  The paper presents a geometrical model for protein secondary structure
analysis which uses only the positions of the $C_{\alpha}$-atoms. We construct
a space curve connecting these positions by piecewise polynomial interpolation
and describe the folding of the protein backbone by a succession of screw
motions linking the Frenet frames at consecutive $C_{\alpha}$-positions. Using
the ASTRAL subset of the SCOPe data base of protein structures, we derive
thresholds for the screw parameters of secondary structure elements and
demonstrate that the latter can be reliably assigned on the basis of a
$C_{\alpha}$-model. For this purpose we perform a comparative study with the
widely used DSSP (Define Secondary Structure of Proteins) algorithm.
