Analyzing gene perturbation screens with nested effects models in R and bioconductor

Abstract

Summary: Nested effects models (NEMs) are a class of probabilistic models introduced to analyze the effects of gene perturbation screens visible in high-dimensional phenotypes like microarrays or cell morphology. NEMs reverse engineer upstream/downstream relations of cellular signaling cascades. NEMs take as input a set of candidate pathway genes and phenotypic profiles of perturbing these genes. NEMs return a pathway structure explaining the observed perturbation effects. Here, we describe the package nem, an open-source software to efficiently infer NEMs from data. Our software implements several search algorithms for model fitting and is applicable to a wide range of different data types and representations. The methods we present summarize the current state-of-the-art in NEMs.

Availability: Our software is written in the R language and freely avail-able via the Bioconductor project at http://www.bioconductor.org.

Contact: rainer.spang@klinik.uni-regensburg.de

1 INTRODUCTION

The analysis of large-scale and high-dimensional phenotyping screens is moving to the center stage of computational systems biology as more and better experimental systems get established in model organisms. Nested effects models (NEM) are a class of models introduced to analyze the effects of gene perturbation screens visible in high-dimensional phenotypes like microarrays or cell morphology. NEMs achieve two goals: (i) to reveal clusters of genes with highly similar phenotypic profiles and (ii) to order (clusters of) genes according to subset relationships between phenotypes. These subset relationships show which genes contribute to global processes in the cell and which genes are only responsible for sub-processes. The NEM structure helps to understand signal flow and internal organization in a cell.

NEMs offer complementary information to traditional graphical models including correlation graphs, Bayesian networks and Gaussian graphical models (Markowetz and Spang, 2007). Thus, they are relevant for theoretical researchers developing methods in systems biology. In addition, a wide range of applications shows the broad impact of NEMs on both molecular biology and medicine: NEMs were successfully applied to data on immune response in Drosophila melanogaster (Markowetz et al., 2005), to the transcription factor network in Saccharomyces cerevisiae (Markowetz et al., 2007), and to the ER-α pathway in human breast cancer cells (Fröhlich et al., 2007, 2008).

2 NEM IMPLEMENTATION

NEMs are two-layered graph models. The first layer consists of a directed graph containing the genes that were experimentally perturbed. The second layer consists of the effects observed in high-dimensional phenotypes. Each node in the second layer is considered to be a specific reporter for the activity of a single gene in the first layer. Current NEM formulations differ in the constraints they pose on the NEM graph in the first layer and on the probabilistic model they assume for effect nodes in the second layer. All current types of NEMs are implemented in the R package nem, which is available from the Bioconductor project (Gentleman et al., 2004; R Development Core Team, 2007).

NEM formulations and inference: A first NEM formulation restricts the NEM graph to be transitively closed. The probabilistic model for effects is either Bernoulli (Markowetz et al., 2005, 2007) or a mixture distribution (Fröhlich et al., 2007, 2008). A second NEM formulation (Tresch and Markowetz, 2008) relaxes the constraints on the NEM graph and allows graphs that are not transitively closed. For each model formulation, the user can choose between different search methods for model inference. Exhaustive enumeration (Markowetz et al., 2005) is feasible for up to eight perturbed genes. For bigger pathways the package provides greedy search heuristics and divide-and-conquer like approaches that divide the graph into smaller units, use exhaustive enumeration for each subgraph and then reassemble the complete model. The division into subgraphs can either be into all pairs or triples of nodes (Markowetz et al., 2007) or data dependent into coherent modules (Fröhlich et al., 2007, 2008).

Extensions and post-processing: on top of the core functions for model formulation and inference, the package nem also implements a feature selection mechanism to discard uninformative effect reporters (Tresch and Markowetz, 2008). The package allows to test the significance of a NEM compared to a random network and its statistical stability by bootstrap and jackknife methods (Fröhlich et al., 2007, 2008). The package nem contains functions for preprocessing and formatting data. Additional post-processing functions are available to simplify the resulting NEM structure by identifying clusters of indistinguishable nodes and computing the transitive reduction of the NEM graph. The package also includes a method to find a transitive approximation of a heuristic search result (Jacob et al., 2008). The exemplary use of nem on Drosophila immune response data (Boutros et al., 2002) is explained in a vignette accompanying the package.

3 AN EXAMPLE SESSION

First, we reproduce the analysis of Markowetz et al. (2005) on the gene expression data of Boutros et al. (2002). We use a discretization function to estimate effects from the control measurements in the data. Then, we infer a NEM graph from the binarized data using estimated error rates.

The core function of the package is nem(). Its output is a list with components containing the highest scoring NEM graph, the marginal likelihoods of all scored models, as well as the estimated positions of effect reporters in the NEM graph. In this example model, search is done by exhaustive enumeration. Specifying inference as ‘pairwise’ or ‘triple’ uses the search heuristics of Markowetz et al. (2007), while ‘nem.greedy’ and ‘ModuleNetwork’ employ the methods of Fröhlich et al. (2007, 2008). These methods extend model search to hundreds of perturbed genes.

The function nem() is applicable to a wide range of data representations. Instead of discretized data, the user can supply it with log-ratios or P-values for seeing an effect. For the example dataset a matrix of precomputed log-ratios (BoutrosRNAiLods) and P-value densities (BoutrosRNAiDens) is contained in the package. All data representations can be used in a MAP estimate (type=“CONTmLLMAP”) or in a model marginalizing over effect positions (type=“CONTmLLBayes”). Additional feature selection to select only informative effect reporters (selEGenes=TRUE) is implemented for all data types. An example application is visualized in Figure 1 by executing:

Fig. 1.

Example of a NEM. The upper part shows the proposed pathway, with gray lines connecting each pathway member to its specific effects. The lower part depicts the phenotypic profiles by a matrix of log-foldchanges of effect reporters (columns) in each gene perturbation experiment (rows). Both differentially up- (black) and down-regulated (white) genes are counted as effects. The group of genes labeled by ‘null’ were automatically discarded as uninformative. The interpretation of this result is: perturbing tak has global effects indicating a central regulatory position, while perturbing mkk4/hep or rel and key affect sub-pathways which branch off the main pathway.

Funding: National Genome Research Network (NGFN) of the German Federal Ministry of Education and Research (BMBF) through the platforms SMP Bioinformatics (01GR0450 to H.F., A.T. and T.B.) and EP-S19T04 to H.F, A.T. and T.B. National Institutes of Health (grant R01 GM071966); National Science Foundation (NSF) (grant IIS-0513552) (Princeton University); National Institute of General Medical Sciences (NIGMS) Center of Excellence (grant P50 GM071508); NSF (grant DBI-0546275).

Conflict of Interest: none declared.