Yarrowia lipolytica is a non-conventional yeast that is extensively investigated for its ability to excrete citrate or to accumulate large amounts of storage lipids, which is of great significance for single cell oil production. Both traits are thus of interest for basic research as well as for biotechnological applications but they typically occur simultaneously thus lowering the respective yields. Therefore, engineering of strains with high lipid content relies on novel concepts such as computational simulation to better understand the two competing processes and to eliminate citrate excretion.Y. lipolytica and optimized it for use in flux balance analysis (FBA), with the aim to simulate growth and lipid production phases of this yeast. We validated our model and found the predictions of the growth behavior of Y. lipolytica in excellent agreement with experimental data. Based on these data, we successfully designed a fed-batch strategy to avoid citrate excretion during the lipid production phase. Further analysis of the network suggested that the oxygen demand of Y. lipolytica is reduced upon induction of lipid synthesis. According to this finding we hypothesized that a reduced aeration rate might induce lipid accumulation. This prediction was indeed confirmed experimentally. In a fermentation combining these two strategies lipid content of the biomass was increased by 80 %, and lipid yield was improved more than four-fold, compared to standard conditions.Using a genome-scale model (GSM) of baker's yeast as a scaffold, we reconstructed the metabolic network of Y. lipolytica to optimize growth conditions for lipid accumulation are demonstrated. Based on these findings, further strategies for engineering Y. lipolytica towards higher efficiency in single cell oil production are discussed.Genome scale network reconstructions provide a powerful tool to predict the effects of genetic modifications and the metabolic response to environmental conditions. The high accuracy and the predictive value of a newly reconstructed GSM of The online version of this article (doi:10.1186/s12918-015-0217-4) contains supplementary material, which is available to authorized users. Saccharomyces cerevisiae, have been used for centuries for biotechnological applications [S. cerevisiae is a Crabtree positive yeast that covers most of its ATP requirement from substrate-level phosphorylation and fermentative metabolism. In contrast, most of the non-conventional yeasts, such as Yarrowia lipolytica, Kluyveromyces lactis or Pichia pastoris, have a respiratory metabolism, resulting in significantly higher biomass yields and no loss of carbon due to ethanol or acetate excretion. Second, S. cerevisiae is highly specialized and evolutionary optimized for the uptake of glucose, but performs poorly on most other carbon sources. Several non-conventional yeasts, on the other hand, are able to grow at high growth rates on alternative carbon sources, like pentoses, C1 carbon sources or glycerol, which may be available as cheap feedstock. Third, non-conventional yeasts are extensively exploited for production processes, for which the productivity of S. cerevisiae is rather low. Prominent examples are the use of P. pastoris for high-level protein expression [Yeasts, especially ications . In recepression  and oleapression .S. cerevisiae for which the broadest spectrum of methods for the engineering of production strains and the best knowledge about manipulation and cultivation are available. One such tool is the use of reconstructed metabolic networks for the computational analysis and optimization of pathways and production processes. These genome-scale models (GSM) are becoming increasingly important as whole genome sequences and deduced pathways are available for many different organisms. In combination with mathematical algorithms like flux balance analysis (FBA) and variants thereof, GSMs have the potential to predict and guide metabolic engineering strategies and significantly improve their success rates [Despite this growing interest in the development of biotechnological processes in other yeast species, the development of tools for the investigation and manipulation of these organisms still lags behind the advances in ss rates . FBA quass rates , 6. A maS. cerevisiae model [P. pastoris and P. stipitis [Yarrowia lipolytica, for which two GSMs have been published [Y. lipolytica is considered to be an excellent candidate for single-cell oil production as it is able to accumulate high amounts of neutral lipids. Furthermore, Y.lipolytica production strains efficiently excrete proteins and organic acids, like the intermediates of the tricarboxylic acid (TCA) cycle citrate, α-ketoglutarate and succinic acid [Y. lipolytica a promising host for the biotech industry.Whereas the yeast community provides continuous updates for the reconstruction of the ae model , hardly stipitis , 9 and fublished , 11. Y. nic acid , 12–14. nic acid –17; the nic acid , 19, makY. lipolytica is known for both efficient citrate excretion and high lipid productivity under stress conditions such as nitrogen limitation. However, due to the undesired by-product citrate, processes aiming at high lipid content suffer from low yields with regard to the carbon conversion, despite the use of mutant strains with increased lipid storage properties. In this study, we reconstructed a new GSM of Y. lipolytica to analyze the physiology of this yeast and to design fermentation strategies towards optimizing the productivity for neutral lipid accumulation by simultaneously reducing the excretion of citrate. These predictions were experimentally confirmed, demonstrating that precisely defined fed batch strategies and oxygen limitation can be used to channel carbon fluxes preferentially towards lipid production.S. cerevisiae with accurately described lipid metabolic pathways, was used as a scaffold for the reconstruction of the Y. lipolytica GSM. For each gene associated with reactions in the scaffold possible orthologs in the Y. lipolytica genome based on the KEGG database were screened. If an orthologous gene was found it was added to the model together with known gene-protein-reaction (GPR) association. Literature was screened for metabolites that can either be produced or assimilated in Y. lipolytica and transport reactions for these metabolites were added. Differences in metabolic reactions between S. cerevisiae and Y. lipolytica were manually edited by adding or deleting the reactions  composition, ranging from 0.4 % NL in biomass to 80 % NL in the biomass, were constructed, keeping the relative amounts of other metabolites in the biomass equation constant.−1 for S. cerevisiae, and divided by the experimentally measured carbon source uptake rate for Y. lipolytica. This resulted in a value of 5.0 mmol ATP/mmol glucose (2.28 mmol ATP/mmol glycerol) to account for non-growth-related maintenance like loss of energy due to inefficiency of enzymes, maintenance of membrane potential and other energy consuming cellular activities, which are not described in the model.In simulations with maximization of lipid accumulation as objective function, the growth rate is reduced to zero. To allow for non-zero maintenance during this phase the maintenance reaction, which is set to 59.28 mmol ATP/g biomass in IND750 , 23, wasIn silico minimal medium (iMM) was used for the calculations, allowing for free uptake of CO2, H2O, H+, inositol, K+, NH4+, Na+, O2, HPO42− and SO42−. Carbon source uptake rates and citric acid excretion rates were set as constraints according to values measured in the laboratory experiments. To compare the calculated growth rates on glucose and glycerol with experimental values, a biomass equation with 1.3 % TAG content in biomass, corresponding to the experimentally determined value, was used.Flux balance analysis (FBA) was used as a tool for assessing the accuracy of the model. Growth predictions on 25 different carbon sources were compared with published data. Boolean values representing growth (true) or no growth  were calculated for each carbon source. For calculations, FBA optimization from the COBRA toolbox [−1 and a carbon source concentration of 20 g L−1 was used. The in silico method is provided in the Additional file Dynamic FBA (dFBA) validation: the function dFBA from COBRA was used for the simulation of growth curves and calculation of biomass yields. In both the prediction and the experiment iMM with an initial biomass of 0.003 g L−1 h−1) and with maximization of the growth rate as objective function, or with a fixed growth rate (0.33 h−1) and glucose uptake minimization as objective function. Flux variability analysis was carried out to evaluate the flexibility of the metabolic network during lipid accumulation conditions.Different biomass compositions were used to analyze the effects of increased TAG content in the range from 0.4 % to 60 % on metabolic fluxes. Calculations were carried out either with the experimentally determined glucose uptake rate (4 mmol g+ was restricted to one of the following reactions: pentose phosphate pathway (PPP), cytosolic isocitrate dehydrogenase, malic enzyme, mannitol dehydrogenase, tetrahydrofolate synthase or succinate semialdehyde dehydrogenase. For malic enzyme, a cytosolic isozyme was added to the network reconstruction. Furthermore, the reactions mannitol-1-phosphate 5-dehydrogenase (1) and mannitol-1-phosphatase (2) were added to complete the mannitol cycle:+ + 1 H < − > 1 fructose + 1 NADPH1 mannitol + 1 NADP2O - > mannitol + 1 Pi1 mannitol-1-phosphate + 1 HFor a comparison of the lipid synthesis rates that can be obtained with different sources of NADPH, the generation of this cofactor from NADPFor modeling fed batch cultivations, the specific citric acid production rate was measured in nitrogen-limited stationary phase of batch cultivation and included as a constraint in the simulation. The difference of the carbon source consumption for maximum lipid productivity between simulations with and without citrate production was determined and used as a basis for the calculation of the feed strategy for fed batch cultivation. The Matlab script used for these calculations is provided as Additional file 2 uptake was performed. A time point at which growth is significantly reduced but lipid accumulation capacity is not affected was determined and used for planning of the fermentation strategy.For modeling oxygen limitation, a robustness analysis for biomass and lipid accumulation in response to changing OYarrowia lipolytica H222 (MATA) wild type strain was used for all studies. For YPD medium, 20 g L−1 glucose, 20 g L−1 peptone and 10 g L−1 yeast extract were dissolved in ddH2O and autoclaved. For batch cultivations mineral salt medium [−1 or 0.40 g L−1 (NH4)2SO4; 3.0 g L−1 KH2PO4; 0.50 g L−1 MgSO4.7H2O; 100 μL Antifoam 204 ; pH 5.0 with 1.5 M KOH. The carbon sources, glucose or glycerol, were prepared separately as 10x stock solutions (200 g L−1) and added after autoclaving. 1 mL L−1 sterile-filtered trace element and 1 mL L−1 vitamin solution, prepared as explained in [−1 ammonium sulfate, corresponding to 1.06 g L−1nitrogen, initial C/N ratio 7.55) or nitrogen-limited .t medium  consistiained in , 28, werA pre-culture was prepared in 5 mL YPD pH 5.5 and incubated overnight at 28 °C on a rotary shaker at 180 rpm. The inoculum was prepared in 50 mL YPD medium pH 5.5 and incubated at 28 °C on a rotary shaker at 180 rpm for 24–34 h until late exponential growth phase, as determined by cell density measurement in a Casy® cell counter equipped with a 60 μm capillary . Prior to inoculation into the fermenter, cells were spun down in a centrifuge and washed twice with sterile deionized water to remove YPD medium components from the culture.max at 1200 rpm. Fermenters were inoculated from precultures to 1.0E05 cells/mL.Batch cultivations were performed in a 0.6 L Sixfors® fermentation system  with scaled round bottom glass vessels with a working volume of 0.4 L. Temperature, aeration and pH were controlled and maintained at 28 °C, 1 volume per liquid volume per minute (1 vvm) and 5.0 (by automatic addition of 1.5 M KOH), respectively. Dissolved oxygen was maintained at >50 % saturation by control of the stirrer speed that was initalliy set to 500 rpm, with vIn the oxygen limitation studies, the same media and fermentation conditions as for the fully aerated batch cultivations were used. When cells reached a cell density of approximately 2.0E08 cells/mL the aeration rate was reduced from 1 vvm to 0.4 vvm and stirring speed was maintained at 500 rpm to maintain oxygen saturation at 1 %. Samples for extracellular metabolite and lipid analyses and dry weight (DW) determination were taken every 12 h after reducing the aeration. The total duration of fermentation was 72 h.−1 glucose and 0.4 g L−1 ammonium sulfate. The feed was started after depletion of glucose, with a glucose solution containing 6.55 g L−1 glucose and at a constant flow rate of 69.4 μL min−1 adding a total of 200 mL of glucose solution to the fermentor. Samples were taken at the beginning of the fed batch phase and after 48 h.For fed-batch fermentations, precultures were inoculated into 300 mL of minimal medium containing 8.0 g LDetermination of biomass: 5 mL samples were withdrawn from the fermenters with a syringe and filtered through nitrocellulose filters , washed twice with deionized water and dried at 97 °C for 24 h and weighted.2SO4 at a flow rate of 0.6 mL min−1 was used as eluent. ChemStation software was used to determine metabolites concentration from the generated chromatograms.Extracellular metabolite concentrations: 1 mL of the fermentation broth was centrifuged at 16000 g at 4 °C for 1 min and the supernatant was stored at −20 °C until further analysis. Extracellular metabolites  were quantified with an Agilent Technologies HP 1100 series HPLC system equipped with an Aminex HPX-87H column , Agilent autosampler, an Agilent UV detector and Knauer differential refractometer (RI detector). The column was maintained at 65 °C, and 5 mM H2O and adjusted to pH 2.0 using HCl (32 %) to quench chemical exchange of the NH4+ protons. The NH4+ concentration was determined by NMR spectroscopy on a Bruker AVIII 300 MHz spectrometer (equipped with a BBI probe head) using a 1D 1H experiment with water suppression and (NH4)2SO4 solutions as external standards . All spectra were processed and analyzed with Topspin 2.1.Determination of the available nitrogen concentration in the growth medium: 450 μL of sample were mixed with 50 μL DLipid analysis: about 20 mg of cell dry weight were harvested from the fermenter and centrifuged at 2000 × g for 5 min at room temperature to remove culture media. Pellets were immediately frozen in liquid nitrogen and stored at −75 °C until further processing. Cells were disrupted with glass beads and extracted with chloroform:methanol 2:1 (v/v) by shaking in a Heidolph Multi Reax test tube shaker  and lipids were extracted with chloroform:methanol 2:1 . NeutralY. lipolytica to simulate and optimize lipid accumulation with constraint based modeling. Since genome scale network reconstructions are not necessarily intended to be used for such a purpose [Y. lipolytica [S. cerevisiae model, iND750, which had been optimized for metabolic modeling in several studies [Y. lipolytica named iMK735 is available in SBML level 2 format in Additional file The aim of this study was to use a GSM of  purpose  and the polytica , 11 were studies –22. The S. cerevisiae scaffold to the Y. lipolytica reconstruction required several changes. The most important ones were the introduction of the alkane assimilation and degradation pathway with gene associations ALK1-ALK12 [LIP2 [Y. lipolytica [2 uptake, which is typically used to simulate ethanol excretion in the S. cerevisiae model, was removed, thus resulting in a fully respiratory metabolism.The conversion of the K1-ALK12  and the 12 [LIP2  allowingpolytica , was delin silico gene deletion study, showing similar results as the scaffold model, and validated with regard to the prediction of growth on different substrates, resulting in an overall accuracy of 80 %  of the normally used concentration, whereas the initial carbon source concentration remained unchanged (20 g L−1). Under these conditions, the carbon to nitrogen ratio is gradually increasing, as required for lipid accumulation. Biomass formation stopped after consumption of ca. 8 g L−1 of glucose, with ca. 10 % lipid content of biomass. The glucose uptake rate dropped from the initial value of 4.0 mmol g−1 h−1 to 0.35 mmol g−1 h−1. Although 26.5 % lipid in dry biomass was obtained at the end of the fermentation, the major product during this phase was not lipid but rather citrate i + 3 NAD+ + 6 H - > 1 citrate + 2 ATP + 3 NADH + 3 H+1 glucose + 2 ADP + 2 P(4)2O + coenzyme A - > 1 oxaloacetate + acetyl-CoA + ADP + Pi1 citrate + ATP + H(5)n-ACP + ATP + 2 NADPH + 2 H+ - > 1acyl(n+2)-ACP + ADP + Pi + 2 NADP+1 acetyl-CoA + 1 acyl49 % of the theoretical maximum yield for citrate were produced. In contrast, the lipid yield was only 16.6 % of the theoretical maximum [Oleaginous yeasts are defined as those species with a neutral lipid content of more than 20 % of their cell dry weight. Such high lipid content, however, is only achieved under specific conditions, which limit or arrest growth when carbon sources are still available. The most frequently used limitation for lipid accumulation is starvation for nitrogen. When cells face such a situation they continue to assimilate the carbon source but, being unable to synthesize nitrogen containing metabolites like amino and nucleic acids, arrest growth and convert the carbon source into storage metabolites, mainly glycogen and neutral lipids. To induce lipid accumulation in a batch fermentation we reduced the nitrogen content in the medium to less than 10 %  in the fermentation with unrestricted glucose uptake. Any further increase of the glucose feed rate above the calculated value resulted in citrate excretion rather than higher lipid synthesis rates (data not shown). These results support the hypothesis that citrate excretion is indeed an overflow reaction; the lipid synthesis rate during nitrogen starvation is thus not high enough to convert all glucose carbon into storage lipid.To experimentally confirm our calculations, we performed a fed-batch fermentation. The initial glucose and nitrogen concentrations were 8 g Led Table . ImportaY. lipolytica with different neutral lipid content in the biomass equation. In this simulation of non-oleaginous and oleaginous states, we varied the TAG content from 0.4 %, as it was found in exponentially growing cells, to a hypothetical value of 60 %. Accordingly, the protein content was reduced, whereas all other biomass constituents, the glucose uptake rate and the objective function (biomass production) were left unchanged. Such high lipid contents are not obtained in exponentially growing cells in vivo, but might provide information regarding the metabolic changes in silico. As expected, an increase in lipid content required increased activity of Acl, the enzyme catalyzing the cleavage of citrate to acetyl-CoA and oxaloacetate, and NADPH synthesis  and variation of the glucose uptake was allowed. In this setup , as predicted by robustness analysis with iMK735.To test experimentally the effect of reduced aeration, the wild type strain H222 was cultivated in stirred bioreactors. After 20 h of cultivation, aeration was reduced from 1 vvm to 0.4 vvm, which caused a drop of the dissolved oxygen concentration from 50 % to 1 %. Samples for analysis of lipid content and extracellular metabolites were withdrawn at the indicated time points  compensates for the reduced NADPH synthesis in the PPP. If the flux through PPP drops below 83 %, however, the rate of lipid synthesis becomes non-optimal.Figure Y. lipolytica have been discussed. Besides the PPP and Idh, malic enzyme (Mae) and the mannitol cycle were regarded as being potentially required or beneficial for high lipid synthesis rates [+ dependent Mae converts malate to pyruvate, which is then converted back to malate through the activities of pyruvate carboxylase and malate dehydrogenase. In the mannitol cycle, for which it is not yet clear in which form it exists in Y. lipolytica [+ and ATP to NAD+, NADPH and ADP + Pi. Both of these pathways were able to provide NADPH for FA synthesis, with a lipid yield similar to the Idh-dependent reaction, but clearly lower than in the simulation with the PPP as source for NADPH  in the production phase is increased by only 50 % to 0.0261 mmol g−1 h−1. Our calculations suggested that only 0.152 mmol g−1 h−1 glucose uptake would be required for this lipid synthesis rate. The remaining glucose is converted to citrate and excreted. These data indicate that the FA synthesis rate of Y. lipolytica wild type is limited to ca. 0.03 mmol g−1 h−1 (ca. 8 mg FA gDW−1 h−1). From the excretion of citrate when the glucose uptake rate is too high, it might be assumed that the activity of ATP:citrate lyase is limiting FA synthesis under nitrogen-limited conditions. Indeed, overexpression of Acl results in improved lipid accumulation [Y. lipolytica as well. Therefore, the classical bottleneck-view fails to characterize the regulation of the pathway for neutral lipid synthesis. Rather, changes in most if not all reactions seem to have an impact on the overall flux. Although some of the engineering strategies mentioned above resulted in yields during the production phase close to 100 % of the theoretical maximum and in strains with high lipid content, the reportedly highest productivities of engineered strains were only ca. 2.5 times higher than the productivity of wild type in our fed-batch fermentation [Y. lipolytica to nitrogen limitation. The reason might be a feedback loop on the post-translational level that down-regulates the activities of hexose transporters and subsequent reactions for glucose catabolism but it could also be a transcriptional response to the depletion of an essential nutrient. In the latter case, overexpression of these genes coding for glucose catabolic functions will be as important as the up-regulation of genes coding for lipogenic enzymes because the observed glucose uptake rate after nitrogen depletion is not sufficient for high lipid synthesis rates. This glucose uptake rate allows for only ca. 2.5 fold higher lipid synthesis rate if all glucose is converted to lipid instead of partial excretion as citrate. In a genetically modified strain with the currently highest productivity [Under nitrogen-limited conditions, the glucose uptake is reduced dramatically to 0.35 mmol gmulation , 39, butmulation –42, increntation . To obtauctivity  such a suctivity  reported+ to NADPH and, therefore, in lower lipid yields. Thus, higher productivities might require alternative pathways for NADP+/NADPH recycling. Calculations with our model, however, indicated that the PPP is the most efficient of the NADPH providing pathways. Only Idh activity in combination with the PPP allows for maximal lipid yields but it is not known whether the cytosolic Idh is subject to the same inhibition under nitrogen-limited conditions as its mitochondrial isozyme [Our simulations showed that an increase in TAG content does not correlate with increased demand for NADPH and acetyl-CoA as it would be expected from stoichiometry of lipid synthesis Fig. . The rea isozyme .+ would be the optimal solution [Y. lipolytica. For a network including such a reaction, the simulation predicts a 7 % higher lipid yield than for the “wild type”. Moreover, this modification would also allow for engineering glycolysis towards higher fluxes because no flux through the PPP is required.In their net stoichiometry, both the Mae and the mannitol cycle can be regarded as energy-dependent transhydrogenase reactions. The lipid yield in these two cycles is lower than in the PPP Fig.  because solution . HoweverY. lipolytica, which were assembled by fully or partly automated reconstruction procedures [S. cerevisiae into the new reconstruction iMK735 by manually changing gene annotations, evaluating reversibilities of reactions and their compartmentalization and by adding or deleting species-specific reactions. This procedure resulted in a GSM that accurately predicts growth behavior of Y. lipolytica and can be used to simulate processes that are of importance for this yeast, like lipid production. However, further efforts regarding both fermentation optimization and genetic engineering will be required to make such a production process competitive with the existing processes. Highly accurate genome scale models will be an important tool for this development.As an alternative approach to available genome scale reconstructions of ocedures , 11, we https://www.ebi.ac.uk/biomodels-main/ where it is stored as MODEL1510060001.The SBML file for iMK735 can be retrieved from the BioModels Database at


Synthetic biology has boomed since the early 2000s when it started being shown that it was possible to efficiently synthetize compounds of interest in a much more rapid and effective way by using other organisms than those naturally producing them. However, to thus engineer a single organism, often a microbe, to optimise one or a collection of metabolic tasks may lead to difficulties when attempting to obtain a production system that is efficient, or to avoid toxic effects for the recruited microorganism. The idea of using instead a microbial consortium has thus started being developed in the last decade. This was motivated by the fact that such consortia may perform more complicated functions than could single populations and be more robust to environmental fluctuations. Success is however not always guaranteed. In particular, establishing which consortium is best for the production of a given compound or set thereof remains a great challenge. This is the problem we address in this paper. We thus introduce an initial model and a method that enable to propose a consortium to synthetically produce compounds that are either exogenous to it, or are endogenous but where interaction among the species in the consortium could improve the production line. Artemisia annua, a type of wormwood, in quantities too small to enable a cheap production of the drug. To address this problem, a living organism, Saccharomyces cerevisiae, was used for such rapid, and therefore much more effective synthetic production. Since the work by J. Keasling, many other species, in particular bacteria, have also been manipulated with a similar objective of more efficiently producing some compounds of interest for health, environmental or industrial purposes.Synthetic biology has been defined by the European Commission as “the application of science, technology, and engineering to facilitate and accelerate the design, manufacture, and/or modification of genetic materials in living organisms to alter living or nonliving materials”. It is a field that has boomed since the early 2000s when in particular Jay Keasling showed that it was possible to efficiently synthetise a compound–artemisinic acid–which after a few more tricks then leads to an effective anti-malaria drug, artemisininHowever, engineering a single microorganism to optimise one or a collection of metabolic tasks may often lead to considerable difficulties in terms either of getting an efficient production system, or of avoiding toxic effects for the recruited microorganism23468In this paper, two types of consortia are studied. The first is a synthetic consortium of strains carrying genetic and/or regulatory modifications. This follows the same spirit as in the work of Jay Keasling for the production of artemisinic acid. In our case, the goal is the synthetic production of two bioactive compounds with antibacterial properties: penicillin and cephalosporin C. Four microorganisms were considered for such production. Notice that already an important question is whether the best option is to use all four in the consortium, or instead only a subset thereof, and of course, which subset is then most efficient. In this first case study, the compounds of interest are exogenous to the consortium.et al.In the second case study addressed, the two microorganisms form an artificial consortium in the sense that the species involved in it do not naturally interact, and both organisms are able to endogenously produce the target compounds. One of these is 1,3-propanediol (PDO), a building block of polymers. Associating microorganisms in a consortium can lead to a better yield of production as already demonstrated by Bizukojc In both cases, it is necessary to infer the transfer of metabolites from one organism to another and, if the compounds are exogenous to the selected organisms, which reactions need to be inserted in the consortium. For such problems, computer models are crucial in providing hints on how to best divide a given metabolic production line among different organisms that are then made to interact with one another. Various methods exist that enable to better understand the metabolic capabilities and the interactions observed in natural communities11et al.14Answer Set Programming (ASP) solverIndeed, the problem of obtaining an optimal consortium includes at least the following two parallel objectives: one is to have a small number of reactions exogenous to the consortium that need to be added to it, the second is to have a small number of compounds that need to be transported across different species of the consortium. Both are indeed costly and should thus be avoided whenever possible. Other aspects would also need to be taken into consideration, such as the efficiency of the consortium in terms of both survival and growth of each species composing it, as well as of production of the compounds of interest. In this paper, we address only the first two objectives of minimising the number of insertions of exogenous reactions and of transitions. Our approach is purely combinatorial and topological. We do not take into account stoichiometry for the moment. This approach however represents a first step that, as we show, leads already to a hard problem. We start by some preliminaries that present the basic notations and definitions used, the model adopted, and a formal description of the problem addressed. Following the idea initially introduced by Fellows V, that corresponds to the compounds, and a set of directed hyperedges, that is of hyperarcs, denoted by A, that corresponds to the reactions. Given a hyperarc a, we denote by src(a) and tgt(a) the sets of source and target vertices of a, respectively, that is the set of substrates and of products. In the problem described below, the main issue comes from the hyperarcs with multiple source vertices. The possible multiplicity of the target vertices of a hyperarc does not affect the complexity of the problem. Moreover, we can, without loss of information, decompose such hyperarcs into ones that each have the same set of source vertices but only one of the target vertices of the original hyperarc . Let then A′ ⊆ A, V(A′) denotes the set of vertices that are involved in at least one hyperarc of A′, that is the set of compounds that participate in at least one of the reactions represented by A′. By abuse of notation, given a set of hyperarcs A′, we often refer to the hypergraph (V(A′), A′) simply as A′.For a subset of hyperarcs Since a reaction needs all its substrates to be activated, we consider that the multiple source vertices of a hyperarc correspond to a multiplicity of tentacles (often used for grasping), each associated to one substrate. A hyperarc is therefore like an octopus, only with a number of tentacles that may be different from eight. The greater the number of tentacles, the more tentacular is the hyperarc considered to be.tentacular hyperarc as follows.We formally introduce the notion of a Definition 1.A hyperarc a is called tentacular with number of tentacles, or spreadness for short, b if b = |src(a)| > 1.total number of tentacles, total spreadness for short, of a directed hypergraph.Finally, we define the notion of the Definition 2.Given a directed hypergraph H, its total spreadness is the sum of the number of sources of the tentacular hyperacs inarc to refer to non tentacular hyperarcs. It will later become clear why we need to consider the total spreadness of the input.For the sake of simplicity, we will use the term T. The compounds of interest may not be produced naturally by the members of the consortium; they are instead produced by other organisms . We denote these two sets by, respectively, Ow  and Oo . As indicated, we may have |Oo| = 0 meaning here that the workers are naturally able to produce the compounds.We recall that the problem we want to address concerns the production by a consortium of organisms, microbes for instance, of a set of compounds denoted by N1, …, Nk be the genome-scale metabolic models (GEMs) for the organisms in Ow, and let V1, …, Vk respectively correspond to the sets of vertices in these networks. Actually, this is a superset of the consortium that may really be required for the production of T and that will be a solution of the problem as defined below. The hyperarcs in Ni have weight wworker, independently of i.Let wworker will be set equal to zero, or to a value that is close to zero for reasons that will be explained later, in the Application part. The set of hyperarcs in the metabolic models for Oo is denoted by Ao.Typically The directed hypergraph N1, …, Nk. Let Ni, and for each hyperarc a ∈ Ao that corresponds to a reaction not already in Ni, we create a copy of it in Ni, and thus in a labelled as ai to Ai. We further add to Vi, and thus to V any vertex corresponding to a compound not already in Ni if such exists. The added hyperarc has weight wother. Typically, wother > wworker: introducing a reaction in the metabolism of an organism that does not contain the corresponding enzyme(s) is indeed costly. Finally, for each pair of vertices vi ∈ Vi and vj ∈ Vj with i, j ≤ k and i ≠ j such that the corresponding compound is the same, we create a hyperarc that has vi for single source and vj for single target (it therefore is an arc) and has weight wtransition. Typically, we will have that wtransition > wworker: making a transition from one organism of the synthetic consortium to another, which implies transporting a compound, is also costly.First, we perform the disjoint union of the networks Oo to an organism from the consortium Ow (when such operation is required) implies a cost that does not depend on the reaction. Similarly, we are considering that any transition from one organism in Ow to another is equally costly. These assumptions may however be refined by making such costs, and thus the weights of the added hyperarcs (tentacular hyperarcs or arcs) depend on the reaction or on the transition (see later for a further discussion on this).It is worth calling attention to the fact that we are considering here that adding a reaction from We first introduce the notion of a directed rooted hypergraph.Definition 3.A directed hypergraphis rooted at S ⊆ V′ if there exists an ordering of its hyperarcs  such that for all i ≤ m, src(ai) ⊆ S ∪  tgt.The problem that we address in this paper is defined as follows:Input: A weighted directed hypergraph Output: A directed hypergraph Notice that the term Directed Steiner Hypertree abuses language in the sense that there may be more than one root. In the case of digraphs, it would correspond to a set of trees, hence to a forest.s if and only if it is an arborescence rooted at s (i.e. a directed tree with an orientation from the root s to the leaves). If there is more than one source, then it is a set of arborescences. In the case of digraphs, the DSH problem coincides with the well-studied Directed Steiner Tree (DST) problem defined as follows:If the directed hypergraph is a digraph, then it is a minimal directed hypergraph rooted at a node Input: A weighted directed graph G = , a source s and a set of targets T.Output: A subset A′ of A of minimum weight such that T ⊆ closureA′(s).X such that X ⊆ V and a set of hyperarcs A′ such that A′ ⊆ A, closureA′(X) is the smallest set C ⊆ V such that X ⊆ C and for each a ∈ A′, if src(a) ⊆ C, then tgt(a) ⊆ C.The closure operation is defined as follows: Given a directed hypergraph A′(X) is the set of vertices that can be reached from X following the hyperarcs in A′. In the context of metabolic networks, it is the set of compounds that the reactions from A′ can produce using only the compounds of X as sources.Intuitively, closureWe start by investigating the complexity of the problem. We first observe that the Directed Steiner Tree problem is NP-hardIn the general setting however, Proposition 1 indicates that the problem is doomed to be intractable when using only parameters related to the solution size. The proofs of the propositions are available in the Proposition 1.The problem is W[1]-hard when parameterised by any combination of: |A′|, weight(A′), |T|, |S|, total number of tentacles of the hyperarcs in A′.Part of the difficulty indeed comes from the choice of tentacular hyperarcs that must belong to the solution. However, taking into account only the number of tentacular hyperarcs in the instance is not sufficient to obtain tractability.Proposition 2.The problem is NP-hard even when |T| = 1 and A contains only one tentacular hyperarc.Overall, the problem remains intractable when either of these constraints applies to the input: there are few targets, or the total number of tentacles of the hyperarcs is bounded. However, there remains the stronger case when both quantities  are bounded. We present a fixed-parameter tractable algorithm for this case in the next section.k tentacular hyperarcs, there are 2kk! such combinations to consider). For each combination, it remains to compute the optimal way of linking these tentacular hyperarcs with regular arcs. This problem is solved by extending the FPT algorithm for the Directed Steiner Tree problem which requires the number of targets as a parameter. In our case, we need the number of targets plus the total number of tentacles of a solution. For a given directed weighted hypergraph x, X) be the best directed Steiner tree of x that has X as set of leaves.We now present our main algorithm that exactly solves the Directed Steiner Hypertree problem provided that the number of targets and the total number of tentacles of the hyperarcs remain small. Intuitively speaking, the algorithm identifies the best combinations of tentacular hyperarcs by trying all those in parallel, and for each such combination, it outputs the solutions (if any exists) having minimum weight. More precisely the algorithm enumerates all possible combinations of tentacular hyperarcs that will be used in a solution, where a combination is a subset of the tentacular hyperarcs ordered according to the topological order of the solution  of the tentacular hyperacs of A′ that uses exactly the tentacular hyperarcs of M following their ordering.Given an ordered subset M must be used, we have that, for all i ≤ k, src(ai) ⊆ tgt(A′) ∪ S, and so the set src(M) can be seen as an additional set of targets. We establish T′ := T ∪ src(M) to be the new set of targets, and for t ∈ T′, we define LayerT(t) := min{i ≤ k: t ∈ src(ai)}. If t ∈ T\src(M), we define LayerT(t) as k + 1, and for a subset X ⊆ T′, we define LayerT(X) := min{LayerT(t): t ∈ X}. Similarly, since all tentacular hyperarcs of M must be used, intuitively tgt(M) can be seen as an additional set of sources. We write S′ := S ∪ tgt(M) and LayerS(s) := min{i ≤ k: s ∈ tgt(ai)} if s ∈ tgt(M)\S, and LayerS(s) := 0 if s ∈ S. To respect the ordering of M, the target of a tentacular hyperarc ai ∈ M can be used to “reach” only the sources of the tentacular hyperarcs that come after ai in M. For all Y ⊆ T′, we define SY := {s ∈ S′|LayerS(s) < LayerT(Y)}.The following definitions are illustrated in A′, the vertices in G(A′) must have in-degree one if they are not in S′, and, by minimality, out-degree at least one if they are not in T′.Observe that for any minimal Directed Steiner Hypertree F, we denote by V(F) and leaves(F) respectively the vertices and the leaves of all the trees of F. For any vertex t, we denote by root the root of the tree in F containing t when t ∈ V(F) (the root is the farthest vertex we can reach starting from t by following only branches of F), or root = t otherwise (t is an isolated node).Given a (directed) forest Y ⊆ T′, we say that a forest F of covers Y if leaves(F) ⊆ Y and root ∈ St for all t ∈ Y.For a set of targets Lemma 1.For any optimal solution A′ of the Directed Steiner Hypertree problem givenas input, if A′ uses exactly the tentacular hyperarcs of an ordered subset M, then G(A′) is a forest covering T′.Proof. Consider a Directed Steiner Hypertree A′. First notice that by minimality, G(A′) is a forest. Indeed, if some vertex x has two incoming arcs in A′, denoted by a and a′, a appearing before a′ in A′, then removing arc a′ yields a strictly better solution to the Directed Steiner Hypertree problem. Furthermore, if any x ∉ T′ is a leaf of G(A′), with incoming arc a, then x is not the head of any arc nor is it part of T′. In this case, a can be deleted and all leaves are in T′.t ∈ T′. Let s = root. Consider the path from s to t: by minimality, the arcs of the path must appear in the same order as in A′ (otherwise some arcs must be deleted), and s must appear in the targets of a tentacular hyperarc ordered before any hyperarc of which t is a source (or s ∈ S). This implies that s ∈ St. ◻Consider now any Lemma 2.Given an ordered subset of tentacular hyperarcs M and any forest F covering T′, there exists a solution A′ of the Directed Steiner Hypertree problem withas input, where A′ uses exactly the tentacular hyperarcs of M in this order, and such that G(A′) = F.Proof. We build A′ as follows. We first insert the tentacular hyperarcs  of M, in this order. We then insert the arcs of F between the tentacular hyperarcs, according to the layer of the root of the tree to which they belong. Formally, let D1, …, Dp be the directed trees in F, and s1, …, sp their respective roots. Observe that since all leaves are in T′, then each si can be written as root for some t ∈ T′, and thus si ∈ S′ and LayerS(si) is well-defined and can be computed. For each j, 1 ≤ j < k , we insert between aj and aj+1 (resp. before a1 or after ak), all arcs of all trees Di such that LayerS(si) = j. Within each tree, the arcs are inserted in topological order. There remains to prove that this ordering has the required properties.t ∈ T, t is reached by some hyperarc (tentacular or not) of A′. Two cases are possible:t = root ), then t ∈ tgt(ai) for some ai ∈ M ⊆ A′, thus t ∈ tgt(A′).If t ∈ tgt(a) for some arc a in F, so a ∈ A′ and t ∈ tgt(A′).Otherwise, We first verify that for any x ∈ src(a) with a ∈ A′, we now need to verify that x ∈ S or x is the target of some hyperarc selected before a. Three cases apply:a ∈ F and x is not the root of any tree Di, then it has an incoming arc appearing in A′ before a .If a ∈ F and x is the root of some tree Di, then x = si. If x ∉ S, then LayerS(x) > 0, and x is produced by the tentacular hyperarc a.If a is not an arc of F, then it is a tentacular hyperarc, x ∈ T′, and a = aj for some j > LayerT(x). Let si = root, then LayerS(si) + 1 ≤ LayerT(x), and the arc producing x is placed before a = aj.If For any vertex M, where, by construction, G(A′) = F.◻Overall, we indeed have a Directed Steiner Hypertree for Lemma 3.For any optimal solution A′ of Directed Steiner Hypertree of, if A′ uses exactly the tentacular hyperarcs of an ordered subset of tentacular hyperarcs M in this order, then G(A′) is a forest covering T′ of minimum weight.Proof. By Lemma 1, F = G(A′) is already a forest, and it has a total weight of weight(F) = weight(A′) − weight(M). Consider any forest F′ of weight w′ covering T′. By Lemma 2, there exists a solution with weight weight(F′) + weight(M), which must be larger than weight(A′), hence w′ ≥ weight(F), i.e. F has minimal weight. ◻Y ⊆ T′, let SHM(Y) be the minimum weight of a forest F covering Y under the ordering M. By Lemma 3, the weight of an optimal solution A′ of the Directed Steiner Hypertree problem given weight(M) + SHM(T′) where M is the ordered set of tentacular hyperarcs used by A′.For a set of targets Theorem 1.The optimal value of an instance ofof the Directed Steiner Hypertree problem has value SHM(T′) + weight(M) for some ordering M. Furthermore, *SHMcan be computed recursively as follows. For any Y ⊆ T′,Proof. Assume first that the optimal forest F covering Y is a tree and let s ∈ SY be its root. Then SHM(Y) = ST = min{ST, s ∈ SY}.F has at least two trees. Let Y′ :=  leaves (F1) where F1 is a tree of F. Notice that since F1 and the other trees of F do not intersect, we have weight(F) = weight(F1) + weight(F\F1). Furthermore, F1 is an optimal forest covering Y′ and F\F1 is an optimal forest covering Y\Y′ since otherwise, the union of two better solutions would lead to a better forest covering Y. We then have that SHM(Y) = SHM(Y′) + SHM(Y\Y′) and Y′ ⊆ Y such that SHM(Y) > SHM(Y′) + SHM(Y\Y′) and let F′ (resp. F′′) be an optimal forest covering Y′ (resp. Y\Y′). Then F′ ∪ F′′ would be forest covering Y of weight weight(F′ ∪ F′′) ≤ SHM(Y′) + SHM(Y\Y′) < F, contradicting the optimality of F. Thus Assume now that Theorem 2.The Directed Steiner hypertree problem is Fixed-Parameter Tractable for the parameters |T| and total number of tentacles of the hypergraph.Proof. The algorithm computes SHM(T′) for each ordered subset M of tentacular hyperarcs. Since the number of tentacular hyperarcs is bounded by the total number of tentacles k of the hypergraph, there are at most 2kk! ordered subsets of tentacular hyperarcs. For a given M, we now compute SHM(T′) using a dynamic programming algorithm induced by the recursion of Theorem 1. We need to store the value of SHM(Y′) for every subset Y′ of T′. Since the size of T′ is bounded by k + |T|, we have at most 2k+|T| such subsets. Finally, since for every vertex s and every Y′ ⊆ T′, the computation of ST is FPT in |Y′| ≤ |T′| ≤ k + |T|, the total running time of the algorithm is FPT in k + |T′|.◻The main objective of microbial consortia engineering is to highlight their capacity to reach enhanced productivity, stability or metabolic functionalityde novo synthesis of bioactive metabolites and to show that the model is able to select the Directed Steiner Hypertree of least cost to produce one or a set of metabolites of interest.We initially focused attention on the production of two bioactive compounds: penicillin and cephalosporin C, useful to the pharmacology industry for their antibiotic properties. For this production, a synthetic consortium defined as a system of metabolically engineered microbes which are modified by genetic manipulations and/or regulatory processesKlebsiella pneumoniae with an acetogenic Archae Methanosarcina mazei. The goal is to obtain a higher yield of 1,3-propanediol. Indeed, production of this compound in a pure culture of K. pneumoniae is associated with production of acetate. The latter has an inhibiting effect on bacterial growth, and ultimately also on the production of PDO. Hence associating K. pneumoniae with a methanogen has been proposed to reduce such effect5We then considered the case of an artificial consortium. This corresponds to a system composed of wild-type populations that do not naturally interacteggetExploreeggAll the genome-scale models (GEMs) used were extracted from Ka priori the fact that endogenous reactions should be easier to use than transport ones (no need to export or to uptake compounds) and than insertions .In the absence of any prior knowledge, the weights were set uniformly using as wworker = 1, wother = 100, wtransition = 100. Notice that the weight of the (hyper)arcs that are present in the organisms forming the consortium is not zero, but instead equal to a value above zero that remains however small in relation to the weights of an insertion or of a transition. The motivation for this is to favour solutions which, while minimising the number of insertion or transition hyperarcs that are used, also minimise the number of hyperarcs corresponding to reactions that are internal to the microorganisms in the consortium.Therefore, the following weights were first applied: In the second application, two sets of transport weights were adopted, one a refinement of the first, as will be explained later on.Streptomyces cattleya, Rhodococcus jostii RAH_1, Rhodococcus erythropolis BG43) and one methanogenic Archaea (Methanosarcina barkeri) was tested to determine which microbial consortium could produce a set of metabolites of interest. In this case, two well-known beta-lactam antibiotics  were selected. Both active compounds belong to the cephalosporin/penicillin pathway and share several metabolic reactions. They also have a common precursor, namely isopenicillin N, are commonly used for their antibacterial properties and are naturally produced by fungi belonging to the Aspergillus and Cephalosporium species In this first application, a synthetic consortium of three Actinobacteria (reference organisms) were used for reaction insertion: Aspergillus nidulans and Streptomyces rapamycinicus. The first is a fungus known to produce penicillin while the second possesses reactions in the penicillin/cephalosporin C pathway, and in particular those needed to produce cephalosporin C. All the reactions present in the reference organisms were added to the four prokaryotes forming the consortium (as described in Model adopted).Microorganisms were chosen because of the availability of Actinobacteria to produce bioactive compounds  and are illustrated in the M. barkeri and L-2-aminodipate is transported into S. cattleya.Four solutions with a minimum cost of 528  are found. All of them are composed of δ-(L-2-aminoadipyl)-L-cysteinyl-D-valine, which is the starting point for the production of penicillin and cephalosporin C. All metabolites previously mentioned can be produced from pyruvate. The requirements to produce the three substrates of N-(5-amino-5-carboxypentanoyl)-L-cysteinyl-D-valine synthase using a solution of minimum weight therefore force to go back into the bacterium producing both amino-acids , in this example S. cattleya. The two other tentacular hyperarcs correspond to the reactions for citrate synthase  and AcetylCoA:2-oxoglutarate C-acetyltransferase (transforms 2-oxoglutarate and AcetylCoA into Homocitrate ((R)-2-hydroxybutane-1,2,4 tricarboxylate).Three tentacular hyperacs are used in this case. One of the reactions is N-(5-amino-5-carboxypentanoyl)-L-cysteinyl-D-valine synthase that converts L-2-aminoadipate, L-valine and L-cysteine into et al.Clostridium butyricum with a methanogenic Archaea, namely Methanosarcina mazei, could lead to a better yield of production. Indeed, in C. butyricum, production of PDO leads to the production of acetate as well as of a side-compound, the latter then participating in the production in M. mazei of methane, which is the main molecule in the composition of biogas.The compound 1,3-propanediol (PDO) is of high interest in biotechnology since it is used as a building block in polymersKlebsiella pneumoniae, is associated with Methanosarcina mazei to produce 1,3-propanediol and methane. Both organisms have the capacity to produce the target compounds. Hence, no reference organisms were used. The weights were first set as in the previous section . The only authorised source was glycerol. Indeed, glycerol is a by-product of biodiesel biodiesel. It therefore is a substrate of choice for biotechnological processesIn this example, another PDO producer and Enterobacteria glycerol scavenger, namely K. pneumoniae, there are two ways of reaching glycerone phosphate from glycerol. Moreover, two different reactions are possible to transform pyruvate into acetyl-CoA, one of them forming also formate. Finally, in the solutions obtained, there is also the possibility to exchange pyruvate instead of Acetyl-CoA. This therefore leads to six solutions (four of them are represented in We obtain six solutions with the same weight of 110 (1 transition and 10 endogenous reactions). In K. pneumoniae. Indeed, Jung et al.K. pneumoniae has an advantage in sharing acetyl-CoA or pyruvate (which is a substrate for the reactions producing acetyl-CoA). However, as stated previously, the production of 1,3-propanediol is associated with the synthesis of acetate and formate. Those by-products are inhibiting for K. pneumoniae and can reduce both its growth and the production of 1,3-propanediol25K. pneumoniae possesses a citrate/acetate exchangerMethanosarcina spp. can grow on acetate although other substrates might be preferred. This indicates the possibility of an exchange of acetate between the two organisms since transport is possible in both species. We therefore decided to diminish the weight of the transport of those organic acids to wtransition = 50.In this case, the community does not exchange acetate but acetyl-CoA or pyruvate. In eukaryotes, transporters of acetyl-CoA are known in several pluricellular organisms and also in yeast. However, no transporter of acetyl-CoA has been detected in organisms close to the ones used in our case. Moreover, a pool of acetyl-CoA is essential to wtransition = 50 and 11 endogenous reactions). They are presented in Two minimum solutions were obtained with a weight of 61  which is then exchanged from E. coli). Without stoichiometric coefficients, we cannot guarantee that the intermediate substrates of the cycles will be all regenerated by a solution. Prohibiting those cycles allows us to ensure that all solutions are feasible by themselves, meaning that all intermediates are at least as much produced as they are consumed (regardless of the remaining of the network).The method introduced in this paper allows to infer topological sub-networks to produce target compounds using one or several microorganisms forming a consortium. Ensuring that a component will be produced as much as it will be consumed according to stoichiometric coefficients leads to a more complex problem. Since we do not use such coefficients, a conservative hypothesis was adopted. This induces the exclusion of some cycles where a substrate used in a reaction is immediately formed again Moreover, Saccharomyces cerevisiae) and in human31Methanosarcina or Streptomyces. Further experiments will therefore be needed to determine whether the two species constituting the microbial consortium do possess the ability to uptake and export 2-oxoadipate. Moreover, if it is confirmed that these two bacterial strains indeed lack this ability, an insertion of ODCs might still be possible, similarly to what was performed in Escherichia coli using human ODCsAs concerns the second exchange, mitochondrial transporters for oxodicarboxylic acids (oxodicarboxylate carrier proteins (ODCs)) such as 2-oxoadipate and 2-oxoglutarate were reported in yeast  of various Gram-positive and Gram-negative bacteria. It further presents a resistance to bacterial beta-lactamases enzymes20S. cattleya could produce the two beta-lactam antibiotics without affecting its bacterial growth.Although the production of two beta-lactam antibiotics destroys the walls of positive Gram bacteria, Streptomyces sp.  and Methanosarcina sp. (with an optimum of growth around 37 °C)One must however call attention here to the fact that cultivating an aerobiose Actinobacteria and an anaerobiose Archaea in a same culture may be difficult. On one hand, several anaerobic-aerobic co-cultures have already been reportedAt their bacterial growth temperature (between 25 °C and 37 °C), we exclude a possible temperature-dependent biosynthetic pathway of antibiotic compounds as already reported for actinorhodinet al.K. pneumoniae. In those experiments, the yield of 2,3-butanediol (BDO) is improved by deletion of pflB, possibly because of the accumulation of pyruvate, a precursor of BDO. Indeed, pflB with ldhA encodes the pyruvate formate-lyase enzyme. Nevertheless in our case, pyruvate is not a precursor of PDO, hence the deletion of the same gene (pflB) would have a negative impact since the growth of the cells would be impaired by the redox imbalance created. Hence the possibility of the association with an acetogenic Archaea is of great interest to regulate acetate production.In the second example, we retrieved a possible network for the joint production of 1,3-propanediol and methane. In Jung et al.in silico simulation of the co-culture of another propanediol producer, namely Clostridium butyricum, with M. mazei showed an improvement in the growth of C. butyricum due to the consumption of acetate by M. mazei. Such consumption alleviates the inhibition of acetate. A similar effect should be expected for Klebsiella pneumoniae. The lighter weight assigned to the exchange of acetate allowed us to retrieve a feasible solution. Although acetate can be utilised almost completely by M. mazei for its growth, it is necessary to have methanol (present in raw glycerol obtained from biodiesel plant) in the medium to produce methane. However, even if the production of methane is low, the association of the two organisms will decrease the concentration of extracellular acetate, which is toxic for K. pneumoniae, hence increasing the yield of PDO. Co-cultures of Clostridium sp. associated to methanogenes such as Methanosarcina sp. CHTI55 have been described in the literature, showing acetate utilisation by methanogene organismsKlebsiella pneumoniae, as the propanediol producer in co-culture with methanogenes has been less described. Hence, more extensive tests on the feasibility using classical optimisation techniques are needed, even though the process and apparatus for such associations have been patentedIn Bizukojc a priori to tune the weights assigned to each reaction is helpful to obtain a realistic solution. Indeed, the weight of an inserted reaction can be set more precisely by taking into account, for example, gene-reaction associations. Reactions catalysed by protein complexes require the insertion of several genes, hence may be harder to handle than those associated to single genes. Using the AND/OR relations available in the SBML models, insertion weights may thus be adapted to reflect those difficulties. Moreover, if information about the inserted organisms is available, more complex weights can be computed, taking into account enzyme promiscuity, catalytic performance, gene compatibilityin silico experiment that is considered.As shown in this second application, we can assign a non uniform weight to the exchange of compounds between organisms, the insertion of exogenous reactions or the use of internal reactions. Using a biological We proposed a new topological method, called MultiPus, to select possible microbial consortia for the production of compounds of interest.With MultiPus, any situation of both exogenous and endogenous compounds might be considered, as well as larger initial consortia whose final composition in terms of species is then optimised by the method. Finally, by setting the sources required, one can test the possibility of using low-cost substrates for the production of high value chemicals.post-processing step, classical methods of flux balance analysis  can be employed to predict product yield424345As a Indeed, the species that are part of the consortium may not have the same growth rate, hence may not reach an equilibrium in terms of composition when all organisms are present. Stable growth and equilibrium in biomass of the community which is being considered is of importance, and stoichiometric models could be used to predict such equilibrium1149e.g. 1,3-propanediol). It is a good starting point, that should be associated in the future with more quantitative methods in order to guarantee maintenance and growth of the organisms in communities .This first model allows to infer topologically possible insertions for heterologous expression and the usage of a mixed culture for the production of exogenous and/or endogenous target compounds. Moreover, MultiPus may thus enable to establish which co-cultures could be interesting to use in order to avoid the inhibition of co-products .


Adaptions were assumed to be required in order to sustain the growth rate. Proteomics indicated that indeed a number of adaptations occurred that included increased expression of ribosomal proteins and 2-oxoglutarate dehydrogenase. The operating space prescribed by a basic flux model that maintained phenotypic traits  within typical bounds of resolution was consistent with the flux implications of the proteomic changes.When the replication of a plasmid based on sucrose selection is deregulated via the  E. coli and can be used as a platform for DNA vaccine production [sacB transcript. Translation of the sacB transcript results in toxicity in a sucrose background unless the plasmid-encoded RNA is produced and then hybridizes with the transcript.The plasmid pNTC8485 replicates in oduction ,2. Antiboduction . The smainc1 and inc2 mutations into this already high copy number plasmid [inc1 and inc2 mutations deregulate plasmid replication by further weakening the RNA I-RNA II interactions [Previously, we reported on the effect of introducing the  plasmid . The incractions . The reaAfter introducing the mutations, plasmid copy numbers (PCNs) ranging from 7,000 (early log phase) to 15,000 (onset of stationary phase) resulted when growth occurred on minimal medium. The growth phase and temperature influenced the PCN. Despite our starting point for copy number being orders of magnitude higher than Tomizawa and Som’s prior work .inc mutant plasmids can be envisioned to be lower than one would expect for conventional β-lactamase expressing plasmids.The low impact on growth rate can be attributed, in part, to the differential expense of protein versus DNA synthesis. A DNA precursor has about three-times the mass of an amino acid. The ATP required per bond during DNA polymerization is about one-third of that needed for protein synthesis . Thus, w3 × 3.7 103/4.6 106 = 5.6). Thus, while the energetics associated with synthesizing and maintaining the deregulated, sucrose-selected plasmids can be estimated to be less expensive than that for a conventional plasmid, the nil impact on nil growth could nonetheless be enabled by metabolic and other adaptations. For example, the de novo synthesis of deoxyribonucleoside triphosphates can require about 10 ATPs per molecule. The transcription from some of the more than 7000 extra genes that are available in a transformed cell will produce RNA. This RNA will degrade and the breakdown products will have to be converted back to ribonucleoside triphosphates prior to repolymerization. Thus, a number of impacts can be envisioned in the aggregate albeit per plasmid, they appear to be less than that normally associated with conventional plasmids.Nonetheless, maintaining copies number ranging from 7,000 to 15,000 for a 3740 base pair plasmid represents the addition of several or more genome equivalents of DNA to the cell (i.e. 7 10−1) subject to measurements and the associated resolution of the by-products and yield on glucose. Such feasible flux scenarios could assist with interpreting the changes in the proteome. Additionally, alterations in nonmetabolic systems could emerge in the proteomic results that could further illuminate how cells may adapt to deregulated plasmid synthesis.To investigate if significant adaptations occurred, we pursued a two-pronged approach: (i) flux modeling and (ii) determining the changes within the proteome. The aim of the modeling was to determine what metabolic flux scenarios would allow for the plasmid-containing cells to grow at the measured rate  of 0.45 g cell/g glucose, the combined precursor load  to deoxyribonucleotides can be estimated to be 0.04 mmol/g cell h, which is quite small compared to the glucose flux that is equal to 2.5 mmol/g h [sacB transcript will also be increasingly synthesized in plasmid-containing cells. However, rapid RNA turnover could allow for extensive recycling thereby reducing the net de novo synthesis burden on precursors. ATP use for repolymerization, however, could increase thereby lowering the ATP yield and increasing the apparent maintenance energy. As for wild-type cells, additional maintenance costs such as leaky membranes [Cells containing deregulated plasmid will experience increased DNA and RNA synthesis. The extra plasmid DNA will exert an increased precursor and ATP demand. However, the precursor load imposed by DNA is not normally high. For a cell growing at 0.2 hmmol/g h . For 10 embranes  might alYX/S, byproduct fluxes, and growth rate.One modeling approach would be to attempt to quantitatively account for all the aforementioned factors. For cells hosting β-lactamase encoding plasmids, such an approach provided yield and flux scenario predictions that spanned a range of promoter strengths and other uncertainties . HoweverYX/S must fall into the experimentally resolved bounds prescribed by, for example, 0.42 ± 0.03 g cell/ g glucose. Essentially this amounts to finding flux scenarios that underlie macroscopically indistinguishable phenotypes (MIPs), which are defined by sets of largely similar measurements and their resolution bounds. These scenarios, in turn, prescribe the adaptive flux space that exists.These scenarios can be generated by initially assuming that precursor fluxes to DNA synthesis in both plasmid-free and -containing cells is not large compared to other fluxes. This still allows for an adaptive space by permitting total ATP production to vary subject to the fluxes must satisfy the phenotypic constraints and their range of resolution. That is, for all the flux scenarios, YX/ATP) might be lower. As noted before, more ATP production subject to fixed growth rate and other phenotypic features could be used to support the ATP costs associated with RNA repolymerization, DNA polymerization, and other processes that contribute to apparent maintenance. Thereafter, the impact of increasing the DNA biosynthetic load can then be tested and how the scenarios change can be determined.Some of the flux scenarios found may turn out to more likely correspond to plasmid-containing cells. For example, in some scenarios the value of the mass yield on ATP (YX/S), and byproducts is fixed by measurements and resolution bounds. From a more mathematical perspective, a related idea is finding clonal solutions that differ by a small “epsilon” value from the true  value [Overall, the different flux scenarios associated with MIPs can be determined. The overarching idea is to see how far a “normal cell” can be stretched in terms of its fluxes while its phenotype in terms of yield, glucose uptake (i.e. l) value . Such soFinding these flux scenarios entails solvingSubject totight: rac = 1 or loose asZ corresponds to an objective function such as minimizing a particular flux. The first constraint , then the flux scenarios that populate the MIPs can be determined. While a mixed integer program could determine the extreme points [If each flux is individually minimized  and plasmid pNTC8485-EGFP  were obtained from the Nature Technology Corporation . The corresponding product identifiers are NTC-DV8485-LV and NTC-DVU-CC1. The inc1 and inc2 (single and double) mutations were introduced to pNTC8485-EGFP as previously described [inc2 mutation was found to have a greater effect; hence, the proteomics experiments compared the untransformed host to that of a cell hosting the plasmid with an inc2 mutation.inc2) plasmid were grown in duplicate in M9 medium with 0.4 and 8% (by weight) glucose and sucrose. Two biological replicates of host and transformed cells were used. When the cultures reached mid-exponential phase (OD ~ 1.5), 250 ml of each culture was harvested by centrifugation . Protein was extracted from culture pellets by the addition of 10 ml/mg pellet (wet weight) of buffer A  plus 1 mg/ml lysozyme. Mixtures were incubated on ice for 10 minutes prior to sonication and centrifugation of debris. Supernatants were decanted, flash-frozen, and stored at −80°C.To generate samples for proteomic analysis, 500 ml cultures of host cells and those harboring a mutant  were pooled and half of the sample (400 μg) composed one 8-plex experimental run. Samples were fractionated by successive strong cation exchange and reverse phase chromatography prior to plate spotting and analysis using the ABI 4800Plus MALDI-TOF/TOF tandem MS system. Protein identification and relative abundance quantitation was performed using ProteinPilot software 3.0 (Applied Biosystems) and searches utilized the E. coli proteome database (Swiss-Prot/UniProt release 2011_11). The data was analyzed using replicate correlation analysis, principal component analysis, and a t-test. A change was considered to be significant if a protein in a cell containing a mutant plasmid was < 0.5 or > 2.0 that of the host, and p < 0.05. The experiments were conducted at the Genomics, Proteomics and Bioinformatics Center  and we wish to thank Dr. Manoj Bhasin for his assistance with the data analysis. In this paper, only the exponential phase cells are compared because these are more amenable to flux analysis.The labeling of protein samples with iTRAQ tags, fractionation using two-dimensional liquid chromatography, identification of differentially expressed proteins by TOF/TOF tandem MS, and statistical analysis were performed as described in a prior report with only slight modification . Briefly1d,e), the results are similar as in Table rac ≤ 1.2 plus the other constraints (1f – 1i).Table YX/S, byproducts) are fairly narrow (~10% variation) and YX/ATP was constrained to be between 7 and 10 g cell/mol ATP. For example, the transaldolase (rTA) and transketolase  fluxes span ca 0.40 mmol/g h to that almost of a knockout (ca 0 mmol/ g h). The flux catalyzed by pyruvate kinase (rPYK) ranges from essentially knocked out (0) to 0.93 mmol/g cell h, which is about one third of the value of the glucose flux. Additionally, a range of solutions arise that offer overall ATP yields of 10, 7.3, or 7 g cell/mol ATP. Increasing the precursor loads for DNA by three-fold did not appreciably alter the number scenarios or the differences between the scenarios (not shown) as would be expected based on the prior remarks on the carbon demands of DNA synthesis.The flux plasticity is intriguingly high given that the resolution limitations of experimental measurements  have coordinated: (i) increased TCA flux, (ii) low pyruvate kinase-catalyzed flux, and (iii) diminished fluxes through transaldolase and transketolase. Two scenarios  provide low (scenario 2) and high (scenario 5) pyruvate kinase flux alternatives to high and lower yields, respectively.p < 0.05 and a two-fold or more change. The correlation between the 69 proteins within the biological replicates was greater than 0.90  [fabG, fabA, and accB. One would expect that if random errors accounted for most of the positives in the data, then the results would not be as extensively and tightly grouped by function.The 69 differentially expressed proteins can be broken down into downregulated Figure a and uprγ:1δ:1ε)  are founE. coli has two phosphoglycerate mutase activities: 2,3-biphosphoglycerate-dependent (gpmA) and cofactor-independent (gpmB). In terms of protein abundance, both have been found to have comparable peak expression during growth in LB medium while the relative amounts of the two enzymes vary during batch growth [inc2 mutant compared to the host. Pyruvate Kinase F, which has greater activity than the pyruvate kinase A [talA gene product Transaldolase 1 also emerged as downregulated.Concerning metabolic enzymes, phosphofructokinase B is downregulated in the transformant Figure a. To proh growth . The cofkinase A , is downIn contrast to the above three enzymes, the E2 subunit of 2-oxoglutarate dehydrogenase is elevated in the transformant. Coinciding with this elevation is the increased expression of dihydyrolipoyl dehydrogenase, which constitutes the E3 component of the functional 2-oxoglutarate dehydrogenase complex . Thus, tE. coli JM101 and found it to enhance the PCN [pykF gene product). In this case, a reduction in flux as denoted by a red arrow is a clear cut consequence and also apart of some scenarios in Table Figure  the PCN . Next totalA product Transaldolase 1is reduced in the transformant. Ow et al. [talA was one of the most highly downregulated genes in plasmid-containing E. coli DH5α. Likewise in chemostat studies with E. coli BL21, the comparison of specific enzyme activities indicated that transaldolase was more than two-fold reduced in a transformant [While comparisons are not easily made due to the plasmid and other differences between studies, the prior reporting of upregulated TCA cycle enzymes corresponds, in part, to our findings. One study reported that transformants had increased levels of several TCA cycle enzymes (e.g. 2-oxoglutarate dehydrogenase) while pyruvate kinase was decreased . We alsow et al.  found thsformant . Thus, arplD, rplF, rplJ, rplQ, rplS, and rplY gene products. The L4, L6, L10, L17, L19, and L25 proteins are all associated with the 50S subunit where L4 participates in the early stages of ribosomal subunit assemblies [infB and infC, IF2 and IF3, are factors involved in the early steps in initiating protein synthesis [rpsC, rpsQ, rpsK, rpsI, and rpsP are also increased in the transformant, which represents a cluster of proteins in the 30S subunit.A large number of proteins related to ribosome assembly, processing, and functionality are upregulated in the transformant. These changes include elevated semblies . The eleynthesis . Within E. coli are Rho-dependent [The clustered outcome for ribosomal factors may enable ribosomes to compete for shared metabolic and energetic resources or to maintain assembly and functionality in a situation of increased cytoplasmic crowding arising from deregulated plasmid replication. Finally, it has been estimated that approximately one-half of the transcription terminations in ependent . In the Considering other protein classes, stress-related factors are either upregulated or downregulated in the transformant.fkpA, tig, cspE, and proX are represented in the upregulated category. The first two assist with protein folding where the tig gene product TF is thought to work in tandem as well as separate from DnaK and specialize in ribosomal and small (<20 kDa) proteins [fabA, fabB, accB) [dnaK, hns, hchA, sodA, dps, osmC, hdeA, and tpx. As noted earlier, elevated TF may be able to provide needed protein chaperone activity. Some can be further grouped as (i) acid resistance factors  [sodA, tpx) [The gene products of proteins ,33. CspEproteins -36. ThatB, accB) -39. Downnd hdeA) ,41 and  .. 2-Oxoglutarate dehydrogenase is not normally highly expressed in E. coli [The link between the modeling Table  and the  E. coli ,44 under E. coli . Thus, iConsidering that exerting flux control is plausible, then increased 2-oxoglutarate dehydrogenase capacity will manifest as increased flux through the TCA cycle. Such increased flux will result in greater ATP production. The outcome of greater glucose use and ATP production per cell mass points towards the lower cell mass yields on glucose and ATP associated with scenarios 3 and 4 in Table E. coli [inc1 and inc2 mutations, we found that an impact on growth rate occurred in a medium that was rich in precursors, but lacking in an energy source such as glucose [Such an additional ATP cost would also translate to a higher effective value of maintenance energy. This is interesting because Ow et al. determined that maximizing the maintenance energy as an objective provided the best fit to the fluxes determined for transformed E. coli . Additio glucose . This ob13C tracer and transcriptome study performed on a pyruvate kinase (pykF) knockout [E. coli strains for either adaption to the presence of plasmid [Looking further at the modeling results Figure c indicatknockout . Additio plasmid   than a wild-type JM101 strain by ~ 40% . The fluoduction , the adarHMP), the difference between this value and the return fluxes represents the net available for biosynthesis, which is also an important characteristic.Concerning transaldolase, this enzyme along with transketolases connects the NADPH-producing steps of the hexose monophosphate (HMP) pathway to glycolysis. The HMP pathway along with malic enzyme and isocitrate dehydrogenase supply the cell with NADPH along with some transhydrogenase-mediated conversion of NADH. The flux solutions in Table Other metabolic aspects now involve fluxes that may not have substantially changed. Phosphofructokinase A is comparable in the host and transformant whereas only the minor phosphofructokinase B activity was found to decrease. An irreversible feedback-regulated enzyme such as Phosphofructokinase A is generally not flux controlling ; hence, E. coli growing on minimal media displays very similar phenotypic characteristics with respect to growth rate, yield on glucose, and byproducts when either transformed with a deregulated plasmid or not transformed. We conclude that within the narrow bounds of experimentally quantitated phenotypic descriptors, significant flux plasticity exists where apparently similar phenotypes can have quite different underlying fluxes. Moreover, we conclude that this plasticity appears to constitute an adaptive space that the cells used to contend with the altered energetics (e.g. RNA turnover/repolymerization) associated with deregulated plasmid replication. A subset of the solutions coordinately presented lower yield on glucose and ATP, low flux through pyruvate kinase, increased TCA cycle flux, and nil transaldolase flux. Proteomic experiments yielded results where increases or decreases in pyruvate kinase, transaldolase 1, and 2-oxoglutarate dehydrogenase paralleled the corresponding predicted fluxes in the subset. These changes and some relationships to prior studies are summarized in Figure In the context of antisense RNA selection for plasmid-containing cells and thus no plasmid-driven protein synthesis, Proteomic characterization also indicated that increases in 30 and 50S ribosomal proteins occurred in the transformant among other clustered changes. We suggest that the increased cytoplasmic crowding imposed by the thousands of plasmids may necessitate adaptations that improve the competiveness of binding and recognition associated with other large macromolecule-based processes. Apart from these particular results and conclusions, including a range for experimental measurements may also be useful for other flux balance analysis/optimization applications in order to fully map the flux solution space.


Methyltransferase (MT) reactions, in which methyl groups are attached to substrates, are fundamental to many aspects of cell biology and human physiology. The universal methyl donor for these reactions is S-adenosylmethionine (SAM) and this presents the cell with an important regulatory problem. If the flux along one pathway is changed then the SAM concentration will change affecting all the other MT pathways, so it is difficult for the cell to regulate the pathways independently.We created a mathematical model, based on the known biochemistry of the folate and methionine cycles, to study the regulatory mechanisms that enable the cell to overcome this difficulty. Some of the primary mechanisms are long-range allosteric interactions by which substrates in one part of the biochemical network affect the activity of enzymes at distant locations in the network (not distant in the cell). Because of these long-range allosteric interactions, the dynamic behavior of the network is very complicated, and so mathematical modeling is a useful tool for investigating the effects of the regulatory mechanisms and understanding the complicated underlying biochemistry and cell biology.We study the allosteric binding of 5-methyltetrahydrofolate (5mTHF) to glycine-N-methyltransferase (GNMT) and explain why data in the literature implies that when one molecule binds, GNMT retains half its activity. Using the model, we quantify the effects of different regulatory mechanisms and show how cell processes would be different if the regulatory mechanisms were eliminated. In addition, we use the model to interpret and understand data from studies in the literature. Finally, we explain why a full understanding of how competing MTs are regulated is important for designing intervention strategies to improve human health.Km values of many MTs also play a role because the reactions then run near saturation and changes in SAM have little effect. Finally, the inhibition of the MTs by the product S-adenosylhomocysteine also stabilizes reaction rates against changes in SAM.We give strong computational evidence that once bound GNMT retains half its activity. The long-range allosteric interactions enable the cell to regulate the MT reactions somewhat independently. The low The online version of this article (doi:10.1186/s12918-015-0215-6) contains supplementary material, which is available to authorized users. Methyltransferase reactions, in which methyl groups are attached to substrates, are fundamental to many aspects of cell biology and human physiology. In mammals there are at least 150 methyl transferases that methylate DNA, RNA, lipids, proteins, and small molecules . For exaMany methyl groups used in the MT reactions come directly from dietary input of methionine, betaine, and choline (to make betaine) in the methionine cycle. See Fig. Km for SAM and it is a methyltransferase that is greatly up regulated when cells divide. Finally, we include AS3MT because the detoxification of arsenic is a special interest of ours. Given the biological importance of the MT reactions, it is not surprising that many regulatory mechanisms have evolved that allow the cell to regulate the methylation fluxes through the different pathways more or less independently. These are: (1) Long-range interactions The long-range interactions are depicted by red arrows in Fig. (2) The binding of 5mTHF to GNMT Zamierowski and Wagner  is A schematic diagram of the mathematical model is shown in Fig. V is a velocity and the subscript indicates which reaction. Each velocity depends on the current value of the concentrations of the indicated variables. The complicated, usually non-linear, form of this dependence depends on the detailed biochemistry of each of the enzymes. Each of the methylation reactions also depends on the concentration of the substrate being methylated, for example glycine for GNMT and guanadino-acetate for GAMT, though we do not indicate these explicitly. These methylation substrates are taken to be constant in the model because our main interest is the regulation of [ SAM] concentration.Each The complete mathematical model that consists of 13 differential equations and explicit formulas for each reaction velocity is given in the Additional file k1 and k2, for the first reaction and k3 and k4, for the second reaction. Thus the differential equations for [ 5mTHF],[ GNMT],[ 5mTHF-GMNT],[5mTHF-GNMT-5mTHF] are: In a series of papers, Wagner, Luka, and colleagues have studied the inhibitory effect of 5mTHF on the activity of GNMT , 23–25. k1=50,k2=1,k3=1,k4=1.6 so that the KD values are those found in Table two of , is a variable in our model. GNMT can be bound by one or two molecules of 5mTHF. Our simulations and the data in [mTHF-GNMT], retains 50 % of it’s activity. The factor 4000 is chosen so that the GNMT has a normal reaction velocity comparable to the reaction velocities of PEMT and GAMT, the two other methyl transferases that carry much of the methylation flux.This formula for  data in  suggest Inorganic arsenic is metabolized in two methylation steps catalyzed by AS3MT. The first step uses utilizes a methyl group from SAM and is followed by a reduction step to produce methylarsonic acid (MMA). The second step uses utilizes a methyl group from SAM and is followed by a reduction step to produce dimethyarsinic acid (DMA), which is readily exported from the liver and cleared in the urine. We have recently studied the biochemistry of these methylation steps that are quite complicated . For, exKm of AS3MT for SAM to be 50 μM as determined in /(Km + [ S]), modified to include the effects of product inhibition, substrate inhibition, or long-range allosteric interactions. All of the explicit formulas are in the Additional file Almost all of our formulas for reactions velocities have Michaelis-Menten form, for example μM of 5mTHF pentaglutamate, 50 % inhibition at 1 μM and 90 % inhibition at 10 μM. Since then, Wagner, Luka, and co-workers have investigated the structure of GNMT and the binding of 5mTHF. In ,[ GNMT],[ 5mTHF-GNMT] and [ 5mTHF-GNMT-5mTHF]. GNMT is 1–3 % of liver protein ,[ 5mTHF-GNMT] and [ 5mTHF-GNMT-5mTHF] as a function of the total concentration of [ 5mTHF] in the medium. Panel b shows our computed model curve of bound 5mTHF versus free 5mTHF along with the data points from Figure 2 of [μM of GNMT in the mixture and the curve and the data rise to 1.7 μM, this shows conclusively that two molecules of 5mTHF can bind to each GNMT. Finally, in Panel c we show the data points from the inhibition curve given in Figure 3 of [Left open was the question of what the activity of the enzyme GNMT is when it is once bound or twice bound with 5mTHF. To investigate this question we used the four differential equations given in  protein  and in [ protein  the GNMTues from . Our resure 2 of . The mature 3 of  and two μM/hr so that the steady state concentration of SAM (23.97) is in the range indicated for humans in [μM [μM [We performed various computational experiments that show the effects of the long-range interactions. Since our results are presented as percentage change from normal, we begin by briefly discussing the normal steady state concentrations and velocities in the model that are indicated in Table umans in , 39. Thes in [μM  and the  [μM [μM . The fra [μM [μM .Table 1μM/hr, is given by the net flux of the reaction from SAH to Hcy. The three major methylation fluxes are those catalyzed by GNMT, PEMT, and GAMT [μM/hr since that is the methionine input.The flux around the methionine cycle, 100.25 and GAMT , 8 and tOur first computational experiments investigate how sudden drastic changes in the amounts of PEMT, GAMT, GNMT, or DNMT affect the other fluxes. In Panel a of Fig. Panel By examining Fig. The opposite scenario happens if DNMT is upregulated by a factor of 20. The steady state value of SAM goes down by 22 %, which removes inhibition from MTHFR, so 5mTHF goes up by 18 %. This drives the reaction of 5mTHF with GNMT towards binding and so the amount of once bound GNMT goes down. Thus less flux goes through the GNMT reaction allowing the the PEMT and GAMT reactions to decrease more modestly Fig. , Panel aThis beautiful mechanism is broken if GNMT is knocked out. As one can see in Panel μM/hr to 100 μM/hr. When the long-range interactions are removed (red curve), the steady state value of SAM increases much more rapidly and accelerates as the methionine input increases. In both cases the SAM concentration increases dramatically at high values of methionine input. This is the behavior seen in the models of [in vitro experiments [Since SAM is the universal methyl group donor, its concentration determines the availability of methyl groups for the transmethylation reactions. This presents a problem for the cell since the precursor of SAM is methionine and the methionine concentration in the blood varies dramatically during the day due to meals. We have previously carried out a fluctuation analysis that showed how the long-range interactions greatly dampen the fluctuations in methionine input and cause the flux through the DNMT reaction to remain quite stable . Here weodels of , 41 whereriments ). As theeriments .Fig. 5DThere is a positive statistical association between liver folate status and liver SAM concentration . Using aVmax values for the velocities around the methionine cycle. We conducted experiments in which each these Vmax values was modified by multiplying it by a number chosen randomly between 0.9 and 1.1 . All the Vmax values were changed simultaneously and independently. The green and red shaded areas in Fig. 66Vmax values one has chosen: the long-range interactions stabilize total methylation rate against folate deficiency. The individual variation of enzyme parameters like Vmax and Km values is not known. We chose 10 % not to represent real biological variation, but simply to show that the model results and conclusions do not depend sensitively on the exact choices of parameters.For all of our model simulations it is natural to ask how sensitive the results are to the exact choices of parameters. The answer is not much. There are 11 Km of DNMT is very small, 1.4 μM [μM, in the model. This means that moderate changes in SAM will hardly affect the velocity of the DNMT reaction, because the velocity curve is very flat for values of SAM considerably higher than the Km. One can see this effect clearly in Fig. Km values for methyltransferases listed in [Km values ≤ 3, and 4 have Km values in the range 3–10 μM. If a methyltransferase has a low Km value, the cell can regulate its flux simply by changing the expression level of the enzyme, independent of the fluxes of the other methyltransferases or the concentration of SAM.A notable feature of the simulations shown in Fig. , 1.4 μM , compareKm values so the discussion in Section Ki of PEMT for SAH is quite small (3.8 μM) so the inhibition by SAH is quite powerful, while the Ki of GAMT for SAH is quite large (16 μM) so the inhibition by SAH is quite weak. Thus, evolution may have tuned the Km and the Ki values of certain methyltransferases for which it was important to buffer the flux against changes in methionine input due to meals.Most methyltransferases are inhibited by SAH, the other product of the MT reaction. Of course, product inhibition is ubiquitous in cell metabolism and this simple mechanism is rightly regarded as a way of preventing the over-accumulation of product. However, the graph of PEMT (Panel gaa) for the GAMT reaction. In our simulations in Section In this paper we have been studying the competition between different methyltransferase reactions for the methyl groups provided by SAM. Each of the methyltransferase reactions has a co-substrate to which the methyl group is given, for example phosphotidylethanolamine for the PEMT reaction or guanadinoacetate  and therefore the GAMT flux becomes zero, then the other MT reactions change modestly, except for GNMT that changes a lot. See the discussion in Section Creatine is produced by a two step process. In the first step the enzyme L-arginine:glycine amidinotransferase (AGAT) makes eactions , 47. Thueactions , 47. HigIn this section we discuss why a full understanding of the regulation of competing methyltransferases is important for human health effects and interventions. Arsenic in drinking water is a major health hazard to millions of people in South and East Asia and in other parts of the world , 49. LonThis is considered a detoxification pathway because DMAs is rapidly exported from the liver to the blood and excreted in urine. Two of us (MVG and MNH) conduct studies whose purpose is to determine which nutritional supplements would increase the rate of the AS3MT reaction and thus lower the arsenic body burden in individuals in Bangladesh. It is known both from experimentation  and fromμg folic acid, 800 μg folic acid, 3 g creatine, 3 g creatine + 400 μg folic acid, or placebo daily [μg folic acid was the only treatment to lower total blood arsenic to a significantly greater extent than placebo. However, 3 g creatine+400 μg folic acid did lower blood arsenic to a greater extent (14 %) than 400 μg folic acid alone (3.7 %) although this finding did not reach statistical significance (p=0.08) [μg folic acid led to decreases in GAA that were correlated with decreases in homocysteine (manuscript in preparation). Treatment effects on As methylation patterns are presently being analyzed. In general, these findings are consistent with the model predictions. Thus, to improve the outcomes, one needs to break one or more of the regulatory mechanisms. A possible way to do this is to give very high levels of folate supplementation along with the creatine supplementation. If one can raise liver folate appreciably, one could shut down the GNMT pathway because of the binding of 5mTHF to GNMT, and then creatine supplementation should have a larger effect. The difficulty is that it is easy to raise plasma folate a lot but it is not known whether this causes liver folate and liver SAM to rise a lot in folate sufficient individuals.This led naturally to the question of whether supplementation with other nutrients, besides folate, would improve these results. The goal is to raise SAM concentrations and thus to increase the availability of methyl groups for AS3MT. A natural candidate is creatine supplementation, which has been shown to downregulate creatine biosynthesis through repression of arginine:glycine amidinotransferase (AGAT) in the kidney, which, in turn, lowers the concentration of guanidinoacetate (GAA), the substrate for GAMT in the liver , 51. Andbo daily . The 622(p=0.08) . FurtherLiver cells are not static but are constantly changing dynamic systems because the cells must continue to operate in the face of dramatically changing inputs due to meals. It is not surprising that liver cells have evolved many complicated and ingeneous mechanisms for accomplishing the homeostasis of important reactions like the methyltransferase reactions. The purpose of our discussion of AS3MT is to illustrate that a thorough understanding of how competing methyltransferases are regulated is necessary for designing successful interventions.There are more than 150 methyltransferase reactions in which a methyl group is transferred from SAM to another substrate. These reactions are important steps in a wide variety of biological mechanisms such as the biosynthesis of a large variety of useful compounds, methylating the cytosines on DNA, and catabolizing neurotransmitters. In any given cell typically only a certain subset of the MTs are expressed depending on cell type, its function, and the tasks that the cell is currently doing. The primary mechanism used by the cell for regulating the MTs is to upregulate and downregulate the expression level of the genes that code for the MTs. However, since all the MTs use the same substrate, SAM, up and down regulation of a particular MT will affect the flux in all MT reactions, i.e. it is hard for the cell to regulate each of MT fluxes independently. It is not surprising that cells have developed a number of different mechanisms that help them meet this challenge. In addition, cells must cope with large changes in amino acid input (i.e. methionine) that happen on a shorter time scale than gene regulation.The long-range interactions ensure that when one MT is greatly upregulated or downregulated the GNMT pathway changes a lot so that the fluxes in the other MT pathways change only modestly Fig. . SAM chaThe long-range interactions act to conserve total mass in the methionine cycle. SAM changes linearly and slowly as methionine input changes Fig. .The long-range interactions stabilize total methylation against folate deficiency Fig. b.We have found that long-range allosteric interactions in which substrates in one part of the network affect enzyme activity in distant parts of the network play an important role: We have provided computational evidence that GNMT that is bound to one 5mTHF molecule retains substantial activity. This remains to be confirmed experimentally.Km values of many MTs for SAM makes them independent of the fluxes through other MT reactions.We explained why the small Ki value of SAH for PEMT stabilizes PEMT flux.We explained why the small In this paper, we have used a mathematical model to investigate the mechanisms that liver cells use to manage the non-independence of the MT fluxes. And finally, we discussed why a full understanding of the regulation of MT fluxes is important for human health interventions to ameliorate arsenic toxicity in Bangladesh.Additional file 1Supplementary material. (PDF 155 KB)