  In the protein sequence space, natural proteins form clusters of families
which are characterized by their unique native folds whereas the great majority
of random polypeptides are neither clustered nor foldable to unique structures.
Since a given polypeptide can be either foldable or unfoldable, a kind of
"folding transition" is expected at the boundary of a protein family in the
sequence space. By Monte Carlo simulations of a statistical mechanical model of
protein sequence alignment that coherently incorporates both short-range and
long-range interactions as well as variable-length insertions to reproduce the
statistics of the multiple sequence alignment of a given protein family, we
demonstrate the existence of such transition between natural-like sequences and
random sequences in the sequence subspaces for 15 domain families of various
folds. The transition was found to be highly cooperative and two-state-like.
Furthermore, enforcing or suppressing consensus residues on a few of the
well-conserved sites enhanced or diminished, respectively, the natural-like
pattern formation over the entire sequence. In most families, the key sites
included ligand binding sites. These results suggest some selective pressure on
the key residues, such as ligand binding activity, may cooperatively facilitate
the emergence of a protein family during evolution. From a more practical
aspect, the present results highlight an essential role of long-range effects
in precisely defining protein families, which are absent in conventional
sequence models.
