Lecture 22 : Space Filling Diagrams

For geometric and topological analysis and for understanding the nonbond interactions between atoms a protein is modeled as a set of spheres in R, each sphere corresponding to one atom of the protein. This model, known as the space-filling diagram, assumes that the exact position of each atom is known. We thus represent a protein P as a set {B1, . . . , Bn} of balls in R. Let zi (resp. ri) denote the center (resp. radius) of Bi. The union ⋃ iBi is the space filled by P. The coordinates of the centers are typically determined using X-ray crystallography and NMR methods. The radius ri is typically the Van der Waals radius, defining the impenetrable volume of an atom. The smallest distance between neighboring atoms (in the crystalline state) that are not covalently bonded is the sum of their van der Waals radii. A range of values is assigned to van der Waals radii because it depends on how the atom is covalently bonded. Typical values are given in Table 22.1, which are originally taken from [1].