  Protein folds are highly designable, in the sense that many sequences fold to
the same conformation. In the present work we derive an expression for the
designability in a 20 letter lattice model of proteins which, relying only on
the Central Limit Theorem, has a generality which goes beyond the simple model
used in its derivation. This expression displays an exponential dependence on
the energy of the optimal sequence folding on the given conformation measured
with respect to the lowest energy of the conformational dissimilar structures,
energy difference which constitutes the only parameter controlling
designability. Accordingly, the designability of a native conformation is
intimately connected to the stability of the sequences folding to them.
