Data structures and methods for modeling Saccharomyces cerevisiae metabolism

This application is a continuation application of U.S. application Ser. No. 10/263,901 filed Oct. 2, 2002 now U.S. Pat. No. 7,751,981, which claims the benefit under 35 USC §119(e) to U.S. Application Ser. No. 60/344,447 filed Oct. 26, 2001. The disclosure of each of the prior applications is considered part of and is incorporated by reference in the disclosure of this application.

This invention was made with government support under Grant No. RO1HL59234 awarded by the National Institutes of Health. The government has certain rights in this invention.

1. Field of the Invention

This invention relates generally to analysis of the activity of a chemical reaction network and, more specifically, to computational methods for simulating and predicting the activity of Saccharomyces cerevisiae ( S. cerevisiae ) reaction networks.

2. Background Information

Saccharomyces cerevisiae is one of the best-studied microorganisms and in addition to its significant industrial importance it serves as a model organism for the study of eukaryotic cells (Winzeler et al. Science 285: 901-906 (1999)). Up to 30% of positionally cloned genes implicated in human disease have yeast homologs.

The first eukaryotic genome to be sequenced was that of S. cerevisiae , and about 6400 open reading frames (or genes) have been identified in the genome. S. cerevisiae was the subject of the first expression profiling experiments and a compendium of expression profiles for many different mutants and different growth conditions has been established. Furthermore, a protein-protein interaction network has been defined and used to study the interactions between a large number of yeast proteins.

S. cerevisiae is used industrially to produce fuel ethanol, technical ethanol, beer, wine, spirits and baker's yeast, and is used as a host for production of many pharmaceutical proteins (hormones and vaccines). Furthermore, S. cerevisiae is currently being exploited as a cell factory for many different bioproducts including insulin.

Genetic manipulations, as well as changes in various fermentation conditions, are being considered in an attempt to improve the yield of industrially important products made by S. cerevisiae . However, these approaches are currently not guided by a clear understanding of how a change in a particular parameter, or combination of parameters, is likely to affect cellular behavior, such as the growth of the organism, the production of the desired product or the production of unwanted by-products. It would be valuable to be able to predict how changes in fermentation conditions, such as an increase or decrease in the supply of oxygen or a media component, would affect cellular behavior and, therefore, fermentation performance. Likewise, before engineering the organism by addition or deletion of one or more genes, it would be useful to be able to predict how these changes would affect cellular behavior.

However, it is currently difficult to make these sorts of predictions for S. cerevisiae because of the complexity of the metabolic reaction network that is encoded by the S. cerevisiae genome. Even relatively minor changes in media composition can affect hundreds of components of this network such that potentially hundreds of variables are worthy of consideration in making a prediction of fermentation behavior. Similarly, due to the complexity of interactions in the network, mutation of even a single gene can have effects on multiple components of the network. Thus, there exists a need for a model that describes S. cerevisiae reaction networks, such as its metabolic network, which can be used to simulate many different aspects of the cellular behavior of S. cerevisiae under different conditions. The present invention satisfies this need, and provides related advantages as well.

The invention provides a computer readable medium or media, including: (a) a data structure relating a plurality of reactants in S. cerevisiae to a plurality of reactions in S. cerevisiae , wherein each of the S. cerevisiae reactions includes a reactant identified as a substrate of the reaction, a reactant identified as a product of the reaction and a stoichiometric coefficient relating the substrate and the product, (b) a constraint set for the plurality of S. cerevisiae reactions, and (c) commands for determining at least one flux distribution that minimizes or maximizes an objective function when the constraint set is applied to the data representation, wherein at least one flux distribution is predictive of a physiological function of S. cerevisiae . In one embodiment, at least one of the cellular reactions in the data structure is annotated to indicate an associated gene and the computer readable medium or media further includes a gene database including information characterizing the associated gene. In another embodiment, at least one of the cellular reactions in the data structure is annotated with an assignment of function within a subsystem or a compartment within the cell.

The invention also provides a method for predicting physiological function of S. cerevisiae , including: (a) providing a data structure relating a plurality of S. cerevisiae to a plurality of S. cerevisiae reactions, wherein each of the S. cerevisiae reactions includes a reactant identified as a substrate of the reaction, a reactant identified as a product of the reaction and a stoichiometric coefficient relating the substrate and the product; (b) providing a constraint set for the plurality of S. cerevisiae reactions; (c) providing an objective function, and (d) determining at least one flux distribution that minimizes or maximizes the objective function when the constraint set is applied to the data structure, thereby predicting a S. cerevisiae physiological function. In one embodiment, at least one of the S. cerevisiae reactions in the data structure is annotated to indicate an associated gene and the method predicts a S. cerevisiae physiological function related to the gene.

Also provided by the invention is a method for making a data structure relating a plurality of S. cerevisiae reactants to a plurality of S. cerevisiae reactions in a computer readable medium or media, including: (a) identifying a plurality of S. cerevisiae reactions and a plurality of reactants that are substrates and products of the reactions; (b) relating the plurality of reactants to the plurality of reactions in a data structure, wherein each of the reactions includes a reactant identified as a substrate of the reaction, a reactant identified as a product of the reaction and a stoichiometric coefficient relating the substrate and the product; (c) determining a constraint set for the plurality of S. cerevisiae reactions; (d) providing an objective function; (e) determining at least one flux distribution that minimizes or maximizes the objective function when the constraint set is applied to the data structure, and (f) if at least one flux distribution is not predictive of a physiological function of S. cerevisiae , then adding a reaction to or deleting a reaction from the data structure and repeating step (e), if at least one flux distribution is predictive of a physiological function of the eukaryotic cell, then storing the data structure in a computer readable medium or media. The invention further provides a data structure relating a plurality of S. cerevisiae reactants to a plurality of reactions, wherein the data structure is produced by the method.

FIG. 1 shows a schematic representation of a hypothetical metabolic network.

FIG. 2 shows the stoichiometric matrix (S) for the hypothetical metabolic network shown in FIG. 1 .

FIG. 3 shows mass balance constraints and flux constraints (reversibility constraints) that can be placed on the hypothetical metabolic network shown in FIG. 1 . (∞, infinity; Y 1 , uptake rate value)

FIG. 4 shows an exemplary metabolic reaction network in S. cerevisiae.

FIG. 5 shows a method for reconstruction of the metabolic network of S. cerevisiae . Based on the available information from the genome annotation, biochemical pathway databases, biochemistry textbooks and recent publications, a genome-scale metabolic network for S. cerevisiae was designed. Additional physiological constraints were considered and modeled, such as growth, non-growth dependent ATP requirements and biomass composition.

FIGS. 6A and 6B show a Phenotypic Phase Plane (PhPP) diagram for S. cerevisiae revealing a finite number of qualitatively distinct patterns of metabolic pathway utilization divided into discrete phases. The characteristics of these distinct phases are interpreted using ratios of shadow prices in the form of isoclines. The isoclines can be used to classify these phases into futile, single and dual substrate limitation and to define the line of optimality. FIG. 6A shows a 3-dimensional S. cerevisiae Phase Plane diagram. FIG. 6B shows a 2-dimensional Phase Plane diagram with the line of optimality (LO) indicated.

FIG. 7 shows the respiratory quotient (RQ) versus oxygen uptake rate (mmole/g-DW/hr) (upper left) on the line of optimality. The phenotypic phase plane (PhPP) illustrates that the predicted RQ is a constant of value 1.06

FIG. 8 shows phases of metabolic phenotype associated with varying oxygen availability, from completely anaerobic fermentation to aerobic growth in S. cerevisiae . The glucose uptake rate was fixed under all conditions, and the resulting optimal biomass yield, as well as respiratory quotient, RQ, are indicated along with the output fluxes associated with four metabolic by-products: acetate, succinate, pyruvate, and ethanol.

FIG. 9A shows anaerobic glucose limited continuous culture of S. cerevisiae . FIG. 9A shows the utilization of glucose at varying dilution rates in anaerobic chemostat culture. The data-point at the dilution rate of 0.0 is extrapolated from the experimental results. The shaded area or the infeasible region contains a set of stoichiometric constraints that cannot be balanced simultaneously with growth demands. The model produces the optimal glucose uptake rate for a given growth rate on the line of optimal solution (indicated by Model (optimal)). Imposition of additional constraints drives the solution towards a region where more glucose is needed (i.e. region of alternative sub-optimal solution). At the optimal solution, the in silico model does not secrete pyruvate and acetate. The maximum difference between the model and the experimental points is 8% at the highest dilution rate. When the model is forced to produce these by-products at the experimental level (Model (forced)), the glucose uptake rate is increased and becomes closer to the experimental values. FIGS. 9B and 9C show the secretion rate of anaerobic by-products in chemostat culture. (q, secretion rate; D, dilution rate).

FIGS. 10A and 10B show aerobic glucose-limited continuous culture of S. cerevisiae in vivo and in silico. FIG. 10A shows biomass yield (Y X ), and secretion rates of ethanol (Eth), and glycerol (Gly). FIG. 10B shows CO 2 secretion rate (q CO2 ) and respiratory quotient (RQ; i.e. q CO2 /q O2 ) of the aerobic glucose-limited continuous culture of S. cerevisiae . (exp, experimental).

The present invention provides an in silico model of the baker's and brewer's yeast, S. cerevisiae , that describes the interconnections between the metabolic genes in the S. cerevisiae genome and their associated reactions and reactants. The model can be used to simulate different aspects of the cellular behavior of S. cerevisiae under different environmental and genetic conditions, thereby providing valuable information for industrial and research applications. An advantage of the model of the invention is that it provides a holistic approach to simulating and predicting the metabolic activity of S. cerevisiae.

As an example, the S. cerevisiae metabolic model can be used to determine the optimal conditions for fermentation performance, such as for maximizing the yield of a specific industrially important enzyme. The model can also be used to calculate the range of cellular behaviors that S. cerevisiae can display as a function of variations in the activity of one gene or multiple genes. Thus, the model can be used to guide the organismal genetic makeup for a desired application. This ability to make predictions regarding cellular behavior as a consequence of altering specific parameters will increase the speed and efficiency of industrial development of S. cerevisiae strains and conditions for their use.

The S. cerevisiae metabolic model can also be used to predict or validate the assignment of particular biochemical reactions to the enzyme-encoding genes found in the genome, and to identify the presence of reactions or pathways not indicated by current genomic data. Thus, the model can be used to guide the research and discovery process, potentially leading to the identification of new enzymes, medicines or metabolites of commercial importance.

The models of the invention are based on a data structure relating a plurality of S. cerevisiae reactants to a plurality of S. cerevisiae reactions, wherein each of the S. cerevisiae reactions includes a reactant identified as a substrate of the reaction, a reactant identified as a product of the reaction and a stoichiometric coefficient relating the substrate and the product.

As used herein, the term “ S. cerevisiae reaction” is intended to mean a conversion that consumes a substrate or forms a product that occurs in or by a viable strain of S. cerevisiae . The term can include a conversion that occurs due to the activity of one or more enzymes that are genetically encoded by a S. cerevisiae genome. The term can also include a conversion that occurs spontaneously in a S. cerevisiae cell. Conversions included in the term include, for example, changes in chemical composition such as those due to nucleophilic or electrophilic addition, nucleophilic or electrophilic substitution, elimination, isomerization, deamination, phosphorylation, methylation, glycolysation, reduction, oxidation or changes in location such as those that occur due to a transport reaction that moves a reactant within the same compartment or from one cellular compartment to another. In the case of a transport reaction, the substrate and product of the reaction can be chemically the same and the substrate and product can be differentiated according to location in a particular cellular compartment. Thus, a reaction that transports a chemically unchanged reactant from a first compartment to a second compartment has as its substrate the reactant in the first compartment and as its product the reactant in the second compartment. It will be understood that when used in reference to an in silico model or data structure, a reaction is intended to be a representation of a chemical conversion that consumes a substrate or produces a product.

As used herein, the term “ S. cerevisiae reactant” is intended to mean a chemical that is a substrate or a product of a reaction that occurs in or by a viable strain of S. cerevisiae . The term can include substrates or products of reactions performed by one or more enzymes encoded by S. cerevisiae gene(s), reactions occurring in S. cerevisiae that are performed by one or more non-genetically encoded macromolecule, protein or enzyme, or reactions that occur spontaneously in a S. cerevisiae cell. Metabolites are understood to be reactants within the meaning of the term. It will be understood that when used in reference to an in silico model or data structure, a reactant is intended to be a representation of a chemical that is a substrate or a product of a reaction that occurs in or by a viable strain of S. cerevisiae.

As used herein the term “substrate” is intended to mean a reactant that can be converted to one or more products by a reaction. The term can include, for example, a reactant that is to be chemically changed due to nucleophilic or electrophilic addition, nucleophilic or electrophilic substitution, elimination, isomerization, deamination, phosphorylation, methylation, reduction, oxidation or that is to change location such as by being transported across a membrane or to a different compartment.

As used herein, the term “product” is intended to mean a reactant that results from a reaction with one or more substrates. The term can include, for example, a reactant that has been chemically changed due to nucleophilic or electrophilic addition, nucleophilic or electrophilic substitution, elimination, isomerization, deamination, phosphorylation, methylation, reduction or oxidation or that has changed location such as by being transported across a membrane or to a different compartment.

As used herein, the term “stoichiometric coefficient” is intended to mean a numerical constant correlating the number of one or more reactants and the number of one or more products in a chemical reaction. Typically, the numbers are integers as they denote the number of molecules of each reactant in an elementally balanced chemical equation that describes the corresponding conversion. However, in some cases the numbers can take on non-integer values, for example, when used in a lumped reaction or to reflect empirical data.

As used herein, the term “plurality,” when used in reference to S. cerevisiae reactions or reactants is intended to mean at least 2 reactions or reactants. The term can include any number of S. cerevisiae reactions or reactants in the range from 2 to the number of naturally occurring reactants or reactions for a particular strain of S. cerevisiae . Thus, the term can include, for example, at least 10, 20, 30, 50, 100, 150, 200, 300, 400, 500, 600 or more reactions or reactants. The number of reactions or reactants can be expressed as a portion of the total number of naturally occurring reactions for a particular strain of S. cerevisiae such as at least 20%, 30%, 50%, 60%, 75%, 90%, 95% or 98% of the total number of naturally occurring reactions that occur in a particular strain of S. cerevisiae.

As used herein, the term “data structure” is intended to mean a physical or logical relationship among data elements, designed to support specific data manipulation functions. The term can include, for example, a list of data elements that can be added combined or otherwise manipulated such as a list of representations for reactions from which reactants can be related in a matrix or network. The term can also include a matrix that correlates data elements from two or more lists of information such as a matrix that correlates reactants to reactions. Information included in the term can represent, for example, a substrate or product of a chemical reaction, a chemical reaction relating one or more substrates to one or more products, a constraint placed on a reaction, or a stoichiometric coefficient.

As used herein, the term “constraint” is intended to mean an upper or lower boundary for a reaction. A boundary can specify a minimum or maximum flow of mass, electrons or energy through a reaction. A boundary can further specify directionality of a reaction. A boundary can be a constant value such as zero, infinity, or a numerical value such as an integer and non-integer.

As used herein, the term “activity,” when used in reference to a reaction, is intended to mean the rate at which a product is produced or a substrate is consumed. The rate at which a product is produced or a substrate is consumed can also be referred to as the flux for the reaction.

As used herein, the term “activity,” when used in reference to S. cerevisiae is intended to mean the rate of a change from an initial state of S. cerevisiae to a final state of S. cerevisiae . The term can include, the rate at which a chemical is consumed or produced by S. cerevisiae , the rate of growth of S. cerevisiae or the rate at which energy or mass flow through a particular subset of reactions.

The invention provides a computer readable medium, having a data structure relating a plurality of S. cerevisiae reactants to a plurality of S. cerevisiae reactions, wherein each of the S. cerevisiae reactions includes a reactant identified as a substrate of the reaction, a reactant identified as a product of the reaction and a stoichiometric coefficient relating the substrate and the product.

The plurality of S. cerevisiae reactions can include reactions of a peripheral metabolic pathway. As used herein, the term “peripheral,” when used in reference to a metabolic pathway, is intended to mean a metabolic pathway that includes one or more reactions that are not a part of a central metabolic pathway. As used herein, the term “central,” when used in reference to a metabolic pathway, is intended to mean a metabolic pathway selected from glycolysis, the pentose phosphate pathway (PPP), the tricarboxylic acid (TCA) cycle and the electron transfer system (ETS), associated anapleurotic reactions, and pyruvate metabolism.

A plurality of S. cerevisiae reactants can be related to a plurality of S. cerevisiae reactions in any data structure that represents, for each reactant, the reactions by which it is consumed or produced. Thus, the data structure, which is referred to herein as a “reaction network data structure,” serves as a representation of a biological reaction network or system. An example of a reaction network that can be represented in a reaction network data structure of the invention is the collection of reactions that constitute the metabolic reactions of S. cerevisiae.

The methods and models of the invention can be applied to any strain of S. cerevisiae including, for example, strain CEN.PK113.7D or any laboratory or production strain. A strain of S. cerevisiae can be identified according to classification criteria known in the art. Classification criteria include, for example, classical microbiological characteristics, such as those upon which taxonomic classification is traditionally based, or evolutionary distance as determined for example by comparing sequences from within the genomes of organisms, such as ribosome sequences.

The reactants to be used in a reaction network data structure of the invention can be obtained from or stored in a compound database. As used herein, the term “compound database” is intended to mean a computer readable medium or media containing a plurality of molecules that includes substrates and products of biological reactions. The plurality of molecules can include molecules found in multiple organisms, thereby constituting a universal compound database. Alternatively, the plurality of molecules can be limited to those that occur in a particular organism, thereby constituting an organism-specific compound database. Each reactant in a compound database can be identified according to the chemical species and the cellular compartment in which it is present. Thus, for example, a distinction can be made between glucose in the extracellular compartment versus glucose in the cytosol. Additionally each of the reactants can be specified as a metabolite of a primary or secondary metabolic pathway. Although identification of a reactant as a metabolite of a primary or secondary metabolic pathway does not indicate any chemical distinction between the reactants in a reaction, such a designation can assist in visual representations of large networks of reactions.

As used herein, the term “compartment” is intended to mean a subdivided region containing at least one reactant, such that the reactant is separated from at least one other reactant in a second region. A subdivided region included in the term can be correlated with a subdivided region of a cell. Thus, a subdivided region included in the term can be, for example, the intracellular space of a cell; the extracellular space around a cell; the periplasmic space; the interior space of an organelle such as a mitochondrium, endoplasmic reticulum, Golgi apparatus, vacuole or nucleus; or any subcellular space that is separated from another by a membrane or other physical barrier. Subdivided regions can also be made in order to create virtual boundaries in a reaction network that are not correlated with physical barriers. Virtual boundaries can be made for the purpose of segmenting the reactions in a network into different compartments or substructures.

As used herein, the term “substructure” is intended to mean a portion of the information in a data structure that is separated from other information in the data structure such that the portion of information can be separately manipulated or analyzed. The term can include portions subdivided according to a biological function including, for example, information relevant to a particular metabolic pathway such as an internal flux pathway, exchange flux pathway, central metabolic pathway, peripheral metabolic pathway, or secondary metabolic pathway. The term can include portions subdivided according to computational or mathematical principles that allow for a particular type of analysis or manipulation of the data structure.

The reactions included in a reaction network data structure can be obtained from a metabolic reaction database that includes the substrates, products, and stoichiometry of a plurality of metabolic reactions of S. cerevisiae . The reactants in a reaction network data structure can be designated as either substrates or products of a particular reaction, each with a stoichiometric coefficient assigned to it to describe the chemical conversion taking place in the reaction. Each reaction is also described as occurring in either a reversible or irreversible direction. Reversible reactions can either be represented as one reaction that operates in both the forward and reverse direction or be decomposed into two irreversible reactions, one corresponding to the forward reaction and the other corresponding to the backward reaction.

Reactions included in a reaction network data structure can include intra-system or exchange reactions. Intra-system reactions are the chemically and electrically balanced interconversions of chemical species and transport processes, which serve to replenish or drain the relative amounts of certain metabolites. These intra-system reactions can be classified as either being transformations or translocations. A transformation is a reaction that contains distinct sets of compounds as substrates and products, while a translocation contains reactants located in different compartments. Thus, a reaction that simply transports a metabolite from the extracellular environment to the cytosol, without changing its chemical composition is solely classified as a translocation, while a reaction such as the phosphotransferase system (PTS) which takes extracellular glucose and converts it into cytosolic glucose-6-phosphate is a translocation and a transformation.

Exchange reactions are those which constitute sources and sinks, allowing the passage of metabolites into and out of a compartment or across a hypothetical system boundary. These reactions are included in a model for simulation purposes and represent the metabolic demands placed on S. cerevisiae . While they may be chemically balanced in certain cases, they are typically not balanced and can often have only a single substrate or product. As a matter of convention the exchange reactions are further classified into demand exchange and input/output exchange reactions.

The metabolic demands placed on the S. cerevisiae metabolic reaction network can be readily determined from the dry weight composition of the cell which is available in the published literature or which can be determined experimentally. The uptake rates and maintenance requirements for S. cerevisiae can be determined by physiological experiments in which the uptake rate is determined by measuring the depletion of the substrate. The measurement of the biomass at each point can also be determined, in order to determine the uptake rate per unit biomass. The maintenance requirements can be determined from a chemostat experiment. The glucose uptake rate is plotted versus the growth rate, and the y-intercept is interpreted as the non-growth associated maintenance requirements. The growth associated maintenance requirements are determined by fitting the model results to the experimentally determined points in the growth rate versus glucose uptake rate plot.

Input/output exchange reactions are used to allow extracellular reactants to enter or exit the reaction network represented by a model of the invention. For each of the extracellular metabolites a corresponding input/output exchange reaction can be created. These reactions can either be irreversible or reversible with the metabolite indicated as a substrate with a stoichiometric coefficient of one and no products produced by the reaction. This particular convention is adopted to allow the reaction to take on a positive flux value (activity level) when the metabolite is being produced or removed from the reaction network and a negative flux value when the metabolite is being consumed or introduced into the reaction network. These reactions will be further constrained during the course of a simulation to specify exactly which metabolites are available to the cell and which can be excreted by the cell.

A demand exchange reaction is always specified as an irreversible reaction containing at least one substrate. These reactions are typically formulated to represent the production of an intracellular metabolite by the metabolic network or the aggregate production of many reactants in balanced ratios such as in the representation of a reaction that leads to biomass formation, also referred to as growth. As set forth in the Examples, the biomass components to be produced for growth include L-Alanine, L-Arginine, L-Asparagine, L-Aspartate, L-Cysteine, L-Glutamine, L-Glutamate, Glycine, L-Histidine, L-Isoleucine, L-Leucine, L-Lysine, L-Methionine, L-Phenylalanine, L-Proline, L-Serine, L-Threonine, L-Tryptophan, L-Tyrosine, L-Valine, AMP, GMP, CMP, UMP, dAMP, dCMP, dTMP, dGMP, Glycogen, alpha,alpha-Trehalose, Mannan, beta-D-Glucan, Triacylglycerol, Ergosterol, Zymosterol, Phosphatidate, Phosphatidylcholine, Phosphatidylethanolamine, Phosphatidyl-D-myo-inositol, Phosphatidylserine, ATP, Sulfate, ADP and Orthophosphate, with exemplary values shown in Table 1.

A demand exchange reaction can be introduced for any metabolite in a model of the invention. Most commonly these reactions are introduced for metabolites that are required to be produced by the cell for the purposes of creating a new cell such as amino acids, nucleotides, phospholipids, and other biomass constituents, or metabolites that are to be produced for alternative purposes. Once these metabolites are identified, a demand exchange reaction that is irreversible and specifies the metabolite as a substrate with a stoichiometric coefficient of unity can be created. With these specifications, if the reaction is active it leads to the net production of the metabolite by the system meeting potential production demands. Examples of processes that can be represented as a demand exchange reaction in a reaction network data structure and analyzed by the methods of the invention include, for example, production or secretion of an individual protein; production or secretion of an individual metabolite such as an amino acid, vitamin, nucleoside, antibiotic or surfactant; production of ATP for extraneous energy requiring processes such as locomotion; or formation of biomass constituents.

In addition to these demand exchange reactions that are placed on individual metabolites, demand exchange reactions that utilize multiple metabolites in defined stoichiometric ratios can be introduced. These reactions are referred to as aggregate demand exchange reactions. An example of an aggregate demand reaction is a reaction used to simulate the concurrent growth demands or production requirements associated with cell growth that are placed on a cell, for example, by simulating the formation of multiple biomass constituents simultaneously at a particular cellular growth rate.

A hypothetical reaction network is provided in FIG. 1 to exemplify the above-described reactions and their interactions. The reactions can be represented in the exemplary data structure shown in FIG. 2 as set forth below. The reaction network, shown in FIG. 1 , includes intrasystem reactions that occur entirely within the compartment indicated by the shaded oval such as reversible reaction R 2 which acts on reactants B and G and reaction R 3 which converts one equivalent of B to two equivalents of F. The reaction network shown in FIG. 1 also contains exchange reactions such as input/output exchange reactions A xt and E xt , and the demand exchange reaction, V growth , which represents growth in response to the one equivalent of D and one equivalent of F. Other intrasystem reactions include R 1 which is a translocation and transformation reaction that translocates reactant A into the compartment and transforms it to reactant G and reaction R 6 which is a transport reaction that translocates reactant E out of the compartment.

A reaction network can be represented as a set of linear algebraic equations which can be presented as a stoichiometric matrix S, with S being an m×n matrix where m corresponds to the number of reactants or metabolites and n corresponds to the number of reactions taking place in the network. An example of a stoichiometric matrix representing the reaction network of FIG. 1 is shown in FIG. 2 . As shown in FIG. 2 , each column in the matrix corresponds to a particular reaction n, each row corresponds to a particular reactant m, and each S mn element corresponds to the stoichiometric coefficient of the reactant m in the reaction denoted n. The stoichiometric matrix includes intra-system reactions such as R 2 and R 3 which are related to reactants that participate in the respective reactions according to a stoichiometric coefficient having a sign indicative of whether the reactant is a substrate or product of the reaction and a value correlated with the number of equivalents of the reactant consumed or produced by the reaction. Exchange reactions such as -E xt and -A xt are similarly correlated with a stoichiometric coefficient. As exemplified by reactant E, the same compound can be treated separately as an internal reactant (E) and an external reactant (E external ) such that an exchange reaction (R 6 ) exporting the compound is correlated by stoichiometric coefficients of −1 and 1, respectively. However, because the compound is treated as a separate reactant by virtue of its compartmental location, a reaction, such as R 5 , which produces the internal reactant (E) but does not act on the external reactant (E external ) is correlated by stoichiometric coefficients of 1 and 0, respectively. Demand reactions such as V growth can also be included in the stoichiometric matrix being correlated with substrates by an appropriate stoichiometric coefficient.

As set forth in further detail below, a stoichiometric matrix provides a convenient format for representing and analyzing a reaction network because it can be readily manipulated and used to compute network properties, for example, by using linear programming or general convex analysis. A reaction network data structure can take on a variety of formats so long as it is capable of relating reactants and reactions in the manner exemplified above for a stoichiometric matrix and in a manner that can be manipulated to determine an activity of one or more reactions using methods such as those exemplified below. Other examples of reaction network data structures that are useful in the invention include a connected graph, list of chemical reactions or a table of reaction equations.

A reaction network data structure can be constructed to include all reactions that are involved in S. cerevisiae metabolism or any portion thereof. A portion of S. cerevisiae metabolic reactions that can be included in a reaction network data structure of the invention includes, for example, a central metabolic pathway such as glycolysis, the TCA cycle, the PPP or ETS; or a peripheral metabolic pathway such as amino acid biosynthesis, amino acid degradation, purine biosynthesis, pyrimidine biosynthesis, lipid biosynthesis, fatty acid metabolism, vitamin or cofactor biosynthesis, transport processes and alternative carbon source catabolism. Examples of individual pathways within the peripheral pathways are set forth in Table 2, including, for example, the cofactor biosynthesis pathways for quinone biosynthesis, riboflavin biosynthesis, folate biosynthesis, coenzyme A biosynthesis, NAD biosynthesis, biotin biosynthesis and thiamin biosynthesis.

Depending upon a particular application, a reaction network data structure can include a plurality of S. cerevisiae reactions including any or all of the reactions listed in Table 2. Exemplary reactions that can be included are those that are identified as being required to achieve a desired S. cerevisiae specific growth rate or activity including, for example, reactions identified as ACO1, CDC19, CIT1, DAL7, ENO1, FBA1, FBP1, FUM1, GND1, GPM1, HXK1, ICL1, IDH1, IDH2, IDP1, IDP2, IDP3, KGD1, KGD2, LPD1, LSC1, LSC2, MDH1, MDH2, MDH3, MLS1, PDC1, PFK1, PFK2, PGI1,PGK1, PGM1, PGM2, PYC1, PYC2, PYK2, RKI1, RPE1, SOL1, TAL1, TDH1, IDH2, TDH3, TKL1, TPI1, ZWF1 in Table 2. Other reactions that can be included are those that are not described in the literature or genome annotation but can be identified during the course of iteratively developing a S. cerevisiae model of the invention including, for example, reactions identified as MET6 — 2, MNADC, MNADD1, MNADE, MNADF — 1, MNADPHPS, MNADG1, MNADG2, MNADH, MNPT1.

Standard chemical names for the acronyms used to identify the reactants in the reactions of Table 2 are provided in Table 3.

Depending upon the particular environmental conditions being tested and the desired activity, a reaction network data structure can contain smaller numbers of reactions such as at least 200, 150, 100 or 50 reactions. A reaction network data structure having relatively few reactions can provide the advantage of reducing computation time and resources required to perform a simulation. When desired, a reaction network data structure having a particular subset of reactions can be made or used in which reactions that are not relevant to the particular simulation are omitted. Alternatively, larger numbers of reactions can be included in order to increase the accuracy or molecular detail of the methods of the invention or to suit a particular application. Thus, a reaction network data structure can contain at least 300, 350, 400, 450, 500, 550, 600 or more reactions up to the number of reactions that occur in or by S. cerevisiae or that are desired to simulate the activity of the full set of reactions occurring in S. cerevisiae . A reaction network data structure that is substantially complete with respect to the metabolic reactions of S. cerevisiae provides the advantage of being relevant to a wide range of conditions to be simulated, whereas those with smaller numbers of metabolic reactions are limited to a particular subset of conditions to be simulated.

A S. cerevisiae reaction network data structure can include one or more reactions that occur in or by S. cerevisiae and that do not occur, either naturally or following manipulation, in or by another prokaryotic organism, such as Escherichia coli, Haemophilus influenzae, Bacillus subtilis, Helicobacter pylori or in or by another eukaryotic organism, such as Homo sapiens . Examples of reactions that are unique to S. cerevisiae compared at least to Escherichia coli, Haemophilus influenzae , and Helicobacter pylori include those identified in Table 4. It is understood that a S. cerevisiae reaction network data structure can also include one or more reactions that occur in another organism. Addition of such heterologous reactions to a reaction network data structure of the invention can be used in methods to predict the consequences of heterologous gene transfer in S. cerevisiae , for example, when designing or engineering man-made cells or strains.

A reaction network data structure or index of reactions used in the data structure such as that available in a metabolic reaction database, as described above, can be annotated to include information about a particular reaction. A reaction can be annotated to indicate, for example, assignment of the reaction to a protein, macromolecule or enzyme that performs the reaction, assignment of a gene(s) that codes for the protein, macromolecule or enzyme, the Enzyme Commission (EC) number of the particular metabolic reaction or Gene Ontology (GO) number of the particular metabolic reaction, a subset of reactions to which the reaction belongs, citations to references from which information was obtained, or a level of confidence with which a reaction is believed to occur in S. cerevisiae . A computer readable medium or media of the invention can include a gene database containing annotated reactions. Such information can be obtained during the course of building a metabolic reaction database or model of the invention as described below.

As used herein, the term “gene database” is intended to mean a computer readable medium or media that contains at least one reaction that is annotated to assign a reaction to one or more macromolecules that perform the reaction or to assign one or more nucleic acid that encodes the one or more macromolecules that perform the reaction. A gene database can contain a plurality of reactions some or all of which are annotated. An annotation can include, for example, a name for a macromolecule; assignment of a function to a macromolecule; assignment of an organism that contains the macromolecule or produces the macromolecule; assignment of a subcellular location for the macromolecule; assignment of conditions under which a macromolecule is being expressed or being degraded; an amino acid or nucleotide sequence for the macromolecule; or any other annotation found for a macromolecule in a genome database such as those that can be found in Saccharomyces Genome Database maintained by Stanford University, or Comprehensive Yeast Genome Database maintained by MIPS.

A gene database of the invention can include a substantially complete collection of genes and/or open reading frames in S. cerevisiae or a substantially complete collection of the macromolecules encoded by the S. cerevisiae genome. Alternatively, a gene database can include a portion of genes or open reading frames in S. cerevisiae or a portion of the macromolecules encoded by the S. cerevisiae genome. The portion can be at least 10%, 15%, 20%, 25%, 50%, 75%, 90% or 95% of the genes or open reading frames encoded by the S. cerevisiae genome, or the macromolecules encoded therein. A gene database can also include macromolecules encoded by at least a portion of the nucleotide sequence for the S. cerevisiae genome such as at least 10%, 15%, 20%, 25%, 50%, 75%, 90% or 95% of the S. cerevisiae genome. Accordingly, a computer readable medium or media of the invention can include at least one reaction for each macromolecule encoded by a portion of the S. cerevisiae genome.

An in silico S. cerevisiae model according to the invention can be built by an iterative process which includes gathering information regarding particular reactions to be added to a model, representing the reactions in a reaction network data structure, and performing preliminary simulations wherein a set of constraints is placed on the reaction network and the output evaluated to identify errors in the network. Errors in the network such as gaps that lead to non-natural accumulation or consumption of a particular metabolite can be identified as described below and simulations repeated until a desired performance of the model is attained. An exemplary method for iterative model construction is provided in Example I.

Thus, the invention provides a method for making a data structure relating a plurality of S. cerevisiae reactants to a plurality of S. cerevisiae reactions in a computer readable medium or media. The method includes the steps of: (a) identifying a plurality of S. cerevisiae reactions and a plurality of S. cerevisiae reactants that are substrates and products of the S. cerevisiae reactions; (b) relating the plurality of S. cerevisiae reactants to the plurality of S. cerevisiae reactions in a data structure, wherein each of the S. cerevisiae reactions includes a reactant identified as a substrate of the reaction, a reactant identified as a product of the reaction and a stoichiometric coefficient relating the substrate and the product; (c) making a constraint set for the plurality of S. cerevisiae reactions; (d) providing an objective function; (e) determining at least one flux distribution that minimizes or maximizes the objective function when the constraint set is applied to the data structure, and (f) if at least one flux distribution is not predictive of S. cerevisiae physiology, then adding a reaction to or deleting a reaction from the data structure and repeating step (e), if at least one flux distribution is predictive of S. cerevisiae physiology, then storing the data structure in a computer readable medium or media.

Information to be included in a data structure of the invention can be gathered from a variety of sources including, for example, the scientific literature or an annotated genome sequence of S. cerevisiae such as the GENBANK, a site maintained by the NCBI (ncbi.nlm.gov), the CYGD database, a site maintained by MIPS, or the SGD database, a site maintained by the School of Medicine at Stanford University, etc.

In the course of developing an in silico model of S. cerevisiae metabolism, the types of data that can be considered include, for example, biochemical information which is information related to the experimental characterization of a chemical reaction, often directly indicating a protein(s) associated with a reaction and the stoichiometry of the reaction or indirectly demonstrating the existence of a reaction occurring within a cellular extract; genetic information which is information related to the experimental identification and genetic characterization of a gene(s) shown to code for a particular protein(s) implicated in carrying out a biochemical event; genomic information which is information related to the identification of an open reading frame and functional assignment, through computational sequence analysis, that is then linked to a protein performing a biochemical event; physiological information which is information related to overall cellular physiology, fitness characteristics, substrate utilization, and phenotyping results, which provide evidence of the assimilation or dissimilation of a compound used to infer the presence of specific biochemical event (in particular translocations); and modeling information which is information generated through the course of simulating activity of S. cerevisiae using methods such as those described herein which lead to predictions regarding the status of a reaction such as whether or not the reaction is required to fulfill certain demands placed on a metabolic network.

The majority of the reactions occurring in S. cerevisiae reaction networks are catalyzed by enzymes/proteins, which are created through the transcription and translation of the genes found on the chromosome(s) in the cell. The remaining reactions occur through non-enzymatic processes. Furthermore, a reaction network data structure can contain reactions that add or delete steps to or from a particular reaction pathway. For example, reactions can be added to optimize or improve performance of a S. cerevisiae model in view of empirically observed activity. Alternatively, reactions can be deleted to remove intermediate steps in a pathway when the intermediate steps are not necessary to model flux through the pathway. For example, if a pathway contains 3 nonbranched steps, the reactions can be combined or added together to give a net reaction, thereby reducing memory required to store the reaction network data structure and the computational resources required for manipulation of the data structure. An example of a combined reaction is that for fatty acid degradation shown in Table 2, which combines the reactions for acyl-CoA oxidase, hydratase-dehydrogenase-epimerase, and acetyl-CoA C-acyltransferase of beta-oxidation of fatty acids.

The reactions that occur due to the activity of gene-encoded enzymes can be obtained from a genome database that lists genes or open reading frames identified from genome sequencing and subsequent genome annotation. Genome annotation consists of the locations of open reading frames and assignment of function from homology to other known genes or empirically determined activity. Such a genome database can be acquired through public or private databases containing annotated S. cerevisiae nucleic acid or protein sequences. If desired, a model developer can perform a network reconstruction and establish the model content associations between the genes, proteins, and reactions as described, for example, in Covert et al. Trends in Biochemical Sciences 26:179-186 (2001) and Palsson, WO 00/46405.

As reactions are added to a reaction network data structure or metabolic reaction database, those having known or putative associations to the proteins/enzymes which enable/catalyze the reaction and the associated genes that code for these proteins can be identified by annotation. Accordingly, the appropriate associations for some or all of the reactions to their related proteins or genes or both can be assigned. These associations can be used to capture the non-linear relationship between the genes and proteins as well as between proteins and reactions. In some cases, one gene codes for one protein which then perform one reaction. However, often there are multiple genes which are required to create an active enzyme complex and often there are multiple reactions that can be carried out by one protein or multiple proteins that can carry out the same reaction. These associations capture the logic (i.e. AND or OR relationships) within the associations. Annotating a metabolic reaction database with these associations can allow the methods to be used to determine the effects of adding or eliminating a particular reaction not only at the reaction level, but at the genetic or protein level in the context of running a simulation or predicting S. cerevisiae activity.

A reaction network data structure of the invention can be used to determine the activity of one or more reactions in a plurality of S. cerevisiae reactions independent of any knowledge or annotation of the identity of the protein that performs the reaction or the gene encoding the protein. A model that is annotated with gene or protein identities can include reactions for which a protein or encoding gene is not assigned. While a large portion of the reactions in a cellular metabolic network are associated with genes in the organism's genome, there are also a substantial number of reactions included in a model for which there are no known genetic associations. Such reactions can be added to a reaction database based upon other information that is not necessarily related to genetics such as biochemical or cell based measurements or theoretical considerations based on observed biochemical or cellular activity. For example, there are many reactions that are not protein-enabled reactions. Furthermore, the occurrence of a particular reaction in a cell for which no associated proteins or genetics have been currently identified can be indicated during the course of model building by the iterative model building methods of the invention.

The reactions in a reaction network data structure or reaction database can be assigned to subsystems by annotation, if desired. The reactions can be subdivided according to biological criteria, such as according to traditionally identified metabolic pathways (glycolysis, amino acid metabolism and the like) or according to mathematical or computational criteria that facilitate manipulation of a model that incorporates or manipulates the reactions. Methods and criteria for subdividing a reaction database are described in further detail in Schilling et al., J. Theor. Biol. 203:249-283 (2000). The use of subsystems can be advantageous for a number of analysis methods, such as extreme pathway analysis, and can make the management of model content easier. Although assigning reactions to subsystems can be achieved without affecting the use of the entire model for simulation, assigning reactions to subsystems can allow a user to search for reactions in a particular subsystem, which may be useful in performing various types of analyses. Therefore, a reaction network data structure can include any number of desired subsystems including, for example, 2 or more subsystems, 5 or more subsystems, 10 or more subsystems, 25 or more subsystems or 50 or more subsystems.

The reactions in a reaction network data structure or metabolic reaction database can be annotated with a value indicating the confidence with which the reaction is believed to occur in S. cerevisiae . The level of confidence can be, for example, a function of the amount and form of supporting data that is available. This data can come in various forms including published literature, documented experimental results, or results of computational analyses. Furthermore, the data can provide direct or indirect evidence for the existence of a chemical reaction in a cell based on genetic, biochemical, and/or physiological data.

The invention further provides a computer readable medium, containing (a) a data structure relating a plurality of S. cerevisiae reactants to a plurality of S. cerevisiae reactions, wherein each of the S. cerevisiae reactions includes a reactant identified as a substrate of the reaction, a reactant identified as a product of the reaction and a stoichiometric coefficient relating the substrate and the product, and (b) a constraint set for the plurality of S. cerevisiae reactions.

Constraints can be placed on the value of any of the fluxes in the metabolic network using a constraint set. These constraints can be representative of a minimum or maximum allowable flux through a given reaction, possibly resulting from a limited amount of an enzyme present. Additionally, the constraints can determine the direction or reversibility of any of the reactions or transport fluxes in the reaction network data structure. Based on the in vivo environment where S. cerevisiae lives the metabolic resources available to the cell for biosynthesis of essential molecules for can be determined. Allowing the corresponding transport fluxes to be active provides the in silico S. cerevisiae with inputs and outputs for substrates and by-products produced by the metabolic network.

Returning to the hypothetical reaction network shown in FIG. 1 , constraints can be placed on each reaction in the exemplary format, shown in FIG. 3 , as follows. The constraints are provided in a format that can be used to constrain the reactions of the stoichiometric matrix shown in FIG. 2 . The format for the constraints used for a matrix or in linear programming can be conveniently represented as a linear inequality such as

β j ≦ν j ≦α j :j=1 . . . n  (Eq. 1)

where v j is the metabolic flux vector, β j is the minimum flux value and α j is the maximum flux value. Thus, α j can take on a finite value representing a maximum allowable flux through a given reaction or β j can take on a finite value representing minimum allowable flux through a given reaction. Additionally, if one chooses to leave certain reversible reactions or transport fluxes to operate in a forward and reverse manner the flux may remain unconstrained by setting β j to negative infinity and α j to positive infinity as shown for reaction R 2 in FIG. 3 . If reactions proceed only in the forward reaction β j is set to zero while α j is set to positive infinity as shown for reactions R 1 , R 3 , R 4 , R 5 , and R 6 in FIG. 3 . As an example, to simulate the event of a genetic deletion or non-expression of a particular protein, the flux through all of the corresponding metabolic reactions related to the gene or protein in question are reduced to zero by setting α j and β j to be zero. Furthermore, if one wishes to simulate the absence of a particular growth substrate, one can simply constrain the corresponding transport fluxes that allow the metabolite to enter the cell to be zero by setting α j and β j to be zero. On the other hand if a substrate is only allowed to enter or exit the cell via transport mechanisms, the corresponding fluxes can be properly constrained to reflect this scenario.

The in silico S. cerevisiae model and methods described herein can be implemented on any conventional host computer system, such as those based on Intel® microprocessors and running Microsoft Windows operating systems. Other systems, such as those using the UNIX or LINUX operating system and based on IBM®, DEC® or Motorola® microprocessors are also contemplated. The systems and methods described herein can also be implemented to run on client-server systems and wide-area networks, such as the Internet.

Software to implement a method or model of the invention can be written in any well-known computer language, such as Java, C, C++, VISUAL BASIC™, FORTRAN or COBOL and compiled using any well-known compatible compiler. The software of the invention normally runs from instructions stored in a memory on a host computer system. A memory or computer readable medium can be a hard disk, floppy disc, compact disc, magneto-optical disc, Random Access Memory, Read Only Memory or Flash Memory. The memory or computer readable medium used in the invention can be contained within a single computer or distributed in a network. A network can be any of a number of conventional network systems known in the art such as a local area network (LAN) or a wide area network (WAN). Client-server environments, database servers and networks that can be used in the invention are well known in the art. For example, the database server can run on an operating system such as UNIX, running a relational database management system, a World Wide Web application and a World Wide Web server. Other types of memories and computer readable media are also contemplated to function within the scope of the invention.

A database or data structure of the invention can be represented in a markup language format including, for example, Standard Generalized Markup Language (SGML), Hypertext markup language (HTML) or Extensible Markup language (XML). Markup languages can be used to tag the information stored in a database or data structure of the invention, thereby providing convenient annotation and transfer of data between databases and data structures. In particular, an XML format can be useful for structuring the data representation of reactions, reactants and their annotations; for exchanging database contents, for example, over a network or internet; for updating individual elements using the document object model; or for providing differential access to multiple users for different information content of a data base or data structure of the invention. XML programming methods and editors for writing XML code are known in the art as described, for example, in Ray, Learning XML O'Reilly and Associates, Sebastopol, Calif. (2001).

A set of constraints can be applied to a reaction network data structure to simulate the flux of mass through the reaction network under a particular set of environmental conditions specified by a constraints set. Because the time constants characterizing metabolic transients and/or metabolic reactions are typically very rapid, on the order of milli-seconds to seconds, compared to the time constants of cell growth on the order of hours to days, the transient mass balances can be simplified to only consider the steady state behavior. Referring now to an example where the reaction network data structure is a stoichiometric matrix, the steady state mass balances can be applied using the following system of linear equations

S·ν= 0  (Eq. 2)

where S is the stoichiometric matrix as defined above and ν is the flux vector. This equation defines the mass, energy, and redox potential constraints placed on the metabolic network as a result of stoichiometry. Together Equations 1 and 2 representing the reaction constraints and mass balances, respectively, effectively define the capabilities and constraints of the metabolic genotype and the organism's metabolic potential. All vectors, ν, that satisfy Equation 2 are said to occur in the mathematical nullspace of S. Thus, the null space defines steady-state metabolic flux distributions that do not violate the mass, energy, or redox balance constraints. Typically, the number of fluxes is greater than the number of mass balance constraints, thus a plurality of flux distributions satisfy the mass balance constraints and occupy the null space. The null space, which defines the feasible set of metabolic flux distributions, is further reduced in size by applying the reaction constraints set forth in Equation 1 leading to a defined solution space. A point in this space represents a flux distribution and hence a metabolic phenotype for the network. An optimal solution within the set of all solutions can be determined using mathematical optimization methods when provided with a stated objective and a constraint set. The calculation of any solution constitutes a simulation of the model.

Objectives for activity of S. cerevisiae can be chosen to explore the improved use of the metabolic network within a given reaction network data structure. These objectives can be design objectives for a strain, exploitation of the metabolic capabilities of a genotype, or physiologically meaningful objective functions, such as maximum cellular growth. Growth can be defined in terms of biosynthetic requirements based on literature values of biomass composition or experimentally determined values such as those obtained as described above. Thus, biomass generation can be defined as an exchange reaction that removes intermediate metabolites in the appropriate ratios and represented as an objective function. In addition to draining intermediate metabolites this reaction flux can be formed to utilize energy molecules such as ATP, NADH and NADPH so as to incorporate any growth dependent maintenance requirement that must be met. This new reaction flux then becomes another constraint/balance equation that the system must satisfy as the objective function. Using the stoichiometric matrix of FIG. 2 as an example, adding such a constraint is analogous to adding the additional column V growth to the stoichiometric matrix to represent fluxes to describe the production demands placed on the metabolic system. Setting this new flux as the objective function and asking the system to maximize the value of this flux for a given set of constraints on all the other fluxes is then a method to simulate the growth of the organism.

Continuing with the example of the stoichiometric matrix applying a constraint set to a reaction network data structure can be illustrated as follows. The solution to equation 2 can be formulated as an optimization problem, in which the flux distribution that minimizes a particular objective is found. Mathematically, this optimization problem can be stated as:

Minimize Z  (Eq. 3)

where

z=Σc i ·ν i   (Eq. 4)

where Z is the objective which is represented as a linear combination of metabolic fluxes ν i using the weights c i in this linear combination. The optimization problem can also be stated as the equivalent maximization problem; i.e. by changing the sign on Z. Any commands for solving the optimization problem can be used including, for example, linear programming commands.

A computer system of the invention can further include a user interface capable of receiving a representation of one or more reactions. A user interface of the invention can also be capable of sending at least one command for modifying the data structure, the constraint set or the commands for applying the constraint set to the data representation, or a combination thereof. The interface can be a graphic user interface having graphical means for making selections such as menus or dialog boxes. The interface can be arranged with layered screens accessible by making selections from a main screen. The user interface can provide access to other databases useful in the invention such as a metabolic reaction database or links to other databases having information relevant to the reactions or reactants in the reaction network data structure or to S. cerevisiae physiology. Also, the user interface can display a graphical representation of a reaction network or the results of a simulation using a model of the invention.

Once an initial reaction network data structure and set of constraints has been created, this model can be tested by preliminary simulation. During preliminary simulation, gaps in the network or “dead-ends” in which a metabolite can be produced but not consumed or where a metabolite can be consumed but not produced can be identified. Based on the results of preliminary simulations areas of the metabolic reconstruction that require an additional reaction can be identified. The determination of these gaps can be readily calculated through appropriate queries of the reaction network data structure and need not require the use of simulation strategies, however, simulation would be an alternative approach to locating such gaps.

In the preliminary simulation testing and model content refinement stage the existing model is subjected to a series of functional tests to determine if it can perform basic requirements such as the ability to produce the required biomass constituents and generate predictions concerning the basic physiological characteristics of the particular organism strain being modeled. The more preliminary testing that is conducted the higher the quality of the model that will be generated. Typically the majority of the simulations used in this stage of development will be single optimizations. A single optimization can be used to calculate a single flux distribution demonstrating how metabolic resources are routed determined from the solution to one optimization problem. An optimization problem can be solved using linear programming as demonstrated in the Examples below. The result can be viewed as a display of a flux distribution on a reaction map. Temporary reactions can be added to the network to determine if they should be included into the model based on modeling/simulation requirements.

Once a model of the invention is sufficiently complete with respect to the content of the reaction network data structure according to the criteria set forth above, the model can be used to simulate activity of one or more reactions in a reaction network. The results of a simulation can be displayed in a variety of formats including, for example, a table, graph, reaction network, flux distribution map or a phenotypic phase plane graph.

Thus, the invention provides a method for predicting a S. cerevisiae physiological function. The method includes the steps of (a) providing a data structure relating a plurality of S. cerevisiae reactants to a plurality of S. cerevisiae reactions, wherein each of the S. cerevisiae reactions includes a reactant identified as a substrate of the reaction, a reactant identified as a product of the reaction and a stoichiometric coefficient relating said substrate and said product; (b) providing a constraint set for the plurality of S. cerevisiae reactions; (c) providing an objective function, and (d) determining at least one flux distribution that minimizes or maximizes the objective function when the constraint set is applied to the data structure, thereby predicting a S. cerevisiae physiological function.

As used herein, the term “physiological function,” when used in reference to S. cerevisiae , is intended to mean an activity of a S. cerevisiae cell as a whole. An activity included in the term can be the magnitude or rate of a change from an initial state of a S. cerevisiae cell to a final state of the S. cerevisiae cell. An activity can be measured qualitatively or quantitatively. An activity included in the term can be, for example, growth, energy production, redox equivalent production, biomass production, development, or consumption of carbon, nitrogen, sulfur, phosphate, hydrogen or oxygen. An activity can also be an output of a particular reaction that is determined or predicted in the context of substantially all of the reactions that affect the particular reaction in a S. cerevisiae cell or substantially all of the reactions that occur in a S. cerevisiae cell. Examples of a particular reaction included in the term are production of biomass precursors, production of a protein, production of an amino acid, production of a purine, production of a pyrimidine, production of a lipid, production of a fatty acid, production of a cofactor, or transport of a metabolite. A physiological function can include an emergent property which emerges from the whole but not from the sum of parts where the parts are observed in isolation (see for example, Palsson Nat. Biotech 18:1147-1150 (2000)).

A physiological function of S. cerevisiae reactions can be determined using phase plane analysis of flux distributions. Phase planes are representations of the feasible set which can be presented in two or three dimensions. As an example, two parameters that describe the growth conditions such as substrate and oxygen uptake rates can be defined as two axes of a two-dimensional space. The optimal flux distribution can be calculated from a reaction network data structure and a set of constraints as set forth above for all points in this plane by repeatedly solving the linear programming problem while adjusting the exchange fluxes defining the two-dimensional space. A finite number of qualitatively different metabolic pathway utilization patterns can be identified in such a plane, and lines can be drawn to demarcate these regions. The demarcations defining the regions can be determined using shadow prices of linear optimization as described, for example in Chvatal, Linear Programming New York, W.H. Freeman and Co. (1983). The regions are referred to as regions of constant shadow price structure. The shadow prices define the intrinsic value of each reactant toward the objective function as a number that is either negative, zero, or positive and are graphed according to the uptake rates represented by the x and y axes. When the shadow prices become zero as the value of the uptake rates are changed there is a qualitative shift in the optimal reaction network.

One demarcation line in the phenotype phase plane is defined as the line of optimality (LO). This line represents the optimal relation between respective metabolic fluxes. The LO can be identified by varying the x-axis flux and calculating the optimal y-axis flux with the objective function defined as the growth flux. From the phenotype phase plane analysis the conditions under which a desired activity is optimal can be determined. The maximal uptake rates lead to the definition of a finite area of the plot that is the predicted outcome of a reaction network within the environmental conditions represented by the constraint set. Similar analyses can be performed in multiple dimensions where each dimension on the plot corresponds to a different uptake rate. These and other methods for using phase plane analysis, such as those described in Edwards et al., Biotech Bioeng. 77:27-36 (2002), can be used to analyze the results of a simulation using an in silica S. cerevisiae model of the invention.

A physiological function of S. cerevisiae can also be determined using a reaction map to display a flux distribution. A reaction map of S. cerevisiae can be used to view reaction networks at a variety of levels. In the case of a cellular metabolic reaction network a reaction map can contain the entire reaction complement representing a global perspective. Alternatively, a reaction map can focus on a particular region of metabolism such as a region corresponding to a reaction subsystem described above or even on an individual pathway or reaction. An example of a reaction map showing a subset of reactions in a reaction network of S. cerevisiae is shown in FIG. 4 .

The invention also provides an apparatus that produces a representation of a S. cerevisiae physiological function, wherein the representation is produced by a process including the steps of: (a) providing a data structure relating a plurality of S. cerevisiae reactants to a plurality of S. cerevisiae reactions, wherein each of the S. cerevisiae reactions includes a reactant identified as a substrate of the reaction, a reactant identified as a product of the reaction and a stoichiometric coefficient relating said substrate and said product; (b) providing a constraint set for the plurality of S. cerevisiae reactions; (c) providing an objective function; (d) determining at least one flux distribution that minimizes or maximizes the objective function when the constraint set is applied to the data structure, thereby predicting a S. cerevisiae physiological function, and (e) producing a representation of the activity of the one or more S. cerevisiae reactions.

The methods of the invention can be used to determine the activity of a plurality of S. cerevisiae reactions including, for example, biosynthesis of an amino acid, degradation of an amino acid, biosynthesis of a purine, biosynthesis of a pyrimidine, biosynthesis of a lipid, metabolism of a fatty acid, biosynthesis of a cofactor, transport of a metabolite and metabolism of an alternative carbon source. In addition, the methods can be used to determine the activity of one or more of the reactions described above or listed in Table 2.

The methods of the invention can be used to determine a phenotype of a S. cerevisiae mutant. The activity of one or more S. cerevisiae reactions can be determined using the methods described above, wherein the reaction network data structure lacks one or more gene-associated reactions that occur in S. cerevisiae . Alternatively, the methods can be used to determine the activity of one or more S. cerevisiae reactions when a reaction that does not naturally occur in S. cerevisiae is added to the reaction network data structure. Deletion of a gene can also be represented in a model of the invention by constraining the flux through the reaction to zero, thereby allowing the reaction to remain within the data structure. Thus, simulations can be made to predict the effects of adding or removing genes to or from S. cerevisiae . The methods can be particularly useful for determining the effects of adding or deleting a gene that encodes for a gene product that performs a reaction in a peripheral metabolic pathway.

A drug target or target for any other agent that affects S. cerevisiae function can be predicted using the methods of the invention. Such predictions can be made by removing a reaction to simulate total inhibition or prevention by a drug or agent. Alternatively, partial inhibition or reduction in the activity a particular reaction can be predicted by performing the methods with altered constraints. For example, reduced activity can be introduced into a model of the invention by altering the α j or β j values for the metabolic flux vector of a target reaction to reflect a finite maximum or minimum flux value corresponding to the level of inhibition. Similarly, the effects of activating a reaction, by initiating or increasing the activity of the reaction, can be predicted by performing the methods with a reaction network data structure lacking a particular reaction or by altering the α j or β j values for the metabolic flux vector of a target reaction to reflect a maximum or minimum flux value corresponding to the level of activation. The methods can be particularly useful for identifying a target in a peripheral metabolic pathway.

Once a reaction has been identified for which activation or inhibition produces a desired effect on S. cerevisiae function, an enzyme or macromolecule that performs the reaction in S. cerevisiae or a gene that expresses the enzyme or macromolecule can be identified as a target for a drug or other agent. A candidate compound for a target identified by the methods of the invention can be isolated or synthesized using known methods. Such methods for isolating or synthesizing compounds can include, for example, rational design based on known properties of the target (see, for example, DeCamp et al., Protein Engineering Principles and Practice , Ed. Cleland and Craik, Wiley-Liss, New York, pp. 467-506 (1996)), screening the target against combinatorial libraries of compounds (see for example, Houghten et al., Nature, 354, 84-86 (1991); Dooley et al., Science, 266, 2019-2022 (1994), which describe an iterative approach, or R. Houghten et al. PCT/US91/08694 and U.S. Pat. No. 5,556,762 which describe a positional-scanning approach), or a combination of both to obtain focused libraries. Those skilled in the art will know or will be able to routinely determine assay conditions to be used in a screen based on properties of the target or activity assays known in the art.

A candidate drug or agent, whether identified by the methods described above or by other methods known in the art, can be validated using an in silico S. cerevisiae model or method of the invention. The effect of a candidate drug or agent on S. cerevisiae physiological function can be predicted based on the activity for a target in the presence of the candidate drug or agent measured in vitro or in vivo. This activity can be represented in an in silico S. cerevisiae model by adding a reaction to the model, removing a reaction from the model or adjusting a constraint for a reaction in the model to reflect the measured effect of the candidate drug or agent on the activity of the reaction. By running a simulation under these conditions the holistic effect of the candidate drug or agent on S. cerevisiae physiological function can be predicted.

The methods of the invention can be used to determine the effects of one or more environmental components or conditions on an activity of S. cerevisiae . As set forth above, an exchange reaction can be added to a reaction network data structure corresponding to uptake of an environmental component, release of a component to the environment, or other environmental demand. The effect of the environmental component or condition can be further investigated by running simulations with adjusted α j or β j values for the metabolic flux vector of the exchange reaction target reaction to reflect a finite maximum or minimum flux value corresponding to the effect of the environmental component or condition. The environmental component can be, for example an alternative carbon source or a metabolite that when added to the environment of S. cerevisiae can be taken up and metabolized. The environmental component can also be a combination of components present for example in a minimal medium composition. Thus, the methods can be used to determine an optimal or minimal medium composition that is capable of supporting a particular activity of S. cerevisiae.

The invention further provides a method for determining a set of environmental components to achieve a desired activity for S. cerevisiae . The method includes the steps of (a) providing a data structure relating a plurality of S. cerevisiae reactants to a plurality of S. cerevisiae reactions, wherein each of the S. cerevisiae reactions includes a reactant identified as a substrate of the reaction, a reactant identified as a product of the reaction and a stoichiometric coefficient relating the substrate and the product; (b) providing a constraint set for the plurality of S. cerevisiae reactions; (c) applying the constraint set to the data representation, thereby determining the activity of one or more S. cerevisiae reactions (d) determining the activity of one or more S. cerevisiae reactions according to steps (a) through (c), wherein the constraint set includes an upper or lower bound on the amount of an environmental component and (e) repeating steps (a) through (c) with a changed constraint set, wherein the activity determined in step (e) is improved compared to the activity determined in step (d).

The following examples are intended to illustrate but not limit the present invention.

Reconstruction of the Metabolic Network of S. cerevisiae

This example shows how the metabolic network of S. cerevisiae can be reconstructed.

The reconstruction process was based on a comprehensive search of the current knowledge of metabolism in S. cerevisiae as shown in FIG. 5 . A reaction database was built using the available genomic and metabolic information on the presence, reversibility, localization and cofactor requirements of all known reactions. Furthermore, information on non-growth-dependent and growth-dependent ATP requirements and on the biomass composition was used.

For this purpose different online reaction databases, recent publications and review papers (Table 5 and 9), and established biochemistry textbooks (Zubay, Biochemistry Wm.C. Brown Publishers, Dubuque, Iowa (1998); Stryer, Biochemistry W. H. Freeman, New York, N.Y. (1988)) were consulted. Information on housekeeping genes of S. cerevisiae and their functions were taken from three main yeast on-line resources:

The MIPS Comprehensive Yeast Genome Database (CYGD) (Mewes et al., Nucleic Acids Research 30(1): 31-34 (2002)); The Saccharomyces Genome Database (SGD) (Cherry et al., Nucleic Acids Research 26(1): 73-9 (1998)); The Yeast Proteome Database (YPD) (Costanzo et al., Nucleic Acids Research 29(1): 75-9 (2001)).

The following metabolic maps and protein databases (available online) were investigated:

Kyoto Encyclopedia of Genes and Genomes database (KEGG) (Kanehisa et al., Nucleic Acids Research 28(1): 27-30 (2000)); The Biochemical Pathways database of the Expert Protein Analysis System database (ExPASy) (Appel et al., Trends Biochem Sci. 19(6): 258-260 (1994)); ERGO from Integrated Genomics (www.integratedgenomics.com) SWISS-PROT Protein Sequence database (Bairoch et al., Nucleic Acids Research 28(1): 45-48 (2000)).

Table 5 lists additional key references that were consulted for the reconstruction of the metabolic network of S. cerevisiae .

All reactions are localized into the two main compartments, cytosol and mitochondria, as most of the common metabolic reactions in S. cerevisiae take place in these compartments. Optionally, one or more additional compartments can be considered. Reactions located in vivo in other compartments or reactions for which no information was available regarding localization were assumed to be cytosol. All corresponding metabolites were assigned appropriate localization and a link between cytosol and mitochondria was established through either known transport and shuttle systems or through inferred reactions to meet metabolic demands.

After the initial assembly of all the metabolic reactions the list was manually examined for resolution of detailed biochemical issues. A large number of reactions involve cofactors utilization, and for many of these reactions the cofactor requirements have not yet been completely elucidated. For example, it is not clear whether certain reactions use only NADH or only NADPH as a cofactor or can use both cofactors, whereas other reactions are known to use both cofactors. For example, a mitochondrial aldehyde dehydrogenase encoded by ALD4 can use both NADH and NADPH as a cofactor (Remize et al. Appl Environ Microbiol 66(8): 3151-3159 (2000)). In such cases, two reactions are included in the reconstructed metabolic network.

Further considerations were taken into account to preserve the unique features of S. cerevisiae metabolism. S. cerevisiae lacks a gene that encodes the enzyme transhydrogenase. Insertion of a corresponding gene from Azetobacter vinelandii in S. cerevisiae has a major impact on its phenotypic behavior, especially under anaerobic conditions (Niessen et al. Yeast 18(1): 19-32 (2001)). As a result, reactions that create a net transhydrogenic effect in the model were either constrained to zero or forced to become irreversible. For instance, the flux carried by NADH dependent glutamate dehydrogenase (Gdh2p) was constrained to zero to avoid the appearance of a net transhydrogenase activity through coupling with the NADPH dependent glutamate dehydrogenases (Gdh1p and Gdh3p).

Once a first generation model is prepared, microbial behavior can be modeled for a specific scenario, such as anaerobic or aerobic growth in continuous cultivation using glucose as a sole carbon source. Modeling results can then be compared to experimental results. If modeling and experimental results are in agreement, the model can be considered as correct, and it is used for further modeling and predicting S. cerevisiae behavior. If the modeling and experimental results are not in agreement, the model has to be evaluated and the reconstruction process refined to determine missing or incorrect reactions, until modeling and experimental results are in agreement. This iterative process is shown in FIG. 5 and exemplified below.

Calculation of the P/O Ratio

This example shows how the genome-scale reconstructed metabolic model of S. cerevisiae was used to calculate the P/O ratio, which measures the efficiency of aerobic respiration. The P/O ratio is the number of ATP molecules produced per pair of electrons donated to the electron transport system (ETS).

Linear optimization was applied, and the in silico P/O ratio was calculated by first determining the maximum number of ATP molecules produced per molecule of glucose through the electron transport system (ETS), and then interpolating the in silico P/O ratio using the theoretical relation (i.e. in S. cerevisiae for the P/O ratio of 1.5, 18 ATP molecules are produced).

Experimental studies of isolated mitochondria have shown that S. cerevisiae lacks site I proton translocation (Verduyn et al., Antonie Van Leeuwenhoek 59(1): 49-63 (1991)). Consequently, estimation of the maximum theoretical or “mechanistic” yield of the ETS alone gives a P/O ratio of 1.5 for oxidation of NADH in S. cerevisiae grown on glucose (Verduyn et al., supra (1991)). However, based on experimental measurements, it has been determined that the net in vivo P/O ratio is approximately 0.95 (Verduyn et al., supra (1991)). This difference is generally thought to be due to the use of the mitochondrial transmembrane proton gradient needed to drive metabolite exchange, such as the proton-coupled translocation of pyruvate, across the inner mitochondrial membrane. Although simple diffusion of protons (or proton leakage) would be surprising given the low solubility of protons in the lipid bilayer, proton leakage is considered to contribute to the lowered P/O ratio due to the relatively high electrochemical gradient across the inner mitochondrial membrane (Westerhoff and van Dam, Thermodynamics and control of biological free - energy transduction Elsevier, New York, N.Y. (1987)).

Using the reconstructed network, the P/O ratio was calculated to be 1.04 for oxidation of NADH for growth on glucose by first using the model to determine the maximum number of ATP molecules produced per molecule of glucose through the electron transport system (ETS) (YATP,max=12.5 ATP molecules/glucose molecule via ETS in silico). The in silico P/O ratio was then interpolated using the theoretical relation (i.e. 18 ATP molecules per glucose molecule are produced theoretically when the P/O ratio is 1.5). The calculated P/O ratio was found to be close to the experimentally determined value of 0.95. Proton leakage, however, was not included in the model, which suggests that the major reason for the lowered P/O ratio is the use of the proton gradient for solute transport across the inner mitochondrial membrane. This result illustrates the importance of including the complete metabolic network in the analysis, as the use of the proton gradient for solute transport across the mitochondrial membrane contributes significantly to the operational P/O ratio.

Phenotypic Phase Plane Analysis

This example shows how the S. cerevisiae metabolic model can be used to calculate the range of characteristic phenotypes that the organism can display as a function of variations in the activity of multiple reactions.

For this analysis, O 2 and glucose uptake rates were defined as the two axes of the two-dimensional space. The optimal flux distribution was calculated using linear programming (LP) for all points in this plane by repeatedly solving the LP problem while adjusting the exchange fluxes defining the two-dimensional space. A finite number of quantitatively different metabolic pathway utilization patterns were identified in the plane, and lines were drawn to demarcate these regions. One demarcation line in the phenotypic phase plane (PhPP) was defined as the line of optimality (LO), and represents the optimal relation between the respective metabolic fluxes. The LO was identified by varying the x-axis (glucose uptake rate) and calculating the optimal y-axis (O 2 uptake rate), with the objective function defined as the growth flux. Further details regarding Phase-Plane Analysis are provided in Edwards et al., Biotechnol. Bioeng. 77:27-36 (2002) and Edwards et al., Nature Biotech. 19:125-130 (2001)).

As illustrated in FIG. 6 , the S. cerevisiae PhPP contains 8 distinct metabolic phenotypes. Each region (P 1 -P 8 ) exhibits unique metabolic pathway utilization that can be summarized as follows:

The left-most region is the so-called “infeasible” steady state region in the PhPP, due to stoichiometric limitations. From left to right: P 1 : Growth is completely aerobic. Sufficient oxygen is available to complete the oxidative metabolism of glucose to support growth requirements. This zone represents a futile cycle. Only CO 2 is formed as a metabolic by-product. The growth rate is less than the optimal growth rate in region P 2 . The P 1 upper limit represents the locus of points for which the carbon is completely oxidized to eliminate the excess electron acceptor, and thus no biomass can be generated. P 2 : Oxygen is slightly limited, and all biosynthetic cofactor requirements cannot be optimally satisfied by oxidative metabolism. Acetate is formed as a metabolic by-product enabling additional high-energy phosphate bonds via substrate level phosphorylation. With the increase of O 2 supply, acetate formation eventually decreases to zero. P 3 : Acetate is increased and pyruvate is decreased with increase in oxygen uptake rate. P 4 : Pyruvate starts to increase and acetate is decreased with increase in oxygen uptake rate. Ethanol production eventually decreases to zero. P 5 : The fluxes towards acetate formation are increasing and ethanol production is decreasing. P 6 : When the oxygen supply increases, acetate formation increases and ethanol production decreases with the carbon directed toward the production of acetate. Besides succinate production, malate may also be produced as metabolic by-product. P 7 : The oxygen supply is extremely low, ethanol production is high and succinate production is decreased. Acetate is produced at a relatively low level. P 8 : This region is along the Y-axis and the oxygen supply is zero. This region represents completely anaerobic fermentation. Ethanol and glycerol are secreted as a metabolic by-product. The role of NADH-consuming glycerol formation is to maintain the cytosol redox balance under anaerobic conditions (Van Dijken and Scheffers Yeast 2(2): 123-7 (1986)). Line of Optimality: Metabolically, the line of optimality (LO) represents the optimal utilization of the metabolic pathways without limitations on the availability of the substrates. On an oxygen/glucose phenotypic phase plane diagram, LO represents the optimal aerobic glucose-limited growth of S. cerevisiae metabolic network to produce biomass from unlimited oxygen supply for the complete oxidation of the substrates in the cultivation processes. The line of optimality therefore represents a completely respiratory metabolism, with no fermentation by-product secretion and the futile cycle fluxes equals zero.

Thus, this example demonstrates that Phase Plane Analysis can be used to determine the optimal fermentation pattern for S. cerevisiae , and to determine the types of organic byproducts that are accumulated under different oxygenation conditions and glucose uptake rates.

Calculation of Line of Optimality and Respiratory Quotient

This example shows how the S. cerevisiae metabolic model can be used to calculate the oxygen uptake rate (OUR), the carbon dioxide evolution rate (CER) and the respiration quotient (RQ), which is the ratio of CER over OUR.

The oxygen uptake rate (OUR) and the carbon dioxide evolution rate (CER) are direct indicators of the yeast metabolic activity during the fermentation processes. RQ is a key metabolic parameter that is independent of cell number. As illustrated in FIG. 7 , if the S. cerevisiae is grown along the line of optimality, LO, its growth is at optimal aerobic rate with all the carbon sources being directed to biomass formation and there are no metabolic by-products secreted except CO 2 . The calculated RQ along the LO is a constant value of 1.06; the RQ in P 1 region is less than 1.06; and the RQ in the remaining regions in the yeast PhPP are greater than 1.06. The RQ has been used to determine the cell growth and metabolism and to control the glucose feeding for optimal biomass production for decades (Zeng et al. Biotechnol. Bioeng. 44:1107-1114 (1994)). Empirically, several researchers have proposed the values of 1.0 (Zigova, J Biotechnol 80: 55-62 (2000). Journal of Biotechnology), 1.04 (Wang et al., Biotechnol & Bioeng 19:69-86 (1977)) and 1.1 (Wang et al., Biotechnol . & Bioeng. 21:975-995 (1979)) as optimal RQ which should be maintained in fed-batch or continuous production of yeast's biomass so that the highest yeast biomass could be obtained (Dantigny et al., Appl. Microbiol. Biotechnol. 36:352-357 (1991)). The constant RQ along the line of optimality for yeast growth by the metabolic model is thus consistent with the empirical formulation of the RQ through on-line measurements from the fermentation industry.

Computer Simulations

This example shows computer simulations for the change of metabolic phenotypes described by the yeast PhPP.

A piece-wise linearly increasing function was used with the oxygen supply rates varying from completely anaerobic to fully aerobic conditions (with increasing oxygen uptake rate from 0 to 20 mmol per g cell-hour). A glucose uptake rate of 5 mmol of glucose per g (dry weight)-hour was arbitrarily chosen for these computations. As shown in FIG. 8A , the biomass yield of the in silico S. cerevisiae strain was shown to increase from P 8 to P 2 , and become optimal on the LO. The yield then started to slowly decline in P 1 (futile cycle region). At the same time, the RQ value declines in relation to the increase of oxygen consumption rate, reaching a value of 1.06 on the LO1 and then further declining to become less than 1.

FIG. 8B shows the secretion rates of metabolic by-products; ethanol, succinate, pyruvate and acetate with the change of oxygen uptake rate from 0 to 20 mmol of oxygen per g (dry weight)-h. Each one of these by-products is secreted in a fundamentally different way in each region. As oxygen increases from 0 in P 7 , glycerol production (data not shown in this figure) decreases and ethanol production increases. Acetate and succinate are also secreted.

Modeling of Phenotypic Behavior in Chemostat Cultures

This example shows how the S. cerevisiae metabolic model can be used to predict optimal flux distributions that would optimize fermentation performance, such as specific product yield or productivity. In particular, this example shows how flux based analysis can be used to determine conditions that would minimize the glucose uptake rate of S. cerevisiae grown on glucose in a continuous culture under anaerobic and under aerobic conditions.

In a continuous culture, growth rate is equivalent to the dilution rate and is kept at a constant value. Calculations of the continuous culture of S. cerevisiae were performed by fixing the in silico growth rate to the experimentally determined dilution rate, and minimizing the glucose uptake rate. This formulation is equivalent to maximizing biomass production given a fixed glucose uptake value and was employed to simulate a continuous culture growth condition. Furthermore, a non growth dependent ATP maintenance of 1 mmol/gDW, a systemic P/O ratio of 1.5 (Verduyn et al. Antonie Van Leeuwenhoek 59(1): 49-63 (1991)), a polymerization cost of 23.92 mmol ATP/gDW, and a growth dependent ATP maintenance of 35.36 mmol ATP/gDW, which is simulated for a biomass yield of 0.51 gDW/h, are assumed. The sum of the latter two terms is included into the biomass equation of the genome-scale metabolic model.

Optimal growth properties of S. cerevisiae were calculated under anaerobic glucose-limited continuous culture at dilution rates varying between 0.1 and 0.4 h −1 . The computed by-product secretion rates were then compared to the experimental data (Nissen et al. Microbiology 143(1): 203-18 (1997)). The calculated uptake rates of glucose and the production of ethanol, glycerol, succinate, and biomass are in good agreement with the independently obtained experimental data ( FIG. 9 ). The relatively low observed acetate and pyruvate secretion rates were not predicted by the in silico model since the release of these metabolites does not improve the optimal solution of the network.

It is possible to constrain the in silico model further to secrete both, pyruvate and acetate at the experimental level and recompute an optimal solution under these additional constraints. This calculation resulted in values that are closer to the measured glucose uptake rates ( FIG. 9A ). This procedure is an example of an iterative data-driven constraint-based modeling approach, where the successive incorporation of experimental data is used to improve the in silico model. Besides the ability to describe the overall growth yield, the model allows further insight into how the metabolism operates. From further analysis of the metabolic fluxes at anaerobic growth conditions the flux through the glucose-6-phosphate dehydrogenase was found to be 5.32% of the glucose uptake rate at dilution rate of 0.1 h −1 , which is consistent with experimentally determined value (6.34%) for this flux when cells are operating with fermentative metabolism (Nissen et al., Microbiology 143(1): 203-218 (1997)).

Optimal growth properties of S. cerevisiae were also calculated under aerobic glucose-limited continuous culture in which the Crabtree effect plays an important role. The molecular mechanisms underlying the Crabtree effect in S. cerevisiae are not known. The regulatory features of the Crabtree effect (van Dijken et al. Antonie Van Leeuwenhoek 63 (3-4):343-52 (1993)) can, however, be included in the in silico model as an experimentally determined growth rate-dependent maximum oxygen uptake rate (Overkamp et al. J. of Bacteriol 182(10): 2823-30 (2000))). With this additional constraint and by formulating growth in a chemostat as described above, the in silico model makes quantitative predictions about the respiratory quotient, glucose uptake, ethanol, CO2, and glycerol secretion rates under aerobic glucose-limited continuous condition ( FIG. 10 ).

Analysis of Deletion of Genes Involved in Central Metabolism in S. cerevsiae

This example shows how the S. cerevisiae metabolic model can be used to determine the effect of deletions of individual reactions in the network.

Gene deletions were performed in silico by constraining the flux(es) corresponding to a specific gene to zero. The impact of single gene deletions on growth was analysed by simulating growth on a synthetic complete medium containing glucose, amino acids, as well as purines and pyrimidines.

In silico results were compared to experimental results as supplied by the Saccharomyces Genome Database (SOD) (Cherry et al., Nucleic Acids Research 26(1):73-79 (1998)) and by the Comprehensive Yeast Genome Database (Mewes et al., Nucleic Acids Research 30(1):31-34 (2002)). In 85.6% of all considered cases (499 out of 583 cases), the in silico prediction was in qualitative agreement with experimental results. An evaluation of these results can be found in Example VIII. For central metabolism, growth was predicted under various experimental conditions and 81.5% (93 out of 114 cases) of the in silico predictions were in agreement with in vivo phenotypes.

Table 6 shows the impact of gene deletions on growth in S. cerevisiae . Growth on different media was considered, including defined complete medium with glucose as the carbon source, and minimal medium with glucose, ethanol or acetate as the carbon source. The complete reference citations for Table 6 can be found in Table 9.

Thus, this example demonstrates that the in silico model can be used to uncover essential genes to augment or circumvent traditional genetic studies.

Large-Scale Gene Deletion Analysis in S. Cerevisiae

A large-scale in silico evaluation of gene deletions in S. cerevisiae was conducted using the genome-scale metabolic model. The effect of 599 single gene deletions on cell viability was simulated in silico and compared to published experimental results. In 526 cases (87.8%), the in silico results were in agreement with experimental observations when growth on synthetic complete medium was simulated. Viable phenotypes were predicted in 89.4% (496 out of 555) and lethal phenotypes are correctly predicted in 68.2% (30 out of 44) of the cases considered.

The failure modes were analyzed on a case-by-case basis for four possible inadequacies of the in silico model: 1) incomplete media composition; 2) substitutable biomass components; 3) incomplete biochemical information; and 4) missing regulation. This analysis eliminated a number of false predictions and suggested a number of experimentally testable hypotheses. The genome-scale in silico model of S. cerevisiae can thus be used to systematically reconcile existing data and fill in knowledge gaps about the organism.

Growth on complete medium was simulated under aerobic condition. Since the composition of a complete medium is usually not known in detail, a synthetic complete medium containing glucose, twenty amino acids (alanine, arginine, asparagine, aspartate, cysteine, glutamine, glutamate, glycine, histidine, isoleucine, leucine, lysine, methionine, phenylalanine, proline, serine, threonine, tryptophane, tyrosine, valine) and purines (adenine and guanine) as well as pyrimidines (cytosine and thymine) was defined for modeling purposes. Furthermore, ammonia, phosphate, and sulphate were supplied. The in silico results were initially compared to experimental data from a competitive growth assay (Winzeler et al., Science 285:901-906 (1999)) and to available data from the MIPS and SGD databases (Mewes et al., Nucleic Acids Research 30(1):31-34 (2002); Cherry et al., Nucleic Acids Research 26(1):73-79 (1998)). Gene deletions were simulated by constraining the flux through the corresponding reactions to zero and optimizing for growth as previously described (Edwards and Palsson, Proceedings of the National Academy of Sciences 97(10):5528-5533 (2000)). For this analysis, a viable phenotype was defined as a strain that is able to meet all the defined biomass requirements and thus grow. Single gene deletion mutants that have a reduced growth rate compared to the wild type simulation are referred to as growth retarded mutants.

The analysis of experimental data was approached in three steps: The initial simulation using the synthetic medium described above, referred to as simulation 1 .

False predictions of simulation 1 were subsequently examined to determine if the failure was due to incomplete information in the in silico model, such as missing reactions, the reversibility of reactions, regulatory events, and missing substrates in the synthetic complete medium. In simulation 2 , any such additional information was introduced into the in silico model and growth was re-simulated for gene deletion mutants whose in silico phenotype was not in agreement with its in vivo phenotype.

A third simulation was carried out, in which dead end pathways (i.e. pathways leading to intracellular metabolites that were not further connected into the overall network), were excluded from the analysis (simulation 3 ).

The effect of single gene deletions on the viability of S. cerevisiae was investigated for each of the 599 single gene deletion mutants. The in silica results were categorized into four groups:

1. True negatives (correctly predicted lethal phenotype);

2. False negatives (wrongly predicted lethal phenotype);

3. True positives (correctly predicted viable phenotypes);

4. False positives (wrongly predicted viable phenotypes).

In simulation 1 , 509 out of 599 (85%) simulated phenotypes were in agreement with experimental data. The number of growth retarding genes in simulation 1 was counted to be 19, a surprisingly low number. Only one deletion, the deletion of TPI1, had a severe impact on the growth rate. Experimentally, a deletion in TPI1 is lethal (Ciriacy and Breitenbach, J Bacteriol 139(1):152-60 (1979)). In silico, a tpi1 mutant could only sustain a specific growth rate of as low as 17% of the wild type. All other growth retarding deletions sustained approximately 99% of wild type growth, with the exception of a deletion of the mitochondrial ATPase that resulted in a specific growth rate of approximately 90% of wild type.

Predictions of simulation 1 were evaluated in a detailed manner on a case-by-case basis to determine whether the false predictions could be explained by:

1. Medium composition used for the simulation;

2. The biomass composition used in the simulation;

3. Incomplete biochemical information; and

4. Effects of gene regulation.

Analysis of the false predictions from simulation 1 based on these possible failure modes resulted in model modifications that led to 526 out of 599 correctly predicted phenotypes (87.8%), i.e., simulation 2 .

Simulation 3 uncovered some 220 reactions in the reconstructed network that are involved in dead end pathways. Removing these reactions and their corresponding genes from the genome-scale metabolic flux balance model, simulation 3 resulted in 473 out of 530 (89.6%) correctly predicted phenotypes of which 91.4% are true positive and 69.8% are true negative predictions.

Table 7 provides a summary of the large-scale evaluation of the effect of in silico single gene deletions in S. cerevisiae on viability.

A comprehensive list of all the genes used in the in silica deletion studies and results of the analysis are provided in Table 8. Table 8 is organized according to the categories true negative, false negative, true positive and false positive predictions. Genes highlighted in grey boxes, such as  corresponded initially to false predictions (simulation 1 ); however, evaluation of the false prediction and simulation 2 identified these cases as true predictions. ORFs or genes that are in an open box, such as  were excluded in simulation 3 , as the corresponding reactions catalysed steps in dead end pathways.

The following text describes the analysis of the initially false predictions of simulation 1 that were performed, leading to simulation 2 results.

Influence of Media Composition on Simulation Results:

A rather simple synthetic complete medium composition was chosen for simulation 1 . The in silico medium contained only glucose, amino acids and nucleotides as the main components. However, complete media often used for experimental purposes, e.g. the YPD medium containing yeast extract and peptone, include many other components, which are usually unknown.

False Negative Predictions: The phenotype of the following deletion mutants: ecm1Δ, yil145cΔ, erg2 Δ, erg24 Δ, fas1 Δ, ura1 Δ, ura2 Δ, ura3 Δ and ura4 Δ were falsely predicted to be lethal in simulation 1 . In simulation 2 , an additional supplement of specific substrate could rescue a viable phenotype in silico and as the supplemented substrate may be assumed to be part of a complex medium, the predictions were counted as true positive predictions in simulation 2 . For example, both Ecm1 and Yil145c are involved in pantothenate synthesis. Ecm1 catalyses the formation of dehydropantoate from 2-oxovalerate, whereas Yil145c catalyses the final step in pantothenate synthesis from β-alanine and panthoate. In vivo, ecm1Δ, and yil145c A mutants require pantothenate for growth (White et al., J Biol Chem 276(14): 10794-10800 (2001)). By supplying pantothenate to the synthetic complete medium in silico, the model predicted a viable phenotype and the growth rate was similar to in silico wild type S. cerevisiae.

Similarly other false predictions could be traced to medium composition:

Mutants deleted in ERG2 or ERG24 are auxotroph for ergosterol (Silve et al., Mol Cell Biol 16(6): 2719-2727 (1996); Bourot and Karst, Gene 165(1): 97-102 (1995)). Simulating growth on a synthetic complete medium supplemented with ergosterol allowed the model to accurately predict viable phenotypes. A deletion of FAS1 (fatty acid synthase) is lethal unless appropriate amounts of fatty acids are provided, and by addition of fatty acids to the medium, a viable phenotype was predicted. Strains deleted in URA1, URA2, URA3, or URA4 are auxotroph for uracil (Lacroute, J Bacterial 95(3): 824-832 (1968)), and by supplying uracil in the medium the model predicted growth.

The above cases were initially false negative predictions, and simulation 2 demonstrated that these cases were predicted as true positive by adjusting the medium composition.

False Positive Predictions: Simulation 1 also contained false positive predictions, which may be considered as true negatives or as true positives. Contrary to experimental results from a competitive growth assay (Winzeler et al., Science 285: 901-906 (1999)), mutants deleted in ADE13 are viable in vivo on a rich medium supplemented with low concentrations of adenine, but grow poorly (Guetsova et al., Genetics 147(2): 383-397 (1997)). Adenine was supplied in the in silico synthetic complete medium. By not supplying adenine, a lethal mutant was predicted. Therefore, this case was considered as a true negative prediction.

A similar case was the deletion of GLN1, which codes a glutamine synthase, the only pathway to produce glutamine from ammonia. Therefore, gln1 Δ mutants are glutamine auxotroph (Mitchell, Genetics 111(2):243-58 (1985)). In a complex medium, glutamine is likely to be deaminated to glutamate, particularly during autoclaving. Complex media are therefore likely to contain only trace amounts of glutamine, and gln1Δ mutants are therefore not viable. However, in silico, glutamine was supplied in the complete synthetic medium and growth was predicted. By not supplying glutamine to the synthetic complete medium, the model predicted a lethal phenotype resulting in a true negative prediction.

Ilv3 and Ilv5 are both involved in branched amino acid metabolism. One may expect that a deletion of ILV3 or ILV5 could be rescued with the supply of the corresponding amino acids. For this, the model predicted growth. However, contradictory experimental data exists. In a competitive growth assay lethal phenotypes were reported. However, earlier experiments showed that ilv3Δ and ilv5Δ mutants could sustain growth when isoleucine and valine were supplemented to the medium, as for the complete synthetic medium. Hence, these two cases were considered to be true positive predictions.

Influence of the Definition of the Biomass Equation

The genome-scale metabolic model contains the growth requirements in the form of biomass composition. Growth is defined as a drain of building blocks, such as amino acids, lipids, nucleotides, carbohydrates, etc., to form biomass. The number of biomass components is 44 (see Table 1). These building blocks are essential for the formation of cellular components and they have been used as a fixed requirement for growth in the in silico simulations. Thus, each biomass component had to be produced by the metabolic network otherwise the organism could not grow in silico. In vivo, one often finds deletion mutants that are not able to produce the original biomass precursor or building block; however, other metabolites can replace these initial precursors or building blocks. Hence, for a number of strains a wrong phenotype was predicted in silico for this reason.

Phosphatidylcholine is synthesized by three methylation steps from phosphatidylethanolamine (Dickinson and Schweizer, The metabolism and molecular physiology of Saccharomyces cerevisiae Taylor & Francis, London; Philadelphia (1999)). The first step in the synthesis of phosphatidylcholine from phosphatidylethanolamine is catalyzed by a methyltransferase encoded by CHO2 and the latter two steps are catalyzed by phospholipid methyltransferase encoded by OPI3. Strains deleted in CHO2 or OPI3 are viable (Summers et al., Genetics 120(4): 909-922 (1988); Daum et al., Yeast 14(16): 1471-1510 (1998)); however, either null mutant accumulates mono- and dimethylated phosphatidylethanolamine under standard conditions and display greatly reduced levels of phosphatidylcholine (Daum et al., Yeast 15(7): 601-614 (1999)). Hence, phosphatidylethanolamine can replace phosphatidylcholine as a biomass component. In silico, phosphatidylcholine is required for the formation of biomass. One may further speculate on whether an alternative pathway for the synthesis of phosphatidylcholine is missing in the model, since Daum et al., supra (1999) detected small amounts of phosphatidylcholine in cho2Δ mutants. An alternative pathway, however, was not included in the in silico model.

Deletions in the ergosterol biosynthetic pathways of ERG3, ERG4, ERG5 or ERG6 lead in vivo to viable phenotypes. The former two strains accumulate ergosta-8,22,24 (28)-trien-3-beta-ol (Bard et al., Lipids 12(8): 645-654 (1977); Zweytick et al., FEBS Lett 470(1): 83-87 (2000)), whereas the latter two accumulate ergosta-5,8-dien-3beta-ol (Hata et al., J Biochem (Tokyo) 94(2): 501-510 (1983)), or zymosterol and smaller amounts of cholesta-5,7,24-trien-3-beta-ol and cholesta-5,7,22,24-trien-3-beta-ol (Bard et al., supra (1977); Parks et al., Crit Rev Biochem Mol Biol 34(6): 399-404 (1999)), respectively, components that were not included in the biomass equations.

The deletion of the following three genes led to false positive predictions: RER2, SEC59 and QIR1. The former two are involved in glycoprotein synthesis and the latter is involved in chitin metabolism. Both chitin and glycoprotein are biomass components. However, for simplification, neither of the compounds was considered in the biomass equation. Inclusion of these compounds into the biomass equation may improve the prediction results.

Incomplete Biochemical Information

For a number of gene deletion mutants (inm1Δ, met6Δ, ynk1Δ, pho84Δ, psd2Δ, tps2Δ), simulation 1 produced false predictions that could not be explained by any of the two reasons discussed above nor by missing gene regulation (see below). Further investigation of the metabolic network including an extended investigation of biochemical data from the published literature showed that some information was missing initially in the in silico model or information was simply not available.

Inm1 catalyses the ultimate step in inositol biosynthesis from inositol 1-phosphate to inositol (Murray and Greenberg, Mol Microbiol 36(3): 651-661 (2000)). Upon deleting INM1, the model predicted a lethal phenotype in contrary to the experimentally observed viable phenotype. An isoenzyme encoded by IMP2 was initially not included in the model, which may take over the function of INM1 and this addition would have led to a correct prediction. However, an inm1 Δimp2Δ in vivo double deletion mutant is not inositol auxotroph (Lopez et al., Mol Microbiol 31(4): 1255-1264 (1999)). Hence, it appears that alternative routes for the production of inositol probably exist. Due to the lack of comprehensive biochemical knowledge, effects on inositol biosynthesis and the viability of strains deleted in inositol biosynthetic genes could not be explained.

Met6Δ mutants are methionine auxotroph (Thomas and Surdin-Kerjan, Microbiol Mol Biol Rev 61(4):503-532 (1997)), and growth may be sustained by the supply of methionine or S-adenosyl-L-methionine. In silico growth was supported neither by the addition of methionine nor by the addition of S-adenosyl-L-methionine. Investigation of the metabolic network showed that deleting MET6 corresponds to deleting the only possibility for using 5-methyltetrahydrofolate. Hence, the model appears to be missing certain information. A possibility may be that the carbon transfer is carried out using 5-methyltetrahydropteroyltri-L-glutamate instead of 5-methyltetrahydrofolate. A complete pathway for such a by-pass was not included in the genome-scale model.

The function of Ynk1p is the synthesis of nucleoside triphosphates from nucleoside diphosphates. YNK1Δ mutants have a 10-fold reduced Ynk1p activity (Fukuchi et al., Genes 129(1):141-146 (1993)), though this implies that there may either be an alternative route for the production of nucleoside triphosphates or a second nucleoside diphosphate kinase, even though there is no ORF in the genome with properties that indicates that there is a second nucleoside diphosphate kinase. An alternative route for the production of nucleoside triphosphate is currently unknown (Dickinson et al., supra (1999)), and was therefore not included in the model, hence a false negative prediction.

PHO84 codes for a high affinity phosphate transporter that was the only phosphate transporter included in the model. However, at least two other phosphate transporters exist, a second high affinity and Na + dependent transporter Pho89 and a low affinity transporter (Persson et al., Biochim Biophys Acta 1422(3): 255-72 (1999)). Due to exclusion of these transporters a lethal pho84□ mutant was predicted. Including PHO89 and a third phosphate transporter, the model predicted a viable deletion mutant.

In a null mutant of PSD2, phosphatidylethanolamine synthesis from phosphatidylserine is at the location of Psd1 (Trotter et al., J Biol Chem 273(21): 13189-13196 (1998)), which is located in the mitochondria. It has been postulated that phosphatidylserine can be transported into the mitochondria and phosphatidylethanolamine can be transported out of the mitochondria. However, transport of phosphatidylethanolamine and phosphatidylserine over the mitochondrial membrane was initially not included in the model. Addition of these transporters to the genome-scale flux balance model allowed in silico growth of a PSD2 deleted mutant.

Strains deleted in TPS2 have been shown to be viable when grown on glucose (Bell et al., J Biol Chem 273(50): 33311-33319 (1998)). The reaction carried out by Tps2p was modeled as essential and as the final step in trehalose synthesis from trehalose 6-phosphate. However, the in vivo viable phenotype shows that other enzymes can take over the hydrolysis of trehalose 6-phosphate to trehalose from Tps2p (Bell et al., supra (1998)). The corresponding gene(s) are currently unknown. Inclusion of a second reaction catalyzing the final step of trehalose formation allowed for the simulation of a viable phenotype.

Strains deleted in ADE3 (C1-tetrahydrofolate synthase) and ADK1 (Adenylate kinase) could not be readily explained. It is possible that alternative pathways or isoenzyme-coding genes for both functions exist among the many orphan genes still present in the S. cerevisiae.

The reconstruction process led to some incompletely modeled parts of metabolism. Hence, a number of false positive predictions may be the result of gaps (missing reactions) within pathways or between pathways, which prevent the reactions to completely connect to the overall pathway structure of the reconstructed model. Examples include:

Sphingolipid metabolism. It has not yet been fully elucidated and therefore was not included completely into the model nor were sphingolipids considered as building blocks in the biomass equation. Formation of tRNA. During the reconstruction process some genes were included responsible for the synthesis of tRNA (DED81, HTS1, KRS1, YDR41C, YGL245W). However, pathways of tRNA synthesis were not fully included. Heme synthesis was considered in the reconstructed model (HEM1, HEM12, HEM13, HEM15, HEM2, HEM3, HEM4). However no reaction was included that metabolized heme in the model. Hence, the incomplete structure of metabolic network may be a reason for false prediction of the phenotype of aur1Δ, lcb1Δ, lcb2Δ, tsc10Δ, ded81Δ, hts1Δ, krs1Δ, ydr41cΔ, ygl245wΔ, hem1Δ, hem12Δ, hem13Δ, hem15Δ, hem2Δ, hem3Δ, and hem4Δ deletion mutants. Reaction reversibility. The CHO1 gene encodes a phosphatidylserine synthase, an integral membrane protein that catalyses a central step in cellular phospholipid biosynthesis. In vivo, a deletion in CHO1 is viable (Winzeler et al., Science 285: 901-906 (1999)). However, mutants are auxotrophic for choline or ethanolamine on media containing glucose as the carbon source (Birner et al., Mol Biol Cell 12(4): 997-1007 (2001)). Nevertheless, the model did not predict growth when choline and/or ethanolamine were supplied. Further investigation of the genome-scale model showed that this might be due to defining reactions leading from phosphatidylserine to phosphatidylcholine via phosphatidylethanolamine exclusively irreversible. By allowing these reactions to be reversible, either supply of choline and ethanolamine could sustain growth in silico.

Gene Regulation

Whereas many false negative predictions could be explained by either simulation of growth using the incorrect in silico synthetic complete medium or by initially missing information in the model, many false positives may be explained by in vivo catabolite expression, product inhibition effects or by repressed isoenzymes, as kinetic and other regulatory constraints were not included in the genome-scale metabolic model.

A total of 17 false positive predictions could be related to regulatory events. For a deletion of CDC19, ACS2 or ENO2 one may usually expect that the corresponding isoenzymes may take over the function of the deleted genes. However, the corresponding genes, either PYK2, ACS1 or ENO1, respectively, are subject to catabolite repression (Boles et al., J Bacteriol 179(9): 2987-2993 (1997); van den Berg and Steensma, Eur J Biochem 231(3): 704-713 (1995); Zimmerman et al., Yeast sugar metabolism: biochemistry, genetics, biotechnology, and applications Technomic Pub., Lancaster, Pa. (1997)). A deletion of GPM1 should be replaced by either of the two other isoenzymes, Gpm2 and Gpm3; however for the two latter corresponding gene products usually no activity is found (Heinisch et al., Yeast 14(3): 203-13 (1998)).

Falsely predicted growth phenotypes can often be explained when the corresponding deleted metabolic genes are involved in several other cell functions, such as cell cycle, cell fate, communication, cell wall integrity, etc. The following genes whose deletions yielded false positive predictions were found to have functions other than just metabolic function: ACS2, BET2, CDC19, CDC8, CYR1, DIM1, ENO2, FAD1, GFA1, GPM1, HIP1, MSS4, PET9, PIK1, PMA1, STT4, TOR2. Indeed, a statistical analysis of the MIPS functional catalogue (http://mips.gsf.de/proj/yeast/) showed that in general it was more likely to have a false prediction when the genes that had multiple functions were involved in cellular communication, cell cycling and DNA processing or control of cellular organization.

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Throughout this application various publications have been referenced. The disclosures of these publications in their entireties are hereby incorporated by reference in this application in order to more fully describe the state of the art to which this invention pertains.

Although the invention has been described with reference to the examples provided above, it should be understood that various modifications can be made without departing from the spirit of the invention. Accordingly, the invention is only limited by the claims.