Modeling Genomic Dna Base Substitution

Many DNA base substitution models have been proposed to describe the evolution of short DNA sequences. Most of these models are special reversible time-continuous Markov chains on the DNA bases. A general reversible model for long genomic DNA sequences, which includes the previous models as special cases, is described in this paper. To estimate the model parameters from pairwise alignments, two numerical maximum likelihood procedures are developed and implemented in MATLAB. The methods are applied to a large collection of local alignments (HSPs) between human chromosome 22 and the mouse genome. The overall estimated rate matrix is nearly strand-symmetric, but the fit is very bad due to the heterogeneous base composition of the HSPs. Dividing the data into three groups according to GC content and estimating the parameters separately gives considerably better fit, and three substitution scores are derived from the estimates. Examining smaller groups of HSPs of certain homogeneous compositions reveals sufficient amount of compositional imbalance in the HSPs to make the fits of the model unsatisfactory. However, removing these nonstationary HSPs from the groups results in very good fits.