Surface hydrophobic groups, stability, and flip-flopping in lattice proteins

Two-dimensional lattice protein models were studied in two approximations of the conformational equilibrium to elucidate the role of surface hydrophobic groups in their stabilities. We demonstrate that stability of any compactly folded sequence is determined by its ability to "flip-flop" (refold) into alternative compact structures. The degree of stability required for folded sequences determines the average numbers of surface hydrophobic groups in stable lattice structures which are in good agreement with ratios of core to surface hydrophobic groups in real proteins. However, the average destabilization of the native structure per surface hydrophobic group is small (0-0.25 kcal/mol), often disagrees with the free energies derived from the ratios of core to surface hydrophobic groups in the same structures, and has a combinatorial entropic nature independent of the strength of structure stabilizing interactions. This suggests that the free energies derived from the core to surface ratios of hydrophobic groups in real proteins have little to do with folding thermodynamics. On average, sequences with highly stable native structures are the least hydrophobic. The results suggest that in designing novel stable proteins hydrophobic groups on the surface should be avoided to reduce the possibility of flip-flopping. The average stability of highly designable structures is never higher than that of some low designability structures, contrary to the accepted view. In the equilibrium approximation with alternative compact and partially unfolded structures, the requirement of high stability selects a unique 5 x 5 structure formed by only a few sequences, suggesting much stronger sequence selectivity than commonly thought.