Designabilities and entropies of structures SA to SD.

Some estimates of how designable are the protein families associated to structures SA, SB, SC, SD: largest eigenvalue of the contact map matrix c (1st column) [25], entropy of the Potts-ACE model (2nd column), shown to be generative in Fig 3A, and mean percentage of identity between sequences in the attached multi-sequence alignments (MSA) (3rd column). The mean identity is defined as the number of sites carrying consensus amino acids, averaged over all sequences in the MSA and divided by the length of the protein (L = 27); low identity corresponds to diverse MSA, and, hence, to large designability. According to our estimates of the entropies, the volumes (Fig 1) associated to structures SB and SC are, respectively, of about 41020 and 8.51024 sequences, while the total number of sequences is 2027 ≃ 1035. For more information about the meanings of designability and entropy, see Section I.B in S1 Text.