Partially Local Multi-way Alignments

Abstract

Multiple sequence alignments are an essential tool in bioinformatics and computational biology, where they are used to represent the mutual evolutionary relationships and similarities between a set of DNA, RNA, or protein sequences. More recently they have also received considerable interest in other application domains, in particular in comparative linguistics. Multiple sequence alignments can be seen as a generalization of the stringto-string edit problem to more than two strings. With the increase in the power of computational equipment, exact, dynamic programming solutions have become feasible in practice also for 3-and 4-way alignments. For the pairwise (2-way) case, there is a clear distinction between local and global alignments. As more sequences are considered, this distinction, which can in fact be made independently for both ends of each sequence, gives rise to a rich set of partially local alignment problems. So far these have remained largely unexplored. Here we introduce a general formal framework that gives raise to a classification of partially local alignment problems. This leads to a generic NR gratefully acknowledges the hospitality of the Santa Fe Institute, where much of this work was performed. scheme that guides the principled design of exact dynamic programming solutions for particular partially local alignment problems.

Bi-alignments with affine gaps costs

“…As noted e.g. in [ 27 , 28 ], the index vector of the penultimate column of the alignment is , where is interpreted as 1 and the gap character − as 0. The Needleman–Wunsch recursions [ 29 ] thus can be written in compact form (see also [ 24 ]) as Notably, in the non-affine case, the scoring function s ( x , c ) is completely determined by a single column.…”

ProbPFP: a multiple sequence alignment algorithm combining hidden Markov model optimized by particle swarm optimization with partition function

“…MSARC use a residue clustering method based on partition function to align multiple sequence [22]. Retzlaff et al [23] use partition function as a part of calculation for partially local multi-way alignments. Partition function is a useful model for alignment.…”

Alignments as Compositional Structures

“…This leads to slight changes in exact algorithms, exemplified by an extra term in the local Smith-Waterman algorithm [50] compared to the global Needleman-Wunsch [44] algorithm. This idea can be generalized to mixed problems in which a user can determine for each of the two ends of each input sequence whether it is to be treated as local or global [48]. For the purpose of the present contribution (partially) local alignments require a slight, trivial extension of the presentation, which we -for the sake of clarity in the presentation -only briefly comment on.…”