Each column in the matrix of perturbation-response genes corresponds to a plane in gene expression space, in which each cell line or tumor sample is located. If you follow its normal vector from the origin, the distance it spans corresponds to the pathway score P each sample is assigned (matrix of samples in rows, pathways in columns). In practice, this is achieved by a simple matrix multiplication between the gene expression matrix (samples in rows, genes in columns, values are expression levels) and the model matrix (genes in rows, pathways in columns, values are our top 100 coefficients):
P = E * G
We then scaled each pathway or gene set score to have a mean of zero and standard deviation of one, in order to factor out the difference in strength of gene expression signatures and thus be able to compare the relative scores across pathways and samples at the same time.
We matched our defined set of pathways to the publicly available pathway databases Reactome 16 and KEGG 31, and Gene Ontology (GO) 17 categories (Supplementary Tables 1-2), to obtain a uniform set across pathway resources that makes them comparable. We calculated pathway scores as Gene Set Variation Analysis (GSVA) scores that are able to assign a score to each individual sample (unlike GSEA that compares groups).
Signaling Pathway Impact Analysis (SPIA) 3 is a method that utilizes the directionality and signs in a KEGG pathway graph to determine if in a given pathway structure the available species are more or less available to transduce a signal. As the species considered for a pathway are usually mRNAs of genes, this method infers signaling activity by the proxy of gene expression. In order to do this, SPIA scores require the comparison with a normal condition in order to compute both their scores and their significance.
We used the SPIA Bioconductor package 3 in our analyses, focussing on a subset of pathways (Supplementary Table 3). We calculated our scores either for each cell line compared to the rest of a given tissue where no normals are available (i.e. for the GDSC and drug response data) or compared to the tissue-matched normals (for the TCGA data used in driver and survival associations).
As Pathifier 5 requires the comparison with a baseline condition in order to compute scores, we computed the GDSC/TCGA scores as with SPIA. As gene sets, we selected Reactome pathways that corresponded to our set of pathways (Supplementary Table 2), where Pathifier calculated the “signal flow” from the baseline and compared it to each sample.
We used the PARADIGM software from the public software repository (https://github.com/sbenz/Paradigm) and a model of the cell signaling network 32 from the corresponding TCGA publication (https://tcga-data.nci.nih.gov/docs/publications/coadread_2012/). We normalized our gene expression data from both GDSC and TCGA using ranks to assign equally spaced values between 0 and 1 for each sample within a given tissue. We then ran PARADIGM inference using the same options as in the above publication for each sample separately. We used nodes in the network representing pathway activity to our set of pathways (Supplementary Table 4) to obtain pathway scores that are comparable to the other methods, averaging scores where there were more than one for a given sample and node.