Hausdorff dimension as a quantification of local roughness of protein surfaces

Based on structural information from the Brookhaven Protein Data Bank, the contact surfaces of the proteins lysozyme, trypsin, and BPTI (bovine pancreatic trypsin inhibitor) with a spherical test particle of the size of a water molecule have been calculated and systematically analyzed. It is our purpose to establish (i) self-similarity as a statistical concept for the characterization of surface roughness and (ii) the Hausdorff dimension as a measure of the local surface complexity. It is found that the proteins statistically show self-similarity within a yardstick range 1.2 A less than R less than 20 A, and that this concept also holds reasonably for parts of the surface which are not too small.