Self-similarity and protein compactness

The hydrophobic effect is the major factor that drives a protein toward collapse and folding. As a consequence of the folding process a hydrophobic core is shielded by the solvent-accessible surface area of the protein. We analyze the solvent-accessible surface area of 1825 nonhomolog protein chains deposited in the Brookhaven Protein Data Bank. This solvent-accessible surface area presents an intrinsic self-similarity behavior. The comparison between the accessible surface area as function of the number of amino acids and the accessible surface area as function of gyration radius supplies a measure of the scaling exponent close to the one observed by volume as function of radius of gyration or by mass-size exponent. The present finding indicates that the fractal analysis describes the protein compactness as an object packing between random spheres in percolation threshold and crumpled wires.