Statistical mechanics of polarizable force fields based on classical Drude oscillators with dynamical propagation by the dual-thermostat extended Lagrangian

Computationally Efficient Polarizable MD Simulations: A Simple Water Model for the Classical Drude Oscillator Polarizable Force Field

An improvement in the computational efficiency of polarizable force field simulations is made through the development of a polarizable Drude water model, SWM3, in combination with the use of Lennard-Jones Particle Mesh Ewald (LJPME) for the treatment of long-range LJ interactions. The experimental bulk properties, density, heat of vaporization, dielectric constant, and self-diffusion constant of the SWM3 model are accurately replicated at ambient condition. The temperature dependence of the bulk properties is also captured except for the density. Microscopic properties, such as hydration free energy, dimer properties, and binding energies of clusters are well represented. The SWM3 model is ∼40% faster than the SWM4 water model traditionally used with the Drude force field, and use of LJPME offers an additional 30% speedup in heterogeneous systems. This combination makes the SWM3-based Drude model only 2.6-fold slower than the TIP3P-based additive simulations.

Revised 4-Point Water Model for the Classical Drude Oscillator Polarizable Force Field: SWM4-HLJ

In this work the 4-point polarizable SWM4 Drude water model is reparametrized. Multiple models were developed using different strategies toward reproduction of specific target data. Results indicate that no individual model can reproduce all the selected target data in the context of the present form of the potential energy function. The changes considered in the new models include, 1) variations in the gas phase dipole moment, 2) variations in the molecular polarizability, 3) variations of the distance between the oxygen and the M site, 4) variation of the oxygen Lennard-Jones (LJ) parameters, 5) introduction of a LJ potential to the hydrogen atoms, and 6) variations of the H-O-H angle. Detailed analysis is presented for 3 new water models from which a final model, SWM4-HLJ, is selected as the future default model for the Drude polarizable force field. The model maintains the gas phase dipole moment as the experimental value while the remaining listed terms were adjusted including a larger H-O-H angle (108.12). Compared to its predecessor, SWM4-NDP, the self-diffusion coefficient, water dimer properties, and water cluster energies are greatly improved. The temperature dependence of the density of the new model also performs better. Overall, the new SWM4-HLJ water model is a general improvement and a good balance between microscopic and bulk properties is achieved.

CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

Simulating the Fluorescence of Di-8-ANEPPS in Solvents of Different Polarity

Voltage-sensitive fluorescent probes, such as di-8-amino-naphthyl-ethylene-pyridinium-propyl-sulfonate (di-8-ANEPPS), are extremely useful for monitoring the membrane potential in biological and biophysical studies. However, because di-8-ANEPPS is very sensitive to its environment, it can be difficult to distinguish the degree to which a given external factor affects the observed fluorescence. Molecular dynamics simulations based on detailed atomic models make it possible to examine the particular characteristics of the system and predict the effects of the surroundings. Here, the sensitivity of the spectra of di-8-ANEPPS to solvent polarity is investigated by modeling the electronic transition between the ground and excited states using classical molecular mechanical force fields. The absorption and emission of di-8-ANEPPS were simulated in 12 solvents of increasing polarity using nonpolarizable and polarizable force fields. While the computational results and experimental data do not match perfectly, classical Lippert plots of both models show the expected increase of the Stokes shift of di-8-ANEPPS with the orientation polarizability of the surrounding solvent.

Simulating the Fluorescence of the Locally Excited State of DMABN in Solvents of Different Polarities

4-(N,N-Dimethylamino)benzonitrile (DMABN) is a luminescent probe that can be used for tracking changes in the surrounding solvent due to the large change in polarity between its ground and excited states. An important characteristic of DMABN is that it exhibits dual fluorescence with two different emission energies that can be monitored, allowing for better characterization of the surrounding system. The first excited state is called the locally excited (LE) state and is characterized by the movement of charge over the conjugated ring structure. In nonpolar solvents and in the gas phase, the fluorescence of DMABN is entirely attributed to the transition from the near-planar LE state. In more polar environments, emission occurs from both the LE and a second excited state, corresponding to a twisted intramolecular charge-transfer (ICT) structure. For the sake of simplicity, this work considers transitions between only the ground and LE state. Molecular mechanical force field models of DMABN in its ground and LE states have been developed to investigate the sensitivity of the LE state to the polarity of the solvent. Both nonpolarizable and polarizable force fields were developed to simulate the molecule in a series of 10 different solvents of different polarities. The calculated Stokes shift of DMABN increases with increasing orientation polarizability of the surrounding solvent, which is the expected trend, as seen in experimental studies.

Symmetrized Drude Oscillator Force Fields Improve Numerical Performance of Polarizable Molecular Dynamics

Drude oscillator potentials are a popular and computationally efficient class of polarizable models that represent each polarizable atom as a positively charged Drude core harmonically bound to a negatively charged Drude shell. We show that existing force fields that place all non-Coulomb forces on the Drude core and none on the shell inadvertently couple the dipole to non-Coulombic forces. This introduces errors where interactions with neutral particles can erroneously induce atomic polarization, leading to spurious polarizations in the absence of an electric field, exacerbating violations of equipartition in the employed Carr-Parinello scheme. A suitable symmetrization of the interaction potential that correctly splits the force between the Drude core and shell can correct this shortcoming, improving the stability and numerical performance of Drude oscillator-based simulations. The symmetrization procedure is straightforward and only requires the rescaling of a few force field parameters.

Electronic Polarization Is Essential for the Stabilization and Dynamics of Buried Ion Pairs in Staphylococcal Nuclease Mutants

Buried charged residues play important roles in the modulation of protein stabilities and conformational dynamics and make crucial contributions to protein functions. Considering the generally nonpolar nature of protein interior, a key question concerns the contribution of electronic polarization to the stabilization and properties of buried charges. We answer this question by conducting free energy simulations using the latest polarizable CHARMM force field based on Drude oscillators for a series of Staphylococcal nuclease mutants that involve a buried Glu-Lys pair in different titration states and orientations. While a nonpolarizable model suggests that the ionized form of the buried Glu-Lys pair is more than 40 kcal/mol less stable than the charge-neutral form, the two titration states are comparable in stability when electronic polarization is included explicitly, a result better reconcilable with available experimental data. Analysis of free energy components suggests that additional stabilization of the ionized Glu-Lys pair has contributions from both the enhanced salt-bridge strength and stronger interaction between the ion-pair and surrounding protein residues and penetrated water. Despite the stronger direct interaction between Glu and Lys, the ion-pair exhibits considerably larger and faster structural fluctuations when polarization is included, due to compensation of interactions in the cavity. Collectively, observations from this work provide compelling evidence that electronic polarization is essential to the stability, hydration, dynamics, and therefore function of buried charges in proteins. Therefore, our study advocates for the explicit consideration of electronic polarization for mechanistic and engineering studies that implicate buried charged residues, such as enzymes and ion transporters.

Global Optimization of the Lennard-Jones Parameters for the Drude Polarizable Force Field

Molecular dynamics (MD) simulations based on atomic models play an important role in the drug-discovery process to screen molecules, estimate binding free energies, and optimize lead compounds in chemical space. Accurate computations of thermodynamic and kinetic properties using MD simulations are highly dependent on the accuracy of the underlying atomic force field. In this context, going beyond the nonpolarizable fixed-charge model by accounting explicitly for induced polarization is highly desirable. The CHARMM polarizable force field based on classical Drude oscillators, in which an auxiliary charged particle is attached via a harmonic spring to its parent nucleus, offers both a computationally convenient and rigorous framework to model explicitly induced electronic polarization in MD simulations. For any molecule of interest, electrostatic partial charges, atomic polarizabilities, and Thole shielding factors, as well as bonded parameters can either be determined from ab initio calculations or ascribed from the knowledge-based library of the CHARMM Generalized force field. While this approach is fairly reliable in general, it is well understood that the overall accuracy of the models with respect to thermodynamic properties such as bulk density, enthalpies, and solvation free energies is particularly sensitive to the nonbonded Lennard-Jones (LJ) parameters. In the present study, we systematically refined the set of LJ parameters for the atom types available in the Drude force field to best match the experimental thermodynamic properties for 416 small druglike organic molecules. To further test the transferability of the optimized parameters, the hydration free energy of 372 molecules was computed. The calculations resulted in a small average error of 0.46 kcal/mol and a Pearson R of 0.9, representing a significant improvement over the additive GAFF force field in our previous study, where an average error of ∼2 kcal/mol was obtained. Such an improvement is consistent with the ability of the polarizable Drude model to more accurately model interactions in different environments. The effort provides a roadmap for the global optimization of force field parameters using experimental data. It is hoped that the present effort will further the application of the Drude polarizable force field in molecular simulations including drug design and discovery.

Hybrid polarizable simulations of a conventional hydrophobic polyelectrolyte. Toward a theoretical tool for green science innovation

Hybrid modeling approaches based on all-atom force fields to handle a solute and coarse-grained models to account for the solvent are promising numerical tools that can be used to understand the properties of large and multi-components solutions and thus to speed up the development of new industrial products that obey the standard of green and sustainable chemistry. Here, we discuss the ability of a full polarizable hybrid approach coupled to a standard molecular dynamics scheme to model the behavior in the aqueous phase and at infinite dilution conditions of a standard hydrophobic polyelectrolyte polymer whose charge is neutralized by explicit counterions. Beyond the standard picture of a polyelectrolyte behavior governed by an interplay between opposite intra-polyelectrolyte and inter-polyelectrolyte/counterion Coulombic effects, our simulations show the key role played by both intra-solute polarization effects and long range solute/solvent electrostatics to stabilize compact globular conformations of that polyelectrolyte. Our full polarizable hybrid modeling approach is thus a new theoretical tool well suited to be used in digital strategies for accelerating innovation for green science, for instance.

The stress in a dispersion of mutually polarizable spheres

Dispersions of dielectric and paramagnetic nanoparticles polarize in response to an external electric or magnetic field and can form chains or other ordered structures depending on the strength of the applied field. The mechanical properties of these materials are of interest for a variety of applications; however, computational studies in this area have so far been limited. In this work, we derive expressions for two important properties for dispersions of polarizable spherical particles with dipoles induced by a uniform external field-the isothermal stress tensor and the pressure. Numerical calculations of these quantities, evaluated using a spectrally accurate Ewald summation method, are validated using thermodynamic integration. We also compare the stress obtained using the mutual dipole model, which accounts for the mutual polarization of particles, to the stress expected from calculations using a fixed dipole model, which neglects mutual polarization. We find that as the conductivity of the particles increases relative to the surrounding medium, the fixed dipole model does not accurately describe the dipolar contribution to the stress. The thermodynamic pressure, calculated from the trace of the stress tensor, is compared to the virial expression for the pressure, which is simpler to calculate but inexact. We find that the virial pressure and the thermodynamic pressure differ, especially in suspensions with a high volume fraction of particles.

Polarization Effects in Water-Mediated Selective Cation Transport across a Narrow Transmembrane Channel

Despite the progress in modeling complex molecular systems of ever-increasing complexity, a quantitatively accurate computational treatment of ion permeation through narrow membrane channels remains challenging. An important factor to reach this goal is induced electronic polarization, which is likely to impact the permeation rate of small ions through narrow molecular pores. In this work, we extended the recently developed polarizable force field based on the classical Drude oscillators to assess the role of induced polarization effects on the energetics of sodium and potassium ion transport across the gramicidin A (gA) ion channel. The inclusion of induced polarization lowers barriers present in 1D potential of mean force (PMF) for cation permeation by ∼50% compared to those obtained with the additive force field. Conductance properties calculated with 1D PMFs from Drude simulations are in better agreement with experimental results. Polarization of single-file water molecules and protein atoms forming the narrow pore has a direct impact on the free-energy barriers and cation-specific solid-state NMR chemical shifts. Sensitivity analysis indicates that small changes to water-channel interactions can alter the free energy barrier for ion permeation. These results, illustrating polarization effects present in the complex electrostatic environment of the gA channel, have broad implications for revising proposed mechanisms of ion permeation and selectivity in a variety of ion channels.

Methylguanidinium at the Air/Water Interface: A Simulation Study with the Drude Polarizable Force Field

Methylguanidinium is an important molecular ion, which also serves as the model compound for the arginine side chain. We studied the structure and dynamics of the methylguanidium ion at the air/water interface by molecular dynamics simulations employing the Drude polarizable force field. We found out that methylguanidinium accumulated at the interface, with a majority adopting tilted conformations. We also demonstrated that methylguanidinium and guanidinium ions had different preference toward the air/water interface. Detailed analysis of induced dipole moments showed how ions adjusted their charge distribution at the interface and revealed how the anisotropy in molecular polarizability impacted the orientation of molecular ions. Our results illustrate the importance of explicitly including the electronic polarization effects in modeling interfacial properties.