Determination of virtual-bond-angle potentials of mean force for coarse-grained simulationsof protein structure and folding from ab initio energy surfaces of terminally-blocked glycine,alanine, and proline

Abstract

We determined the potentials of mean force corresponding to the bending of virtual-bond angles (θ) for use in our united-residue (UNRES) force field. The potentials were determinedby integrating the ab initio energy surfaces of terminally-blocked glycine,alanine, and proline calculated in our earlier work at the MP2/6-31G(d, p)level (Ołdziej et al 2003 J. Phys. Chem. A 107 8035), where alanine representsall types of amino-acid residues except for glycine and proline. This resulted in27 different free-energy surfaces. The potentials were found to depend both onθ and on the two virtual-bond dihedral angles (γ1 andγ2) whose axesare the edges of θ, as well as on the types of all three consecutive amino-acid residues whoseCα atoms definethe angle θ. The type of residue at the second and third position of a triad has a major influence onthe potentials, while that in the first position is less important. Each surface was fitted wellby a three-dimensional Fourier series in the trigonometric functions of multiplicities ofθ/2,γ1,and γ2; these analytical expressions can readily be implemented in the UNRES forcefield, thus replacing our earlier knowledge-based virtual-bond valence potentials.