Determination of side-chain-rotamer and side-chain and backbone virtual-bond-stretching potentials of mean force from AM1 energy surfaces of terminally-blocked amino-acid residues, for coarse-grained simulations of protein structure and folding. II. Results, comparison with statistical potentials, and implementation in the UNRES force field.

Using the harmonic-approximation approach of the accompanying article and AM1 energy surfaces of terminally blocked amino-acid residues, we determined physics-based side-chain rotamer potentials and the side-chain virtual-bond-deformation potentials of 19 natural amino-acid residues with side chains. The potentials were approximated by analytical formulas and implemented in the UNRES mesoscopic dynamics program. For comparison, the corresponding statistical potentials were determined from 19,682 high-resolution protein structures. The low free-energy region of both the AM1-derived and the statistical potentials is determined by the valence geometry and the L-chirality, and its size increases with side-chain flexibility and decreases with increasing virtual-bond-angle theta. The differences between the free energies of rotamers are greater for the AM1-derived potentials compared with the statistical potentials and, for alanine and other residues with small side chains, a region corresponding to the C(ax)(7) conformation has remarkably low free-energy for the AM1-derived potentials, as opposed to the statistical potentials. These differences probably result from the interactions between neighboring residues and indicate the need for introduction of cooperative terms accounting for the coupling between side-chain rotamer and backbone interactions. Both AM1-derived and statistical virtual-bond-deformation potentials are multimodal for flexible side chains and are topologically similar; however, the regions of minima of the statistical potentials are much narrower, which probably results from imposing restraints in structure determination. The force field with the new potentials was preliminarily optimized using the FBP WW domain (1E0L) and the engrailed homeodomain (1ENH) as training proteins and assessed to be reasonably transferable. 2009 Wiley Periodicals, Inc.