Polarizable Force Fields for Biomolecular Modeling

Abstract

Classical electrostatics models that take into account polarization appeared as early as the 1950s. Barker in his 1953 paper "Statistical Mechanics of Interacting Dipoles" discussed the electrostatic energy of molecules in terms of "permanent and induced dipoles". 13 Currently, polarizable models generally fall into three categories: those based on induced point dipoles, 9, 14-23 the classical Drude oscillators, 24-26 and fluctuating charges. 27-30 More sophisticated force fields that are "electronic structure-based" 31, 32 or use "machine learning methods" 33 also exist, but incur higher computational costs. Discussions of the advantages and disadvantages of each model and their applications will be presented in the following sections. Compared to fixed charge models, the polarizable models are still in a relatively early stage. Only in the past decade or so has there been a systematic effort to develop general polarizable force fields for molecular modeling. A number of reviews have been published to discuss various aspects of polarizable force fields and their development. 9, 34-40 Here, we focus on the recent development and applications of different polarizable force fields. We begin with a brief introduction to the basic principles and formulae underlying alternative models. Next, the recent progress of several well-developed polarizable force fields is reviewed. Finally, applications of polarizable models to a range of molecular systems, including water and other small molecules, ion solvation, peptides, proteins and lipid systems are presented.

Quantum mechanical force fields for condensed phase molecular simulations

“…The metenkephalin solute is solvated in a 42 3 Å 3 box of TIP4P/Ew waters. The U5A3 system is solvated in a 46 3 Å 3 box of TIP4P/Ew waters and an ion environment of 7 Na + and 6 Cl − .…”

“…The U5A3 system is solvated in a 46 3 Å 3 box of TIP4P/Ew waters and an ion environment of 7 Na + and 6 Cl − . These systems were prepared by performing pure-MM simulations (1 fs/step) for 1 ns at 298 K and 1 atm to equilibrate the density.…”

A Boundary‐Integral Approach for the Poisson–Boltzmann Equation with Polarizable Force Fields

“…Recently, there has been an increasing amount of research developing polarizable force fields . Among the most popular ones is atomic multipole optimized energetics for biomolecular applications (AMOEBA), which is available in several packages, such as Tinker, Force Field X, OpenMM, and AMBER .…”

Toward polarizable AMOEBA thermodynamics at fixed charge efficiency using a dual force field approach: application to organic crystals

“…23 Thus, to apply the configurational sampling algorithms needed to quantify thermodynamics, multipolar force fields must address transferability of their multipole moments as a function of molecular conformation, while also consistently treating both intra- and intermolecular polarization. 23, 24 A few examples of multipolar energy functions include AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) 24–26 , GMM (Gaussian Multipolar Model) 27, 28 , SIBFA (Sum of Interactions Between Fragments Ab Initio Computed) 29, 30 and NEMO (Non-empirical Molecular Orbital) 31 , which are described in recent reviews 32–34 . The accuracy and transferability improvements of AMOEBA relative to FC force fields have been demonstrated in the context of water 25, 35 , ion solvation 36 , the properties of small organic molecules 24, 26, 36–38 and for protein energetics.…”

“…The accuracy and transferability improvements of AMOEBA relative to FC force fields have been demonstrated in the context of water 25, 35 , ion solvation 36 , the properties of small organic molecules 24, 26, 36–38 and for protein energetics. 34, 39 …”