By enumerating all sequences of length 20, we study the designability of
structures in a two-dimensional Hydrophobic-Polar (HP) lattice model in a wide
range of inter-monomer interaction parameters. We find that although the
histogram of designability depends on interaction parameters, the set of highly
designable structures is invariant. So in the HP lattice model the High
Designability should be a purely geometrical feature. Our results suggest two
geometrical properties for highly designable structures, they have maximum
number of contacts and unique neighborhood vector representation. Also we show
that contribution of perfectly stable sequences in designability of structures
plays a major role to make them highly designable.Comment: 6 figure, To be appear in JC