The aerobic energy metabolism of cardiac muscle cells is of major importance for the contractile function of the heart. Because energy metabolism is very heterogeneously distributed in heart tissue, especially during coronary disease, a method to quantify metabolic fluxes in small tissue samples is desirable. Taking tissue biopsies after infusion of substrates labeled with stable carbon isotopes makes this possible in animal experiments. However, the appreciable noise level in NMR spectra of extracted tissue samples makes computational estimation of metabolic fluxes challenging and a good method to define confidence regions was not yet available.in vivo. Isotopic enrichment of glutamate was measured by NMR spectroscopy in tissue samples taken at a single time point after the timed infusion of 13C labeled substrates for the TCA cycle. The NMR intensities for glutamate were analyzed with a computational model describing carbon transitions in the TCA cycle and carbon exchange with amino acids. The model dynamics depended on five flux parameters, which were optimized to fit the NMR measurements. To determine confidence regions for the estimated fluxes, we used the Metropolis-Hastings algorithm for Markov chain Monte Carlo (MCMC) sampling to generate extensive ensembles of feasible flux combinations that describe the data within measurement precision limits. To validate our method, we compared myocardial oxygen consumption calculated from the TCA cycle flux with in vivo blood gas measurements for 38 hearts under several experimental conditions, e.g. during coronary artery narrowing.Here we present a computational analysis method for nuclear magnetic resonance (NMR) measurements of tricarboxylic acid (TCA) cycle metabolites. The method was validated using measurements on extracts of single tissue biopsies taken from porcine heart Despite the appreciable NMR noise level, the oxygen consumption in the tissue samples, estimated from the NMR spectra, correlates with blood-gas oxygen uptake measurements for the whole heart. The MCMC method provides confidence regions for the estimated metabolic fluxes in single cardiac biopsies, taking the quantified measurement noise level and the nonlinear dependencies between parameters fully into account. Metabolic fluxes in animal tissues can be identified by measuring the incorporation of stable isotopes in intracellular metabolite pools. To quantify metabolic fluxes, isotope label incorporation is usually measured at several time points , among o13C) in metabolic intermediates can be detected by nuclear magnetic resonance (NMR) spectroscopy or mass spectrometry (MS). The data is then analyzed with computational methods that require (i) detailed mathematical models of carbon transitions between the metabolites in the system and (ii) sophisticated optimization procedures for estimating the flux parameters. In the past, we have developed a bioinformatics method to estimate metabolic fluxes in aerobic metabolism from very noisy NMR measurements resulting from the Labelling with Isotope for a Pre-Steady-State Snapshot (LIPSSS) protocol [The incorporation of stable isotopes  coronary artery of anesthetized pigs [13C] acetate for 4 minutes and  acetate for 1.5 minutes. After exactly 5.5 minutes of 13C enriched acetate infusion, metabolism was arrested by freeze-clamping part of the left ventricular wall of the heart before the isotopic steady state was reached. Biopsies from different regions of this part of the left ventricular wall were cut from the tissue slab after freeze-drying, and divided into approximately nine samples per heart with around 0.1 g dry mass per sample. After extraction with perchloric acid, the 13C NMR multiplets of glutamate were measured. 13C-NMR spectra were obtained at 100.62 MHz and analyzed with the MRUI/AMARES software package .Up to nine separate multiplet intensities were detected for glutamate. For independent testing of the LIPSSS method and the associated parameter estimation procedures, “gold standard” myocardial oxygen uptake was calculated from blood flow, hemoglobin content and blood-gas measurements taken before and during acetate infusion . Note th2O of positive end-expiratory pressure (PEEP) was applied before opening the thorax. The thorax was opened via a midsternal incision and the heart exposed by opening the pericardium. The left hemiazygos vein was tied off to prevent mixing of noncoronary venous blood with coronary venous blood. The LAD was dissected free over a distance of about 2 cm and was catheterized with a 24G catheter. In the stenosis and adenosine + stenosis groups, a custom-made adjustable aluminium occluder was placed around the artery, and LAD pressure was measured.In all groups, sedation was performed with ketamine 15 mg/kg and midazolam 1 mg/kg intramuscularly, and anesthesia was maintained by continuous infusion of sufentanil (4 μg/kg/hr), midazolam (0.5 mg/kg/hr), and pancuronium (0.2 mg/kg/hr). The trachea was intubated and the lungs were ventilated with a mixture of 60% oxygen/40% air. Fluid-filled catheters were introduced and hemodynamic parameters collected as previously described (see ). A cont141Ce or 103Ru, in random order) was injected into the left atrium for baseline blood flow measurements. The intervention was performed and 30 minutes later a second batch of microspheres was injected for final blood flow measurements. Throughout the procedure hemodynamic data were recorded continuously.After finishing instrumentation the animal was allowed to stabilize for at least 15 minutes, the first batch of microspheres  and represent reaction fluxes through the TCA cycle and exchange reactions with amino acids, respectively. The dynamics of incorporation of 13C label from acetate into the acetyl-CoA pool depends on transport in the blood vessels, permeation of the cell membrane, the flux of the conversion of acetate into acetyl-CoA, the flux of acetyl-CoA into the TCA cycle and the acetate and acetyl-CoA pool sizes. Fortunately, the time course of incorporation of 13C label into the acetate pool is almost mono-exponential  and anddil istimates  and its Parametric sensitivity analysis is commonly applied in systems biology . In thisThe challenge in analyzing the data in this study was the high noise level. Up to seven of the nine measured multiplet intensities could sometimes not be detected. Ensemble modeling proved to be a feasible method to separate samples with flux parameters that could be estimated from samples with poor information on the fluxes in the system. This ensemble approach made it possible to identify 262 out of 347 samples that gave useful estimates for the primary parameters. The quality selection of the samples allowed us to use the best-fit parameters from each sample as a point estimate for the primary parameters. The MCMC approach allowed us to define confidence bounds on all estimated parameter values taking their correlations into account. This is a significant advantage compared with previous approaches, where linearized or analytical methods were used to calculate errors on estimated model parameters ,6,8.Adding the Monte Carlo ensemble sampling to the LIPSSS framework enables us to estimate the confidence regions of flux parameters in a single sample. The small size of the tissue samples makes it feasible to identify the spatial variation of flux parameters expected because of the known heterogeneity in the tissue. The physiological meaning of our measurements of heterogeneity in metabolism in heart muscle will be addressed in future studies.In this study we improved the LIPSSS method in order to quantify metabolic fluxes using stable isotope labeling integrated with mathematical models of carbon transitions: auxiliary information was taken into account in the form of Bayesian priors and emphasis was placed on the uncertainty analysis of the estimated flux parameters. The method was used to quantify TCA cycle fluxes from noisy NMR measurements in porcine hearts under different physiological conditions. Two important metabolic fluxes could be determined in single biopsies taken during animal experiments and confidence regions could be calculated for single samples.The authors declare that they have no competing interests.in silico experiments, HH and TWB performed the in silico experiments. HH, DJA, JH and JHGMvB analyzed the data. HH and JHGMvB wrote the manuscript. All authors read and approved the final manuscript.DJA, ABJG and JHGMvB designed and conducted the animal experiments. HH, TWB and JHGMvB designed and conceived the Model equations. In this supplemental text, we give a detailed description of the computational model and list all model ODEs.Click here for fileCode and data. In this supplemental file we provide all R code and part of the experimental data used to produce the results of this study. The zip file contains a file README.txt which describes all code and data.Click here for fileEstimation of auxiliary model parameters. In this supplemental text, the results of estimating the auxiliary model parameters Panap and Jexch are presented and discussed.Click here for file


Several methods have been developed for analyzing genome-scale models of metabolism and transcriptional regulation. Many of these methods, such as Flux Balance Analysis, use constrained optimization to predict relationships between metabolic flux and the genes that encode and regulate enzyme activity. Recently, mixed integer programming has been used to encode these gene-protein-reaction (GPR) relationships into a single optimization problem, but these techniques are often of limited generality and lack a tool for automating the conversion of rules to a coupled regulatory/metabolic model.Saccharomyces cerevisiae.We present TIGER, a Toolbox for Integrating Genome-scale Metabolism, Expression, and Regulation. TIGER converts a series of generalized, Boolean or multilevel rules into a set of mixed integer inequalities. The package also includes implementations of existing algorithms to integrate high-throughput expression data with genome-scale models of metabolism and transcriptional regulation. We demonstrate how TIGER automates the coupling of a genome-scale metabolic model with GPR logic and models of transcriptional regulation, thereby serving as a platform for algorithm development and large-scale metabolic analysis. Additionally, we demonstrate how TIGER's algorithms can be used to identify inconsistencies and improve existing models of transcriptional regulation with examples from the reconstructed transcriptional regulatory network of The TIGER package provides a consistent platform for algorithm development and extending existing genome-scale metabolic models with regulatory networks and high-throughput data. Constraint-Based Reconstruction and Analysis (COBRA) methods have allowed the study of metabolism on a genome-wide scale . These min silico genetic state. Turning genes "off" can be used to simulate significant reductions in expression levels or complete knockouts. The GPR for each reaction, represented as a binary rule, determines if a sufficient collection of proteins  is present for the reaction to carry flux. All reactions with satisfied GPR rules are collected into a stoichiometric matrix. The second stage of FBA uses linear programming to calculate a thermodynamically-feasible, mass-balanced flux distribution that maximizes the flux through an objective reaction. The objective reactions used in FBA vary among organisms, ranging from ATP maintenance to biomass production [COBRA models often contain two sets of biological information, a matrix of stoichiometric data for metabolic reactions, and a mapping between gene-encoding enzymes and the reactions they catalyze . Predicting the metabolic capabilities of a COBRA model is possible with Flux Balance Analysis (FBA), a two-stage mathematical technique based on the observation that metabolic networks often display optimal dynamics . In the oduction . By assuSaccharomyces cerevisiae [The GPR rules do not always describe a one-to-one mapping between genes and reactions . For example, a COBRA reconstruction for the yeast revisiae  containsE. coli with optimal production of a metabolic byproduct. Ideally, OptKnock would operate by removing genes, not reactions, since it is not straightforward to independently remove reactions from a biological system without genetic manipulations. An optimization using genes as decision variables would require a method for encoding the GPR logic into a set of linear inequalities. This encoding was developed as SR-FBA [Because of the complexity of the GPR mappings, early extensions to FBA were reaction, rather than gene, centric. For example, the OptKnock  algoriths SR-FBA  using a s SR-FBA . Other gs SR-FBA -14. HoweThe accuracy of COBRA models has been improved through the addition of transcriptional regulatory networks (TRNs) ,16. The Escherichia coli [Saccharomyces cerevisiae [E. coli and S. cerevisiae TRNs used an iterative approach [The first genome-scale TRNs were applied to models of hia coli  and Saccrevisiae  metaboliapproach  - applyiS. cerevisiae [A second obstacle with TRN integration is that the explicit rule formulation used by previous studies  can overrevisiae :(1)mth1 is repressed by mig1 and promotes expression of rgt1. Extracellular L-glutamine (gln-L) represses rgt1 expression. The original iMH805 study required this set of constraints be described with the following set of explicit rules [Transcription factor it rules :An implicit representation of (1) is4 = 16 possible states. As shown in Table The three transcription factors and one metabolite in these rules can be arranged in 2TIGER). TIGER automatically converts a list of implicit or explicit GPR and TRN rules into a set of linear inequalities; these equations are integrated with an existing COBRA model. The software allows rules to be written in a generalized Boolean format, enabling TRN logic to more accurately reflect the underlying biology. We demonstrate how this increased expressivity can overcome inconsistencies in existing TRN models. We will also show how TIGER simplifies the development of gene-centric extensions to FBA by improving three algorithms for integrating high-throughput expression data with a COBRA model.Software suites have been developed to enable COBRA analyses. Packages such as CellNetAnalyzer , the BioTIGER are shown in Figure TIGER converts a GPR and additional regulatory rules into an equivalent mixed integer linear program (MILP). The MILP constraints are added to a COBRA metabolic model to create a TIGER model that combines metabolism, GPR associations, and transcriptional regulation. This integrated model serves as a platform for applying many gene-centric extensions to FBA, including algorithms that incorporate "omics" data for model refinement. In this section, we describe how the rules parsed by TIGER are constructed, and how they are converted to an MILP. Sample files depicting a COBRA model, GPR, and TRN are provided in the "test/samples" directory of the TIGER distribution.The primary functions of gene a, enzyme A, and reaction 1. If gene a is expressed, FBA assumes that reaction 1 can carry any physiologically feasible flux. Some enzymes, such as enzyme B, can catalyze two or more separate reactions. Other reactions, such as reaction 4, require two enzymes (C and D) to carry any flux. Enzymes C and D are commonly protein subunits of an enzymatic complex; if either is absent, no substrate conversion is possible. Genes e and f encode isozymes; either protein can independently catalyze reaction 5.The GPR uses Boolean logic to describe the nonlinear relationship among genes, their protein products, and the reactions they catalyze. Examples of GPR relationships appear in Figure expression using the standard operators and and or. For example, a reaction that is catalyzed by either of two isozymes, the second of which is composed of two subunits, would have a GPR of the form "isozyme1 or (isozyme2a and isozyme2b)". Two expressions are joined with an implication operator (⇒ or ⇔ corresponding to "if" and "if and only if"), to form a rule. For GPR associations, rules are formed as "GPR ⇔ reaction", where reaction is an indicator variable that constrains the flux through a reaction to be zero when the GPR expression is false.These GPR relationships can be described as a Boolean TIGER expressions allow additional features to describe logical relationships that are more complex than those typically found in GPRs. The not operator allows logical negation, which is often used to construct rules for transcriptional repression. Expressions can also contain conditionals that compare the numerical values of individual variables. If a gene g was known to be expressed when glucose uptake is greater than 10 flux units, this relationship could be represented by the rule "glc_ex >10 ⇒ g", where "glc_ex" is the glucose exchange reaction in the metabolic model. Any two expressions of arbitrary complexity can be combined as a rule and parsed by TIGER. The grammar used by TIGER for rules was designed to resemble logical operations in common programming languages and to be compatible with the GPRs of widely-used COBRA models. A complete description of the TIGER syntax appears in Additional File crp to cAMP in E. coli, display multiple levels of activity and cannot be easily described with Boolean logic [TIGER allows multilevel variables. If a transcription factor t activates target genes glow at low levels of expression and ghigh at high levels of expression, then this relationship could be described with the rulesSome transcriptional regulators, such as the response of an logic . Rather t = 0, 1, and 2 corresponds to no, low, and high expression. Logical operators have a different interpretation when applied to multilevel variables. If proteins x and y form a promoter complex for expression of gene z, then the corresponding rule for z expression would be "x and y ⇒ z", since both x and y are required for z transcription. If x and y were multilevel, one would assume that z expression would be proportional to the promoter subunit in lower abundance, since this species would limit the amount of complete promoter complex that could be formed. Thus, the and operation often corresponds to a minimization:where or operation would be used in situations where either factor can independently induce expression. In this situation, the species in higher abundance determines the target gene's transcription level. TIGER implements the multilevel or as a maximization:The not operator can have two interpretations when applied to multilevel variables:The x and the quantity notx always sum to the maximum value that x can occupy. In this case, notx is a measure of how far x is from its upper bound. Users are able to select the pseudo-binary or inversion representation depending on which interpretation is a better approximation of the biological context. For example, consider a gene/repressor relationship R ⇒ not G, where the repressor R can take on three biologically distinct levels - "off," "low," and "high". If both "low" and "high" levels of R prevent any expression of G, then the pseudo-binary not operator would be appropriate as G is off whenever R is not "off". However, if G also has the same three levels of expression, then the inversion interpretation of the not operator is more appropriate. This choice implies thatwhere TIGER model can be declared with multiple levels. Such declarations are made when rules are added to a model using the add_rule function in two ways: 1.) setting the default upper bound to all variables to any integer greater than one, or 2.) providing a list of variable names and a set of upper and lower bounds.Any variable in a Simple Boolean rules can be represented by systems of linear inequalities of integer variables . A generx) or a negated variable (not x). If a not operator appears before an expression that is not atomic, TIGER applies DeMorgan's laws to move the negation onto atomic expressions  becomes the equivalent expression (not x) or (not y)). A simple rule then conforms to one of the following patternsWe define an "atomic" expression as either a variable . Non-simple rules are converted to simple rules through a series of recursive substitutions. For example, the rulewhere x or (not y) is not atomic. By defining an indicator variable I, which is true if and only if the expression x or (not y) is true, equation (14) can be written as two simple rules:is not simple, since the expression I are determined by the bounds of x and y. If The bounds of x and y are binary, I is binary as well.Thus, if TIGER applies the above substitutions recursively, creating indicator variables as necessary until all rules are simple. Each simple rule is converted to a set of linear inequalities that are added as constraints to the model structure. If a variable name already appears in the model, TIGER assumes that these variables represent the same quantity and thus allows new rules to be added to an existing model without recompiling previous rules. At the same time, TIGER creates variables to substitute for negated variables. For efficiency, TIGER ensures that only one negated variable is created for each original variable, regardless of the number of times the negated expression appears in the set of simple rules. Details of the conversion between simple rules and inequalities, along with methods for handling conditionals, are provided in Additional File i Rare defined, where i R= 0 if the GPR for reaction i is not satisfied, and i >R0 otherwise. To enforce the GPR's effect on flux, TIGER adds the constraintIf the GPR expression for a reaction is not satisfied, the reaction is not allowed to carry flux. To enforce this relationship during an optimization, a set of discrete variables i vis the flux through the ith reaction, with lower and upper bounds where TIGER models are represented as Matlab structures. The layout of this structure is shown in Figure obj, A, b, lb, and ub that correspond to the values in the following MILP problem:A is determined by the character vector ctype. The type of variable for each entry in x is specified by the field vartype, where 'c', 'b', and 'i' denote continuous, binary, and general integer variables. Reaction fluxes are continuous variables, while all other variables are either binary or integer depending on the corresponding upper bound. The fields rownames and varnames contain descriptive names of the constraints and variables, stored as cell arrays of strings. Functions in TIGER allow variables to be interchangeably referenced by their name, column index, or through Matlab's logical indexing features.The type of (in)equality for each constraint in TIGER models is designed for compatibility with the model structure for the COBRA Toolbox [TIGER can use a COBRA Toolbox model as a starting point for converting a genome-scale reconstruction; therefore, any model in a file format supported by the COBRA Toolbox  can be converted to a TIGER model.The format for  Toolbox . TIGER cTIGER uses a custom Matlab class CMPI  to create and solve mathematical programming problems. CMPI defines a consistent structure for MILP  problems, providing independence from the underlying MILP solver software. TIGER currently supports the CPLEX, Gurobi (via Gurobi MEX), and GLPK (via GLPK Mex) software packages, all of which are freely available for academic use. Porting TIGER to use a new solver requires modifying only the CMPI method solve_mip to specify the new interface. CMPI also provides a standardized method for configuring common solver parameters .solve_multiple_milps, to preserve the solver state between successive calls to the CPLEX optimizer and reduce runtime in this manner. (Gurobi and GLPK currently do not support this feature in their Matlab interfaces.) If the CPLEX optimizer is not installed, CMPI will automatically make successive calls to the installed optimizer. While this removes the potential speed increase from using solver restarts, it allows TIGER code to remain solver independent and portable.Previous work has indicated that the computation time of some FBA-related algorithms, such as Flux Variability Analysis , can be TIGER source code and installation instructions are available online at http://bme.virginia.edu/csbl/downloads/ or http://csbl.bitbucket.org/tiger The version of TIGER used for the examples in this study is included as Additional File TIGER website. The software includes a testing suite to verify the installation. These tests contain examples that build a TIGER structure from a simple COBRA model, add a set of TRN rules, call a MILP solver, and display the solution.TIGER was used to couple the 1266 reactions in iND750 [Saccharomyces cerevisiae metabolism, with 750 metabolic genes. The resulting TIGER model contained 4498 constraints in 3214 variables. A model of S. cerevisiae transcriptional regulation, iMH805 [TIGER model. The conversion took 53.66 s for iND750 and 20.31 s to add the TRN using an Intel 3.2 GHz i7-quad core processor running Linux.n iND750 , a genom, iMH805 , was adda priori [TIGER solves the TRN and FBA problems simultaneously, so the resulting gene state is always stable .As mentioned above, previous methods for integrating TRNs involve an iterative process, alternating between calculating gene states from a given environment and determining an environment based on metabolic byproducts . Howevera priori . In factTIGER includes the function find_infeasible_rules to identify rules that prevent feasible solutions to the resulting MILP. Given a model and a set of rules that prevent a feasible solution, find_infeasible_rules creates a MILP that preserves the logic of the rules but allows each rule to be artificially satisfied. The objective of this MILP is to minimize the number of rules that must be artificially satisfied while finding a feasible solution for the model.  was originally derived from Turi & Loper . Re-examerg11 expression was re-written to only exhibit ROX1 repression under low oxygen conditions:where "EX_o2(e)" is the iND750 name for the oxygen exchange reaction, and the maximum oxygen uptake rate for growth on glucose is 2.44 mol/(g dry cell weight)/h (negative flux through exchange reactions indicate uptake by the cell). Rule (21) for TIGER: 1.) apply the existing TRN to a COBRA model, 2.) use the find_infeasible_rules function to identify rules that cause the model to differ from a known phenotype, and 3.) re-examine the evidence for these rules and make appropriate modifications. As shown in the previous example, new biological information can often be incorporated into existing rules using TIGER's support for complex logical expressions.The set of refined rules  reproduces the correct growth phenotype in aerobic glucose conditions. This example demonstrates a three-step procedure for refining existing TRN models using TIGER package contains implementations of three of these methods.Coupling the GPR with a metabolic model is a starting point for several algorithms designed to refine metabolic models by integrating high-throughput gene or protein expression data. The GIMME was designed to generate context-specific metabolic networks by designating each reaction as "on" or "off" . Given eTIGER provides a gimme function that implements this gene-centric approach. Similar to the original algorithm, TIGER's GIMME uses the distance below the expression threshold as a weight when selecting genes for re-activation. In addition to removing discrepancies caused by the averaging of gene expression values over each reaction, TIGER's integrated approach allows GIMME to identify each gene as either "on" or "off" in the resulting network .The GIMME algorithm is an excellent candidate for conversion to a gene-centric approach. Rather than average the gene expression values for each reaction, a simpler approach is to turn genes "on" or "off" if their expression is above or below a threshold. Using an integrated GPR/metabolic model, an optimization problem could re-activate "off" genes to allow the network to produce an objective flux. We applied GIMME to the prototypic network shown in Figure g5a and g7b. Because reaction 7 is the only method of producing metabolite E (the metabolic objective), this reaction must be active and both subunits (g7a and g7b) must be expressed. Production of E also requires metabolite B and either reaction 5 or reaction 6. The expression data showed that both genes g5a and g6 were below the expression threshold; GIMME chose to activate g5a since its expression was closer to the threshold.The expression data applied to this network are shown in Table et al. [Shlomi, et al. , introdui vand some small flux ε. The optimization attempted to preserve the reaction classifications while enforcing that the resulting set of reaction fluxes be feasible . The mass-balance approach attempts to yield functional models in multicellular organisms that lack a clearly defined metabolic objective.for each reaction flux TIGER includes a gene-centric version of the iMAT algorithm. Because TIGER allows multilevel variables, each gene in the GPR is allowed to occupy a state of low (0), medium (1), or high (2) activity. The multilevel operators in the GPR then combine the gene expression values to create a reaction indicator with the same three levels. Rules are added to enforce the constraints in equation (24). Additionally, if a metabolic objective is available for the organism, the flux through the corresponding objective reaction can be constrained above a minimum value.g8b requires that reactions 8 and 10 carry flux. Because production of metabolite G is not a part of the system's metabolic objective, reaction 8 would most likely not carry flux in the FBA flux distribution for this network; the activity seen in this side pathway is enforced by the iMAT constraints.iMAT was used to integrate the activity data in Table Metabolic Adjustment by Differential Expression (MADE) removes the need for a pre-defined "on"/"off" threshold when integrating expression data . InsteadTIGER implementation of MADE offers two improvements. First, genes are allowed to be multilevel instead of binary. The user is allowed to define a mapping between the multiple levels of gene expression and the flux constraints for the corresponding reactions. Second, TIGER MADE allows comparisons among states that do not appear as a linear sequence. The original MADE algorithm used a series of n conditions C1, C2, ..., nC, and n - 1 sets of expression data describing the changes C1 → C2, C2 → C3, ..., Cn-1 → nC. TIGER MADE allows any number of connections between the n states.The TIGER MADE's capabilities is presented in Figure A and B were evolved from the same parent strain P. Strain A later gave rise to two additional strains, A1 and A2. A matrix containing the differential expression between each strain and its predecessor is calculated. A transition matrix T is defined as follows: if T = k, then the kth column of the differential expression matrix was calculated between strains i and j. Values greater than one in this column indicate that expression is higher in strain j than in strain i. These two matrices are used by TIGER MADE to create a single optimization problem. The result is a functional gene state for each condition that maximizes the significant changes in gene expression between each strain and its parent.A conceptual example of Figure test/gimme_imat_made_examples.m of the TIGER distribution.Source code for all of the examples in Figure TIGER, a software platform for converting generalized Boolean and multilevel rules to mixed-integer linear programs, and coupling these rules to genome-scale models of metabolism. The flexibility of TIGER's generalized rule format allows for a more accurate description of biological processes such as catalysis by isozymes and multi-meric proteins, metabolic flux control, and transcriptional regulation. These features were used to identify and correct inconsistencies within an existing TRN model of Saccharomyces cerevisiae. We have also demonstrated how TIGER can be used as a starting point for implementing and improving existing algorithms for genome-scale analysis.We have presented TIGER, we are exploring methods to improve the solution efficiency of the generated MILP. Possible strategies include exploiting indicator constraints, specially-ordered-sets (SOS), and other solver optimizations through CMPI.In addition to adding implementations of other gene-centric algorithms to Project name: TIGERProject home page: http://bme.virginia.edu/csbl/downloads or http://csbl.bitbucket.org/tigerOperating system: Platform independentProgramming language: MatlabOther requirements: Matlab v7.0 or higher, a Mixed-Integer Linear Programming solver License: MITNon-academic use restrictions: NoneSaccharomyces cerevisiae metabolism; iMH805: Genome-scale transcriptional regulatory network for Saccharomyces cerevisiae.; CMPI: Common Mathematical Programming Interface; GIMME: Gene Inactivity Moderated by Metabolism and Expression; iMAT: Integrative Metabolic Analysis Tool; MADE: Metabolic Adjustment by Differential Expression.TIGER: Toolbox for Integrating Genome-scale metabolism, Expression, and Regulation; COBRA: COnstraint-Based Reconstruction and Analysis; FBA: Flux Balance Analysis; GPR: Gene-Protein-Reaction; TRN: Transcriptional Regulatory Network; MILP: Mixed-Integer Linear Program; SR-FBA: Steady-State Regulatory FBA; iND750: Genome-scale model of TIGER software and performed the simulations. KAL prepared the TRN validation study and contributed TIGER functions. The project was conceived by PAJ and JP, and advised by JP. All authors wrote and reviewed the manuscript.PAJ designed and wrote the Supplementary Methods. Detailed grammar for TIGER rules and specifics on the rule to MILP conversion process.Click here for fileTIGER source code. Source code, documentation, and tutorials are also available online at http://bme.virginia.edu/csbl/downloads/ or http://csbl.bitbucket.org/tiger.Click here for file


Escherichia coli and Saccharomyces cerevisiae. For a small number of fluxes for which the predictions were poor, the corresponding enzyme-coding transcripts were also found to be distinctly regulated, showing the ability of structural fluxes in capturing the underlying regulatory principles. Exploiting the observed correspondence between in vivo fluxes and structural fluxes, we propose an in silico metabolic engineering approach, iStruF, which enables the identification of gene deletion strategies that couple the cellular biological objective with the product flux while considering optimal as well as sub-optimal routes and their efficiency.Identification of optimal genetic manipulation strategies for redirecting substrate uptake towards a desired product is a challenging task owing to the complexity of metabolic networks, esp. in terms of large number of routes leading to the desired product. Algorithms that can exploit the whole range of optimal and suboptimal routes for product formation while respecting the biological objective of the cell are therefore much needed. Towards addressing this need, we here introduce the notion of structural flux, which is derived from the enumeration of all pathways in the metabolic network in question and accounts for the contribution towards a given biological objective function. We show that the theoretically estimated structural fluxes are good predictors of experimentally measured intra-cellular fluxes in two model organisms, namely,  However, given the complexity of metabolic networks in terms of their structure and regulation, identification of optimal strategies for redirecting fluxes towards desired products is a challenging task.Microorganisms that produce a desirable product, either naturally, or because they have been engineered through insertion of heterologous pathways, often have low yields and productivities. Only after the introduction of appropriate genetic modifications, production strains may become available that can meet the demands of economic production in silico metabolic engineering problem have been proposed in recent years. The OptKnock algorithm Several solutions to the in vivo. Additionally, the presence of futile cycles can cause certain fluxes to have an infinite range of variation One of the key requirements for successful metabolic engineering target identification is the ability to predict biologically meaningful flux distributions following genetic perturbations such as gene knockouts. In OptKnock/OptGene, this requirement is explicit in terms of the biological objective function included in the optimization problem. Current approaches typically assume that microbes have evolved for achieving a flux distribution that leads to maximum growth (or another flux-based objective). The biological feasibility of a solution thus depends on the validity of the assumption that the formulated objective function correctly represents the system. Although the assumption of optimality for a wild-type microorganism is justifiable, it may not be valid for mutants in silico metabolic engineering problem using pathway analysis is limited to few. Trinh and co-workers Linear programming based methods can be used to tackle some of the above-mentioned limitations, for example, by using flux-cone sampling methods In this study, we aim at combining the advantages of both objective function-centered and pathway enumeration-centered approaches. To this end, we first address the question of biological relevance of sub-optimal routes and flux distributions predicted by computational methods. We introduce the notion of structural fluxes, which account for a biological objective function and are derived from the enumeration of all pathways in a given metabolic network. Structural fluxes are inspired from the concept of control effective flux (CEF) that uses efficiency and elementary modes to understand changes in transcriptional regulation Escherichia coli and Saccharomyces cerevisiae. Building upon the ability of structural fluxes to predict genetically perturbed biological networks, we propose an in silico metabolic engineering algorithm, iStruF, where the objective is to identify deletion targets that increase the structural flux of a desired product. iStruF leads to solutions that couple biological objectives, such as growth, with product formation while considering optimal as well as sub-optimal routes and their efficiency. As a biotechnologically relevant case study, we present the results of iStruF for improving production of ethanol and succinate in baker’s yeast. Finally, we discuss the use of Generating Vectors (GVs) We show that structural fluxes are good predictors of experimentally measured fluxes in in silico metabolic engineering procedure is given in An overview of the proposed ε of each elementary mode i is defined as the ratio of the EM’s output e  to the investment required to establish the EM  for a specific carbon source:In the original formulation of CEF k is then obtained by the weighted average of the product of mode-specific efficiencies and reaction-specific fluxes over the sum of all mode efficiencies:X) production and/or ATP generation for cellular maintenance on substrate S). In order to find a measure that can predict fluxes across mutants, we propose three modifications to the definition of CEFs and thereby introduce the concept of Structural Fluxes.The control effective flux of each reaction Two flavors of structural flux definitions are introduced, namely, SF and StruF. SF is introduced in the context of application on a single given network, while StruF is introduced for cases where comparison across different networks (e.g. wild-type versus mutant) is required.In metabolic systems, the cellular network of reactions, together with constraints on the reversibility of enzymes, determine the space of all possible steady-state phenotypes. In actuality, the cell does not invoke the large majority of those in a given condition. For example, for growth on a given substrate, several of the reversible reactions across the network are usually constrained to either backward or forward directions. We use this fact in order to derive heuristics for restricting reaction directionalities. Such restrictions, together with splitting of bi-directional reactions into two unidirectional reactions allowed us to obtain a pointed cone and thereby to avoid re-computation of GVs following each network perturbation (gene deletions).In the concept of structural fluxes, we first split up the fluxes of reversible reactions into forward (f) and backward (b) directions as a way to consider biologically relevant directionalities for growth on a given substrate:in vivo. Hereto, we define the reversibility score rs of a reaction as the smallest divided by the greatest SF:Our hypothesis is that the greatest SF of a particular reaction (either forward or backward) matches the directionality A reversibility score of 0 indicates that the reaction is irreversible and a score of 1 indicates that the reaction may be active in both directions. We assume that the directionality of a particular reaction may flip in mutants as compared with wild-type for a high reversibility score; otherwise we assume the directionality to be equal for mutant and wild-type (irreversible). Based on the reversibility score (Eq. 4), we impose additional restrictions on the reaction directionalities : split up the reaction above a threshold of 0.05; otherwise restrict the reaction to either forward or backward direction.E. coli was found to be the maintenance reaction (i.e. ATP requirement for maintenance). However, this normalization is not suitable for the identification of metabolic engineering targets, as the algorithm would tend to minimize the use of the maintenance reaction in the mutant EMs when maximizing the product formation. We chose the glucose (substrate) uptake rate as the normalization factor for predicting fluxes and in metabolic engineering applications:Although elementary modes are normalized to the substrate uptake rate, control effective fluxes are not. SF and CEF values tend to be larger for smaller networks. If the CEFs as such would be used to find deletion targets for the production of a target metabolite, the algorithm would tend to minimize network size, besides maximizing product formation. It would thereby favor deletion of reactions that are present in many elementary modes and lead to a biased set of deletion targets. We show the importance of normalization in a case study on succinate production using yeast in Table S3 of Zhao and Kurata E. coli central carbon metabolism . GVs were computed using METATOOL in vivo13C labeling experiments for S. cerevisiae and E. coli: both with respect to reversibility of reactions for growth on different substrates, and with respect to the measured fluxes across different mutants.In this section, we compare the calculated structural fluxes with the experimental data from S. cerevisiae under three different conditions: growth on glucose, glycerol, or acetate as the sole carbon sources. Under these conditions, the net directionality of some of the fluxes varies. For instance, growth on glucose involves a net flux through the glycolysis from DHAP to PEP, whereas growth on acetate involves the reverse (net flux through the gluconeogenesis). As the same enzymes are used in all cases, the favored flux directions estimated based on the structural flux reversibility scores should also change.We evaluate reaction directions in the central carbon metabolism of We observed that the direction given by the greatest structural flux when the reversibility score is smaller than 0.5 matches well with the measured reaction directionality for growth on glucose (100% match), glycerol (90% match), and acetate (100% match) as sole carbon sources. SF thus correctly captures the experimental observations on the reaction directionalities. E. coli model . Hence, the biological objective used for structural fluxes calculation must at least contain growth. In the current study, we use growth as the objective for C fluxes . We founA limitation of the use of the CEF and StruF definitions based on EMs is current computational intractability of EMs for large-scale metabolic networks 13C-based in vivo flux measurements in the following manner: for every pair of strains, all experimentally measured flux changes greater than a cut-off value C . Consequently, for the purpose of comparing fluxes of particular reactions across different mutants, variability in the data is a limiting factor. With respect to our main objective of identifying metabolic intervention strategies, however, it is more important to determine whether a given flux will be increased or decreased in comparison with the wild type or with another mutant, as opposed to flux magnitude comparisons within the same mutant. We therefore evaluate the performance of the predictions of the structural fluxes in comparison with the Since for metabolic engineering purposes it is also of importance to determine whether a given flux remains constant in comparison with the wild type (or with another mutant) we define a similar measure for the unchanged fluxes:G improved with increasing magnitude of flux change, demonstrating that structural fluxes successfully capture large flux changes in the network. Furthermore, the overall prediction of up or down regulation of fluxes across mutants was also found to be good . Interestingly, the true match rate TM be good . Table 1G) from StruFs against random predictions in a binomial test with the expected true match rate for the random model being 50%. Concerning E. coli, S. cerevisiae, As a performance indicator, we tested the true match rates . We hypothesized that these fluxes are likely to be regulated by other means than those taken into account by the structural properties of the network. For example, the transcriptional regulation for these fluxes may display a different pattern than for the other fluxes. To test this hypothesis, we employ statistical analysis to detect enzyme-coding transcripts that are differently regulated by using mRNA measurements from the a priori information on regulation, e.g. the absence of fermentation reactions at low specific growth rates, would improve the predictions, because the structural fluxes represent a “capacity” for each flux, whereas the measurements reflect a particular situation.Outliers of the principal component analysis are marked in The objective of the metabolic engineering algorithm iStruF is to identify deletion targets that increase the structural flux of the desired product. For the metabolic networks under study, it was feasible to perform an exhaustive search and compute all potential reaction deletions up to the combinations of three reaction deletions. For each gene deletion mutant, the structural fluxes of each reaction  were recomputed by excluding the modes that contain the deleted reaction(s). For large-scale networks or higher number of gene deletions, search algorithms like controlled random search in silico metabolic engineering strategies, we selected i) production of ethanol through single reaction deletions and ii) production of succinate through triple deletions in baker’s yeast. Both compounds are interesting bio-based alternatives for replacing products that are currently manufactured from fossil fuels.As case studies for the While considering the biomass producing modes, we note that the maximum theoretical structural flux towards ethanol is 1.68 mole ethanol/mole glucose. Whereas, the structural flux for the wild-type is 0.36, thus setting a theoretical limit of 4.5 fold improvement in production . We present the results of an exhaustive search for single reaction deletions using iStruF and contrast it with the results from OptGene  . Using OIt is relevant to couple product formation to growth for a viable mutant. Depending on the mode of fermentation, a mutant may be chosen that exhibits fast or slow growth. If one aims to produce a compound in two-stage fermentation with a growth and a production phase, one may opt for a reversible knockout with low growth, because a high growth rate reduces the achievable product yield. If on the other hand, one aims to produce a compound while growing, a mutant with a high growth rate may be the better choice to obtain higher productivity. Amongst the viable mutants with enhanced ethanol production, growth was predicted to be between 79% and 100% of the wild-type rate. Deletion of one of the top ranked candidate reaction, GDH1, has been shown to experimentally contribute to a higher ethanol yield with good growth in vivo as part of a deletion strategy to improve succinate production The maximum theoretical structural flux towards succinate is 0.74 mole succinate/mole glucose while considering the biomass producing modes, whereas the structural flux for the wild-type is 0.093. Thus, theoretically, eight fold improvement in production  can be ain vivo flux measurements and predict preferred reaction directionalities on a given substrate. In future, we expect that structural fluxes can be further verified as more experimental flux measurements become available, spanning multiple gene knockout mutants, larger networks, and with higher accuracy. In addition, structural fluxes can be used for understanding the type of regulation occurring in a given reaction.Systematic consideration of the contribution of each pathway towards the cellular biological objective leads to the concept of structural fluxes. We have shown here that these structural fluxes reflect in silico metabolic engineering algorithm, iStruF, which is able to find solutions for metabolic engineering targets that couple growth with product formation while considering optimal as well as sub-optimal routes and their efficiency. These solutions were found to include targets that have been partially validated in vivo. Together, structural fluxes and iStruF constitute a novel and promising toolset for metabolic engineering.Building on the predictive power of structural fluxes, we present a formulation of a novel Supplement S1E. coli model (ME Model).(PDF)Click here for additional data file.Supplement S2Alignment of fluxes. Table S1, E. coli. Table S2, S. cerevisiae.(PDF)Click here for additional data file.Supplement S3Biological objectives.(PDF)Click here for additional data file.Supplement S4Normalization and succinate production. Table S3, CEFs vs. StruFs.(PDF)Click here for additional data file.Supplement S5Structural fluxes based on generating vectors. Table S4, Pearson correlations for StruFs, CEFs, and FBA in E. coli. Table S5, Pearson correlations for StruFs, CEFs, and FBA in S. cerevisiae. Fig. S1, Pearson correlations for StruFs in E. coli and S. cerevisiae. Fig. S2, Phenotypic phase plane analysis in E. coli. Fig. S3, Phenotypic phase plane analysis in S. cerevisiae. Fig. S4, Reaction participation in elementary modes vs. generating vectors.(PDF)Click here for additional data file.Supplement S6True match rates yeast. Table S6, True match rates yeast.(PDF)Click here for additional data file.Supplement S7Thermodynamic feasibility. Fig. S5, Thermodynamic constraints in central metabolism of E. coli. Table S7, Overview of classified reactions based on thermodynamics. References.(PDF)Click here for additional data file.


Yarrowia lipolytica is an oleaginous yeast which has emerged as an important microorganism for several biotechnological processes, such as the production of organic acids, lipases and proteases. It is also considered a good candidate for single-cell oil production. Although some of its metabolic pathways are well studied, its metabolic engineering is hindered by the lack of a genome-scale model that integrates the current knowledge about its metabolism.in silico tools and expert manual curation, we have produced an accurate genome-scale metabolic model for Y. lipolytica. Using a scaffold derived from a functional metabolic model of the well-studied but phylogenetically distant yeast S. cerevisiae, we mapped conserved reactions, rewrote gene associations, added species-specific reactions and inserted specialized copies of scaffold reactions to account for species-specific expansion of protein families. We used physiological measures obtained under lab conditions to validate our predictions.Combining Y. lipolytica iNL895 represents the first well-annotated metabolic model of an oleaginous yeast, providing a base for future metabolic improvement, and a starting point for the metabolic reconstruction of other species in the Yarrowia clade and other oleaginous yeasts. It is possible to find oleaginous organisms among plants, algae, bacteria and yeasts. Plants and algae are technically difficult  to modify genetically, while oleaginous bateria present a low growth rate. On the other side, oleaginous yeasts enjoy well-developed genetic tools for their improvement and grow quickly. Also, oleaginous yeasts can accumulate up to 70% of their dry mass as lipids [Even if lipid metabolism is common to all microorganisms, we call s lipids , making Yarrowia lipolytica, normally found as a food contaminant, has been extensively studied experimentally. It is easy to modify genetically, and presents many opportunities for metabolic engineering. For example, Y. lipolytica has been used as a food supplement, given its easily modifiable lipid composition. It is also studied as a potential source of biodiesel [Y. lipolytica is a hemiascomycete yeast, it is phylogenetically distant from S. cerevisiae and other well-studied yeasts, manifesting many metabolic differences: it is an obligate aerobic yeast, that can use normal hydrocarbons and various fats as carbon sources; it secretes diverse hydrolytic enzymes ; its perixosome is constitutive.One of those oleaginous yeasts, iodiesel -4, becauMetabolic models are an important tool for metabolic engineering. Their uses include the guidance of metabolic engineering, the contextualization of high-throughput data and helping hypothesis-driven discovery.Genome-scale metabolic models have up to now been principally produced for bacterial species and for a few higher organisms . We performed a manual curation of the initial draft model, adding species-specific metabolic reactions, in particular those related with central carbon and fatty acid metabolism. To assess the predictive power of our model, we compared our predictions against published experimental results of growth under different media conditions and gene knockouts. This comparison shows high degree of agreement between predictions and experimental results.In this work we present the first genome-scale functional metabolic model for families ,9 and coYarrowia lipolytica iNL895 describes 2 002 reactions encoded by 895 Y. lipolytica genes, the 1 847 metabolites consumed and produced by those reactions, the 16 compartments in which those reactions take place and a biomass function which describes the metabolic requirements for growth.Our functional genome-scale metabolic model for From the total of reactions, 139 (7%) are transport reactions with a gene association, 286 (14.3%) transport reactions that are spontaneous or without a known gene association, 171 (8.5%) are exchanges with the media, 1 055 (52.7%) enzymatic reactions with a gene association and 351 (17.5%) without.S. cerevisiae.The 1 055 enzymatic reactions with associated genes in the curated model were distributed into 39 biological processes, based on the associated GO Slim annotation of the closest ortholog in For alkane degradation we have introduced the ω-oxidation pathway including cytochrome P450 oxidases (12 genes ALK1–ALK12) and the cytochrome P450 reductase (CPR) reaction from each alkane  to the corresponding alcohol. We added reactions from alcohols to aldehydes then aldehydes to corresponding fatty acids, following .Y. lipolytica secretes lipases that are either extracellular (Lip2p) or membrane-bound (Lip7 and Lip8). These are part of a 19-gene multi-gene family [For triglyceride degradation e family .For fatty acid synthesis we have included in reaction r_2008 the effect of a new gene that codes a member of the type 1 acyl-CoA:diacylglycerol acyltransferase family (DGAT1), which has not previously been identified in yeasts, but is commonly found in mammals and plants, and proposed in  to give For transport and export of hydrophobic substrates we have included reactions for binding, export , and meY. lipolytica of genes linked to glycerol 3 phosphate (G3P), following [For oleaginous character, we have taken into account the loss in ollowing , specifiY. lipolytica due to missing genes (compared to S. cerevisiae), in particular Y. lipolytica cannot use sucrose as a sole carbon source due to the lack of the corresponding invertase. Note that transformation of Y. lipolytica strains is made possible through the inclusion of a selective marker built from a fusion of the S. cerevisiae SUC2 gene with the promoter and signal sequence of Y. lipolytica alkaline extracellular protease XPR2 [For galactose and sucrose substrates we verified the absence of reactions that are not present in ase XPR2 .S. cerevisiae, Y. lipolytica uses ethanol only with difficulty and does not produce it. These losses are reflected in reactions r_0176 through r_0190 concerning acetaldehyde to ethanol transformation.For ethanol production, unlike Y. lipolytica, and approved in terms of agreement with the literature: This model is not capable of producing ethanol, it cannot grow anaerobically, fatty acid metabolism presented expansions and contractions of protein families, and new species-specific reactions for the intake of alkanes were automatically detected.The draft model was verified by experts in Also, to assess the completeness of our model, we compared its phenotypic predictions in terms of growth/no growth, against published experimental results of observed growth, under several carbon sources and gene knockouts  of 0.65.In order to facilitate comparison, quantitative results from experiments and from simulations of biomass production were simplified into binary values (growth/no growth). Corresponding binary results were obtained for 98 experiments paired with simulations, with exact agreement in 64 cases (39 true positives and 25 true negatives). The 18 false negatives we observed may be attributed to missing reactions, corresponding to We stress that this qualitative validation does not substitute for quantitative comparison, but does show that each of the tested conditions is connected from uptake through to the biomass function. It thus serves to validate the completeness of the model, in particular with respect to overall network topology.in silico tools and expert manual curation, we produced an accurate genome-scale metabolic model of the oleaginous yeast Y. lipolytica, using a functional metabolic model of the phylogenetically related yeast S. cerevisiae as a scaffold for the reconstruction. The method developed in the present work can be used for genome-scale metabolic model reconstruction of other organisms, making it a useful tool for biotechnology and research.Combining S. cerevisiae reactions not present in Y. lipolytica was short, there was an important number of changes in the gene associations between both organisms. Also, the loss of some phenotypes in Y. lipolytica, compared to S. cerevisiae, was characterized by a loss of a small number of genes.We noticed that, even if the list of Y. lipolytica genes with unknown function, will provide evidence for some of them. The lack of accuracy at predicting some experiments could be explained by missing reactions in the model, especially regarding the transport of specific carbon sources. This gives us hints about possible ways to improve our model.Thirteen new transport reactions were added to the new model in order to connect enzymatic reactions inside the peroxisome with molecular species in the cytosol, and to import species from extracellular space to the cytosol. We could not find genes encoding for all those transports, but we expect that the eventual characterization of the 1 034 (16%) The modifications to the draft model performed by the manual curators allowed us to formalize a set of edit operations over metabolic models. This facilitated an automatic iteration process, from improvements to the reconstruction method, to improved draft models, to automatic application of curator edits, to automatic assertion of accuracy.Y. lipolytica metabolism. Data from high-throughput experiments, like microarrays and metabolomics, can be mapped to this model to have an overview of metabolic changes under different media conditions.The present model can be used to predict growth under different media conditions and gene knock-outs. It can also be used as a general description of the state-of-the-art in Y. lipolytica is constantly improving, and a number of features of its metabolism are the subject of ongoing work and consequently improvements to the model. Multigene families such as POX1–POX6 in peroxisomal β-oxidation could be modeled with better precision, since there are enzymatic specificities linked to the length of the carbon chain . This iric acid .et al.[S. cerevisiae sphingolipid metabolism; more recently, Gupta et al.[Y. lipolytica metabolic pathways with the same precision as dynamic differential equation models, but does have the merit of permitting a whole-genome model.Expansion of families of isozymes is detectable through expansion of paralogous protein families, but the method used here cannot detect these differences because FBA does not differentiate isoenzyme activities in the same reaction. Dynamic models that describe the kinetics of individual enzymes in reactions must be developed. This will require acquiring and integrating metabolic and transcriptomic data for targeted pathways, and developing models. Alvarez-Vasquez et al., for exata et al. developeY. lipolytica is described as growing on n-alkane paraffin (petroleum distillate) containing n-alkane oil (C12 to C18 n-akanes) and also n-paraffin wax  in [Y. lipolytica could use very long alkane chains above C20.The most pressing need in further iterations of the model is refinement of alkane degradation for decane and hexadecane. Indeed the analysis of alkane growth of ANT1 and ABC1 mutants were performed on n-alkane from C10 to C16, including C11, C13, and C15, in [kane) in . This suGenome-scale metabolic models describe the network of enzymatic and transport reactions in an organism. The main idea of most metabolic model reconstruction algorithms is to look for the presence of enzymatic reactions in the annotated genome of the organism to be modeled, and create a network of those reactions, representing the interconnected production and consumption of metabolites .Pathway Tools[The construction of metabolic models is costly and time consuming, so tools have been developed to automatically create initial, draft versions of the models, to be further improved by manual curation. Some of the current methods and platforms are way Tools, The SEEway Tools, AUTOGRAway Tools, and sevway Tools.These methods are mostly designed for bacterial organisms and are not always adequate for reconstruction of yeasts models. In particular, some of them lack proper handling of compartments, rewriting of gene associations, or rely on the strong functional relations provided by operons. Also, fine tuning existing programs was not always possible, given the lack of public source code availability. To cover these shortcomings, we implemented our own automatic reconstruction method (to be published separately). See Briefly, the method developed for the present work uses a scaffold model for the reconstruction. For each one of the genes associated to reactions described in the scaffold, we look for possible orthologs in the target organism. If certain conditions are met, the reaction is considered to be conserved, and added to the network of the target organism.This method of projection can be applied to any pair of phylogenetically close species. Given a set of ortholog maps between two genomes, and a well-annotated metabolic model for one of them, it automatically produces a draft model for the target, providing a well-documented starting point for manual curation.S. cerevisiae reaction R_0005  can be performed by either the product of gene YLR342W (FKS1) or the product of gene YGR032W (GSC2), so its Gene Association is “(YGR032W or YLR342W)”.Well-curated models include information about the dependency of each reaction on proteins and genes, which is called Gene-Protein-Reaction associations (GPR). The Gene Association is the dependency of a reaction on the presence of a combination of genes, described as a logical formula between gene identifiers. For example, Y. lipolytica model, we used three functional models published for S. cerevisiae: iMM904 [consensus model version 4.36 [Y. lipolytica metabolic model, and will be referenced as the ‘scaffold model’ in what follows. We used the detailed fatty acid metabolism described in iIN800 [Y. lipolytica fatty acid metabolism. From the scaffold model, we extracted the reactions predicted to be present in Y. lipolytica, the metabolites consumed and produced by them, the cellular compartments and all the non-enzymatic transport reactions. To make our model functional, we produced a list of genes that restored connectivity between the metabolites imported by the organism and the metabolic requirements of the biomass function. This list of genes provided as a starting point for the manual curation of the model.During the reconstruction of the iNL895 : iMM904 , iIN800 : iMM904  and the n iIN800  as a scaOrthology detection based on sequence similarity is the most used approach to predict if a biological function, encoded by genes, is conserved between two organisms . Some spS. cerevisiae) and the genome of the target (Y. lipolytica), we determine if the original genes that encode the protein required for the enzymatic activity are conserved. Our method determines a) if a reaction is conserved, b) if a re-written gene association formula for the reaction is necessary , and synteny (SONS ) This inIn the cases of divergent predictions, consensus was determined by the following election procedure: From the different methods we produce a tally of the number of times each paralog group appears between all existing homolog map.Our translator, using the rules described in Table The formulas that could not be resolved where reported to manual curation, as a possible loss of function  and the results of gap-filling analysis were also used as part of the manual curation.To assess the predictive power of our metabolic model, we compared growth predictions, obtained using Flux Balance Analysis (FBA) , againstWhen growth curves were provided, we calculated a boolean value representing growth (true) or no growth , where the threshold was decided based on 1/3 of the average of growth in time (OD), for all mutants studied ,44. The S. cerevisiae iIN800 [A confusion matrix and geometric mean  was usede iIN800  and iLL6e iIN800 .From the list of experimental results from the literature we produced a table of experiments, summarizing media conditions, gene knockouts, and observed growth . This was modified for each simulation, controlling the availability of different carbon sources. The name of media conditions used in We used FBA from COBRA Tools  to predihttp://biomodels.org), searching for the model id MODEL1111190000.We called our reconstructed model iNL895, following the rules defined in . We prodThe authors declare that they have no competing interests.NL and DJS conceived the study and wrote the paper. NL implemented the reconstruction method and produced the model. TD and JMN provided expert knowledge in the form of manual curation. All authors read and approved the final manuscript.underlined in the gene association column. Manual curation of lost reactions. In many cases, orthology results fail to associate a target gene to an enzyme-coding gene in the scaffold model, suggesting that the reaction is absent. Each of these predictions were manually reviewed, where a reaction was confirmed as being absent (‘Lost’), or was upheld (‘Retained’) when empirical evidence was available. Genes for which no ortholog could be found are Click here for fileValidation of the iNL895 model. This table lists 152 experiments extracted from the literature, detailing media conditions, gene KOs, and observed growth (as yes/no). It also includes our simulations of the same experiments, obtained using FBA/COBRA Tools, and the comparison between observed and the simulated growth. Click here for fileY. lipolytica iNL895. The three main parts of our pipeline for the reconstruction of the Y. lipolytica model are: Projection, where the S. cerevisiae scaffold model and the information from different sources of orthology between S. cerevisiae and Y. lipolytica are used to produce a draft model, Curation, where the expert curators revised the candidates for gap-filling and added species-specific reactions and Validation, where experiments obtained from the literature were compared with our simulations, producing a detailed accuracy report. Projection pipeline from S. cerevisiae scaffold model to Click here for fileS. cerevisiae reactions to Y. lipolytica. Pipeline for gene-association rewriting, as part of the projection of Y. lipolytica iNL895 model. From the 4 ortholog maps provided by different methods, a map of votes of possible ortholog mappings is created. Then, from the scaffold model, we extracted gene associations for each reaction, and re-wrote them based on our map of homologs (e.g.: Reaction1: (SourceGene1 or SourceGene2) ↔ (TargetGene1)). The new reactions, this time associated with Y. lipolytica genes, constituted the base of the reconstructed model. Gene Association rewrite from Click here for fileSelected gene annotations inY. lipolytica  . This table lists Y. lipolytica genes used in the manual curation of the metabolic model.Click here for fileComplete validation tests forY. lipolytica.   This MATLAB file runs the validation tests of the Y. lipolytica metabolic model. It requires the COBRA Toolbox (2.0+). Each of the 152 tests is declared as a MATLAB function, in order to help the curation process. All tests can be ran in batch mode using: matlab -nodisplay -nosplash -nojvm -r “model0=runTests; exit;” Click here for fileY. lipolytica  iNL895 SBML model. SBML representation of the reconstructed model of Y. lipolytica. This XML file is compatible with SBML Level 2, Version 4, and has been tested with COBRA Toolbox (2.0) and CellDesigner (4.1). This model can also be retrieved from the BioModels database (http://biomodels.org), under model id MODEL1111190000.Click here for file


Scheffersomyces stipitis is a yeast able to ferment pentoses to ethanol, unlike Saccharomyces cerevisiae, it does not present the so-called overflow phenomenon. Metabolic features characterizing the presence or not of this phenomenon have not been fully elucidated. This work proposes that genome-scale metabolic response to variations in NAD(H/+) availability characterizes fermentative behavior in both yeasts. Thus, differentiating features in S. stipitis and S. cerevisiae were determined analyzing growth sensitivity response to changes in available reducing capacity in relation to ethanol production capacity and overall metabolic flux span. Using genome-scale constraint-based metabolic models, phenotypic phase planes and shadow price analyses, an excess of available reducing capacity for growth was found in S. cerevisiae at every metabolic phenotype where growth is limited by oxygen uptake, while in S. stipitis this was observed only for a subset of those phenotypes. Moreover, by using flux variability analysis, an increased metabolic flux span was found in S. cerevisiae at growth limited by oxygen uptake, while in S. stipitis flux span was invariant. Therefore, each yeast can be characterized by a significantly different metabolic response and flux span when growth is limited by oxygen uptake, both features suggesting a higher metabolic flexibility in S. cerevisiae. By applying an optimization-based approach on the genome-scale models, three single reaction deletions were found to generate in S. stipitis the reducing capacity availability pattern found in S. cerevisiae, two of them correspond to reactions involved in the overflow phenomenon. These results show a close relationship between the growth sensitivity response given by the metabolic network and fermentative behavior. Scheffersomyces stipitis is a yeast well known for its ability to ferment xylose to ethanol and has been a matter of research in a broad number of studies, including two recently published genome-scale metabolic reconstructions S. stipitis does not present the so-called Crabtree effect or overflow phenomenon Saccharomyces cerevisiae does. This phenomenon refers to the occurrence of fermentative metabolism along with aerobic respiration (respiro-fermentative metabolism) triggered by high glucose uptake rates S. stipitis, it induces ethanol production only when growth is limited by oxygen availability S. stipitis's strong dependency between ethanol production and oxygen availability, regardless of carbon source availability levels, has been widely described in literature S. cerevisiae is driven by the overflow phenomenon and in S. stipitis by the oxygen limiting conditions. S. stipitis presents the proton translocating NADH dehydrogenase complex I (NDH1) and an alternative oxidase (AOX) at the respiratory chain, both absent in S. cerevisiae. This determines in S. stipitis a higher respiratory capacity than S. cerevisiaePentoses fermenting yeasts are important due to their relevance in the production of second generation biofuels, since xylose is the main pentose found in hemicelluloses and its fermentation to ethanol is key to obtain economically viable processes S. stipitis from S. cerevisiae may help the understanding of fermentative behavior and the metabolic engineering of ethanol producing strains. Fermentative metabolism is affected by NAD(H/+) cofactors and there is evidence showing that high NADH availability promotes fermentation. This is supported by a number of reports indicating that cofactor manipulation is a useful tool for improving fermentation performance E. coli that an increment in NADH availability induces fermentation by stimulating pathways which are normally inactive under aerobic conditions S. cerevisiae that the oxidation capacity of NADH is directly related to the occurrence of the overflow phenomenon, they were able to reduce it in a great extent by introducing a heterologous alternative oxidase (AOX) at the mitochondrion. Furthermore, Hou et al. S. cerevisiae strain disabled for formate anabolism, and modified to overexpress the native NAD dependent formate dehydrogenase, were able to induce fermentation by increasing intracellular NADH concentration via formate supplementation.Although fermentative metabolism has been widely studied in yeast, overall metabolic properties characterizing the occurrence of the overflow phenomenon are not fully understood S. stipitis the first two steps of xylose consumption produces an stoichiometric imbalance yielding a positive NADH balance. S. stipitis may prevent this NADH excess by converting NADH to NADPH through a bypass at the tricarboxylic acids cycle (TCA) S. cerevisiae strains, often leading to xylitol accumulation S. stipitis may be able to use the arabinose assimilation pathway backwards, oxidizing NADH and producing polyols. Accumulation of polyols in S. stipitis is several fold greater than in S. cerevisiae in aerobic batch culture  Aspergillus niger polyols are synthesized under oxygen limiting conditions, where they play a role in the balance of redox metabolism. Hence, evidence suggests that the metabolism of S. stipitis efficiently recycles NAD(H/+) cofactors, so that ethanol production under oxygen limiting conditions may be related to a compromise in the use of NADH for growth. On the other hand, NAD(H/+) availability is related to the flexibility of the flux network. Regarding this, using genome-scale metabolic modeling, Ghosh et al.S. cerevisiae, finding that cofactor imbalance increases the range of flux variability (flux span). Thus, an excess of NADH can lead to an increase in metabolic flexibility, allowing the induction of fermentative metabolism. Overall, the availability levels of NADH in both yeasts could lead to a metabolic response that determines whether NADH is used for growth or not. Therefore, growth sensitivity response to changes in NADH metabolic availability might be different in each yeast and may serve characterizing fermentative behavior.Regarding cofactor usage in S. cerevisiae, Reznik et al. A helpful way to study overall metabolic properties is by using genome-scale metabolic reconstructions +) availability affects fermentative behavior considering the genome-scale metabolic network Despite the amount of reports concerning fermentation in yeast, there are a few studies on how NAD(H/S. stipitis and S. cerevisiae regarding NAD(H/+) availability patterns in relation to ethanol production capacity and overall metabolic flux span. By considering the difference between NADH and NAD shadow prices as an index for available reducing capacity, which defines the ability of the flux-carrying pathways for supplying the NADH demand for growth, NAD(H/+) availability was studied. Ethanol production capacity was analyzed using production envelope analysis to characterize the relationship between growth and the production rate of ethanol. Flux variability analysis S. cerevisiae. From shadow price and phenotypic phase planes analyses differences in reducing capacity availability patterns were found. In S. cerevisiae an excess in available reducing capacity for growth was observed at every metabolic phenotype where growth is limited by oxygen uptake rate, while in S. stipitis this was found only at some of those phenotypes. Thus, phenotypes at exponential growth mapped in production envelope analysis are allocated in phenotypic phases of excess and limitation of available reducing capacity, for S. cerevisiae and S. stipitis respectively. Flux variability analysis showed an increased metabolic flux span in S. cerevisiae when growth is limited by oxygen uptake rate, while in S. stipitis flux span was invariant. This increased flux span along with the excess of available reducing capacity suggest high flexibility of the metabolic network of S. cerevisiae, allowing the overflow phenomenon. Furthermore, the relationship between these differentiating features to a metabolic function: the overflow phenomenon, was studied by seeking modifications able to generate excess of available reducing capacity in all phenotypes where growth is limited by oxygen uptake rate, and verifying their involvement in the phenomenon. Thus, deletions in S. stipitis generating the pattern of excess found in S. cerevisiae were searched for. By using an optimization-based approach it was found that the deletion of reactions in S. stipitis, which are negatively regulated during overflow phenomenon in S. cerevisiae, allowed the replication of the sought reducing capacity availability pattern.This work aims to determine the differentiating metabolic features between Hence, the relevance of the results of this work is that they allow establishing a close relationship between growth sensitivity response, regarding available reducing capacity, and fermentative behavior.S. stipitis (−1 h−1 (26.7 C-mmol gDW−1 h−1) and unbounded oxygen uptake rate were considered. As −1 is predicted by the model, which is close to the value reported by Papini et al. −1, at aerobic conditions where no ethanol production is observed. This envelope shows that in S. stipitis there is no coupling between growth and ethanol production at aerobic batch conditions. For S. cerevisiae, envelope 1 in −1 h−1 (84.5 C-mmol gDW−1 h−1) and unbounded oxygen uptake rate, while envelope 2 shows the one calculated considering an upper bound of 2.8 mmol gDW−1 h−1 for oxygen uptake rate, fitting the envelope close to the experimental values reported by Papini et al. −1 and a specific ethanol productivity of 19.90 mmol gDW−1 h−1 . As it can be observed, in contrast to S. stipitis, ethanol production and growth rate are coupled in S. cerevisiae, accounting for the presence of the overflow phenomenon. Arrows in +) availability patterns, phenotypic phase planes (PhPPs) and shadow price analyses were carried out for each yeast.stipitis  a glucosS. stipitis and S. cerevisiae. Each phase plane represents a qualitatively distinct phenotype having different optimal use of the flux network S. stipitis's metabolism is on the line of optimality, indicating a fully respiratory metabolism, while in S. cerevisiae, the occurrence of the overflow phenomenon, allocates its metabolism in a state characterized by high glucose uptake rate and growth limited by oxygen uptake rate.PhPPs analysis was performed characterizing growth rate as a function of glucose and oxygen uptake rates. S. stipitis  of the respiratory metabolism with the aim of forcing it to avoid the use of available reducing capacity for biomass production. Two approaches were used to find deletions: Firstly, an a priori approach which considered the modification of the mitochondrial NADH-consuming related pathways, with the purpose of decreasing respiratory capacity, expecting to generate the pattern found in S. cerevisiae. These modifications were:  cofactor recycling in S. stipitis, by using pathways such as: NADH to NADPH conversion through a by-pass at the TCA cycle, the alternative oxidase at the respiratory chain and polyol synthesis From production envelope analysis of biomass and ethanol fluxes, coupling for ake rate , this exS. cerevisiae, while in S. stipitis flux span was almost invariant (+) cofactors availability and overall flux span has been established by Ghosh et al. S. cerevisiae, finding that the modified model  presents larger overall metabolic flux span than the wildtype, showing that cofactor imbalance was responsible for this increase in flux span. In this work, the characteristic excess of available reducing capacity found in S. cerevisiae, as in the case of the cofactor imbalanced model studied by Ghosh et al. S. cerevisiae at all phenotypes with growth limited by oxygen uptake, the number of feasible alternate optimal states increases, thus increasing the metabolic network flexibility. On the other hand, available reducing capacity in S. stipitis is not always in excess, and metabolic flexibility is not increased. Reznik et al.S. cerevisiae than in S. stipitis. This along with the increased flux span of S. cerevisiae may provide the metabolic flexibility to allow the overflow phenomenon.Flux variability was evaluated for both yeasts in phenotypic phases where growth is limited by oxygen uptake rate. A large increase in overall flux span was found in nvariant . Then, tS. stipitis the S. cerevisiae were found. COX single deletion resulted in a phenotype with high growth rates associated with high ethanol flux and excess of available reducing capacity  have been described to account for the fermentative behavior of yeast, the approach presented in this work contributes to the characterization of yeast metabolism from the point of view of the entire flux network sensitive response, namely the available reducing capacity pattern. Therefore, a relationship between a property of the metabolic network: the shadow price, and a metabolic function: fermentative behavior, has been established.In conclusion, the results of this research allow relating metabolic sensitivity response to changes in available reducing capacity, to fermentative behavior. It was found that S. stipitis and S. cerevisiae. Thus, a number of in silico analyses were carried out: ethanol-biomass production envelopes, sensitivity analysis regarding available reducing capacity, flux variability analysis and ethanol overproducing phenotypes calculation.Genome-scale metabolic models S. cerevisiae and iBB814 S. stipitis. These models were chosen because they were constructed using experimental data, and have been empirically validated by a number of studies http://opencobra.sourceforge.net/).Genome-scale metabolic models used in this work were: iMM904 S. stitpitis and (−1 h−1) for S. cerevisiae.Production envelopes were determined using COBRA function productionEnvelope. Envelopes for ethanol production were calculated in two different ways: (Phenotypic phase planes (PhPPs) analysis Shadow price  S. stipitis the S. cerevisiae, flux value for certain reactions of the respiratory chain of S. stipitis were fixed to zero in the FBA to simulate metabolic deletions. These modifications were NDH1/AOX double-deletion and COX single-deletion.With the purpose of replicating in In-silico strains which enhance ethanol production were obtained via optimization-based approach by using Genetic Design through Local Search (GDLS) algorithm −1.S. stipitis in-silico strains to show an excess in available reducing capacity, as found in S. cerevisiae. For the NADH sink reaction fluxes between 0.1 and 0.6 mmol gDW−1 h−1, and a minimal growth rate of 0.20 h−1 were considered. Strains with single deletions which maximize ethanol flux were obtained using the modified model. The obtained deletions configured phenotypes with enhanced ethanol flux compensating for the low NADH availability generated by the sink. These single reaction deletions were applied to the non-modified model  enhancing ethanol flux and also increasing available reducing capacity.Since an excess in available reducing capacity is searched for, it was attempted to force an increase in the available NADH. By means of adding an artificial sink reaction the metabolism was driven to function with a low availability of NADH. Then modifications (deletions) were sought in the direction of compensating for the NADH demanded by the sink. These modifications were searched for using a bilevel optimization aproach (GDLS), because it finds deletions leading to flux coupling, in this case ethanol to biomass production. The formulation of the problem using this approach considered the maximization of both ethanol and biomass fluxes. In this way, considering the modified model (with the NADH sink), the modifications are conditioned not only by the metabolic NADH demand for growth and ethanol, but also for the sink. Thus, an increment in the available NADH is expected by applying those modifications to the original model. This strategy was used with the purpose of finding more deletions leading