Inferring gene regulatory networks from transcriptomic profiles

1. Dirk Husmeier Inferring gene regulatory networks from transcriptomic profiles Biomathematics & Statistics Scotland

2. Overview • Introduction • Limitations • Methodology • Application to morphogenesis • Application to synthetic biology

3. Objective: reverse engineering regulatory networks From Sachs et al Science 2005

4. Network reconstruction from postgenomic data

5. Model Parameters q Probability theory  Likelihood

6. Mechanistic model: description with differential equations Concentrations Kinetic parameters q Rates

7. Model Parameters q Probability theory  Likelihood

8. 1) Practical problem: numerical optimization q 2) Conceptual problem: overfitting ML estimate increases on increasing the network complexity

9. Overfitting problem True pathway Poorer fit to the data Equal or better fit to the data Poorer fit to the data

10. Regularization E.g.: Bayesian information criterion (BIC) Regularization term Data misfit term Maximum likelihood parameters Number of parameters Number of data points

11. Likelihood BIC Complexity Complexity

12. Model selection: find the best pathway Select the model with the highest posterior probability: This requires an integration over the whole parameter space:

13. MCMC based schemes q Problem: excessive computational costs

14. Accuracy Mechanistic models DynamicBayesian networks Computational complexity

15. Marriage between graph theory and probability theory Friedman et al. (2000), J. Comp. Biol. 7, 601-620

16. Bayes net ODE model

17. Model Parameters q Bayesian networks: integral analytically tractable!

18. UAI 1994

19. Example: 2 genes 16 different network structures Compute

20. Identify the best network structure Ideal scenario: Large data sets, low noise

21. Uncertainty about the best network structure Limited number of experimental replications, high noise

22. Sample of high-scoring networks

23. Sample of high-scoring networks Feature extraction, e.g. marginal posterior probabilities of the edges

24. Sample of high-scoring networks Feature extraction, e.g. marginal posterior probabilities of the edges Uncertainty about edges High-confident edge High-confident non-edge

25. Sampling with MCMC Number of structures Number of nodes

26. Overview • Introduction • Limitations • Methodology • Application to morphogenesis • Application to synthetic biology

27. Model Parameters q Bayesian networks: integral analytically tractable!

28. Homogeneity assumption Parameters don’t change with time

29. Homogeneity assumption Parameters don’t change with time

30. Limitations of the homogeneity assumption

31. Overview • Introduction • Limitations • Methodology • Application to morphogenesis • Application to synthetic biology

32. Example: 4 genes, 10 time points

33. Standard dynamic Bayesian network: homogeneous model

34. Limitations of the homogeneity assumption

35. Our new model: heterogeneous dynamic Bayesian network. Here: 2 components

36. Changepoint model Parameters can change with time

37. Changepoint model Parameters can change with time

38. Our new model: heterogeneous dynamic Bayesian network. Here: 2 components

39. Our new model: heterogeneous dynamic Bayesian network. Here: 3 components

40. Extension of the model q

41. Extension of the model q Allocation vector h k Number of components (here: 3)

42. Analytically integrate out the parameters q Allocation vector h k Number of components (here: 3)

43. RJMCMC within Gibbs P(network structure | changepoints, data) P(changepoints | network structure, data) Birth, death, and relocation moves

46. Model extension So far:non-stationarity in the regulatory process

47. Non-stationarity in the network structure

48. Flexible network structure .

49. Model Parameters q

50. Model Parameters q Use prior knowledge!