1. Reverse engineering of regulatory networks Dirk Husmeier & Adriano Werhli

2. Systems biology Learning signalling pathways and regulatory networks from postgenomic data

3. Reverse Engineering of Regulatory Networks Can we learn the network structure from postgenomic data themselves? Statistical methods to distinguish between –Direct correlations –Indirect correlations Challenge: Distinguish between –Correlations –Causal interactions Breaking symmetries with active interventions: –Gene knockouts (VIGs, RNAi)

8. Shrinkage estimation and the lemma of Ledoit-Wolf

13. Bayesian networks versus Graphical Gaussian models Directed versus undirected graphs Score based versus constrained based inference

14. Evaluation On real experimental data, using the gold standard network from the literature On synthetic data simulated from the gold- standard network

16. Evaluation: Raf signalling pathway Cellular signalling network of 11 phosphorylated proteins and phospholipids in human immune systems cell Deregulation  carcinogenesis Extensively studied in the literature  gold standard network

18. Data Laboratory data from cytometry experiments Down-sampled to 100 measurements Sample size indicative of microarray experiments

20. Two types of experiments

22. Evaluation On real experimental data, using the gold standard network from the literature On synthetic data simulated from the gold- standard network

23. Comparison with simulated data 1

24. Raf pathway

25. Comparison with simulated data 2

26. Steady-state approximation

30. Evaluation 1: AUC scores

31. Evaluation 2: TP scores We set the threshold such that we obtained 5 spurious edges (5 FPs) and counted the corresponding number of true edges (TP count).

35. AUC scores

36. TP scores

37. Raf pathway

38. Conclusions 1 BNs and GGMs outperform RNs, most notably on Gaussian data. No significant difference between BNs and GGMs on observational data. For interventional data, BNs clearly outperform GGMs and RNs, especially when taking the edge direction (DGE score) rather than just the skeleton (UGE score) into account.

39. Conclusions 2 Performance on synthetic data better than on real data: Real data: more complex Real interventions are not ideal Errors in the gold-standard network

41. Reconstructing gene regulatory networks with Bayesian networks by combining microarray data with biological prior knowledge

42. MOTIVATION

43. Use TF binding motifs in promoter sequences

44. Use prior knowledge from KEGG

45. Prior knowledge

47. Biological prior knowledge matrix Biological Prior Knowledge Indicates some knowledge about the relationship between genes i and j

48. Biological prior knowledge matrix Biological Prior Knowledge Define the energy of a Graph G Indicates some knowledge about the relationship between genes i and j

49. Prior distribution over networks Energy of a network

50. Rewriting the energy Energy of a network

51. Approximation of the partition function

52. Multiple sources of prior knowledge

53. Rewriting the energy Energy of a network

54. Approximation of the partition function

55. MCMC sampling scheme

56. Sample networks and hyperparameters from the posterior distribution Metropolis-Hastings scheme Proposal probabilities

57. Metropolis-Hastings scheme

59. MCMC with one prior Sample graph and the parameter . Separate in two samples to improve the acceptance: 1.Sample graph with  fixed. 2.Sample  with graph fixed.

60. Sample graph and the parameter . BGe BDe MCMC with one prior Separate in two samples to improve the acceptance: 1.Sample graph with  fixed. 2.Sample  with graph fixed.

61. Sample graph and the parameter . BGe BDe MCMC with one prior Separate in two samples to improve the acceptance: 1.Sample graph with  fixed. 2.Sample  with graph fixed.

62. Sample graph and the parameter . BGe BDe MCMC with one prior Separate in two samples to improve the acceptance: 1.Sample graph with  fixed. 2.Sample  with graph fixed.

63. Sample graph and the parameter . BGe BDe MCMC with one prior Separate in two samples to improve the acceptance: 1.Sample graph with  fixed. 2.Sample  with graph fixed.

64. Approximation of the partition function

65. MCMC with two priors Sample graph and the parameters    and  2 Separate in three samples to improve the acceptance: 1.Sample graph with  1 and  2 fixed. 2.Sample  1 with graph and  2 fixed. 3.Sample  2 with graph and  1 fixed.

66. Application to real data

67. Flow cytometry data and KEGG

69. Data available: –Intracellular multicolour flow cytometry. –Measured protein concentrations. –1200 data points. We sample 5 data sets with 100 data points each.

70. Flow cytometry data and KEGG KEGG PATHWAYS are a collection of manually drawn pathway maps representing our knowledge of molecular interactions and reaction networks.

71. Flow cytometry data and KEGG

72. Prior distribution

73. Sampled values of the hyperparameters

74. Idealized network population

76. Sampled values of the hyperparameters

77. Performance evaluation: AUC scores

78. Flow cytometry data and KEGG

79. Comparison: AUC for fixed and sampled hyperparameters on real data

80. Comparison: AUC for fixed and sampled hyperparameters on synthetic data

81. Future work

83. Thank you