An Alternative Model of Amino Acid Replacement
  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. 
Gavin E. Crooks, Steven E. Brenner