An Empirical Polarizable Force Field Based on the Classical Drude Oscillator Model: Development History and Recent Applications

Abstract

Molecular mechanics force fields that explicitly account for induced polarization represent the next generation of physical models for molecular dynamics simulations. Several methods exist for modeling induced polarization, and here we review the classical Drude oscillator model, in which electronic degrees of freedom are modeled by charged particles attached to the nuclei of their core atoms by harmonic springs. We describe the latest developments in Drude force field parametrization and application, primarily in the last 15 years. Emphasis is placed on the Drude-2013 polarizable force field for proteins, DNA, lipids, and carbohydrates. We discuss its parametrization protocol, development history, and recent simulations of biologically interesting systems, highlighting specific studies in which induced polarization plays a critical role in reproducing experimental observables and understanding physical behavior. As the Drude oscillator model is computationally tractable and available in a wide range of simulation packages, it is anticipated that use of these more complex physical models will lead to new and important discoveries of the physical forces driving a range of chemical and biological phenomena.

Balancing the Interactions of Mg2+ in Aqueous Solution and with Nucleic Acid Moieties For a Polarizable Force Field Based on the Classical Drude Oscillator Model

“…20 The PMF profiles (Figure 4) confirm the previous observation 10 that CHARMM36 overestimates the free energy barrier, with a value of 13.1 ± 0.2 kcal mol −1 . In contrast, the Drude-2013 force field 16 (which includes ion parameters from Yu et al 20 ) underestimated the free energy barrier (4.7 ± 0.7 kcal mol −1 ), comparable to the value produced by the AMOEBA force field. 9, 13, 15 The application of the NBFIX described above to Mg 2+ -water interactions yields a value 10.4 ± 0.3 kcal mol −1 , in good agreement with the experimental activation barrier.…”

“…The application of an NBFIX to the interaction of Mg 2+ and the Drude oscillator of water (MAGD-DOH2) was needed due to the observation that water molecules frequently dissociated from [Mg•(H 2 O) 6 ] 2+ complexes in bulk solution in < 10 ns using the Drude-2013 force field 16 (data not shown). As the off-rate for inner-shell water molecules is 6.7 × 10 5 s −1 in bulk solution, 8 such exchanges should only occur on the µs scale.…”

“…16, 28, 30, 31 Instead, we parametrized interactions with Mg 2+ using pair-specific LJ terms (called NBFIX in CHARMM), including terms between the water Drude oscillators and Mg 2+ . Additionally, for some interactions, through-space Thole dipole screening factors (NBTHOLE) were applied for some atom pairs (see Results and Discussion), as was done previously in the parametrization of monovalent and divalent ions in the force field.…”

“…The NBFIX parameters (ε and R min ) were allowed to vary freely in the ranges of −0.250 < ε < −0.001 kcal mol −1 and 2.0 < R min < 5.0 Å. The initial value of the NBTHOLE term was 2.6, which is a default value for the sum of atom-based Thole terms in the Drude-2013 force field; 16 this value was allowed to vary from 0.5 to 3.0, a range of values typically used to screen ion interactions. Target data for the fitting protocol were the minimum distances between the ligating atom on the nucleic acid base or DMP and the Mg 2+ ion, as well as a characteristic angle that was established for each complex (see below).…”

“…21 Details of this force field and its development history are reviewed elsewhere. 16 Yu et al previously parametrized a series of monovalent and divalent ions using the Drude oscillator model. 20 The present work is a refinement of those parameters, specifically for Mg 2+ and its interactions with water, ions, and nucleic acid moieties.…”