Figure 1.
Predicting Pair-wise Interaction Using Quantitative Nested Effects.
(A) Hypothetical example with four S-genes, A, B, C, and D. The graph contains one inhibitory link, B⊣D (left). A heatmap of E-gene expression under knockdown of each S-gene shows both inhibitory and stimulatory effects (middle). Scatter plots of the C, A, B, and D knock-outs show that expression fits in the shaded preferred regions of each interaction (right). The inhibitory link explains some of the “observed” data: expression changes under ΔD (bright red or bright green entries in the heatmap) occur in a subset of the E-genes for which the opposite changes occur in ΔB. (B) Data from a known inhibitory interaction. Expression levels of effect genes under the DIG1/DIG2 knock-out (y-axis) plotted against their levels under the STE2 knock-out (x-axis) as detected in [17]. Expression changes significant at α = 0.05 indicated in gray lines. DIG1/DIG2 is known to inhibit STE12. (C) Interaction modes. Observed E-gene expression changes are compared to five possible types of interactions between two S-genes, A and B (i–v). The top row illustrates the expected nested effects relationship for each type of interaction mode: circles represent sets of E-genes with expression changes consistent with either activation (blue circles) or inhibition (yellow circles). Scatter-plots for each interaction mode show the hypothetical expression changes under ΔA (x-axis) and ΔB (y-axis) for all E-genes (circles). E-gene levels are either consistent (filled) or inconsistent (open) with the mode. Shaded regions demark expression levels consistent with each interaction model. The example shows expression changes that most closely match the inhibition mode (indicated by the greatest number of closed circles).
Figure 2.
Structure of the factor graph for network inference.
The factor graph consists of three classes of variables (circles) and three classes of factors (squares). XeAr is a continuous observation of E-gene e's expression under ΔA and replicate r. YeA is the hidden state of E-gene e under ΔA, and is a discrete variable with domain {up, ∅, down}. φAB is the interaction between two S-genes A and B. Expression Factors model expression as a mixture of Gaussian distributions. Interaction Factors constrain E-gene states to the allowed regions shown in Figure 1C. Transitivity Factors constrain pair-wise interactions to form consistent triangles. The arrows labeled μ and μ′ are messages encoding local belief potentials on φAB and are propagated during factor graph inference.
Figure 3.
Accuracy of artificial network recovery and expansion.
(A) Influence of inhibition on network recovery. AUC (y-axis) plotted as a function of the percent of inhibitory links (x-axis). Four replicate hybridizations were used in all simulations. Points and error bars represent means and standard deviations computed across 500 synthetically generated networks respectively. Lines in each plot represent the performance of FG-NEM (red) and uFG-NEM run on the original data (green) or on AVT data (blue) for both structure recovery (solid lines) and sign recovery (dotted lines). (B) Accuracy of FG-NEM network expansion compared to Template Matching. The percentile of an S-gene obtained from Template Matching was subtracted from the percentile of the LAR score (see Methods) assigned by FG-NEM and uFG-NEM obtained from the leave-one-out expansion test. A smoothed histogram for FG-NEM (red), uFG-NEM run on the original data (green) and the AVT data (blue) was plotted and shows the proportion of S-genes (y-axis) with a particular difference in method percentile (x-axis). The underlying simulated network had 32 S-genes, eight S-genes were used for network recovery, and twenty E-genes were attached to each S-gene.
Figure 4.
Yeast knock-out compendium predictions.
(A) Precision/recall comparison. Each method's ability to expand a pathway was compared. Thick lines indicate mean precision and shaded regions represent standard error of mean calculated over the networks with the five highest AUCS from any of the tested methods. (B) Network expansion comparison. Networks were predicted for a non-redundant set of GO categories containing four or more S-genes in the Hughes et al. (2000) compendium and used to predict held-out genes from the same category (see Methods). The area under the curve (AUC) for each pathway was calculated for each method. AUC ratios (y-axis) were calculated for each method relative to the lowest AUC. (C) Compatibility of physical evidence and predicted S-gene interactions. Each point is the margin of compatibility (MOC, see Methods) of a predicted genetic interaction to high-throughput physical interaction data when physical interaction evidence was used (y-axis) and when it was not used (x-axis). Coloring indicates two-dimensional density estimation of points. Inset shows detail of the highest density region. Prediction methods that are significantly better than the lowest performing method, excluding random, at the 0.05 level (*) and 0.01 level (**) were determined by a proportions test on the top 30 predictions from each method. (D) Predicted S-gene networks for the ion homeostasis pathway. Shown are predicted networks from the FG-NEM method (Signed) and the uFG-NEM method (Unsigned). Arrows indicate activating interactions and tees indicate inhibiting interactions. The absence of a link between a pair of S-genes indicates the most likely mode for the pair was the non-interaction mode. Equivalence interactions are indicated with double lines and S-genes connected by equivalence are grouped into dashed ovals.
Figure 5.
Invasive colon cancer network predictions.
(A) Expression changes of selected E-genes following targeted S-gene knock-downs in HT29 colon cancer cells. Gene expression was measured in HT29 cells treated with a shRNA specifically targeting an S-gene (column of the matrix) relative to cells treated with a scrambled control shRNA (Irby et al., 2005). Colors indicate putatively inhibited E-genes (rows of the matrix) with up-regulated levels relative to control (red), activated E-genes with down-regulated levels relative to control (green), and unaffected E-genes with expression levels not significantly different from control (black). Biological replicates were available for KRT20, TFDP1, and GLS knock-downs. Genes were sorted by their attachment point and then by their LAR scores. (B) Cancer invasion network predicted by FG-NEM. For each pair of S-genes, the most likely interaction mode is shown. The same conventions used for illustrating interactions predicted for the yeast networks were used here. Some interactions were found to be significant at the 0.05 level (*) or 0.01 level (**) using a permutation test (see Methods). KRT20 and RPL32 were predicted to be equivalent and are therefore grouped together in a dashed oval. (C) Matrigel invasion assay in HT29 colon cancer cells. Genes predicted to be significantly attached to the network, CAPN12 and expressed sequence tag AA099748, resulted in a loss of the invasiveness phenotype when knocked-down by RNA interference. Genes not significantly attached to the network, MYO1G, BMPR1A, and COLEC12, did not result in significant loss of the invasive phenotype. A scrambled non-sense sequence also served as a negative control and did not result in a loss of HT29 cell invasiveness. Gene knock-downs in HT29 cells were validated by quantitative real time RT-PCR where mRNA levels of targeted genes were decreased by 70–80% compared to scrambled control shRNA-treated cells (data not shown). Data shown are the mean±S.E. of five independent experiments performed in quadruplicate. *Significantly different from scrambled control shRNA-treated cells (P<0.05) by ANOVA and post hoc Tukey test.
Table 1.
Top frontier genes for colon cancer invasiveness ranked by LAR score (see Methods) and filtered for significance as determined by data permutation test (see Methods).