Protein secondary structure analysis with a coarse-grained model

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.