Motivation: One of the challenging questions in modelling biological systems is to characterize the functional forms of the processes that control and orchestrate molecular and cellular phenotypes. Recently proposed methods for the analysis of metabolic pathways, for example, dynamic flux estimation, can only provide estimates of the underlying fluxes at discrete time points but fail to capture the complete temporal behaviour. To describe the dynamic variation of the fluxes, we additionally require the assumption of specific functional forms that can capture the temporal behaviour. However, it also remains unclear how to address the noise which might be present in experimentally measured metabolite concentrations.Results: Here we propose a novel approach to modelling metabolic fluxes: derivative processes that are based on multiple-output Gaussian processes (MGPs), which are a flexible non-parametric Bayesian modelling technique. The main advantages that follow from MGPs approach include the natural non-parametric representation of the fluxes and ability to impute the missing data in between the measurements. Our derivative process approach allows us to model changes in metabolite derivative concentrations and to characterize the temporal behaviour of metabolic fluxes from time course data. Because the derivative of a Gaussian process is itself a Gaussian process, we can readily link metabolite concentrations to metabolic fluxes and vice versa. Here we discuss how this can be implemented in an MGP framework and illustrate its application to simple models, including nitrogen metabolism in Escherichia coli.Availability and implementation: R code is available from the authors upon request.Contact:j.norkunaite@imperial.ac.uk; m.stumpf@imperial.ac.ukSupplementary information:Supplementary data are available at Bioinformatics online. In gene expression assays, for example, we typically measure messenger RNA expression, but not the activity of transcription factors and/or the occupancy of transcription-factor binding sites. Similarly, in metabolomic analyses , key met13C and 15N metabolic flux analysis) metabolites through the metabolic network  belong to the armoury of non–parametric Bayesian methods and have been widely used to describe dynamical processes  and to ix (or concentrations) and fluxes Here we develop a more general framework that uses so-called derivative GPs (Gaussian process regression (GPR) can be applied to recover an underlying dynamical process from noisy observations. A GP defines a prior distribution over all possible functions, and to specify a GP, we need expressions for the mean and covariance function that describe the behaviour of the system output over time . Below wx and outputs z via functions, n-dimensional real-valued vectors. The observed values of the dependent variable, z, can be related to the independent variables, ε is a noise term, which is here assumed to be independent and identically distributed according to a Gaussian distribution, K,In a typical regression problem, we connect inputs ace a GP  prior ovI the identity matrix. The unknown set of hyper-parameters, θ, can be estimated from the data by evaluating the following log-likelihood function,Different functional forms can be chosen for the covariance function , either  methods .For any finite number of input (test) points, f evaluated at inputs y are jointly distributed as whey, it remains unclear how to deal with several variables simultaneously: if outputs are correlated then the standard GPR framework may fail in providing an adequate description.Although h(t), and the output z(t) can be expressed via convolution integral,h(t) must be absolutely integrable, i.e.Dealing with linear filters is central to signal processing where such filters describe a physical systems that can generate an output signal in response to a given input signal . Linear X(t) is specified to be a Gaussian white noise process, the output process, Z(t), will also be a GP.Then if the input M white noise processes as inputs, K outputs, kth output. As discussed previously, the observed variables might differ from expected variables owing to the measurement noise, and we thus considerSpecifying a stable linear time-invariant filter with GP model . A multiijC permits the definition of a positive definite symmetric covariance matrix C between K variables,Multiple-input multiple-output filters are able to capture the relationships between several variables iN the number of observations of variable i. Having defined the covariance matrix, we can use the log-likelihood, which has the form (1) for the inference of the hyper-parameters i, predictions can be made using the appropriate marginal distribution, which is Gaussian, with mean Here X(t) is a white noise GP, h(t) is a kernel function and W(t) is an additive noise, it is easy to formulate the expression of a derivative process. Taking a derivative of Y with respect to t, it is possible to obtain a new process U that is also a GP  with a derivative kernel function g(t). This definition enables us to consider derivative processes and the corresponding original processes as a collection of dependent GPs. This is true because the derivative processes and the original processes are derived from exactly the same input, X(t).Thus, it is possible to construct the derivative process by convolving a white noise GP iUAutocovariance function of derivative process iU and jUCross-covariance function between two derivative processes iY and corresponding derivative process iUCovariance between original process iY and derivative process jUCovariance between original process To construct a dependent model for several related variables R denote a block matrix,H denoteZ1 and Z2 evaluated at a finite set of test points ijDDC consists of auto/cross-correlations between derivative variables U1 and U2. The matrices H are building components of the overall covariance matrix K, which is symmetric and positive definite,Let Y, functions Z and derivatives U,At a finite number of input points i and its derivative process at any input point Evaluating a GP posteriorRwww.r-project.org.To demonstrate the performance of derivative processes, we consider two simulation examples—a system of two oscillating signals and a simple model of linear metabolic pathway—before turning to a more complicated metabolic process and, finally, some real metabolic network data. The derivative processes can be used to address the flux estimation problem from time course data. Here GPs describe the dynamics of metabolites, and the corresponding derivative processes capture the functional forms of the associated fluxes. Below, all examples were implemented using the free statistical computing platform A is the amplitude, iA of each Gaussian kernel to be A simple oscillating signal can be expressed as lgorithm . DependeSupplementary Material for details), which is summarized in x1 to x2 is negatively regulated by metabolite x3, and x3 increases the transformation of x2 into x3. A set of ordinary differential equations (ODEs) can be used to describe the dynamics of these two metabolites, x2 and x3 ,Next we consider a linear metabolic pathway with two regulatory signals ; x3 inhibits the conversions of x1 into x2, and x2 positively regulates reaction v4. The following ODE model describes the dynamics of the metabolites that are involved in this pathway,v4,We now turn to an example of metabolic pathway that was originally proposed by  pathway b, the chv1 and v4. In this example, we will focus only on estimation of fluxes v2 and v3 from available data rather than try to address a uniqueness problem of v1 and v4.These expressions define a system of linear equations that is underdetermined, as we have more fluxes to estimate than available equations, and it cannot be solved using standard Gaussian elimination techniques. For this reason, additional information is required to uniquely determine fluxes x2 and x3 with added random Gaussian noise x2 and x3 dynamics; the green lines describe the derivatives of the same metabolites and can be understood as a slope estimates. In v2 and v3 under consideration of pathway The above ODE model enables us to generate simulated time course data using the initial conditions E. coli, where we have measurements of the abundance of several key metabolites involved in nitrogen assimilation. Nitrogen is one of the key chemical elements that acts as a nutrient for the cells; ammonium is a preferred source of nitrogen for E. coli growth  that operates during cell growth in ammonium-rich environments, and glutamine synthetase-glutamate synthase (GS-GOGAT) that operates during cell growth in low-ammonium conditions (α-ketoglutarade (glutamate (GLU) and glutamine (GLN) metabolites over the time after ammonium spike; red dots correspond to a wild-type (WT) E. coli metabolic measurements, and in squares—isogenic glnG deletion (ΔglnG) measurements. Below we focus on the pathway summarized in v3 and v4 can be summarized by the overall flux v3 that describes the flow from GLU to GLN, as there is not enough information to discriminate between them. From the pathway, we can construct a system of linear equations that describe the dependencies between fluxes and metabolites,Finally, we apply our technique to the experimental data from GLU and the third one describes additive noise; GLN is modelled similarly. However, GLU is modelled as the sum of four GPs, where the first three describe GLU; the dependence between GLU and GLU and GLN; and the fourth is an additive noise. Choosing kernel functions to be Gaussian E. coli, and green lines for ΔglnG. Using the relationship v1, v2 and v3 . In E. coli, glnG encodes the transcription factor, NtrC (nitrogen regulator) that controls GS expression levels, and in its active form, GS catalyses glutamine synthesis . Because there is less enzyme available to catalyse the reaction in ΔglnG, the flux v3 in the mutant will be noticeably reduced compared with the WT flux v3 .To evaluate our predictions, we can compare flux Flux estimation has become central to many analyses into the metabolic processes and mechanisms. Typically, the estimates for a set of fluxes are obtained in a point-wise manner at discrete time points. It is clear that this fails to capture the temporal behaviour of the fluxes and additional consideration of parametric models is compulsory to fully explain the fluxes; further, this approach is susceptible to noise that is present in experimentally measured metabolite data.Here we have addressed these problems and proposed a novel non-parametric Bayesian approach to modelling metabolic fluxes. This is based on MGPs that enable the construction of derivative processes. Because the derivative processes and original processes share the same input source, we can complement the dependent GP model and make joint predictions about original and derivative processes at any finite number of input points. Such derivative processes can be applied to characterize the temporal behaviour of metabolic fluxes from time course data—without having to make reference, e.g. transcriptomic data, to explain temporal variation—and here we have demonstrated the applicability on simple models and a real-world example.GPs, including our approach, propagate uncertainty in line with the assumed covariance structures. This can lead to large confidence intervals, especially if the dependencies among different observations are not considered explicitly. With increasing number of metabolic species within the pathway, the derivative process approach might become computationally costly due to the inference of a large number of hyper-parameters and a matrix inversion step; however, this limitation potentially might be addressed by considering a sparse approximation for the full covariance matrix of all metabolic species . These c


Toxoplasma gondii is a human pathogen prevalent worldwide that poses a challenging and unmet need for novel treatment of toxoplasmosis. Using a semi-automated reconstruction algorithm, we reconstructed a genome-scale metabolic model, ToxoNet1. The reconstruction process and flux-balance analysis of the model offer a systematic overview of the metabolic capabilities of this parasite. Using ToxoNet1 we have identified significant gaps in the current knowledge of Toxoplasma metabolic pathways and have clarified its minimal nutritional requirements for replication. By probing the model via metabolic tasks, we have further defined sets of alternative precursors necessary for parasite growth. Within a human host cell environment, ToxoNet1 predicts a minimal set of 53 enzyme-coding genes and 76 reactions to be essential for parasite replication. Double-gene-essentiality analysis identified 20 pairs of genes for which simultaneous deletion is deleterious. To validate several predictions of ToxoNet1 we have performed experimental analyses of cytosolic acetyl-CoA biosynthesis. ATP-citrate lyase and acetyl-CoA synthase were localised and their corresponding genes disrupted, establishing that each of these enzymes is dispensable for the growth of T. gondii, however together they make a synthetic lethal pair. Toxoplasma gondii, which chronically infects about 30% of humans worldwide. Through a semi-automatic reconstruction we have developed ToxoNet1, a comprehensive metabolic model of Toxoplasma gondii, and we have performed an extensive computational analysis to explore the properties of Toxoplasma metabolism. In particular, we have identified and classified the minimal set of substrates the parasite utilizes for growth, along with the genes and pairs of genes that are essential for cellular functions such as growth and energy metabolism. We have validated our computational predictions that the genes encoding acetyl-CoA synthase and ATP-citrate lyase enzymes serve complementary function but their simultaneous disruption does not allow cell growth. This study presents a number of hypotheses generated using ToxoNet1, which can lead to the discovery of novel antiparasitic drug targets.Understanding the metabolism of disease-causing microorganisms can guide drug design through the identification of metabolic enzymes whose activity is indispensable for important cellular functions. Such understanding can come from the reconstruction and computational analysis of metabolic networks. In this study we have focused on the metabolism of an opportunistic human pathogen,  Toxoplasma gondii, is a ubiquitous opportunistic pathogen responsible for one of the most common parasitic infections in humans and warm-blooded animals. It is estimated that up to 30% of the human population is chronically infected [The phylum of Apicomplexa comprises a large number of obligate intracellular parasites that can infect organisms across the whole animal kingdom. An important member of this phylum, infected . Toxoplainfected .T. gondii possesses a complex life cycle, which is composed of an asexual replicative stage in the intermediate host and a sexually replicative stage within the definitive feline host. During the asexual phase, T. gondii can switch from a fast-replicative tachyzoite form, which causes acute disease, to a slow-growing bradyzoite stage, which forms cysts that are characteristic of chronic infection. The encysted, slow growing form is resistant to commonly used drugs and immune system attack. Few efficient medicines are available to treat toxoplasmosis and they mainly treat the acute phase of the disease. Furthermore, poor tolerance of these drugs promotes the search for novel drug targets.Plasmodium species, T. gondii is able to invade and asexually replicate within virtually any nucleated cell of warm-blooded animals. The broad range of cells amenable to infection by T. gondii reflects the plasticity of the parasite’s metabolism and versatility in accessing and utilising nutrients to support its intracellular growth [T. gondii.Unlike other notorious apicomplexan parasites that infect a narrow range of host cell types, such as the r growth ,4. The cT. gondii replication and which of these are dispensable; 2) in which intracellular compartments do the enzymatic activities annotated at the genome level occur; 3) which of these enzymatic activities are indispensable for replication or other vital processes of the parasite. While achievable, the application of high-throughput gene knockout or knockdown strategies to globally determine gene essentiality in T. gondii remains a major undertaking.Currently, no adequate experimental approaches exist to answer comprehensively the following important questions: 1) what substrates are available within the host cell that are necessary for in silico) metabolic modelling coupled with systematic analyses facilitates the study of biological systems. This modern approach of systems biology has been extensively exerted to predict gene essentiality in various bacteria, including numerous pathogenic species [In silico metabolic models offer a cost-effective pipeline to identify putatively indispensable metabolic processes that, in the case of pathogens, represent potential targets for therapeutic intervention [Computational  database. The databases used for identification of “gap” reactions were KEGG [For the compartmentalization process we consulted the models of lciparum ,13 and ulciparum –16 as weere KEGG  and LLAMere KEGG . Recon 2ere KEGG  was usedReconstruction of the metabolic network was achieved by combination of the state-of-the-art algorithm for a semi-automated generation of metabolic networks  and a coThe reconstructed metabolic network accounted for 527 open-reading frames (ORFs) that were linked to 867 unique metabolic reactions present in the KEGG  databaseIn ToxoNet1, the majority of reactions were associated with genes that encode corresponding metabolic enzymes . IntraceT. gondii and present within ToxoNet1, the transferases (class 2) and oxidoreductases (class 1) were the most numerous . Hydrolases (class 3), lyases (class 4) and ligases were significantly less represented , experimental data was available only for a limited number of proteins: 60 out of the 527 included in ToxoNet1. Thus the only reasonable option for building a compartmentalized metabolic model was to make use of sequence-based localization predictors. To define putative localizations of the enzymes with no experimental evidence we generated sequence-based predictions using three software algorithms: TargetP [Relatively straightforward experimental methods exist to determine the localization of proteins in . gondii , however TargetP , MitoPro TargetP , and Api TargetP . We thenComparison of these predictions with 60 experimentally established subcellular localizations available from ApiLoc uncovered two issues: (i) not all the computational predictions matched their experimental data . This enzyme interconverts IPP into its more reactive isomer—DMAPP. In T. gondii, as well as in Plasmodium spp. this enzyme is absent [In ToxoNet1 a majority of the reactions (c.a. 69%) occur in the cytosolic compartment. We also considered this compartment as a default for enzymes with a subcellular localization remaining unclear from the rganelle . We connrganelle ; (ii) exs absent . Thus, bcheckTasks and fitTask functions), which verifies that specific tasks are fulfilled and, if necessary, it fills the gaps in the metabolic pathways to meet the required functionality.A major limitation of all algorithms for automatic reconstruction of metabolic models is the number of missing reactions  that disrupt metabolic pathways. The RAVEN Toolbox offers a functionality called metabolic tasks (de novo synthesis was possible in the model). The second group contains the metabolites whose synthesis required a precursor with a specific moiety (e.g. hypoxanthine or other source of purine moiety for purine nucleotides and their derivatives). The third group are the biomass constituents that could not be produced even with the maximum set of host-supplied substrates, and therefore they were directly taken up from the host .We created metabolic tasks for the synthesis of every metabolite included in the biomass reaction  from the list of host-supplied molecules, enabled production of the necessary biomass precursors in ToxoNet1. Nevertheless, several biomass building blocks could not be produced in the model even when all the 230 host-supplied substrates were provided simultaneously, indicating that the parasite is likely auxotrophic for these molecules.According to ToxoNet1, no acids . When tafillGaps) and manual gap-filling based on the information from the LLAMP database [In the cases when metabolic tasks could not be accomplished despite literature evidence (mainly acquired from the LLAMP database ), we perdatabase . For insdatabase . ToxoNetT. gondii. We manually built such a model prior to this study based on the genome annotation from ToxoDB and refined it according to the relevant primary literature. This model contained a number of recent experimental findings as well as manually assembled complex gene-reaction associations. Among these were the pyruvate dehydrogenase activity that can be carried out by the branched-chain keto-acid dehydrogenase complex (BCKDH) in the mitochondrion [Importantly, some of the information necessary for a metabolic model could not be easily deduced from the genome sequences alone. This is why we merged the draft output metabolic network from the RAVEN Toolbox with a small-scale model of central carbon metabolism in hondrion , mitochohondrion –30 and tin silico is the unknown range of metabolites available for the parasite within the host cell. As extracellular replication (axenic cultivation) of T. gondii is not possible, it remains undefined which of the substrates are dispensable for the parasite and which are not.One of the major challenges in simulation of parasite metabolism in silico, we developed a method to enumerate all of the smallest/ minimal metabolite sets , which could enable simulation of growth in ToxoNet1. In brief, the algorithm applied iterative rounds of biomass production using the fewest number of substrates possible. After each of the iterations we added a constraint to ensure that the next IMM included at least one substrate uncommon from the preceding ones .To address this issue T. gondii replication in ToxoNet1. We also observed a relatively large number (2592) of alternative sets of 19 substrates with 10 metabolites being constitutively present in all the IMMs. The other 9 substrates could be substituted by at least one other host-supplied metabolite  are listed in Gene essentiality predictions depend on the following important aspects of metabolism as represented in the model: (1) range of substrates that can enter the model (i.e. molecules that the parasite can take up from the infected host cell); (2) composition of the parasite cell represented as a set of biomass precursor molecules (the concept of biomass objective functions is explained in ); (3) thT. gondii observed experimentally in tissue culture, we chose to assess the importance of the two independent routes of cytosolic acetyl-CoA production in the rapidly dividing tachyzoite stage  by introducing a 3xTy-epitope tag at the C-terminal end of both genes in the RHku80ko (Ku80ko) background strain, which limits random integration in the genome hence facilitating recovery of homologous recombination events  monolayers. Indeed, both ACLko and ACSko parasites formed lysis plaques of similar sizes when compared to wild type (Ku80ko) parasites  in Ku80ko . For botarasites . Moreovearasites . FinallyT. gondii as suggested by ToxoNet1, we first attempted to disrupt ACL by single homologous recombination in the middle of the ORF in the ACSko parasite background , the signal was lost immediately after the first passage of these cultures (P1 and P2)  indicatiT. gondii FASI was disrupted in wild type RH strain parasites by CRISPR/Cas9 mediated genome editing [To determine whether the deleterious phenotype and loss of pellicle integrity could be attributed to a block in type I fatty acid synthesis following depletion in cytosolic acetyl-CoA, the gene coding for  editing . TrangenT. gondii, which can simulate growth of the parasite in silico and infer essentiality of its genes. It considerably extends the scope of previous work [T. gondii, in the present study we reconstructed an independent model that represents the potential scope of the metabolic capabilities of the parasite independently of the life-stage and strain-type. Aiming at the most reliable gene essentiality predictions we used many alternative assumptions on the range of accessible substrates and transportability of metabolites. We have also achieved more comprehensive coverage of all the metabolic capabilities of the parasite and implemented functional gene-protein-reaction associations enabling rigorous gene deletions studies. Hereafter we provide a more in depth discussion on the key aspects of our approach.ToxoNet1 constitutes a full genome-scale reconstruction of metabolism within ous work  and contP. falciparum [There are two distinct approaches for model reconstruction process that are commonly referred to as top-down and bottom-up . The toplciparum  used as lciparum ) as wellT. gondii protein-coding genes, which is comparable but greater than in the genome-scale models of P. falciparum (7%) [L. major (6.7%) [Cryptosporidium hominis (5.5%) [T. gondii [P. falciparum [T. gondii possesses broader metabolic capabilities  of the rum 7%) , L. major (6.7%)  and Cryp% , L. ma. gondii . Comparilciparum ,9,13 con% of the bilities . These d-141 and bit-score 479). Accordingly, an orthologous gene (PF3D7_0621200) is annotated as pyridoxine biosynthesis protein (PDX1) in P. falciparum, yet without an E.C. number assigned. There was also a set of genes with low confidence in their function, despite their annotation in ToxoDB . These two examples demonstrate the potential of the RAVEN Toolbox to improve genome annotation and produce models with confidence estimates that enable evaluation and, potentially, future corrections of the existing models.ToxoNet1 contains confidence estimates  for each gene annotated as encoding certain metabolic activities. This has allowed us to suggest a number of metabolic functions for genes that did not have annotations with E.C. numbers in the ToxoDB database . For exaToxoNet1 contains 260 unique dead-end metabolites, which currently can be only produced or only consumed in the network. We kept them in the model in order to allow future developments and expansion of the scope of the model. Further definition of the metabolic routes can utilise these dead-end metabolites and contribute to a more complete understanding of the metabolic capabilities of the parasite. For instance, the tRNAs loaded with the respective amino acids were included to enable future extension of the model to the representation of protein synthesis.T. gondii. Our objective of this work is to provide ToxoNet1 as a resource for the community and therefore we avoided imposing constraints and hypotheses, which are not well-tested and confirmed that could contaminate the model and our results.We chose to impose relaxed constraints in terms of subcellular compartments due to rather high uncertainty in subcellular localisation of the enzymes as well as largely unknown capabilities of the parasite to transport metabolites across its organellar membranes. We assigned the enzymes with the corresponding reactions to their putative compartments and allowed a broad range of metabolites to be transported across the compartment boundaries. This approach to compartmentalisation ensures minimal bias in our results due to underestimated transport capabilities or incorrect assignment of enzymes to subcellular compartments. We expect subsequent refinements of ToxoNet1 with more stringent compartmentalisation as more reliable, high-throughput computational and experimental methods are becoming available for subcellular localisation of enzymes and functional annotation of transporter proteins in T. gondii, we implemented an algorithm that identifies and ranks the minimal number of substrates required for growth in ToxoNet1. The results indicate that uptake of as few as 19 of 230 substrates allows the model to produce all biomass building blocks. Moreover, we identified 2592 sets of 19 substrates that can allow growth, and 10 substrates common to all these sets . Among the alternative substrates we identified 7 carbon sources: five hexoses and two pentoses (ribose and deoxyribose), which can be incorporated into the metabolism by a ribokinase enzyme. Uptake of pentoses through a hexose transporter has been reported in the protozoan parasite L. major and may potentially represent an additional level of versatility in meeting the need of a carbon source, similarly to the previously observed in T. gondii utilization of glutamine [To understand the nutritional requirements of ese sets . These 1lutamine ,46. We cde novo biomass building blocks from glucose and inorganic substances. Interestingly, almost all the cofactors of metabolic enzymes, with the exception of pyridoxal phosphate cannot be produced de novo. Their synthesis required precursors that contained certain chemical moieties . Notably, T. gondii lacks the pathway for arginine synthesis, which can be produced by human cells, however arginine is growth limiting for human cells because its de novo synthesis is insufficient and thus supplemental uptake is required [Validation of genome-scale models using metabolic tasks is an approach developed to evaluate metabolic capabilities of the models in a systematic manner. To date it has been applied to several models ,47,48 fomoieties . This surequired . This suT. gondii can potentially produce. However, this pathway includes the enzyme homoserine dehydrogenase (E.C. 1.1.1.3), the encoding gene for which is not identified to date in the genome of the parasite. Data from ToxoDB suggests that the genes encoding the enzymes of the threonine biosynthesis pathway, namely aspartokinase (TGME49_227090), threonine synthase (TGME49_220840), homoserine kinase (TGME49_216640) and aspartate-semialdehyde dehydrogenase (TGME49_205420), are expressed at low levels in the tachyzoite stage. Homoserine kinase has been detected in the proteome of oocysts [T. gondii could be a conditional threonine auxotroph. Should threonine biosynthesis also be active in the other life stages it could represent a selective drug target for inhibition of parasite replication without affecting the mammalian host cells. Maintenance of some metabolite pools in T. gondii may be a result of both uptake and de novo production. Hence, if the complete set of genes of a metabolic pathway is present in the genome of the parasite, this pathway is not necessarily active and will not meet the demands of the parasite regarding the products of the pathway. Fox et al. showed that salvage of pyrimidine nucleotides from the host cell can support in vitro but not in vivo survival of T. gondii mutants with disrupted de novo pyrimidine synthesis pathways [T. gondii.Threonine is the only amino acid essential for human cells and which  oocysts , the inf oocysts . Taken tpathways . TherefoT. gondii. The earlier efforts to infer essentiality of genes in this parasite were reported by Gautam et al. [Our study represents the first model-based gene essentiality predictions for m et al. . Their am et al. ,54. NeveP. falciparum and 32 of them were predicted as essential in the existing metabolic models [T. gondii is currently scarce, thus, we could not test the majority of our essentiality predictions  have orthologs in the malaria parasite c models . Evidencdictions . However. gondii . The datWe predicted synthetic essentiality of 20 pairs of genes, which represent two distinct cases. In the first case the pair of genes encode two isoenzymes that catalyse the same reaction in the same compartment. For example, the genes TGME49_318580 and TGME49_285980 encode isoenzymes, which catalyse the phosphoglucomutase reaction (E.C. 5.4.2.2) and both were experimentally localised to the cytosol . This reT. gondii acetyl-CoA transporter (AT1) is localized in the membrane of the ER and is anticipated to deliver acetyl-CoA to the secretory pathway. It would be interesting to examine the importance AT1 for parasite survival. In contrast, the mitochondrion and the apicoplast should not be affected since these compartments have their own routes for production of acetyl-CoA: (i) in the apicoplast it is produced by the pyruvate dehydrogenase (PDH) complex [Moreover given that deletion of the genes coding for elongases previously reported  did not  complex , and , the enzymatic reactions associated with the corresponding KEGG orthology ID were added to the draft metabolic network. As a result we have obtained a set of metabolic reactions linked to genetic loci of T. gondii. At this stage the model did not contain information about either subcellular compartments, or about transport of metabolites. We next merged this model with a manually curated, small-scale metabolic reconstruction that we previously built based on the P. falciparum model [The reconstruction process started with generation of a draft metabolic network of database . Within database  orthologdatabase . In the um model .et al [Similarly to Huthmatcher et al ., we remT. gondii from the host cell cytosol, is the outermost compartment represented in ToxoNet1. Extracellular compartment of the model corresponds to the PV space. A eukaryotic organization of intracellular space of the parasite also includes a number of compartments, among which we chose to represent in ToxoNet1 the most relevant to metabolism, namely: mitochondrion, apicoplast and cytosol. The following sequence-based localization predictors were used to suggest putative subcellular localization of the enzymes: TargetP [T. gondii and P. falciparum in the cases when the latter were available (see The parasitophorous vacuole (PV) space, which secludes  TargetP   or Coenzyme A (CoA) moiety attached .de novo synthesis of ATP” was formulated as following: given unlimited uptake of glucose, oxygen, inorganic phosphate, sulfate and ammonium, can the model produce ATP. The model failed to accomplish this task, which is consistent with the literature knowledge about auxotrophy of T. gondii for purines [Testing metabolic tasks is a built-in functionality of the RAVEN Toolbox  meant fo purines . Thus, tWe simulated metabolism of the host cell using the most recent tissue-unspecific model of human metabolism . The Recde novo production in the parasite and sequestered towards biomass from the cytosol.In order to simulate replication of the parasite and assess the essentiality of genes, reactions and substrates, we assumed maximisation of flux through the biomass reaction to be the objective function of ToxoNet1. It represents cellular replication as a reaction that consumes pre-defined amounts of metabolites defined as small-molecule biomass precursors as well as energy in the form of ATP. We used the biomass reaction from the previous study  as a temFBA is a standard computational approach for exploration of the metabolic capabilities represented in constraint-based models; principles, computational implementation of FBA as well as the key assumptions are extensively described elsewhere .In the absence of clear knowledge on the scope of substrates that the parasite can take up from the host we made the following assumption: all the metabolites present in the host cell cytosol are potentially accessible for the parasite except those that are phosphorylated, bound to coenzyme A, acyl-carrier protein or carnitine. A list of molecules that satisfy these criteria was generated using the recent tissue-unspecific model of human metabolism Recon2  the lis.Minimal sets of metabolites necessary for the production of biomass were explored using an in-house developed mixed-integer linear programming algorithm. For each of the exchange reactions that allowed uptake of a substrate into the model (i.e. 230 host-supplied metabolites) we added one binary variable that denoted its utilization. Our algorithm solved the model subject to minimization of the sum of the binary variables thus yielding a minimal set of uptakes that allowed the model to simulate growth. After each iteration the algorithm added one new constraint to the model to assure that the following set would include at least one different uptake reaction compared to all the previously generated ones. The iterations were repeated until no more alternative sets of the same length could be found.-1). Similar approaches were used for double gene deletion studies—simultaneously blocking reactions associated with all pairs of genes that were not predicted as singularly essential. In reaction deletion simulations we blocked flux through every single reaction in ToxoNet1 one at a time. Subsequent attempts at achieving the wild-type doubling time in the absence of the reaction indicated whether the gene was dispensable or not.We performed simulation of gene deletion using a conventional approach  that impT. gondii tachyzoites (RHku80-ko (Ku80ko), RHku80-ko/ACS-ko (ACSko), RHku80-ko/ACL-ko (ACLko), RHku80-ko/ACL3Ty-LoxP3’UTRLoxP-U1 (ACL-lox), RHku80-ko/ACS-ko/ACL3Ty-LoxP3’UTRLoxP-U1 (ACSko/ACL-lox), RH/FASIko (FASIko)) were grown in confluent Human Foreskin Fibroblasts (HFF) and maintained in Dulbecco’s Modified Eagle’s Medium  supplemented with 5% foetal calf serum, 2 mM glutamine and 25 μg/ml gentamicin in a humidified incubator at 37°C with 5% CO2.All amplifications were performed with LA Taq (TaKaRa) polymerase and primers used are listed in Knock-in of ACS: (pKI-ACS-3Ty) The genomic fragment of ACS (TGME49_266640) was amplified using primers ACS-1 and ACS-2 prior to digestion with with KpnI and SbfI and subsequent cloning in the same sites of pTub8MIC13-3Ty-HXGPRT [SnaBI.y-HXGPRT  to introKnock-in of AT1: (pKI-AT1-3Ty) The genomic fragment of AT-1 (TGME49_215940) was amplified using primers AT1-1 and AT1-2 prior to digestion with KpnI and NsiI and subsequent cloning in the same sites of pTub8MIC13-3Ty-HXGPRT [HindIII.y-HXGPRT  to introKnock-in and knock-down of ACL: (pKI-ACL-3Ty and pKI-ACL-3Ty-LoxP-3’UTR-LoxP-U1) Genomic fragment of ACL (TGME49_223840) was amplified using primers ACL-1/ACL-2 and subsequently digested with KpnI and NsiI prior to cloning in the same sites of the pTub8MIC13-3Ty-HXGPRT for 3Ty-tag knock-in [XhoI.knock-in , or the knock-in . Prior tKnockout of ACS: (pTub-CAT-ACS-ko) around 1.5kb of the 5’ and 3’ flanking regions of ACS were amplified using primers ACS-3/ACS-4 and ACS-5/ACS-6 respectively. The 5’ flanking region was then cloned between KpnI and XhoI restriction sites of the pTub5-CAT and the 3’ flanking region between the BamHI and NotI sites. The plasmid was cut with KpnI and NotI prior to transfection.Knockout of ACL: (pTub-HXGPRT-ACL-ko) around 1.5kb of the 5’ and 3’ flanking regions of ACL were amplified using primers ACL-3/ACL-4 and ACL-5/ACL-6 respectively. The 5’ flanking region was then cloned between the KpnI and XhoI sites of the p2855-HXGPRT plasmid and the 3’ flanking region between the BamHI and NotI sites. The plasmid was cut with KpnI and NotI restriction enzymes prior to transfection.Frameshift knockout of FASI using CRISPR/CAS9 plasmid : This vector has been generated using the Q5 site-directed mutagenesis kit (New England Biolabs) with the vector pSAG1::CAS9-U6::sgUPRT as template (a gift from Dr. L.D. Sibley). The UPRT-targeting gRNA was replaced by the FASI (TGME49_294820) specific gRNA using the primer pairs gRNA-FASI/gRNA-rev (gRNA highlighted in red in hxgprt gene was used as a positive selectable marker in the presence of mycophenolic acid (25 μg/mL) and xanthine (50 μg/mL) for pKI-ACS-3Ty, pKI-AT1-3Ty, pKI-ACL-3Ty, pKI-ACL-3Ty-LoxP-3’UTR-LoxP-U1 and pTub-HXGPRT-ACL-ko vectors transfected in Ku80ko or ACSko, as previously described [Parasite transfections were performed by electroporation as previously described .The hxgpescribed .Ku80ko was transfected with pTub-CAT-ACS-ko and 20μM chloramphenicol was used to select resistant parasites.Resistant parasites were cloned by limiting dilution in 96 well plates and clones were assessed by genomic PCR.FASI locus, 30 ug of the FASI gRNA-specific CRISPR/CAS9 vector was transfected into wild type RH parasites. 48 hours after transfection, GFP positive parasites were sorted by flow cytometry and cloned into 96-well plates using a Moflo Astrios (Beckman Coulter). Individual clones were then analysed by sequencing.To efficiently disrupt the Genomic DNA was prepared from tachyzoites using the Wizard SV genomic DNA purification system (Promega). Correct integration of the different constructs into the genome of the various strains was determined by genomic PCR using GoTaq Green Master Mix (Promega).The antibodies used in this study were described previously as follows: polyclonal rabbit anti-GAP45, rabbit anti-TgProfilin , monocloParasite-infected HFF cells seeded on cover slips were fixed with 4% paraformaldehyde/0.05% glutaraldehyde (PFA/Glu) in PBS. Fixed cells were then processed as previously described . ConfocaParasites were lysed in PBS-1% Triton X-100 and mixed with SDS–PAGE loading buffer under reducing conditions. The suspension was subjected to sonication on ice. SDS-PAGE was performed using standard methods. Separated proteins were transferred to nitrocellulose membranes and probed with appropriate antibodies in 5% non-fat milk in PBS-0.05% Tween20. Bound secondary peroxidase conjugated antibodies were visualized using the SuperSignal (Pierce).Plaque assays: HFF monolayers were infected with parasites and let to develop for 7 days before fixation with PFA/Glu and Crystal Violet staining to visualize plaques.Intracellular growth assays: HFFs were inoculated with parasites, washed 4h post infection and coverslips were fixed at 24 h post-infection with 4% PFA/Glu and stained by IFA with rabbit anti-TgGAP45. Number of parasites per vacuole was counted in triplicate for each condition (n = 3). More than 200 vacuoles were counted per replicate.http://129.16.106.142/tools.php?c=raven). Input data was taken from KEGG database , ToxoDB , ApiLoc database , and LLAMP portal .Flux-balance analysis was performed using MATLAB  with CPLEX  and Mosek (version 7) solvers; RAVEN Toolbox was used within Matlab environment  PCR for sequencing was done using primers FAS-1/FAS-2 . The gRN(EPS)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.S6 Table(XLSX)Click here for additional data file.S7 Table(PDF)Click here for additional data file.


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.