In addition to Hi-C linkages, we tried to find further regulatory connections by relating the activity of TFs to target genes (Fig. 5A). In particular, for each potential target of a TF, we created a linkage if it had a “good binding site” (matching the TF’s motif) in gene-proximal open chromatin regions (either promoters or brain-active enhancers) and if it had a high coefficient in a regularized, elastic net regression, relating TF activity to target expression (fig. S42) (21). Elastic net regression assumes that target gene expression is determined by a linear combination of the expression levels of its regulating TFs, via regression coefficients (using sparsified L1 and L2 regularization). Overall, we found that a subset of regulatory connections could predict the expression of 8930 genes with a mean square error (MSE) of <0.05 (fig. S43). For example, we could predict the expression of the ASD-associated gene CHD8 with MSE = 0.034 (equivalent to coefficient of determination R2 = 0.77 over the population) (21). Lastly, the enhancer-binding TFs with high regression coefficients—implying a high chance for TF regulation of the target genes via particular bound enhancers—provide a third set of putative enhancer-to-gene links.
