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

Gerhard König,Sereina Riniker

doi:10.1098/rsfs.2019.0121

Gerhard König, Sereina Riniker

Open Access

https://doi.org/10.1098/rsfs.2019.0121

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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.

Highlights

Computer simulations have become an indispensable tool to study processes involving proteins, nucleic acids, lipid membranes, and drug-like molecules
The molecular structure is maintained by harmonic functions for bond stretching, bond-angle bending, and out-of-plane distortions, while Fourier expansions are used for the dihedral-angle torsions
Non-bonded interactions include the van der Waals interactions, which are modelled by a Lennard-Jones potential, and electrostatic interactions based on point charges

Summary

Introduction

Computer simulations have become an indispensable tool to study processes involving proteins, nucleic acids, lipid membranes, and drug-like molecules. MM force fields are fast and well suited for sampling, but involve many approximations that limit their accuracy (see, e.g., Ref. 4 for a review) Their potential-energy function U is a sum of simple terms.[5] The molecular structure is maintained by harmonic functions for bond stretching, bond-angle bending, and out-of-plane distortions (improper dihedrals), while Fourier expansions are used for the dihedral-angle torsions. QM approaches[6,7,8,9,10,11,12,13,14] are based on molecular orbital calculations and combine a heavy computational burden with highly accurate interactions They capture the correct physical behaviour, but are limited in terms of the size and time scale of the processes that can be studied (usually only hundreds of atoms on the time scale of picoseconds)

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