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Inferring gene regulatory networks from transcriptomic profiles

Dirk Husmeier. Inferring gene regulatory networks from transcriptomic profiles. Biomathematics & Statistics Scotland. Overview. Introduction Methodology Circadian regulation in Arabidopsis Application to synthetic biology DREAM. Network reconstruction from postgenomic data. Accuracy.

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Inferring gene regulatory networks from transcriptomic profiles

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

  2. Overview • Introduction • Methodology • Circadian regulation in Arabidopsis • Application to synthetic biology • 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)

  9. Correlation Partial correlation high high high high high low highlow high low

  10. 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

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

  12. Regulatory network

  13. Description with differential equations Concentrations Kinetic parameters q Rates

  14. Model Parameters q Probability theory  Likelihood

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

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

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

  18. Likelihood BIC Complexity Complexity

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

  20. MCMC based schemes q Problem: excessive computational costs

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

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

  23. Bayes net ODE model

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

  25. UAI 1994

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

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

  28. Uncertainty about the best network structure Limited 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. Sampling with MCMC Number of structures Number of nodes

  33. UAI 1994

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

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

  36. Homogeneity assumption Parameters don’t change with time

  37. Homogeneity assumption Parameters don’t change with time

  38. Limitations of the homogeneity assumption

  39. Overview • Introduction • Methodology • Circadian regulation in Arabidopsis • Application to synthetic biology • DREAM

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

  41. Example: 4 genes, 10 time points

  42. Standard dynamic Bayesian network: homogeneous model

  43. Limitations of the homogeneity assumption

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

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

  46. Extension of the model q

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

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

  49. Non-homogeneous model  Non-linear model

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