Accurate Reproduction of Quantum Mechanical Many-Body Interactions in Peptide Main-Chain Hydrogen-Bonding Oligomers by the Polarizable Gaussian Multipole Model

Abstract

A key advantage of polarizable force fields is their ability to model the atomic polarization effects that play key roles in the atomic many-body interactions. In this work, we assessed the accuracy of the recently developed polarizable Gaussian Multipole (pGM) models in reproducing quantum mechanical (QM) interaction energies, many-body interaction energies, as well as the nonadditive and additive contributions to the many-body interactions for peptide main-chain hydrogen-bonding conformers, using glycine dipeptide oligomers as the model systems. Two types of pGM models were considered, including that with (pGM-perm) and without (pGM-ind) permanent atomic dipoles. The performances of the pGM models were compared with several widely used force fields, including two polarizable (Amoeba13 and ff12pol) and three additive (ff19SB, ff15ipq, and ff03) force fields. Encouragingly, the pGM models outperform all other force fields in terms of reproducing QM interaction energies, many-body interaction energies, as well as the nonadditive and additive contributions to the many-body interactions, as measured by the root-mean-square errors (RMSEs) and mean absolute errors (MAEs). Furthermore, we tested the robustness of the pGM models against polarizability parameterization errors by employing alternative polarizabilities that are either scaled or obtained from other force fields. The results show that the pGM models with alternative polarizabilities exhibit improved accuracy in reproducing QM many-body interaction energies as well as the nonadditive and additive contributions compared with other polarizable force fields, suggesting that the pGM models are robust against the errors in polarizability parameterizations. This work shows that the pGM models are capable of accurately modeling polarization effects and have the potential to serve as templates for developing next-generation polarizable force fields for modeling various biological systems.

Transferability of the Electrostatic Parameters of the Polarizable Gaussian Multipole Model

“…Two desirable properties of molecular mechanical force fields are accuracy and transferability. Various previous works have demonstrated the accuracy of the pGM models. ,, In this work, we assessed the transferability of the electrostatic parameters of the pGM-ind and pGM-perm models by exploring whether the pGM models can accurately reproduce the electrostatic properties of larger molecular systems or different molecular conformations other than the molecules or conformations used for parametrizations. Encouragingly, as measured by RRMS μ and ARRMS V , both the pGM-ind and pGM-perm models show significantly better transferability than the point-charge additive model.…”

“…56 A recent work assessed the accuracy of the pGM models in reproducing QM interaction energies, many-body interaction energies, as well as the nonadditive and additive contributions to the manybody interactions for peptide main-chain hydrogen-bonding conformers, which showed that the pGM models outperform all other tested and widely used polarizable and additive force fields. 55 However, there has been no work assessing the transferability of the pGM models, that is, whether the pGM models can accurately reproduce the electrostatic properties of larger molecular systems or different molecular conformations other than the molecules or conformations used for parametrizations. This is the primary focus of this work.…”

“…The induced dipole model is one of the most studied polarizable models, which has been incorporated into various Amber polarizable force fields, including ff02, ff02rl, and ff12pol. − In this model, the induced dipole μ i of atom i subject to the external electric field E i that comes from all the atoms other than i is where α i is the isotropic polarizability of atom i and T ij is the dipole field tensor with the matrix form where I is the identity matrix; x , y , and z are the Cartesian components along the vector between atoms i and j at distance r ij ; and f e and f t are distance-dependent damping functions that modify T ij to avoid the so-called “polarization catastrophe” problem, which is the phenomenon that induced dipole diverges due to the cooperative induction between induced dipoles at short distances. , Various damping schemes have been proposed by Thole, which have been incorporated into the Amber ff12pol force field. − However, one disadvantage of Thole’s schemes is that they only screen the interactions between induced dipoles, leading to an inconsistent treatment of the polarizations due to fixed charges and permanent multipoles. About a decade ago, a damping scheme that models atomic electric multipoles using Gaussian electron densities was proposed by Elking et al, − which was later named the polarizable Gaussian multipole (pGM) model. − The pGM model overcomes the disadvantage of Thole’s schemes by screening all short-range electrostatic interactions in a physically consistent manner, including the interactions of charge–charge, charge–dipole, charge–quadrupole, dipole–dipole, and so on. The formula of damping functions f e and f t for the pGM model is as follows where is the inverse of the pGM “radius” of the Gaussian density distribution of atom i ; s is a constant screening factor; and is the error function of S ij .…”

“…Moreover, the electrostatic parameterizations on various molecules with various electrostatic models using the PyRESP program show that the pGM models consistently produce ESPs and molecular electric moments with a better agreement with QM-calculated results than the point-charge additive model . A recent work assessed the accuracy of the pGM models in reproducing QM interaction energies, many-body interaction energies, as well as the nonadditive and additive contributions to the many-body interactions for peptide main-chain hydrogen-bonding conformers, which showed that the pGM models outperform all other tested and widely used polarizable and additive force fields …”

Optimal Scheme to Achieve Energy Conservation in Induced Dipole Models

“…Polarizable force fields, encapsulating interactions between charges and induced higher moments like dipoles and quadrupoles, have shown superiority in depicting atomistic interactions over previous fixed-charge additive force field models, per comparisons with high-level quantum mechanical calculations. Strategies for polarizable force field development are varied, involving Drude oscillators, , fluctuating charges, induced dipoles, − and continuum dielectrics. , Recently, the polarizable Gaussian multipole (pGM) model − has emerged as a promising alternative approach, employing Gaussian-shaped multipoles to consistently treat intra- and intermolecular electrostatic interactions and circumvent “polarization catastrophe”. , …”