Alignments with non-overlapping moves, inversions and tandem duplications in O(n 4) time

Abstract

Sequence alignment is a central problem in bioinformatics. The classical dynamic programming algorithm aligns two sequences by optimizing over possible insertions, deletions and substitutions. However, other evolutionary events can be observed, such as inversions, tandem duplications or moves (transpositions). It has been established that the extension of the problem to move operations is NP-complete. Previous work has shown that an extension restricted to non-overlapping inversions can be solved in O(n 3) with a restricted scoring scheme. In this paper, we show that the alignment problem extended to non-overlapping moves can be solved in O(n 5) for general scoring schemes, O(n 4 log n) for concave scoring schemes and O(n 4) for restricted scoring schemes. Furthermore, we show that the alignment problem extended to non-overlapping moves, inversions and tandem duplications can be solved with the same time complexities. Finally, an example of an alignment with non-overlapping moves is provided.

Homoplastic microinversions and the avian tree of life

“…Otherwise estimates of the amount of evolutionary change will be distorted, potentially resulting in incorrect phylogenetic estimation [19]. Algorithms for sequence alignment that include the possibility of inversions have been proposed [55-57], and they have the potential advantage of incorporating explicit penalties for inversion events. However, the optimal inversion penalty to limit false positives may be difficult to determine and the available algorithms are limited to the identification of non-overlapping microinversions.…”

Enumeração de traces e identificação de breakpoints

“…Os algoritmos clássicos de alinhamento global requerem que a ordem e a orientação de nucleotídeos homólogos sejam as mesmas nas duas sequências e, além disso, um nucleotídeo pode ser alinhado uma única vez. Existem algoritmos exatos que realizam a detecção de rearranjos (inversões e translocações) e/ou duplicações [33,99,161]. Contudo, eles lidam apenas com pequenos rearranjos locais e duplicações em tandem e, devido a complexidade que apresentam, não são viáveis para a realização de alinhamentos com sequências de genomas completos.…”