A set of van der Waals and Coulombic radii of protein atoms for molecular and solvent-accessible surface calculation, packing evaluation, and docking

We analyze the contact distance distributions between nonbonded atoms in known protein structures. A complete set of van der Waals (VDW) radii for 24 protein atom types and for crystal-bound water is derived from the contact distance distributions of these atoms with a selected group of apolar atoms. In addition, a set of Coulombic radii for polar atoms is derived from their contacts with water. The contact distance distributions and the two sets of radii are derived in a systematic and self-consistent manner using an iterative procedure. The Coulombic radii for polar atoms are, on average, 0.18 Å smaller than their VDW radii. The VDW radius of water is 1.7 which is 0.3 Å larger than its Coulombic radius. We show that both the VDW and the Coulombic radii of polar atoms are needed in calculating the molecular and solvent-accessible surfaces of proteins. The VDW radii are needed to generate the apolar portions of the surface and the Coulombic radii for the polar portions. The fact that polar atoms have two apparent sizes implies that a hydrophobic cavity has to be larger than a polar cavity in order to accommodate the same number of water molecules. Most surface area calculations have used only one radius for each polar atom. As a result, unreal cavities, grooves, or pockets may be generated if the Coulombic radii of polar atoms are used. On the other hand, if the VDW radii of polar atoms are used, the details of the polar regions of the surface may be lost. The accuracy of the molecular and the solvent-accessible surfaces of proteins can be improved if the radii of polar atoms are allowed to change depending on the nature of their contacting neighbors. The surface of a protein at a protein-protein interface differs from that in solution in that it has to be generated using at least two kinds of probes, one representing a typical apolar atom and the other a typical polar atom. This observation has important implications for docking, which relies on surface complementarily at the interface.