Quantification and visualization of molecular surface flexibility.

Two new methods for the quantification and visualization of the flexibility of molecular surfaces are presented. Both methods rely on results of molecular dynamics (MD) simulations. Whereas method I is based on a simple but fast grid-counting algorithm, method II uses a mapping function that allows for a sharp and clear visualization of atomic RMS fluctuations on a molecular surface. To demonstrate the scope of the methods, MD simulations of two proteins, PTI and ubiquitin, were performed. The flexibility data are mapped onto the molecular surfaces of the proteins and visualized using texture mapping technology available on modern workstations.

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.