Continuing
our effort to introduce d-amino-acid residues
in the united residue (UNRES) force field developed in our laboratory,
in this work the Cα ··· Cα ··· Cα backbone-virtual-bond-valence-angle
(θ) potentials for systems containing d-amino-acid
residues have been developed. The potentials were determined by integrating
the combined energy surfaces of all possible triplets of terminally
blocked glycine, alanine, and proline obtained with ab initio molecular
quantum mechanics at the MP2/6-31G(d,p) level to calculate the corresponding
potentials of mean force (PMFs). Subsequently, analytical expressions
were fitted to the PMFs to give the virtual-bond-valence potentials
to be used in UNRES. Alanine represented all types of amino-acid residues
except glycine and proline. The blocking groups were either the N-acetyl and N′,N′-dimethyl or N-acetyl and pyrrolidyl group,
depending on whether the residue next in sequence was an alanine-type
or a proline residue. A total of 126 potentials (63 symmetry-unrelated
potentials for each set of terminally blocking groups) were determined.
Together with the torsional, double-torsional, and side-chain-rotamer
potentials for polypeptide chains containing d-amino-acid
residues determined in our earlier work (Sieradzan et al. J.
Chem. Theory Comput., 2012, 8, 4746), the new
virtual-bond-angle (θ) potentials now constitute the complete
set of physics-based potentials with which to run coarse-grained simulations
of systems containing d-amino-acid residues. The ability
of the extended UNRES force field to reproduce thermodynamics of polypeptide
systems with d-amino-acid residues was tested by comparing
the experimentally measured and the calculated free energies of helix
formation of model KLALKLALxxLKLALKLA peptides, where x denotes any d- or l- amino-acid residue. The obtained results demonstrate
that the UNRES force field with the new potentials reproduce the changes
of free energies of helix formation upon d-substitution but
overestimate the free energies of helix formation. To test the ability
of UNRES with the new potentials to reproduce the structures of polypeptides
with d-amino-acid residues, an ab initio replica-exchange
folding simulation of thurincin H from Bacillus thuringiensis, which has d-amino-acid residues in the sequence, was carried
out. UNRES was able to locate the native α-helical hairpin structure
as the dominant structure even though no native sulfide–carbon
bonds were present in the simulation.