Inference of phylogenetic distances from DNA-walk divergences

A formalism for the analysis of DNA-sequences is presented. It develops the concept of a composition vector potential which incorporates intrinsic double-strand and four-base symmetries. The vector potential allows for straightforward coarse graining and graphical representation of whole genomes. Its projections are mapped onto DNA-walks. It is shown that distances due to mutation between sequences can be estimated from mean square differences between walks. A computer program for global alignment of sequences (DNAWD) is thus developed and applied to a set of toy sequences representing evolution under mutation. The distance matrix output of DNAWD is shown to provide a good estimate of the associated phylogenetic tree.