Some useful statistical properties of position-weight matrices.

Position-weight matrices (or profiles) are simple mathematical objects traditionally used to capture the information about local sequence patterns (or motifs) characteristic of a given structure or function. Although weight matrices can lead to fast database scanning algorithms their usage has been limited, due to the lack of a reliable method to assess the statistical significance of the matching scores. In this article I first review 3 different computation scheme for designing weight matrices from a block-alignment of any (small or large) number of sequences. I then show that, for patterns spanning 10 positions or more, the best scores expected from matching random sequences are distributed according to the extreme value (Gumbel) distribution. The threshold of statistical significance assessed from this distribution perfectly delineate the range of scores characterizing "true positive" sequences (biological significant matches). This result allows weight matrices to be used to scan an entire protein database for patterns in a highly sensitive way. MODEST (MOtif DEsign and Search Tools), a suite of programs in Unix/C, implements these statistical improvements and is available upon E-mail request (jmc@ncbi.nlm.nih.gov).