Pichia pastoris is one of the most widely used organisms for heterologous protein expression. There are different GEMs for this methylotrophic yeast of which the most relevant and complete in the published literature are iPP668, PpaMBEL1254 and iLC915. However, these three models differ regarding certain pathways, terminology for metabolites and reactions and annotations. Moreover, GEMs for some species are typically built based on the reconstructed models of related model organisms. In these cases, some organism-specific pathways could be missing or misrepresented.Genome-scale metabolic models (GEMs) are tools that allow predicting a phenotype from a genotype under certain environmental conditions. GEMs have been developed in the last ten years for a broad range of organisms, and are used for multiple purposes such as discovering new properties of metabolic networks, predicting new targets for metabolic engineering, as well as optimizing the cultivation conditions for biochemicals or recombinant protein production. P. pastoris, we have reconstructed and validated a consensus model integrating and merging all three existing models. In this step a comprehensive review and integration of the metabolic pathways included in each one of these three versions was performed. In addition, the resulting iMT1026 model includes a new description of some metabolic processes. Particularly new information described in recently published literature is included, mainly related to fatty acid and sphingolipid metabolism, glycosylation and cell energetics. Finally the reconstructed model was tested and validated, by comparing the results of the simulations with available empirical physiological datasets results obtained from a wide range of experimental conditions, such as different carbon sources, distinct oxygen availability conditions, as well as producing of two different recombinant proteins. In these simulations, the iMT1026 model has shown a better performance than the previous existing models.In order to provide an updated and more comprehensive GEM for  Genome-Scale metabolic models (GEMs) have become one of the most useful and widely employed tools in systems biology in the last fifteen years . Since tPichia pastoris has become more extensively used for industrial applications [AOX promoter, inducible with methanol [P. pastoris is able to grow up to high cell densities, resulting in high protein production yields [Regarding the expression of heterologous proteins, ications , 14. It ications , 16 thatications –19. Moreications , 21. Spen yields , 23. DueP. pastoris were limited to the central carbon metabolism and were used for 13C flux data analysis [The first metabolic models for analysis –27. In 2analysis  and GS11analysis , was seqanalysis  showing analysis  correspoanalysis  based onanalysis . Moreoveanalysis , 35 whicP. pastoris’ GEM models are potentially useful platforms for bioprocess design and optimization, as well as for strain metabolic engineering [ineering , 37. In ineering  have alrP. pastoris specific gene-protein-reaction associations and hence, a larger number of genes, but several extracellular and nuclear reactions are missing. In general terms, these models cover the same metabolic processes, but iLC915 is more detailed. Nevertheless, there still exist some critical issues in these models, such as missing and divergent information or reactions that require manual revision and curation.Each one of the three currently available models is fully compartmentalized, but they differ in the number of reactions and metabolites. The first two models, iPP668 and PpaMBEL1254 have a comparable number of associated genes, reactions and metabolites, as well as similar metabolite and reaction identifications and nomenclature. On the other hand, iLC915 incorporates more Saccharomyces cerevisiae, new versions and updated models integrate previous versions and incorporate new features and information from newly published literature. In the case of S. cerevisiae, despite the existence of other versions, a consensus metabolic model was developed [th version [Similar to other organisms, such as eveloped  and it w version –43.P. pastoris and provide an upgraded version. As mentioned above two different strains were used to obtain these models. Nonetheless, there is a high degree of identity at the amino acid coding sequences level (93.7%) and functional annotation between the two genome sequences [P. pastoris physiology and metabolism enabled to complete sphingolipid biosynthesis metabolism and glycosylation pathways, as well as the oxidative phosphorylation electron transport chain. Furthermore, we included different biomass compositions specific for each of the alternative carbon sources used. Finally, the model accuracy was tested in a variety of physiological conditions.In this work, we compare the models of equences . In addiequences . TherefoFor the model comparison, an initial step of metabolite nomenclature unification was required. In PpaMBEL1254 only the identifier (ID) was available in the SBML file, i.e. neither the complete name of metabolites nor any association to a reference database was included. These metabolite IDs, were mostly the standard IDs most commonly used and therefore also included in both in BiGG  and The S. cerevisiae GEMs [S. cerevisiae GEM [P. pastoris or S. cerevisiae literature. The P. pastoris high quality sequence annotation [P. pastoris [Once all metabolite names were unified, PpaMBEL1254 and iPP668 were compared using ModelBorgifier , therebyiae GEMs , 43 or isiae GEM . Divergenotation  and the pastoris , 35 werepastoris , 53, 54.Eventually, the network was loaded into a convenient environment for debugging . Thus, bThe biomass reaction is defined by the sum of biomass components, grouped in macromolecules , essential cofactors and ATP consumption associated to growth. This equation was adapted depending on culture conditions or carbon source used in accordance to the available literature experimental data , 61. In GAP promoter [Rhizopus oryzae lipase (ROL), regulated by the methanol inducible AOX promoter [5 between recombinant DNA (gene copies), mRNA and heterologous protein was assumed, as described in [The model was also tested for the expression of two different recombinant proteins under different growth conditions: i) the antibody fragment 2F5 (FAB), expressed constitutively under the promoter  and, ii)promoter . The datpromoter , 66, whepromoter , 61. Rearibed in . These eribed in . Details-1·h-1) was represented against the specific growth rate using data from [y-intercept of the linear regression line to this data corresponds to the amount of glucose needed for maintenance by non-growing cells. Using this value and the model, the NGAME can be calculated by maximization of the ATP turnover per mmol of glucose for the case of no biomass growth. Using the obtained value as fixed value for the non-growth associated maintenance, GAME is determined by adjusting the ATP consumption coefficient in biomass equation to fit biomass-substrate yields using experimental data (including CO2 and O2 constrains) from [Before the validation step, classic energetic parameters were estimated using experimental data. These parameters are the growth-associated maintenance energy (GAME) and non-growth-associated maintenance energy (NGAME). Both are represented as ATP consumption in the model. For the NGAME calculation, a classical approach was used . For theata from , 69, 70.ns) from .However, for the case of glycerol:methanol growth conditions NGAME was directly taken from the calculated values reported in . This waModel analysis and validation were performed using both RAVEN  and COBR-1·h-1 except were otherwise stated.Carbon assimilation capabilities were determined maximizing growth rate and arbitrarily constraining the carbon source influx to 10 mmol·gDCWKO = growthKO/growthWT). The ratios obtained allowed to classify each reaction into three categories: i) essential (GRKO = 0), ii) partially-essential (0 < GRKO < 1) iii) non-essential (GRKO = 1).Reaction essentiality was determined performing an additional set of simulations. The procedure consisted on sequentially deleting each reaction of the model, maximizing biomass production and calculating the ratio of the resulting growth rate over the wild type result , they present significant differences in their metabolic capabilities. Thus, besides P. pastoris well known additional pathways such as the methanol incorporation steps, other significant metabolic differences exist. More specifically, in this work, pathways such as sphingolipid biosynthesis, oxidative phosphorylation and glycosylation pathway, were adapted and redefined, as described below.In the case of  limited , with moinferred . DespiteP. pastoris, it was assumed that most of S. cerevisiae fatty acid pathways were identical in the P. pastoris case. According to Hiltunen and co-workers [S. cerevisiae [de novo biosynthesis and elongation. Despite it is well known that mitochondrial FAS type II synthetizes at least up to C8 fatty acid, some evidences suggest that this system can synthesize longer fatty acids [S. cerevisiae 7th version of the consensus model [8, this model also include reactions for up to C18 biosynthesis.Due to the limited information on specific fatty acid (FA) metabolic pathways in -workers , the lat-workers  and iTO9revisiae , fatty arevisiae . FAS typty acids , 76. Whius model  mitochon14 to C18 acyl-CoAs, mainly because they are the main fatty acids found in P. pastoris [14, C16 and C18 acyl-CoAs). In addition to de novo biosynthesis, P. pastoris also has fatty acid elongation enzymes, which are able to extend C12-14 fatty acids and generate very long chain fatty acids (up to C26).On the other hand, cytosolic FAS is a complex formed by Fas1p and Fas2p within which the successive elongation reactions take place and only the final acyl-CoA is released . The finpastoris . The bio14, C16 and C18 FFA, as well as their respective acyl-CoA hydrolysis. Finally, only acyl-CoA desaturations were included (that is not acyl-ACP or FFA) according to the pathway defined in S. cerevisiae [Activation of free fatty acids (FFA) was considered to take place in cytosol only for Crevisiae .12 chain length) and, on the other hand, long and very long chain fatty acids are translocated as acyl-CoA concomitant with the corresponding ATP hydrolysis [Two different transport mechanisms are commonly described depending on the FA chain length –80, bothdrolysis . For thedrolysis , 88, per18:3 to C18:2 was taken from iLC915.Each cycle of β-oxidation is represented by 4 reactions. Nevertheless, for unsaturated fatty acid degradation, and due to its highly complex degradation steps which depend on the position of its double bounds , 90, lumS. cerevisiae and they are extensively described in the literature [S. cerevisiae, some yeasts such as P. pastoris, are able to produce glucosylceramides (GlcCer) from sphingolipid bases [General sphingolipid biosynthetic pathways in yeast are partially homologous to terature , 92. Nevid bases –96.P. pastoris.None of the three models include GlcCer biosynthesis. Ternes and co-workers , 98 idenSphingoid bases can be derived from palmitoyl-CoA and stearoyl-CoA. However, only a 5% of the detected species correspond to the last one. In fact, Ternes and co-workers  characteP. pastoris. Only iLC915 partially included N-glycosylation, O-glycosylation and glycosylphosphatidylinositol-anchor (GPI-anchor) biosynthesis pathways. However, compartmentalization of several reactions of this pathway also required revision.Protein glycosylation pathways are not accurately described in previous models of N-glycosylation process is highly conserved among eukaryotes [P. pastoris [N-Acetylglucosamine polymer). Both contribute to the biomass formation as a specific component of the carbohydrate fraction.The first part of the karyotes , 102. Itkaryotes . In the karyotes , 105. Thpastoris , 107. Aspastoris –110 and pastoris . Due to N-glycosylation in mannan formation, O-glycosylation is included assuming an average of 3 Man oligosaccharides [O-glycosylation is also represented by a pseudo-reaction forming the compound (Man)1(Ser/Thr)1 in which Ser/Thr represents a serine or threonine residue of a protein.Similarly to charides –115. O-gFinally, GPI-anchor biosynthesis was also reviewed and compartments reassigned according to Orlean and Menon .P. pastoris specific traits in respiratory chain that should be included in the GEM. As an example, while complex I is not present in S. cerevisiae [P. pastoris [P. pastoris models include respiratory complex I and so, an important proton translocation step was missing. In general, two main traits of oxidative phosphorylation were deeply analyzed: the proton stoichiometry and the complexes integrating the electron transport chain.There are revisiae , it is dpastoris , 119. NoP. pastoris models shows a different stoichiometry for proton translocation. After a review of the stoichiometry and relevant literature it was decided to apply a stoichiometry that satisfies the H+ balance of the metabolites’ charged formula and including complex I stoichiometry considerations proposed by Wikström and Hummer [complex I translocating 4 H+ to the intermembrane space [In this model the mitochondrial intermembrane space has been included. Hence proton translocation is assumed to occur from the mitochondrial matrix to the intermembrane space. Thus, protons pumped out from the mitochondria do not merge with the high amount of protons from the cytosolic space. Regarding the electron transfer chain reactions, each of the previous d Hummer . This inne space , 121.+ translocating outer and inner mitochondrial membrane NAD(P)H dehydrogenases (cytoplasmic side and matrix side) were also included. While inner NADH dehydrogenase appears in all three models, outer NADH dehydrogenase was only present in iPP668 and PpaMBEL1254, despite both dehydrogenases have been previously reported [Kluyveromyces lactis [In the present model, reactions for non Hreported , 123. Wes lactis , 125 ands lactis .complex III and IV are included in all three models, but several discrepancies exist on the details of the H+ balance due to the consideration of alternative metabolite’s molecular formulas or the result of using different criteria when considering chemical and translocated protons [complex III equations is the complexity on the stoichiometric representation of Q-cycle [complex III and IV reactions were chosen with special attention to the proton balance. The selected stoichiometry was of 2H+/2e- for complex III and 4H+/2e- for complex IV according to recent literature [On the other hand,  protons . An addi Q-cycle , 129. Thterature , 129.P. pastoris is the presence of an alternative oxidase that could bypass complex III and IV in the respiratory chain [+/ATP, resulting in a final maximum theoretical stoichiometry of 2.5e-/ATP) as its H+ balance is in agreement with the available literature [One additional characteristic of ry chain , 130 whiry chain , 131. Alterature .P. pastoris and reported non growth for these carbon sources. Consequently reasons for their metabolization were revised and discarded reactions are detailed in P. stipitis [Metabolization of some sugars was also updated. Sugars such as starch, maltose or cellobiose were able to be assimilated in some of the previous models. However, Kurtzman  and Naumstipitis , 136.A full list of modifications from the original models, also including some additional pathways and subsystems not discussed above such as phosphatidylinositol synthesis or transport reactions, is provided in P. pastoris’ GEMs, which is provided in After following all the steps described above, an extended model (iMT1026) is obtained that integrates previous In the first place this model includes an increased number of gene-protein-reaction relationships as can be seen in Our final model incorporated 185 new reactions that didn’t appear in previous models and has 614 common reactions in all three models . Reactioy-intercept from a representation of glucose uptake rate versus growth rate was 0.0878 mmol glucose/(gDCW·h) which corresponds to 2.81 mmol ATP/(gDCW·h) using the glucose-ATP conversion factor obtained in the initial step. This calculated glucose NGAME value is similar to the 2.3 mmol ATP/(gDCW·h), previously proposed by [Pichia (Scheffersomyces) stipitis also growing in glucose [As described in Materials and Methods, data from , 69, 70 posed by  for gluc glucose .P. pastoris [S. cerevisiae of 62–71 mmol ATP/gDCW [in silico estimated [On the other hand, GAME for glucose was estimated by fitting the calculated biomass-substrate yields to experimental data. This way a value of 72 mmol ATP/gDCW was obtained. This amount of ATP associated to cell growth is also similar to 70.5 mmol ATP/gDCW calculated previously for pastoris  and closATP/gDCW , 139, an-1 growth rates), therefore a specific GAME was calculated for each case. The obtained values ranged within the 69.8 and 125.6 mmol ATP/gDCW interval. These GAME values increase with the fraction of methanol in the mixed feeding and are in agreement with those calculated by Caspeta and co-workers [For the case of the glycerol and methanol co-feeding cultivations, ATP maintenance values calculated by Jordà and co-workers  were use-workers , who estP. pastoris utilization of different carbon sources was tested and compared to experimental data [in silico minimal medium, with ammonium, phosphate and biotin. The model successfully predicts carbon assimilation for all sources tested.The model agreement with tal data , 133. A An interesting trait of the obtained GEMs is the identification of those reactions critical or essential for biomass growth . Simulations to determine reaction essentiality were performed for glucose in normoxia, limited oxygen and hypoxia conditions and also for mixtures of glycerol and methanol at different growth rates. No significant difference in reaction essentiality was observed in all the conditions tested. Thus, similar patterns of distribution of essential reactions in each pathway are observed for all the cases. The results, grouped into major metabolic pathways, are summarized in S. cerevisiae, extending the model and including more detailed biomass composition results in an increase of essential reactions directly linked to the biomass related metabolites. Nevertheless, this essentiality could be overestimated in silico, due to the fact that in vivo systems are able to replace de missing species with other similar biomass components.The results show that there are 312 condition independent essential reactions, which are essential in all the performed simulations. These essential reactions can be grouped in three main groups: in the first group, most of them are associated with lipid metabolism (40%), in the second group most reactions belong to the amino acid metabolism (18.6%) while the third group mostly includes cofactor related essential reactions as a 14.1% of all common essential reactions. Similarly to other GEM models, such as An additional step of model validation was performed by comparing the model predicted values with an additional set of experimental data including diverse combinations of glucose, glycerol and methanol chemostats , 66.2 production were successfully predicted with errors lower than 6% for both FAB expressing and non-expressing strains H regeneration, could be one of the key factors for the production of those alternative products [13C-labelling data [For the glucose chemostats, simulations with different oxygen availabilities, growth rates and CO strains . Accordi strains . In addioenzymes , 144, anproducts , 146. Coing data  as well ing data  would be2 consumption and CO2 production rates were predicted within a 11% of deviation, as shown + for maximum biomass production.For the second dataset, (glycerol:methanol mixtures), specific growth rate, together with specific O2 production and O2 consumption (only in the glycerol:methanol simulations) were compared to the experimental values [In order to compare the accuracy of our model with the previous existing models a set of simulations were performed for glucose and glycerol:methanol cultivations . The saml values , 66. As P. pastoris integrating the three preexisting models has been obtained. Importantly, the new GEM, iMT1026, is more complete and includes a comprehensive revision and upgrading of several metabolic processes  based on new information emerged from recent literature. Furthermore, the new GEM has been validated using different sets of experimental data corresponding to a wider range of physiological states than previous GEMs. From our point of view this GEM improves the capabilities in terms of accuracy of predictions/simulations in relation to previous models. Overall, we provide an improved tool to the P. pastoris community for the physiological analysis and understanding of this yeast. It is expected that on-going efforts in the functional (re)annotation of the P. pastoris genome will allow for further improvements of its GEMs by all the P. pastoris community. From a wider perspective, it also has to be pointed out the importance of curating and manually revising new GEMs of non-model organisms that are based on GEM scaffolds from related model organisms. Despite the comprehensiveness of these scaffolds, an exhaustive analysis of specific metabolic traits of the non-model organism is still essential to construct a GEM describes/predicts its metabolic phenotype accurately.In summary, a consensus GEM of the yeast S1 FigSummary of reaction essentiality results grouped into major pathways.(PDF)Click here for additional data file.S1 FilePichia pastoris GEM model in xlsx format for use in the RAVEN toolbox.(XLSX)Click here for additional data file.S2 FileDetails of biomass composition for cultivations on glucose and glycerol:methanol mixtures.(XLSX)Click here for additional data file.S3 FileP. pastoris and tested in the model.DNA, RNA and amino acid compositions for the FAB and ROL recombinant proteins expressed in (XLSX)Click here for additional data file.S4 FileList of modified, added and excluded reactions in iMT1026.(XLSX)Click here for additional data file.S5 FilePichia pastoris GEM model in SBML format generated with the RAVEN toolbox.(XML)Click here for additional data file.S6 FileAnalysis of the prediction capabilities and deviations from experimental data in simulations performed with iMT1026 and the previous models.(PDF)Click here for additional data file.


During the last 10 years, systems biology has matured from a fuzzy concept combining omics, mathematical modeling and computers into a scientific field on its own right. In spite of its incredible potential, the multilevel complexity of its objects of study makes it very difficult to establish a reliable connection between data and models. The great number of degrees of freedom often results in situations, where many different models can explain/fit all available datasets. This has resulted in a shift of paradigm from the initially dominant, maybe naive, idea of inferring the system out of a number of datasets to the application of different techniques that reduce the degrees of freedom before any data set is analyzed. There is a wide variety of techniques available, each of them can contribute a piece of the puzzle and include different kinds of experimental information. But the challenge that remains is their meaningful integration. Here we show some theoretical results that enable some of the main modeling approaches to be applied sequentially in a complementary manner, and how this workflow can benefit from evolutionary reasoning to keep the complexity of the problem in check. As a proof of concept, we show how the synergies between these modeling techniques can provide insight into some well studied problems: Ammonia assimilation in bacteria and an unbranched linear pathway with end-product inhibition. The complexity of high-throughput datasets has reached a level, where mathematical models are needed to understand biochemical networks. The most common way of modeling metabolic networks, if regulation is to be included, is a system of differential equations describing the dynamics of certain variables, normally metabolite concentrations. These state variables are collected as a vector of dependent variables ructions . The equThe function of reaction rates If we were walking among the tables during a chess championship without having any knowledge about the game, we might wonder why some moves are recurrent and some are never seen or why some pieces tend to be in certain areas of the board. Most games start with the same movements, advancing one of the central pawns, and no game ever starts with some pawn at the side. Moreover, the pawns are never seen behind their starting positions and the bishops have a tendency to show up along the main diagonals. Some of these questions can be easily explained from the rules themselves. Pawns can only move forwards and that is why they cannot reach any position behind their starting point. But nothing in the rules prevent the player from starting the game with the leftmost pawn, so why doesn’t that ever happen? In order to understand this, we would have to think in terms of winning and losing strategies. Moving the central pawns satisfies two important goals: controlling the center of the board and clearing the way for other pieces. Domination of the center can also be achieved by moving a knight towards it, and that is also an opening move that is sometimes seen. Advancing the leftmost pawn, however legal a move, does not follow any strategy with chances of winning and it is therefore not done. Chess masters do not think in terms of isolated moves but in sets of concerted moves that pursue certain goals. Independent moves can be much better understood within the context of these strategies, which are sometimes complementary but can also be conflicting: should I make an offensive move or surrender the initiative to defend my king by “castling”?et al. [et al. showed that phenotypes tend to be in the Pareto space and large areas of perfectly possible phenotypes are never found in nature.Just as the rules of chess constrain the possible moves in a game, physics and chemistry constrain all the possible phenotypes available to evolution. Moreover, just as the most frequent moves in a game are those that enable successful strategies, the most frequent genotypes are those that enable its own propagation. Finally, just as the chess games of our example only covered a fraction of all possible combinations, so can metabolic networks, as products of evolution, be expected to concentrate in those “designs” that enable a certain performance. This prevalence of successful strategies has been observed in many biological systems. The analysis by Shoval et al.  shows thIn this work, we will try to show how the sequential application of several well established strategies see  for the In growing microbes, fitness can be equated to growth rate. It is therefore reasonable to start considerations on evolutionary strategies for microbes by inspecting potential for growth of a given metabolic network.In the steady state, since Equation  that desLet’s define the production of biomass, One approach to this problem is to establish an arbitrary upper limit for lsewhere  or overfAnother popular aproach is to establish a reasonable limit for the uptake rate of the carbon source. This may however obscure the meaning of the solution, since it implies that the limiting factor for growth is limited uptake rate. Even if the result of this optimization matches the data, it can lead to a misinterpretation of the results. To help clarify this point, we will reformulate the problem in an equivalent version. Swapping the objective function and one of the constraints yields the following problem: Here, the former limiting factor,  problem  is often problem . Since tEquation  defines Equation . A detaiE. coli on glucose under limited oxygen availability). While the solutions to Problem  is performed and show with an example how it constrains but also complements FBA.Thermodynamic descriptions of a system at equilibrium are built upon pairs of conjugate variables, one intensive (x) and one extensive (y), so that the product xdy has units of energy or work—e.g., pressure (P) and volume (V). Thus, the contribution of each pair to a thermodynamic potential is the product of a certain driving force (x) and the displacement or flow (y) it provokes, like in PdV. This force/flow relationship is also present in non-equilibrium thermodynamics, so any system admits many different representations depending on the chosen combination of flows and forces. e.g., entropy is often replaced with temperature through a Legendre transform. Models of biochemical processes have also been shown to be amenable to such alternative representations both in the linear  and non-But thermodynamics goes beyond filtering solutions. The framework, called Thermodynamic Feasibility Analysis ,19,20, eKM  or the eKM ,22. The Feasible states are defined as a set of linear inequalities, which can be explored using the same tools that make FBA possible:g=g0+RTSTB as the B is, by definition, the minimal driving force. If we try to maximize its magnitude, it is easy to see that B must be below both curves (grayed area) and its maximum value is found for the concentration of The net reaction rate of a reaction l to |ΔG|. So evenproposed  as the MEquation . This enEquation  will looears ago  and receears ago , the priears ago . AccordiAfter sequential application of FBA and TFA, the system is described by a steady state flux distribution together with admissible intervals for Equation  would yiPractically all enzyme rates can be factored  as a conetc.—and depends also on a series of parameters, like Hill coefficients, saturation constants, etc. For some rate laws, it is difficult to factor allosteric and saturation terms separately, but it has been shown that the allosteric and other terms can always be factored out as a Hill-like term using a special type of Taylor series [θ is the distance to equilibrium, i—positive for products and negative for substrates—and θ) as a function of the metabolites or just of the The product of the catalytic constant r series . Finallyain flux . KnowledBeing the building blocks of metabolism, it is certain that enzymes must be the subject of some evolutionary pressure. It is however far from trivial to establish the magnitude of such pressure and in which direction it aims. Mutations will change the detailed behavior of the function presented above but which changes can be considered improvements from an evolutionary point of view? In many cases, the answer depends on the enzyme as well as the milieu in which the enzyme operates, in this context represented by the concentrations of substrate and product. For instance, if the enzyme is operating at saturation, its rate will be mal kcat ,30. The mization ,31,32. Tmization , and addmization ,35. Accof 1010s−1,37,38. Mf 1010s−1 on the bet al. estimated the average enzyme to have a While some enzymes, like Triosephosphate Isomerase, have lived up to the most optimistic theoretical calculations, the great majority of  of 10s−1. EnzymesE. coli. The expression of all the proteins in the cell follows a log-normal distribution, which is also appropriate to describe the subset of enzymes for which a catalytic constant value is provided, as can be seen in The disagreement between theoretical limits and actual observations makes it especially relevant to develop a feeling for which values of ata from  can be ported in ,40, and The approaches discussed so far have been extremely successful for two main reasons: First, they are based on linear equations. The simplicity and structural regularity of the linear formalism enables the use of very general techniques and its application to really big systems. Second, the amount of information necessary to set up a model is not too high and can be obtained in the omics scale. In spite of their undeniable usefulness, a very important feature is missing in both cases: regulation. Only introducing kinetics in the model can shed light into regulation and dynamics but identifying all the functions and parameters in Equation  is extrevs. the corresponding variable in a log-log plot and x at the reference steady state. We can also undo the logarithmic transformation to obtain the following rate law: Reaction kinetics are non-linear, and linearizing them would result in unrealistic representations of the problem. The next best option is to obtain a linear representation in logarithmic coordinates.g parameters and rate constants for the αs. Kinetic orders in a power law model, unlike in mass action kinetics, can have any real value. Kinetic orders are very often referred to as elasticities in the context of Metabolic Control Analysis (MCA) [The kind of rate in Equation  is knownis (MCA) ,44, wherUsing separable reaction rates like Equation  as the srium see .In order to do numeric analysis and simulations with such a system, the space of possible kinetic orders could be sampled using Monte Carlo methods but much can already be done without attributing numerical values to the parameters. This is a consequence of a well known property of systems like this (S-systems), namely that in spite of being fully non-linear, its steady states can easily be expressed as a system of linear equations in terms of the logarithms of its variables (yi=lnxi) .The availability of analytic solutions for the steady state brings the possibility of performing many different analysis symbolically without the need for numeric methods, like sensitivity analysis. Two kinds of sensitivities are normally defined: Logarithmic gains, Another consequence of the structural regularity of power-law models is that linearization is straightforward and the Routh-Hurwitz stability criterion  can be fIf we want to understand the kind of strategy that can be evolutionarily successful, we will have to compare alternatives. Comparing objects requires defining some criteria, according to which the objects can be ranked. Comparing classes or sets, however, is a much more complex problem, since two objects from the same class can rank different on the same criterion. Comparing the most honest and virtuous feudal lord with the a bunch of corrupt politicians may give the impression that the feudal system is preferable to a democracy . So how Internal equivalence The reference and alternative system belong to different classes due to differences in one or more reactions/processes—e.g., the first reaction of the reference system is inhibited by the end product of the pathway, while the alternative system does not have this feedback loop. Since those distinctive reactions have been modified from one system to another, their parameters may differ. We will keep the notation, where, if p is a parameter or a property of the reference system, then External equivalence Two systems satisfying the internal equivalence condition will have identical values for most parameters except for the handful involved in processes distinctive of their class. These degrees of freedom are further reduced by ensuring that both systems are perceived by their environments as being as similar as possible. That eliminates differences that are not inherent of the class but characteristic of some particular cases. Let’s imagine a pathway that has an optimal flux to provide a certain precursor for biomass. Introducing a feedback inhibition will decrease the flux through the whole pathway, making it suboptimal. Does it mean that the feedback is deletereous for the cell? Obviously not. The system with feedback is perfectly capable to supply the precursor in the same amounts, but that will require an increase in the activity of the inhibited enzyme. Only after setting the fluxes equal in both systems, can the comparison between the two alternative architectures be considered fair. An additional boon of this approach is that the degrees of freedom for the choices of parameter values is reduced, so the free parameters of the alternative system become a function of those of the reference system, and comparisons are made practically on a one to one basis. Typical requirements for external equivalence would be that both systems carry the same fluxes, have the same concentrations of initial and end product in the steady state, or that they have as many identical logarithmic gains as possible.MCC provides clear cut analytical solutions, when a systemic property is always better in one of the alternatives being compared or when both alternatives are always identical. In cases, where a quantitative prediction is wanted or when there is a trend for one system to outperform the other, a statistical approach to MCC can be followed .The use of constraint based approaches as a stepping stone towards dynamic models has so far been limited to stoichiometric constraints ,49,50. Nθ provided in Equation ∏j|θ in mathematically controlled comparison, we will have to take it into account, when the equivalence conditions are established (see case study 2 for an example).Finally, if we intend to use Thermodynamic shortening As has been shown above, as a reaction approaches equilibrium, its rate becomes hypersensitive to perturbations of substrates and products, their kinetic orders tending to infinite magnitude in the sense that counters the perturbation, positive for substrate and negative for product. Also, by definition, the mass action quotient will tend to the value of the equilibrium constant. This enables to reformulate the model in a reduced form that will, nevertheless, be consistent with the behavior of the full metabolic network, as has been established using perturbation theory [n theory .The first step is to establish which reactions are close to equilibrium. Then, we can partition the fluxes of the system into those close to equilibrium, Equation  into: and then proceeds to transfer the NH3 to α-ketoglutaric acid by Glutamate Synthase (GOGAT). The sum of these two reactions are equivalent to the action of GDH plus the hydrolysis of one ATP. Viewing this small network  that catalyzes the reductive amination of work see  from a sThe longer pathway needs two enzymes, that is twice as much protein assuming all enzymes have the same 3 available, as we’ll see below.terature ,20 and tterature  32) enforEquivalence conditions Due to internal equivalence, only the parameters involved in the second reaction can change with θ, which leaves four degrees of freedom: θ, θ are automatically fulfilled, since neither the concentration of θ. So no reduction in the degrees of freedom comes from those conditions. The thermodynamic conditions in Equations x3, remaiTo eliminate the last degree of freedom we start writing the rate law for the reaction: Introducing the thermodynamic formulation of the kinetic orders from Equation  and rearθ is negligible, can be taken as a reference and then equivalence conditions can be established. When elevant, 8limθ→0|vSystemic properties Once the equivalence conditions have been set, the behavior of the pathway, when a reaction approaches equilibrium, can be checked analytically by taking limits of the systemic properties, when  to zero ),(40)liθ and for those that do: The response of the pathway to supply and demand remains the same, since most logarithmic gains do not depend on Thermodynamic shortening It has been shown that pathways with feedback inhibition tend to have a narrower margin of stability—right hand side of Equation (Equation —as they When a reaction of the system, in this case  p1=x1+x2. The difNow the old variables must be eliminated. We combine the equilibrium relation with the definition of the pool, Defining n, de facto shortening it.In this particular case, the margin of stability of the starting pathway was wide due to the small number of intermediates but becomes infinity after the reduction. If et al. [per se; increasing the margin means that the feedback loop can be several times stronger without causing instability, making the shortened pathway even more robust and responsive.The unbranched pathway with end-product inhibition illustrates the concept of archetypes as defined by Shoval et al. . On the Comparing a priori knowledge.Biology seems to be the science of exceptions, a bazaar offering a thousand different solutions for every problem. But the continuous recurrence of certain patterns is as characteristic of biology as diversity itself. The same counter current mechanism that concentrates urine in the kidney serves as a heat saving mechanism in the feet of the penguins. These patterns can also find their way across levels of organization: feedback inhibition is ubiquitous in the nervous system but it is also a fixture in metabolic pathways as we have discussed above. In this work, we have tried to show that the recurrence of some patterns are often the product of evolution. These patterns can, not only be recognized, but also predicted from first principles. Few problems have a unique solution and some problems have several that are equally good. But most problems have alternative solutions that fulfill different goals and the phenotypes we observe are different trade-offs between them. Identifying the relevant goals of a certain process and the “design principles” relevant to achieve them enables a higher level of understanding and a much more efficient use of available data by building upon In the case of metabolic pathways, modern methods have provided new ways for computers to do, what biochemists have always done. FBA is a way of following the traffic of molecules, just on a big scale. TFA applies the same principle to thermodynamics while BST/MCA add regulation to the picture. Applying these methods together within an integrative framework enables the analysis to be performed at the whole network level, rather than one pathway at a a time. This has been illustrated through small classical examples, like ammonia assimilation or a very simple pathway, but all the methods discussed have the potential to be used on a large scale. FBA is routinely performed on genome scale models and TFA is catching up fast, thanks to methods that approximate thermodynamic information for cases, where experimental data are not available . The tra


Glycosylation is a key post-translational modification that can affect critical properties of proteins produced in biopharmaceutical manufacturing, such as stability, therapeutic efficacy or immunogenicity. However, unlike a protein's amino acid sequence, glycosylation is hard to engineer since it does not follow any direct equivalent of a genetic code. Instead, its complex biogenesis in the Golgi apparatus Figure  integratWe use the COBRA toolbox to generate an in-silico representation of the N-glycosylation network. The stochastic transition of glycans through this reaction network is modeled as a Markov chain where secreted glycans are represented as absorbing states Figure . After tOur model is capable of creating N-glycosylation reaction networks that are complex enough to cover typical glycoprofiles found in biopharmaceutical manufacturing including tetra-antennary, highly sialylated or polylactosamine carrying glycans. The probabilistic framework implemented in this model proves to outperform knockout predictions derived from pure constraints-based modeling. Tests on experimental knockout glycoprofiles both from the literature and our laboratory show that the model yields sound predictions of glycoprofile change upon genetic modification which are in good congruence with corresponding experiments Figure .The model has the potential to provide a cheap and fast guidance tool to help find host conditions that can yield a desired glycoprofile, thus providing an important step towards the in-silico process of glycoengineering. So far, the reaction network considered is specific for CHO cells but can be easily modified to include reactions occurring in other hosts. In addition, it could be integrated into whole-cell metabolic models. This would enable comprehensive in-silico representations of the entire cell-culture setup, allowing one to simulate the effects on the glycoprofile of a wide range of both intracellular and extracellular modifications to the growth conditions.This work was funded from a generous gift from the Novo Nordisk Foundation to the Center for Biosustainability. A provisional patent has been filed concerning this work. In addition, we wish to thank H. Clausen and his group from Copenhagen University for valuable discussions and sharing unpublished data.


Progress in systems biology offers sophisticated approaches toward a comprehensive understanding of biological systems. Yet, computational analyses are held back due to difficulties in determining suitable model parameter values from experimental data which naturally are subject to biological fluctuations. The data may also be corrupted by experimental uncertainties and sometimes do not contain all information regarding variables that cannot be measured for technical reasons.Arabidopsis. The dynamic behaviors obtained by predictive simulations agreed with actually available metabolomic time-series data, identified probable errors in the experimental datasets, and estimated probable behavior of unmeasurable metabolites in a qualitative manner. The model could also predict metabolic responses of Arabidopsis with altered network structures due to genetic modification.We show here a streamlined approach for the construction of a coarse model that allows us to set up dynamic models with minimal input information. The approach uses a hybrid between a pure mass action system and a generalized mass action (GMA) system in the framework of biochemical systems theory (BST) with rate constants of 1, normal kinetic orders of 1, and -0.5 and 0.5 for inhibitory and activating effects, named Unity (U)-system. The U-system model does not necessarily fit all data well but is often sufficient for predicting metabolic behavior of metabolites which cannot be simultaneously measured, identifying inconsistencies between experimental data and the assumed underlying pathway structure, as well as predicting system responses to a modification of gene or enzyme. The U-system approach was validated with small, generic systems and implemented to model a large-scale metabolic reaction network of a higher plant, The U-system approach can effectively predict metabolic behaviors and responses based on structures of an alleged metabolic reaction network. Thus, it can be a useful first-line tool of data analysis, model diagnostics and aid the design of next-step experiments. Systems biology have advanced far enough that it is becoming possible to gain a comprehensive understanding of a metabolic system, and to use this knowledge for developing rational treatment options for diseases or devising strategies for increasing the productivity of foods and chemicals. While the main hallmark of systems biology is often portrayed as a means for predicting systems responses to external or internal stimuli, a similarly important aspect is its abilities to envisage all relevant information and integrate experimental data into logical and computable structures. As an example, suppose that three metabolites, A, B, and C, form a linear pathway Figure . SupposiThe exploitation of logical concepts for the prediction of probable behaviors of unmeasurable data and identification of uncertainties in datasets becomes much more complicated and important if the pathway systems are large. Large-scale datasets, and in particular time series data characterizing metabolic systems, are also becoming more and more commonplace to assist the investigation. To acquire such datasets with reasonable efforts, the high-throughput analytical instruments have been developed in recent times -3. GivenIt is therefore useful to explore to what degree it might be possible to employ the logic of the pathway to address these issues. Such an analysis seems to be feasible in principle, because the biologist executing the experiments usually has a relatively well-supported concept of the topology of the pathway system. The challenge is that even small pathways quickly become too complicated for intuitive assessments, and larger and more complicated pathway systems simply prevent us from testing assumptions or hypotheses without computational support. Such computational support of course requires mathematical models, which immediately leads to the challenge of setting up detailed, quantitatively appropriate models with a minimum of input requirements. The goal of such models is not necessarily to provide a quantitatively perfect picture of a pathway or to fit all data with great accuracy. Instead, these models should be easy to construct, robust, and merely able to identify how data within a large dataset could probably be.Power-law models within Biochemical Systems Theory  possessArabidopsis. This pathway system contains 351 metabolites and 441 fluxes, which are subject to various regulatory mechanisms. Apart from these, we have measurements from two different analytical methods, one comprising 268 metabolites, including 21 amino acids, and the other one accounting for 16 amino acids. As expected, although a large number of data can be measured, it is clear that not all data can be obtained. Also, none of the obtained data contain exactly the same values even in the replicated samples, mainly due to high biological variation among samples. In most cases, the measured time series are qualitatively the same, but in some cases they differ. We show that the U-system analysis estimates the probable behaviors of unmeasurable data and identifies at least some of the unreliable data. Besides, the U-system model is also applicable to predict metabolic responses when a metabolic reaction is altered.Here we capitalize on these two features of BST and propose a coarse test for the prospect of metabolic time-series data and consistency between the data and an alleged pathway diagram. The purpose is not to establish optimally fitting models but to identify how the unmeasurable data of metabolites located in a focused pathway probably behave, which time-series data within the dataset may be inconsistent with the understanding of pathway, as well as which data within a large dataset are probably reliable and which, if any, are most likely imprecise. We use a hybrid between a pure mass action system and a generalized mass action (GMA) system in the framework of BST with kinetic orders of 1, which allows for inhibitory and activating effects that are modeled with kinetic orders of -0.5 and 0.5. The rate constants are at first set to 1, but may be later subjected to order-of-magnitude adjustments, which obviously improve the model representation of the data. Once the parameter values are fixed, their effects are to some degree compensated by adjustments in metabolite concentrations according to the network structure so that we named this simplified method unity (U)-system. The diagram for U-system approach is also exhibited in Figure in vitro experiment . Additig13 and h34, respectively. When g13 is changed, only the magnitudes of normalized metabolite concentrations are changed but almost no difference is observed in temporal changes in time-course patterns of metabolite concentrations. Similar results are also observed for g21, g32, g41, h111, h112, h22, h33 and h44 , is a major primary methyl-group donor and also a precursor for a plant hormone ethylene and polyamines. To increase the sulfur-containing amino acids methionine and cysteine in crops, numerous researches in the field of genetics and metabolic engineering have been carried out for more than two decades, and the objectives have been partially realized. However, the results are not quite satisfactory yet, because the amino acids and related metabolites in the obtained transgenic crops are not well balanced. One of the major causes for not achieving a good balance is an incomplete understanding of the whole regulatory mechanisms of amino acid accumulation, as well as the regulatory feedback structure of the system, although it is well known that the accumulation of methionine, a member of the aspartate-family amino acids together with lysine and threonine, is tightly controlled by negative feedback by lysine and threonine [in vitro data into kinetic models for specific pathways [Arabidopsis metabolic system. In this study, therefore, we exploited the U-system approach to construct a large-scale mathematical model based on available metabolic reaction networks  for 351 metabolites was constructed by U-system approach on the basis of only structures of metabolic reaction networks available in databases          Figure  does not) Figure  clearly ) Figure  and AdoM) Figure  temporar) Figure  and sacc) Figure  increase Figure X0  exhibited small biological fluctuations among sample replicates, increasing from its steady-state level to a maximum at around 24 h, from where it decreased back to its steady-state level. The lysine concentrations (X93) contained more biological fluctuations among the sample replications, but it is still possible to detect a clear pattern over time. The glutamate concentration (X37) increased within 2 h and then seemed to be constant. The aspartate concentration (X78) increased slightly, then decreased, and finally tended to increase considerably.The modified U-system includes various approximations so that it is necessary to validate whether it is practicability and conformable to experimental data. Figure X26) and lysine (X93) agreed with the metabolic behaviors of experimental data obtained by metabolome analysis with significant correlations  was not consistent with metabolome data , lysine (X93) and glutamate (X37), both methods yielded similar results in terms of the metabolic trajectories, although the simulations were in better agreement with the time-courses of metabolite concentrations measured by amino acid analysis. For example, lysine concentration (X93) measured by metabolome analysis  exhibited high standard deviations. This assumption may be indirectly supported by the results of correlation analysis. For example, the correlation between the U-system simulation and the time-series data obtained by the amino acid analysis  slightly increased and then decreased to its initial concentration level or steady-state  after lysine and threonine supplementation were also indirectly supported by the increase of proline (X50) observed both in simulation and metabolome analysis  in this case) agree well with the experimental data, those of intermediate metabolites (glutamate (X37) and aspartate (X78) in this case) are likely to be correct. This consistency implies that the prediction of metabolic behavior by our approach is reliable even if the quality of the experimental data for some metabolites is not very high.As mentioned above, the relative concentrations observed for several amino acids such as aspartate and glutamate were scattered mainly because of biological variability and possibly due to analytical limitations, and it was difficult to precisely capture the time courses of their concentrations Figure  and 6d. e Figure  and 2. Te Figure . The fluntration . Thus, is Figure . One couThe 86 out of 268 metabolite concentrations measured by metabolome analysis  measured by metabolome analysis   started increasing at around t=55 h and then 4-methoxy-3-indolylmethyl GSL concentration (X261) increased around t=60 h. In this case, the dynamic behaviors of 1-hydroxy-3-indolylmethyl GSL (X257) from model prediction were inconsistent with the relative concentrations obtained by metabolome analysis. In the metabolic map, the reactions between X257 and X261 are linearly connected without any regulations, i.e., inhibition and activation  might have not be reliably analyzed.Figure s Figure  did not ) Figure  started X80)   Figure , which cArabidopsis metabolic system predicted that the supplementation of lysine and threonine did not affect 4-methoxy-3-indolylmethyl GSL concentration (X261) until t=60 h  in pyrimidine biosynthesis until t=40 h  and ureidoproprionate (X344) in purine and pyrimidine biosynthesis , glutarate (X152), and pipecolate (X141) in lysine degradation  the U-system model is presented in a normalized form, and 2) the U-system model constructed only using partial, currently-available metabolic pathways. Recent advances in metabolomics technology have enabled us to obtain large-scale semi-quantitative datasets for hundreds of metabolite concentrations. The first characteristic is essential to establish mathematical models for actual metabolic systems consisting of hundreds to thousands of metabolites, whose concentrations cannot be measured practically by existing methods of measurement other than metabolomics. The second characteristic is desirable for the coarse characterization of complicated systems, because metabolic responses mainly depend on the network structure, rather than parameter values, as we have shown in this study. Thus, the U-system approach is not only informatively useful for data analysis and model diagnostics but it also can aid the design of next-step experiments.BST uses ordinary differential equation systems of a specific format: Each process is represented with a product of power-law functions. This format is the result of Taylor approximation in a logarithmic space ,9,19,20.i X are dependent variables , j Y are independent variables , αik  and βik  are the non-negative rate constants for influxes and effluxes, respectively, ijk g and ijk h are real-valued kinetic orders associated with dependent variables in influxes and effluxes, respectively, while ijk G and ijk H are those associated with independent variables. n and m are the numbers of dependent and independent variables, respectively, p and q are the maximum numbers of influxes and effluxes, respectively, and t is time. Details have been documented in the literature many times, e.g. in [Here,  e.g. in ,7,9,21.Since the power-law format in BST appears to be quite restrictive, the accuracy of different model variants within BST has been assessed many times. As Taylor approximations, the models are mathematically guaranteed to be correct at an operating point of choice, but their ranges of validity were also tested against results from more traditional formulations like the Michaelis-Menten formalism. These comparisons demonstrated sufficient accuracy of BST models over quite large ranges in variation of the involved variables -25. ApplVmax, Michaelis constant KM, etc.) are not explicitly visible, but they are instead distributed to the rate constants and kinetic orders. The BST parameters have their own meaning either as turn-over rates or as the specific effect that a variable has on the flux term in which it is involved. Thus, if a kinetic order is negative, the variable with which it is associated has a negative (inhibitory) effect on the flux term. This effect is given exclusively by the one appropriate kinetic order, thereby reducing the number of kinetic parameters in the system, which can be much higher in traditional rate functions. Still, the simplified BST parameters are able to capture time-transient behaviors of metabolite concentrations and other characteristics of metabolic reaction systems very well.Model parameters of pathway systems are usually estimated from kinetic information or from metabolic time series data. In Eq. (5), the familiar kinetic parameters involved in Michaelis-Menten kinetics  can be estimated directly from time-series data of metabolite concentrations, and subsequently convey important information about the system characteristics. In some cases, traditional kinetic parameters from the literature, such as 1 is converted into X2 and X4, so that the equation is dX1/dt = VinX1 - VoutX1-1 - VoutX1-2. Since most of the parameters are set at unity in the proposed approach, we name this system as Unity-system or U-system.It was recently shown  that a cFixing the parameters values is to some degree compensated by adjustments in metabolite concentrations. In other words, if the kinetic orders are forced to be 1, +0.5, or -0.5, a data fit will lead to adjusted metabolite concentrations.Monte-Carlo simulations were employed to test in an unbiased manner whether the qualitative behavior of a model is consistent with the U-system representation. Most Monte-Carlo simulations were calculated for 1,000 loops. The parameter values were generated randomly from uniform distributions. The ranges for rate constants and kinetic orders were between 0.5 and 20, and ±0.2 and ±0.8, respectively.Differential equations were solved using automatic switching for stiff and non-stiff problems (LSODA)  using th(Scientific Tools for Python) . All visArabidopsis thaliana liquid callus culture derived from accession Col-0 was prepared as described in Murota et al. [a et al.  with slia et al.  was usedFor both metabolome and amino acid analyses, calli were collected prior to lysine and threonine treatment (0 h), and 2, 6, 12, 24, 36, 48, 60, 72, 84 and 96 h after the treatment. The calli were immediately frozen in liquid nitrogen and stored at -80°C. Prior to analyses, the frozen samples were lyophilized using a freeze dryer  in a vacuum.Metabolites were extracted by homogenizing lyophilized callus in 500 uL 80% methanol in 0.1% formic acid per 2 mg dry weight callus with 5 mm zirconia beads  in 2.0 mL sampling tubes  for 5 min using shake master NEO . After centrifugation using a high speed refrigerated micro centrifuge (TOMY MX-300) at 14,000 r.p.m. at 4°C, 250 uL supernatant was dried up in 96 well plate and the residue was dissolved in 120 uL ultrapure water . One uL of the solution was subjected to widely targeted metabolome analysis  by LC-MSMetabolites were extracted by homogenizing lyophilized callus in 500 uL of the extraction solution (methanol: milliQ water = 4:1) per 2 mg dry weight in 2.0 mL sampling tubes using Mixer Mill MM300. After centrifugation at 15,000 r.p.m. at 25°C for 10 min, the 400 uL supernatant was used for the analysis performed according to the protocol based on the EZ:faast amino acid derivatization technique for GC-MS  with slight modification. The reagent 1  was diluted to 10-fold while the reagent 6 (re-dissolution solvent) was added only 50uL to concentrate amino acid concentrations in samples. Then, 1 uL of solution was subjected to amino acid analysis by GC-MS using GCMS-QP2010 Plus .t continuous random variable based on a survival function were calculated for comparing model simulations with experimental data.The correlation coefficients, testing for the significance of the correlation coefficients, and student's http://www.genome.jp/kegg/) [http://arabidopsis.org/tools/aracyc/) [Information for metabolic pathways including their inhibition and activation was assembled from KEGG (p/kegg/) ,38 and Aaracyc/)  databaseThe present study employs a GMA-system model to which the U-system approach was applied for characterizing metabolic behaviors in a large-scale metabolic reaction network related to aspartate-derived amino acids, namely, aspartate, lysine, threonine, and methionine. The effects of feedback inhibition and activation were also included based on information available from the literature and pertinent databases ,40. KineThe authors declare that they have no competing interests.SN and MYH conceived the experimental concepts and designed callus culture experiment. KS, EOV, FS and MYH conceived the theoretical concepts and designed modeling approach. YC, YY and HO planned and performed callus culture experiments. YS conducted metabolome analysis by LC-MS. KS conducted amino acid analysis by GC-MS, and performed modeling and simulations. KS, TF, SN, EOV, FS and MYH performed data analyses. KS, SK, HO, TF, SN, EOV, FS and MYH performed data interpretation. KS, YS, SN, EOV, FS, MYH wrote and edited the manuscript. All authors read and approved the final manuscript.X1 and X2 represent metabolites whereas Y1 and Y2 represent enzyme activities for the X1 influx and X2 efflux, respectively. Figure S2. Comparisons of time courses of X1 and X2 obtained by the Michaelis-Menten model and those by the simplified U-system approach of the corresponding GMA model. The x-axis represents time, while the y-axis represents the concentrations of iX. The red lines pertain to the actual system in left and bottom axes whereas the blue dotted lines are for U-system in right and top axes. a The X1 U-system concentration compared with real concentration when the values of X1 was increased two-fold at t=0. b The X2 U-system concentration compared with real concentration when the values of X1 was increased two-fold at t=0. c The X1 U-system concentration compared with real concentration when the values of X2 was increased two-fold at t=0. d The X2 U-system concentration compared with real concentration when the values of X2 was increased two-fold at t=0. Figure S3. Normalized concentrations of i Xwith variations of parameters i αwhich value from 0.5 (red), 1, 5, 10, 15, 20, 25, 50, 75 to 100 (blue). Figure S4. Normalized concentrations of i Xwith variations of parameters i βwhich value from 0.5 (red), 1, 5, 10, 15, 20, 25, 50, 75 to 100 (blue). Figure S5. Normalized concentrations of i Xwith variations of parameters ij gwhich range from 0.1  to 1.0 . Figure S6. Normalized concentrations of i Xwith variations of parameters ij hwhich range from 0.1 (red) to 1.0 (blue).Usystem_SupplementaryInformation.pdf. Additional figures for the branched pathway model. Figure S1. Linear pathway with inhibition (⊖). Click here for fileArabidopsis model.Usystem_SupplementaryModel.pdf. The details for Click here for fileUsystem_SupplementaryFigures.pdf. The U-system simulations comparing with experimental data from metabolome and amino acids analysis.Click here for file


Rhodosporidium toruloides can accumulate lipids up to 70% of its cell mass under certain conditions. However, our understanding of lipid production in this yeast is still much limited, especially for growth with mixed substrates at the level of metabolic network. In this work, the potentials of several important carbon sources for TAG production in R.toruloides are first comparatively studied in silico by means of elementary mode analysis followed by experimental validation.Microbial lipids  have received large attention for a sustainable production of oleochemicals and biofuels. R.toruloides was reconstructed based on a combination of genome and proteome annotations. Optimal metabolic space was studied using elementary mode analysis for growth on glycerol, glucose, xylose and arabinose or in mixtures. The in silico model predictions of growth and lipid production are in agreement with experimental results. Both the in silico and experimental studies revealed that glycerol is an attractive substrate for lipid synthesis in R. toruloides either alone or in blend with sugars. A lipid yield as high as 0.53 (C-mol TAG/C-mol) has been experimentally obtained for growth on glycerol, compared to a theoretical maximum of 0.63 (C-mol TAG/C-mol). The lipid yield on glucose is much lower  vs. 0.58 (predicted) C-mol TAG/C-mol). The blend of glucose with glycerol decreased the lipid yield on substrate but can significantly increase the overall volumetric productivity. Experimental studies revealed catabolite repression of glycerol by the presence of glucose for the first time. Significant influence of oxygen concentration on the yield and composition of lipids were observed which have not been quantitatively studied before.A simplified metabolic network of R.toruloides and its detailed in silico analysis for growth on different carbon sources for their potential of TAG synthesis. Experimental studies revealed the phenomenon of catabolite repression of glycerol by glucose and the importance of oxygen supply on the yield and composition of lipids. More systematic studies are needed to understand the mechanisms which should help to further optimize the lipid production in this strain of industrial interest.This study provides for the first time a simplified metabolic model of The online version of this article (doi:10.1186/s12934-015-0217-5) contains supplementary material, which is available to authorized users. During the past years fuel production from biomass has gained enormous interest due to the escalating cost and scarcity of fossil fuels. Biodiesel industry has become important and the use of plant oils as raw materials is not ecologically sustainable because of the relatively high production costs and their competition with global supply of food. Despite the expected high production capacity of biodiesel the anticipated target has increased at a slower rate , mainly nd generation biofuels based on cheaper and more abundant lignocellulosic biomass. In fact, several oleaginous microorganisms were reported for efficient lipid production using industrial wastes and biomass hydrolysate [On the other hand, microbial lipids are being explored as raw materials for the production of biodiesel and functional oils with comparable properties of those produced from plant oils -11. Morerolysate ,13-18. SCryptococcus albidus, Lipomyces lipofera, Lipomyces starkeyi, Rhodosporidium toruloides, Rhodotorula glutinis, Trichosporon pullulan, and Yarrowia lipolytica [R. toruloides and R. glutinis were shown to be the most promising. Y. lipolytica was also proven to be a potential lipid producer, especially after improvement with genetic tools.Several yeast strains are known for lipids production, which include polytica . Ageitospolytica  comparedRhodosporidium toruloides has a high capability for growth and lipid synthesis on a range of carbon sources from glucose, fructose and xylose to glycerol [w/w) in cell mass of R. toruloides. Its ability to simultaneously assimilate sugars, especially glucose and glycerol has not been studied in detail. Studies on a closely related species R. glutinis showed that glucose and glycerol can be utilized simultaneously with preference toward glycerol which is similar to Y. lipolytica [The red yeast glycerol -22. Lipipolytica .R. toruloides grown on different substrates and substrate mixtures, using detailed biochemical knowledge on genome scale. Elementary mode analysis was used to elucidate the optimal pathway and the various fluxes for lipid accumulation from different substrates. Validation experiments were then performed and the kinetics of growth, lipid production and substrate uptake were evaluated. Experiments with biomass hydrolysate as pure substrates or with glycerol were also compared. Since lipid production is a process requiring intensive reducing power and energy, the control of oxygen supply on lipid accumulation and composition is important and studied in a well-controlled bioreactor system. An understanding of these metabolic processes can open doors for metabolic engineering of this yeast and for process optimization.With substrate cost and availability being continually changing, the utilization of multiple feed stocks is crucial for process viability. Therefore the aim of this study was to analyze the metabolic network and fluxes of in silico modeling of R. toruloides. With the genome annotation and other metabolic capacities in available literature and experiments, a draft metabolic network model was validated and curated manually until a high-quality metabolic network model of R. toruloides was constructed . The numbers of elementary modes obtained from the metabolic network for each substrate are shown in Table The large quantity of information featured in public databases, like details about genomes, pathways and proteins were first used for the reconstruction of the metabolic network and the −1 on the basis of an assumed TAG molecule size of 51 carbons . Taking the molecular weight of the assumed TAG (C51H92O6 = 801.27 g.mol−1) into account the resulting maximum yield is 0.30 g.g−1 glucose. For the production of one mol of TAG, 42 moles of NADPH and 21 moles of ATP are required. From the flux distribution map . About 10% ATP is generated by the respiratory chain reaction using the mitochondrial NADH.With glucose as the sole carbon and energy source, the computed optimum flux distribution is shown in Figure 2 formation. Glycerol is channeled into glycolysis via the dihydroxyacetone to glyceraldehydes 3-phosphate. Most of the fluxes pass through the lower part of the glycolysis into the pyruvate dehydrogenase complex. Two more optimal modes (data not shown) were identified where similar maximum TAG yields were observed with a succinate to fumarate interconversion in the mitochondrion and cytoplasm. The required ATP is also generated by both the respiratory chain reactions in the mitochondrion.On the other hand, with glycerol as the sole substrate Figure , the NADSimilarly, the optimal flux distributions with xylose and arabinose as substrates are shown in Additional file R. toruloides were performed using blend of substrates. The maximum TAG yield obtained is 0.58 Cmol. Cmol−1 substrate with a blend of glucose and glycerol , whereas glycerol as a sole carbon source has the lowest CO2 production (30.7 mol/mol TAG), indicating that glycerol is a desirable substrate in terms of efficiency of carbon utilization. CO2 production is proportional to the flux entering into the PP pathway as clearly observed from the in silico predictions.Using the same method, optimal flux distributions and EFM analysis with the proposed metabolic network of l Figure , comparein silico predictions regarding the use of different substrates an initial set of cultivations was performed using glucose and glycerol as the sole carbon and energy source. The time profiles of the cultivations are shown in Figure To compare the −1 compared to 0.12 h−1 with glycerol as the sole carbon source. The lipid concentration on the other hand, was similar in both substrates  of cell mass. On the other hand lower cell mass but higher lipid content was observed with glycerol and a maximum lipid content of 57% (on cell mass basis) was achieved. Moreover, the lipid yield on glycerol consumed (0.27 g.g−1) is more closer to the theoretical maximum value (0.32 g.g−1) predicted than the lipid yield on glucose . It should be emphasized that the maximum yield of TAG given in Table R. toruloides strains on different substrates and conditions. The lipid yield on glucose could be improved by proper process control, especially by applying nitrogen or phosphorous limitations as demonstrated in literature. We found in this work that the lipid yield on glucose can be significantly improved by using blend with glycerol.The results shown that glucose supported a higher cell mass concentration with a maximum specific growth rate of 0.16 hin silico analysis was all done with a fixed P:O ratio of 1.2. The effects of oxidative phosphorylation (with varied P:O ratio) on TAG yields using glucose as a substrate were analyzed using the proposed model. The change in P:O ratios (from 1.2 to 2) neither showed significant effect on the TAG yields (from 0.58 to 0.60 Cmol.Cmol−1 glucose), nor cell mass yield (0.67 to 0.71 Cmol.Cmol−1 glucose), respectively. Hence, it can be concluded that ATP generated by oxidative phosphorylation is not a major limiting factor for TAG synthesis. In agreement with the in silico analysis, controlling the oxygen concentration at 50% air saturation in the fermentation broth of R. toruloides grown either on glucose or glycerol throughout the cultivation process did not have any significant effect on the yield  with higher lipid content . The lipid yields on the substrate consumed and the specific lipid productivities on cell mass are higher when glucose and glycerol are used in mixture rather than only glucose  with the lowest lipid content (32%). Similarly, with a closely related yeast strain R. glutinis, Easterling [R. glutinis. However, it should be stressed that, on mixtures of carbohydrates and with the sequential utilization of sugars, the sugar is being consumed with more nitrogen available (and hence more cell mass formation), followed by glycerol consumption during a period of nitrogen restricted growth which will have a positive effect on the lipid yield. Still, the mechanism of the positive role of glycerol for the lipid synthesis of cells grown in blends deserves more detailed studies. Glycerol can be utilized as a source of carbon and energy. But under certain conditions (e.g. in pO2-controlled culture with glucose as the sole carbon source), R. toruloides can produce glycerol extracellularly up to 5 g/L (data not shown). The two most important functions of glycerol synthesis in yeast are related to redox balancing and the hyperosmotic stress response [Saccharomyces cerevisiae, production of glycerol occurs to maintain the redox balance. Interestingly, glycerol production is found to be higher in a minimal medium than in a complex medium [de novo synthesis of amino acids from glucose and ammonia leads to an excess of NADH which is re-oxidized by glycerol formation. In osmotolerant yeasts, glycerol plays a crucial role in their survival [S. cerevisiae adapts to hyperosmotic stress by activating the HOG signaling cascade, which controls glycerol accumulation, production and import. Moreover, it was also shown that glycerol transport depends on the strain and the growth conditions. Glycerol production has been never reported in R. toruloides, and hence transcriptomic analysis is being further performed in our laboratory.In the above blend substrate fermentation experiments, glucose was used at a concentration of 10% of the added carbon source. The effect of different combinations of the substrates on the lipid yield was further investigated in flask experiments. As compared to mono-substrate fermentation with glucose, a 26% increase of lipid yield was observed if glycerol is added , about 65% of the fatty acid measured is unsaturated (oleic acid and linoleic acid) if glycerol or blend are used, compared to 57% of saturated fatty acids  if glucose is the sole carbon source. Oxygen limitation has significantly influenced the fraction of saturated and un-saturated fatty acid composition in the lipid produced by R.toruloides especially on glycerol or mixed substrates. Oxygen controlled conditions derived fatty acid compositions that are suitable for biodiesel conversion [The effects of different growth substrates and culture conditions on the fatty acid composition were also studied Figure . In oxygR. toruloides is a known lipogenic yeast and the results presented here confirm its ability to accumulate over 60% of its cell mass as lipid. However, lipid accumulation was strongly affected by the nature of the carbon source provided. The recently sequenced and annotated genome of R. toruloides, its proteomic analysis and the available protein annotation have opened doors to understand the underlying mechanism of this organism for lipid production [R. toruloides. Maximum theoretical TAG yields on hexoses (glucose), pentose (xylose and arabionse), glycerol and on mixture of hexoses & glycerol, pentose & glycerol have been estimated  which is inactive in the predicted optimal flux distribution of glucose  on glucose and glycerol (0.32 g.g−1 to 0.27 g.g−1). However, the theoretical maximum yield retained to 0.30 g.g−1 on glucose and 0.32 g.g−1 on glycerol if a NADP-dependent acetaldehyde dehydrogenase (ALD6) is incorporated. This enzyme constitutively catalyzes the conversion of acetaldehyde to acetate, generating an NADPH in the cytoplasm. Another alternate route for supplying NADPH as proposed by Ratledge [−1 glucose. A third possible target could be a heterologous NADPH generating enzyme or an endogenous engineered NADPH generating enzyme, both in the glycolytic pathway [One of the key processes for fatty acid biosynthesis is the provision of reducing power (e.g. NADPH) to reduce the acetyl group and channel it into the acyl chain of fatty acid. In c enzyme  and the c enzyme . In R. te Figure . A singlRatledge  can be a pathway  which coRhodotorula glutinis ATCC 204091 [GOT2B1. This protein is 84% identical to an uncharacterized protein of R. toruloides (RHTO_06438). A theoretical analysis of the metabolic implications of a transhydrogenase reaction was investigated using the R. toruloides model. About 10% higher theoretical maximum yields were calculated on all the substrates when a transhydrogenase activity was introduced  in C 204091  with a U342 in C in silico analysis for determining and understanding the potential and metabolic pathways for lipid production in R. toruloides grown on different substrates, especially for substrate blends. Cultivations of R. toruloides were carried out with different substrates and in a well-controlled bioreactor system. The experimental results are in general agreement with model predictions in terms of lipid yield.The present work describes the successful application of reconstruction of metabolic network and it’s The constructed metabolic model can be used to guide further optimization of lipid synthesis in this strain. The maximal lipid yield experimentally achieved is still significantly below the theoretical maximum, especially for growth on glucose (0.29 vs. 0.58 C-Mol/C-Mol) and its blend with glycerol. Several strategies to increase the lipid yield are identified and discussed with the help of the metabolic model.R. toruloides DSMZ 4444 was used for the current study. The strain was maintained at −80°C on potato dextrose medium with 20% glycerol (v/v). The medium for seed cultures and main cultures was a nitrogen limited medium which is similar to that reported previously [3 and CaCl2 solutions and inoculated immediately. Spruce BH  was also used in co-substrate fermentation with glycerol. An enzymatic hydrolysis of spruce was done without buffer. The hydrolysate was then heated at 80°C for 15–20 min to inactivate the enzymes. The supernatant was removed and filtered with a centrifuge with filter bag. The sample was then concentrated by vacuum evaporation at 60°C. The concentrated hydrolysate contained 550 g/L glucose and 35 g/L xylose.eviously . Carbon Seed cultures and cultivations in flasks were performed in baffled shake flasks incubated at 30°C and 180 rpm for 24 h. Batch cultivations were performed in a 1.5 L well-equipped parallel bioreactor system  with 1 L initial working volume. Cultivations were started by inoculating 30 mL (3%) from the seed cultures grown for 24 h. pH was maintained at 6.0 using 5 N NaOH and 2 M HCL. Dissolved oxygen was maintained at 50% air saturation. Carbon dioxide evolution rates and oxygen uptake rates were automatically evaluated by the online DASGIP off gas analyzing system equipped with sensors from Bluesens.-1, [2SO4 and detection via refractive index or by UV absorption at 210 nm. Ammonia concentration in the supernatant was determined by photometric measurements using a kit from Macherey Nagel, Germany. GC analysis of the fatty acid methyl esters was performed as reported [Cell growth was recorded as optical density at 600 nm. Cell mass was harvested during the cultivations after centrifugation . Cell dry weight was determined gravimetrically after drying the harvested cells in an oven at 80°C to a constant weight. Extraction of lipids was performed with a modified method described previously using Folsch solution  as shown in the reaction network , the influx of substrates  and efflux of products  are considered. The P/O ratio is taken as 1.2 and the cell mass equation is taken from S.cerevisiae’s data [A metabolic network with the most important reactions of e’s data . EFMs wee’s data  in MATLAe’s data ,46.Figur−1.h−1 normalized to the substrate uptake rate.The metabolic network with D-glucose as a substrate comprises of 69 reactions, of which 27 are reversible with 61 internal metabolites and 8 external metabolites. With glycerol as a sole carbon source, the network is comprised of 71 reactions (28 reversible) of which 61 are internal and 8 external metabolites. The network with D-xylose and L-arabinose comprises 71 and 73 reactions respectively. Theoretical maximum yields were calculated based on the obtained fluxes. All fluxes are given in mmol.g