📝 SummarXiv

Abstract

Sequence matching algorithms such as BLAST and FASTA have been widely used in searching for evolutionary origin and biological functions of newly discovered nucleic acid and protein sequences. As parts of these search tools, alignment scores and E values are useful indicators of the quality of search results from querying a database of annotated sequences, whereby a high alignment score (and inversely a low E value) reflects significant similarity between the query and the subject (target) sequences. For cross-comparison of results from sufficiently different queries however, the interpretation of alignment score as a similarity measure and E value a dissimilarity measure becomes somewhat nuanced, and prompts herein a judicious distinction of different types of similarity. We show that an adjustment of E value to account for self-matching of query and subject sequences corrects for certain ostensibly anomalous similarity comparisons, resulting in canonical dissimilarity and similarity measures that would be more appropriate for database applications, such as all-on-all sequence alignment or selection of diverse subsets. In actual practice, the canonicalization of E value dissimilarity improves clustering and the diversity of subset selection. While both E value and the canonical E value share positivity and symmetry, two of the four axiomatic properties of a metric space, the canonical E value itself is also reflexive and meets the condition of triangle inequality, thus an appropriate distance function for a metric space of protein sequences.