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HYPE Hybrid method for parameter estimation In biochemical models

HYPE Hybrid method for parameter estimation In biochemical models. Anne Poupon Biology and Bioinformatics of Signalling Systems PRC, Tours, France. k 0. A. y 0. The question. k 1. k 2. k 3. B. y 1. y 2. k 4. C. y 3.

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HYPE Hybrid method for parameter estimation In biochemical models

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  1. HYPE Hybridmethod for parameter estimation In biochemicalmodels Anne Poupon Biology and Bioinformatics of SignallingSystems PRC, Tours, France

  2. k0 A y0 The question k1 k2 k3 B y1 y2 k4 C y3 How to simulate the evolutions of the differentquantities as a function of time ?

  3. The question A B

  4. The question A B This is the topology of the model • Or • static model • inference graph • influence graph • ...

  5. The question The dynamical model: topology + time-evolutionrules k0 A B k1 Ordinarydifferentialequation (ODE)

  6. The question k0 A B k1 Ordinarydifferentialequation (ODE) Using mass action law :

  7. The question C k0 k0 A A B B k1 k1 Ordinarydifferentialequation (ODE) Using mass action law :

  8. The question k0 A B k1 k0 = 1 k1 = 1 [A](0) = 10 [B](0] =0

  9. The question k0 A B k1 k0 = 2 k1 = 1 [A](0) = 10 [B](0] =0

  10. The question What if wedon’t know the values of the parameters ? k0 A B k1

  11. The question What if wedon’t know the values of the parameters ? k0 A B k1 Experimental values

  12. The question What if wedon’t know the values of the parameters ? k0 A B k1 Experimental values Try to find k0 and k1such as the simulatedcurves fit withexperimental values

  13. The question What if wedon’t know the values of the parameters ? k0 A B k1 Experimental values Try to find k0 and k1such as the simulatedcurves fit withexperimental values That’sparameter estimation !

  14. The question Initial k0, k1 Iterativemethodology Simulate Compare withexp. values Objective function Change k0, k1 Done !

  15. The question Why do wewant to simulate ? k0 A B k1

  16. The question Why do wewant to simulate ? k0 A B k1 If wecanfindwithsufficientprecision the parameters of the model, wecansimulateitsbehavior in any condition withoutdoing the experiments !

  17. The question However... • In order to parameterizebiochemicalmodels, weneed a parameter estimation method : • fast, sodifferent topologies canbeexplored • robust, wewant to make sure that the parameterfoundis correct, and thatit’s unique • flexible, sodifferent types of data canbeused : dose-response, time series, relative mesurments, etc.

  18. Test models • In order to develop the method, weneed a benchmark ... • Wecannot use real systemsbecause the parameters are unknown ! • Wewill use syntheticmodels. • Syntheticmodelsallow to evaluate the influence of experimentaluncertainty. • Wealsodesigned the differentmodels in order to evaluate the importance of 2 differentfeatures: • the number of molecularspecies • the range betweensmallest and biggestparameter value

  19. k0 A y0 Test models k1 k2 k3 B y1 y2 k5 = A + y0 4 equations 8 parameters k4 k6 = B + y1 + y2 C y3 k7 = C + y3 Model 3 parametersfrom 5.10-7 to 1.105 (12 logs) Model 1 1 for all parameters Model 2 parametersfrom 2.10-3 to 1,28.102 (5 logs)

  20. A k10 = A + y0 k11 = B + y1 k12 = C + y2 + y3 k13 = D + y4 k0 k1 C y0 k6 k7 k2 Test models y2 B y1 Model 4 5 equations 14 parameters k3 k8 k9 k4 D y4 y3 k5

  21. Test models k20 = A + y0 k21 = B + y1 + y2 k22 = C + y3 k23= D + y4 + y5 k24 = E + y6 + y7 k25 = F + y8 k26 = G + y9 B A E k3 k2 k0 k1 k12 k13 y1 y0 y6 k5 k4 k15 k14 k6 y2 C y3 y7 k7 k8 k10 D y4 y5 k9 k11 Model 5 10 equations 27 parameters k16 F y8 k17 k18 G y9

  22. A B k1 k0 k2 k5 k4 k3 y0 y1 y2 k6 k8 k10 C y3 y4 D y5 k7 k9 k11 k17 k13 k12 k16 k15 k18 k20 y7 y6 E y8 y9 k14 k19 k21 k22 F y10 k23 k24 k26 G y11 y12 k25 k27 k28 k30 k32 H y13 y14 y15 k29 k31 k33 Test models k34 = A + y0 k35 = B + y1 + y2 k36= C + y3 + y4 k37 = D + y5 + y6 + y7 k38 = E + y8 + y9 k39 = F + y10 k40 = G + y11 + y12 k41 = H + y13 + y14 + y15 Model 6 16 equations 42 parameters

  23. Principle Theoretical parameters ODE Integration Concentrations at chosen time points Add perturbation (pert) « Experimental » data HYPE Parameter estimation Observed error Real error

  24. Objective function The objective functioniswhatweneed to minimize

  25. Objective function Normalized difference between observed and simulated in %

  26. Objective function Sum on all the time point for this observable Normalized difference between observed and simulated in %

  27. Objective function Divided by the number of time points for this observable Sum on all the time point for this observable Normalized difference between observed and simulated in %

  28. Objective function Sum on observables Divided by the number of time points for this observable Sum on all the time point for this observable Normalized difference between observed and simulated in %

  29. Objective function Divided by the nb of observables Sum on observables Divided by the number of time points for this observable Sum on all the time point for this observable Normalized difference between observed and simulated in %

  30. Objective function Divided by the nb of observables Depends on standard deviation Sum on observables Divided by the number of time points for this observable Sum on all the time point for this observable Normalized difference between observed and simulated in %

  31. Objective function

  32. Objective function

  33. Optimizationmethod Nowweneed an optimizationmethod.... Evolutionnarymethods are usuallyvery good atfinding extrema in a large and rought solution space ! Most popular: geneticalgorithm

  34. Geneticalgorithm 1 individual = (x, y); Parameter 2 Parameter 1

  35. Geneticalgorithm Mutation Parameter 2 Parameter 1

  36. Geneticalgorithm Cross-over Parameter 2 Parameter 1

  37. Geneticalgorithm New parents Parameter 2 Parameter 1

  38. Geneticalgorithm • Cross-over : global exploration • Mutation : local exploration • Afterenoughtgenerations, all the individuals are close to the global minimum.

  39. Geneticalgorithm

  40. Geneticalgorithm Not sobad ... But not that good !

  41. CMA-ES Parameter 2 Parameter 1

  42. CMA-ES Parameter 2 Parameter 1

  43. CMA-ES Parameter 2 Parameter 1

  44. CMA-ES New parent : weightedaverage Parameter 2 Parameter 1

  45. CMA-ES Best direction Parameter 2 Parameter 1

  46. CMA-ES Parameter 2 Parameter 1

  47. CMA-ES New generation Parameter 2 Parameter 1

  48. Geneticalgorithm

  49. Geneticalgorithm When CMA-ES converges itsvery good, but...

  50. Hybridmethod • Geneticalgorithmalways converges, but not very close to the solution • CMA-ES doesn’t converge often, but whenitdoes, itgetsvery close Let’stry to combine them !

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