Efficient characterization of protein secondary structure in terms of screw motions

A simple and efficient method is presented to describe the secondary structure of proteins in terms of orientational distances between consecutive peptide planes and local helix parameters. The method uses quaternion-based superposition fits of the protein peptide planes in conjunction with Chasles' theorem, which states that any rigid-body displacement can be described by a screw motion. The helix parameters are derived from the best superposition of consecutive peptide planes and the `worst' fit is used to define the orientational distance. Applications are shown for standard secondary-structure motifs of peptide chains for several proteins belonging to different fold classes and for a description of structural changes in lysozyme under hydrostatic pressure. In the latter case, published reference data obtained by X-ray crystallography and by structural NMR measurements are used.