where pJ(r) is a number density of protein atoms of type j at distance r from an arbitrary point in a protein. The reference sphere with radius R must be entirely filled with protein atoms since solvent exposure of the reference sphere, which is no longer centered at a specific ligand atom, would introduce arbitrary solvent effects. ( )pro, designates an average over protein complexes of the PDB. In order to assure that Aij(r) approaches zero with decreasing r, an additional set of protein atom dependent correction factors C j must be added to the reference state which is referred to below as Ref2. This is necessary since, in contrast to p j(r), the spherical volumes in which the pbuik(r) are calculated do not contain any solvent. Note that the reference number densities no longer depend on the ligand atoms.

In order to derive pj bun we find the average number of protein heavy atoms to entirely fill a spherical reference volume of radius R = 12 Ä, to be about fW = 400. The average number of protein atoms of any type at a distance r from an arbitrary reference point in the protein can then be calculated by using the expression

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