  We study the designability of all compact 3x3x3 and 6x6 lattice-protein
structures using the Miyazawa-Jernigan (MJ) matrix. The designability of a
structure is the number of sequences that design the structure, i.e. sequences
that have that structure as their unique lowest-energy state. Previous studies
of hydrophobic-polar (HP) models showed a wide distribution of structure
designabilities. Recently, questions were raised concerning the use of a
2-letter (HP) code in such studies. Here we calculate designabilities using all
20 amino acids, with empirically determined interaction potentials (MJ matrix),
and compare with HP model results. We find good qualitative agreement between
the two models. In particular, highly designable structures in the HP model are
also highly designable in the MJ model--and vice versa--with the associated
sequences having enhanced thermodynamic stability.
