A coupled two-dimensional main chain torsional potential for protein dynamics: generation and implementation

Abstract

Main chain torsions of alanine dipeptide are parameterized into coupled 2-dimensional Fourier expansions based on quantum mechanical (QM) calculations at M06 2X/aug-cc-pvtz//HF/6-31G** level. Solvation effect is considered by employing polarizable continuum model. Utilization of the M06 2X functional leads to precise potential energy surface that is comparable to or even better than MP2 level, but with much less computational demand. Parameterization of the 2D expansions is against the full main chain torsion space instead of just a few low energy conformations. This procedure is similar to that for the development of AMBER03 force field, except unique weighting factor was assigned to all the grid points. To avoid inconsistency between quantum mechanical calculations and molecular modeling, the model peptide is further optimized at molecular mechanics level with main chain dihedral angles fixed before the calculation of the conformational energy on molecular mechanical level at each grid point, during which generalized Born model is employed. Difference in solvation models at quantum mechanics and molecular mechanics levels makes this parameterization procedure less straightforward. All force field parameters other than main chain torsions are taken from existing AMBER force field. With this new main chain torsion terms, we have studied the main chain dihedral distributions of ALA dipeptide and pentapeptide in aqueous solution. The results demonstrate that 2D main chain torsion is effective in delineating the energy variation associated with rotations along main chain dihedrals. This work is an implication for the necessity of more accurate description of main chain torsions in the future development of ab initio force field and it also raises a challenge to the development of quantum mechanical methods, especially the quantum mechanical solvation models.

Correct folding of an α-helix and a β-hairpin using a polarized 2D torsional potential

“…The model peptide primarily adopts extended conformations, including β and PPII, under the AMBER03 2D force field39. This intrinsic conformational propensity of the AMBER03 2D force field results directly from the quantum mechanical potential energy surface of the alanine dipeptide and agrees with experimental observations445455.…”

“…We adopt the tactic of fitting the secondary structure propensity according to high level quantum mechanical calculations of short model peptides and accounting for the non-pairwise effect in long peptide chains by using electrostatic polarization. The feasibility of this tactic and the reliability of this new force field have been justified in this study as well as in our previous work39. These studies pave the way for the future development of polarizable force fields.…”

“…Moreover, the lack of an explicit polarization effect in pairwise force fields impedes the occurrence of ordered secondary structures. Recently, we optimized the AMBER force fields by replacing the uncoupled main chain torsion energy with a set of two-dimensional Fourier expansions, of which the parameters are fitted to the potential energy map resulting from high level quantum mechanical calculations of an alanine dipeptide39. Other force field parameters are kept intact as in the original AMBER force field.…”

“…A detailed explanation of the implementation and parameterization of this coupled 2D torsion potential can be found in our previous work39. Here we give a brief introduction.…”

“…As these two main chain torsion energies are not physically separable in the potential energy map, a more desirable choice is to expand the torsion energy function by using orthogonal basis sets of both φ and ψ in a coupled fashion. Recently, we calibrated the AMBER03 and AMBER99SB force fields by replacing the one-dimensional Fourier series for φ and ψ with a coupled 2-dimensional (2D) main chain torsion energy (denoted AMBER03 2D and AMBER99SB 2D )39. These two force fields are more balanced among various conformations than the original AMBER force fields.…”