The Smith-Waterman algorithm for local sequence alignment is one of the most important t e c hniques in computational molecular biology. This ingenious dynamic programming approach w as designed to reveal the highly conserv ed fragments by discarding poorly conserved initial and terminal segments. Ho w ever, the existing notion of local similarity has a serious aw: it does not discard poorly conserv edintermediate segments. The Smith-Waterman algorithm nds the local alignment with maximal score but it is unable to nd local alignment with maximum degree of similarity (e.g., maximal percent o f m a t c hes). Moreover, there is still no e cient algorithm that answers the follo wing natural question: do tw o sequences share a (su ciently long) fragment with more than 70% of similarity? As a result, the local alignment sometimes produces a mosaic of wellconserved fragments arti cially connected by poorlyconserv ed or ev en unrelated fragmen ts. This may l e a d to problems in comparison of long genomic sequences and comparative gene prediction as recently poin ted out by Zhang et al., 1999 33]. In this paper we propose a new sequence comparison algorithm (normalized local alignment) that reports the regions with maximum degree of similarity. The algorithm is based on fractional programming and its running time is O(n 2 log n). In practice, normalized local alignment is only 3-5 times slow er than the standard Smith-Waterman algorithm.
Recently, the fractional programming approach has been used to determine normalized local sequence alignments based on the classical Smith-Waterman algorithm REF .
A new approach to sequence comparison: normalized sequence alignment
Bioinformatics
Bioinformatics
Mathematics Medicine Computer Science