SELF-SIMILARITY OF SOLVENT-ACCESSIBLE SURFACES OF BIOLOGICAL AND SYNTHETIC MACROMOLECULES

The quantification of surface roughness of globular proteins and synth etical macromolecules in the globular state is discussed using the con cept of fractality. The Hausdorff dimension as a measure for local and global fractality of surfaces is applied. To calculate the Hausdorff dimension of any surface at a high level of accuracy, a new algorithm is presented that is based on a triangulated solvent-accessible molecu lar surface. It can be demonstrated that protein surfaces (as calculat ed on the basis of experimentally determined structures) as well as su rfaces of globular polyethylene (PE) conformers (calculated on the bas is of structural information basing on extensive Monte Carlo and molec ular dynamics simulations) in fact show self-similarity within a reaso nable yardstick range, at least in a global statistical sense. The sam e is true for parts of a protein surface provided that these regions a re not too small. The concept of self-similarity breaks down when indi vidual surface points are considered. The results obtained for the fra ctal dimension of PE surfaces (average fractal dimension D = 2.23) lea d to the conclusion that protein surfaces probably do not exhibit a un ique and specific degree of geometrical complexity (or surface roughne ss) characterized by a fractal dimension of approximately D = 2.2 as w as argued in the past. It is clear that the concept of self-similarity is helpful for the classification of surface roughness of large molec ules, but it seems questionable whether this concept is useful for the identification of active sites or other questions related to the fiel d of molecular recognition. (C) 1993 by John Wiley & Sons, Inc.