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The multiple sequence alignment (MSA) of a protein family provides a wealthof information in terms of the conservation pattern of amino acid residues notonly at each alignment site but also between distant sites. In order tostatistically model the MSA incorporating both short-range and long-rangecorrelations as well as insertions, I have derived a lattice gas model of theMSA based on the principle of maximum entropy. The partition function, obtainedby the transfer matrix method with a mean-field approximation, accounts for allpossible alignments with all possible sequences. The model parameters forshort-range and long-range interactions were determined by a self-consistentcondition and by a Gaussian approximation, respectively. Using this model withand without long-range interactions, I analyzed the globin and V-set domains byincreasing the "temperature" and by "mutating" a site. The correlations betweenresidue conservation and various measures of the system's stability indicatethat the long-range interactions make the conservation pattern more specific tothe structure, and increasingly stabilize better conserved residues.

A unified statistical model of protein multiple sequence alignment integrating direct coupling and insertions