Non-occurring and rare quads in PDB and translated introns from XPro with possible applications in nanostructure design

Exhaustive search over 17313 unique protein sequences in the database PDB indicates the absence of 4036 of the 160000 possible subsequences of four residues (quads). When the polypeptides obtained by translating 100000 prion sequences in the database XPro are searched the number drops to 424, which still exceeds what would be obtained by pure chance. More generally there are 11444 quads that occur 3 or fewer times in PDB. Using the Kyte-Doolittle hydrophobicity index, the 4036 quads (including the 424 absent in XPro) are divided into 16 groups, five of which can form unbroken helices or sheets by repetition. Most of the 16 groups are evenly distributed, one exception being quads with all-apolar residues, which are significantly less frequent. The helical and sheet structures so formed are artificial polypeptides not observed in nature. By using patterns from the other 11 groups more complex structures can be formed. Such structures could potentially serve as tubules and substrates in nanostructure design.