Mapping all-atom models onto one-bead Coarse Grained Models: general properties and applications to a minimal polypeptide model.

In the one and two beads Coarse Grained (CG) models for proteins, the two conformational dihedrals ϕ and ψ that describe the backbone geometry are no longer present as explicit internal coordinates, thus the information contained in the Ramachandran plot cannot be used directly. We derive an analytical mapping between these dihedrals and the internal variable describing the backbone conformation in the one(two) beads CG models, namely the pseudo-bond angle and pseudo-dihedral between subsequent Cαs. This is used to derive a new density plot that contains the same information as the Ramachandran plot and can be used with the one(two) beads CG models. The use of this mapping is then illustrated with a new one bead polypeptide model that accounts for transitions between α-helices and β-sheets.