A Frenet frame analysis of protein geometry: hints for secondary structure assignments

Abstract

This paper deepens into the analysis of the protein secondary structure using Frenet frame to describe the curvature and torsion of the discrete curve formed by the protein $\alpha$-carbons. We show how a simple criterion based on the evaluation of the curvature and torsion of the discrete curve can be useful to pinpoint the presence of some secondary and supersecondary structures in proteins. Moreover, the description of proteins as fixed points of an effective action inspired by an $U(1)$ gauge model is strongly supported by the curvature and torsion observed over a large dataset of proteins in the Protein Data Bank.