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.

A newly developed AMBER compatible force field with coupled backbone torsion potential terms (AMBER032D) is utilized in a folding simulation of a mini-protein Trp-cage. Through replica exchange and direct molecular dynamics (MD) simulations, a multi-step folding mechanism with a synergetic folding of the hydrophobic core (HPC) and the α-helix in the final stage is suggested. The native structure has the lowest free energy and the melting temperature predicted from the specific heat capacity C v is only 12 K higher than the experimental measurement. This study, together with our previous study, shows that AMBER032D is an accurate force field that can be used for protein folding simulations.

A new modification to the AMBER force field that incorporates the coupled two-dimensional main chain torsion energy has been evaluated for the balanced representation of secondary structures. In this modified AMBER force field (AMBER032D), the main chain torsion energy is represented by 2-dimensional Fourier expansions with parameters fitted to the potential energy surface generated by high-level quantum mechanical calculations of small peptides in solution. Molecular dynamics simulations are performed to study the folding of two model peptides adopting either α-helix or β-hairpin structures. Both peptides are successfully folded into their native structures using an AMBER032D force field with the implementation of a polarization scheme (AMBER032Dp). For comparison, simulations using a standard AMBER03 force field with and without polarization, as well as AMBER032D without polarization, fail to fold both peptides successfully. The correction to secondary structure propensity in the AMBER03 force field and the polarization effect are critical to folding Trpzip2; without these factors, a helical structure is obtained. This study strongly suggests that this new force field is capable of providing a more balanced preference for helical and extended conformations. The electrostatic polarization effect is shown to be indispensable to the growth of secondary structures.

The accuracy of force fields is of utmost importance in molecular modeling of proteins. Despite successful applications of force fields for about the past 30 years, some inherent flaws lying in force fields, such as biased secondary propensities and fixed atomic charges, have been observed in different aspects of biomolecular research; hence, a correction to current force fields is desirable. Because of the simplified functional form and the limited number of parameters for main chain torsion (MCT) in traditional force fields, it is not easy to propose an exquisite force field that is well-balanced among various conformations. Recently, AMBER-compatible force fields with coupled MCT term have been proposed, which show some improvement over AMBER03 and AMBER99SB force fields. In this work, further calibration of the torsional parameters has been conducted by changing the solvation model in quantum mechanical calculation and minimizing the deviation from the nuclear magnetic resonance experiments for some benchmark model systems and a folded protein. The results show that the revised force fields give excellent agreement with experiments in J coupling, chemical shifts, and secondary structure populations. In addition, the polarization effect is found to be crucial for the systems with ordered secondary structures.