In the past, tasks of model based yield optimization in metabolic engineering were either approached with stoichiometric models or with structured nonlinear models such as S-systems or linear-logarithmic representations. These models stand out among most others, because they allow the optimization task to be converted into a linear program, for which efficient solution methods are widely available. For pathway models not in one of these formats, an Indirect Optimization Method (IOM) was developed where the original model is sequentially represented as an S-system model, optimized in this format with linear programming methods, reinterpreted in the initial model form, and further optimized as necessary.S. cerevisiae, while the second describes the dynamics of the tryptophan operon in E. coli. Both models have previously been used for benchmarking purposes, thus facilitating comparisons with the proposed new method. In these comparisons, the geometric programming method was found to be equal or better than the earlier methods in terms of successful identification of optima and efficiency.A new method is proposed for this task. We show here that the model format of a Generalized Mass Action (GMA) system may be optimized very efficiently with techniques of geometric programming. We briefly review the basics of GMA systems and of geometric programming, demonstrate how the latter may be applied to the former, and illustrate the combined method with a didactic problem and two examples based on models of real systems. The first is a relatively small yet representative model of the anaerobic fermentation pathway in GMA systems are of importance, because they contain stoichiometric, mass action and S-systems as special cases, along with many other models. Furthermore, it was previously shown that algebraic equivalence transformations of variables are sufficient to convert virtually any types of dynamical models into the GMA form. Thus, efficient methods for optimizing GMA systems have multifold appeal. Model based optimization of biotechnological processes is a key step towards the establishment of rational strategies for yield improvement, be it through genetic engineering, refined setting of operating conditions or both. As such, it is a key element in the rapidly emerging field of metabolic engineering ,2. OptimThe most straightforward attempts toward improved efficiency have been based, in one form or another, on the reduction of the originally nonlinear task to linearity, because linear optimization tasks are rather easily solved, even if they involve thousands of variables. One variant of this approach is the optimization of stoichiometric flux distribution models . The twoAn alternative is the use of S-system models within the modeling framework of Biochemical Systems Theory -7. TheseAn extension of these linear approaches is the Indirect Optimization Method . In thisAn alternative to using S-system models is the General Mass Action (GMA) representation within BST. GMA systems are very interesting for several reasons. First, they contain both stoichiometric and S-system models as direct special cases, which would allow the optimization of combinations of the two. Second, mass action systems are special cases of GMA models, so that, in some sense, Michaelis-Menten functions and other kinetic rate laws are special cases, if they are expressed in their elemental, non-approximated form. Third, it was shown that virtually any system of differential equations may be represented exactly as a GMA system, upon equivalence transformations of some of the functions in the original system. Thus, GMA systems, as a mathematical representation, are capable of capturing any differentiable nonlinearity that one might encounter in biological systems. We show here that GMA systems, while highly nonlinear, are structured enough to permit the application of efficient optimization methods based on geometric programming.Pertinent optimization problems in metabolic engineering can be stated as the targeted manipulation of a system in the following way:subject to:In this generic representation, (1) usually targets a flux or a yield. The optimization must occur under several constraints. The first set (2) ensures that the system will operate under steady-state conditions. Other constraints (3) are imposed to retain the system within a physically and chemically feasible state and so that the total protein or metabolite levels do not impede cell growth. Yet other constraints (4) guarantee that no metabolites are depleted below minimal required levels or accumulate to toxic concentrations. These sets of constraints are designed to allow sustained operation of the system.X is represented as:Biological processes are usually modeled as systems of differential equations in which the variation in metabolites ni,j of the stoichiometric matrix N are constant. The vector v contains reaction rates, which are in general functions of the variables and parameters of the system. This structure is usually associated with metabolic systems, but it is similarly valid for models describing gene expression, bioreactors, and a wide variety of other processes in biotechnology. In typical stoichiometric analyses, the reaction rates are considered constant. Furthermore, the analysis is restricted to steady-state operation, with the consequence that (5) is set equal to 0 and thereby becomes a set of linear algebraic equations, which are amenable to a huge repertoire of analyses.The elements In analyses accounting for regulation, the reaction rates become functions that depend on system variables and outside influences. Even at steady state, these may be very complex, thereby rendering direct analysis of the system a formidable task . As a reγi is called the rate constant and fi,j are kinetic orders, which may be any real numbers. Positive kinetic orders indicate augmentation, whereas negative values are indicative of inhibition. Kinetic orders of 0 result in automatic removal of the corresponding variable from the term. In the notation of BST, the first n variables are often considered the dependent variables, which change dynamically under the action of the system, while the remaining variables Xi for i = n + 1 ... m + n are considered independent variables and typically remain constant throughout any given simulation study. Thus, metabolites, enzymes, membrane potentials or other system components can easily be made dependent or independent by the modeler without requiring alterations in the structure of the equations. BST is very compact and explicitly distinguishes variables from parameters.In analogy with chemical kinetics, monomial. If this monomial is an approximation of reaction rate V, its parameters can be directly related to V, by virtue of the fact that the monomial is in fact a Taylor linearization in logarithmic space [Because we will later introduce concepts of geometric programming, it is noted that the power-law term in Eq. 6 is also called a ic space . Thus, cThus, it follows directly from 7 that the parameters of a power-law  term can be computed asSystem equations in BST may be designed in slightly different ways. For the GMA form, each reaction is represented by its own monomial, and the result is thereforeaggregated terms are now represented as monomials, and the result isNote that this is actually a spelled-out version of Eq. 5, where the reaction rates are monomials as in Eq. 6. As an alternative to the GMA format, one may, for each dependent variable, collect all incoming reactions in one term Thus, there are at most one positive and one negative term in each S-system equation.The conversion of a GMA into an S-system will become important later. It is achieved by collecting the aggregated fluxes into vectorsN+ and N- are matrices containing respectively the positive and negative coefficients of N such that N = N+ - N-. With these definitions, we can derive the matrices of kinetic orders of S-systems from those of the corresponding GMA representation. Namely,where V, V+ and V- are square matrices of zeros having the corresponding vectors as their main diagonals. G and H contain the kinetic orders of the S-system while F contains those of the GMA [recasting technique, consider a simple equation where production and degradation are formulated as traditional Michaelis-Menten rate laws:where  the GMA . GMA sys the GMA . First,  the GMA . As an eX0 is a dependent or independent variable describing the substrate for the generation of X1. To effect the transformation into a GMA equation, define auxiliary variables as X2 = KM,2 + X1 and X3 = KM,1 + X0. The equation then becomeswhere X0 is a constant, independent variable. Thus, X3 is also constant and does not need its own equation. By contrast, X2 is a new dependent variable and from its definition we can calculate its initial value and see that its derivative must be equal to that of X1. Therefore the equations:For simplicity of discussion, suppose that form a system that is an exact equivalent of the original system but in GMA format.X0 is independent or to three if it is a dependent variable.Recasting can be useful with equations that are difficult to handle otherwise or for purposes of streamlining a model structure and its analysis. One must note though that often the number of variables increases significantly. In the case shown, the number of equations rises from one to two if The overall task is to reset some of the independent variables so that some objective is optimized. The independent variables in question are typically enzyme activities, which are experimentally manipulated through genetic means, such as the application of customized promoters or plasmids. The objective is usually the maximization of a metabolite concentration or a flux. Three approaches have been proposed in the literature.Among a number of convenient properties, the steady states of an S-system can be computed analytically by solving a system of algebraic linear equation . Equatinwhich is a monomial of the formMonomial equations become linear by taking logarithms on both sides thus reducing the steady-state computation to a linear task:whereMonomial objective functions become linear by taking logarithms and so holds for many constraints on metabolites or fluxes. Therefore, constrained optimization of pathways modeled as S-systems becomes a straightforward linear program .Any other relevant constraint or objective function that is not a power law can also be approximated using the abovementioned methods. Then logarithms can be taken and Eqns 1–4 can be rewritten as:Subject to:F is the logarithm of the flux or variable to be optimized, and superscripts L and U refer to lower and upper bounds. Eq. 20 assures operation at steady state. Matrix B and vector d account for additional equality constraints and C and e are analogous constraints for additional inequalities, which could, for instance, limit the magnitude of a metabolite concentration or flux, and improve the chances of viability. Optimization problems of this type are called linear programs (LPs) and can be solved very efficiently for large numbers of variables and constraints [Where straints .The advantage of the pure S-system approach is its great speed combined with the fact that S-system models have proven to be excellent representations of many pathways. The disadvantage is that the optimization process, by design, moves the system away from the chosen operating point, so that questions arise as to how accurate the S-system representation is at the steady state suggested by the optimization.If the pathway is not modeled as an S-system, the reduction of the optimization task to linearity is jeopardized. A compromise solution that has turned out to be quite effective is the Indirect Optimization Method (IOM) . The firA global optimization method for GMA systems  has beenGeometric programming (GP)  addresseposynomials. If some of the monomials enter the sum with negative signs, the collection is called a signomial. The peculiarities of convexity and GP methods render the difference between posynomials and signomials crucial.GP addresses optimization programs where the objective function and the constraints are sums of monomials, i.e., power-law terms as shown in Eq. 6. Because of their importance in GP, sums of monomials, all with positive sign, are called A GP problem has the generic form:Subject to:Pi(x) and Mi(x) must fulfill strict conditions. Every function Mi(x) must be a monomial, while the objective function P0(x) and the functions Pi(x) involved in inequalities must be posynomials. Signomials are not permitted, and optimization problems involving them require additional effort.where The equivalence between monomials and power laws immediately suggests the potential use of GP for optimization problems formulated within BST. In the next sections, several methods will be proposed to develop such potential.It is easy to see that steady-state equations of S-systems are readily arranged as monomials as shown in Eq 18 and that optimization tasks for S-systems directly adhere to the format of a GP, except that GP mandates minimization. However, this is easily remedied for maximization tasks by minimizing the inverse of the objective, which again is a monomial. By contrast, steady-state GMA equations as shown in Eq. 10 do not automatically fall within the GP structure, because GMA systems usually include negative terms, thus making them signomials. Furthermore, inversion of an objective that contains more than one monomial is not equivalent to a monomial.When the objective or some restriction falls outside the GMA formalism, it can be recast into proper form as has been discussed above and will be shown in one of the case studies.condensation [The proposed solutions for adapting GP solvers to treat GMA systems rely on ensation , but theand, in the terminology of Eqs. 10 and 11, defined as:αi and gi,j are chosen such that equality holds at a chosen operating point; thus, the result is equivalent to the Taylor linearization that is fundamental in BST as was shown in eqn. 7 [where n eqn. 7 ,7,12. Asand therefore, the condensed form is an understimation of the original.Objective functions can only be minimized in GP, this is seldom a problem given that the functions to maximize are often monomials that can be inverted: a variable, a reaction rate or a flux ratio. Posynomial objectives are usually entitled for minimization, like the sum of certain variables. Nonetheless, it is also relevant in metabolic engineering to consider the maximization of posynomials, such as the sum of variables or fluxes. In such cases, condensation or recasting can be used. For en extensive introduction on GP modelling see .The steady-state equation of a GMA system may be written as the single difference of two posynomials:If both posynomials are condensed, every equation will be reduced to the standard form for monomial equations:Because the division of a monomial by another is itself a monomial.Since the steady state equations of the GMA have been condensed to those of an s-system, this method could be regarded as a direct generalization of classical IOM methods. One of the advantages of this approach is the possibility of keeping posynomial inequalities and objectives as they are and therefore reduce the amount of condensation (approximation) needed, but there is another interesting possibility. When a posynomial is approximated by condensation, the A-G inequality, Eq. 30, guarantees that the monomial is an underestimation of the constraint. Furthermore, the posynomial structure is not altered when divided by a monomial so the quotient between a posynomial and its condensed form is always greater than or equal to 1 and provides the exact error as a posynomial function. Therefore the problem can be constrained to allow a maximum error per condensed constraint:So the original problem is solved as a series of GPs in which the GMA equations are successively condensed using the previous solution as the reference point. To assure validity an extra set of constraints is added to ensure that every iteration will only explore the neighborhood of the feasible region in which error due to condensation remains below an arbitrary tolerance set by the user.A similar yet distinct strategy that minimizes the use of condensation is an extension of the penalty treatment method , a classwhere P and Q are posynomials, is replaced by two posynomial equalities through the creation of an ancilliary variable t:These are not valid GP constraints, so the following relaxed version is used:t, the feasible area of the original problem is contained in the feasible area of the new relaxed version and aproximation by condensation is not needed. In order to force these inequalities to be tight in the final solution, the objective function is augmented with penalty terms that grow with the slackness of the constraints, namely the inverses of the condensation of the relaxed constraints. The result of this procedure is a legal GP:Upon dividing by Where the condensed terms are calculated at the basal steady state. If the obtained solution falls within the feasible area of the original problem, it is taken as a solution, if it does not , which is disconnected from the true optimal solution. While both IOM and the Controlled-Error method reported the initial point as the solution, the penalty treatment algorithm found the global optimum at .The feasible region of this problem consists of two points  and , of which clearly the first solution is superior, because In this case, most methods failed to find the optimal solution because the approximated s-system had the operating point as the only feasible solution while the relaxed problem for the penalty treatment algorithm had a feasible area  maximization of the ethanol production rate,  see Fig . Being pThe results are sumarized in Table E. coli, as illustrated in Fig. The third example addresses the tryptophan operon in A model of the system was recently presented by  and inclX1, X2 and X3 are dimensionless quantities representing mRNA, enzyme levels and the tryptophan concentration, respectively. The rate equations are:Here The GMA format is obtained by defining the following ancillary variables:which turns the rates into power laws:v8, which may be regarded as an aggregate term for growth and tryptophan excretion.The objective function consists simply of A recurrent feature of previously found IOM solutions was the noticeable violation of a constraint retaining a minimum tryptophan concentration. This discrepancy is a feature for comparisons between methods beyond computational efficiency. The Appendix contains a complete formulation of the optimization problem.In order to test the effectiveness of the controlled error approach, two variants were used in this model:• Fixed tolerance. The standard method in which every iteration is limited to a maximum condensation error of 10% by constraints described in Eq. 33.• Fixed step. No limit on the condensation error. The variation of the variables in every iteration is limited to 10% distance from the reference state.a priori. The fixed step method remains within a lower margin of error in this case due to the good quality of the condensed approximation but this margin is not under direct control and will depend on the size of the subintervals and on the model in an unforeseeable way. When the error tolerance was lowered to match the values observed for the fixed step method, both performed very similarly with a slight advantage of the fixed tolerance.When the constraints were absent (fixed step), the variation of the variables was restricted to a fraction of the total range in every iteration, in order to prevent them from moving too far from the operating point. Fig. Both the controlled error and penalty treatment methods yielded the same results while SQP returned a solution that was feasible but yielded a lower flux. As can be seen in Table ad hoc tricks such as subdividng the system in many subsystems, finding convex relaxations of the constraints, adding extra variables or a combination of several of these strategies.The main challenge of non-linear optimization is dealing with non-convexities. In some cases, like GP, there is an elegant transformation that convexifies the problem without adding undue complexity. But this is seldom the case and dealing with non-convexities usually implies developing Geometric programming provides a simple and efficient tool for the optimization of biotechnological systems that takes advantage of the structural regularity and flexibility of GMA systems. In this work we have presented two different strategies to do so, of which the penalty treatment seems to be the most promising. The methods are quite general, as this treatment of GP and recasting can be applied to any rational function, which in fact include almost all rate functions used in representations of metabolic processes.The use of geometric programming also provides a solution for the problem of constraint violations in the two strategies considered. The possibility of keeping an arbitrarily small approximation error in every iteration prevents the buildup of discrepancies in the Controlled Error Method which results in a "safer" condensation while the Penalty treatment doesn't rely on condensation to define the feasible area. It has been shown elsewhere  that GP Geometric programming is a relatively recent and active area in operations research, which implies that further improvements and refinements for the optimization of GMA systems are to be expected. But even with existing methods, the optimization of this large class of systems, which is further expanded by the technique of recasting, has become feasible for execution of moderately sized tasks even on simple desktop computers.The author(s) declare that they have no competing interests.


Genome-scale metabolic reconstructions under the Constraint Based Reconstruction and Analysis (COBRA) framework are valuable tools for analyzing the metabolic capabilities of organisms and interpreting experimental data. As the number of such reconstructions and analysis methods increases, there is a greater need for data uniformity and ease of distribution and use.We describe BiGG, a knowledgebase of Biochemically, Genetically and Genomically structured genome-scale metabolic network reconstructions. BiGG integrates several published genome-scale metabolic networks into one resource with standard nomenclature which allows components to be compared across different organisms. BiGG can be used to browse model content, visualize metabolic pathway maps, and export SBML files of the models for further analysis by external software packages. Users may follow links from BiGG to several external databases to obtain additional information on genes, proteins, reactions, metabolites and citations of interest.http://bigg.ucsd.edu.BiGG addresses a need in the systems biology community to have access to high quality curated metabolic models and reconstructions. It is freely available for academic use at  Metabolism is the structure and behavior of chemical reaction networks that occur in living organisms in order to maintain life. It is intrinsically linked to many other cellular functions and metabolic abnormalities are implicated as the cause of various diseases. Over the last 100 years, the list of reactions comprising an organism's metabolism has largely been catalogued. This reductionist process has focused on characterizing individual reactions in great detail. However, as the body of metabolic knowledge grew, so did the desire to integrate it into comprehensive models to simulate, predict and ultimately understand its behavior on a systems level. Kinetic models utilizing a system of differential equations are an established method of modeling biochemical pathways -5 as welIn contrast, constraint based modeling based on genome-scale metabolic reconstructions aim to include every known reaction for an organism, through the integration of genome annotation and biochemical knowledge. Reactions are defined simply by their reaction stoichiometry, and the networks are easily converted to mathematical models on which constraint-based analysis can be applied. In this paradigm, model predictions depend on constraints through reaction fluxes and an inferred metabolic objective, rather than on precisely defined kinetic parameters. Metabolic reconstructions have proven broadly useful for a number of applications. Case studies have been reviewed in .biochemically, genetically and genomically structured (BiGG) knowledgebase of metabolic reconstructions.In recent years, the publication of hundreds of genomes, with various databases such as KEGG , Biocyc S matrix) of the reconstruction is created and used to validate network structure by testing functionality, such as growth under some condition or the ability to produce a specific metabolite. Furthermore, gap analysis identifies possible missing reactions by finding so called 'dead end' metabolites which can be produced by the network but not consumed. Failure of network validation tests and the existence of gaps suggest targeted literature searches or experiments, which can be used to improve the model. Each reaction is verified individually and a confidence score can be assigned by the curator. A model may undergo several iterative rounds of validation and changes before it reaches a satisfactory state and is published, a process which can take up to a year of time. Because of the great effort involved, there have been attempts to partially automate the process [A general bottom-up metabolic reconstruction process has been formulated and detailed in ,17. Init process -31 and s process .Most biological reactions require enzymatic catalysis to occur. Thus the 'on' or 'off' state of each reaction in the network is controlled by the genotype and expression level of associated genes. In the simplest case, a reaction is catalyzed by only a single enzyme which is coded for by a single gene. The expression and translation of that gene implies the feasibility of the reaction, and vice versa. More complex cases involve multiple genes and proteins whose relationship is described using Boolean logic. A single protein may be composed of subunits coded by two (or more) genes. If all of these subunits are required for the catalytic activity of the protein, the activity is modeled as an 'and' logic ('gene A and gene B'). Alternatively, the model allows for equivalent proteins (isozymes) to catalyze the same reaction. In this case, the presence of either protein is sufficient to establish the activity of the reaction and an 'or' logic is used ('protein A or protein B'). Other phenomena, which are representable in the Boolean framework, are alternative splicing ('or' logic) and obligate protein complexes ('and' logic). Collectively, these Boolean logic statements relating genes, proteins, and reactions are named GPRs. If a GPR statement of a reaction evaluates to 'true,' then its corresponding reaction is said to be feasible. Thus, GPRs may be used to evaluate the effects of gene knockouts and gene regulation on the metabolic reconstructions, ruling out reactions whose genes are not available. GPRs may also be displayed graphically. Figure Homo sapiens Recon 1 [Escherichia coli iJR 904 [iAF1260 [Saccharomyces cerevisiae iND750 [Staphylococcus aureus iSB619 [Methanosarcina barkeri iAF692 [Helicobacter pylori iIT341 [BiGG is currently capable of browsing and exporting the contents of seven different genome-scale reconstructions of six organisms  supplied server running an Oracle™ database. Access to this database is provided by a read-only client with several tables and views for accessing information on Reactions, Metabolites, Genes, Proteins, Maps and Citations Figure . All queThe two main functions of BiGG are browsing content and exporting whole reconstructions. The browser is designed for querying the content and comparing different reconstructions whereas the exporter is primarily designed to enable further computational analysis by other software packages.http://graphviz.org. Hyperlinks to other databases are included whenever provided by the authors of the reconstructions. These include NCBI Entrez gene database [http://www.cas.org identifications for metabolites.The BiGG browser contains entries for metabolic reactions, metabolites, genes, proteins, and literature citations Figure . Reactiodatabase , Uniprotdatabase  for geneReactions and metabolites can be searched through the Search Reactions and Search Metabolites pages. Reactions may be searched for by name, EC number, or associated gene. Alternatively, all reactions in a model may be listed by using the model name as the only search parameter. It is also possible to specify compartment, pathway, or metabolite participation. Results may be limited by only including reactions with known gene associations, high or low confidence, or by excluding transport reactions. In addition, reactions may be searched across reconstructions allowing for model comparison. Lists of reactions matching a set of criteria may be exported as a tab delimited flat file. The exported files can contain information for multiple models, simplifying model comparison.Metabolites may be searched for by name, KEGG ID, CAS ID, or charge. Just as for reactions, limiting searches by compartment, pathway, and organism is possible. In addition to basic metabolite information such as formula and charge, lists of reactions in which the metabolite participates are listed and categorized by the metabolite's role as a reactant or a product. Lists of metabolites matching a set of search criteria may be exported as tab delimited flat file, and contain information such as metabolite name, abbreviation, formula, KEGG ID, and CAS ID. The browser interface is shown in Figure For visualization, curated metabolic maps are provided for many organisms in BiGG. These maps show metabolites, reactions, and text markup. Some large reconstructions (in particular human Recon 1) have several maps for different metabolic subsystems. Maps are rendered with Scalable Vector Graphics (SVG) for smooth scaling and are hyperlinked back to the entries in the database. A small portion of a metabolic map from the human reconstruction is shown in Figure The second function of the BiGG knowledgebase is exporting reconstructions as Systems Biology Markup Language (SBML) files , which apartially decompartmentalized reconstruction removes these internal compartments and relocates their reactions and metabolites to the Cytosol. A full decompartmentalization removes internal compartments as well as the boundary between the Extraorganism and Cytosol compartments, creating a single-compartment system. In either case, internal transporters are removed.A reconstruction may be exported as a decompartmentalized model. A compartment in a metabolic reconstruction is a distinct pool of metabolites and their reactions. Metabolites are exchanged among compartments by transporter reactions. All reconstructions included in BiGG have at least two compartments: Cytosol and Extra-organism. Additionally, reconstructions of eukaryotic organisms have internal compartmentalization modeling subcellular organelles. A It should be noted that the utility of decompartmentalization lies in model comparison rather than a basis for simulations. For instance, reactions such as ATP synthase are driven by an electrochemical gradient across compartment boundaries. In the decompartmentalized model there can be no gradients thus the ATP Synthase reaction becomes thermodynamically incorrect, creating unpredictable outcomes with some optimizations. As a rule, decompartmentalization should only be used for comparative purposes. Computational studies should only be performed on the full models.The exported SBML file may include information on genes, proteins and citations. Because the SBML specification does not include fields for this kind of data, this information is stored in the 'notes' field of the reaction entries.The notes field of the Reaction entries in the exported SBML file can include Boolean strings corresponding to the GPR statements. The GPR field is read and interpreted by the COBRA toolbox but should be ignored by other programs.Reconstructions are the basis for computational models. The process of converting a reconstruction into a model is performed by the curator and is reviewed in ,49. UppeMost of the simulations are run by default under parameters simulating aerobic growth condition in glucose minimal medium. This is modeled by the constraints on fluxes of the model's exchange reactions. For instance, modeling of an aerobic environment with glucose minimal media must allow for glucose, oxygen, ammonium ion, salts, and other ions to be up-taken but other carbon sources only excreted. These bounds are included in the SBML file along with the objective coefficients of each reaction and flux distribution. For simulating other conditions there is a web based interface for changing the bounds on any reaction by pressing the "refine" button. In this way, SBML files corresponding to different media compositions can be created.SBML files conform to the level 2 version 1 specification and are compatible with the COBRA toolbox  which coH. pylori, to 3743 reactions in the human reconstruction. The total number of metabolites in BiGG is 2556, of which more than half (1509) are found in the Human Reconstruction  share a total of 240 reactions, 80 of which are exchange reactions  which are also not gene associated. These two have been replaced with elementary reactions. This leaves 44 reactions with missing gene associations in iJR904. Fourteen now have genes in iAF1260 while the remaining 30 do not. Twelve of these 30 are found in at least one other reconstruction, forming the basis for further searching. Analyses like these provide an overview of the state of reconstructions and can pinpoint areas of future focus. Performing this analysis without the BiGG knowledgebase would be possible although cumbersome.All reconstructions have knowledge gaps where information on components is not available. One example is orphan reactions which are reactions for which the catalyzing enzyme is unknown. The BiGG knowledgebase can be used to study and help fill in these knowledge gaps by 1) listing all orphan reactions and 2) displaying any other reconstruction that use these reactions. complete . The iJRBacillus subtilis and Haemophilus influenzae. As they become available, they will be added to BiGG as well. Currently, only E. coli has more than one reconstruction version, but in the future, we plan on hosting different (older) versions of other reconstructions as well. Currently, it is only possible to host reconstructions created within the Simpheny software and at the moment there is no way to import other groups' reconstructions. This may change in the future.Two notable reconstructions in development are The BiGG knowledgebase is designed to work with the COBRA toolbox. Version 2.0 of this toolbox will be released soon and will include a visualization component. The BiGG maps will be downloadable in a custom text format containing coordinates of all metabolites and reaction control points. This is imported into COBRA and displayed in a customizable fashion. Colors and sizes can be changed on a per-reaction basis to visualize biological results.At present, exported models contain one set of lower and upper flux bounds. Lower bounds of irreversible reactions are automatically set to 0 and upper bounds are either set to arbitrarily large values (eg. 999999) or physiologically determined rates. However, to run meaningful simulations, the bounds of the exchange fluxes must be specified to match the environment. For instance, modeling of an aerobic environment with glucose minimal media must allow for glucose, oxygen, ammonium ion, and salts to be taken up, but not other extracellular species. Currently, this must be done manually via the export "refine" button, but in the future, libraries of bounds (constraint) vectors will be added to the SBML files to allow the user to specify media conditions.+ and H2O are simply ignored [The reconstructions and models in BiGG have several specific features necessary to compute within the COBRA framework: 1) Each reconstruction in BiGG is manually curated. Exotic transformations unique to an organism may be absent from databases and must be pulled from primary literature. 2) BiGG uses both genetics and literature based data to assess whether a reaction is present. If the genetic basis for a reaction is unknown but the reaction is described in the literature, it will be included without associated genes (an "orphan reaction"). 3) The curators of BiGG reconstructions have the option of providing confidence levels for reactions which can be used when evaluating resultant models. These levels, along with reaction notes, provide an assessment of the confidence that a reaction is correctly included in the model. 4) Boolean relationships between genes, proteins and reactions (GPRs) are described in BiGG. This information is necessary for the proper modeling of mutations or gene knockouts. 5) All reactions in BiGG are mass and charge balanced. In some metabolic databases, simple species such as H ignored . Failure ignored . 7) BiGG ignored ), and ot ignored . The advhttp://bigg.ucsd.edu/. A JavaScript enabled browser is required for browsing and exporting. The map viewer requires SVG support. BiGG data and results require a password which is made freely available for academic use.The BiGG knowledgebase is available online at BiGG: Biochemically, Genetically and Genomically structured; CAS: Chemical Abstracts Service; COBRA: Constraint Based Reconstruction and Analysis; GPR: Gene, Protein, Reactions; KEGG: Kyoto Encyclopedia of Genes and Genomes; SBML: Systems Biology Markup Language.JS built the database interface and content browser. TC and JP wrote the export tool and GPR visualization. JP wrote the map visualization. JS and TC drafted the manuscript. All authors read and approved the final manuscript.Table 1 - Contents of BiGG. BiGG currently contains 7 reconstructions including two versions of E. coli. There are a total of 7234 unique reactions and exchanges in the database. Exchange reactions carry metabolites from the extracellular 'compartment' across the system boundary and are not technically part of the metabolic reconstruction. Translocation reactions carry a metabolite between compartments (possibly performing other transformations). Reactions can be gene associated or not. Every reconstruction contains the 'cytosol' and 'extracellular' compartment. Human and yeast contain 'endoplasmic reticulum', 'mitochondria', 'peroxisome', 'nucleus'. The 'periplasm' in iAF1260, vacuole in yeast, and lysosome in human are unique to these reconstructions.Click here for fileTable 2 - Orphan reactions. 58 E. coli iJR904 orphan (non-gene associated) reactions are categorized by current status. 'Found in 1260' shows whether the reactions are found in reconstruction iAF1260. 'Y*' indicates that the reaction is found in iAF1260 in modified form . Notes: spont. -spontaneous, lump - lumped reaction, virtual - virtual reaction, P - H. pylori, S - S. aureus, Y - S. cerevisiae, H - H. sapiens,Click here for file


Geobacter sulfurreducens suggested the existence of several redundant pathways. Here, we identified eight sets of redundant pathways that included redundancy for the assimilation of acetate, and for the conversion of pyruvate into acetyl-CoA. These equivalent pathways and two other sub-optimal pathways were studied using 5 single-gene deletion mutants in those pathways for the evaluation of the predictive capacity of the model. The growth phenotypes of these mutants were studied under 12 different conditions of electron donor and acceptor availability. The comparison of the model predictions with the resulting experimental phenotypes indicated that pyruvate ferredoxin oxidoreductase is the only activity able to convert pyruvate into acetyl-CoA. However, the results and the modeling showed that the two acetate activation pathways present are not only active, but needed due to the additional role of the acetyl-CoA transferase in the TCA cycle, probably reflecting the adaptation of these bacteria to acetate utilization. In other cases, the data reconciliation suggested additional capacity constraints that were confirmed with biochemical assays. The results demonstrate the need to experimentally verify the activity of key enzymes when developing in silico models of microbial physiology based on sequence-based reconstruction of metabolic networks.Previous model-based analysis of the metabolic network of  Geobacter sulfurreducens is a member of the Geobacteraceae family of micro-organisms that breathe metals and have a unique mode of metabolism. Stimulation of the activity of this species in the environment has been shown to result in the removal of radioactive contaminants in groundwater. Similarly, the respiration of these micro-organisms also has been linked to electricity generation in a microbial fuel cell. Both the rate of electricity generation and the efficiency of ground water clean-up can be enhanced through the improved understanding of the growth and metabolism of Geobacteraceae. In order to better understand the growth and metabolism of this organism, we had constructed a large-scale mathematical model of the metabolic network of this organism. Using this model, we identified reaction alternates that sustain metabolism in the event of gene deletions. We then experimentally confirmed the role of these metabolic reactions through gene deletion mutants and biochemical assays and improved the predictive ability of the mathematical model. Such an integrated computational and experimental approach can be used to study the activity and function of metabolic network in a rapid manner for other poorly characterized organisms of environmental relevance. Geobacter species are of interest because of their natural role in carbon and mineral cycling, their ability to remediate organic and metal contaminants in the subsurface, and their capacity to harvest electricity from waste organic matter [Geobacter sulfurreducens [c matter –3. Geobareducens  is the mreducens , the comreducens , whole greducens  and genoreducens  are avaireducens –14.G. sulfurreducens can use either acetate or hydrogen as the sole electron donors for Fe(III) reduction, and fumarate or malate can also be used as terminal electron acceptors [Geobacter species is required because acetate, secreted by fermenting organisms, is the dominant electron donor for Geobacteraceae in soils and sediments [Geobacter species [Geobacter species, and the closely related Desulfuromonas acetoxidans, oxidize acetate via the TCA cycle [G. sulfurreducens, a constraint-based genome-scale metabolic model was constructed and used to investigate the unique physiology associated with the reduction of extracellular electron acceptors, such as Fe(III) [cceptors . An undeediments , and bec species ,17. PrevCA cycle –20. Howe Fe(III) . The gen Fe(III) .G. sulfurreducens [E. coli, where four metabolic gene deletion mutants had significantly different metabolic flux distributions, but similar overall growth rates [Furthermore, the network reconstruction revealed the existence of a number of redundant or alternate pathways in the central metabolism of reducens . Recent reducens –26. Expeth rates . Hence, G. sulfurreducens. We demonstrate the need for redundancy in the acetate assimilation pathways, due to a coupling between the TCA cycle and acetate activation to acetyl-CoA, and also the inactivity of some of the predicted alternatives for pyruvate oxidation to acetyl-CoA. We also show that by using this information to constrain the model, its predictive capacity can be improved.Here we report on a coupled computational and experimental evaluation of potential redundant pathways during acetate metabolism in G. sulfurreducens , which are conserved across different Growth of the mutants with acetate as the donor, the condition used for redundant pathway identification, was evaluated. In addition, to further evaluate the predictive capacity of the model, the mutants were grown on combinations of acetate, pyruvate, and hydrogen as the carbon source/electron donor with either fumarate or Fe(III) citrate as the electron acceptor . This reG. sulfurreducens could grow in the presence of pyruvate and hydrogen with either acceptor. This indicated that pyruvate can be transported and used as a carbon source but it cannot serve as carbon and electron donor. The reason for this phenotype is not known and contrasted with predictions of the previously published model based on the presence of the transporter and enzymes needed for pyruvate oxidation [The wild type strain could grow on all combinations of donors/acceptors except when pyruvate was the sole donor/carbon source with either fumarate or Fe(III) citrate as the acceptor A and 5A.xidation . Thus, ixidation ., pyruvate dehydrogenase (Pdh) and pyruvate formate lyase (Pfl), which could potentially substitute for pyruvate ferredoxin oxidoreductase activity, but with the production of different reduced electron carriers (G. sulfurreducens [The pyruvate ferredoxin oxidoreductase (Por) reaction was evaluated because examination of the mutant phenotypes when growing on pyruvate as carbon source, would provide information about the functionality of the alternative reactionscarriers A. It is reducens .Methanosarcina mazei Go1, 42% identity for CAE09839 from Wolinella succinogenes DSM 1740). Furthermore, in both cases a gene coding for a phenylacetate CoA ligase, an enzyme involved in the metabolism of phenylalanine or in the aromatic catabolism of phenylacetic acid, is present immediately downstream, suggesting a putative role for the product of these genes in the reduction of a 2-oxoacid of the aromatic type. Therefore, the best Por candidate was GSU0097, encoding a putative homodimeric type enzyme [Nostoc sp. PCC 7120), where this enzyme has a role in providing electrons to ferredoxin or flavodoxin, the electron donors for nitrogenase [There were three putative Por encoded in the genome, two of them of the heterodimeric type, (gene clusters GSU1859–62 and GSU2052–54), and one of the homodimeric type (GSU0097 gene). The first two are more similar to indolpyruvate ferredoxin oxidoreductases, enzymes involved in the metabolism of aromatic amino acids  eliminated malate dehydrogenase activity  citrate is the electron acceptor was predicted by the model. Although there is a predicted alternative pathway for conversion of malate to oxaloacetate involving the malic enzyme and pyruvate carboxylase C, this aFor growth on fumarate, the model predicted that, in order to compensate for the lack of Mdh, the flux through the pyruvate carboxylase would have to increase over 50 fold relative to the wild type flux distribution. The measured activity of the pyruvate carboxylase was low in the wild type, ca. 5 μmol/mg of protein/min. When pyruvate carboxylase flux is constrained at levels for the wild type cells, the model correctly predicts that MDH1 should not be able to grow with acetate as the carbon source, even with fumarate as the electron donor .G. sulfurreducens genome  whereas there were two genes whose products putatively code for Ack, GSU2707 and GSU3348 [In order to evaluate the potential redundancy in pathways for converting acetate to acetyl-CoA B, the gePTA1 was unable to grow with acetate as the electron donor E and 5E.In order to further evaluate this phenotype of PTA1, the predicted alternative pathway for succinyl-CoA synthesis catalyzed by succinyl-CoA synthetase was investigated. No succinyl-CoA synthetase activity was detected in cell extracts , consistThe model simulations with an inactivated succinyl-CoA synthetase match the experimental observations in all the cases, except for growth in the presence of both acetate and pyruvate, or acetate, pyruvate and hydrogen. It may be that PTA1 accumulates acetyl phosphate, in a manner similar to mutants in other organisms that lack phosphotransacetylase . Acetyl In order to further evaluate the mechanisms for formation of acetyl-CoA, the acetyl-CoA transferase activity B was invG. sulfurreducens genome. These genes are also similar to well characterized acetyl-CoA hydrolases from S. cerevisiae , anddentical ). The mu2 medium than the wild type, an observation which could not be explained based on the Flux Balance Analysis model. ATO3, which completely lacked acetyl-CoA transferase activity, could only grow with hydrogen as the electron donor  predicted the growth phenotype in 47 of the 72 growth conditions evaluated . One of n source . With thated see . The modated see . While tIn addition, an alternative approach for simulating the phenotype of knock-out mutations , in whicG. sulfurreducens. Such integrated analysis of computational and experimental data can provide valuable insights on the activity and function of metabolic pathways in a rapid manner for poorly characterized organisms of environmental significance.In summary, the results demonstrate that the iterative comparison of the in silico and the in vivo phenotypes has led to additional information on the role and activity of the central metabolic pathways in G. sulfurreducens [G. sulfurreducens can grow on pyruvate only if an electron donor, such as hydrogen is also present (see −1 and 0.043 hr−1 for fumarate and Fe(III) citrate reduction, respectively, and were found to be consistent with experimental observations. If a particular substrate was not present in an environment, the uptake rate corresponding to the substrate was constrained to be zero.The previously described constraint-based in silico model of reducens  served asent see . In orde−1 were considered to be lethal.Two different approaches to the prediction of a deletion mutant growth rate have been proposed in the past based on the assumptions of the cellular objective after a gene deletion ,42,43. GThe range of variation in fluxes for all various reactions in the model at the predicted optimal (maximum possible) growth rate was calculated with the previously described  Flux Variability Analysis (FVA) algorithm. Briefly, this algorithm involves the maximization and minimization of every flux in the network subject to the stoichiometric constraints and an additional constraint that forces an optimal growth rate. The solution of this series of optimization problems results in the maximum and the minimum value of flux allowed for every reaction in the network, given the constraint that the growth rate is optimal . SimulatG. sulfurreducens strains used in this study (is study  were groG. sulfurreducens strain DL1 (ATCC 51573) [Mutations were introduced into the chromosome of C 51573)  by homol2, 10% CO2, and 83% N2 atmosphere at 30 °C. A single isolate of each mutant was selected for detailed analysis and maintained with the adequate antibiotic. All the insertion-deletions were confirmed by PCR analysis.Primers used for the construction of the various linear fragments utilized for gene disruption are listed and described in In order to generate a mutant strain completely lacking the acetate:succinate Coenzyme-A transferase activity, a double mutant (ATO3) was constructed by electroporation of ATO2 mutant with the DNA fragment used to construct ATO1 (Supplementary Information: Protein content was determined by a modification of the method of  using boGenomic DNA was purified using the MasterPure Complete DNA & RNA purification kit (Epicentre Technologies) PCR product purification and gel extraction were carried out using the PCR purification kit and the Qiaquick gel extraction kit (Qiagen). Primers were purchased from Sigma-Genosys. All PCR amplifications were done using Taq DNA polymerase (Qiagen).−1).Cell-free extracts were prepared from 100 ml mid-log cultures. Cells were harvested by centrifugation , washed with 50 mM potassium phosphate buffer, pH 7.3, containing 2.5 mM dithiothreitol, and centrifuged again. The cells were resuspended in 3 ml of the same buffer and were disrupted by sonication ; the cell debris was removed by centrifugation , and the supernatant was further clarified by ultracentrifugation . The cell-free extracts used to determine pyruvate-ferredoxin oxidoreductase and pyruvate formate lyase activities were prepared under strict anoxic conditions using the same protocol except that the cells were disrupted in a French press at 40,000 kPa (two passages). All enzymatic assays were carried out at 30 °C. All specific activities are expressed in units per milligram of protein (1U = 1 μmol min340 = 6.22 mM−1cm−1) in 1 ml assay mixtures containing 50 mM Tris-HCl, pH 8, 0.2 mM NADH, 2.5 mM oxaloacetate and cell extract.Malate dehydrogenase activity (Mdh) was measured in the direction of oxaloacetate reduction  by monit2, 50 mM NaHCO3, 5 mM sodium pyruvate, 2 mM ATP, 0.1 mM NADH, 2 U porcine malate dehydrogenase (Sigma-Aldrich), and cell extract [2, 0.5 mM MnCl2, 1 mM DTT, 50 mM NaHCO3, 0.25 mM NADH, 2.5 mM phosphoenolpyruvate, 2.5 mM GDP (or ADP), 10 U porcine malate dehydrogenase (Sigma-Aldrich), and cell extract [Pyruvate carboxylase (Pc) and phosphoenolpyruvate carboxykinase (Ppck) activities were monitored at 340 nm in assays coupled to the NADH dependent reduction of oxaloacetate by malate dehydrogenase. The Pyc assay mixture (1 ml) contained 100 mM Tris-HCl pH 7.8, 5 mM MgCl extract .600 = 12 mM−1cm−1) using a modified version of the method reported by [2, 1 mM thiamine pyrophosphate, 1 mM Coenzyme A (CoASH), 10 mM methyl viologen, and 10 mM sodium pyruvate. This assay was carried out in under anoxic conditions in sealed 1 ml cuvettes and all solutions were sparged with oxygen-free nitrogen.Pyruvate-ferredoxin oxidoreductase (Por) activity was measured at 600 nm as the pyruvate-dependent reduction of methyl viologen , and 1.4 U of porcine citrate synthase (Sigma-Aldrich).Phosphotransacetylase (Pta) activity was measured in a coupled assay by monitoring reduction of NAD at 340 nm as previously described . The rea412 = 13.6 mM−1cm−1). The reaction mixture contained 100 mM potassium phosphate buffer, pH 7.0, 200 mM, 1 mM oxaloacetate, 1 mM DTNB, 0.1 mM succinyl-CoA, and 3 U of porcine citrate synthase (Sigma-Aldrich).Acetate-succinate CoA transferase (Ato) activity was determined as described by Sohling and Gottschalk , via a c2, 0.4 mM ATP, 0.1 mM CoASH, and 20 mM sodium succinate [235 = 4 mM−1cm−1).Succinyl-CoA synthetase (Sucoas) was assayed in 50 mM Tris-HCl, pH 7.2, 100 mM KCl, 10 mM MgCluccinate . SuccinaSuccinyl-CoA hydrolase (Sucoh) activity was measured by monitoring the liberation of free CoASH with DTNB at 412 nm . The assG. sulfurreducens, these pathways can be determined by manual inspection as shown in One approach to maintaining robustness of metabolism is through alternate pathways that can readily substitute in the event of loss of function. Metabolic modeling based on linear programming known as Flux Balance Analysis is effective in predicting large-scale growth phenotypes in different organisms. Flux Variability Analysis is an algorithm to identify those reactions that participate in alternate metabolic pathways. In this algorithm, in addition to the stoichiometric and capacity constraints, a growth rate constraint that forces the growth rate to be optimal is incorporated. Then, the flux through every reaction in the model is maximized and minimized in the formulation. If a reaction has an alternate pathway, then the flux through this reaction can be zero and yet optimal growth can be maintained as the flux gets rerouted through the alternate pathway. The range of flux is calculated as the difference between the maximum and the minimum possible value. Therefore, any reaction that has a non-zero range in the FVA problem has an alternate pathway. These reactions are compiled and augmented with the reactions in the reverse direction and used as the input to the Extreme Pathway Analysis algorithm. The redundant pathways are then identified from the list of predicted pathways. Further details are available in a previously published manuscript . However, if the number of reactions identified is small such as in the case of Figure S1 Glutamate to alphaketoglutarate.(C) Glutamate to alphaketoglutarate and glutamine.(D) Alphaketoglutarate to succinyl-CoA.(E) AMP to ADP.(F) Folate to tetrahydrofolate(G) Malate to pyruvate, a set of reactions that are equivalent only if fumarate is assumed to be transported via a fumarate symport mechanism.Adk1, Adenylate kinase; Adk2, Adenylate kinase (pyrophosphate); Akgd, Alphaketoglutarate dehydrogenase; Alad_L, L-alanine dehydrogenase; Alata_L, Alanine transaminase; Aspta1, Asparate transaminase; Aspt, Aspartase; DHFR, Folate reductase (2NADPH); DHFOR2, Folate reductase; DHFOR3, Dihydrofolate reductase; Fnor Ferredoxin: NADP oxidoreductase; Fum, Fumarase; Gludx, Glutamate dehydrogenase (NAD dependent); Gludy, Glutamate dehydrogenase (NADP dependent); Glusy, Glutamate synthase (NAD dependent); Glusz, glutamate synthase (ferredoxin dependent); Me, Malic enzyme; Mdh, Malate dehydrogenase; NADPH5, NADPH dehydrogenase, NADH5, NADH dehydrogenase; Oor, Oxaglutarate oxidoreductase; Ppck, Phosphoenolpyruvate carboxykinase; Ppik, polyphosphate kinase; Pyk, Pyruvate kinase. Other abbreviations are explained in (397 KB TIF)Click here for additional data file.Figure S2mdh and pta genes were inactivated inserting a kanamycin resistance cassette in mutants MDH1 and PTA1 respectively; por and ato1 were replaced with a gentamycin resistance cassette in mutants POR1 and ATO1, respectively; and a chloramphenicol cassette was used for the inactivation of pckA and ato2 in mutants PPCK1 and ATO2, respectively. ATO3 mutant contained both rato1::Gm and rato2::Cm insertions. The transcriptional orientation of the inserted cassettes is the same as that of the target genes.The structure of the gene clusters containing the inactivated genes, their transcriptional orientation, and the relative sizes of the deletions–insertions are shown. Black arrows represent the target genes and white blocks and arrows show the inserted cassettes. The (160 KB TIF)Click here for additional data file.Table S1(1.6 MB TIF)Click here for additional data file.Table S2The list was calculated for acetate limiting growth with 1) acetate (5 mmol/gdwh) and fumarate and 2) acetate (10 mmol/gdwh) and Fe(III) citrate. Abbreviations are explained in (25 KB TIF)Click here for additional data file.Table S3Abbreviations are explained in (20 KB TIF)Click here for additional data file.Table S4(53 KB TIF)Click here for additional data file.http://www.ncbi.nlm.nih.gov/) accession numbers for the G. sulfurreducens proteins described in this report are as follows: Por (GSU0097), AAR33432.1; Ppck (GSU3385), AAR36775.1; Pta (GSU2706), AAR36078.1; Ato1 (GSU0490), AAR33822.1; Ato2 (GSU0174), AAR33509.1; and Mdh (GSU1466), AAR34840.1.The GenBank Database (


This paper presents a metabolic model describing the production of polyhydroxyalkanoate (PHA) copolymers in mixed microbial cultures, using mixtures of acetic and propionic acid as carbon source material. Material and energetic balances were established on the basis of previously elucidated metabolic pathways. Equations were derived for the theoretical yields for cell growth and PHA production on mixtures of acetic and propionic acid as functions of the oxidative phosphorylation efficiency, P/O ratio. The oxidative phosphorylation efficiency was estimated from rate measurements, which in turn allowed the estimation of the theoretical yield coefficients.The model was validated with experimental data collected in a sequencing batch reactor (SBR) operated under varying feeding conditions: feeding of acetic and propionic acid separately (control experiments), and the feeding of acetic and propionic acid simultaneously. Two different feast and famine culture enrichment strategies were studied: (i) either with acetate or (ii) with propionate as carbon source material. Metabolic flux analysis (MFA) was performed for the different feeding conditions and culture enrichment strategies. Flux balance analysis (FBA) was used to calculate optimal feeding scenarios for high quality PHA polymers production, where it was found that a suitable polymer would be obtained when acetate is fed in excess and the feeding rate of propionate is limited to ~0.17 C-mol/(C-mol.h). The results were compared with published pure culture metabolic studies.Acetate was more conducive toward the enrichment of a microbial culture with higher PHA storage fluxes and yields as compared to propionate. The P/O ratio was not only influenced by the selected microbial culture, but also by the carbon substrate fed to each culture, where higher P/O ratio values were consistently observed for acetate than propionate. MFA studies suggest that when mixtures of acetate and propionate are fed to the cultures, the catabolic activity is primarily guaranteed through acetate uptake, and the characteristic P/O ratio of acetate prevails over that of propionate. This study suggests that the PHA production process by mixed microbial cultures has the potential to be comparable or even more favourable than pure cultures. Polyhydroxyalkanoates are biopolymers with physico-chemical properties similar to polypropylene but with the advantage of being biodegradable and biocompatible. Industrial PHA production technology is currently based on bacteria cultivation using pure cultures grown in well-defined nutrient deficient synthetic media with single substrates . The relPotential strategies for reducing both the operational and capital expenses of PHA production are the use of open mixed cultures of microorganisms instead of pure cultures, and the use of waste materials as the carbon substrate. Activated sludge is known to accumulate up to 65% PHA per cell dry weight -4. There1), growth on acetyl-CoA (R4), catabolism (R6), oxidative phosphorylation (R8), maintenance (R7) and PHB production (RPHB). A metabolic model based on these reactions was comprehensively validated with experimental data . The steady state material balances to the m intracellular intermediates  are:The metabolic network of Figure From acetyl-CoA* and propionyl-CoA*, the resulting PHA polymer can be comprised of either PHB (2 acetyl-CoA* molecules), PHV (one acetyl-CoA* and one propionyl-CoA*) and PH2MV (2 propionyl-CoA*). The PHA composition depends on whether selective or random condensation of acetyl-CoA* and propionyl-CoA* takes place. In the propionate enriched culture selective condensation was observed, where acetyl-CoA* preferentially bounds with propionyl-CoA*, forming PHV . Since aRPH2MV = 0 (Eq. 2c), Eqs. (2a–b) are linearly dependent to Eqs. (1a–f), only a single additional constraint is introduced with RPH2MV = 0.since In the acetate enriched culture, the PHA composition consisted of a lower PHV fraction and a higher PH2MV and PHB fraction, as is expected by microorganisms performing random condensation of acetyl-CoA* and propionyl-CoA*. In this latter case the following three equations are applied :R9 and R10 fluxes are sufficient to calculate the fluxes of RPHB, RPHV and RPH2MV.The On the other hand, constraints (3a–c) automatically obey the material balances (1a–f)  and intracellular contents of PHB, PHV and PH2MV are the following:K1, K2 and y, the ratio of propionate flux to total carbon flux (see Eq. 5):The theoretical yields and VFA and oxygen maintenance coefficients were derived analytically from the material balance equations (1a–f). The expressions are compiled in Table q = 13 fluxes and a total number of 7 constraints. Therefore, at least 6 fluxes must be defined a priori in order to calculate the network fluxes. Table As stated above, the metabolic network has R4) is limited by the concentrations of acetate and ammonia.• Growth on acetyl-CoA (R5) is limited by the concentrations of propionate and ammonia.• Growth on propionyl-CoA (R6) is limited by total VFA concentration. The kinetic equation for catabolism is only used for mixtures of acetate and propionate to fulfil the 6 fluxes required to perform MFA.• Catabolism (R7) is limited by total VFA concentration.• Maintenance (R9) is limited by total VFA concentration and inhibited by the intracellular PHA content. Intracellular PHA inhibition has been validated experimentally by several authors ; mATP: maintenance coefficient on ATP [mol-ATP/(C-mol.h)]; N: ammonia/ammonia concentration (N-mmol/l); O2: oxygen/oxygen concentration (mmol/l); Prop: propionate/propionate concentration (C-mmol/l); Ri: specific rate of reaction on compound i [C-mol/(C-mol.h)]; Ri, max: maximum specific rate of reaction on compound i [C-mol/(C-mol.h)]; S: total VFA/total VFA concentration (C-mmol/l); t: culture runtime (h); X: active biomass/active biomass concentration (C-mmol/l); y: fraction of propionate uptake rate in the total VFA uptake rate; i/jY: yield of component i on component j (C-mol/C-mol); α: PHB production saturation order constant (dimensionless); δ: efficiency of oxidative phosphorylation (mol-ATP/mol-NADH2).All authors read and approved the final manuscript. JMLD and RO developed the software. JMLD, AO and RO participated in the model implementation. LSS and PCL performed experimental work. MAMR and RO designed and coordinated the study. JMLD, AO and RO drafted the manuscript.


Saccharomyces cerevisiae, each differing in scope and content. The recent community-driven reconstruction, while rigorously evidenced and well annotated, under-represented metabolite transport, lipid metabolism and other pathways, and was not amenable to constraint-based analyses because of lack of pathway connectivity.To date, several genome-scale network reconstructions have been used to describe the metabolism of the yeast in vivo experiments and to those of previous reconstructions.We have expanded the yeast network reconstruction to incorporate many new reactions from the literature and represented these in a well-annotated and standards-compliant manner. The new reconstruction comprises 1102 unique metabolic reactions involving 924 unique metabolites - significantly larger in scope than any previous reconstruction. The representation of lipid metabolism in particular has improved, with 234 out of 268 enzymes linked to lipid metabolism now present in at least one reaction. Connectivity is emphatically improved, with more than 90% of metabolites now reachable from the growth medium constituents. The present updates allow constraint-based analyses to be performed; viability predictions of single knockouts are comparable to results from http://www.comp-sys-bio.org/yeastnet/.We report the development of the most complete reconstruction of yeast metabolism to date that is based upon reliable literature evidence and richly annotated according to MIRIAM standards. The reconstruction is available in the Systems Biology Markup Language (SBML) and via a publicly accessible database  A central goal of integrative systems biology is the accurate representation of molecular interaction networks. Ultimately, such networks can be used to underpin mathematical models, consisting of stochastic or ordinary differential equations that permit the simulation of biological behaviour. The first step in generating such models is constructing a network of biochemical reactions and interactions between molecular components of the system to form a qualitative (unparameterised) model. Several groups have reconstructed the metabolic network of baker's yeast from genomic and literature data -3. VariaA limitation of Yeast 1.0 came about through the very generation of the consensus; the network became considerably fragmented as reactions that could not be readily annotated  were removed. This led to underrepresentation of a number of pathways, particularly those involved in lipid biosynthesis. Since Yeast 1.0, many improvements have been made to the reconstruction. The latest release, described here, is considerably larger (in terms of numbers of metabolites and reactions), of higher quality (by reference to literature evidence), exhibits greater coverage of known metabolic enzymes, and is better connected than all previous efforts.The reconstruction is described and made available in Systems Biology Markup Language (SBML) , an estaImprovements in the representation of yeast metabolism in this release as compared to Yeast 1.0 primarily consist of its enhanced representation of lipid metabolism and greater connectivity, thereby permitting constraint-based flux analyses. Many of the extensions to Yeast 1.0 are reactions garnered from the literature, which are entirely novel to any genome-wide yeast metabolic reconstruction. Data were also incorporated, when backed up by traceable evidence, from two other reconstructions: iMM904  and iIN8Careful curation does not simply involve increasing the scope of the reconstruction. Indeed, 32 enzymes from Yeast 1.0 were considered insufficiently evidenced and have been removed, whilst a number of metabolites were relocalised to a different compartment. A typical example of an enzyme removed from the reconstruction is Gpm2p; whilst a homologue of Gpm1p, its phosphoglycerate mutase activity could not be evidenced and may be non-functional . Four reThe correct and complete representation of lipid metabolism is important, not only to meet the ultimate goal of genome-scale coverage, but also because understanding and engineering lipid metabolism through systems and synthetic biology is likely to play a major role in the replacement of fossil energy sources and chemical feedstocks with biofuels and bioplastics . In Yeaset al. improved upon the original community reconstruction (Yeast 1.0) by increasing set coverage from 48% to 62% (with at least one reaction being associated with each enzyme). In the present release set coverage has further improved to 87%. Coverage of the lipid enzyme set by the various reconstructions is summarised in Figure With reference to this set of lipid enzymes, the iIN800 reconstruction of Nookaew The 34 remaining lipid enzymes   to assesThe model was used to predict single knockout viability through flux balance analysis (FBA). Growth conditions exactly followed those set out in iMM904, namely a glucose-limited minimal medium. Cellular biomass was defined as in iIN800 (carbon-limited version), due to its high level of detail regarding lipid composition. As the reaction producing biomass does not represent a real metabolic process it is semantically annotated as such using SBO (Systems Biology Ontology)  identifiCloser inspection of predictions reveals that relatively subtle network variations often underlie prediction differences. Four experimentally lethal knockouts were not initially predicted as such by the new reconstruction, but are correctly predicted using iMM904. Three of these genes encode enzymes that are essential to riboflavin biosynthesis. The capacity of iMM904 to predict lethality correctly is due to its biomass definition including a small contribution from riboflavin, whereas this was not part of the initial iIN800 or current network's biomass definition. Subsequent addition of riboflavin to the  biomass description has resolved these differences. Note that this is not therefore a reflection of the quality of the underlying network but only of the empirical biomass estimation, which is itself dependent on the growth conditions.acs2 gene, encoding acetyl-coA synthetase (Acs2p). By experiment this should be lethal, yet in the current network the cytoplasmic reaction is also catalysed by Acs1p, consistent with experimental data [acs2 knockout. The proper basis of the inviability of the acs2 mutant is that ACS1 is transcriptionally repressed in the high glucose conditions of viability experiments and so is unable to compensate for the loss of ACS2 [In places, the added richness of the new reconstruction combines with certain known limitations to defeat total agreement with experiment. An example is seen by knocking out the tal data . When th of ACS2 . Transcrin silico knockouts that are overcome by alternative routings in the network but are actually lethal in vivo. This is, however, tempered by a decrease in false negative outcomes , addition of isoenzymes of specific reactions that do not exist in earlier reconstructions can reduce the predictive power of the model. Nonetheless, such enzymes are included due to literature support. This reconstruction continues the shifting focus, started with the consensus model Yeast 1.0, toward realistic representation and proof-based selection of reactions, rather than creating a reconstruction with simulation in mind. Reactions with a lower level of confidence (e.g. biomass definition) are characterised with specialised evidence codes and SBO terms, allowing the easy extraction of subsets of the network from the SBML code for specific purposes.network.reconstruction@manchester.ac.uk. We also highlight gaps in the network that cannot be resolved from current literature, as well as the little-studied enzymes for which we have not yet identified any function  for backward compatibility.Click here for filePoorly characterised genes. Excel spreadsheet. The network is built upon intensive literature mining to identify reactions. Many genes still do not have detailed literature describing the functions of their products, yet  they appear likely to be involved in metabolism. The attached list describes these genes.Click here for file