Figure 3. Degree of Interpenetration of Subchains.

Defined as follows: given a labeled subchain (say chain AB in the inset at the lower right), determine the fraction of the number of units (or residues) of the loop or protein enclosed within a sphere (dashed circle) that does not belong to the subchain. The radius of this enclosing sphere is equal to the gyration radius of the subchain. The degree of interpenetration is then defined as an average of this quantity over all subchains of the given length, taken within a single protein chain and from all other protein chains. As in the results for the mean square end-to-end distance, for each chain of length N, we consider subchains of length up to N^2/3. The degree of interpenetration for proteins, lattices (average from five globular loop sizes from 4 × 4 × 4 to 12 × 12 × 12, and separately for 4 × 4 × 4, 6 × 6 × 6, and 8 × 8 × 8) and linear equilateral random walks of length N = 100 and N = 200 are shown.