AMOEBA Force Field Research Articles

Polarizable Multipole-Based Force Field for Dimethyl and Trimethyl Phosphate.

Phosphate groups are commonly observed in biomolecules such as nucleic acids and lipids. Due to their highly charged and polarizable nature, modeling these compounds with classical force fields is challenging. Using quantum mechanical studies and liquid-phase simulations, the AMOEBA force field for dimethyl phosphate (DMP) ion and trimethyl phosphate (TMP) has been developed. On the basis of ab initio calculations, it was found that ion binding and the solution environment significantly impact both the molecular geometry and the energy differences between conformations. Atomic multipole moments are derived from MP2/cc-pVQZ calculations of methyl phosphates at several conformations with their chemical environments taken into account. Many-body polarization is handled via a Thole-style induction model using distributed atomic polarizabilities. van der Waals parameters of phosphate and oxygen atoms are determined by fitting to the quantum mechanical interaction energy curves for water with DMP or TMP. Additional stretch-torsion and angle-torsion coupling terms were introduced in order to capture asymmetry in P–O bond lengths and angles due to the generalized anomeric effect. The resulting force field for DMP and TMP is able to accurately describe both the molecular structure and conformational energy surface, including bond and angle variations with conformation, as well as interaction of both species with water and metal ions. The force field was further validated for TMP in the condensed phase by computing hydration free energy, liquid density, and heat of vaporization. The polarization behavior between liquid TMP and TMP in water is drastically different.

Microhydration of Protonated Nα-Acetylhistidine: A Theoretical Approach.

Extensive exploration of the potential energy surfaces of protonated Nα-acetylhistidine hydrated by 0-3 molecules of water was performed. The methodology combined hierarchical and genealogical (Darwin family tree) approaches using polarizable AMOEBA force field and M06 functional. It is demonstrated that this mixed approach allows recovering a larger number of conformers than the number recovered by using any one of the two methods alone. Hydration enthalpies of protonated Nα-acetylhistidine and of model compounds have been computed using higher theoretical methods, up to the G4MP2 procedure. Excellent agreement with experiment is observed for successive hydration of methylamonium and imidazolium cations using MP2/6-311++G(2d,2p)//M06/6-311++G(d,p) and G4MP2 methods, thereby validating the theory levels used for hydrated protonated Nα-acetylhistidine. It is found that the first hydration enthalpy of protonated Nα-acetylhistidine is ca. 10 kJ mol(-1) lower than that of imidazolium, a result explained by the local environment of the positively charged imidazolium moiety.

Development of an AMOEBA water model using GEM distributed multipoles

Distributed multipoles obtained from the Gaussian electrostatic model (GEM) have been previously shown to be amenable for use in the AMOEBA force field [JCTC(2012) 12, 5072]. GEM distributed multipoles (GEM-DM) were determined for several systems including water. This previous AMOEBA water model with GEM-DM included only monopoles on the hydrogens and multipoles up to quadrupoles on the oxygen. This model showed good agreement with experiment for several properties at room temperature, but not at higher temperatures. In this contribution, we present the development of an AMOEBA water model using GEM-DM with distributed multipoles for each atomic site up to the quadrupole level. Quantum mechanical energy decomposition analysis has been employed to compare each term of the force field for parametrization. The inclusion of higher-order multipoles on hydrogen atoms is shown to provide better agreement with experiment on a number of properties including liquid density ( $$\rho$$ ), enthalpy of vaporization ( $$\Delta H_\mathrm{vap}$$ ), heat capacity ( $$C_{p}$$ ), and self-diffusion coefficient (D) for a range of temperatures.

Dead-End Elimination with a Polarizable Force Field Repacks PCNA Structures

A balance of van der Waals, electrostatic, and hydrophobic forces drive the folding and packing of protein side chains. Although such interactions between residues are often approximated as being pairwise additive, in reality, higher-order many-body contributions that depend on environment drive hydrophobic collapse and cooperative electrostatics. Beginning from dead-end elimination, we derive the first algorithm, to our knowledge, capable of deterministic global repacking of side chains compatible with many-body energy functions. The approach is applied to seven PCNA x-ray crystallographic data sets with resolutions 2.5–3.8 Å (mean 3.0 Å) using an open-source software. While PDB_REDO models average an Rfree value of 29.5% and MOLPROBITY score of 2.71 Å (77th percentile), dead-end elimination with the polarizable AMOEBA force field lowered Rfree by 2.8–26.7% and improved mean MOLPROBITY score to atomic resolution at 1.25 Å (100th percentile). For structural biology applications that depend on side-chain repacking, including x-ray refinement, homology modeling, and protein design, the accuracy limitations of pairwise additivity can now be eliminated via polarizable or quantum mechanical potentials.

Structural evolution of nucleobase clusters using force field models and density functional theory

We report global minima for all nucleobase clusters (nucleobase)n, with 2≤n≤4. The global minima are predicted using force field based global optimization methods followed by local optimizations using the dispersion corrected DFT method. In this study, we use both non-polarizable (OPLS-AA) and polarizable (AMOEBA) force fields for global optimization. Here we emphasize on the reliability of AMOEBA force field used for predicting accurate global minima of nucleobase clusters. The average deviation in binding energies using AMOEBA is 3kcal/mol from the DFT while the average deviation using OPLS-AA is 8kcal/mol from DFT.

Scalable evaluation of polarization energy and associated forces in polarizable molecular dynamics: II. Toward massively parallel computations using smooth particle mesh Ewald.

In this article, we present a parallel implementation of point dipole-based polarizable force fields for molecular dynamics (MD) simulations with periodic boundary conditions (PBC). The smooth particle mesh Ewald technique is combined with two optimal iterative strategies, namely, a preconditioned conjugate gradient solver and a Jacobi solver in conjunction with the direct inversion in the iterative subspace for convergence acceleration, to solve the polarization equations. We show that both solvers exhibit very good parallel performances and overall very competitive timings in an energy and force computation needed to perform a MD step. Various tests on large systems are provided in the context of the polarizable AMOEBA force field as implemented in the newly developed Tinker-HP package, which is the first implementation of a polarizable model that makes large-scale experiments for massively parallel PBC point dipole models possible. We show that using a large number of cores offers a significant acceleration of the overall process involving the iterative methods within the context of SPME and a noticeable improvement of the memory management, giving access to very large systems (hundreds of thousands of atoms) as the algorithm naturally distributes the data on different cores. Coupled with advanced MD techniques, gains ranging from 2 to 3 orders of magnitude in time are now possible compared to nonoptimized, sequential implementations, giving new directions for polarizable molecular dynamics with periodic boundary conditions using massively parallel implementations.

Quantum Mechanical Molecular Mechanical Calculations using AMOEBA Force Fields

We report an implementation of quantum mechanical molecular mechanical (QM/MM) calculations with AMOEBA force field applied to water molecules in the molecular mechanics region. Three AMOEBA parameter sets (AMOEBA03, iAMOEBA, and AMOEBA14) are employed, and compared to TIP3P and other water models in terms of their performance in QM/MM calculations. The effect of the MM polarization (MM induced dipoles due to QM electron density) will also be discussed.

Structure and thermodynamics of Mg:phosphate interactions in water: a simulation study.

The association of Mg(2+) and H2 PO4 (-) in water can give insights into Mg:phosphate interactions in general, which are very widespread, but for which experimental data is surprisingly sparse. It is studied through molecular dynamics simulations (>100 ns) by using the polarizable AMOEBA force field, and the association free energy is computed for the first time. Explicit consideration of outer-sphere and two types of inner-sphere association provides considerable insight into the dynamics and thermodynamics of ion pairing. After careful assessment of the computational approximations, the agreement with experimental values indicates that the methodology can be extended to other inorganic and biological Mg:phosphate interactions in solution.

AMOEBA force field parameterization of the azabenzenes

We present an extension of the AMOEBA force field to several common organic heterocycles, namely pyridine, pyrazine, pyrimidine, pyridazine, the three unique triazines, and the two unique tetrazines. Atomic multipoles for newly defined atom types were obtained from quantum chemical calculations on the isolated molecules. Atomic polarizability parameters are maintained at their standard AMOEBA values for corresponding atomic classes while standard van der Waals parameters are rescaled to reproduce CCSD(T) intermolecular interaction energies of selected dimer structures. In order to improve vibrational frequencies that are important both spectroscopically and for flexible dynamics, parameters for covalent terms, i.e., bond-stretching, angle-bending, and stretch-bend terms, were optimized and added to the existing AMOEBA force field. We validate our force field through comparison of molecular structural, vibrational, electrostatic, and energetic properties—including intermolecular interaction energies—to reliable quantum chemical data for the various systems of interest.

Solvation structure and dynamics of Ni2+(aq) from a polarizable force field

An aqueous solution of Ni2+ has often been used as a prototypic transition-metal system for experimental and theoretical studies in nuclear and electron-spin magnetic resonance (NMR and ESR). Molecular dynamics (MD) simulation of Ni2+(aq) has been a part of many of these studies. As a transition metal complex, its MD simulation is particularly difficult using common force fields. In this work, we parameterize the Ni2+ ion for a simulation of the aqueous solution within the modern polarizable force field AMOEBA. We show that a successful parameterization is possible for this specific case when releasing the physical interpretation of the electrostatic and polarization parameters of the force field. In doing so, particularly the Thole damping parameter and also the ion charge and polarizability were used as fitting parameters. The resulting parameterizations give in a MD simulation good structural and dynamical properties of the [Ni(H2O)6]2+ complex, along with the expected excellent performance of AMOEBA for the water solvent. The presented parameterization is appropriate for high-accuracy simulations of both structural and dynamic properties of Ni2+(aq). This work documents possible approaches of parameterization of a transition metal within the AMOEBA force field.

Current status of protein force fields for molecular dynamics simulations.

The current status of classical force fields for proteins is reviewed. These include additive force fields as well as the latest developments in the Drude and AMOEBA polarizable force fields. Parametrization strategies developed specifically for the Drude force field are described and compared with the additive CHARMM36 force field. Results from molecular simulations of proteins and small peptides are summarized to illustrate the performance of the Drude and AMOEBA force fields.

Development of AMOEBA force field for 1,3-dimethylimidazolium based ionic liquids.

The development of AMOEBA (a multipolar polarizable force field) for imidazolium based ionic liquids is presented. Our parametrization method follows the AMOEBA procedure and introduces the use of QM intermolecular total interactions as well as QM energy decomposition analysis (EDA) to fit individual interaction energy components. The distributed multipoles for the cation and anions have been derived using both the Gaussian distributed multipole analysis (GDMA) and Gaussian electrostatic model-distributed multipole (GEM-DM) methods.1 The intermolecular interactions of a 1,3-dimethylimidazolium [dmim(+)] cation with various anions, including fluoride [F(-)], chloride [Cl(-)], nitrate [NO(3)(-)], and tetraflorouborate [BF(4)(-)], were studied using quantum chemistry calculations at the MP2/6-311G(d,p) level of theory. Energy decomposition analysis was performed for each pair using the restricted variational space decomposition approach (RVS) at the HF/6-311G(d,p) level. The new force field was validated by running a series of molecular dynamic (MD) simulations and by analyzing thermodynamic and structural properties of these systems. A number of thermodynamic properties obtained from MD simulations were compared with available experimental data. The ionic liquid structure reproduced using the AMOEBA force field is also compared with the data from neutron diffraction experiment and other MD simulations. Employing GEM-DM force fields resulted in a good agreement on liquid densities ρ, enthalpies of vaporization ΔH(vap), and diffusion coefficients D(±) in comparison with conventional force fields.

Finite Temperature Infrared Spectra from Polarizable Molecular Dynamics Simulations.

Infrared spectra of biomolecules are obtained from molecular dynamics simulations at finite temperature using the AMOEBA force field. Diverse examples are presented such as N-methylacetamide and its derivatives and a helical peptide. The computed spectra from polarizable molecular dynamics are compared in each case to experimental ones at various temperatures. The role of high-level electrostatic treatment and explicit polarization, including parameters improvements, is highlighted for obtaining spectral sensitivity to the environment including hydrogen bonds and water molecules and a better understanding of the observed experimental bands.

Quasichemical analysis of the cluster-pair approximation for the thermodynamics of proton hydration.

A theoretical analysis of the cluster-pair approximation (CPA) is presented based on the quasichemical theory of solutions. The sought single-ion hydration free energy of the proton includes an interfacial potential contribution by definition. It is shown, however, that the CPA involves an extra-thermodynamic assumption that does not guarantee uniform convergence to a bulk free energy value with increasing cluster size. A numerical test of the CPA is performed using the classical polarizable AMOEBA force field and supporting quantum chemical calculations. The enthalpy and free energy differences are computed for the kosmotropic Na(+)/F(-) ion pair in water clusters of size n = 5, 25, 105. Additional calculations are performed for the chaotropic Rb(+)/I(-) ion pair. A small shift in the proton hydration free energy and a larger shift in the hydration enthalpy, relative to the CPA values, are predicted based on the n = 105 simulations. The shifts arise from a combination of sequential hydration and interfacial potential effects. The AMOEBA and quantum chemical results suggest an electrochemical surface potential of water in the range -0.4 to -0.5 V. The physical content of single-ion free energies and implications for ion-water force field development are also discussed.

Hydration Free Energy from Orthogonal Space Random Walk and Polarizable Force Field.

The orthogonal space random walk (OSRW) method has shown enhanced sampling efficiency in free energy calculations from previous studies. In this study, the implementation of OSRW in accordance with the polarizable AMOEBA force field in TINKER molecular modeling software package is discussed and subsequently applied to the hydration free energy calculation of 20 small organic molecules, among which 15 are positively charged and five are neutral. The calculated hydration free energies of these molecules are compared with the results obtained from the Bennett acceptance ratio method using the same force field, and overall an excellent agreement is obtained. The convergence and the efficiency of the OSRW are also discussed and compared with BAR. Combining enhanced sampling techniques such as OSRW with polarizable force fields is very promising for achieving both accuracy and efficiency in general free energy calculations.

Ab initio calculation of the electronic absorption spectrum of liquid water.

The electronic absorption spectrum of liquid water was investigated by coupling a one-body energy decomposition scheme to configurations generated by classical and Born-Oppenheimer Molecular Dynamics (BOMD). A Frenkel exciton Hamiltonian formalism was adopted and the excitation energies in the liquid phase were calculated with the equation of motion coupled cluster with single and double excitations method. Molecular dynamics configurations were generated by different approaches. Classical MD were carried out with the TIP4P-Ew and AMOEBA force fields. The BLYP and BLYP-D3 exchange-correlation functionals were used in BOMD. Theoretical and experimental results for the electronic absorption spectrum of liquid water are in good agreement. Emphasis is placed on the relationship between the structure of liquid water predicted by the different models and the electronic absorption spectrum. The theoretical gas to liquid phase blue-shift of the peak positions of the electronic absorption spectrum is in good agreement with experiment. The overall shift is determined by a competition between the O-H stretching of the water monomer in liquid water that leads to a red-shift and polarization effects that induce a blue-shift. The results illustrate the importance of coupling many-body energy decomposition schemes to molecular dynamics configurations to carry out ab initio calculations of the electronic properties in liquid phase.

Dipeptide Aggregation in Aqueous Solution from Fixed Point-Charge Force Fields.

The description of aggregation processes with molecular dynamics simulations is a playground for testing biomolecular force fields, including a new generation of force fields that explicitly describe electronic polarization. In this work, we study a system consisting of 50 glycyl-l-alanine (Gly-Ala) dipeptides in solution with 1001 water molecules. Neutron diffraction experiments have shown that at this concentration, Gly-Ala aggregates into large clusters. However, general-purpose force fields in combination with established water models can fail to correctly describe this aggregation process, highlighting important deficiencies in how solute–solute and solute–solvent interactions are parametrized in these force fields. We found that even for the fully polarizable AMOEBA force field, the degree of association is considerably underestimated. Instead, a fixed point-charge approach based on the newly developed IPolQ scheme [Cerutti et al. J. Phys. Chem.2013, 117, 2328] allows for the correct modeling of the dipeptide aggregation in aqueous solution. This result should stimulate interest in novel fitting schemes that aim to improve the description of the solvent polarization effect within both explicitly polarizable and fixed point-charge frameworks.

Scalable Evaluation of Polarization Energy and Associated Forces in Polarizable Molecular Dynamics: II.Towards Massively Parallel Computations using Smooth Particle Mesh Ewald.

In this paper, we present a scalable and efficient implementation of point dipole-based polarizable force fields for molecular dynamics (MD) simulations with periodic boundary conditions (PBC). The Smooth Particle-Mesh Ewald technique is combined with two optimal iterative strategies, namely, a preconditioned conjugate gradient solver and a Jacobi solver in conjunction with the Direct Inversion in the Iterative Subspace for convergence acceleration, to solve the polarization equations. We show that both solvers exhibit very good parallel performances and overall very competitive timings in an energy-force computation needed to perform a MD step. Various tests on large systems are provided in the context of the polarizable AMOEBA force field as implemented in the newly developed Tinker-HP package which is the first implementation for a polarizable model making large scale experiments for massively parallel PBC point dipole models possible. We show that using a large number of cores offers a significant acceleration of the overall process involving the iterative methods within the context of spme and a noticeable improvement of the memory management giving access to very large systems (hundreds of thousands of atoms) as the algorithm naturally distributes the data on different cores. Coupled with advanced MD techniques, gains ranging from 2 to 3 orders of magnitude in time are now possible compared to non-optimized, sequential implementations giving new directions for polarizable molecular dynamics in periodic boundary conditions using massively parallel implementations.

Anisotropic Coarse-Grained Model for Proteins Based On Gay–Berne and Electric Multipole Potentials

Gay–Berne anisotropic potential has been widely used to evaluate the nonbonded interactions between coarse-grained particles being described as elliptical rigid bodies. In this paper, we are presenting a coarse-grained model for twenty kinds of amino acids and proteins, based on the anisotropic Gay–Berne and point electric multipole (EMP) potentials. We demonstrate that the anisotropic coarse-grained model, namely GBEMP model, is able to reproduce many key features observed from experimental protein structures (Dunbrack Library), as well as from atomistic force field simulations (using AMOEBA, AMBER, and CHARMM force fields), while saving the computational cost by a factor of about 10–200 depending on specific cases and atomistic models. More importantly, unlike other coarse-grained approaches, our framework is based on the fundamental intermolecular forces with explicit treatment of electrostatic and repulsion-dispersion forces. As a result, the coarse-grained protein model presented an accurate description of nonbonded interactions (particularly electrostatic component) between hetero/homodimers (such as peptide–peptide, peptide–water). In addition, the encouraging performance of the model was reflected by the excellent correlation between GBEMP and AMOEBA models in the calculations of the dipole moment of peptides. In brief, the GBEMP model given here is general and transferable, suitable for simulating complex biomolecular systems.

Accelerated Molecular Dynamics Simulations with the AMOEBA Polarizable Force Field on Graphics Processing Units

The accelerated molecular dynamics (aMD) method has recently been shown to enhance the sampling of biomolecules in molecular dynamics (MD) simulations, often by several orders of magnitude. Here, we describe an implementation of the aMD method for the OpenMM application layer that takes full advantage of graphics processing units (GPUs) computing. The aMD method is shown to work in combination with the AMOEBA polarizable force field (AMOEBA-aMD), allowing the simulation of long time-scale events with a polarizable force field. Benchmarks are provided to show that the AMOEBA-aMD method is efficiently implemented and produces accurate results in its standard parametrization. For the BPTI protein, we demonstrate that the protein structure described with AMOEBA remains stable even on the extended time scales accessed at high levels of accelerations. For the DNA repair metalloenzyme endonuclease IV, we show that the use of the AMOEBA force field is a significant improvement over fixed charged models for describing the enzyme active-site. The new AMOEBA-aMD method is publicly available (http://wiki.simtk.org/openmm/VirtualRepository) and promises to be interesting for studying complex systems that can benefit from both the use of a polarizable force field and enhanced sampling.