  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 show that the ratio for real and
well-designed proteins is universal and equal to 0.491\pm0.005. 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.
