Amino acid substitution matrices from an information theoretic perspective

Protein sequence alignments have become an important tool for molecular biologists. Local alignments are frequently constructed with the aid of a "substitution score matrix" that specifies a score for aligning each pair of amino acid residues. Over the years, many different substitution matrices have been proposed, based on a wide variety of rationales. Statistical results, however, demonstrate that any such matrix is implicitly a "log-odds" matrix, with a specific target distribution for aligned pairs of amino acid residues. In the light of information theory, it is possible to express the scores of a substitution matrix in bits and to see that different matrices are better adapted to different purposes. The most widely used matrix for protein sequence comparison has been the PAM-250 matrix. It is argued that for database searches the PAM-120 matrix generally is more appropriate, while for comparing two specific proteins with suspected homology the PAM-200 matrix is indicated. Examples discussed include the lipocalins, human alpha 1 B-glycoprotein, the cystic fibrosis transmembrane conductance regulator and the globins.