Protein backbone. (a) Full-atom representation described by the Ramachandran φ and ψ angles (in red); the ω torsion and τ stretching angles are also shown (in green). (b) The joint distribution of the Ramachandran φ and ψ angles with the allowed (light grey) and favoured (dark grey) regions according to Lovell et al. (2003); the nomenclature of different regions is according to Hollingsworth & Karplus (2010). (c) Five-atom (double-plane) representation with the conformationally variable interatomic distances shown in red; the distance-geometry based concept used in this work is depicted by a 5 × 5 interatomic distance matrix.