Substitution Matrices and Mutual Information Approaches to Modeling Evolution

Substitution matrices are at the heart of Bioinformatics: sequence alignment, database search, phylogenetic inference, protein family classification are all based on BLOSUM, PAM, JTT, mtREV24 and other matrices. These matrices provide means of computing models of evolution and assessing the statistical relationships amongst sequences. This paper reports two results; first we show how Bayesian and grid settings can be used to derive novel specific substitution matrices for fish and insects and we discuss their performances with respect to standard amino acid replacement matrices. Then we discuss a novel application of these matrices: a refinement of the mutual information formula applied to amino acid alignments by incorporating a substitution matrix into the calculation of the mutual information. We show that different substitution matrices provide qualitatively different mutual information results and that the new algorithm allows the derivation of better estimates of the similarity along a sequence alignment. We thus express an interesting procedure: generating ad hoc substitution matrices from a collection of sequences and combining the substitution matrices and mutual information for the detection of sequence patterns.