  The observed correlations between pairs of homologous protein sequences are
typically explained in terms of a Markovian dynamic of amino acid substitution.
This model assumes that every location on the protein sequence has the same
background distribution of amino acids, an assumption that is incompatible with
the observed heterogeneity of protein amino acid profiles and with the success
of profile multiple sequence alignment. We propose an alternative model of
amino acid replacement during protein evolution based upon the assumption that
the variation of the amino acid background distribution from one residue to the
next is sufficient to explain the observed sequence correlations of homologs.
The resulting dynamical model of independent replacements drawn from
heterogeneous backgrounds is simple and consistent, and provides a unified
homology match score for sequence-sequence, sequence-profile and
profile-profile alignment.
