Methods and systems for the identification of components of mammalian biochemical networks as targets for therapeutic agents

Abstract

Systems and methods for modeling the interactions of the several genes, proteins and other components of a cell, employing mathematical techniques to represent the interrelationships between the cell components and the manipulation of the dynamics of the cell to determine which components of a cell may be targets for interaction with therapeutic agents. A first such method is based on a cell simulation approach in which a cellular biochemical network intrinsic to a phenotype of the cell is simulated by specifying its components and their interrelationships. The various interrelationships are represented with one or more mathematical equations which are solved to simulate a first state of the cell. The simulated network is then perturbed by deleting one or more components, changing the concentration of one or more components, or modifying one or more mathematical equations representing the interrelationships between one or more of the components. The equations representing the perturbed network are solved to simulate a second state of the cell which is compared to the first state to identify the effect of the perturbation on the state of the network, thereby identifying one or more components as targets. A second method for identifying components of a cell as targets for interaction with therapeutic agents is based upon an analytical approach, in which a stable phenotype of a cell is specified and correlated to the state of the cell and the role of that cellular state to its operation. A cellular biochemical network believed to be intrinsic to that phenotype is then specified by identifying its components and their interrelationships and representing those interrelationships in one or more mathematical equations. The network is then perturbed and the equations representing the perturbed network are solved to determine whether the perturbation is likely to cause the transition of the cell from one phenotype to another, thereby identifying one or more components as targets.

1 . A method for identifying one or more components of a cell as putative targets for interaction with one or more agents, comprising the steps of: 
 (a) specifying a biochemical network believed to be intrinsic to a phenotype of said cell;    (b) simulating said network by 
 (i) specifying the components of said network, and  
 (ii) representing interrelationships between said components in one or more mathematical equations;  
   (c) solving the mathematical equations to simulate a first state of the cell;    (d) perturbing the simulated network by deleting one or more components thereof, changing the concentration of one or more components thereof or modifying one or more mathematical equations representing interrelationships between one or more of said components;    (e) solving the equations representing the perturbed net-work to simulate a second state of the cell; and    (f) comparing said first and second simulated states of the network to identify the effect of said perturbation on the state of the network, and thereby identifying one or more components for interaction with one or more agents.    
   
   
       2 . A method as recited in  claim 1  wherein said mathematical equations are solved using stochastic or differential equations.  
   
   
       3 . A method as recited in  claim 1  wherein the concentrations of one or more of the several proteins and genes in the biochemical network are selectively perturbed to identify which ones of said proteins or genes cause a change in the time course of the concentration of a gene or protein implicated in a disease state of said cell.  
   
   
       4 . A method as recited in  claim 3  wherein a series of perturbations are made, each of said perturbations changing the concentration of a protein or gene in said network to a perturbed value, to determine whether that protein or gene is implicated in causing a change in the time course of the concentration of a gene or protein implicated in a disease state of said cell.  
   
   
       5 . A method as recited in  claim 4  wherein the concentration of each of said proteins and genes is reduced to zero in each respective perturbation.  
   
   
       6 . A method as recited in  claim 1  wherein the concentrations of one or more of the components of the said biochemical network are optimized by determining the minima or multiple minima of said concentrations.  
   
   
       7 . A method as recited in  claim 1  wherein the concentrations and or the parameters of one or more of the several proteins and genes in the biochemical network are systematically perturbed to identify which ones of said proteins or genes cause a change in the time course of the concentration of a gene or protein implicated in a disease state of said cell.  
   
   
       8 . A method for identifying one or more components of a cell as putative targets for interaction with one or more agents, comprising the steps of: 
 (a) specifying a stable phenotype of a cell;    (b) correlating said phenotype to the state of the cell;    (c) specifying a cellular biochemical network believed to be intrinsic to said phenotype;    (d) characterizing said network by 
 (i) specifying the components thereof, and  
 (ii) specifying interrelationships between said components and representing said interrelationships in one or more mathematical equations;  
   (e) perturbing the characterized network by deleting one or more components thereof, changing the concentration of one or more components thereof or modifying one or more mathematical equations representing inter-relationships between one or more of said components; and    (f) solving the equations representing the perturbed network to determine whether said perturbation is likely to cause the transition of said cell from one phenotype to another, and thereby identifying one or more components for interaction with one or more agents.    
   
   
       9 . A method as recited in  claim 8  wherein the stable attractors include at least one of an equilibrium state characterized by steady state values, a periodically changing state characterized by periodically changing values, and a chaotically changing state having a peculiar signature.  
   
   
       10 . A method as recited in  claim 8  wherein the concentrations of one or more of the several proteins and genes in the biochemical network are selectively perturbed to identify which ones of said proteins or genes are implicated in causing an attractor of the biochemical network to become unstable.  
   
   
       11 . A method as recited in  claim 8  comprising carrying out a series of perturbations, each of said perturbations changing the concentration of a protein or gene in said network to a perturbed value to determine whether that protein or gene is implicated in causing a change in the time course of the concentration of a gene or protein implicated in a disease state of said cell.  
   
   
       12 . A method as recited in  claim 8  wherein the concentration of each of said proteins and genes is reduced to zero in each respective perturbation.  
   
   
       13 . A method as recited in  claim 8  wherein a bifurcation analysis is performed using eigen values of a Jacobian matrix based upon said equations to characterize the stability of one or more attractors.  
   
   
       14 . A method as recited in  claim 8  wherein the step of characterizing said network includes at least one of: 
 (iii) identifying new and missing links and components in the network;    (iv) constraining parameter values in the network; and    (v) determining parameter values in the network.    
   
   
       15 . A method for identifying one or more components of a cell as putative targets for interaction with one or more agents, comprising the steps of: 
 (a) specifying a biochemical network believed to be intrinsic to a phenotype of said cell;    (b) inferring new links and components in the network using experimental data;    (c) simulating said network by 
 (i) specifying the components of said network, and  
 (ii) specifying interrelationships between said components and representing said interrelationships in one or more mathematical equations;  
   (d) inferring new and missing links and components in the network;    (e) constraining and or determining parameter values in the network by (i) sampling a set of networks and parameter values, (ii) simulating the said networks as described in (c), and (iii) determining the network and parameter values that optimally fits a given set or sets of experimental data;    (f) solving those equations representing the network to simulate a first state of the cell;    (g) perturbing the simulated network by deleting one or more components thereof, changing the concentration of one or more components thereof or modifying one or more mathematical equations representing interrelationships between one or more of said components;    (h) solving the equations representing the perturbed net-work to simulate a second state of the cell; and    (i) comparing said first and second simulated states of the network to identify the effect of said perturbation on the state of the network, and thereby identifying one or more components for interaction with one or more agents.    
   
   
       16 . A method as recited in  claim 15  wherein the experimental data includes at least one of a DNA sequence, protein sequence, microarray data, expression data, time course expression data, and a protein structure.  
   
   
       17 . A method as recited in  claim 1  including the steps of storing said mathematical formulae in computer memory, storing algorithms in computer memory for solving said mathematical formulae, said solving step or steps each comprising retrieving said algorithms and applying them to solve said formulae.  
   
   
       18 . A method as recited in  claim 17  in which said perturbing step includes storing in computer memory a plurality of values for use in said perturbing step, and using an algorithm to apply said values separately or in combination with one another to automatically change the perturbations in accordance with a predetermined sequence.  
   
   
       19 . A method as recited in  claim 8  including the steps of storing said mathematical formulae in computer memory, storing algorithms in computer memory for solving said mathematical formulae, said solving step or steps each comprising retrieving said algorithms and applying them to solve said formulae.  
   
   
       20 . A method as recited in  claim 19  in which said perturbing step includes storing in computer memory a plurality of values for use in said perturbing step and using an algorithm to apply said values separately or in combination with one another to automatically change the perturbations in accordance with a predetermined sequence.  
   
   
       21 . A method as recited in  claim 15  including the steps of storing said mathematical formulae in computer memory, storing algorithms in computer memory for solving said mathematical formulae, said solving step or steps each comprising retrieving said algorithms and applying them to solve said formulae.  
   
   
       22 . A method as recited in  claim 21  in which said perturbing step includes storing in computer memory a plurality of values for use in said perturbing step and using an algorithm to apply said values separately or in combination with one another to automatically change the perturbations in accordance with a predetermined sequence.  
   
   
       23 . A method as recited in  claim 1  wherein experiments are conducted to confirm the identified component as a target.  
   
   
       24 . A method as recited in  claim 8  wherein experiments are conducted to confirm the identified component as a target.  
   
   
       25 . A method for creating an optimized mathematical simulation of a biochemical network of a cell comprising: 
 (a) specifying a biochemical network of a cell;    (b) simulating said network by 
 (i) specifying the components of said network, and  
 (ii) representing interrelationships between said components in one or more mathematical equations and setting the quantitative parameters of said components; and  
   (c) optimizing said simulated biochemical network by determining and constraining the parameter values set therein.    
   
   
       26 . A method for creating an optimized mathematical simulation of a biochemical network of a cell as recited in  claim 25  wherein optimization algorithms are used to con-strain the parameter values to fit the measured data.  
   
   
       27 . A method as recited in  claim 25  comprising the further steps of 
 (d) fitting the parameter values to said data and assessing how good the fit is; and    (e) performing an error analysis to determine it there are other parameter values or the populatoin of parameter values which fit the data but yield a different prediction and identifying that prediction.    (f) experimentally verifying predictions from the model in order to validate a single prediction or disceren between various predictions or hypotheses and/or using the experimentally derived results to iteratively refine the model.    
   
   
       28 . A method as recited in  claim 27  wherein experiments are conducted to validate that prediction.  
   
   
       29 . A method as recited in  claim 26  including the steps of storing said mathematical formulae in computer memory, storing said optimization algorithms in computer memory, storing in computer memory values corresponding to said quantitative parameters, and applying said algorithms to said parameters to optimize said simulated biochemical network.  
   
   
       30 . A method for identifying one or more components of a cell as putative targets for interaction with one or more agents, comprising the steps of: 
 (a) specifying a biochemical network of a cell;    (b) simulating said network by 
 (i) specifying the components of said network, and  
 (ii) representing interrelationships between said components in one or more mathematical equations and setting the quantitative parameters of said components; and  
   (c) optimizing said simulated biochemical network by determining and constraining the values of the parameters of said components; and    (d) solving the mathematical equations to simulate a state of said cell.    
   
   
       31 . A method as recited in  claim 30  including the steps of storing said mathematical formulae in computer memory, storing algorithms in computer memory for solving said mathematical formulae, said solving step or steps each comprising retrieving said algorithms and applying them to solve said formulae.  
   
   
       32 . A method as recited in  claim 31  including the step of storing optimization algorithms in computer memory, storing in computer memory values corresponding to said quantitative parameters, and applying said algorithms to said parameters to optimize said simulated biochemical network.  
   
   
       33 . A method of predicting the physiological state of a cell comprising the steps of: 
 (a) specifying a biochemical network of a cell;    (b) simulating said network by 
 (i) specifying the components of said network, and  
 (ii) representing interrelationships between said components in one or more mathematical equations and setting the quantitative parameters of said components;  
   (c) optimizing said first simulated biochemical network by determining and constraining the values of the parameters of said components; and    (d) determining the state of said cell by solving the mathematical equations and thereby simulating the physiological state of said cell.    
   
   
       34 . A method as recited in  claim 33  wherein said cell is a cancer cell.  
   
   
       35 . A method as recited in  claim 33  in which said perturbing step includes storing in computer memory a plurality of values for use in said perturbing step and using an algorithm to apply said values separately or in combination with one another to automatically change the perturbations in accordance with a predetermined sequence.  
   
   
       36 . A method as recited in  claim 35  including the step of storing optimization algorithms in computer memory, storing in computer memory values corresponding to said quantitative parameters, and applying said algorithms to said parameters to optimize said simulated biochemical network.  
   
   
       37 . A method of predicting an altered physiological state of a cell comprising the steps of: 
 (a) specifying a biochemical network of a cell;    (b) simulating said network by 
 (i) specifying the components of said network, and  
 (ii) representing interrelationships between said components in one or more mathematical equations and setting the quantitative parameters of said components;  
   (c) optimizing said first simulated biochemical network by determining and constraining the values of the parameters of said components;    (d) perturbing the optimized simulated network by adding or deleting one or more components thereof, changing the concentration of one or more components thereof or modifying one or more mathematical equations representing interrelationships between one or more of said components;    (e) solving the equations representing the perturbed net-work to simulate a second state of the cell; and    (f) comparing said first and second simulated states of the network to identify the effect of said perturbation on the state of the network.    
   
   
       38 . A method as recited in  claim 37  wherein the simulated network is systematically perturbed.  
   
   
       39 . A method as recited in  claim 37  wherein the simulated network is systematically perturbed by deleting two or more components.  
   
   
       40 . A method as recited in  claim 37  wherein the physiological state is proliferation.  
   
   
       41 . A method as recited in  claim 37  wherein said physiological state is G1-S and wherein Cyclin E-CDK2 is used as the marker for said determination.  
   
   
       42 . A method as recited in  claim 37  wherein said physiological state is G2-M and wherein Cyclin B-CDK1 is used as the marker for said determination.  
   
   
       43 . A method as recited in  claim 37  wherein said physiological state is S phase arrest and wherein Cyclin A-CDK2 is used as the marker for said determination.  
   
   
       44 . A method as recited in  claim 37  wherein said physiological state is apoptosis and wherein caspase 3 and cleaved PARP are the markers of said state.  
   
   
       45 . A method as recited in  claim 37  including the steps of storing said mathematical formulae in computer memory, storing algorithms in computer memory for solving said mathematical formulae, said solving step or steps each comprising retrieving said algorithms and applying them to solve said formulae including the step of storing optimization algorithms in computer memory, storing in computer memory values corresponding to said quantitative parameters, and applying said algorithms to said parameters to optimize said simulated biochemical network.  
   
   
       46 . A method as recited in  claim 45  in which said perturbing step includes storing in computer memory a plurality of values for use in said perturbing step and using an algorithm to apply said values separately or in combination with one another to automatically change the perturbations in accordance with a predetermined sequence.  
   
   
       47 . A method of simulating the physiological state of a cancer cell comprising the steps of: 
 (a) specifying a biochemical network of a cell;    (b) simulating said network by 
 (i) specifying the components of said network, and  
 (ii) representing interrelationships between said components in one or more mathematical equations and setting the quantitative parameters of said components; and  
   (c) solving the mathematical equations to simulate a first state of the cell.    
   
   
       48 . A method as recited in  claim 47  wherein the physiological state is manifested by Erk a high level of proliferative signals.  
   
   
       49 . A method as recited in  claim 48  wherein said signal is Erk.  
   
   
       50 . A method as recited in  claim 47  wherein said physiological state is manifested by a high level of pro-apoptotic proteins.  
   
   
       51 . A method as recited in  claim 50  wherein said proapoptotic protein is Bcl2.  
   
   
       52 . A method as recited in  claim 47  wherein after simulating the first state of the cell the method further comprises: 
 (d) perturbing the simulated network by deleting one or more components thereof, changing the concentration of one or more components thereof or modifying one or more mathematical equations representing interrelationships between one or more of said components;    (e) solving the equations representing the perturbed net-work to simulate a second physiological state of the cell; and    (f) comparing said first and second simulated states of the network to identify the effect of said perturbation on the state of the network.    
   
   
       53 . A method as recited in  claim 52  wherein the second simulated state of the network is analyzed to determine whether the cells have gone through G1-S arrest, G2-M arrest, S phase arrest and/or apoptosis.  
   
   
       54 . A method as recited in  claim 52  wherein said method is used to predict the sensitivity of said cell to a particular state.  
   
   
       55 . A method as recited in  claim 53  wherein said state is apoptosis.  
   
   
       56 . A method is recited in  claim 52  wherein in step (e) two or more components are perturbed.  
   
   
       57 . A method as recited in  claim 47  including the steps of storing said mathematical formulae in computer memory, storing algorithms in computer memory for solving said mathematical formulae, said solving step or steps each comprising retrieving said algorithms and applying them to solve said formulae.  
   
   
       58 . A method as recited in  claim 57  in which said perturbing step includes storing in computer memory a plurality of values for use in said perturbing step and using an algorithm to apply said values separately or in combination with one another to automatically change the perturbations in accordance with a predetermined sequence.  
   
   
       59 . A method for testing a substance for possible use as a therapeutic by simulating its effect on the physiological state of a cell, comprising the steps of: 
 (a) specifying a biochemical network of a cell;    (b) simulating said network by 
 (i) specifying the components of said network, and  
 (ii) representing interrelationships between said components in one or more mathematical equations and setting the quantitative parameters of said components; and  
   (c) solving the mathematical equations to simulate a first physiological state of the cell;    (d) modifying the simulated network created in step (b) by representing the interrelationships between said chosen substance and other cell components in mathematical equations and setting forth the quantitative parameters of said components;    (e) solving the mathematical equations of said modified simulated network.    
   
   
       60 . A method as recited in  claim 59  further comprising perturbing the modified simulated network by deleting one or more components thereof, changing the concentration of one or more components thereof or modifying one or more mathematical equations representing interrelationships between one or more of said components.  
   
   
       61 . A method as recited in  claim 59  wherein said sub-stance is exogenous to said cell.  
   
   
       62 . A method as recited in  claim 59  in which said perturbing step includes storing in computer memory a plurality of values for use in said perturbing step and using an algorithm to apply said values separately or in combination with one another to automatically change the perturbations in accordance with a predetermined sequence.  
   
   
       63 . A method as recited in  claim 60  in which said perturbing step includes storing in computer memory a plurality of values for use in said perturbing step and using an algorithm to apply said values separately or in combination with one another to automatically change the perturbations in accordance with a predetermined sequence.  
   
   
       64 . A method as recited in  claim 59  wherein experiments are conducted to confirm the therapeutic value of a sub-stance identified by the method.  
   
   
       65 . An iterative method of from 2−n steps for simulating the physiological state of a cell under iteratively modified conditions comprising the steps of 
 (a) specifying a biochemical network of a cell;    (b) simulating said network by 
 (i) specifying the components of said network, and  
 (ii) representing interrelationships between said components in one or more mathematical equations and setting the quantitative parameters of said components; and  
   (c) solving the mathematical equations to simulate a first state of the cell;    (d) perturbing the simulated network by adding or deleting one or more components thereof, changing the concentration of one or more components thereof or modifying one or more mathematical equations representing interrelationships between one or more of said components;    (e) solving the equations representing the perturbed net-work to simulate a second physiological state of the cell;    (f) comparing said first and second simulated states of the network to identify the effect of said perturbation on the state of the network; and    (g) repeating steps (d)-(f) from one to n times to create further modified simulated networks.