Protein structures and optimal folding from a geometrical variational principle

A novel approach, validated by an analysis of barnase and chymotrypsin inhibitor, is introduced to elucidate the paramount role played by the geometry of the protein backbone in steering the folding to the native state. It is found that native states of proteins, compared with compact artificial backbones, have an exceedingly large number of conformations with a given amount of structural overlap with them; moreover, the density of overlapping conformations, at a given overlap, of unrelated proteins of the same length are nearly equal. These results suggest an extremality principle underlying protein evolution, which, in turn, is shown to be possibly associated with the emergence of secondary structures.