Concavity is computed by an algorithm similar to Connolly's (Connolly, M.L. (1986), J. Mol. Graphics 4, 3-6), in which a sphere with a large radius RC is placed around each atom. Concavity at that atom's location is defined as proportional to the solid angle on the sphere occluded by its neighboring atoms. The solid angle varies from 0 (lone atom) to 4π square radians (deeply buried). We use RC = 10Å, which approximates the sizes of typical substrate binding sites.
We modified Connolly's algorithm by replacing the solid angle with its ranking relative to all other exposed atoms in that protein. This is intended to correct for proteins that have unusually large or numerous pockets. A ranking of 0.5 would be median concavity, and 1.0 would be maximum concavity among exposed atoms in that protein. A value of 0.0 means maximum convexity. Buried atoms get no value.