Extension of UNRES Force
Field to Treat Polypeptide
Chains with d‑Amino Acid Residues
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Abstract
Coarse-grained force fields for protein simulations are
usually
designed and parametrized to treat proteins composed of natural l-amino acid residues. However, d-amino acid residues
occur in bacterial, fungal (e.g., gramicidins), as well as human-designed
proteins. For this reason, we have extended the UNRES coarse-grained
force field developed in our laboratory to treat systems with d-amino acid residues. We developed the respective virtual-bond-torsional
and double-torsional potentials for rotation about the C<sup>α</sup>···C<sup>α</sup> virtual-bond axis and two consecutive
C<sup>α</sup>···C<sup>α</sup> virtual-bond
axes, respectively, as functions of virtual-bond-dihedral angles γ.
In turn, these were calculated as potentials of mean force (PMFs)
from the diabatic energy surfaces of terminally blocked model compounds
for glycine, alanine, and proline. The potential-energy surfaces were
calculated by using the <i>ab initio</i> method of molecular
quantum mechanics at the Møller–Plesset (MP2) level of
theory and the 6-31G(d,p) basis set, with the rotation angles of the
peptide groups about C<sub><i>i</i>–1</sub><sup>α</sup>···C<sub><i>i</i></sub><sup>α</sup> (λ<sup>(1)</sup>) and C<sub><i>i</i></sub><sup>α</sup>···C<sub><i>i</i>+1</sub><sup>α</sup> (λ<sup>(2)</sup>) used as variables, and the energy was minimized
with respect to the remaining degrees of freedom. The PMFs were calculated
by numerical integration for all pairs and triplets with all possible
combinations of types (glycine, alanine, and proline) and chirality
(d or l); however, symmetry relations reduce the
number of nonequivalent torsional potentials to 13 and the number
of double-torsional potentials to 63 for a given C-terminal blocking
group. Subsequently, one- (for torsional) and two-dimensional (for
double-torsional potentials) Fourier series were fitted to the PMFs
to obtain analytical expressions. It was found that the torsional
potentials of the x–Y and X–y types, where X and Y are
Ala or Pro, respectively, and a lowercase letter denotes d-chirality, have global minima for small absolute values of γ,
accounting for the double-helical structure of gramicidin A, which
is a dimer of two chains, each possessing an alternating d-Tyr–l-Tyr sequence, and similar peptides. The side-chain
and correlation potentials for d-amino acid residues were
obtained by applying the reflection about the C<sub><i>i</i>–1</sub><sup>α</sup>···C<sub><i>i</i></sub><sup>α</sup>···C<sub><i>i</i>+1</sub><sup>α</sup> plane
to the respective potentials for the l-amino acid residues