We can use these comparisons of variation between highly similar kmers to construct de novo motifs representing sequences associated with variation in chromatin accessibility. In brief, we start with highly variable “seed” kmers, and use the covariance between the seed kmer and kmers either differing by one mismatch or partially overlapping the seed kmer to assign weights to different nucleotide bases at each position of the motif model (Supplementary Fig. 11; see methods). Importantly, many de novo motifs assembled using this approach closely match known motifs (Figs. 3c–f, Supplementary Fig. 11). For motifs that do not closely match to a known TF, we confirmed that the constructed motifs were also associated with variation in DNase hypersensitivity between different samples represented in the Roadmap Epigenomics Project18 (Supplementary Fig. 12), demonstrating that these de novo motifs are associated with chromatin accessibility variation in two distinct accessibility assays. To further validate the discovery of these putative trans-regulators we calculated aggregate TF “footprints”, a measure of the DNase or Tn5 cut density around the given motif, and found a diverse set of accessibility profiles
