Relation between weight matrix and substitution matrix: motif search by similarity

The discovery of patterns shared by several sequences that differ greatly is a basic task in sequence analysis, and still a challenge. Several methods have been developed for detecting patterns. Methods commonly used for motif search include the Gibbs sampler, Expectation-Maximization (EM) algorithm and some intuitive greedy approaches. One cannot guarantee the optimality of the result produced by the Gibbs sampler in a single run. The deterministic EM methods tend to get trapped by local optima. Solutions found by greedy approaches are rarely sufficiently good.

A simple model describing a motif or a portion of local multiple sequence alignment is the weight matrix model, in which a motif is characterized with position-specific probabilities. Two substitution matrices are proposed to relate the sequence similarity with the weight matrix. Combining the substitution matrix and weight matrix, we examine three typical sets of protein sequences with increasing complexity. At a low score threshold for pair similarity, sliding windows are compared with a seed window to find the score sum, which provides a measure of statistical significance for multiple sequence comparison. Such a similarity analysis reveals many aspects of motifs. Blocks determined by similarity can be used to deduce a primary weight matrix or an improved substitution matrix. The algorithm successfully obtains the optimal solution for the test sets by just greedy iteration.