Polarizable Force Field Research Articles

Structural and electronic analysis of the octarepeat region of prion protein with four Cu2+ by polarizable MD and QM/MM simulations.

Prions have been linked to neurodegenerative diseases that affect various species of mammals including humans. The prion protein, located mainly in neurons, is believed to play the role of metal ion transporter. High levels of copper ions have been related to structural changes. A 32-residue region of the N-terminal domain, known as octarepeat, can bind up to four copper ions. Different coordination modes have been observed and are strongly dependent on Cu2+ concentration. Many theoretical studies carried out so far have focused on studying the coordination modes of a single copper ion. In this work we investigate the octarepeat region coordinated with four copper ions. Molecular dynamics (MD) and hybrid quantum mechanics/molecular mechanics (QM/MM) simulations using the polarizable AMOEBA force field have been carried out. The polarizable MD simulations starting from a fully extended conformation indicate that the tetra-Cu2+/octarepeat complex forms a globular structure. The globular form is stabilized by interactions between Cu2+ and tryptophan residues resulting in some coordination sites observed to be in close proximity, in agreement with experimental results. Subsequent QM/MM simulations on several snapshots suggests the system is in a high-spin quintet state, with all Cu2+ bearing one single electron, and all unpaired electrons are ferromagnetically coupled. NMR simulations on selected structures provides insights on the chemical shifts of the first shell ligands around the metals with respect to inter-metal distances.

Multiscale polarizable coarse-graining water models on cluster-level electrostatic dipoles.

The development of a coarse-grained (CG) water model is increasingly important in CG studies of biological processes. In this work, we developed a generic CG force field of liquid water on cluster-level electrostatic dipoles. An exponential term is introduced in the non-bonded potential to adjust the well depth. The whole force field is parametrized on the AMOEBA simulation and then refined on the experimental density, dielectric permittivity and isothermal compressibility. The new CG water force field is suitable for the construction of multi-resolution water models and here the NC = 4/5/10 systems are taken as examples. The results show that the NC = 4/5/10 models can correctly reproduce the density and relative dielectric permittivity. The models can well predict the pressure-density/density-temperature relationships close to the all-atom or experiment results. However, the new models behave differently from other CG models in several water properties such as the air-water surface tension. Through dipole distributions, two representative polarizable configurations are captured after the NC = 4/5/10 systems are dynamically equilibrated. Besides, the NC = 4 model is coupled with the Martini Na+/Cl- models to predict ion-relevant radial distribution functions in comparison to the Martini result. Lastly, CPU tests suggest that the new CG models can enhance simulation efficiency by factors of 20-42, compared to the TIP3P force field. The newly proposed polarizable water force field is practical and transferable and can be flexibly extended to higher coarse-graining of liquid water.

Thermodynamics of ion binding and occupancy in potassium channels.

Potassium channels modulate various cellular functions through efficient and selective conduction of K+ ions. The mechanism of ion conduction in potassium channels has recently emerged as a topic of debate. Crystal structures of potassium channels show four K+ ions bound to adjacent binding sites in the selectivity filter, while chemical intuition and molecular modeling suggest that the direct ion contacts are unstable. Molecular dynamics (MD) simulations have been instrumental in the study of conduction and gating mechanisms of ion channels. Based on MD simulations, two hypotheses have been proposed, in which the four-ion configuration is an artifact due to either averaged structures or low temperature in crystallographic experiments. The two hypotheses have been supported or challenged by different experiments. Here, MD simulations with polarizable force fields validated by ab initio calculations were used to investigate the ion binding thermodynamics. Contrary to previous beliefs, the four-ion configuration was predicted to be thermodynamically stable after accounting for the complex electrostatic interactions and dielectric screening. Polarization plays a critical role in the thermodynamic stabilities. As a result, the ion conduction likely operates through a simple single-vacancy and water-free mechanism. The simulations explained crystal structures, ion binding experiments and recent controversial mutagenesis experiments. This work provides a clear view of the mechanism underlying the efficient ion conduction and demonstrates the importance of polarization in ion channel simulations.

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.

Comparisons of different force fields in conformational analysis and searching of organic molecules: A review

This review aims to examine literature where different force fields are compared by their performances in conformational analysis and searching of organic molecules. Conformational analysis studies are those where energies and/or geometries of conformers are evaluated with force fields; the closer the values are to experiment or ab initio calculations, the better the force field performance. In conformational searching, an algorithm alters the geometry of a chemical system, followed by force field energy minimisation, then the process repeats, ideally until all conformations of the system are found. For conformational analysis, MM2, MM3 and MMFF94 often showed strong performances and their use is recommended. The polarisable AMOEBA force field consistently had strong performance and further comparisons including AMOEBA are advised. UFF showed very weak performance and is not recommended. For conformational searching, a distinct lack of comparisons were found, and the need for more work is emphasised.

General formulation of polarizable embedding models and of their coupling.

We propose a general formalism for polarizable embedding models that can be applied to either continuum or atomistic polarizable models. After deriving such a formalism for both variational and non-variational models, we address the problem of coupling two polarizable models among themselves and to a quantum mechanical (QM) description in the spirit of multiscale quantum chemistry. We discuss general, model-independent coupling hypotheses and derive coupled polarization equations for all combinations of variational and non-variational models and discuss the embedding contributions to the analytical derivatives of the energy, with a particular focus on the elements of the Fock or Kohn-Sham matrix. We apply the general formalism to the derivation of the working equations for a three-layered, fully polarizable QM/MM/continuum strategy using the non-variational atomic multipole optimized energetics for biomolecular applications polarizable force field and the domain decomposition conductor-like screening model.

Removing artifacts in polarizable embedding calculations of one- and two-photon absorption spectra of fluorescent proteins.

The multiscale calculations involving excited states may suffer from the electron spill-out (ESO) problem. This seems to be especially the case when the environment of the core region, described with the electronic structure method, is approximated by a polarizable force field. The ESO effect often leads to incorrect physical character of electronic excitations, spreading outside the quantum region, which, in turn, results in erroneous absorption spectra. In this work, we investigate means to remove the artifacts in one-photon absorption (OPA) and two-photon absorption (TPA) spectra of green and yellow fluorescent protein representatives. This includes (i) using different basis sets, (ii) extending the core subsystem beyond the chromophore, (iii) modification of polarization interaction between the core region and its environment, and (iv) including the Pauli repulsion through effective core potentials (ECPs). Our results clearly show that ESO is observed when diffuse functions are used to assemble the multielectron wave function regardless of the exchange-correlation functional used. Furthermore, extending the core region, thus accounting for exchange interactions between the chromophore and its environment, leads to even more spurious excited states. Also, damping the interactions between the core subsystem and the polarizable force field is hardly helpful. In contrast, placing ECPs in the position of sites creating the embedding potential leads to the removal of artificious excited states that presumably should not be observed in the OPA and TPA spectra. We prove that it is a reliable and cost-effective approach for systems where the covalent bond(s) between the core region and its environment must be cut.

Ion Binding Properties and Dynamics of the bcl-2 G-Quadruplex Using a Polarizable Force Field.

G-quadruplexes (GQs) are topologically diverse, highly thermostable noncanonical nucleic acid structures that form in guanine-rich sequences in DNA and RNA. GQs are implicated in transcriptional and translational regulation and genome maintenance, and deleterious alterations to their structures contribute to diseases such as cancer. The expression of the B-cell lymphoma 2 (Bcl-2) antiapoptotic protein, for example, is under transcriptional control of a GQ in the promoter of the bcl-2 gene. Modulation of the bcl-2 GQ by small molecules is of interest for chemotherapeutic development but doing so requires knowledge of the factors driving GQ folding and stabilization. To develop a greater understanding of the electrostatic properties of the bcl-2 promoter GQ, we performed molecular dynamics simulations using the Drude-2017 polarizable force field and compared relevant outcomes to the nonpolarizable CHARMM36 force field. Our simulation outcomes highlight the importance of dipole-dipole interactions in the bcl-2 GQ, particularly during the recruitment of a bulk K+ ion to the solvent-exposed face of the tetrad stem. We also predict and characterize an "electronegative pocket" at the tetrad-long loop junction that induces local backbone conformational change and may induce local conformational changes at cellular concentrations of K+. These outcomes suggest that moieties within the bcl-2 GQ can be targeted by small molecules to modulate bcl-2 GQ stability.

Coarse-Grained Simulation of the Adsorption of Water on Au(111) Surfaces Using a Modified Stillinger-Weber Potential.

For reproducing the behavior of water molecules adsorbed on gold surfaces in terms of density of both bulk and interfacial water and in terms of structuring of water on top of gold atoms, the implementation of a multibody potential is necessary, thus the Stillinger–Weber potential was tested. The goal is using a single nonbonded potential for coarse-grained models, without the usage of explicit charges. In order to modify the angular part of the Stillinger–Weber potential from a single cosine to a piecewise function accounting for multiple equilibrium angles, employed for Au–Au–Au and Au–Au–water triplets, it is necessary to create a version of the simulation package LAMMPS that supports the assignment of multiple favored angles. This novel approach is able to reproduce the data obtained using quantum mechanical calculations and density profiles of both bulk and adsorbed water molecules obtained using classical polarizable force fields.

A Many-Body, Fully Polarizable Approach to QM/MM Simulations.

We present a new development in quantum mechanics/molecular mechanics (QM/MM) methods by replacing conventional MM models with data-driven many-body (MB) representations rigorously derived from high-level QM calculations. The new QM/MM approach builds on top of mutually polarizable QM/MM schemes developed for polarizable force fields with inducible dipoles and uses permutationally invariant polynomials to effectively account for quantum-mechanical contributions (e.g., exchange-repulsion and charge transfer and penetration) that are difficult to describe by classical expressions adopted by conventional MM models. Using the many-body MB-pol and MB-DFT potential energy functions for water, which include explicit two-body and three-body terms fitted to reproduce the corresponding CCSD(T) and PBE0 two-body and three-body energies for water, we demonstrate a smooth energetic transition as molecules are transferred between QM and MM regions, without the need of a transition layer. By effectively elevating the accuracy of both the MM region and the QM/MM interface to that of the QM region, the new QM/MB-MM approach achieves an accuracy comparable to that obtained with a fully QM treatment of the entire system.

Polarizable and non-polarizable force fields: Protein folding, unfolding, and misfolding.

Molecular dynamics simulations are an invaluable tool to characterize the dynamic motions of proteins in atomistic detail. However, the accuracy of models derived from simulations inevitably relies on the quality of the underlying force field. Here, we present an evaluation of current non-polarizable and polarizable force fields (AMBER ff14SB, CHARMM 36m, GROMOS 54A7, and Drude 2013) based on the long-standing biophysical challenge of protein folding. We quantify the thermodynamics and kinetics of the β-hairpin formation using Markov state models of the fast-folding mini-protein CLN025. Furthermore, we study the (partial) folding dynamics of two more complex systems, a villin headpiece variant and a WW domain. Surprisingly, the polarizable force field in our set, Drude 2013, consistently leads to destabilization of the native state, regardless of the secondary structure element present. All non-polarizable force fields, on the other hand, stably characterize the native state ensembles in most cases even when starting from a partially unfolded conformation. Focusing on CLN025, we find that the conformational space captured with AMBER ff14SB and CHARMM 36m is comparable, but the ensembles from CHARMM 36m simulations are clearly shifted toward disordered conformations. While the AMBER ff14SB ensemble overstabilizes the native fold, CHARMM 36m and GROMOS 54A7 ensembles both agree remarkably well with experimental state populations. In addition, GROMOS 54A7 also reproduces experimental folding times most accurately. Our results further indicate an over-stabilization of helical structures with AMBER ff14SB. Nevertheless, the presented investigations strongly imply that reliable (un)folding dynamics of small proteins can be captured in feasible computational time with current additive force fields.

AMOEBA binding free energies for the SAMPL7 TrimerTrip host-guest challenge.

As part of the SAMPL7 host-guest binding challenge, the AMOEBA force field was applied to calculate the absolute binding free energy for 16 charged organic ammonium guests to the TrimerTrip host, a recently reported acyclic cucurbituril-derived clip host structure with triptycene moieties at its termini. Here we report binding free energy calculations for this system using the AMOEBA polarizable atomic multipole force field and double annihilation free energy methodology. Conformational analysis of the host suggests three families of conformations that do not interconvert in solution on a time scale available to nanosecond molecular dynamics (MD) simulations. Two of these host conformers, referred to as the "indent" and "overlap" structures, are capable of binding guest molecules. As a result, the free energies of all 16 guests binding to both conformations were computed separately, and combined to produce values for comparison with experiment. Initial ranked results submitted as part of the SAMPL7 exercise had a mean unsigned error (MUE) from experimental binding data of 2.14kcal/mol. Subsequently, a rigorous umbrella sampling reference calculation was used to better determine the free energy difference between unligated "indent" and "overlap" host conformations. Revised binding values for the 16 guests pegged to this umbrella sampling reference reduced the MUE to 1.41kcal/mol, with a correlation coefficient (Pearson R) between calculated and experimental binding values of 0.832 and a rank correlation (Kendall τ) of 0.65. Overall, the AMOEBA results demonstrate no significant systematic error, suggesting the force field provides an accurate energetic description of the TrimerTrip host, and an appropriate balance of solvation and desolvation effects associated with guest binding.

Accurate Nonlinear Optical Properties of Solvated para-Nitroaniline Predicted by an Electrostatic Discrete Local Field Approach.

A general computational protocol for accurate predictions of nonlinear optical (NLO) properties of solvated molecules based on the rigorous local field (RLF) approach taking all relevant effects into account is presented. para-Nitroaniline (pNA) was taken as a model NLO system dissolved in cyclohexane, tetrahydrofuran, and 1,4-dioxane. Molecular dynamics (MD) simulations employing either non-polarizable or polarizable force fields were used to generate representative sets of structures of the solutions. The static NLO properties of the solute were calculated at the MP2/aug-cc-pVDZ level of theory with the multiplicative scaling method used to account for the frequency dispersion of the properties. Focusing on the electric field-induced second harmonic generation (EFISH) and hyper-Rayleigh scattering (HRS), a good agreement between calculated results and experimental measurements was achieved with a polarizable force field. While the solvent effects on the vibrational contributions to the static molecular properties are significant, they remain small for both EFISH and HRS. Our results show that the proposed approach yields reliable predictions of dynamic NLO properties of solvated chromophores, which paves a route to further applications of the RLF approach to study a wide range of NLO phenomena in heterogeneous environments.

Molecular dynamics simulations of liquid-liquid interfaces in an electric field: The water-1,2-dichloroethane interface.

The polarized interface between two immiscible liquids plays a central role in many technological processes. In particular, for electroanalytical and ion extraction applications, an external electric field is typically used to selectively induce the transfer of ionic species across the interfaces. Given that it is experimentally challenging to obtain an atomistic insight into the ion transfer process and the structure of liquid-liquid interfaces, atomistic simulations have often been used to fill this knowledge gap. However, due to the long-range nature of the electrostatic interactions and the use of 3D periodic boundary conditions, the use of external electric fields in molecular dynamics simulations requires special care. Here, we show how the simulation setup affects the dielectric response of the materials and demonstrate how by a careful design of the system it is possible to obtain the correct electric field on both sides of a liquid-liquid interface when using standard 3D Ewald summation methods. In order to prove the robustness of our approach, we ran extensive molecular dynamics simulations with a rigid-ion and polarizable force field of the water/1,2-dichloroethane interface in the presence of weak external electric fields.

Benchmarking polarizable and non-polarizable force fields for Ca2+-peptides against a comprehensive QM dataset.

Explicit description of atomic polarizability is critical for the accurate treatment of inter-molecular interactions by force fields (FFs) in molecular dynamics (MD) simulations aiming to investigate complex electrostatic environments such as metal-binding sites of metalloproteins. Several models exist to describe key monovalent and divalent cations interacting with proteins. Many of these models have been developed from ion-amino-acid interactions and/or aqueous-phase data on cation solvation. The transferability of these models to cation-protein interactions remains uncertain. Herein, we assess the accuracy of existing FFs by their abilities to reproduce hierarchies of thousands of Ca2+-dipeptide interaction energies based on density-functional theory calculations. We find that the Drude polarizable FF, prior to any parameterization, better approximates the QM interaction energies than any of the non-polarizable FFs. Nevertheless, it required improvement in order to address polarization catastrophes where, at short Ca2+-carboxylate distances, the Drude particle of oxygen overlaps with the divalent cation. To ameliorate this, we identified those conformational properties that produced the poorest prediction of interaction energies to reduce the parameter space for optimization. We then optimized the selected cation-peptide parameters using Boltzmann-weighted fitting and evaluated the resulting parameters in MD simulations of the N-lobe of calmodulin. We also parameterized and evaluated the CTPOL FF, which incorporates charge-transfer and polarization effects in additive FFs. This work shows how QM-driven parameter development, followed by testing in condensed-phase simulations, may yield FFs that can accurately capture the structure and dynamics of ion-protein interactions.

On the Interplay between Electronic Structure and Polarizable Force Fields When Calculating Solution-Phase Charge-Transfer Rates.

We present a comprehensive analysis of the interplay between the choice of an electronic structure method and the effect of using polarizable force fields vs. nonpolarizable force fields when calculating solution-phase charge-transfer (CT) rates. The analysis is based on an integrative approach that combines inputs from electronic structure calculations and molecular dynamics simulations and is performed in the context of the carotenoid-porphyrin-C60 molecular triad dissolved in an explicit tetrahydrofuran (THF) liquid solvent. Marcus theory rate constants are calculated for the multiple CT processes that occur in this system based on either polarizable or nonpolarizable force fields, parameterized using density functional theory (DFT) with either the B3LYP or the Baer-Neuhauser-Livshits (BNL) density functionals. We find that the effect of switching from nonpolarizable to polarizable force fields on the CT rates is strongly dependent on the choice of the density functional. More specifically, the rate constants obtained using polarizable and nonpolarizable force fields differ significantly when B3LYP is used, while much smaller changes are observed when BNL is used. It is shown that this behavior can be traced back to the tendency of B3LYP to overstabilize CT states, thereby pushing the underlying electronic transitions to the deep inverted region, where even small changes in the force fields can lead to significant changes in the CT rate constants. Our results demonstrate the importance of combining polarizable force fields with an electronic structure method that can accurately capture the energies of excited CT states when calculating charge-transfer rates.

Efficient formulation of polarizable Gaussian multipole electrostatics for biomolecular simulations.

Molecular dynamics simulations of biomolecules have been widely adopted in biomedical studies. As classical point-charge models continue to be used in routine biomolecular applications, there have been growing demands on developing polarizable force fields for handling more complicated biomolecular processes. Here, we focus on a recently proposed polarizable Gaussian Multipole (pGM) model for biomolecular simulations. A key benefit of pGM is its screening of all short-range electrostatic interactions in a physically consistent manner, which is critical for stable charge-fitting and is needed to reproduce molecular anisotropy. Another advantage of pGM is that each atom's multipoles are represented by a single Gaussian function or its derivatives, allowing for more efficient electrostatics than other Gaussian-based models. In this study, we present an efficient formulation for the pGM model defined with respect to a local frame formed with a set of covalent basis vectors. The covalent basis vectors are chosen to be along each atom's covalent bonding directions. The new local frame can better accommodate the fact that permanent dipoles are primarily aligned along covalent bonds due to the differences in electronegativity of bonded atoms. It also allows molecular flexibility during molecular simulations and facilitates an efficient formulation of analytical electrostatic forces without explicit torque computation. Subsequent numerical tests show that analytical atomic forces agree excellently with numerical finite-difference forces for the tested system. Finally, the new pGM electrostatics algorithm is interfaced with the particle mesh Ewald (PME) implementation in Amber for molecular simulations under the periodic boundary conditions. To validate the overall pGM/PME electrostatics, we conducted an NVE simulation for a small water box of 512 water molecules. Our results show that to achieve energy conservation in the polarizable model, it is important to ensure enough accuracy on both PME and induction iteration. It is hoped that the reformulated pGM model will facilitate the development of future force fields based on the pGM electrostatics for applications in biomolecular systems and processes where polarization plays crucial roles.

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

Polarizable force fields based on classical Drude oscillators offer a practical and computationally efficient avenue to carry out molecular dynamics (MD) simulations of large biomolecular systems. To treat the polarizable electronic degrees of freedom, the Drude model introduces a virtual charged particle that is attached to its parent nucleus via a harmonic spring. Traditionally, the need to relax the electronic degrees of freedom for each fixed set of nuclear coordinates is achieved by performing an iterative self-consistent field (SCF) calculation to satisfy a selected tolerance. This is a computationally demanding procedure that can increase the computational cost of MD simulations by nearly one order of magnitude. To avoid the costly SCF procedure, a small mass is assigned to the Drude particles, which are then propagated as dynamic variables during the simulations via a dual-thermostat extended Lagrangian algorithm. To help clarify the significance of the dual-thermostat extended Lagrangian propagation in the context of the polarizable force field based on classical Drude oscillators, the statistical mechanics of a dual-temperature canonical ensemble is formulated. The conditions for dynamically maintaining the dual-temperature properties in the case of the classical Drude oscillator are analyzed using the generalized Langevin equation.

Systematic Parameterization and Simulation of Boronic Acid-β-Lactamase Aqueous Solution in Developing the ABEEMσπ Polarizable Force Field.

Boronic acid, an inhibitor of β-lactamase, has begun to be applied to the treatment of biological infections and tumors. Scientists are working to develop new and more effective boronic acid. Molecular dynamics (MD) simulation provides a powerful auxiliary tool for drug design. However, the current force fields have no boron-related parameters. In this work, an atom-bond electronegativity equalization method at the σπ level (ABEEMσπ) polarizable force field (ABEEMσπ PFF) of boronic acid and β-lactamase has been developed to determine the potential functions and parameters. The interaction between boron and serine in β-lactamase is regarded as a bonded mode. The interaction between them is simulated by the Morse potential energy function, which is close to the experimental change of the stretching potential energy in a large range. The potential energy surfaces of the bond length, bond angle, and dihedral angle of boronic acid-β-lactamase have the same stability point and change trend as M06-2X/6-311G**. For 47 boronic acid-β-lactamase training molecules, the linear correlation coefficient (R) of the charge distribution between the ABEEMσπ PFF and HF/STO-3G is greater than 0.96. Attributed to the fact that the charge distribution of the ABEEMσπ PFF can fluctuate with the change of geometry and environment, the polarization effect and charge-transfer effect are well reflected. The binding ability of different boronic acids with the same β-lactamase is different. A total of 10 boronic acid-β-lactamase model molecules and 10 boronic acid-β-lactamase and water complexes are simulated. The order of binding energy of five large model molecules calculated by the ABEEMσπ PFF is consistent with that of the MP2 method. The binding energies of boronic acid-β-lactamase and water complexes are close to those of the MP2 method. The results of MD simulation of five aqueous boronic acid-β-lactamase complexes in the NVT ensemble verify the rationality of boron-related parameters of the ABEEMσπ PFF, which have a good application prospect. This study lays a solid theoretical foundation for further study of the inhibition of boronic acid on β-lactamase.

Enantiomerization of Axially Chiral Biphenyls: Polarizable MD Simulations in Water and Butylmethylether.

In this study, we investigate the influence of chiral and achiral cations on the enantiomerization of biphenylic anions in n-butylmethylether and water. In addition to the impact of the cations and solvent molecules on the free energy profile of rotation, we also explore if chirality transfer between a chiral cation and the biphenylic anion is possible, i.e., if pairing with a chiral cation can energetically favour one conformer of the anion via diastereomeric complex formation. The quantum-mechanical calculations are accompanied by polarizable MD simulations using umbrella sampling to study the impact of solvents of different polarity in more detail. We also discuss how accurate polarizable force fields for biphenylic anions can be constructed from quantum-mechanical reference data.