Reconstructing gene regulatory networks with probabilistic models

1. Reconstructing gene regulatory networkswith probabilistic models Dirk Husmeier MarcoGrzegorczyk

4. Regulatory network

5. Network unknown High-throughput experiments Postgenomic data Machine learning Statistics

6. Overview • Introduction • Bayesian networks • Comparative evaluation • Integration of biological prior knowledge • A non-homogeneous Bayesian network for non-stationary processes • Current work

7. Overview • Introduction • Bayesian networks • Comparative evaluation • Integration of biological prior knowledge • A non-homogeneous Bayesian network for non-stationary processes • Current work

8. Elementary molecular biological processes

9. Description with differential equations Concentrations Kinetic parameters q Rates

10. Given: Gene expression time series Can we infer the correct gene regulatory network?

11. Parameters q known: Numerically integrate the differential equations for different hypothetical networks

12. Model selection for known parameters q Gene expression time series predicted with different models Measured gene expression time series Compare Highest likelihood: best model

13. Model selection for unknown parameters q Gene expression time series predicted with different models Measured gene expression time series Highest likelihood: over-fitting

14. Bayesian model selection Select the model with the highest posterior probability: This requires an integration of the whole parameter space: This integral is usually intractable

16. Marginal likelihoods for the alternative pathways Computational expensive, network reconstruction ab initio unfeasible

17. Overview • Introduction • Bayesian networks • Comparative evaluation • Integration of biological prior knowledge • A non-homogeneous Bayesian network for non-stationary processes • Current work

18. Objective:Reconstruction of regulatory networks ab initio Higher level of abstraction: Bayesian networks

19. Bayesian networks • Marriage between graph theory and probability theory. • Directed acyclic graph (DAG) representing conditional independence relations. • It is possible to score a network in light of the data: P(D|M), D:data, M: network structure. • We can infer how well a particular network explains the observed data. NODES A B C EDGES D E F

20. Bayes net ODE model

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

22. Nonlinear discretized model P1 Activator P2 Activation Repressor Allow for noise: probabilities P1 Activator P2 Inhibition Conditional multinomial distribution Repressor

23. Model Parameters q Integral analytically tractable!

26. Example: 2 genes 16 different network structures Best network: maximum score

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

28. Uncertainty about the best network structure Limted number of experimental replications, high noise

29. Sample of high-scoring networks

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

31. 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

32. Can we generalize this scheme to more than 2 genes? In principle yes. However …

33. Number of structures Number of nodes

34. Complete enumeration unfeasible  Hill climbing Accept move when increases

35. Local optimum Configuration space of network structures

36. Local change MCMC If accept If accept with probability Configuration space of network structures

37. Algorithm converges to

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

39. Problem: Local changes  small steps  slow convergence, difficult to cross valleys. Configuration space of network structures

40. Problem: Global changes  large steps  low acceptance  slow convergence. Configuration space of network structures

41. Can we make global changes that jump onto other peaks and are likely to be accepted? Configuration space of network structures

43. MCMC trace plots Conventional scheme New scheme against iteration number Plot of

44. Overview • Introduction • Bayesian networks • Comparative evaluation • Integration of biological prior knowledge • A non-homogeneous Bayesian network for non-stationary processes • Current work

47. Example: Protein signalling pathway Cell membran phosphorylation nucleus TF TF -> cell response

48. Evaluationon the Raf signalling pathway Receptor molecules Cell membrane Activation Interaction in signalling pathway Phosphorylated protein Inhibition From Sachs et al Science 2005

49. Flow cytometry data • Intracellular multicolour flow cytometry experiments: concentrations of 11 proteins • 5400 cells have been measured under 9 different cellular conditions (cues) • Downsampling to 100 instances (5 separate subsets): indicative of microarray experiments

50. Simulated data or “gold standard” from the literature