For assembling de novo motifs, we start with the kmer associated with the greatest variability in chromatin accessibility across the cells as a “seed” kmer. We first find the distribution of the normalized covariances between that seed kmer and all other kmers with an edit distance from that seed kmer of at least 3; these values are used as a null distribution for testing the significance of the observed covariances for kmers with a single nucleotide mismatch using a Z-test. For each position along the kmer, the nucleotide of the seed kmer is given a weight of 1. Each alternate nucleotides is given a weight of zero if the p-value for the normalized covariance of the kmer with that mismatch is greater than 0.05; if the p-value is less than 0.05 the nucleotide is given a weight equal to the square of the normalized covariance. The weights for each base pair are then normalized to sum to 1. To further extend the de novo motif, we used kmers overlapping the seed kmer with an offset of 1 or 2 bases.
