  The multiple sequence alignment (MSA) of a protein family provides a wealth
of information in terms of the conservation pattern of amino acid residues not
only at each alignment site but also between distant sites. In order to
statistically model the MSA incorporating both short-range and long-range
correlations as well as insertions, I have derived a lattice gas model of the
MSA based on the principle of maximum entropy. The partition function, obtained
by the transfer matrix method with a mean-field approximation, accounts for all
possible alignments with all possible sequences. The model parameters for
short-range and long-range interactions were determined by a self-consistent
condition and by a Gaussian approximation, respectively. Using this model with
and without long-range interactions, I analyzed the globin and V-set domains by
increasing the "temperature" and by "mutating" a site. The correlations between
residue conservation and various measures of the system's stability indicate
that the long-range interactions make the conservation pattern more specific to
the structure, and increasingly stabilize better conserved residues.
