PWMs

PWMs, or position weight matrices, are a common representation of sequence motifs used to model the preferences of DNA- and RNA-binding proteins. They summarize how likely each symbol is at each position within a motif, enabling quantitative assessment of how well a sequence matches the motif. In DNA contexts, a PWM is typically an L by 4 matrix, where L is the motif length and the four columns correspond to the nucleotides A, C, G, and T. Each entry represents either a probability, a count, or a log-odds score against a background distribution.

PWMs are usually derived from a set of known motif instances. Counts at each position generate position-specific scores, often with pseudocounts to avoid zero values. These counts can be converted to probabilities or to log-odds scores by comparing observed frequencies to a background model, such as the overall genomic nucleotide frequencies. The resulting matrix allows uniform scoring across motif positions and supports comparisons between sequences of the same length.

To score a candidate sequence, the base at each motif position is mapped to its corresponding weight in the column for that position, and the scores are summed over the motif length. Higher scores indicate better matches to the motif. PWMs underpin motif scanning, genome annotation, and motif discovery, and are frequently used with thresholding or p-value estimation to identify potential binding sites. Limitations include the independence assumption between positions, sensitivity to the chosen background model, and reliance on the quality and representativeness of the training data. Extensions include information content analyses, sequence logos, and alternative, non-independent models.