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

Siebourg-Polster J, Mudrak D, Emmenlauer M, Rämö P, Dehio C, Greber U, Fröhlich H, Beerenwinkel N - PLoS Comput. Biol. (2015)

Bottom Line: Nested effects models have been used successfully for learning subcellular networks from high-dimensional perturbation effects that result from RNA interference (RNAi) experiments.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.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland; SIB Swiss Institute of Bioinformatics, Basel, Switzerland.

ABSTRACT
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.

No MeSH data available.


Related in: MedlinePlus

NEM versus NEMix.A schematic example is shown comparing the classical nested effects model (NEM; panel A) with the new nested effects mixture model (NEMix; panel B) on six features observed in 15 individual cells. Blue nodes in the graph depict the signaling genes S1, S2, and S3 that have been silenced and whose dependency structure is sought. The observed features E1, …, E6 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 A and B), the pathway has been activated via S2, whereas in cells 3, 4, and 5 (right in both A and B) it has remained inactivated. In the latter case, the effects of silencing S2 are masked and the resulting silencing scheme then differs from the one where the pathway is stimulated. Classic NEMs (A) 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), both observed patterns can be explained by the same signaling graph Φ, because the hidden pathway stimulation Z (shown in red) is modeled explicitly. In the NEMix model, Z is a hidden binary random variable indicating pathway activation (Z = 1), which occurs with probability P(Z = 1) = p1.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4400057&req=5

pcbi.1004078.g001: NEM versus NEMix.A schematic example is shown comparing the classical nested effects model (NEM; panel A) with the new nested effects mixture model (NEMix; panel B) on six features observed in 15 individual cells. Blue nodes in the graph depict the signaling genes S1, S2, and S3 that have been silenced and whose dependency structure is sought. The observed features E1, …, E6 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 A and B), the pathway has been activated via S2, whereas in cells 3, 4, and 5 (right in both A and B) it has remained inactivated. In the latter case, the effects of silencing S2 are masked and the resulting silencing scheme then differs from the one where the pathway is stimulated. Classic NEMs (A) 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), both observed patterns can be explained by the same signaling graph Φ, because the hidden pathway stimulation Z (shown in red) is modeled explicitly. In the NEMix model, Z is a hidden binary random variable indicating pathway activation (Z = 1), which occurs with probability P(Z = 1) = p1.

Mentions: We developed NEMix, a new model based on NEMs, which allows to estimate activity of a pathway in individual cells. A NEM is a graphical model, consisting of two graphs. The transitively closed graph Φ encodes dependencies among signaling gene nodes Ss ∊ 𝓢, which are silenced one by one. The bipartite graph Θ connects a set of observable feature nodes Ee ∊ 𝓔 uniquely to the signaling genes (Fig. 1A). We seek the structure of Φ, i.e., the topology of the signaling pathway, by inferring it from the nested structure of observed effects. For a data set 𝒟 = (dek) of a set of knock-down experiments k ∊ {1, …, K} and observed features e ∊ {1, …, m}, the likelihood function given Φ and θ isP(𝒟∣Φ,θ)=∏e=1m∏k=1KP(dek∣Φ,θe=s),(1)where θe = s indicates that feature e is connected to signaling gene s ∊ 𝓢.


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

Siebourg-Polster J, Mudrak D, Emmenlauer M, Rämö P, Dehio C, Greber U, Fröhlich H, Beerenwinkel N - PLoS Comput. Biol. (2015)

NEM versus NEMix.A schematic example is shown comparing the classical nested effects model (NEM; panel A) with the new nested effects mixture model (NEMix; panel B) on six features observed in 15 individual cells. Blue nodes in the graph depict the signaling genes S1, S2, and S3 that have been silenced and whose dependency structure is sought. The observed features E1, …, E6 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 A and B), the pathway has been activated via S2, whereas in cells 3, 4, and 5 (right in both A and B) it has remained inactivated. In the latter case, the effects of silencing S2 are masked and the resulting silencing scheme then differs from the one where the pathway is stimulated. Classic NEMs (A) 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), both observed patterns can be explained by the same signaling graph Φ, because the hidden pathway stimulation Z (shown in red) is modeled explicitly. In the NEMix model, Z is a hidden binary random variable indicating pathway activation (Z = 1), which occurs with probability P(Z = 1) = p1.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4400057&req=5

pcbi.1004078.g001: NEM versus NEMix.A schematic example is shown comparing the classical nested effects model (NEM; panel A) with the new nested effects mixture model (NEMix; panel B) on six features observed in 15 individual cells. Blue nodes in the graph depict the signaling genes S1, S2, and S3 that have been silenced and whose dependency structure is sought. The observed features E1, …, E6 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 A and B), the pathway has been activated via S2, whereas in cells 3, 4, and 5 (right in both A and B) it has remained inactivated. In the latter case, the effects of silencing S2 are masked and the resulting silencing scheme then differs from the one where the pathway is stimulated. Classic NEMs (A) 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), both observed patterns can be explained by the same signaling graph Φ, because the hidden pathway stimulation Z (shown in red) is modeled explicitly. In the NEMix model, Z is a hidden binary random variable indicating pathway activation (Z = 1), which occurs with probability P(Z = 1) = p1.
Mentions: We developed NEMix, a new model based on NEMs, which allows to estimate activity of a pathway in individual cells. A NEM is a graphical model, consisting of two graphs. The transitively closed graph Φ encodes dependencies among signaling gene nodes Ss ∊ 𝓢, which are silenced one by one. The bipartite graph Θ connects a set of observable feature nodes Ee ∊ 𝓔 uniquely to the signaling genes (Fig. 1A). We seek the structure of Φ, i.e., the topology of the signaling pathway, by inferring it from the nested structure of observed effects. For a data set 𝒟 = (dek) of a set of knock-down experiments k ∊ {1, …, K} and observed features e ∊ {1, …, m}, the likelihood function given Φ and θ isP(𝒟∣Φ,θ)=∏e=1m∏k=1KP(dek∣Φ,θe=s),(1)where θe = s indicates that feature e is connected to signaling gene s ∊ 𝓢.

Bottom Line: Nested effects models have been used successfully for learning subcellular networks from high-dimensional perturbation effects that result from RNA interference (RNAi) experiments.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.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland; SIB Swiss Institute of Bioinformatics, Basel, Switzerland.

ABSTRACT
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.

No MeSH data available.


Related in: MedlinePlus