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. For the two bases immediately outside the seed kmer, the weighting of each nucleotide is given by x * y2 + (1 − x)) * 0.25, where y2 is the square of the normalized covariance for the kmer with the given nucleotide offset (if significant at 0.05 and otherwise 0) and x is the maximum value of the normalized covariances for the four kmers (bounded by 0 and 1). For the bases offset by two from the seed kmer, the weighting is computed in the same way except that there are four possible kmers with a given nucleotide at that position that overlap the seed kmer; only the kmer with the maximum normalized covariance with the seed kmer is used (Figure S11).
