On the faithfulness of molecular mechanics representations of proteins towards quantum-mechanical energy surfaces

Abstract

Force fields based on molecular mechanics (MM) are the main computational tool to study the relationship between protein structure and function at the molecular level. To validate the quality of such force fields, high-level quantum-mechanical (QM) data are employed to test their capability to reproduce the features of all major conformational substates of a series of blocked amino acids. The phase-space overlap between MM and QM is quantified in terms of the average structural reorganization energies over all energy minima. Here, the structural reorganization energy is the MM potential-energy difference between the structure of the respective QM energy minimum and the structure of the closest MM energy minimum. Thus, it serves as a measure for the relative probability of visiting the QM minimum during an MM simulation. We evaluate variants of the AMBER, CHARMM, GROMOS and OPLS biomolecular force fields. In addition, the two blocked amino acids alanine and serine are used to demonstrate the dependence of the measured agreement on the QM method, the phase, and the conformational preferences. Blocked serine serves as an example to discuss possible improvements of the force fields, such as including polarization with Drude particles, or using tailored force fields. The results show that none of the evaluated force fields satisfactorily reproduces all energy minima. By decomposing the average structural reorganization energies in terms of individual energy terms, we can further assess the individual weaknesses of the parametrization strategies of each force field. The dominant problem for most force fields appears to be the van der Waals parameters, followed to a lesser degree by dihedral and bonded terms. Our results show that performing a simple QM energy optimization from an MM-optimized structure can be a first test of the validity of a force field for a particular target molecule.

Keywords: AMBER; CHARMM; GROMOS; OPLS; molecular mechanics; quantum mechanics.

Figure 1.

(a) Snapshots from free-energy calculations based on molecular mechanics (MM) simulations can be post-processed in a highly parallel fashion with quantum-mechanical (QM) potential-energy evaluations to obtain QM-corrected free-energy differences. Each arrow represents an alchemical transformation from the MM Hamiltonian to the QM Hamiltonian. (b) The alchemical transformation at each snapshot converts the MM potential-energy function (red) to the QM potential (blue). Depending on the position along the one-dimensional reaction coordinate that connects the two end states, different potential-energy differences between MM and QM can be obtained. A simple metric for the convergence of free-energy calculations is the structural reorganization energy ($\mathrm{\Delta }{\mathrm{U}}_{\mathrm{reorg}}$) [28]. It is characterized by the MM potential-energy difference between the QM optimal structure and the MM optimal structure. Thus, it directly measures the energetic costs for the MM force field to sample the correct QM structure. $\mathrm{\Delta }{\mathrm{U}}_{\mathrm{reorg}}$ is also related to the variance of the potential-energy difference distribution, which determines the variance of the free-energy estimate.