Probabilistic modelling in computational biology

1. Dirk Husmeier Probabilistic modelling in computational biology Biomathematics & Statistics Scotland

2. James Watson & Francis Crick, 1953

3. Frederick Sanger, 1980

7. Network reconstruction from postgenomic data

8. Model Parameters q

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

10. Bayes net ODE model

11. Model Parameters q Probability theory  Likelihood

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

13. UAI 1994

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

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

16. Sample of high-scoring networks

17. 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

18. Sampling with MCMC Number of structures Number of nodes

19. Madigan & York (1995), Guidici & Castello (2003)

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

22. Homogeneity assumption Interactions don’t change with time

23. Limitations of the homogeneity assumption

24. Example: 4 genes, 10 time points

25. Supervised learning. Here: 2 components

26. Changepoint model Parameters can change with time

27. Changepoint model Parameters can change with time

28. Unsupervised learning. Here: 3 components

29. Extension of the model q

30. Extension of the model q

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

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

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

35. 2 Dynamic programming, complexity N

37. Collaborationwith theInstitute of Molecular Plant Sciences at Edinburgh University (Andrew Millar’s group) Circadian rhythms in Arabidopsis thaliana - Focus on: 9 circadian genes: LHY, CCA1, TOC1, ELF4, ELF3, GI, PRR9, PRR5, and PRR3 - Transcriptional profiles at 4*13 time points in 2h intervals under constant light for - 4 experimental conditions

38. Comparison with the literature Precision Proportion of identified interactions that are correct Recall = Sensitivity Proportion of true interactions that we successfully recovered Specificity Proportion of non-interactions that are successfully avoided

39. Which interactions from the literature are found? ELF3 True positive CCA1 True positives (TP) = 8 False negatives (FN) = 5 LHY PRR9 Recall= 8/13= 62% GI Blue: activations Red: Inhibitions TOC1 PRR5 PRR3 ELF4 False negative

40. Which proportion of predicted interactions are confirmed by the literature? True positives (TP) = 8 False positives (FP) = 13 Precision = 8/21= 38% True positive Blue: activations Red: Inhibitions False positives

41. Precision= 38% Recall= 62% ELF3 CCA1 LHY PRR9 GI TOC1 PRR5 PRR3 ELF4

42. True positives (TP) = 8 False positives (FP) = 13 False negatives (FN) = 5 True negatives (TN) = 9²-8-13-5= 55 Sensitivity = TP/[TP+FN] = 62% Specificity = TN/[TN+FP] = 81% Recall Proportion of avoided non-interactions

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

44. Non-stationarity in the network structure

45. Flexible network structure .

46. Model Parameters q

47. Model Parameters q Use prior knowledge!

48. Flexible network structure .

49. Flexible network structure with regularization Hyperparameter Normalization factor

50. Flexible network structure with regularization Exponential prior versus Binomial prior with conjugate beta hyperprior