How alike are the shapes of two random chains?

Two completely flexible random chains containing N atoms joined by links of length L can be superimposed by rigid‐body motions to match their structures as closely as possible. The statistics of the root‐mean‐square best‐fit distance D are discussed. For long chains, D2 tends of 0.125L2N. Thus, for a protein of 100 residues, where the Cα‐Cα distance is L = 3.8 Å, the expected root‐mean‐square atomic distance is 13.4 Å. This result gives a surprisingly good fit to the observed results for unrelated structures.