Approximate Abelian periods to find motifs in biological sequences

Abstract

A problem that has been gaining importance in recent years is that of computing the Abelian periods in a string. A string w has an Abelian period p if it is a sequence of permutations of a length-p string. In this paper, we define an approximate variant of Abelian periods which allows variations between adjacent elements of the sequence. Particularly, we compare two adjacent elements in the sequence using δ- and γ- metrics. We develop an algorithm for computing all the δγ- approximate Abelian periods in a string under two proposed definitions. We also show a preliminary application to the problem of identifying genes with periodic variations in their expression levels.