Metabolic Network Analysis

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Metabolic Network Analysis

  1. 1. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsSome computational systems biology techniques tostudy regulation of metabolismAreejit Samal and Sanjay JainDepartment of Physics and Astrophysics,University of DelhiPresentation at:Heraeus International Summer School – “Statistical Physics of Gene Regulation”July 25–26, 2007Jacobs University, Bremen, GermanyAreejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  2. 2. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsOutline1 Introduction to FBABasics of FBAStoichiometric matrix2 Examples of FBA implementation3 Blocked Reactions4 UP-UC clusters5 Boolean dynamicsAreejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  3. 3. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsBasics of FBAMetabolic networkMetabolic network is an exampleof input-output network. Inprinciple, the organism has thecapability in terms of transporterproteins to uptake variousmetabolites from the externalenvironment. The main purposeof the metabolic network is toingest a subset of inputs (whichare all available in theenvironment) and produce alloutputs in the required ratios thatforms the ‘biomass’ for growthand maintenance of the cell.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  4. 4. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsBasics of FBAFlux Balance Analysis (FBA)Flux balance analysis (FBA) is a computational technique thatallows you to compute the fluxes of all reactions inside the metabolicnetwork and the growth rate for a given environmental condition.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  5. 5. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsBasics of FBAFlux Balance Analysis (FBA)Flux balance analysis (FBA) is a computational technique thatallows you to compute the fluxes of all reactions inside the metabolicnetwork and the growth rate for a given environmental condition.Flux of a reaction is defined as the amount of substrate that isconverted to product in unit time. Flux of a reaction is a measure ofthe activity of a reaction under certain condition.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  6. 6. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsBasics of FBAFlux Balance Analysis (FBA)Flux balance analysis (FBA) is a computational technique thatallows you to compute the fluxes of all reactions inside the metabolicnetwork and the growth rate for a given environmental condition.Flux of a reaction is defined as the amount of substrate that isconverted to product in unit time. Flux of a reaction is a measure ofthe activity of a reaction under certain condition.The method has been primarily developed by the group of BernhardPalsson at UCSD (http://gcrg.ucsd.edu/).Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  7. 7. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsBasics of FBAFlux Balance Analysis (FBA)Flux balance analysis (FBA) is a computational technique thatallows you to compute the fluxes of all reactions inside the metabolicnetwork and the growth rate for a given environmental condition.Flux of a reaction is defined as the amount of substrate that isconverted to product in unit time. Flux of a reaction is a measure ofthe activity of a reaction under certain condition.The method has been primarily developed by the group of BernhardPalsson at UCSD (http://gcrg.ucsd.edu/).The growth rate and fluxes predicted by FBA have been shown tomatch well with experimentally obtained values.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  8. 8. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsBasics of FBAFlux Balance Analysis (FBA)Flux balance analysis (FBA) is a computational technique thatallows you to compute the fluxes of all reactions inside the metabolicnetwork and the growth rate for a given environmental condition.Flux of a reaction is defined as the amount of substrate that isconverted to product in unit time. Flux of a reaction is a measure ofthe activity of a reaction under certain condition.The method has been primarily developed by the group of BernhardPalsson at UCSD (http://gcrg.ucsd.edu/).The growth rate and fluxes predicted by FBA have been shown tomatch well with experimentally obtained values.The method has the advantage that it does not require theknowledge of kinetic information such as rate constants, etc. whichare still largely unknown and may vary across population of cells.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  9. 9. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsBasics of FBAKey ingredients for FBAWe need the complete list of metabolic reactions along with thestoichiometric coefficients of the metabolites involved in eachreaction.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  10. 10. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsBasics of FBAKey ingredients for FBAWe need the complete list of metabolic reactions along with thestoichiometric coefficients of the metabolites involved in eachreaction.We need the biomass composition of the cell in terms of aminoacids, lipids, nucleotides, etc.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  11. 11. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsBasics of FBAKey ingredients for FBAWe need the complete list of metabolic reactions along with thestoichiometric coefficients of the metabolites involved in eachreaction.We need the biomass composition of the cell in terms of aminoacids, lipids, nucleotides, etc.We need to know which metabolites the cell can uptake from theexternal environment and their maximum uptake rates.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  12. 12. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsBasics of FBAAssumptions used in FBAWe determine the fluxes of all reactions and growth rate under theassumption of steady state. A steady state is defined as one whereinconcentrations of all metabolites in the network are constant.Hence,dXidt= 0where Xi is the concentration of metabolite i.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  13. 13. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsBasics of FBAAssumptions used in FBAWe determine the fluxes of all reactions and growth rate under theassumption of steady state. A steady state is defined as one whereinconcentrations of all metabolites in the network are constant.Hence,dXidt= 0where Xi is the concentration of metabolite i.The organism tries to adjust its intracellular machinery so as tomaximize its ‘growth rate’.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  14. 14. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsBasics of FBAOutput of FBAA theoretical prediction of the steady state fluxes of all reactions inthe metabolic network in the given medium.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  15. 15. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsBasics of FBAOutput of FBAA theoretical prediction of the steady state fluxes of all reactions inthe metabolic network in the given medium.The maximum growth rate possible for the specified medium.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  16. 16. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsStoichiometric matrixStoichiometric MatrixThe set of metabolic reactions for a given organism along withstoichiometric coefficients can be compactly represented in the form ofthe stoichiometric matrix S. The rows of the stoichiometric matrix Scorrespond to metabolites and the columns to reactions in the metabolicnetwork. For example, the matrix element Sij is −2 if 2 molecules ofmetabolite i gets consumed in reaction j. Similarly, the matrix elementSij is 3 if 3 molecules of metabolite i gets produced in reaction j.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  17. 17. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsStoichiometric matrixExample of a reaction networkThis reaction network was designed to mimicthe central metabolism inside any typical cell.The reactions of a metabolic network can beclassified into internal reactions and transportreactions. The internal reactions involve onlyinternal metabolites and the transportreactions are used to uptake metabolites fromthe external environment. The Growthreaction represents the biomass compositionof the cell.Covert MW, Schilling CH, PalssonBO: Regulation of Gene Expression inFlux Balance Models of Metabolism.J. Theor. Biol. 2001, 213:73–78.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  18. 18. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsStoichiometric matrixStoichiometric matrix for the example networkAreejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  19. 19. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsStoichiometric matrixStoichiometric constraintsIn steady state, the rate of production of a any metabolite is equal to its rate of consumption. This can beexpressed in the form of the equationdXidt=jSij Vj = 0where,X is the column vector of metabolite concentrations with dimension m × 1,S is the stoichiometric matrix with dimension m × n andV is the column vector of fluxes with dimension n × 1.Each row of the stoichiometric matrix (corresponding to a metabolite in the network) gives a linear equationrelating various fluxes. For example, in the last example the first row gives the linear equation−VR1 + VTc1 + VTc2 = 0.The unknowns of the system are the n fluxes. The fluxes are related by m linear equations (one linear equation foreach metabolite). Typically, in metabolic networks, the number of metabolites is less than the number of reactionsor fluxes, or, the number of equations is less than the number of unknowns and the system is under-determined.Note that the stoichiometric constraints are hard nonadjustable constraints and need to be always satisfied.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  20. 20. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsStoichiometric matrixAdditional ConstraintsIn most cases, the stoichiometric constraints are not enough to geta solution in terms of fluxes of all metabolic reactions and growthrate for a given medium. For real metabolic networks, the null spaceis quite large.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  21. 21. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsStoichiometric matrixAdditional ConstraintsIn most cases, the stoichiometric constraints are not enough to geta solution in terms of fluxes of all metabolic reactions and growthrate for a given medium. For real metabolic networks, the null spaceis quite large.To limit the solution space, we can impose additional constraintssuch as maximum uptake rates, etc.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  22. 22. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsStoichiometric matrixLinear OptimizationTo get a particular solution, we use the technique of linearoptimization. In this technique, we find a solution such that itmaximizes a objective function such as growth rate.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  23. 23. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsStoichiometric matrixLinear OptimizationTo get a particular solution, we use the technique of linearoptimization. In this technique, we find a solution such that itmaximizes a objective function such as growth rate.Note that linear optimization is also unable to fix all fluxes in realmetabolic networks (e.g. E. coli metabolic network). Hence, in thiscase as well we get a particular solution and not a unique solution.However, the technique is able fix most fluxes in the metabolicnetworks.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  24. 24. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsOutline1 Introduction to FBA2 Examples of FBA implementationToy model of central metabolismE. coli metabolic network3 Blocked Reactions4 UP-UC clusters5 Boolean dynamicsAreejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  25. 25. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismReaction networkCovert MW, Schilling CH, Palsson BO: Regulation of Gene Expression in Flux Balance Models ofMetabolism. J. Theor. Biol. 2001, 213:73–78.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  26. 26. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismList of reactionsThis reaction network was designedto mimic the central metabolisminside any typical cell.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  27. 27. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismList of reactionsThis reaction network was designedto mimic the central metabolisminside any typical cell.The reactions of a metabolic networkcan be classified into internalreactions and transport reactions.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  28. 28. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismList of reactionsThis reaction network was designedto mimic the central metabolisminside any typical cell.The reactions of a metabolic networkcan be classified into internalreactions and transport reactions.There are 5 metabolites (Carbon1,Carbon2, F, H and Oxygen) that thecell can uptake from the externalenvironment.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  29. 29. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismList of reactionsThis reaction network was designedto mimic the central metabolisminside any typical cell.The reactions of a metabolic networkcan be classified into internalreactions and transport reactions.There are 5 metabolites (Carbon1,Carbon2, F, H and Oxygen) that thecell can uptake from the externalenvironment.There are 2 metabolites (D and E)that the cell can excrete to theexternal environment.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  30. 30. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismList of reactionsThis reaction network was designedto mimic the central metabolisminside any typical cell.The reactions of a metabolic networkcan be classified into internalreactions and transport reactions.There are 5 metabolites (Carbon1,Carbon2, F, H and Oxygen) that thecell can uptake from the externalenvironment.There are 2 metabolites (D and E)that the cell can excrete to theexternal environment.The Growth reaction gives the ratiosof various metabolites required for themaintenance and growth of the cell.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  31. 31. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismModified Reaction List for FBAIn order to implement Flux Balance Analysis (FBA), we needto convert every reversible reaction into two one-wayreactions. This is done so as to restrict the flux values topositive real numbers.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  32. 32. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismModified Reaction List for FBAIn order to implement Flux Balance Analysis (FBA), we needto convert every reversible reaction into two one-wayreactions. This is done so as to restrict the flux values topositive real numbers.Further, we need to add reactions that represent theexchange of external metabolites across the boundary. Thesereactions have been highlighted in the table.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  33. 33. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismModified Reaction List for FBAIn order to implement Flux Balance Analysis (FBA), we needto convert every reversible reaction into two one-wayreactions. This is done so as to restrict the flux values topositive real numbers.Further, we need to add reactions that represent theexchange of external metabolites across the boundary. Thesereactions have been highlighted in the table.The metabolite ’ZZZZ’ is a fictitious metabolite thatrepresents an infinite source or sink, i.e., we do notimplement the steady state constraintdXdt= 0on this metabolite.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  34. 34. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismModified Reaction List for FBAIn order to implement Flux Balance Analysis (FBA), we needto convert every reversible reaction into two one-wayreactions. This is done so as to restrict the flux values topositive real numbers.Further, we need to add reactions that represent theexchange of external metabolites across the boundary. Thesereactions have been highlighted in the table.The metabolite ’ZZZZ’ is a fictitious metabolite thatrepresents an infinite source or sink, i.e., we do notimplement the steady state constraintdXdt= 0on this metabolite.The modified reaction list is contained in the fileDATA/Rxnlist iMCJTB.txt.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  35. 35. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismStoichiometric MatrixStarting from the modified reaction list of the metabolic network,construct the stoichiometric matrix S for the network.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  36. 36. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismStoichiometric MatrixStarting from the modified reaction list of the metabolic network,construct the stoichiometric matrix S for the network.The stoichiometric matrix for the modified reaction list is containedin the file DATA/SIJ.txt. The dimensions of the stoichiometricmatrix is 18 × 27.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  37. 37. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismStoichiometric MatrixStarting from the modified reaction list of the metabolic network,construct the stoichiometric matrix S for the network.The stoichiometric matrix for the modified reaction list is containedin the file DATA/SIJ.txt. The dimensions of the stoichiometricmatrix is 18 × 27.The rows of the stoichiometric matrix correspond to the metaboliteslisted in the file DATA/SUB.txt. For example, the first row of thestoichiometric matrix corresponds to the metabolite listed on thefirst line of the file DATA/SUB.txt.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  38. 38. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismStoichiometric MatrixStarting from the modified reaction list of the metabolic network,construct the stoichiometric matrix S for the network.The stoichiometric matrix for the modified reaction list is containedin the file DATA/SIJ.txt. The dimensions of the stoichiometricmatrix is 18 × 27.The rows of the stoichiometric matrix correspond to the metaboliteslisted in the file DATA/SUB.txt. For example, the first row of thestoichiometric matrix corresponds to the metabolite listed on thefirst line of the file DATA/SUB.txt.The number of equations that we get by imposing thestoichiometric constraints is 18. The unknowns are the 27 fluxes.The number of unknowns are more than the number of equations.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  39. 39. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismFormulation of LP problemSince the number of equations are less than the number of unknowns, we use linear optimization to get aparticular solution.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  40. 40. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismFormulation of LP problemSince the number of equations are less than the number of unknowns, we use linear optimization to get aparticular solution.In Flux Balance Analysis, we determine the flux distribution and growth rate for a given environmentalcondition.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  41. 41. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismFormulation of LP problemSince the number of equations are less than the number of unknowns, we use linear optimization to get aparticular solution.In Flux Balance Analysis, we determine the flux distribution and growth rate for a given environmentalcondition.The environmental condition in this case is decided by which of the subset of 5 metabolites(Carbon1,Carbon2, F, H and Oxygen) are available to the cell for uptake and the maximum possible uptakerate for each metabolite from the environment.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  42. 42. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismFormulation of LP problemSince the number of equations are less than the number of unknowns, we use linear optimization to get aparticular solution.In Flux Balance Analysis, we determine the flux distribution and growth rate for a given environmentalcondition.The environmental condition in this case is decided by which of the subset of 5 metabolites(Carbon1,Carbon2, F, H and Oxygen) are available to the cell for uptake and the maximum possible uptakerate for each metabolite from the environment.The environment imposes additional constraints in form of range of values for certain fluxes and furtherlimits the solution space.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  43. 43. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismFormulation of LP problemSince the number of equations are less than the number of unknowns, we use linear optimization to get aparticular solution.In Flux Balance Analysis, we determine the flux distribution and growth rate for a given environmentalcondition.The environmental condition in this case is decided by which of the subset of 5 metabolites(Carbon1,Carbon2, F, H and Oxygen) are available to the cell for uptake and the maximum possible uptakerate for each metabolite from the environment.The environment imposes additional constraints in form of range of values for certain fluxes and furtherlimits the solution space.The linear programming problem can be posed in the following way:Given the 18 linear equations relating 27 fluxes and additional constraintson ranges of possible values for certain fluxes, find a flux vector such thatit satisfies the above constraints and maximizes the growth rate reaction.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  44. 44. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismFormulation of LP problemSince the number of equations are less than the number of unknowns, we use linear optimization to get aparticular solution.In Flux Balance Analysis, we determine the flux distribution and growth rate for a given environmentalcondition.The environmental condition in this case is decided by which of the subset of 5 metabolites(Carbon1,Carbon2, F, H and Oxygen) are available to the cell for uptake and the maximum possible uptakerate for each metabolite from the environment.The environment imposes additional constraints in form of range of values for certain fluxes and furtherlimits the solution space.The linear programming problem can be posed in the following way:Given the 18 linear equations relating 27 fluxes and additional constraintson ranges of possible values for certain fluxes, find a flux vector such thatit satisfies the above constraints and maximizes the growth rate reaction.Mathematically, the linear programming problem can be written as:maximize VGrowth subject to S.V = 0 and 0 ≤ Vj ≤ αj .Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  45. 45. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismWe can solve any linear programming (LP) problem using one of thefollowing solvers.Linear Programming (LP) SolversMany free and commercial optimization software packages are available which can be used on wide rangeof platforms:GLPK http://www.gnu.org/software/glpk/glpk.htmlLINDO http://www.lindo.com/cgi/frameset.cgi?leftdwnld.html;downloadf.htmlLinSolve ftp://garbo.uwasa.fi/pc/ts/tslin35c.zipLP-Optimizer http://www.mynetcologne.de/∼nc-weidenma/readme.htmC-WHIZ http://www.ketronms.com/LP SOLVE http://www.cs.sunysb.edu/∼algorith/implement/lpsolve/implement.shtmlQsopt http://www2.isye.gatech.edu/∼wcook/qsopt/index.htmlMATLAB Optimization Toolbox http://www.mathworks.com/products/optimization/MAPLE and Mathematica also provide some linear programming routines.. . .Further details about various optimization packages is available at:http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html.Most of these softwares accept input in MPS and LP file formats.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  46. 46. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismWe can solve any linear programming (LP) problem using one of thefollowing solvers.Linear Programming (LP) SolversMany free and commercial optimization software packages are available which can be used on wide rangeof platforms:GLPK http://www.gnu.org/software/glpk/glpk.htmlLINDO http://www.lindo.com/cgi/frameset.cgi?leftdwnld.html;downloadf.htmlLinSolve ftp://garbo.uwasa.fi/pc/ts/tslin35c.zipLP-Optimizer http://www.mynetcologne.de/∼nc-weidenma/readme.htmC-WHIZ http://www.ketronms.com/LP SOLVE http://www.cs.sunysb.edu/∼algorith/implement/lpsolve/implement.shtmlQsopt http://www2.isye.gatech.edu/∼wcook/qsopt/index.htmlMATLAB Optimization Toolbox http://www.mathworks.com/products/optimization/MAPLE and Mathematica also provide some linear programming routines.. . .Further details about various optimization packages is available at:http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html.Most of these softwares accept input in MPS and LP file formats.We will use the GNU Linear Programming Kit (GLPK) solver.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  47. 47. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismThe MPS FormatThe MPS format unlike the LP format does not vary across solversand has become a standard in the field of operational research.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  48. 48. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismThe MPS FormatThe MPS format unlike the LP format does not vary across solversand has become a standard in the field of operational research.Most solvers take in the linear programming problem in the form ofMPS format.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  49. 49. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismThe MPS FormatThe MPS format unlike the LP format does not vary across solversand has become a standard in the field of operational research.Most solvers take in the linear programming problem in the form ofMPS format.MPS is not a free format. Fields start in column 2, 5, 15, 25, 40and 50.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  50. 50. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismThe MPS FormatThe MPS format unlike the LP format does not vary across solversand has become a standard in the field of operational research.Most solvers take in the linear programming problem in the form ofMPS format.MPS is not a free format. Fields start in column 2, 5, 15, 25, 40and 50.Sections of an MPS file are marked by so-called header cards, whichare distinguished by their starting in column 1.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  51. 51. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismVarious sections of a MPS fileThe NAME record can have any value, starting in column 15.The ROWS section defines the names of all the constraints. Entries in column 2 or 3 are E for equalityrows, L for less-than, G for greater-than, and N for non-constraining rows (the first of which would beinterpreted as the objective function).The COLUMNS section contains the entries of the stoichiometric matrix.The RHS section allows one or more right-hand-side vectors to be defined. Rows not mentioned in an RHSvector would be assumed to have a right-hand-side of zero.The optional BOUNDS section specifies lower and upper bounds on individual variables, if they are notgiven by rows in the matrix. A bound of type UP means a upper bound is applied. A bound type of FX(“fixed”) means that the variable has upper and lower bounds equal to a single value.Another optional section called RANGES specifies double-inequalities.The final card must be ENDATA.An example of a MPS file is iMCJTB.mps for the reaction network underconsideration.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  52. 52. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismRun FBAStepsInvoke the command sh FBA MCJTB.sh.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  53. 53. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismRun FBAStepsInvoke the command sh FBA MCJTB.sh.Enter the configuration of the external environment.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  54. 54. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismRun FBAStepsInvoke the command sh FBA MCJTB.sh.Enter the configuration of the external environment.Specify the reactions if any to be knocked out from the originalnetwork.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  55. 55. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismRun FBAStepsInvoke the command sh FBA MCJTB.sh.Enter the configuration of the external environment.Specify the reactions if any to be knocked out from the originalnetwork.You get the flux vector and growth rate as output.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  56. 56. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismBrief description of the programThe program PROG/FBA MCJTB.cpp is used to generate the MPS filewhich is then used as an input to GLPK solver to obtain the optimal fluxdistribution.Various FunctionsThe function readsmatrix() reads in the stoichiometric matrix.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  57. 57. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismBrief description of the programThe program PROG/FBA MCJTB.cpp is used to generate the MPS filewhich is then used as an input to GLPK solver to obtain the optimal fluxdistribution.Various FunctionsThe function readsmatrix() reads in the stoichiometric matrix.The function knockreaction() determines the reactions to beknocked off from the original network.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  58. 58. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismBrief description of the programThe program PROG/FBA MCJTB.cpp is used to generate the MPS filewhich is then used as an input to GLPK solver to obtain the optimal fluxdistribution.Various FunctionsThe function readsmatrix() reads in the stoichiometric matrix.The function knockreaction() determines the reactions to beknocked off from the original network.In the main program, we first determine the metabolites availablefor uptake with their maximum uptake rates.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  59. 59. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsToy model of central metabolismBrief description of the programThe program PROG/FBA MCJTB.cpp is used to generate the MPS filewhich is then used as an input to GLPK solver to obtain the optimal fluxdistribution.Various FunctionsThe function readsmatrix() reads in the stoichiometric matrix.The function knockreaction() determines the reactions to beknocked off from the original network.In the main program, we first determine the metabolites availablefor uptake with their maximum uptake rates.Next we write out the MPS file.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  60. 60. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkE. coli metabolic network iJR904The E. coli metabolic network iJR904 has 761 metabolites and 931metabolic reactions.Reed JL, Vo TD, Schilling CH, Palsson BO: An expanded genome-scale model of Escherichia coli K-12(iJR904 GSM/GPR). Genome Biology 2003, 4:R54.1–R54.12.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  61. 61. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkE. coli metabolic network iJR904The E. coli metabolic network iJR904 has 761 metabolites and 931metabolic reactions.The biomass composition is further specified in terms of a growthrate reaction that is used as the optimization function.Reed JL, Vo TD, Schilling CH, Palsson BO: An expanded genome-scale model of Escherichia coli K-12(iJR904 GSM/GPR). Genome Biology 2003, 4:R54.1–R54.12.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  62. 62. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkE. coli metabolic network iJR904The E. coli metabolic network iJR904 has 761 metabolites and 931metabolic reactions.The biomass composition is further specified in terms of a growthrate reaction that is used as the optimization function.The enzymes for the 931 metabolic reactions are coded by 904metabolic genes.Reed JL, Vo TD, Schilling CH, Palsson BO: An expanded genome-scale model of Escherichia coli K-12(iJR904 GSM/GPR). Genome Biology 2003, 4:R54.1–R54.12.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  63. 63. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkE. coli metabolic network iJR904The E. coli metabolic network iJR904 has 761 metabolites and 931metabolic reactions.The biomass composition is further specified in terms of a growthrate reaction that is used as the optimization function.The enzymes for the 931 metabolic reactions are coded by 904metabolic genes.The growth rate reaction gives the composition of biomass in termsof 49 internal metabolites.Reed JL, Vo TD, Schilling CH, Palsson BO: An expanded genome-scale model of Escherichia coli K-12(iJR904 GSM/GPR). Genome Biology 2003, 4:R54.1–R54.12.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  64. 64. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkE. coli metabolic network iJR904The E. coli metabolic network iJR904 has 761 metabolites and 931metabolic reactions.The biomass composition is further specified in terms of a growthrate reaction that is used as the optimization function.The enzymes for the 931 metabolic reactions are coded by 904metabolic genes.The growth rate reaction gives the composition of biomass in termsof 49 internal metabolites.There are 143 metabolites that the cell can uptake from theexternal environment according to the insilico model.Reed JL, Vo TD, Schilling CH, Palsson BO: An expanded genome-scale model of Escherichia coli K-12(iJR904 GSM/GPR). Genome Biology 2003, 4:R54.1–R54.12.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  65. 65. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkList of metabolic reactionsFor purposes of FBA, we convert each reversible reaction in the metabolic network into two one-wayreactions. The number of one-way reactions in the metabolic network is 1176.Reed JL, Vo TD, Schilling CH, Palsson BO: An expanded genome-scale model of Escherichia coli K-12(iJR904 GSM/GPR). Genome Biology 2003, 4:R54.1–R54.12.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  66. 66. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkList of metabolic reactionsFor purposes of FBA, we convert each reversible reaction in the metabolic network into two one-wayreactions. The number of one-way reactions in the metabolic network is 1176.Next we append to these 1176 reactions, 286 reactions (143 × 2) for uptake and excretion of 143 externalmetabolites with the infinite source and sink (i.e., ‘ZZZZ’).Reed JL, Vo TD, Schilling CH, Palsson BO: An expanded genome-scale model of Escherichia coli K-12(iJR904 GSM/GPR). Genome Biology 2003, 4:R54.1–R54.12.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  67. 67. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkList of metabolic reactionsFor purposes of FBA, we convert each reversible reaction in the metabolic network into two one-wayreactions. The number of one-way reactions in the metabolic network is 1176.Next we append to these 1176 reactions, 286 reactions (143 × 2) for uptake and excretion of 143 externalmetabolites with the infinite source and sink (i.e., ‘ZZZZ’).To this list we append the Growth rate reaction, which gives a list of 1463 reactions (1176 + 286 + 1).Reed JL, Vo TD, Schilling CH, Palsson BO: An expanded genome-scale model of Escherichia coli K-12(iJR904 GSM/GPR). Genome Biology 2003, 4:R54.1–R54.12.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  68. 68. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkList of metabolic reactionsFor purposes of FBA, we convert each reversible reaction in the metabolic network into two one-wayreactions. The number of one-way reactions in the metabolic network is 1176.Next we append to these 1176 reactions, 286 reactions (143 × 2) for uptake and excretion of 143 externalmetabolites with the infinite source and sink (i.e., ‘ZZZZ’).To this list we append the Growth rate reaction, which gives a list of 1463 reactions (1176 + 286 + 1).The list of reactions is contained in the file DATA/Rxnlist iJR904.txt.Reed JL, Vo TD, Schilling CH, Palsson BO: An expanded genome-scale model of Escherichia coli K-12(iJR904 GSM/GPR). Genome Biology 2003, 4:R54.1–R54.12.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  69. 69. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkList of metabolic reactionsFor purposes of FBA, we convert each reversible reaction in the metabolic network into two one-wayreactions. The number of one-way reactions in the metabolic network is 1176.Next we append to these 1176 reactions, 286 reactions (143 × 2) for uptake and excretion of 143 externalmetabolites with the infinite source and sink (i.e., ‘ZZZZ’).To this list we append the Growth rate reaction, which gives a list of 1463 reactions (1176 + 286 + 1).The list of reactions is contained in the file DATA/Rxnlist iJR904.txt.The stoichiometric matrix is contained in the file DATA/SIJ ECJR904.txt and the rows of thestoichiometric matrix correspond to the metabolites listed in the file DATA/SUB ECJR904.txt.Reed JL, Vo TD, Schilling CH, Palsson BO: An expanded genome-scale model of Escherichia coli K-12(iJR904 GSM/GPR). Genome Biology 2003, 4:R54.1–R54.12.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  70. 70. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkList of metabolic reactionsFor purposes of FBA, we convert each reversible reaction in the metabolic network into two one-wayreactions. The number of one-way reactions in the metabolic network is 1176.Next we append to these 1176 reactions, 286 reactions (143 × 2) for uptake and excretion of 143 externalmetabolites with the infinite source and sink (i.e., ‘ZZZZ’).To this list we append the Growth rate reaction, which gives a list of 1463 reactions (1176 + 286 + 1).The list of reactions is contained in the file DATA/Rxnlist iJR904.txt.The stoichiometric matrix is contained in the file DATA/SIJ ECJR904.txt and the rows of thestoichiometric matrix correspond to the metabolites listed in the file DATA/SUB ECJR904.txt.The file DATA/Rxnlist iJR904.txt also contains the Gene-Protein-Reaction (GPR) association for eachmetabolic reaction.Reed JL, Vo TD, Schilling CH, Palsson BO: An expanded genome-scale model of Escherichia coli K-12(iJR904 GSM/GPR). Genome Biology 2003, 4:R54.1–R54.12.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  71. 71. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkList of metabolic reactionsFor purposes of FBA, we convert each reversible reaction in the metabolic network into two one-wayreactions. The number of one-way reactions in the metabolic network is 1176.Next we append to these 1176 reactions, 286 reactions (143 × 2) for uptake and excretion of 143 externalmetabolites with the infinite source and sink (i.e., ‘ZZZZ’).To this list we append the Growth rate reaction, which gives a list of 1463 reactions (1176 + 286 + 1).The list of reactions is contained in the file DATA/Rxnlist iJR904.txt.The stoichiometric matrix is contained in the file DATA/SIJ ECJR904.txt and the rows of thestoichiometric matrix correspond to the metabolites listed in the file DATA/SUB ECJR904.txt.The file DATA/Rxnlist iJR904.txt also contains the Gene-Protein-Reaction (GPR) association for eachmetabolic reaction.The file DATA/iJR904 Genes contains the list of 904 genes coding for enzymes in the metabolic network.Reed JL, Vo TD, Schilling CH, Palsson BO: An expanded genome-scale model of Escherichia coli K-12(iJR904 GSM/GPR). Genome Biology 2003, 4:R54.1–R54.12.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  72. 72. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkRun FBAStepsEnter the configuration of the external environment in the tab separated file DATA/Media.txt. Note thatfor growth some of the inorganic metabolites should always be available for uptake.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  73. 73. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkRun FBAStepsEnter the configuration of the external environment in the tab separated file DATA/Media.txt. Note thatfor growth some of the inorganic metabolites should always be available for uptake.Invoke the command sh FBA ECJR904.sh.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  74. 74. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkRun FBAStepsEnter the configuration of the external environment in the tab separated file DATA/Media.txt. Note thatfor growth some of the inorganic metabolites should always be available for uptake.Invoke the command sh FBA ECJR904.sh.Decide if you want to perform pure FBA or knock reactions or genes and observe the effect ofperturbations.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  75. 75. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkRun FBAStepsEnter the configuration of the external environment in the tab separated file DATA/Media.txt. Note thatfor growth some of the inorganic metabolites should always be available for uptake.Invoke the command sh FBA ECJR904.sh.Decide if you want to perform pure FBA or knock reactions or genes and observe the effect ofperturbations.The program lets you knock off more than one gene or reaction at the same time. Remember that if aknockout of a reaction or gene results in zero growth rate then the reaction or gene is deemed ‘essential’for the simulated medium.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  76. 76. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkRun FBAStepsEnter the configuration of the external environment in the tab separated file DATA/Media.txt. Note thatfor growth some of the inorganic metabolites should always be available for uptake.Invoke the command sh FBA ECJR904.sh.Decide if you want to perform pure FBA or knock reactions or genes and observe the effect ofperturbations.The program lets you knock off more than one gene or reaction at the same time. Remember that if aknockout of a reaction or gene results in zero growth rate then the reaction or gene is deemed ‘essential’for the simulated medium.The resultant flux vector is stored in the file Flux.txt. The program also prints out the growth rateobtained.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  77. 77. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkBrief description of the programThe program PROG/FBA ECJR904.cpp is used to generate the MPS filewhich is then used as an input to GLPK solver to obtain the optimal fluxdistribution. The program requires the configuration of the externalenvironment which is contained in the file DATA/Media.txt. Theprogram GR.cpp is used to determine the subset of enzymatic reactionsavailable when a gene is knocked off.Various FunctionsThe function readsmatrix() reads in the stoichiometric matrix.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  78. 78. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkBrief description of the programThe program PROG/FBA ECJR904.cpp is used to generate the MPS filewhich is then used as an input to GLPK solver to obtain the optimal fluxdistribution. The program requires the configuration of the externalenvironment which is contained in the file DATA/Media.txt. Theprogram GR.cpp is used to determine the subset of enzymatic reactionsavailable when a gene is knocked off.Various FunctionsThe function readsmatrix() reads in the stoichiometric matrix.The function knockreaction() determines the reactions to be knocked off from the original network.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  79. 79. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkBrief description of the programThe program PROG/FBA ECJR904.cpp is used to generate the MPS filewhich is then used as an input to GLPK solver to obtain the optimal fluxdistribution. The program requires the configuration of the externalenvironment which is contained in the file DATA/Media.txt. Theprogram GR.cpp is used to determine the subset of enzymatic reactionsavailable when a gene is knocked off.Various FunctionsThe function readsmatrix() reads in the stoichiometric matrix.The function knockreaction() determines the reactions to be knocked off from the original network.In the main program, we first determine if we are simulating pure FBA or wish to knock off reactions orknock off genes based on the command line argument.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  80. 80. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkBrief description of the programThe program PROG/FBA ECJR904.cpp is used to generate the MPS filewhich is then used as an input to GLPK solver to obtain the optimal fluxdistribution. The program requires the configuration of the externalenvironment which is contained in the file DATA/Media.txt. Theprogram GR.cpp is used to determine the subset of enzymatic reactionsavailable when a gene is knocked off.Various FunctionsThe function readsmatrix() reads in the stoichiometric matrix.The function knockreaction() determines the reactions to be knocked off from the original network.In the main program, we first determine if we are simulating pure FBA or wish to knock off reactions orknock off genes based on the command line argument.Next we write out the MPS file.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  81. 81. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkReferencesVarma A, Palsson BO: Metabolic flux balancing: Basic concepts, scientific and practical use.Biotechnology 1994, 12:994–998.Edwards JS, Palsson BO: The Escherichia coli MG1655 in silico metabolic genotype: its definition,characteristics, and capabilities. Proc. Natl. Acad. Sci. USA 2000, 97:5528–5533.Edwards JS, Ibarra RU, Palsson BO: In silico predictions of Escherichi coli metabolic capabilities areconsistent with experimental data. Nat. Biotechnol. 2001, 19:125–130.Covert MW, Schilling CH, Palsson BO: Regulation of Gene Expression in Flux Balance Models ofMetabolism. J. Theor. Biol. 2001, 213:73–78.Segre D, Vitkup D, Church GM: Analysis of optimality in natural and perturbed metabolic networks.Proc. Natl. Acad. Sci. USA 2002, 99:15112–15117.Reed JL, Vo TD, Schilling CH, Palsson BO: An expanded genome-scale model of Escherichia coli K-12(iJR904 GSM/GPR). Genome Biology 2003, 4:R54.1–R54.12.Samal A, Singh S, Giri V, Krishna S, Raghuram N, Jain S: Low degree metabolites explain essentialreactions and enhance modularity in biological networks. BMC Bioinformatics 2006, 7:118.Palsson BO: Systems Biology: Properties of Reconstructed Networks. (Cambridge University Press) 2006.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  82. 82. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkExerciseFind the growth rate when acetate (ac) is provided at 10mmol/gDW-hr with oxygen in excess.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  83. 83. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkExerciseFind the growth rate when acetate (ac) is provided at 10mmol/gDW-hr with oxygen in excess.Find the growth rate when succinate (succ) is provided at 10mmol/gDW-hr with oxygen in excess.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  84. 84. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkExerciseFind the growth rate when acetate (ac) is provided at 10mmol/gDW-hr with oxygen in excess.Find the growth rate when succinate (succ) is provided at 10mmol/gDW-hr with oxygen in excess.Find the growth rate when glucose (glc-D) is provided at 10mmol/gDW-hr with no oxygen (anaerobic condition).Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  85. 85. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkExerciseFind the growth rate when acetate (ac) is provided at 10mmol/gDW-hr with oxygen in excess.Find the growth rate when succinate (succ) is provided at 10mmol/gDW-hr with oxygen in excess.Find the growth rate when glucose (glc-D) is provided at 10mmol/gDW-hr with no oxygen (anaerobic condition).Find the growth rate when you knock off reaction 1176 underglucose aerobic condition.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  86. 86. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsE. coli metabolic networkExerciseFind the growth rate when acetate (ac) is provided at 10mmol/gDW-hr with oxygen in excess.Find the growth rate when succinate (succ) is provided at 10mmol/gDW-hr with oxygen in excess.Find the growth rate when glucose (glc-D) is provided at 10mmol/gDW-hr with no oxygen (anaerobic condition).Find the growth rate when you knock off reaction 1176 underglucose aerobic condition.Find the growth rate when you knock off gene b0031 under glucoseaerobic condition.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  87. 87. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsOutline1 Introduction to FBA2 Examples of FBA implementation3 Blocked ReactionsAlgorithmImplementation4 UP-UC clusters5 Boolean dynamicsAreejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  88. 88. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsAlgorithmDefinitionA blocked reaction is a reaction that cannot have a nonzero flux valueunder any steady state condition. These reactions are also referred to as‘strictly detailed balanced’ reactions. A reaction is blocked for any givencondition due to stoichiometric reasons. This is mainly due to dead endmetabolites in the reconstructed metabolic networks.Schuster S, Schuster R: Detecting strictly detailed balanced subnetworks in open chemical reactionnetworks. J. Math. Chem. 1991, 6:17–40.Burgard AP, Nikolaev EV, Schilling CH, Maranas CD: Flux coupling analysis of genome-scale metabolicnetwork reconstructions. Genome Res 2004, 14:301–312.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  89. 89. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsAlgorithmAlgorithm to find blocked reactionsThe linear programming problem to compute blocked reactions can beformulated as follows:maximize Vk subject to S.V = 0 and 0 ≤ Vj ≤ αj .If the maximum flux obtained for reaction k is zero, the reaction isdeemed blocked for the simulated external environment. Note that weneed to fix the flux of reactions that are exactly reverse of the reactionbeing checked for ‘blocked’ status to zero so as to avoid trivial cycles.Burgard AP, Nikolaev EV, Schilling CH, Maranas CD: Flux coupling analysis of genome-scale metabolicnetwork reconstructions. Genome Res 2004, 14:301–312.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  90. 90. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsImplementationStepsEnter the configuration of the external environment in the tabseparated file DATA/Media.txt. Note that for growth some of theinorganic metabolites should always be available for uptake.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  91. 91. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsImplementationStepsEnter the configuration of the external environment in the tabseparated file DATA/Media.txt. Note that for growth some of theinorganic metabolites should always be available for uptake.Invoke the command sh Blocked.sh.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  92. 92. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsImplementationStepsEnter the configuration of the external environment in the tabseparated file DATA/Media.txt. Note that for growth some of theinorganic metabolites should always be available for uptake.Invoke the command sh Blocked.sh.Specify the reaction to be tested for ‘blocked’ status.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  93. 93. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsImplementationStepsEnter the configuration of the external environment in the tabseparated file DATA/Media.txt. Note that for growth some of theinorganic metabolites should always be available for uptake.Invoke the command sh Blocked.sh.Specify the reaction to be tested for ‘blocked’ status.If the maximum value of the flux obtained is zero, the reaction isdeemed blocked for the simulated environmental condition.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  94. 94. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsImplementationBrief description of the programThe program PROG/Blocked.cpp is used to generate the MPS filewhich is then used as an input to GLPK solver. The fileDATA/Reversible.txt contains the list of exact reverse of each ofthe 1176 reactions in the E. coli metabolic network. When a givenreaction is specified so as to be checked for the ‘blocked’ status,the file DATA/Reversible.txt is used to fix the flux of exact reverseof the specified reaction to zero in order to avoid trivial cycles.Also, note that in the MPS file we specify the optimizationfunction as the flux of the reaction being tested.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  95. 95. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsOutline1 Introduction to FBA2 Examples of FBA implementation3 Blocked Reactions4 UP-UC clustersDefinitionsDetermine UP-UC clusters5 Boolean dynamicsAreejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  96. 96. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDefinitionsUP-UC metabolitesA metabolite is designated as ‘uniquely produced’ or ‘UP’ if, in thebipartite graph of reactions and metabolites, the node correspondingto the metabolite has in-degree equal to unity. In other words, ifthere is only one reaction in the network that produces themetabolite.A metabolite is designated as ‘uniquely consumed’ or ‘UC’ if, in thebipartite graph of reactions and metabolites, the node correspondingto the metabolite has out-degree equal to unity. In other words, ifthere is only one reaction in the network that consumes themetabolite.A metabolite that is both UP and UC is designated as a ‘UP-UCmetabolite’ and has the lowest degree in the network.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  97. 97. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDefinitionsUP/UC reactionsA reaction was designated as ‘uniquely producing’ or ‘UP’ if itproduced a UP metabolite.A reaction was designated as ‘uniquely consuming’ or ‘UC’ if itconsumed a UC metabolite.A reaction that is either ‘UP’ or ‘UC’ is designated as ‘UP/UCreaction’.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  98. 98. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDefinitionsUP-UC clusterA ‘UP-UC cluster’ of reactions may be defined as a set of reactionsconnected by UP-UC metabolites.In a steady state fixing the flux of any reaction in the UP-UC clusterfixes the fluxes of all other reactions in the cluster. UP-UCmetabolites give rise to a situation wherein the inclusion of onereaction in a set implies the inclusion of another.Each UP-UC cluster of reactions can be replaced by an effectivereaction without affecting the steady state performance and can beused to coarse-grain metabolic networks.Samal A, Singh S, Giri V, Krishna S, Raghuram N, Jain S: Low degree metabolites explain essentialreactions and enhance modularity in biological networks. BMC Bioinformatics 2006, 7:118.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  99. 99. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDefinitionsExample of UP-UC clusterNote that UP-UC clusters include linear pathways but can also havebranched or cyclic structure.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  100. 100. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersAlgorithm1 Starting from stoichiometric matrix of the metabolic network,determine all the UP-UC metabolites in the network.Harary F: Graph Theory. (Addison Wesley, Reading) 1969.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  101. 101. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersAlgorithm1 Starting from stoichiometric matrix of the metabolic network,determine all the UP-UC metabolites in the network.2 Delete all links in the bipartite graph except those involving UP-UCmetabolites.Harary F: Graph Theory. (Addison Wesley, Reading) 1969.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  102. 102. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersAlgorithm1 Starting from stoichiometric matrix of the metabolic network,determine all the UP-UC metabolites in the network.2 Delete all links in the bipartite graph except those involving UP-UCmetabolites.3 Create the reaction-reaction graph (i.e., adjacency matrix of theunipartite graph with nodes as reactions) from the bipartite graphcontaining only the links involving UP-UC metabolites.Harary F: Graph Theory. (Addison Wesley, Reading) 1969.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  103. 103. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersAlgorithm1 Starting from stoichiometric matrix of the metabolic network,determine all the UP-UC metabolites in the network.2 Delete all links in the bipartite graph except those involving UP-UCmetabolites.3 Create the reaction-reaction graph (i.e., adjacency matrix of theunipartite graph with nodes as reactions) from the bipartite graphcontaining only the links involving UP-UC metabolites.4 The weak components [1] of size ≥ 2 of this graph are the UP-UCclusters.Harary F: Graph Theory. (Addison Wesley, Reading) 1969.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  104. 104. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersStepsChange your current directory to UPUC.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  105. 105. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersStepsChange your current directory to UPUC.Compile the program as g++ PROG/UPUC.cpp.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  106. 106. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersStepsChange your current directory to UPUC.Compile the program as g++ PROG/UPUC.cpp.Run the program by invoking the command ./a.out.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  107. 107. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersStepsChange your current directory to UPUC.Compile the program as g++ PROG/UPUC.cpp.Run the program by invoking the command ./a.out.The program creates three files as output:Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  108. 108. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersStepsChange your current directory to UPUC.Compile the program as g++ PROG/UPUC.cpp.Run the program by invoking the command ./a.out.The program creates three files as output:1 UPUCmet.txt: This contains the list of UP-UC metabolites.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  109. 109. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersStepsChange your current directory to UPUC.Compile the program as g++ PROG/UPUC.cpp.Run the program by invoking the command ./a.out.The program creates three files as output:1 UPUCmet.txt: This contains the list of UP-UC metabolites.2 UPUCreac.txt: This contains the list of UP/UC reactions.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  110. 110. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersStepsChange your current directory to UPUC.Compile the program as g++ PROG/UPUC.cpp.Run the program by invoking the command ./a.out.The program creates three files as output:1 UPUCmet.txt: This contains the list of UP-UC metabolites.2 UPUCreac.txt: This contains the list of UP/UC reactions.3 UPUCcluster.txt: This contains the list of UPUC clusters.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  111. 111. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersStepsChange your current directory to UPUC.Compile the program as g++ PROG/UPUC.cpp.Run the program by invoking the command ./a.out.The program creates three files as output:1 UPUCmet.txt: This contains the list of UP-UC metabolites.2 UPUCreac.txt: This contains the list of UP/UC reactions.3 UPUCcluster.txt: This contains the list of UPUC clusters.In additions, the program prints out the number of UP-UCmetabolites, the number of UP/UC reactions and the sizedistribution of UP-UC clusters.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  112. 112. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersBrief description of the programVarious FunctionsThe function readsmatrix() reads in the stoichiometric matrix.These functions are used to determine the UP-UC clusters in the E. coli metabolic network.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  113. 113. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersBrief description of the programVarious FunctionsThe function readsmatrix() reads in the stoichiometric matrix.The function upucmetabolite() determines the UP-UC metabolites.These functions are used to determine the UP-UC clusters in the E. coli metabolic network.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  114. 114. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersBrief description of the programVarious FunctionsThe function readsmatrix() reads in the stoichiometric matrix.The function upucmetabolite() determines the UP-UC metabolites.The function upucreaction() determines the UP/UC reactions.These functions are used to determine the UP-UC clusters in the E. coli metabolic network.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  115. 115. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersBrief description of the programVarious FunctionsThe function readsmatrix() reads in the stoichiometric matrix.The function upucmetabolite() determines the UP-UC metabolites.The function upucreaction() determines the UP/UC reactions.The function deletelink() is used to delete all links in the bipartite graph except those involving the UP-UCmetabolites.These functions are used to determine the UP-UC clusters in the E. coli metabolic network.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  116. 116. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersBrief description of the programVarious FunctionsThe function readsmatrix() reads in the stoichiometric matrix.The function upucmetabolite() determines the UP-UC metabolites.The function upucreaction() determines the UP/UC reactions.The function deletelink() is used to delete all links in the bipartite graph except those involving the UP-UCmetabolites.The function adj() constructs the reaction-reaction graph.These functions are used to determine the UP-UC clusters in the E. coli metabolic network.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  117. 117. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDetermine UP-UC clustersBrief description of the programVarious FunctionsThe function readsmatrix() reads in the stoichiometric matrix.The function upucmetabolite() determines the UP-UC metabolites.The function upucreaction() determines the UP/UC reactions.The function deletelink() is used to delete all links in the bipartite graph except those involving the UP-UCmetabolites.The function adj() constructs the reaction-reaction graph.The function connect(i) is used to determine all nodes that can be reached starting from node idisregarding the directionality of links.These functions are used to determine the UP-UC clusters in the E. coli metabolic network.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  118. 118. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsOutline1 Introduction to FBA2 Examples of FBA implementation3 Blocked Reactions4 UP-UC clusters5 Boolean dynamicsDescription of the dynamical systemAttractors of the dynamical systemAreejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  119. 119. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDescription of the dynamical systemTranscriptional regulatory network iMC1010v1We have studied the transcriptional regulatory network (TRN) controllingE. coli metabolism contained in the database iMC1010v1 [1] as booleandynamical system [2]. The database has been constructed by the groupof Bernhard Palsson at UCSD and is available athttp://gcrg.ucsd.edu/organisms/ecoli/regulation/iMC1010v1.xls. Theregulatory network iMC1010v1 can be interfaced with the metabolicnetwork iJR904 [3] to study the gene regulation of metabolism.Covert MW, Knight EM, Reed JL, Herrgard MJ, Palsson BO: Integrating high-throughput andcomputational data elucidates bacterial networks. Nature 2004, 429:92–96.Samal A, Jain S: The regulatory network of E. coli metabolism as a boolean dynamical system exhibitsboth homeostasis and flexibility of response. arxiv:q-bio.MN/0703059.Reed JL, Vo TD, Schilling CH, Palsson BO: An expanded genome-scale model of Escherichia coli K-12(iJR904 GSM/GPR). Genome Biology 2003, 4:R54.1–R54.12.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  120. 120. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDescription of the dynamical systemEffective boolean dynamical systemThe database iMC1010v1 also provides the boolean input-output map at each node, e.g., the configuration of eachgene (on or off), as a function of the on-off states of all its inputs.Using this information we construct the following discrete dynamical system describing E. coli’s TRN:gi (t + 1) = Gi (g(t), m); i = 1, 2, . . . , 583.Here, gi (t) is the configuration of gene i at time t.Time is measured in discrete units: t = 0, 1, 2, . . ..gi (t) = 1 (0) means that at time t gene i is on (off).The vector g(t) collectively denotes the configurations of all the genes at time t; its ithcomponent is gi (t).The vector m denotes the configuration of external metabolites; its ithcomponent mi = 1 if metabolite i(i = 1, 2, . . . , 96) is present in the external environment for uptake into the cell, and mi = 0 if it is absent.Samal A, Jain S: The regulatory network of E. coli metabolism as a boolean dynamical system exhibitsboth homeostasis and flexibility of response. arxiv:q-bio.MN/0703059.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  121. 121. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDescription of the dynamical systemExample of a Boolean RuleAreejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  122. 122. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDescription of the dynamical systemOrganization of the database iMC1010v1The database accounts for 583 genes of which 479 genes code for the enzymes of the metabolic networkand 104 genes code for 103 transcription factors (TFs).Covert MW, Knight EM, Reed JL, Herrgard MJ, Palsson BO: Integrating high-throughput andcomputational data elucidates bacterial networks. Nature 2004, 429:92–96.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  123. 123. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDescription of the dynamical systemOrganization of the database iMC1010v1The database accounts for 583 genes of which 479 genes code for the enzymes of the metabolic networkand 104 genes code for 103 transcription factors (TFs).The database further accounts for 96 external metabolites whose presence or absence affects the state ofthe genes.Covert MW, Knight EM, Reed JL, Herrgard MJ, Palsson BO: Integrating high-throughput andcomputational data elucidates bacterial networks. Nature 2004, 429:92–96.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  124. 124. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDescription of the dynamical systemOrganization of the database iMC1010v1The database accounts for 583 genes of which 479 genes code for the enzymes of the metabolic networkand 104 genes code for 103 transcription factors (TFs).The database further accounts for 96 external metabolites whose presence or absence affects the state ofthe genes.The flux values of 21 reactions affect the state of the genes in the network. The flux values are a surrogatefor concentration of internal metabolites in the model as Flux Balance Analysis (FBA) cannot be used tocompute the concentrations of internal metabolites.Covert MW, Knight EM, Reed JL, Herrgard MJ, Palsson BO: Integrating high-throughput andcomputational data elucidates bacterial networks. Nature 2004, 429:92–96.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  125. 125. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDescription of the dynamical systemOrganization of the database iMC1010v1The database accounts for 583 genes of which 479 genes code for the enzymes of the metabolic networkand 104 genes code for 103 transcription factors (TFs).The database further accounts for 96 external metabolites whose presence or absence affects the state ofthe genes.The flux values of 21 reactions affect the state of the genes in the network. The flux values are a surrogatefor concentration of internal metabolites in the model as Flux Balance Analysis (FBA) cannot be used tocompute the concentrations of internal metabolites.There are 19 condition variables that affect the state of genes in the network. Of these 19 conditionvariables, 17 are determined by the state of the external metabolites, TFs and fluxes. The remaining twocondition variables are Growth and pH.Covert MW, Knight EM, Reed JL, Herrgard MJ, Palsson BO: Integrating high-throughput andcomputational data elucidates bacterial networks. Nature 2004, 429:92–96.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  126. 126. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDescription of the dynamical systemOrganization of the database iMC1010v1The database accounts for 583 genes of which 479 genes code for the enzymes of the metabolic networkand 104 genes code for 103 transcription factors (TFs).The database further accounts for 96 external metabolites whose presence or absence affects the state ofthe genes.The flux values of 21 reactions affect the state of the genes in the network. The flux values are a surrogatefor concentration of internal metabolites in the model as Flux Balance Analysis (FBA) cannot be used tocompute the concentrations of internal metabolites.There are 19 condition variables that affect the state of genes in the network. Of these 19 conditionvariables, 17 are determined by the state of the external metabolites, TFs and fluxes. The remaining twocondition variables are Growth and pH.There are 9 stimuli such as stress, etc. that affect the state of genes in the network.Covert MW, Knight EM, Reed JL, Herrgard MJ, Palsson BO: Integrating high-throughput andcomputational data elucidates bacterial networks. Nature 2004, 429:92–96.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  127. 127. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDescription of the dynamical systemOrganization of the database iMC1010v1The database accounts for 583 genes of which 479 genes code for the enzymes of the metabolic networkand 104 genes code for 103 transcription factors (TFs).The database further accounts for 96 external metabolites whose presence or absence affects the state ofthe genes.The flux values of 21 reactions affect the state of the genes in the network. The flux values are a surrogatefor concentration of internal metabolites in the model as Flux Balance Analysis (FBA) cannot be used tocompute the concentrations of internal metabolites.There are 19 condition variables that affect the state of genes in the network. Of these 19 conditionvariables, 17 are determined by the state of the external metabolites, TFs and fluxes. The remaining twocondition variables are Growth and pH.There are 9 stimuli such as stress, etc. that affect the state of genes in the network.The regulatory network provides the boolean function for each of the 583 genes in terms of the state ofeach gene’s input transcription factors, external metabolites, flux values, condition variables and stimulithat control the state of the genes.Covert MW, Knight EM, Reed JL, Herrgard MJ, Palsson BO: Integrating high-throughput andcomputational data elucidates bacterial networks. Nature 2004, 429:92–96.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  128. 128. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDescription of the dynamical systemPicture of the complete regulatory networkIn this picture, the genes coding for theenzymes have been coloured brown, the genescoding for TFs have been coloured pink, theexternal metabolites have been colouredgreen, the internal fluxes have been coloureddark blue, the condition variables have beencoloured light blue and the stimuli have beencoloured yellow.Areejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism
  129. 129. Introduction to FBA Examples of FBA implementation Blocked Reactions UP-UC clusters Boolean dynamicsDescription of the dynamical systemPicture of the largest connected clusterAreejit Samal and Sanjay Jain Department of Physics and Astrophysics,University of DelhiSome computational systems biology techniques to study regulation of metabolism

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