  Using an off-lattice model, we fully enumerate folded conformations of
polypeptide chains of up to N = 19 monomers. Structures are found to differ
markedly in designability, defined as the number of sequences with that
structure as a unique lowest-energy conformation. We find that designability is
closely correlated with the pattern of surface exposure of the folded
structure. For longer chains, complete enumeration of structures is
impractical. Instead, structures can be randomly sampled, and relative
designability estimated either from designability within the random sample, or
directly from surface-exposure pattern. We compare the surface-exposure
patterns of those structures identified as highly designable to the patterns of
naturally occurring proteins.
