Universal geometrical factor of protein conformations as a consequence of energy minimization

The biological activity and functional specificity of proteins depend on their native three-dimensional structures determined by inter- and intra-molecular interactions. In this paper, we investigate the geometrical factor of protein conformation as a consequence of energy minimization in protein folding. Folding simulations of 10 polypeptides with chain length ranging from 183 to 548 residues manifest that the dimensionless ratio (V/A〈r〉) of the van der Waals volume V to the surface area A and average atomic radius 〈r〉 of the folded structures, calculated with atomic radii setting used in SMMP (Eisenmenger F. et al., Comput. Phys. Commun., 138 (2001) 192), approach 0.49 quickly during the course of energy minimization. A large scale analysis of protein structures shows that the ratio for real and well-designed proteins is universal and equal to 0.4910.005. The fractional composition of hydrophobic and hydrophilic residues does not affect the ratio substantially. The ratio also holds for intrinsically disordered proteins, while it ceases to be universal for polypeptides with bad folding properties.