Recurring shapes in the folding of the polypeptide chain in the tertiary structures of proteins

The tertiary structure and folding of proteins are interpreted in terms of the amino acid sequence. A representation of the tertiary sequence is presented in terms of the torsional angles of αii+1 about the fixed-length virtual bonds connecting the next neighbor Cα atoms i and i + 1. The virtual-bond angle Θi changes throughout all sterically allowed dipeptide conformations, depending only on the conformation of the ith amino acid residue; however αii+1 assumes a whole range of values and involves conformation of amino acid residues i and i + 1. The position of side chains is not particularly sensitive to the conformation of a pair of amino acid residues with similar αii+1 values. Folding is analyzed as a spatial distribution of sites where the intrinsic properties of the amino acids (molar vol., hydrophobicity, polarity, etc.) can be assocd. The conformation of 4 proteins was calcd. as to the distribution of the angles αii+1 and compared with folding which would result from random choices. The distributions were approx. identical. In expt. diagrams where the spatial position of the Cα atoms of 5 amino acid residues were considered, protein fragments having similar values of 2, 3, 4, etc. had similar folding over 6, 7, 8, etc. residues.