Coarse-grained torsional potential of polypeptide backbone by fragment molecular orbital method: Dependence on coarse-graining scheme

Coarse graining of polymer chains involves a usually arbitrary assignment of atoms to extended sites. In this work, we use the scale-consistent theory of coarse graining, in which all-atom potential energy surfaces are mapped to the effective coarse-grained energy surfaces by partitioning the potential of mean force of a system into Kubo cluster-cumulant functions, to analyze the dependence of polypeptide-backbone coarse-grained torsional potential on the definition of coarse-grained sites. The polypeptide-backbone unit is modeled by a glycine residue and is divided into CH3–CONHCH2–CONHCH3 (CH3–BN1–BN2) or CH3CONH–CH2CONH–CH3 (BC1–BC2–CH3) sites, with methyl as a capping group. We use the fragment molecular orbital method to partition the all-atom potential energies into single- (site), two-body (site-pair), and three-body (site-triad) contributions to eliminate those involving the capping group. We demonstrate that the torsional potential corresponding to the BC1–BC2–CH3 partition differs remarkably from that of the CH3–BN1–BN2 partition and that obtained from the energy surface of whole terminally blocked glycine. This difference is caused by the electron-density leak outside the interacting BC1 and BC2 units, resulting from their borders running across the single N–C bonds. Consequently, a preferable choice of the boundary between connected sites is to set it across a bond between atoms with a similar electronegativity.