Correlations between designability and various structural characteristics of protein lattice models

Using six kinds of lattice types (4 x 4, 5 x 5, and 6 x 6 square lattices; 3 x 3 x 3 cubic lattice; and 2+3+4+3+2 and 4+5+6+5+4 triangular lattices), three different size alphabets (HP, HNUP, and 20 letters), and two energy functions, the designability of protein structures is calculated based on random samplings of structures and common biased sampling (CBS) of protein sequence space. Then three quantities stability (average energy gap), foldability, and partnum of the structure, which are defined to elucidate the designability, are calculated. The authors find that whatever the type of lattice, alphabet size, and energy function used, there will be an emergence of highly designable (preferred) structure. For all cases considered, the local interactions reduce degeneracy and make the designability higher. The designability is sensitive to the lattice type, alphabet size, energy function, and sampling method of the sequence space. Compared with the random sampling method, both the CBS and the Metropolis Monte Carlo sampling methods make the designability higher. The correlation coefficients between the designability, stability, and foldability are mostly larger than 0.5, which demonstrate that they have strong correlation relationship. But the correlation relationship between the designability and the partnum is not so strong because the partnum is independent of the energy. The results are useful in practical use of the designability principle, such as to predict the protein tertiary structure.