Probabilistic Models that uncover the hidden Information Flow in Signalling Networks Achim Tresch

-2- A model that explains the data merely finds associations E.g.: Epidemiology (predict colon cancer risk from SNPs) Which model? A model that explains the mechanism finds explanations E.g.: Physics, Systems Biology (predict the signal flow through a cascade of transcription factors)

-3- Which model? ? Our choice: Graphical Models nodes correspond to physical entities, arrows correspond to interactions Need for inter- ventional data Two different types of nodes: Observable components Perturbed components (signals) 1 st Idea

-4- How do marionettes walk?

-5- How do marionettes walk? This is what we observeThis is the true model ? Both models explain the observations perfectly. What makes the right model (biologically) more plausible?

-6- How do marionettes walk? This is what we observeThis is the true model ? Both models explain the observations perfectly. What makes a model (biologically) more plausible? Signal transmission is expensive! Find a consistent model with a most parsimonious effects graph Signals, Signal graph Γ Observables, Effects graph Θ 2 nd Idea

-7- Signal graph, Adjacency matrix Γ= (with 1´s in the diagonal) Effects graph, Adjacency matrix Θ = Signals Predicted effects F t Observables Parsimony Assumption: Each observable is linked to exactly one action Definition [Markowetz, Bioinformatics 2005]: A Nested Effects Model (NEM) is a model F for which F = Γ Θ Nested Effects Models

-8- Signals Predicted effects F t Observables Nested Effects Models Why „nested“ ? If the signal graph is transitively closed, then the observed effects are nested in the sense that a → b implies effects(a)  effects(b) The present formulation of a NEM drops the transitivity requirement. █  █  █ Predicted effects

-9- s a Signals Observables Effect of signal s on observable a R a,s Predicted effects = F t Measured effects = R t Nested Effects Models The final ingredient: A quantification of the measured effect strength R a,s > 0 if the data favours an effect of s on a

-10- Assuming independent data, it follows that Note: Missing data is handeled easily: set R s,a = 0 Nested Effects Models

-11- NEM Estimation There are two ways of finding a high scoring NEM: Maximum Likelihood: Bayesian, posterior mode: For n≤5 signals, an exhaustive parameter space search is possible. For larger n, apply standard optimization strategies: Gradient ascent, Simulated annealing or heuristics tailored to NEMs: Module networks [Fröhlich et al., BMC Bioinformatics 2007], Triplet search [Markowetz at al., Bioinformatics 2007] Theorem (Tresch, SAGeMB 2008): For ideal data, is unique up to reversals (Corollary: if Γ is a DAG).

-12- True graphs Γ,Θ simulated measure- ments (R) ideal measure- ments (ΓΘ) R/Bioconductor package: Nessy Simulation

-13- True graphEstimated graph Distribution of the likelihoods 12 edges, 2 12 =4096 signal graphs, ~ 4seconds Simulation

-14- a b Hypotheses: SL between two genes occurs if the genes are located in different pathways Genes sharing the same synthetic lethality partners have an increased chance of being located in the same pathway [Ye, Bader et al., Mol.Systems Biology 2005] Pathway I Pathway II Pathway I Pathway II synthetic lethality Consequence: A gene b whose SL partners are nested into the SL partners of another gene a is likely to be located beneath a in the same pathway. Application: Synthetic Lethality

-15- Application: Synthetic Lethality Pan et al., Cell 2006

-16- Application: Synthetic Lethality 7 of 10 Genes directly linked to DNA repair Tresch, unpublished

-17- References: Structure Learning in Nested Effects Models. A. Tresch, F. Markowetz, to appear in SAGeMB 2008, avaliable on the ArXive Nested Effects Models as a Means to learn Signaling Networks from Intervention Effects. H. Fröhlich, A. Tresch, F. Markowetz, M. Fellmann, R. Spang, T. Beissbarth, in preparation Computational identification of cellular networks and pathways F. Markowetz, Olga G. Troyanskaya, Dennis Kostka, Rainer Spang. Molecular BioSystems, Bioinformatics 2007 Non-transcriptional Pathway Features Reconstructed from Secondary Effects of RNA Interference. F. Markowetz, J. Bloch, R. Spang, Bioinformatics 2005 R/Bioconductor packages: NEM (Markowetz, Fröhlich, Beissbarth) Nessy (Tresch) Software, References

-18- Research & Teaching Activities Research related to the theory of NEMs Integration of multiple data sources Time-dependent NEMs Allow for arbitrary signalling model Teaching Lectures & Exercises in Bioinformatics, Machine Learning, Statistics for Physicians, Group Theory, Microarray Analysis E-learning Core Group of the Faculty Bachelor-/Master- and PhD theses Other Research Topics Software for data acquisition, -processing & -visualization for high-density technologies Design and analysis of biological/clinical experiments, consulting

-19- Florian Markowetz Lewis-Sigler Institute, Princeton Tim Beissbarth, Holger Fröhlich German Cancer Research Center, Heidelberg Rainer Spang Computational Diagnostics Group, Regensburg Acknowledgements

-20- Thank You! Conclusion Exercise: Why is this administration model inefficient? Construct a model that scores better!

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-22- What I did not show … Automatic Feature Selection, without Control experiment: Estimated graph (120 genes selected)

-23- The „observed“ graph of the Fellmann estrogen receptor dataset What I did not show …

Genes 17 Knockdown Experiments 6 of them double Knockdowns What I did not show …

-25- Same Data, With prior knowledge. What I did not show …