0.58 to 0.63 d-1  delivered comparable results since both measuring points overlap . The simth rates . At low 0.63 d-1 . For hyd67 day-1 . Pure cuNitrobacter was coupled to the nitrite concentrations in the reactor .Simulations on the concentration in the reactor showed that the delayed washout of  reactor . Howeverwth rate . At the robacter . The ranNitrobacter  would have led to a washout only when the dilution rate exceeded the maximal growth rate  and hence very close to the μmax of Nitrospira (0.67 day-1). The value of the affinity constant had a more severe effect on the competition (Nitrobacter (Nitrospira occurred at significantly lower dilution rates (0.3 day-1) than the μmax of Nitrospira (0.67 day-1)  , zone IINitrobacter at higher dilution rates matched the simulation results very well, hence providing a reliable starting point for further simulation studies evaluating for various operational strategies, which would have been very time consuming to be tested experimentally. In this study, the chosen dilution rate was not close enough to the μmax of Nitrospira in order to provoke its washout by competition, which is nevertheless possible as shown in Figs Nitrospira at a dilution rate close to its μmax would have been easily interpreted as washout due to high dilution rate (e.g. due to inaccuracies of the pumps). Our simulation results show that the sludge retention time (SRT) has a big impact on the substrate concentrations, hence severely influencing the competition between Nitrospira and Nitrobacter. Under these circumstances it was shown here that the bacterium with the highest substrate affinity (Nitrospira) does not necessarily win the competition at low substrate concentrations as commonly perceived in literature [Nitrobacter) and can even be reverted from one to another species as shown in the simulation studies  can be controlled independently from the hydraulic retention time . The J criterion can also be applied in systems in which the SRT is not equal to the HRT but still the same for all bacteria , 34. NatNitrobacter is capable of mixotrophic growth, hence using other substrates than nitrite [Earlier modelling studies, investigating the growth of bacteria on multiple substrates, have shown that the coexistence of several species at steady state is possible due to niche differentiation by substrate inhibition, even when all the organisms strongly prefer one substrate . In addi nitrite  increasi nitrite .Nitrobacter) winning the competition at low substrate concentrations. In biotechnological processes the bacterial retention time is often uncoupled from dilution rate by using biofilm systems, which retain high biomass concentrations. However, in these biofilm systems suspended biomass is present as well and the selection for different nitrifying populations based on biofilms and/or suspended biomass and the impact on ecophysiological population dynamics is poorly understood. Therefore one must better comprehend what conditions bacteria experience when growing in suspension versus in a biofilm. Recent studies insinuate that suspended biomass plays different functional roles in biofilm systems, and that suspended biomass and biofilms can coexists in a single system [Despite of the complexity of substrate competition between different species, the outcome of this can study give an explanation for situations in which a r-strategist is dominating a system at low substrate concentrations. In this study, it was shown that the dilution rate within an ecosystem creates a selection pressure favouring the most adapted species under given environmental conditions, hence out-competing other less adapted species , 40, whie system –44. Since system , 46, ande system  and a vaIn conclusion, it was demonstrated that not only the substrate concentrations but also the dilution rate in natural habitats and engineered systems drives interspecies competition and must be taken into consideration, while investigating the competition between k and r strategists.S1 Table(DOCX)Click here for additional data file.S2 Tablei) of a component i is related to the process rates (ρj) through Ri = ∑jAijρj.The conversion rate (R(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.S4 Table(DOCX)Click here for additional data file.S5 Table(DOCX)Click here for additional data file.