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

Abstract

Mg2+ ions are important in biological systems, particularly in stabilizing compact RNA folds. Mg2+ is strongly polarizing, and representing its interactions in heterogeneous environments is a challenge for empirical force field development. To date, the most commonly used force fields in molecular dynamics simulations utilize a pairwise-additive approximation for electrostatic interactions, which cannot account for the significant polarization response in systems containing Mg2+. In the present work, we refine the interactions of Mg2+ with water, Cl− ions, and nucleic acid moieties using a polarizable force field based on the classical Drude oscillator model. By targeting gas-phase quantum mechanical interaction energies and geometries of hydrated complexes, as well as condensed-phase osmotic pressure calculations, we present a model for Mg2+ that yields quantitative agreement with experimental measurements of water dissociation free energy and osmotic pressure across a broad range of concentrations. Notable is the direct modeling of steric repulsion between the water Drude oscillators and Mg2+ to treat the Pauli exclusion effects associated with overlap of the electron clouds of water molecules in the first hydration shell around Mg2+. Combined with the refined interactions with nucleic acid moieties, the present model represents a significant advancement in simulating nucleic acid systems containing Mg2+.

Polarizable Force Field for DNA Based on the Classical Drude Oscillator: II. Microsecond Molecular Dynamics Simulations of Duplex DNA

“…68 Co-solutes such as polyamines were removed. Orthorhombic crystals (P2 1 2 1 2 1 space group) were constructed by applying the prescribed symmetry operations using the CRYSTAL BUILD facility in CHARMM.…”

Polarizable force field for RNA based on the classical drude oscillator

“…The equilibrated systems were converted to the Drude polarizable model, adding Drude oscillators to all non‐hydrogen atoms and constructing lone pairs using CHARMM. This process also converted TIP3P water to polarizable SWM4‐NDP water and ions to their polarizable forms, with monovalent ion parameters taken from Yu et al and Mg 2+ parameters taken from our recent work . The polarizable systems were again subjected to energy minimization in CHARMM to relax the Drude oscillators, after which an additional 1‐ns of restrained equilibration was carried out in NAMD, using the extended Lagrangian method for integrating Drude particle positions, implemented in NAMD as Langevin dynamics .…”

Molecular dynamics simulations using the drude polarizable force field on GPUs with OpenMM: Implementation, validation, and benchmarks

“…The Drude functional form shares many features with the additive CHARMM force field, 24 including treatment of bonded forces, the Lennard-Jones form to treat pairwise van der Waals interactions and corresponding off-diagonal (NBFIX) terms, including terms involving Drude particles, 25,26 and Coulomb’s Law to treat electrostatic interactions between point charges. Additional elements of the functional form include explicit inclusion of screened 1–2 and 1–3 dipole-dipole interactions and anisotropic polarization.…”

“…We evaluated protein (ubiquitin, PDB 1UBQ) 35 , DNA (Dickerson-Drew dodecamer, EcoRI, PDB 1BNA), 36 and 1 M MgCl 2 systems, all taken from previous studies. 25,37,38 Each system was solvated in SWM4-NDP water 39 and the EcoRI system included ~100 mM NaCl. The differences between forces computed by the two programs were evaluated for each atom in the systems using the relative errors defined by the L2 norm between its (x,y,z) component: $$e=\sqrt{{\sum }_{i=x,y,z}{\left(\frac{F_i^{\text{OpenMM}}-F_i^{\text{CHARMM}}}{F_i^{\text{CHARMM}}}\right)}^2}$$…”