AMOEBA Polarizable Force Field Research Articles

Proton disorder and elasticity of hexagonal ice and gas hydrates.

This work is devoted to the study of the mechanical properties of hexagonal ice Ih and gas hydrate frameworks sI, sII and sH, taking into account the disorder in the positions of the hydrogen atoms (protons). The article emphasizes the critical role of the elastic energy for the evaluation of the relative energy of the proton configurations. The calculations are performed with the help of the TINKER package using the AMOEBA polarizable force field. The elastic constants, elastic modulus, and anisotropy indices are calculated. It is shown that all gas hydrate frameworks are very isotropic due to their cage-like structure. It was established that one of the reasons for the higher anisotropy of ice Ih is the presence of a large number of highly symmetric proton configurations. The purpose of the article is to overcome the apparent contradiction between the ab initio and force field methods in predicting the relative stability of the proton configurations of ice structures at low temperature. The other purpose is to evaluate the effect of proton disorder on the elastic properties of ice and gas hydrate structures. Graphical abstract Proton configurations in hexagonal ice: fixed (a) and free (b) unit cell parametersᅟ.

Coupled hydroxyl and ether functionalisation in EAN derivatives: the effect of hydrogen bond donor/acceptor groups on the structural heterogeneity studied with X-ray diffractions and fixed charge/polarizable simulations.

We present a study by energy-dispersive X-ray diffraction of liquid 2-(2-hydroxyethoxy)ethan-1-ammonium nitrate, NH3CH2CH2(OCH2CH2OH)+NO3- (22HHEAN). This ionic liquid is derived from the parent ethylammonium nitrate (EAN) with an ether link in the chain and a hydroxyl group in the terminal position. The absence of peaks at low-q values in the experimental diffraction curve indicates that the added polar groups and the high conformational isomerism of the cations alter strongly the nanosegregation of the parent EAN liquid. Aggregation between ionic species may involve hydrogen bonding between cations and anions and a variety of intermolecular hydrogen bonds between cations. Diffraction patterns are compared with the results of molecular dynamics simulations with two different force fields: the fixed point charge force field (GAFF) with different charge scaling protocols and the polarizable AMOEBA force field. Most point charge models lead to the appearance of a quite evident low q-peak which decreases gradually, when the percentage and type of the scaling (uniform vs. non-uniform) are increased. In the polarisable model and in the model where only anion charges are scaled to 20%, instead, the pre-peak is absent in agreement with our experiments.

A fragment-based approach to evaluate the performance of AMOEBA polarizable force field on charge-carrier electronic polarization

Electrostatic polarization effect plays a crucial role in determining the charge-carrier energy levels in organic electronics devices. The polarizable force field (PFF) is one of the popular methods to explicitly calculate charge carrier’s energy levels in condensed phase. It is a challenge to evaluate the performance of PFFs on estimation the carrier’s site energies due to the lack of accurate photoelectron spectroscopy (PES) data. As such, developing the first-principle based method is an alternative option to estimate the performance of PFFs on electronic polarization effect. In this paper, we applied the block-localized wavefunction (BLW) coupled with DFT to solve the charge localized energy in some oligoacene clusters, which provide a nice reference to evaluate the performance of AMOEBA PFF. Our results demonstrate that the AMOEBA PFF can well describe the electronic polarization in some small cluster systems.

Electrostatic Polarization Energies of Charge Carriers in Organic Molecular Crystals: A Comparative Study with Explicit State-Specific Atomic Polarizability Based AMOEBA Force Field and Implicit Solvent Method.

The electrostatic polarization plays an important role in determining the energy levels of charge carriers in organic solids, which is controlled by the atomic polarizability in AMOEBA polarizable force field. QTAIM-based space partitioning of molecular polarizability is utilized to uniformly parametrize the state-specific atomic polarizability (SSAP) of π-conjugated organic small molecules to avoid fitting molecular polarizability of some artificial training set. Herein, the SSAPs are applied to explicitly extrapolate the electrostatic polarization energy ( E pol) of the charge carriers of nine π-conjugated organic crystals including six p-type transfer materials, oligoacenes and TIPS-substituted oligoacenes, and three n-type transfer materials, F-substituted oligoacenes and TCNQ. Our results demonstrate that the electrostatic polarization energies of the hole carrier ( E+pol) are smaller than that of the electron carrier ( E-pol) for p-type molecules while E+pol are larger than E-pol for n-type molecules. SSAP-based E pol values of oligoacenes behave as a nearly unvaried feature with the increase of conjugation length which is similar to implicit polarizable continuum model (PCM) results, while E pol obtained from the default atomic polarizability behaves with a notable decrease. Implicit PCM can correctly capture most of electrostatic polarization of ions in bulk system although it slightly underestimates the gap between the electrostatic polarization of hole and electron carriers in oligoacene crystals. Our results demonstrate that this unified parametrized SSAP provides a reliable and cheap tool to estimate the energy landscape of charge carriers in condensed-phase organic solids.

Elucidating the Phosphate Binding Mode of Phosphate-Binding Protein: The Critical Effect of Buffer Solution.

Phosphate is an essential component of cell functions, and the specific transport of phosphorus into a cell is mediated by phosphate-binding protein (PBP). The mechanism of PBP-phosphate recognition remains controversial: on the basis of similar binding affinities at acidic and basic pHs, it is believed that the hydrogen network in the binding site is flexible to adapt to different protonation states of phosphates. However, only hydrogen (1H) phosphate was observed in the sub-angstrom X-ray structures. To address this inconsistency, we performed molecular dynamics simulations using the AMOEBA polarizable force field. Structural and free energy data from simulations suggested that 1H phosphate was the preferred bound form at both pHs. The binding of dihydrogen (2H) phosphate disrupted the hydrogen-bond network in the PBP pocket, and the computed affinity was much weaker than that of 1H phosphate. Furthermore, we showed that the discrepancy in the studies described above is resolved if the interaction between phosphate and the buffer agent is taken into account. The calculated apparent binding affinities are in excellent agreement with experimental measurements. Our results suggest the high specificity of PBP for 1H phosphate and highlight the importance of the buffer solution for the binding of highly charged ligands.

AMOEBA Polarizable Force Field Parameters of the Heme Cofactor in Its Ferrous and Ferric Forms.

We report the first parameters of the heme redox cofactors for the polarizable AMOEBA force field in both the ferric and ferrous forms. We consider two types of complexes, one with two histidine side chains as axial ligands and one with a histidine and a methionine side chain as ligands. We have derived permanent multipoles from second-order Møller-Plesset perturbation theory (MP2). The sets of parameters have been validated in a first step by comparison of AMOEBA interaction energies of heme and a collection of biologically relevant molecules with MP2 and Density Functional Theory (DFT) calculations. In a second validation step, we consider interaction energies with large aggregates comprising around 80 H2O molecules. These calculations are repeated for 30 structures extracted from semiempirical PM7 DM simulations. Very encouraging agreement is found between DFT and the AMOEBA force field, which results from an accurate treatment of electrostatic interactions. We finally report long (10 ns) MD simulations of cytochromes in two redox states with AMOEBA testing both the 2003 and 2014 AMOEBA water models. These simulations have been carried out with the TINKER-HP (High Performance) program. In conclusion, owing to their ubiquity in biology, we think the present work opens a wide array of applications of the polarizable AMOEBA force field on hemeproteins.

AMOEBA Polarizable Atomic Multipole Force Field for Nucleic Acids.

The AMOEBA polarizable atomic multipole force field for nucleic acids is presented. Valence and electrostatic parameters were determined from high-level quantum mechanical data, including structures, conformational energy, and electrostatic potentials, of nucleotide model compounds. Previously derived parameters for the phosphate group and nucleobases were incorporated. A total of over 35 μs of condensed-phase molecular dynamics simulations of DNA and RNA molecules in aqueous solution and crystal lattice were performed to validate and refine the force field. The solution and/or crystal structures of DNA B-form duplexes, RNA duplexes, and hairpins were captured with an average root-mean-squared deviation from NMR structures below or around 2.0 Å. Structural details, such as base pairing and stacking, sugar puckering, backbone and χ-torsion angles, groove geometries, and crystal packing interfaces, agreed well with NMR and/or X-ray. The interconversion between A- and B-form DNAs was observed in ethanol-water mixtures at 328 K. Crystal lattices of B- and Z-form DNA and A-form RNA were examined with simulations. For the RNA tetraloop, single strand tetramers, and HIV TAR with 29 residues, the simulated conformational states, 3 J-coupling, nuclear Overhauser effect, and residual dipolar coupling data were compared with NMR results. Starting from a totally unstacked/unfolding state, the rCAAU tetranucleotide was folded into A-form-like structures during ∼1 μs molecular dynamics simulations.

Simulations of the OKE Response in Simple Liquids Using a Polarizable and a Nonpolarizable Force Field.

Recently polarizable force fields are becoming increasingly popular for molecular dynamics simulations. As the signal obtained in the optical Kerr effect (OKE) experiment is due to the polarizability dynamics of the investigated system, a study is conducted in order to compare the experimental results with those obtained with the polarizable AMOEBA force field. The comparison is made in the frequency domain; however, time domain data are also included. The selected molecular systems are the isotropic carbon tetrachloride molecule, the anisotropic chloroform, carbon disulfide and acetone molecules, and the hydrogen-bonded water and methanol molecules. Different dipole-induced-dipole (DID) method variants are used for calculation of the OKE response, showing the importance of use of the all-atom approach with preoptimized atomic polarizabilities. In order to obtain a good intermolecular to intramolecular components amplitude ratio, the isotropic polarizability in the Thole correction needs to be updated between iterations. The convergence of the spectra calculated with different DID variants is also considered, and the approach that appears to be the best gives a very good approximation after three iterations. The comparison of the experimental and simulated spectra shows a rather good agreement for the non-hydrogen-bonded molecules, although the contribution of the reorientation of anisotropic molecules is overestimated. In the case of the hydrogen-bonded molecules, the theoretical spectra are far from the experimental ones. The highly overestimated librational bands indicate excessive polarizability anisotropy introduced by the potential model. Finally, in order to verify the significance of different components of the AMOEBA model, it is gradually simplified and compared with a simple reference potential model. Removal of polarizability shows a tremendous change in the case of hydrogen-bonded liquids, whereas for the other molecules it is of minor importance. The non-hydrogen-bonded liquids are, however, more sensitive to the presence of atomic multipoles in the model.

Strategy for Modeling the Infrared Spectra of Ion-Containing Water Drops.

Hydrated ions are ubiquitous in environmental and biological media. Understanding the perturbation exerted by an ion on the water hydrogen bond network is possible in the nanodrop regime by recording vibrational spectra in the O-H bond stretching region. This has been achieved experimentally in recent years by forming gaseous ions containing tens to hundreds of water molecules and recording their infrared photodissociation spectra. In this paper, we demonstrate the capabilities of a modeling strategy based on an extension of the AMOEBA polarizable force field to implement water atomic charge fluctuations along with those of intramolecular structure along the dynamics. This supplementary flexibility of nonbonded interactions improves the description of the hydrogen bond network and, therefore, the spectroscopic response. Finite temperature IR spectra are obtained from molecular dynamics simulations by computing the Fourier transform of the dipole moment autocorrelation function. Simulations of 1-2 ns are required for extensive sampling in order to reproduce the experimental spectra. Furthermore, bands are assigned with the driven molecular dynamics approach. This method package is shown to compare successfully with experimental spectra for 11 ions in water drops containing 36-100 water molecules. In particular, band frequency shifts of the free O-H stretching modes at the cluster surface are well reproduced as a function of both ion charge and drop size.

Computational Insight into Calcium–Sulfate Ion Pair Formation

The thermodynamics of ion pair formation between Ca2+ and SO42– has been studied using a rigid ion force field, the polarizable AMOEBA force field, and ab initio molecular dynamics simulation. The results obtained from the three methods are remarkably similar and consistent with the available experimental data and show that the ion association is driven by an increase in entropy, which can be related to the release of water molecules as previously found for Ca2+ and CO32–. Two new rigid ion force fields targeting different solvation free energies for sulfate have been developed. The comparison between static and dynamic properties of the solvated anion, as well as the pairing free energy with Ca2+, suggest that the model with the strongest solvation is more realistic, which may help to resolve the inconsistency in the current literature.

Transfer Learning from Markov Models Leads to Efficient Sampling of Related Systems.

We recently showed that the time-structure-based independent component analysis method from Markov state model literature provided a set of variationally optimal slow collective variables for metadynamics (tICA-metadynamics). In this paper, we extend the methodology toward efficient sampling of related mutants by borrowing ideas from transfer learning methods in machine learning. Our method explicitly assumes that a similar set of slow modes and metastable states is found in both the wild type (baseline) and its mutants. Under this assumption, we describe a few simple techniques using sequence mapping for transferring the slow modes and structural information contained in the wild type simulation to a mutant model for performing enhanced sampling. The resulting simulations can then be reweighted onto the full-phase space using the multistate Bennett acceptance ratio, allowing for thermodynamic comparison against the wild type. We first benchmark our methodology by recapturing alanine dipeptide dynamics across a range of different atomistic force fields, including the polarizable Amoeba force field, after learning a set of slow modes using Amber ff99sb-ILDN. We next extend the method by including structural data from the wild type simulation and apply the technique to recapturing the effects of the GTT mutation on the FIP35 WW domain.

Hybrid QM/MM Molecular Dynamics with AMOEBA Polarizable Embedding.

We present the implementation of a Born-Oppenheimer (BO) hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) strategy using density functional theory (DFT) and the polarizable AMOEBA force field. This approach couples the Gaussian and Tinker suite of programs through a variational formalism allowing for a full self-consistent relaxation of both the AMOEBA induced dipoles and the DFT electron density at each MD step. As the DFT SCF cycles are the limiting factor in terms of computational efforts and MD stability, we focus on the latter aspect and compare the time-reversible BO (TR-BO) and the extended BO Lagrangian approaches (XL-BO) to the MD propagation. The XL-BO approach allows for stable, energy-conserving trajectories offering various perspectives for hybrid simulations using polarizable force fields.

Estimating and modeling charge transfer from the SAPT induction energy.

Recent studies using quantum mechanics energy decomposition methods, for example, SAPT and ALMO, have revealed that the charge transfer energy may play an important role in short ranged inter-molecular interactions, and have a different distance dependence comparing with the polarization energy. However, the charge transfer energy component has been ignored in most current polarizable or non-polarizable force fields. In this work, first, we proposed an empirical decomposition of SAPT induction energy into charge transfer and polarization energy that mimics the regularized SAPT method (ED-SAPT). This empirical decomposition is free of the divergence issue, hence providing a good reference for force field development. Then, we further extended this concept in the context of AMOEBA polarizable force field, proposed a consistent approach to treat the charge transfer phenomenon. Current results show a promising application of this charge transfer model in future force field development. © 2017 Wiley Periodicals, Inc.

Polarizable and Non-Polarizable Force Field Representations of Ferric Cation and Validations.

The AMOEBA polarizable force field of ferric ion was optimized and applied to study the hydration of ferric ion and its complexation with porphine in the aqueous phase. The nonpolarizable force field was also optimized for comparison. The AMOEBA force field was found to give a more accurate hydration free energy than the nonpolarizable force field with respect to experimental data, and correctly predict the most stable electronic state of hydrated Fe3+, which is the sextet state, and of the Fe(III)-Por complex, which is the quartet state, consistent with the literature that was carried out using the DFT method. The explicit inclusion of charge transfer between Fe3+ and ligand was found to be important in order to obtain a precise picture of polarization energy and van der Waals energy, which otherwise deviate from the corresponding energy components derived from ab initio calculations. The successful application of the AMOEBA force field in the characterization of aquo Fe(III)-Por complexes suggests that its use may be extended to the study of the dynamics of metalloenzyme containing highly charged metal ions in the condensed phase with reliable treatment of the interactions between metal atom and protein.

Improved Polarizable Dipole-Dipole Interaction Model for Hydrogen Bonding, Stacking, T-Shaped, and X-H···π Interactions.

The polarizable dipole-dipole interaction model was formulated in our laboratory to rapidly simulate hydrogen bonding in biosystems. In this paper, this model is improved and further parametrized for stacking, T-shaped, and X-H···π interactions by adding the orbital overlap term and fitting to 19 CCSD(T)/CBS interaction energy curves of training dimers. The performance of our model is assessed through its application to more than 100 complexes, including hydrogen-bonded, stacked, T-shaped, and X-H···π complexes. For 124 relatively small testing complexes, our model reproduces benchmark equilibrium intermolecular distances with a root-mean-square deviation (RMSD) of 0.08 Å, and it reproduces benchmark interaction energies with a 0.64 kcal/mol RMSD. For 14 large noncovalent complexes, our model reproduces benchmark equilibrium intermolecular distances with a RMSD of 0.05 Å, and it reproduces benchmark interaction energies with a 0.80 kcal/mol RMSD. Extensive comparisons are made to interaction energies calculated via the M06-2X and M06-2X-D3 methods, via the well-known nonpolarizable AMBER99 force field method, via the popular polarizable AMOEBA force field method, and via semiempirical quantum mechanical (SQM) methods. Our statistical evaluations show that our model outperforms the AMBER99, AMOEBA, and SQM methods and is as accurate as the M06-2X and M06-2X-D3 methods. In summary, the model developed in this work is reasonable, and the newly introduced orbital overlap term is effective in the accurate modeling of the noncovalent interactions. Our testing results also indicate that the polarization interaction term is important in the evaluation of hydrogen bonding, whereas the orbital overlap is important in examining short hydrogen bonding, T-shaped, and X-H···π interactions. Our model may serve as a new tool for modeling biological systems where hydrogen bonding, stacking, T-shaped, and X-H···π interactions are of general importance.

The Importance of the Scaffold for de Novo Enzymes: A Case Study with Kemp Eliminase.

We report electric field values relevant to the reactant and transition states of designed Kemp eliminases KE07 and KE70 and their improved variants from laboratory directed evolution (LDE), using atomistic simulations with the AMOEBA polarizable force field. We find that the catalytic base residue contributes the most to the electric field stabilization of the transition state of the LDE variants of the KE07 and KE70 enzymes, whereas the electric fields of the remainder of the enzyme and solvent disfavor the catalytic reaction in both cases. By contrast, we show that the electrostatic environment plays a large and stabilizing role for the naturally occurring enzyme ketosteroid isomerase (KSI). These results suggest that LDE is ultimately a limited strategy for improving de novo enzymes since it is largely restricted to optimization of chemical positioning in the active site, thus yielding a ∼3 order magnitude improvement over the uncatalyzed reaction, which we suggest may be an absolute upper bound estimate based on LDE applied to comparable de novo Kemp eliminases and other enzymes like KSI. Instead de novo enzymatic reactions could more productively benefit from optimization of the electrostatics of the protein scaffold in early stages of the computational design, utilizing electric field optimization as guidance.

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory.

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes-in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.

Polarizable Amoeba Force Field Metadynamics with Minimization Predicts Missing Protein Loops

Computational methods developed to find the global free energy minimum of amino acid sequences are increasingly successful, but limitations in both accuracy and efficiency remain. Optimization algorithms are typically focused on proteins of modest size (i.e. of approximately 100 residues) and utilize potential energy functions based on fixed charged force fields, statistical or knowledge based potentials, and/or potentials incorporating experimental data. Although the aforementioned methods are widely used, known limitations include 1) search protocols that are inefficient or not deterministic due to rough energy landscapes characterized by large energy barriers between multiple minima and 2) use of a target function whose global minimum does not correspond to the actual free energy minimum. To overcome the first limitation, this work describes a global optimization approach based on metadynamics to drive the search of conformational space toward unexplored regions by adding a time-dependent bias to the objective function. To overcome the second limitation, a hybrid objective function is defined as the sum of the polarizable AMOEBA polarizable force field and an experimental X-ray crystallography target. As metadynamics drives the search, periodic quenching via local minimization is used to access structure quality via evaluation of Rwork. Thus, the overall method is called AMOEBA Metadynamics with Minimization (AMM), and is suitable for optimization of side-chains, ligand binding poses, protein loops or even protein complexes. Here we focus on characterizing the ability of AMM to elucidate the structural details of missing protein loops, which are often excluded from experimental X-ray crystallography structures due to conformational heterogeneity and/or limitations in the resolution of the data. We first show that the correlation between experimental data and AMOEBA structural minima is stronger than that for OPLS-AA/L (i.e. a fixed charge force field). Next, missing protein loops are optimized using 5 nsec of sampling for both AMM and simulated annealing with OPLS-AA/L. The AMM procedure provides more accurate structures in terms of both experimental (i.e. lower Rfree values) and structural metrics (i.e. MolProbity). In addition to providing more accurate loop conformations, AMM converged faster than the simulated annealing protocol. Overall, this work suggests that AMM is well-suited to refine or predict the coordinates of missing amino acid residues and/or protein loops due to both the increased accuracy of the target function relative to OPLS-AA/L and more rapid convergence of the metadynamics driven search compared to simulation annealing.

Dynamics of ions in a water drop using the AMOEBA polarizable force field

Various ions carrying a charge from −2 to +3 were confined in a drop of 100 water molecules as a way to model coordination properties inside the cluster and at the interface. The behavior of the ions has been followed by molecular dynamics with the AMOEBA polarizable force field. Multiply charged ions and small singly charged ions are found to lie inside the droplet, while bigger monovalent ions sit near the surface. The results provide a coherent picture of average structural properties as well as residence times for which a general trend is proposed, especially for the anions.

Evaluation of solvation free energies for small molecules with the AMOEBA polarizable force field.

The effects of electronic polarization in biomolecular interactions will differ depending on the local dielectric constant of the environment, such as in solvent, DNA, proteins, and membranes. Here the performance of the AMOEBA polarizable force field is evaluated under nonaqueous conditions by calculating the solvation free energies of small molecules in four common organic solvents. Results are compared with experimental data and equivalent simulations performed with the GAFF pairwise‐additive force field. Although AMOEBA results give mean errors close to “chemical accuracy,” GAFF performs surprisingly well, with statistically significantly more accurate results than AMOEBA in some solvents. However, for both models, free energies calculated in chloroform show worst agreement to experiment and individual solutes are consistently poor performers, suggesting non‐potential‐specific errors also contribute to inaccuracy. Scope for the improvement of both potentials remains limited by the lack of high quality experimental data across multiple solvents, particularly those of high dielectric constant. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.