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White Box Function Estimation using Convenience Kinetics

White Box Function Estimation using Convenience Kinetics. COMP 150GA – Class Project Fall 2011 Tufts University Prof. Soha Hassoun, soha@cs.tufts.edu. Goal.

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White Box Function Estimation using Convenience Kinetics

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  1. White Box Function Estimationusing Convenience Kinetics COMP 150GA – Class Project Fall 2011 Tufts University Prof. Soha Hassoun, soha@cs.tufts.edu

  2. Goal • Develop approximate expressions for rate change of concentrations in metabolic networks, when given measurement data (data sets that correspond to various operating conditions).

  3. “White Box” approximationAssume you have *all* measurements! ATP ADP FDP d[D-Glucose]/dt = ? d[G6P]/dt =vGlk - vPgi d[F6P]/dt = vPgi -vPfkA d[FDP]/dt = ? d[ATP]/dt = ? d[ADP]/dt = ? d[D-Glucose]/dt = -vGlk d[G6P]/dt =vGlk - vPgi d[F6P]/dt = vPgi -vPfkA d[FDP]/dt = vPfkA d[ATP]/dt = -vGlk -vPfkA d[ADP]/dt = vGlk + vPfkA

  4. Each rate equation maybe a function is of the concentration of one or more of compound on the boundaries or inside the cell • GOAL: • What is the best form that describes these concentrations? • Minimize the number of variables in the rate equations ATP d[D-Glucose]/dt = ? d[FDP]/dt = ? d[ATP]/dt = ? d[ADP]/dt = ? ADP FDP

  5. Shape of theconcentrations for some data sets we have SET2 SET1 ATP FDP SET4 SET3

  6. Convenience Kinetics* • A systematic way of generating rate equations. • Apply convenience kinetics to determine rate for each input and output metabolite. • Each metabolite can influence one or more other metabolites either as: (a) a reactant or product (b) an activator (c) an inhibitor • Narrowing down parameter choices: • We can look up Vmax for each reaction using Brenda. Vmax may dominate and can be used to seed guesses. • We can use Gibbs free energy to constraint the solution space *http://www.tbiomed.com/content/pdf/1742-4682-3-41.pdf

  7. Convenience Kinetics – reactant/product relationship example • Given equation: A + X ↔ B + Y • We have 6 parameters for this equation: those involved with ~a, ~x, ~b, ~y, and k+, and k- =

  8. Convenience Kinetics – reactant/product relationship (general) Assume that α and β (stoichiometric coefficients) are known Each kM is a parameter represents binding energy known as dissociation constant as If irreversible, then kM goes to infinity… ~b goes to zero and products disappear from the equations

  9. Convenience Kinetics – Activators/Inhibitors • Activators modify the rate equation by a factor, where d is the concentration of the modifier and kA is the activation (binding) constant • Inhibitors modify the rate equation by a factor, where d is the concentration of the modifier and kI is the inhibition (binding) constant

  10. Convenience Kinetics – General Form • For an equation l with m metabolites, Metabolites in the reactant set Metabolites in the product set Inhibitor pre-factors Activator pre-factors Set of all activators Set of all inhibitors * El does not need to be an independent parameter, assume k+cat and k-cat are modified to account for E

  11. Thermodynamic Constraints limit parameter solution space.We can re-write the rate equation Is kiG known for a particular metabolite or does it need to be estimated? Can klV be obtained from a data base (??)

  12. Genetic Programming • Each solution has a list of reactants (R), products (P), inhibitors (I), activators (A), and associated parameters. • Capture information using three matrices: each column is a reaction and each row is a compound. • N matrix: Each entry shows how a metabolite participates in a particular reaction (Given) • Regulation matrix: Each entry is +1, or -1 for activation or inhibition (guess!) • K matrix: Each entry describes an AFFINITY, if that relationship exists An order of magnitude estimate is useful (.1, 1, 10). • To evolve form: • Mutations: add/remove R, P, I, A • Crossover: move from R/P to I/A ???? • Should be able to perform parameter estimation for convenience kinetics format (an independent parameter estimation problem).

  13. Test Case #1 • D-Glucose + 2 ATP ↔ 2 ADP + FDP ATP ADP FDP

  14. Test Case #2 • S ↔ P

  15. GLUC6P GAP Test Case #3 • GLUC + 2NAD + NADP + ADP ↔ 2Ethanol + 2NADH + NADPH + ATP • GLUC6P + 2NAD + NADP + 2ADP ↔ 2Ethanol + 2NADH + NADPH + 2ATP • GAP + NAD + 2ADP ↔ 2Ethanol + NADH + 2ATP

  16. END • Old slides follow – please ignore

  17. Test Case #1

  18. Test Case #1Equation Rates

  19. Network

  20. Parameters Used in the Paper (Data generated used similar K and n values)

  21. Test case #2

  22. Input concentrations are P and M2, E2 We simplified the equations P

  23. Test Case #3

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