An assessment of substitution scores for protein profile–profile comparison

Pairwise protein sequence alignments are generally evaluated using scores defined as the sum of substitution scores for aligning amino acids to one another, and gap scores for aligning runs of amino acids in one sequence to null characters inserted into the other. Protein profiles may be abstracted from multiple alignments of protein sequences, and substitution and gap scores have been generalized to the alignment of such profiles either to single sequences or to other profiles. Although there is widespread agreement on the general form substitution scores should take for profile-sequence alignment, little consensus has been reached on how best to construct profile-profile substitution scores, and a large number of these scoring systems have been proposed. Here, we assess a variety of such substitution scores. For this evaluation, given a gold standard set of multiple alignments, we calculate the probability that a profile column yields a higher substitution score when aligned to a related than to an unrelated column. We also generalize this measure to sets of two or three adjacent columns. This simple approach has the advantages that it does not depend primarily upon the gold-standard alignment columns with the weakest empirical support, and that it does not need to fit gap and offset costs for use with each substitution score studied.