Asymmetry in the shapes of folded and denatured states of proteins

The asymmetry in the shapes of folded and unfolded states are probed using two parameters, Δ (a measure of the sphericity) and S that describes the shape (S > 0 corresponds to prolate and S < 0 represents oblate). For the folded states, whose interiors are densely packed, the radii of gyration (Rg), Δ, and S are calculated using the coordinates of the experimentally determined structures. Although Rg scales as N1/3, as expected for maximally compact structures, the distributions of Δ and S show that there is considerable asymmetry in the shapes of folded structures. The degree of asymmetry is greater for proteins that form oligomers. Analysis of the two- and three-body contacts in the native structures shows that the presence of near equal number of contacts between backbone and side-chains and between side-chains gives rise to dense packing. We suggest that proteins with relatively large values of Δ and S can tolerate volume mutations without greatly affecting the network of contacts or their stability. ...