Fig. 3

Functional properties of disease gene sets are tested using gene set enrichment (top panels) and co-expression network connectivity (bottom panels). a Gene set enrichment is calculated with a hypergeometric test. A large number (34%) of the genes in the de novo loss-of-function set overlap with essential genes (hypergeometric test p ~ 9.8e-10). b This is repeated across all disease gene sets (a subset shown here). Sample size is controlled through downsampling. Gene sets with the higher effect sizes also have the higher functional convergences. c We can now demonstrate how to calculate the functional convergence trend for the “essential genes” test. The disease gene sets are ordered by an estimate of the average effect size of genes within the set (from low to high on the x-axis) and the functional convergence of that disease gene set is plotted (y-axis). A trend between the effect size of the candidate genes and their essentiality can be clearly observed. The network connectivity functional test (d) consists of calculating the ratio of disease genes’ total connectivity (node degrees calculated from the whole network; sum of their connections) to their internal connectivity (node degrees of their subnetwork; sum of their connections to one another). The line (in grey) reflects the expected values if there is no preferential connectivity within the set. We see that a large number (72%) of the genes lie above the identity line. The Wilcoxon p value of the mean residuals is shown in the inset (p ~ 7.83e-41). e Once again, controlling for sample size through downsampling, the functional convergence of each gene set is calculated (subset shown). f A weak trend between the effect size of the candidate genes and their degree of co-expression is visible. Empirical nulls are calculated by permuting disease gene sets and FDRs through a Benjamini–Hochberg correction against the resultant functional convergence trends