Reverse engineering of regulatory networks Dirk Husmeier & Adriano Werhli

Systems biology Learning signalling pathways and regulatory networks from postgenomic data

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)

Shrinkage estimation and the lemma of Ledoit-Wolf

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

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

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

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

Two types of experiments

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

Comparison with simulated data 1

Raf pathway

Comparison with simulated data 2

Steady-state approximation

Evaluation 1: AUC scores

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).

AUC scores

TP scores

Raf pathway

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.

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

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

MOTIVATION

Use TF binding motifs in promoter sequences

Use prior knowledge from KEGG

Prior knowledge

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

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

Prior distribution over networks Energy of a network

Rewriting the energy Energy of a network

Approximation of the partition function

Multiple sources of prior knowledge

Rewriting the energy Energy of a network

Approximation of the partition function

MCMC sampling scheme

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

Metropolis-Hastings scheme

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.

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.

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.

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.

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.

Approximation of the partition function

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.

Application to real data

Flow cytometry data and KEGG

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

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

Flow cytometry data and KEGG

Prior distribution

Sampled values of the hyperparameters

Idealized network population

Sampled values of the hyperparameters

Performance evaluation: AUC scores

Flow cytometry data and KEGG

Comparison: AUC for fixed and sampled hyperparameters on real data

Comparison: AUC for fixed and sampled hyperparameters on synthetic data

Future work

Thank you