Topological analysis of hydrogen bonding in protein structure

A recent study has shown that topological stereoisomers exist for the polypeptide chain in disulfide-containing proteins that are represented by non-planar graphs. This topological stereochemistry is demonstrated in the structure of variant 3 toxin in the venom of the North American scorpion Centruroides sculpturatus Ewing and the structure of toxin I1 from the North African scorpion Androctonus australis Hector. In this report, we found that a similar topological analysis can be applied to the hydrogen bonding in a-helices and /I-sheets within protein molecules, and we described the topological characteristics of chiral properties of protein secondary structure elements. Specifically, a closed right-handed a-helix of more than six residues long is shown formally to be nonplanar and has the L topology. Antiparallel /I-sheets are planar. Two parallel /I-strands each of at least three residues in length, however, constitute a non-planar structural element and can have either L or D topology. The favored right-handed crossover for parallel P-sheets has the L form, the same as the right-handed a-helix. This topological description of the hydrogen bonding in secondary structures may be extended to higher levels of protein structure and may provide a conceptual framework for studying complex protein architecture in general. d The covalent structure of polypeptide chains in folded proteins, including any disulfide linkages, can be represented by a graph in which LX carbon atoms of disulfide linked cysteine residues are vertices and covalent linkages between these car