NEMix: single-cell nested effects models for probabilistic pathway stimulation

Nested effects models have been used successfully for learning subcellular networks from high-dimensional perturbation effects that result from RNA interference (RNAi) experiments. Here, we further develop the basic nested effects model using high-content single-cell imaging data from RNAi screens of cultured cells infected with human rhinovirus. RNAi screens with single-cell readouts are becoming increasingly common, and they often reveal high cell-to-cell variation. As a consequence of this cellular heterogeneity, knock-downs result in variable effects among cells and lead to weak average phenotypes on the cell population level. To address this confounding factor in network inference, we explicitly model the stimulation status of a signaling pathway in individual cells. We extend the framework of nested effects models to probabilistic combinatorial knock-downs and propose NEMix, a nested effects mixture model that accounts for unobserved pathway activation. We analyzed the identifiability of NEMix and developed a parameter inference scheme based on the Expectation Maximization algorithm. In an extensive simulation study, we show that NEMix improves learning of pathway structures over classical NEMs significantly in the presence of hidden pathway stimulation. We applied our model to single-cell imaging data from RNAi screens monitoring human rhinovirus infection, where limited infection efficiency of the assay results in uncertain pathway stimulation. Using a subset of genes with known interactions, we show that the inferred NEMix network has high accuracy and outperforms the classical nested effects model without hidden pathway activity. NEMix is implemented as part of the R/Bioconductor package 'nem' and available at www.cbg.ethz.ch/software/NEMix

Inferred MAPK networks on HRV infection data.

<p>Best networks of the 5 top scoring siRNAs from the MAPK pathway for HRV infection for the different compared methods are displayed. (A) shows the known KEGG pathway. (B) is the inferred NEM and (C) the sc-NEM. (D) left shows the known network with the most likely attachment of the hidden variable <i>Z</i> (blue) and (E) is the inferred NEMix. For all networks their performance is summarized in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004078#pcbi.1004078.t001" target="_blank">Table 1</a>. Subfigure (F) summarizes robustness of the MAPK network inference. For the inferred MAPK signaling networks on the HRV infection data, we assessed robustness of the accuracy for edge recovery. Box-plots display the result of 50 bootstrap samples for the three compared methods, on the 5 gene (<i>n</i> = 5) and 8 gene (<i>n</i> = 8) network.</p

Performance summary of the 5 gene MAPK network.

<p>The first column gives the log-likelihood for each model, showing that the true network is much less likely than the inferred networks. The second and third column show performance of the networks in terms of accuracy (ACC) and area under curve (AUC). The inferred <i>p</i>₀ for the NEMix models is displayed in column four. Column five indicates the corresponding sub-figure of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004078#pcbi.1004078.g003" target="_blank">Fig. 3</a>. The network ‘KEGG Graph + Z’ denotes the structure of the known KEGG network, where only the position of <i>Z, p</i>₀, and <i>θ</i> are inferred.</p><p>Performance summary of the 5 gene MAPK network.</p

NEM versus NEMix.

<p>A schematic example is shown comparing the classical nested effects model (NEM; panel <b>A</b>) with the new nested effects mixture model (NEMix; panel <b>B</b>) on six features observed in 15 individual cells. Blue nodes in the graph depict the signaling genes <i>S</i>₁, <i>S</i>₂, and <i>S</i>₃ that have been silenced and whose dependency structure is sought. The observed features <i>E</i>₁, …, <i>E</i>₆ are shown in green. Each box below the graphs indicates the observed (noisy) features (e.g., image-based read-outs) for a single cell. Within each box, dark entries indicate an effect of the knock-down on the feature, light entries indicate no effect. In cells 1 and 2 (left in both <b>A</b> and <b>B</b>), the pathway has been activated via <i>S</i>₂, whereas in cells 3, 4, and 5 (right in both <b>A</b> and <b>B</b>) it has remained inactivated. In the latter case, the effects of silencing <i>S</i>₂ are masked and the resulting silencing scheme then differs from the one where the pathway is stimulated. Classic NEMs (<b>A</b>) could explain such a heterogeneous cell population only by two different signaling graphs Φ. By contrast, with the NEMix model proposed in this work (<b>B</b>), both observed patterns can be explained by the same signaling graph Φ, because the hidden pathway stimulation <i>Z</i> (shown in red) is modeled explicitly. In the NEMix model, <i>Z</i> is a hidden binary random variable indicating pathway activation (<i>Z</i> = 1), which occurs with probability <i>P</i>(<i>Z</i> = 1) = <i>p</i>₁.</p

Simultaneous analysis of large-scale RNAi screens for pathogen entry

Large-scale RNAi screening has become an important technology for identifying genes involved in biological processes of interest. However, the quality of large-scale RNAi screening is often deteriorated by off-targets effects. In order to find statistically significant effector genes for pathogen entry, we systematically analyzed entry pathways in human host cells for eight pathogens using image-based kinome-wide siRNA screens with siRNAs from three vendors. We propose a Parallel Mixed Model (PMM) approach that simultaneously analyzes several non-identical screens performed with the same RNAi libraries.; We show that PMM gains statistical power for hit detection due to parallel screening. PMM allows incorporating siRNA weights that can be assigned according to available information on RNAi quality. Moreover, PMM is able to estimate a sharedness score that can be used to focus follow-up efforts on generic or specific gene regulators. By fitting a PMM model to our data, we found several novel hit genes for most of the pathogens studied.; Our results show parallel RNAi screening can improve the results of individual screens. This is currently particularly interesting when large-scale parallel datasets are becoming more and more publicly available. Our comprehensive siRNA dataset provides a public, freely available resource for further statistical and biological analyses in the high-content, high-throughput siRNA screening field