  We examined what determines the designability of 2-letter codes (H and P)
lattice proteins from three points of view. First, whether the native structure
is searched within all possible structures or within maximally compact
structures. Second, whether the structure of the used lattice is bipartite or
not. Third, the effect of the length of the chain, namely, the number of
monomers on the chain. We found that the bipartiteness of the lattice structure
is not a main factor which determines the designability. Our results suggest
that highly designable structures will be found when the length of the chain is
sufficiently long to make the hydrophobic core consisting of enough number of
monomers.
