A new approach to sequence comparison: normalized sequence alignment

Abstract

The Smith-Waterman algorithm for local sequence alignment is one of the most important techniques in computational molecular biology. This ingenious dynamic programming approach was designed to reveal the highly conserved fragments by discarding poorly conserved initial and terminal segments. However, the existing notion of local similarity has a serious flaw: it does not discard poorly conserved intermediate segments. The Smith-Waterman algorithm finds the local alignment with maximal score but it is unable to find local alignment with maximum degree of similarity (e.g. maximal percent of matches). Moreover, there is still no efficient algorithm that answers the following natural question: do two sequences share a (sufficiently long) fragment with more than 70% of similarity? As a result, the local alignment sometimes produces a mosaic of well-conserved fragments artificially connected by poorly-conserved or even unrelated fragments. This may lead to problems in comparison of long genomic sequences and comparative gene prediction as recently pointed out by Zhang et al. (Bioinformatics, 15, 1012-1019, 1999). 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(n2log n). In practice, normalized local alignment is only 3-5 times slower than the standard Smith-Waterman algorithm.

Accurate statistics for local sequence alignment with position-dependent scoring by rare-event sampling

“…While this still prohibits interactive use, we see a lot of potential for our method to provide an improved version of the tool [22] and to explore the statistics of normalized sequence alignment [7]. …”

“…In this paper, we explain and extend an efficient and generally applicable numerical technique that solves this problem in many different sequence comparison settings, such as for a BLAST-like database search [5] with a fixed query, for position-specific scoring and/or gap-cost schemes (essentially HMMs), or for normalized alignment [7]. In each of those settings a variety of null models in addition to the i.i.d.…”

“…Our framework is readily applicable to the (RQGS), (FQPS) and (HMM) models, but also to more exotic settings, such as normalized alignment [7], where the score is not additive, but normalized by the alignment length, for which no statistical framework exists so far. Very recently Eddy [24] studied the distributions of Viterbi and Forward scores under probabilistic local alignment, for which a numerical analysis of the rare-event tail would be of interest as well.…”

Normalized Similarity of RNA Sequences

“…While the LCS metric is a suitable metric for global comparison, in many real-life applications one is often interested in finding local regions of high similarity [16]. One approach for transforming the global LCS metric into a local version, is to calculate the normalized longest common subsequence [3,7]. Here, one divides the LCS score of two substrings by the sum of their lengths.…”

“…Specifically, we consider the local normalized LCS metric for RNA sequences which measures the highest LCS scoring consecutive subsequences divided by their length. The advantages of the normalized approach in the context of strings [3,7] also apply for RNAs. We present an O(n 2 m lg m) time algorithm for this problem which is conceptually inspired by the algorithm given in [7].…”