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## Reverse engineering gene regulatory networks

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**Reverse engineering gene regulatory networks**Dirk Husmeier Adriano Werhli Marco Grzegorczyk**Systems biology**Learning signalling pathways and regulatory networks from postgenomic data**unknown**high-throughput experiments postgenomic data**unknown**data data machine learning statistical methods**extracted network**true network Does the extracted network provide a good prediction of the true interactions?**Reverse Engineering of Regulatory Networks**• Can we learn the network structure from postgenomic data themselves? • Statistical methods to distinguish between • Direct interactions • Indirect interactions • Challenge: Distinguish between • Correlations • Causal interactions • Breaking symmetries with active interventions: • Gene knockouts (VIGs, RNAi)**direct**interaction common regulator indirect interaction co-regulation**Relevance networks**• Graphical Gaussian models • Bayesian networks**Relevance networks**• Graphical Gaussian models • Bayesian networks**Relevance networks(Butte and Kohane, 2000)**• Choose a measure of association A(.,.) • Define a threshold value tA • For all pairs of domain variables (X,Y) compute their association A(X,Y) 4. Connect those variables (X,Y) by an undirected edge whose association A(X,Y) exceeds the predefined threshold value tA**1**2 ‘direct interaction’ X 1 2 1 2 X X ‘common regulator’ 1 1 2 2 ‘indirect interaction’ strong correlation σ12**Pairwise associations without taking the context of the**system into consideration**Relevance networks**• Graphical Gaussian models • Bayesian networks**1**2 direct interaction 1 2 Graphical Gaussian Models strong partial correlation π12 Partial correlation, i.e. correlation conditional on all other domain variables Corr(X1,X2|X3,…,Xn)**Distinguish between direct and indirect interactions**direct interaction common regulator indirect interaction co-regulation A and B have a low partial correlation**1**2 direct interaction 1 2 Graphical Gaussian Models strong partial correlation π12 Partial correlation, i.e. correlation conditional on all other domain variables Corr(X1,X2|X3,…,Xn) Problem: #observations < #variables**Graphical Gaussian Models**direct interaction common regulator indirect interaction P(A,B)=P(A)·P(B) But: P(A,B|C)≠P(A|C)·P(B|C)**Undirected versus directed edges**• Relevance networks and Graphical Gaussian models can only extract undirected edges. • Bayesian networks can extract directed edges. • But can we trust in these edge directions? It may be better to learn undirected edges than learning directed edges with false orientations.**Relevance networks**• Graphical Gaussian models • Bayesian networks**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**Bayesian networks versus causal networks**Bayesian networks represent conditional (in)dependence relations - not necessarily causal interactions.**Node A unknown**A A True causal graph B C B C Bayesian networks versus causal networks**Bayesian networks versus causal networks**A A A B C B C B C • Equivalence classes: networks with the same scores: P(D|M). • Equivalent networks cannot be distinguished in light of the data. A B C**A**C B Equivalence classes of BNs A C B A C A B P(A,B)≠P(A)·P(B) P(A,B|C)=P(A|C)·P(B|C) C B A C completed partially directed graphs (CPDAGs) B v-structure A P(A,B)=P(A)·P(B) P(A,B|C)≠P(A|C)·P(B|C) C B**Symmetry breaking**A A A B C B C B C A • Interventions • Priorknowledge B C**Symmetry breaking**A A A B C B C B C A • Interventions • Priorknowledge B C**Interventional data**A and B are correlated A B inhibition of A A B A B A B down-regulation of B no effect on B**Learning Bayesian networks from data**P(M|D) = P(D|M) P(M) / Z M: Network structure. D: Data**Learning Bayesian networks from data**P(M|D) = P(D|M) P(M) / Z M: Network structure. D: Data**Evaluation**• On real experimental data, using the gold standard network from the literature • On synthetic data simulated from the gold-standard network**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**Raf regulatory network**From Sachs et al Science 2005**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