Hindawi Publishing Corporation EURASIP Journal on Bioinformatics and Systems Biology Volume 2009, Article ID 195272, 8 pages doi:10.1155/2009/195272 Research Article A Bayesian Network View on Nested Effects Models Cordula Zeller, 1 Holger Fr¨ ohlich, 2 and Achim Tresch 3 1 Department of Mathematics, Johannes Gutenberg University, 55099 Mainz, Germany 2 Division of Molecular Genome Analysis, German Cancer Research Center, 69120 Heidelberg, Germany 3 Gene Center, Ludwig Maximilians University, 81377 Munich, Germany Correspondence should be addressed to Achim Tresch, tresch@lmb.uni-muenchen.de Received 27 June 2008; Revised 23 September 2008; Accepted 24 October 2008 Recommended by Dirk Repsilber Nested effects models (NEMs) are a class of probabilistic models that were designed to reconstruct a hidden signalling structure from a large set of observable effects caused by active interventions into the signalling pathway. We give a more flexible formulation of NEMs in the language of Bayesian networks. Our framework constitutes a natural generalization of the original NEM model, since it explicitly states the assumptions that are tacitly underlying the original version. Our approach gives rise to new learning methods for NEMs, which have been implemented in the R/Bioconductor package nem. We validate these methods in a simulation study and apply them to a synthetic lethality dataset in yeast. Copyright © 2009 Cordula Zeller et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction Nested effects models (NEMs) are a class of probabilis- tic models. They aim to reconstruct a hidden signalling structure (e.g., a gene regulatory system) by the analysis of high-dimensional phenotypes (e.g., gene expression profiles) which are consequences of well-defined perturbations of the system (e.g., RNA interference). NEMs have been introduced by Markowetz et al. [1], and they have been extended by Fr¨ ohlich et al. [2] and Tresch and Markowetz [3], see also the review of Markowetz and Spang [4]. There is an open- source software package “nem” available on the platform R/Bioconductor [5, 13], which implements a collection of methods for learning NEMs from experimental data. The utility of NEMs has been shown in several biological applica- tions (Drosophila melanogaster [1], Saccharomyces cerevisiae [6], estrogen receptor pathway, [7]). The model in its original formulation suffers from some ad hoc restrictions which seemingly are only imposed for the sake of computability. The present paper gives an NEM formulation in the con- text of Bayesian networks (BNs). Doing so, we provide a motivation for these restrictions by explicitly stating prior assumptions that are inherent to the original formulation. This leads to a natural and meaningful generalization of the NEM model. The paper is organized as follows. Section 2 briefly recalls the original formulation of NEMs. Section 3 defines NEMs as a special instance of Bayesian networks. In Section 4, we show that this definition is equivalent to the original one if we impose suitable structural constraints. Section 5 exploits the BN framework to shed light onto the learning problem for NEMs. We propose a new approach to parameter learning, and we introduce structure priors that lead to the classical NEM as a limit case. In Section 6, a simulation study compares the performance of our approach to other implementations. Section 7 provides an application of NEMs to synthetic lethality data. In Section 8, we conclude with an outlook on further issues in NEM learning. 2. The Classical Formulation of Nested Effects Models For the sake of self-containedness, we briefly recall the idea and the original definition of NEMs, as given in [3]. NEMs are models that primarily intend to establish causal relations between a set of binary variables, the signals S. The signals are not observed directly rather than through their consequences on another set of binary variables, the effects E . A variable assuming the value 1, respectively, 0 is called active, respectively, inactive. NEMs deterministically