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 II 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 alpha-helices and beta-sheets within protein molecules, and we described the topological characteristics of chiral properties of protein secondary structure elements. Specifically, a closed right-handed alpha-helix of more than six residues long is shown formally to be non-planar and has the L topology. Antiparallel beta-sheets are planar. Two parallel beta-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 beta-sheets has the L form, the same as the right-handed alpha-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.