Inferring gene regulatory networks from transcriptomic profiles

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

2. Overview • Introduction • Application to synthetic biology • Lessons from DREAM

3. Network reconstruction from postgenomic data

4. Accuracy Mechanistic models Bayesian networks Conditional independence graphs Methods based on correlation and mutual information Computational complexity

5. Accuracy Mechanistic models Bayesian networks Conditional independence graphs Methods based on correlation and mutual information Computational complexity

6. Shortcomings Pairwise associations do not take the context of the systeminto consideration direct interaction common regulator indirect interaction co-regulation

7. Accuracy Mechanistic models Bayesian networks Conditional independence graphs Methods based on correlation and mutual information Computational complexity

8. 1 2 Direct interaction 1 2 Conditional Independence Graphs (CIGs) Inverse of the covariance matrix strong partial correlation π12 Partial correlation, i.e. correlation conditional on all other domain variables Corr(X1,X2|X3,…,Xn) Problem: #observations < #variables  Covariance matrix is singular

9. Accuracy Mechanistic models Bayesian networks Conditional independence graphs Methods based on correlation and mutual information Computational complexity

10. Model Parameters q Probability theory  Likelihood

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

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

13. Regularization E.g.: Bayesian information criterion Regularization term Data misfit term Maximum likelihood parameters Number of parameters Number of data points

14. Likelihood BIC Complexity Complexity

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

16. Problem: huge computational costs q

17. Accuracy Mechanistic models Bayesian networks Conditional independence graphs Methods based on correlation and mutual information Computational complexity

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

19. Bayes net ODE model

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

21. UAI 1994

22. Linearity assumption [A]= w1[P1]+ w2[P2] + w3[P3] + w4[P4] + noise P1 w1 P2 A w2 w3 P3 w4 P4

23. Homogeneity assumption

24. Accuracy Mechanistic models Bayesian networks Conditional independence graphs Methods based on correlation and mutual information Computational complexity

25. Example: 4 genes, 10 time points

26. Standard dynamic Bayesian network: homogeneous model

27. Limitations of the homogeneity assumption

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

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

30. Learning with MCMC q Allocation vector h k Number of components (here: 3)

31. Learning with MCMC q Allocation vector h k Number of components (here: 3)

32. Non-homogeneous model  Non-linear model

33. BGe: Linear model [A]= w1[P1]+ w2[P2] + w3[P3] + w4[P4] + noise P1 w1 P2 A w2 w3 P3 w4 P4

34. Can we get an approximate nonlinear model without data discretization? y x

35. Can we get an approximate nonlinear model without data discretization? Idea: piecewise linear model y x

36. Inhomogeneous dynamic Bayesian network with common changepoints

37. Inhomogenous dynamic Bayesian network with node-specific changepoints

38. NIPS 2009

39. Non-stationarity in the regulatory process

40. Non-stationarity in the network structure

41. Flexible network structure .

42. Flexible network structure with regularization

43. Flexible network structure with regularization

44. Flexible network structure with regularization

45. ICML 2010

46. Morphogenesis in Drosophila melanogaster • Gene expression measurements over 66 time steps of 4028 genes (Arbeitman et al., Science, 2002). • Selection of 11 genes involved in muscle development. Zhao et al. (2006), Bioinformatics22

47. Transition probabilities: flexible structure with regularization Morphogenetic transitions: Embryo  larva larva pupa pupa  adult

50. Overview • Introduction • Application to synthetic biology • Lessons from DREAM