For each HGNC symbol, we calculated a model based on mean and standard deviation of the gene expression level, and computed the z-score as average number of standard deviations that the expression level in the perturbed array was shifted from the basal arrays. We then performed LOESS smoothing for all z-scores in a given experiment using our null model, as described previously 12.
From the z-scores of all experiments and all pathways, we performed a multiple linear regression with the pathway as input and the z-scores as response variable for each gene separately:
Zg ~ M ... g
Where Zg is the z-score for a given gene g across all input experiments (as a column vector of experiments). M is a coefficients matrix (rows are experiments, columns pathways, Fig. 1b) that has the coefficient 1 if the the experiment had a pathway activated, -1 if inhibited, and 0 otherwise. For instance, the Hypoxia pathway had experiments with low oxygen conditions set as 1, HIF1A knockdown as -1, and all other experiments as 0. The same is true for EGFR and EGF treatment vs. EGFR inhibitors respectively, with the additional coefficients of MAPK and PI3K pathways set to 1 because of known cross-talk (for a full structure of the cross-talk modeled, see Fig. 1c). As these are fold changes, we do not allow an intercept.
From the result of the linear model, we selected the top 100 genes per pathway according to their p-value and took their estimate (the fitted z-scores) as coefficient. We set all other gene coefficients to 0, so this yielded a matrix with HGNC symbols in rows and pathways in columns, where each pathway had 100 non-zero gene coefficients (Supplementary Table 9).