An Algorithm to Solve the Motif Alignment Problem for Approximate Nested Tandem Repeats

An approximate nested tandem repeat (NTR) in a string T is a complex repetitive structure consisting of many approximate copies of two substrings x and X ("motifs") interspersed with one another. NTRs have been found in real DNA sequences and are expected to have applications for evolutionary studies, both as a tool to understand concerted evolution, and as a potential marker in population studies. In this paper we describe software tools developed for database searches for NTRs. After a first program NTRF inder identifies putative NTR motifs, a confirmation step requires the application of the alignment of the putative NTR against exact NTRs built from the putative template motifs x and X. In this paper we describe an algorithm to solve this alignment problem in O(vertical bar T vertical bar (vertical bar x vertical bar + vertical bar X vertical bar)) space and time. Our alignment algorithm is based on Fischetti et al.'s wrap-around dynamic programming.