Computing a new family of shape descriptors for protein structures

The large-scale 3D structure of a protein can be represented by the polygonal curve through the carbon alpha atoms of the protein backbone. We introduce an algorithm for computing the average number of times that a given configuration of crossings on such polygonal curves is seen, the average being taken over all directions in space. Hereby, we introduce a new family of global geometric measures of protein structures, which we compare with the so-called generalized Gauss integrals.