Methods and systems for genome-scale kinetic modeling

Abstract

Embodiments of the present invention generally relate to the construction, analysis, and characterization of dynamical states of biological networks at the cellular level. Methods are provided for analyzing the dynamical states by constructing matrices using high-throughput data types, such as fluxomic, metabolomic, and proteomic data. Some embodiments relate to an individual, while others relate to a plurality of individuals.

What is claimed is: 
     
         1 . A computer-implemented method for developing a dynamic network model of a biological network, the method comprising:
 providing, at a computer system, a network data structure relating a plurality of reactants to a plurality of reactions, the plurality of reactions comprising one or more flux distributions, wherein each of the reactions comprises one or more reactants identified as a substrate of the reaction, one or more reactants identified as a product of the reaction and a stoichiometric coefficient relating the substrate and the product;   providing, at a computer system, a constraint set for the plurality of reactions in said biological network associated with the plurality of reactions;   providing, at a computer system, a constraint set for a plurality of constraints, wherein said constraint set comprises at least one physical constraint;   providing, at a computer system, a constraint set for a plurality of kinetic constants associated with the plurality of reactions;   providing, at a computer system, a constraint set for a plurality of equilibrium constants associated with the plurality of reactions;   integrating, at a computer system, the sets of constraints to form stoichiometric, gradient, and Jacobian matrices;   providing, at a computer system, an objective function; and   predicting, at a computer system, a physiological function related to said biological network by determining using the computer system at least one flux distribution, from the one or more flux distributions, that minimizes or maximizes the objective function when at least one constraint set from the sets of constraints is applied to the data structure.   
     
     
         2 . The method of  claim 1 , wherein said at least one physical constraint is mass balance. 
     
     
         3 . The method of  claim 1 , wherein said constraint set for said plurality of reactions in said biological network reflects enzymatic interconversions of small metabolites, enzyme reaction schemes, allosteric enzyme interactions, signaling pathways, or macromolecular biochemical reactions. 
     
     
         4 . A computer-implemented method for developing a dynamic network model, the method comprising:
 accessing archetype data for a plurality of reactions of a network;   developing a stoichiometric data structure for the reactions based on the archetype data;   accessing physiological data reflecting a specific context;   performing a steady state simulation using the stoichiometric data structure and the physiological data;   incorporating metabolic data and equilibrium constant data based on the steady state simulation;   deriving a gradient matrix and dynamic rate equations based on the stoichiometric data structure and the incorporated data; and   deriving a concentration Jacobian matrix and a flux Jacobian matrix based on the stoichiometric data structure and the gradient matrix so as to characterize dynamic properties of the network.   
     
     
         5 . The method of  claim 4 , wherein an i th  column of the stoichiometric data structure contains stoichiometric coefficients of an i th  reaction in the network and an i th  row in the gradient matrix contains partial derivatives of the i th  reaction with respect to all reactants in the network. 
     
     
         6 . The method of  claim 4 , wherein the stoichiometric data structure is derived from genomic, proteomic and metabolomic data. 
     
     
         7 . The method of  claim 4 , wherein the gradient matrix is derived from fluxomic and metabolomic data, kinetic characterization of individual reactions and assessment of thermodynamic properties. 
     
     
         8 . The method of  claim 4 , wherein the stoichiometric data structure is derived from a stoichiometry of reactions, and the gradient matrix is based on kinetic data and thermodynamic information. 
     
     
         9 . The method of  claim 4 , wherein the stoichiometric data structure is based on the content of a genome and is a property of a species, and the gradient matrix is based on kinetic information and is genetically derived. 
     
     
         10 . The method of  claim 4 , wherein a reaction comprises a representation of a chemical conversion that consumes a substrate or produces a product, and a reactant comprises a representation of a chemical that is a substrate or a product of a reaction that occurs in a cell. 
     
     
         11 . The method of  claim 4 , wherein a reaction comprises a conversion that occurs due to the activity of one or more enzymes that are genetically encoded by the human genome, a conversion that occurs spontaneously in a human or mammalian cell, or conversions based on 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 one or more reactants within the same compartment or from one cellular compartment to another. 
     
     
         12 . The method of  claim 4 , wherein the biological network reflects a  H. sapiens  cell type at any stage of differentiation. 
     
     
         13 . The method of  claim 4 , wherein the method is applied to normal cells or pathological cells. 
     
     
         14 . The method of  claim 4 , wherein the concentration Jacobian matrix is calculated by post-multiplication of the stoichiometric data structure by the gradient matrix, and the flux Jacobian matrix is calculated by pre-multiplication of the stoichiometric data structure by the gradient matrix. 
     
     
         15 . A computer-implemented method for developing data-driven dynamic models of biological networks, the method comprising:
 providing, at a computer system, a data structure relating a plurality of biological network reactants to a plurality of biological network reactions, the plurality of biological network reactions comprising one or more flux distributions, wherein each of the biological network reactions comprises one or more biological network reactants identified as a substrate of the reaction, one or more biological network reactants identified as a product of the biological network reaction and a stoichiometric coefficient relating the substrate and the product;   providing, at a computer system, a constraint set for the plurality of biological network reactions;   providing, at a computer system, a constraint set for a plurality of concentrations associated with the plurality of biological network reactions;   providing, at a computer system, a constraint set for a plurality of kinetic constants associated with the plurality of biological network reactions;   providing, at a computer system, a constraint set for a plurality of equilibrium constants associated with the plurality of biological network reactions;   integrating, at a computer system, the sets of constraints, thereby forming stoichiometric, gradient, and Jacobian matrices;   providing, at a computer system, an objective function; and   predicting, at a computer system, a physiological function related to at least one of the biological networks by determining using the computer system at least one flux distribution, from the one or more flux distributions, that minimizes or maximizes the objective function when at least one constraint set from the sets of constraints is applied to the data structure, wherein one or more of said constraint sets reflects a perturbation.   
     
     
         16 . The method of  claim 15 , wherein one or more of said constraint sets has been altered to reflect genetic or environmental perturbations. 
     
     
         17 . The method of  claim 15 , wherein at least one of said kinetic constants or at least one of said concentrations has been altered to reflect a genetic perturbation. 
     
     
         18 . The method of  claim 15 , additionally comprising modifying, at a computer system, at least one of the reaction constraint set, the concentration constraint set, the kinetic constant set and the equilibrium constant set based at least partly on genetic variations. 
     
     
         19 . The method of  claim 15 , additionally comprising modifying, at a computer system, at least one of the reaction constraint set, the concentration constraint set, the constraint set for a plurality of kinetic constants and the set for a plurality of equilibrium constants based at least partly on altered environmental conditions. 
     
     
         20 . The method of  claim 15 , additionally comprising simulating the effects of adding or removing genes on at least one of the plurality of biological networks. 
     
     
         21 . The method of  claim 15 , additionally comprising simulating the effects of one or more environmental perturbations on at least one of the plurality of biological networks. 
     
     
         22 . The method of  claim 18 , additionally comprising determining dynamics and consequences of genetic variations selected from the group consisting of deficiencies in metabolic enzymes and metabolic transporters. 
     
     
         23 . The method of  claim 22 , wherein the genetic variations comprise functioning of a compound selected from the group consisting of phosphofructokinase, phosphoglycerate kinase, phosphoglycerate mutase, lactate dehydrogenase adenosine deaminase, ABC transporters, the SLC class of transporters, and the cytochrome P450 class of enzymes. 
     
     
         24 . The method of  claim 15 , wherein providing a constraint set for a plurality of concentrations comprises measuring metabolite levels at steady state. 
     
     
         25 . The method of  claim 15 , wherein providing a constraint set for a plurality of kinetic constants comprises solving a steady state mass conservation relationship comprising a stoichiometric matrix and flux vector. 
     
     
         26 . The method of  claim 19 , wherein the modified sets of constraints correspond to an individual. 
     
     
         27 . The method of  claim 19 , wherein the modified sets of constraints correspond to a group or plurality of individuals. 
     
     
         28 . The method of  claim 18 , wherein a therapeutic regime is applied to regulate a physiological function based on at least one of the modified sets based at least partly on genetic variations. 
     
     
         29 . The method of  claim 15 , wherein a genetic variation results in alterations of kinetic parameters or concentrations of variables. 
     
     
         30 . The method of  claim 19 , wherein a therapeutic regime is applied to regulate a physiological function based on at least one of the modified sets based at least partly on altered environmental conditions. 
     
     
         31 . The method of  claim 15 , wherein the altered environmental conditions result in changes in measured variables. 
     
     
         32 . The method of  claim 15 , additionally comprising:
 factorizing the gradient matrix into a kappa matrix and a gamma matrix; and   analyzing the gradient, Jacobian, kappa and gamma matrices to characterize time scales of the network model.   
     
     
         33 . The method of  claim 32 , wherein the kappa matrix is a diagonal matrix of kinetic constants. 
     
     
         34 . The method of  claim 15 , additionally comprising:
 modifying, at a computer system, at least one of metabolite measurement or a kinetic parameter measurement based on a genetic influence, the kinetic parameter comprising a rate constant;   generating a new set of reaction rate expressions and a new gradient matrix; and   analyzing a pathological state of the network model based on a simulation of the new set of reaction rate expressions and the new gradient matrix.   
     
     
         35 . A computer-implemented method for the analysis of pathological states due to genetic influences, the method comprising:
 providing, at a computer system, a data structure relating a plurality of reactants to a plurality of reactions, the plurality of reactions comprising one or more flux distributions, wherein each of the reactions comprises one or more reactants identified as a substrate of the reaction, one or more reactants identified as a product of the reaction and a stoichiometric coefficient relating the substrate and the product;   providing, at a computer system, a constraint set for the plurality of reactions;   providing, at a computer system, a constraint set for a plurality of concentrations associated with the plurality of reactions;   providing, at a computer system, a constraint set for a plurality of kinetic constants associated with the plurality of reactions;   providing, at a computer system, a constraint set for a plurality of equilibrium constants associated with the plurality of reactions;   integrating, at a computer system, the sets of constraints, thereby forming stoichiometric, gradient, and Jacobian matrices;   providing, at a computer system, an objective function;   modifying, at a computer system, at least one of the reaction constraint set, the concentration constraint set, the kinetic constant set and the equilibrium constant set based at least partly on genetic variations; and   predicting, using a computer system, a physiological function related to a pathological state by determining at least one flux distribution, from the one or more flux distributions, that minimizes or maximizes the objective function when at least one constraint set from the sets of constraints is applied to the data structure.   
     
     
         36 . The method of  claim 35 , additionally comprising determining dynamics and consequences of genetic variations selected from the group consisting of deficiencies in metabolic enzymes and metabolic transporters. 
     
     
         37 . The method of  claim 36 , wherein the genetic variations comprise functioning of a compound selected from the group consisting of phosphofructokinase, phosphoglycerate kinase, phosphoglycerate mutase, lactate dehydrogenase adenosine deaminase, ABC transporters, the SLC class of transporters, and the cytochrome P450 class of enzymes. 
     
     
         38 . The method of  claim 35 , wherein providing a constraint set for a plurality of concentrations comprises measuring metabolite levels at steady state. 
     
     
         39 . The method of  claim 35 , wherein providing a constraint set for a plurality of kinetic constants comprises solving a steady state mass conservation relationship comprising a stoichiometric matrix and flux vector. 
     
     
         40 . The method of  claim 35 , wherein the modified sets of constraints correspond to an individual. 
     
     
         41 . The method of  claim 35 , wherein the modified sets of constraints correspond to a group or plurality of individuals. 
     
     
         42 . The method of  claim 35 , wherein a therapeutic regime is applied to regulate a physiological function based on at least one of the modified sets based at least partly on genetic variations. 
     
     
         43 . The method of  claim 35 , wherein the genetic variations result in alterations of kinetic parameters or concentrations of variables. 
     
     
         44 . A computer-implemented method for the analysis of pathological states due to environmental influences, the method comprising:
 providing, at a computer system, a data structure relating a plurality of reactants to a plurality of reactions, the plurality of reactions comprising one or more flux distributions, wherein each of the reactions comprises one or more reactants identified as a substrate of the reaction, one or more reactants identified as a product of the reaction and a stoichiometric coefficient relating the substrate and the product;   providing, at a computer system, a constraint set for the plurality of reactions;   providing, at a computer system, a constraint set for a plurality of concentrations associated with the plurality of reactions;   providing, at a computer system, a constraint set for a plurality of kinetic constants associated with the plurality of reactions;   providing, at a computer system, a constraint set for a plurality of equilibrium constants associated with the plurality of reactions;   integrating, at a computer system, the sets of constraints, thereby forming stoichiometric, gradient, and Jacobian matrices;   providing, at a computer system, an objective function;   modifying, at a computer system, at least one of the reaction constraint set, the concentration constraint set, the constraint set for a plurality of kinetic constants and the set for a plurality of equilibrium constants based at least partly on altered environmental conditions; and   predicting, using a computer system, a physiological function related to a pathological state by determining at least one flux distribution, from the one or more flux distributions, that minimizes or maximizes the objective function when at least one constraint set from the sets of constraints is applied to the data structure.   
     
     
         45 . The method of  claim 44 , wherein providing a constraint set for a plurality of concentrations comprises measuring metabolite levels at steady state. 
     
     
         46 . The method of  claim 44 , wherein the modified sets of constraints correspond to an individual. 
     
     
         47 . The method of  claim 44 , wherein the modified sets of constraints correspond to a group or plurality of individuals. 
     
     
         48 . The method of  claim 44 , wherein a therapeutic regime is applied to regulate a physiological function based on at least one of the modified sets based at least partly on altered environmental conditions. 
     
     
         49 . The method of  claim 44 , wherein the altered environmental conditions result in changes in measured variables. 
     
     
         50 . A computer-implemented method for the analysis of a pathological state of a data-driven model of a biological network due to a genetic influence, the method comprising:
 providing, at a computer system, a data structure relating a plurality of reactants to a plurality of reactions, the plurality of reactions comprising one or more flux distributions, wherein each of the reactions comprises one or more reactants identified as a substrate of the reaction, one or more reactants identified as a product of the reaction and a stoichiometric coefficient relating the substrate and the product;   providing, at a computer system, a constraint set for the plurality of reactions;   providing, at a computer system, a constraint set for a plurality of concentrations associated with the plurality of reactions;   providing, at a computer system, a constraint set for a plurality of kinetic constants associated with the plurality of reactions;   providing, at a computer system, a constraint set for a plurality of equilibrium constants associated with the plurality of reactions;   integrating, at a computer system, the sets of constraints, thereby forming stoichiometric, gradient, and Jacobian matrices;   modifying, at a computer system, at least one of metabolite measurement or a kinetic parameter measurement based on a genetic influence, the kinetic parameter comprising a rate constant;   generating a new set of reaction rate expressions and a new gradient matrix; and   analyzing of the pathological state of the network model based on a simulation of the new set of reaction rate expressions and the new gradient matrix.   
     
     
         51 . A computer-implemented method for the analysis of an effect of a drug or chemical agent on a physiological function, the method comprising:
 providing, at a computer system, a data structure relating a plurality of reactants to a plurality of reactions, the plurality of reactions comprising one or more flux distributions, wherein each of the reactions comprises one or more reactants identified as a substrate of the reaction, one or more reactants identified as a product of the reaction and a stoichiometric coefficient relating the substrate and the product;   providing, at a computer system, a constraint set for the plurality of reactions;   providing, at a computer system, a constraint set for a plurality of concentrations associated with the plurality of reactions;   providing, at a computer system, a constraint set for a plurality of kinetic constants associated with the plurality of reactions;   providing, at a computer system, a constraint set for a plurality of equilibrium constants associated with the plurality of reactions;   integrating, at a computer system, the sets of constraints, thereby forming the stoichiometric, gradient, and Jacobian matrices;   providing, at a computer system, an objective function;   adding a reaction to the data structure, removing a reaction from the data structure, or adjusting a constraint for a reaction in at least one of the sets of constraints to reflect a measured effect of a drug or chemical agent on the activity of the reaction; and   predicting, at a computer system, a physiological function related to the drug or chemical agent by determining at least one flux distribution, from the one or more flux distributions, that minimizes or maximizes the objective function when a constraint set is applied to the data structure.   
     
     
         52 . A computer-implemented method for developing a dynamic network model, the method comprising:
 accessing archetype data for a plurality of reactions of a network;   developing a stoichiometric data structure for the reactions based on the archetype data;   accessing physiological data reflecting a specific context;
 performing a steady state simulation using the stoichiometric data structure and the physiological data; 
   incorporating metabolic data and equilibrium constant data based on the steady state simulation;   deriving a gradient matrix and dynamic rate equations based on the stoichiometric data structure and the incorporated data; and   deriving a concentration Jacobian matrix and a flux Jacobian matrix based on the stoichiometric data structure and the gradient matrix so as to characterize dynamic properties of the network, wherein at least some of the stoichiometric, metabolic or equilibrium constant data is obtained by sampling a solution space.   
     
     
         53 . A computer-implemented method for the analysis of an effect of a drug or chemical agent on a physiological function, the method comprising:
 accessing archetype data for a plurality of reactions of a biological network;   developing a stoichiometric data structure for the reactions based on the archetype data;   accessing physiological data reflecting a specific context;   performing a steady state simulation using the stoichiometric data structure and the physiological data;   incorporating metabolic data and equilibrium constant data based on the steady state simulation;   adding a reaction to the stoichiometric data structure, removing a reaction from the stoichiometric data structure, or adjusting a constraint for a reaction in at least a set of constraints for reactions in the stoichiometric data structure to reflect a measured effect of a drug or chemical agent on the activity of the reaction;   deriving a gradient matrix and dynamic rate equations based on the stoichiometric data structure and the incorporated data;   deriving a concentration Jacobian matrix and a flux Jacobian matrix based on the stoichiometric data structure and the gradient matrix so as to characterize dynamic properties of the network; and   predicting, at a computer system, a physiological function related to the drug or chemical agent based on a simulation including at least the added reaction, removed reaction, or adjusted constraint.   
     
     
         54 . A computer-implemented method for developing a dynamic network model, the method comprising:
 accessing archetype data for a plurality of reactions of a network;   developing a stoichiometric data structure for the reactions based on the archetype data;
 performing a steady state simulation using the stoichiometric data structure and physiological data; 
   obtaining metabolic data and equilibrium constant data based on the steady state simulation;   deriving a gradient matrix and dynamic rate equations based on the stoichiometric data structure and the obtained data; and   deriving a concentration Jacobian matrix and a flux Jacobian matrix based on the stoichiometric data structure and the gradient matrix so as to characterize dynamic properties of the network, wherein unknown concentrations of metabolites are determined by solving a steady state mass conservation relationship S·v=0, where S is a the stoichiometric data structure and v is a flux vector.