Extension of UNRES Force Field to Treat Polypeptide Chains with d‑Amino Acid Residues

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^α···C^α virtual-bond axis and two consecutive C^α···C^α 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_<i>i</i>–1^α···C_<i>i</i>^α (λ⁽¹⁾) and C_<i>i</i>^α···C_<i>i</i>+1^α (λ⁽²⁾) 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_<i>i</i>–1^α···C_<i>i</i>^α···C_<i>i</i>+1^α plane to the respective potentials for the l-amino acid residues