Motivation: Amino acid substitution matrices play a central role in protein alignment methods. Standard log-odds matrices, such as those of the PAM and BLOSUM series, are constructed from large sets of protein alignments having implicit background amino acid frequencies. However, these matrices frequently are used to compare proteins with markedly different amino acid compositions, such as transmembrane proteins or proteins from organisms with strongly biased nucleotide compositions. It has been argued elsewhere that standard matrices are not ideal for such comparisons and, furthermore, a rationale has been presented for transforming a standard matrix for use in a non-standard compositional context.
Results: This paper presents the mathematical details underlying the compositional adjustment of amino acid or DNA substitution matrices.