Classifying molecular sequences using a linkage graph with their pairwise similarities

Abstract

This paper presents a method for classifying a large and mixed set of uncharacterized sequences provided by genome projects. As the measure of sequence similarity, we use similarity score computed by a method based on the dynamic programming (DP), such as the Smith-Waterman local alignment algorithm. Although comparison by DP based method is very sensitive, when given sequences include a family of sequences that are much diverged in evolutionary process, similarity among some of them may be hidden behind spurious similarity of some unrelated sequences. Also the distance derived from the similarity score may not be metric (i.e., triangle inequality may not hold) when some sequences have multi-domain structure. To cope with these problems, we introduce a new graph structure called p-quasi complete graph for describing a family of sequences with a confidence measure. We prove that a restricted version of the p-quasi complete graph problem (given a positive integer k, whether a graph contains a 0.5-quasi complete subgraph of which size ⩾ k or not) is NP-complete. Thus we present an approximation algorithm for classifying a set of sequences using p-quasi complete subgraphs. The effectiveness of our method is demonstrated by the result of classifying over 4000 protein sequences on the Escherichia coli genome that was completely determined recently.