  Protein molecules can be approximated by discrete polygonal chains of amino
acids. Standard topological tools can be applied to the smoothening of the
polygons to introduce a topological classification of proteins, for example,
using the self-linking number of the corresponding framed curves. In this paper
we add new details to the standard classification. Known definitions of the
self-linking number apply to non-singular framings: for example, the Frenet
framing cannot be used if the curve has inflection points. Meanwhile in the
discrete proteins the special points are naturally resolved. Consequently, a
separate integer topological characteristics can be introduced, which takes
into account the intrinsic features of the special points. For large number of
proteins we compute integer topological indices associated with the
singularities of the Frenet framing. We show how a version of the Calugareanu's
theorem is satisfied for the associated self-linking number of a discrete
curve. Since the singularities of the Frenet framing correspond to the
structural motifs of proteins, we propose topological indices as a technical
tool for the description of the folding dynamics of proteins.
