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

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Presentation on theme: "Probabilistic modelling in computational biology Dirk Husmeier Biomathematics & Statistics Scotland."— Presentation transcript:

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

2 James Watson & Francis Crick, 1953

3 Frederick Sanger, 1980

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7 Network reconstruction from postgenomic data

8 Model Parameters q

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

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 Feature extraction, e.g. marginal posterior probabilities of the edges High-confident edge High-confident non-edge Uncertainty about edges

18 Number of structures Number of nodes Sampling with MCMC

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

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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 t1t1 t2t2 t3t3 t4t4 t5t5 t6t6 t7t7 t8t8 t9t9 t 10 X (1) X 1,1 X 1,2 X 1,3 X 1,4 X 1,5 X 1,6 X 1,7 X 1,8 X 1,9 X 1,10 X (2) X 2,1 X 2,2 X 2,3 X 2,4 X 2,5 X 2,6 X 2,7 X 2,8 X 2,9 X 2,10 X (3) X 3,1 X 3,2 X 3,3 X 3,4 X 3,5 X 3,6 X 3,7 X 3,8 X 3,9 X 3,10 X (4) X 4,1 X 4,2 X 4,3 X 4,4 X 4,5 X 4,6 X 4,7 X 4,8 X 4,9 X 4,10

25 Supervised learning. Here: 2 components t1t1 t2t2 t3t3 t4t4 t5t5 t6t6 t7t7 t8t8 t9t9 t 10 X (1) X 1,1 X 1,2 X 1,3 X 1,4 X 1,5 X 1,6 X 1,7 X 1,8 X 1,9 X 1,10 X (2) X 2,1 X 2,2 X 2,3 X 2,4 X 2,5 X 2,6 X 2,7 X 2,8 X 2,9 X 2,10 X (3) X 3,1 X 3,2 X 3,3 X 3,4 X 3,5 X 3,6 X 3,7 X 3,8 X 3,9 X 3,10 X (4) X 4,1 X 4,2 X 4,3 X 4,4 X 4,5 X 4,6 X 4,7 X 4,8 X 4,9 X 4,10

26 Changepoint model Parameters can change with time

27 Changepoint model Parameters can change with time

28 t1t1 t2t2 t3t3 t4t4 t5t5 t6t6 t7t7 t8t8 t9t9 t 10 X (1) X 1,1 X 1,2 X 1,3 X 1,4 X 1,5 X 1,6 X 1,7 X 1,8 X 1,9 X 1,10 X (2) X 2,1 X 2,2 X 2,3 X 2,4 X 2,5 X 2,6 X 2,7 X 2,8 X 2,9 X 2,10 X (3) X 3,1 X 3,2 X 3,3 X 3,4 X 3,5 X 3,6 X 3,7 X 3,8 X 3,9 X 3,10 X (4) X 4,1 X 4,2 X 4,3 X 4,4 X 4,5 X 4,6 X 4,7 X 4,8 X 4,9 X 4,10 Unsupervised learning. Here: 3 components

29 Extension of the model q

30 q

31 q k h Number of components (here: 3) Allocation vector

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

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

35 Dynamic programming, complexity N 2

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37 Collaboration with the Institute of Molecular Plant Sciences at Edinburgh University (Andrew Millar’s group) - 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 Circadian rhythms in Arabidopsis thaliana

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

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

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

42 True positives (TP) = 8 False positives (FP) = 13 False negatives (FN) = 5 True negatives (TN) = 9² = 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 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

51 NIPS 2010

52 Overview Introduction Limitations Methodology Application to morphogenesis Application to synthetic biology

53 Morphogenesis in Drosophila melanogaster Gene expression measurements at 66 time points during the life cycle of Drosophila (Arbeitman et al., Science, 2002). Selection of 11 genes involved in muscle development. Zhao et al. (2006), Bioinformatics 22

54 Can we learn the morphogenetic transitions: embryo  larva larva  pupa pupa  adult ?

55 Average posterior probabilities of transitions Morphogenetic transitions: Embryo  larva larva  pupa pupa  adult

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57 Can we learn changes in the regulatory network structure ?

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59 Overview Introduction Limitations Methodology Application to morphogenesis Application to synthetic biology

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62 Can we learn the switch Galactose  Glucose? Can we learn the network structure?

63 Task 1: Changepoint detection Switch of the carbon source: Galactose  Glucose

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65 Task 2: Network reconstruction Precision Proportion of identified interactions that are correct Recall Proportion of true interactions that we successfully recovered

66 BANJO: Conventional homogeneous DBN TSNI: Method based on differential equations Inference: optimization, “best” network

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68 Sample of high-scoring networks

69 Marginal posterior probabilities of the edges P=1 P=0 P=0.5

70 P=1 True network Thresh0.9 Prec1 Recall1/2 Precision Recall

71 P=1 P=0.5 True network Thresh Prec12/3 Recall1/21 Precision Recall

72 P=1 P=0 P=0.5 True network Thresh Prec12/31/2 Recall1/211 Precision Recall

73

74 Future work

75 How are we getting from here …

76 … to there ?!

77 Input: Learn: MCMC Prior knowledge


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