Estimating Similarities in DNA Strings Using the Efficacious Rank Distance Approach

Abstract

In general, when a new DNA sequence is given, the first step taken by a biologist would be to compare the new sequence with sequences that are already well studied and annotated. Sequences that are similar would probably have the same function, or, if two sequences from different organisms are similar, there may be a common ancestor sequence. Traditionally, this is made by using a distance function between the DNA chains, which implies in most cases that we apply it between two DNA sequences and try to interpret the obtained score. The standard method for sequence comparison is by sequence alignment. Sequence alignment is the procedure of comparing two sequences (pairwise alignment) or more sequences (multiple alignment) by searching for a series of individual characters or characters patterns that are in the same order in the sequences. Algorithmically, the standard pairwise alignment method is based on dynamic programming; the method compares every pair of characters of the two sequences and generates an alignment and a score, which is dependent on the scoring scheme used, i.e. a scoring matrix for the different base-pair combinations, match and mismatch scores, or a scheme for insertion or deletion (gap) penalties. The underlying string distance is called edit distance or also Levenshtein distance. Although dynamic programming for sequence alignment is mathematically optimal, it is far too slow for comparing a large number of bases. Typical DNAdatabase today contains billions of bases, and the number is still increasing rapidly. To enable sequence search and comparison to be performed in a reasonable time, fast heuristic local alignment algorithms have been developed, e.g. BLAST, freely available at http://www.ncbi.nlm.nih.gov/BLAST. With respect to the standard approach to the alignment and string matching problems as dealt with in computer science, alternative approaches might be explored in biology, provided one is able to give a positive answer to the following question: can one exhibit a sequence distance which is at the same time easily computed and non-trivial? The ranking of this problem on the first position in two lists of major open problems in bioinformatics (J.C. Wooley. Trends in computational biology: a summary based on a RECOMB plenary lecture. J. Comput. Biology, 6, 459-474, 1999 and E.V. Koonin. The emerging paradigm and open problems in comparative 6