Classical Drude Oscillator Model Research Articles

Drude Model Based Polarizable Force Field for Lipids

Incorporation of electronic polarization of atoms induced by local electric fields in the empirical potential function used to generate molecular dynamics simulations is important for accurate studies of various biological processes such as ion transfer, binding and selectivity. In this work, we present new polarizable force fields for the simulations of zwitterionic lipids membranes based on the classical Drude oscillator model. The lipids considered include: dipalmitoyl phosphatidylcholine (DPPC), dipalmitoyl phosphatidylethanolamine (DPPE), and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC).The parameterization strategy relies on the properties of small model compound analogs of functional groups in the molecules. The polar head group parameters are based on the molecular ions dimethyl phosphate and tetramethyl ammonium, methyl acetate for the glycerol linker region and linear alkanes as well as alkenes for the aliphatic tail of the lipid. The small molecule parameters are optimized and validated against a suite of experimental properties. The resulting lipid force field is applied to the simulation of lipid bilayers and monolayers for each lipid. For the lipid bilayer, the area per lipid, deuterium order parameters and electron density profile, and for the monolayers, the surface pressure and dipole potentials are all found to be in good agreement with experimental data when available. Thus, we have successfully validated our force field for a number of lipids.

Solvent Boundary Potentials for Hybrid QM/MM Computations Using Classical Drude Oscillators: A Fully Polarizable Model.

Accurate quantum mechanical/molecular mechanical (QM/MM) treatments should account for MM polarization and properly include long-range electrostatic interactions. We report on a development that covers both these aspects. Our approach combines the classical Drude oscillator (DO) model for the electronic polarizability of the MM atoms with the generalized solvent boundary Potential (GSBP) and the solvated macromolecule boundary potential (SMBP). These boundary potentials (BP) are designed to capture the long-range effects of the outer region of a large system on its interior. They employ a finite difference approximation to the Poisson-Boltzmann equation for computing electrostatic interactions and take into account outer-region bulk solvent through a polarizable dielectric continuum (PDC). This approach thus leads to fully polarizable three-layer QM/MM-DO/BP methods. As the mutual responses of each of the subsystems have to be taken into account, we propose efficient schemes to converge the polarization of each layer simultaneously. For molecular dynamics (MD) simulations using GSBP, this is achieved by considering the MM polarizable model as a dynamical degree of freedom, and hence contributions from the boundary potential can be evaluated for a frozen state of polarization at every time step. For geometry optimizations using SMBP, we propose a dual self-consistent field approach for relaxing the Drude oscillators to their ideal positions and converging the QM wave function with the proper boundary potential. The chosen coupling schemes are evaluated with a test system consisting of a glycine molecule in a water ball. Both boundary potentials are capable of properly reproducing the gradients at the inner-region atoms and the Drude oscillators. We show that the effect of the Drude oscillators must be included in all terms of the boundary potentials to obtain accurate results and that the use of a high dielectric constant for the PDC does not lead to a polarization catastrophe of the DO models. Optimum values for some key parameters are discussed. We also address the efficiency of these approaches compared to standard QM/MM-DO calculations without BP. In the SMBP case, computation times can be reduced by around 40% for each step of a geometry optimization, with some variation depending on the chosen QM method. In the GSBP case, the computational advantages of using the boundary potential increase with system size and with the number of MD steps.

Development of CHARMM Polarizable Force Field for Nucleic Acid Bases Based on the Classical Drude Oscillator Model

A polarizable force field for nucleic acid bases based on the classical Drude oscillator model is presented. Parameter optimization was performed to reproduce crystallographic geometries, crystal unit cell parameters, heats of sublimation, vibrational frequencies and assignments, dipole moments, molecular polarizabilities and quantum mechanical base-base and base-water interaction energies. The training and validation data included crystals of unsubstituted and alkyl-substituted adenine, guanine, cytosine, uracil, and thymine bases, hydrated crystals, and hydrogen bonded base pairs. Across all compounds, the RMSD in the calculated heats of sublimation is 4.1%. This equates to an improvement of more than 2.5 kcal/mol in accuracy compared to the nonpolarizable CHARMM27 force field. However, the level of agreement with experimental molecular volume decreased from 1.7% to 2.1% upon moving from the nonpolarizable to the polarizable model. The representation of dipole moments is significantly improved with the Drude polarizable force field. Unlike in additive force fields, there is no requirement for the gas-phase dipole moments to be overestimated, illustrating the ability of the Drude polarizable force field to treat accurately differently dielectric environments and indicating the improvements in the electrostatic model. Validation of the model was performed on the basis of the calculation of the gas-phase binding enthalpies of base pairs obtained via potential of mean force calculations; the additive and polarizable models both performed satisfactorily with average differences of 0.2 and 0.9 kcal/mol, respectively, and rms differences of 1.3 and 1.7 kcal/mol, respectively. Overall, considering the number of significant improvements versus the additive CHARMM force field, the incorporation of explicit polarizability into the force field for nucleic acid bases represents an additional step toward accurate computational modeling of biological systems.

Polarizable empirical force field for sulfur-containing compounds based on the classical Drude oscillator model.

Condensed-phase computational studies of molecules using molecular mechanics approaches require the use of force fields to describe the energetics of the systems as a function of structure. The advantage of polarizable force fields over nonpolarizable (or additive) models lies in their ability to vary their electronic distribution as a function of the environment. Toward development of a polarizable force field for biological molecules, parameters for a series of sulfur-containing molecules are presented. Parameter optimization was performed to reproduce quantum mechanical and experimental data for gas phase properties including geometries, conformational energies, vibrational spectra, and dipole moments as well as for condensed phase properties such as heats of vaporization, molecular volumes, and free energies of hydration. Compounds in the training set include methanethiol, ethanethiol, propanethiol, ethyl methyl sulfide, and dimethyl disulfide. The molecular volumes and heats of vaporization are in good accordance with experimental values, with the polarizable model performing better than the CHARMM22 nonpolarizable force field. Improvements with the polarizable model were also obtained for molecular dipole moments and in the treatment of intermolecular interactions as a function of orientation, in part due to the presence of lone pairs and anisotropic atomic polarizability on the sulfur atoms. Significant advantage of the polarizable model was reflected in calculation of the dielectric constants, a property that CHARMM22 systematically underestimates. The ability of this polarizable model to accurately describe a range of gas and condensed phase properties paves the way for more accurate simulation studies of sulfur-containing molecules including cysteine and methionine residues in proteins.

Polarizable Empirical Force Field for Alkanes Based on the Classical Drude Oscillator Model

Recent extensions of potential energy functions used in empirical force field calculations have involved the inclusion of electronic polarizability. To properly include this extension into a potential energy function it is necessary to systematically and rigorously optimize the associated parameters based on model compounds for which extensive experimental data are available. In the present work, optimization of parameters for alkanes in a polarizable empirical force field based on a classical Drude oscillator is presented. Emphasis is placed on the development of parameters for CH3, CH2, and CH moieties that are directly transferable to long chain alkanes, as required for lipids and other biomolecules. It is shown that a variety of quantum mechanical and experimental target data are reproduced by the polarizable model. Notable is the proper treatment of the dielectric constant of pure alkanes by the polarizable force field, a property essential for the accurate treatment of, for example, hydrophobic solvation in lipid bilayers. The present alkane force field will act as the basis for the aliphatic moieties in an extensive empirical force field for biomolecules that includes the explicit treatment of electronic polarizability.

Molecular Dynamics Study of Hydration in Ethanol−Water Mixtures Using a Polarizable Force Field

The abnormal physicochemical characteristics of ethanol solvation in water are commonly attributed to the phenomenon of hydrophobic hydration. To investigate the structural organization of hydrophobic hydration in water-ethanol mixtures, we use molecular dynamics simulations based on detailed atomic models. Induced polarization is incorporated into the potential function on the basis of the classical Drude oscillator model. Water-ethanol mixtures are simulated at 11 ethanol molar fractions, from 0.05 to 0.9. Although the water and ethanol models are parametrized separately to reproduce the vaporization enthalpy, static dielectric constant, and self-diffusion constant of neat liquids at ambient conditions, they also reproduce the energetic and dynamical properties of the mixtures accurately. Furthermore, the calculated dielectric constant for the various water-alcohol mixtures is in excellent agreement with experimental data. The simulations provide a detailed structural characterization of the mixtures. A depletion of water-water hydrogen bonding in the first hydration shell of ethanol is compensated by an enhancement in the second hydration shell. The structuring effect from the second solvation shell gives rise to a net positive hydrogen-bonding excess for ethanol molar fractions up to approximately 0.5. For larger molar fractions, the second hydration shell is not sufficiently populated to overcome the net H-bond depletion from the first shell.

Determination of Electrostatic Parameters for a Polarizable Force Field Based on the Classical Drude Oscillator.

A procedure to determine the electrostatic parameters has been developed for a polarizable empirical force field based on the classical Drude oscillator model. Atomic charges and polarizabilities for a given molecule of interest were derived from restrained fitting to quantum-mechanical electrostatic potentials (ESP) calculated at the B3LYP/ cc-pVDZ or B3LYP/aug-cc-pVDZ levels on grid points located on concentric Connolly surfaces. The determination of the atomic polarizabilities requires a series of perturbed ESP maps, each one representing the electronic response of the molecule in the presence of a background charge placed on Connolly surfaces primarily along chemical bonds and lone pairs. Reference values for the partial atomic charges were taken from the CHARMM27 additive all-atom force field, and those for the polarizabilities were based on adjusted Miller's ahp atomic polarizability values. The fitted values of atomic polarizabilities were scaled to reflect the reduced polarization expected for the condensed media and/or to correct for the systematic underestimation of experimental molecular polarizabilities by B3LYP calculations. Following correction of the polarizabilities, the atomic charges were adjusted to reproduce gas-phase dipole moments. The developed scheme has been tested on a set of small molecules representing functional moieties of nucleic acids. The derived electrostatic parameters have been successfully applied in a preliminary polarizable molecular dynamics simulation of a DNA octamer in a box of water with sodium counterions. Thus, this study confirms the feasibility of the use of a polarizable force field based on a classical Drude model for simulations of biomolecules in the condensed phase.

Modeling induced polarization with classical Drude oscillators: Theory and molecular dynamics simulation algorithm

A simple treatment for incorporating induced polarization in computer simulations is formulated on the basis of the classical Drude oscillator model. In this model, electronic induction is represented by the displacement of a charge-carrying massless particle attached to a polarizable atom under the influence of the local electric field. The traditional self-consistent field (SCF) regime of induced polarization is reproduced if these auxiliary particles are allowed to relax instantaneously to their local energy minima for any given fixed configuration of the atoms in the system. In practice, such treatment is computationally prohibitive for generating molecular dynamics trajectories because the electric field must be recalculated several times iteratively to satisfy the SCF condition, and it is important to seek a more efficient way to simulate the classical Drude oscillator model. It is demonstrated that a close approximation to the SCF regime can be simulated efficiently by considering the dynamics of an extended Lagrangian in which a small mass is attributed to the auxiliary particles, and the amplitude of their oscillations away from the local energy minimum is controlled with a low-temperature thermostat. A simulation algorithm in this modified two-temperature isobaric–isothermal ensemble is developed. The algorithm is tested and illustrated using a rigid three-site water model with one additional Drude particle attached to the oxygen which is closely related to the polarizable SPC model of Ahlström et al. [Mol. Phys. 68, 563 (1989)]. The tests with the extended Lagrangian show that stable and accurate molecular dynamics trajectories for large integration time steps (1 or 2 fs) can be generated and that liquid properties equivalent to SCF molecular dynamics can be reproduced at a fraction of the computational cost.