Protein chain packing and percolation threshold

The major factor that drives a protein chain toward collapse and folding is the hydrophobic effect. Amino acids with apolar side chains join forming a solvent-shielded hydrophobic core. This process pack the structure in the native one. Here we investigate the average packing density of 5526 protein chains deposited in the Brookhaven Protein Data Bank. This analysis is carried out from the scaling analysis of the mass-size exponent and it shows that the exponent is δ=2.47δ=2.47. This fractal dimension of the protein chain is close to the one obtained in the randomly packed spheres near their percolation threshold. The present findings supply a measure of the protein compactness, that tends to a constant protein chain packing. The average packing density tends to ρ=0.86a.u./Å3.