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.