Towards accurate solvation dynamics of divalent cations in water using the polarizable amoeba force field: From energetics to structure

Probing pH-Dependent Dehydration Dynamics of Mg and Ca Cations in Aqueous Solutions with Multi-Level Quantum Mechanics/Molecular Dynamics Simulations

The dehydration of aqueous calcium and magnesium cations is the most fundamental process controlling their reactivity in chemical and biological phenomena, such as the formation of ionic solids or passing through ion channels. It holds particular relevance in light of recent advancements in the development of carbon capture techniques that rely on mineralization for long-term carbon storage. Specifically, dehydration of Ca2+ and Mg2+ is a key step in proposed carbon capture processes aiming to exploit the relatively high concentration of dissolved carbon dioxide in seawater via the formation of carbonate minerals from solvated Ca2+ and Mg2+ cations for sequestration and storage. Nevertheless, atomic-scale understanding of the dehydration of aqueous Ca2+ and Mg2+ cations remains limited. Here, we utilize rare event sampling via density functional theory molecular dynamics and embedded wavefunction theory calculations to elucidate the dehydration dynamics of aqueous Ca2+ and Mg2+. Emphasis is placed on the investigation of the effect pH has on the stability of the different coordination environments. Our results reveal significant differences in the dehydration dynamics of the two cations and provide insight into how they may be modulated by pH changes.

Classical Exchange Polarization: An Anisotropic Variable Polarizability Model

Polarizability, or the tendency of the electron distribution to distort under an electric field, often depends on the local chemical environment. For example, the polarizability of a chloride ion is larger in gas phase compared to a chloride ion solvated in water. This effect is due to the restriction the Pauli exclusion principle places on the allowed electron states. Because no two electrons can occupy the same state, when a highly polarizable atom comes in close contact with other atoms or molecules, the space of allowed states can dramatically decrease. This constraint suggests that an accurate molecular mechanics polarizability model should depend on the radial distance between neighboring atoms. This paper introduces a variable polarizability model within the framework of the HIPPO (Hydrogen-like Intermolecular Polarizable Potential) force field, by damping the polarizability as a function of the orbital overlap of two atoms. This effectively captures the quantum mechanical exchange polarization effects, without explicit utilization of antisymmetrized wave functions. We show that the variable polarizability model remarkably improves the two-body polarization energies and three-body energies of ion-ion and ion-water systems. Under this model, no manual tuning of atomic polarizabilities for monatomic ions is required; the gas-phase polarizability can be used because an appropriate damping function is able to correct the polarizability at short range.

The influence of L-aspartic acid on calcium carbonate nucleation and growth revealed by in situ liquid phase TEM

In situ transmission electron microscopy has permitted the study of nanomaterials in liquid environments with high spatial and temporal resolutions, allowing chemical reaction visualization in real time. The aim of...

Manifolds of low energy structures for a magic number of hydrated sulfate: SO42-(H2O)24

Low energy structures of SO₄^2-(H₂O)₂₄ have been obtained using a combination of classical molecular dynamics simulations and refinement of structures and energies by quantum chemical calculations. Extensive exploration of the potential energy surface led to a number of low-energy structures, confirmed by accurate calibration calculations. An overall analysis of this large set was made after devising appropriate structural descriptors such as the numbers of cycles and their combinations. Low energy structures bear common motifs, the most prominent being fused cycles involving alternatively four and six water molecules. The latter adopt specific conformations which ensure the appropriate surface curvature to form a closed cage without dangling O-H bonds and at the same time provide 12-coordination of the sulfate ion. A prominent feature to take into account is isomerism via inversion of hydrogen bond orientations along cycles. This generates large families of ca. 100 isomers for this cluster size, spanning energy windows of 10-30 kJ mol^-1. This relatively ignored isomerism must be taken into account to identify reliably the lowest energy minima. The overall picture is that the magic number cluster SO₄^2-(H₂O)₂₄ does not correspond to formation of a single, remarkable structure, but rather to a manifold of structural families with similar stabilities. Extensive calculations on isomerization mechanisms within a family indicate that large barriers are associated to direct inversion of hydrogen bond networks. Possible implications of these results for magic number clusters of other anions are discussed.

Computational predictions of metal-macrocycle stability constants require accurate treatments of local solvent and pH effects

Rational design of molecular chelating agents requires a detailed understanding of physicochemical ligand-metal interactions in solvent phase. Computational quantum chemistry methods should be able to provide this, but computational reports have shown poor accuracy when determining absolute binding constants for many chelating molecules. To understand why, we compare and benchmark static- and dynamics-based computational procedures for a range of monovalent and divalent cations binding to a conventional cryptand molecule: 2.2.2-cryptand ([2.2.2]). The benchmarking comparison shows that dynamics simulations using standard OPLS-AA classical potentials can reasonably predict binding constants for monovalent cations, but these procedures fail for divalent cations. We also consider computationally efficient static procedure using Kohn-Sham density functional theory (DFT) and cluster-continuum modeling that accounts for local microsolvation and pH effects. This approach accurately predicts binding energies for monovalent and divalent cations with an average error of 3.2 kcal mol-1 compared to experiment. This static procedure thus should be useful for future molecular screening efforts, and high absolute errors in the literature may be due to inadequate modeling of local solvent and pH effects.

Assessing the Intrinsic Strengths of Ion–Solvent and Solvent–Solvent Interactions for Hydrated Mg2+ Clusters

Information resulting from a comprehensive investigation into the intrinsic strengths of hydrated divalent magnesium clusters is useful for elucidating the role of aqueous solvents on the Mg2+ ion, which can be related to those in bulk aqueous solution. However, the intrinsic Mg–O and intermolecular hydrogen bond interactions of hydrated magnesium ion clusters have yet to be quantitatively measured. In this work, we investigated a set of 17 hydrated divalent magnesium clusters by means of local vibrational mode force constants calculated at the ωB97X-D/6-311++G(d,p) level of theory, where the nature of the ion–solvent and solvent–solvent interactions were interpreted from topological electron density analysis and natural population analysis. We found the intrinsic strength of inner shell Mg–O interactions for [Mg(H2O)n]2+ (n = 1–6) clusters to relate to the electron density at the bond critical point in Mg–O bonds. From the application of a secondary hydration shell to [Mg(H2O)n]2+ (n = 5–6) clusters, stronger Mg–O interactions were observed to correspond to larger instances of charge transfer between the lp(O) orbitals of the inner hydration shell and the unfilled valence shell of Mg. As the charge transfer between water molecules of the first and second solvent shell increased, so did the strength of their intermolecular hydrogen bonds (HBs). Cumulative local vibrational mode force constants of explicitly solvated Mg2+, having an outer hydration shell, reveal a CN of 5, rather than a CN of 6, to yield slightly more stable configurations in some instances. However, the cumulative local mode stretching force constants of implicitly solvated Mg2+ show the six-coordinated cluster to be the most stable. These results show that such intrinsic bond strength measures for Mg–O and HBs offer an effective way for determining the coordination number of hydrated magnesium ion clusters.

Determination of van der Waals Parameters Using a Double Exponential Potential for Nonbonded Divalent Metal Cations in TIP3P Solvent

A double exponential (DE) functional form for Lennard-Jones (LJ) interactions, proposed in our previous study, has many advantages over LJ potentials including a natural softcore characteristic for the convenience of the pathway-based free-energy calculations, fast convergence, and flexibility in use. In this work, we put the first step on the application of the DE functional form by identifying a DE potential, coined DE-TIP3P, for molecular simulations using the TIP3P water model. The developed DE-TIP3 potential was better than LJ potential in reproducing the experimental water properties. Afterward, we developed the nonbonded models of 15 divalent metal ions, which frequently appear and play vital roles in biological systems, to be consistent with the DE-TIP3P potential and TIP3P water model. Our nonbonded models were as good as the complicated nonbonded dummy cationic models by Jiang et al. and the nonbonded 12-6-4 LJ models by Li and Merz in reproducing the experimental properties of those ions. Moreover, our nonbonded models achieved a better performance than the compromise (CM) LJ models and 12-6-4 LJ models, developed by Li and Merz, in reproducing the properties of MgCl₂ in aqueous solution.

Characterization of a TP53 Somatic Variant of Unknown Function From an Ovarian Cancer Patient Using Organoid Culture and Computational Modeling

In our proof-of-concept study of 1 patient with stage IIIC carcinosarcoma of the ovary, we discovered a rare mutation in the tumor suppressor, TP53, that results in the deletion of N131. Immunofluorescence imaging of the organoid culture revealed hyperstaining of p53 protein. Computational modeling suggests this residue is important for maintaining protein conformation. Drug screening identified the combination of a proteasome inhibitor with a histone deacetylase inhibitor as the most effective treatment. These data provide evidence for the successful culture of a patient tumor and analysis of drug response ex vivo.

Transferable interactions of Li+ and Mg2+ ions in polarizable models

Therapeutic implications of Li⁺, in many cases, stem from its ability to inhibit certain Mg²⁺-dependent enzymes, where it interacts with or substitutes for Mg²⁺. The underlying details of its action are, however, unknown. Molecular simulations can provide insights, but their reliability depends on how well they describe relative interactions of Li⁺ and Mg²⁺ with water and other biochemical groups. Here, we explore, benchmark, and recommend improvements to two simulation approaches: the one that employs an all-atom polarizable molecular mechanics (MM) model and the other that uses a hybrid quantum and MM implementation of the quasi-chemical theory (QCT). The strength of the former is that it describes thermal motions explicitly and that of the latter is that it derives local contributions from electron densities. Reference data are taken from the experiment, and also obtained systematically from CCSD(T) theory, followed by a benchmarked vdW-inclusive density functional theory. We find that the QCT model predicts relative hydration energies and structures in agreement with the experiment and without the need for additional parameterization. This implies that accurate descriptions of local interactions are essential. Consistent with this observation, recalibration of local interactions in the MM model, which reduces errors from 10.0 kcal/mol to 1.4 kcal/mol, also fixes aqueous phase properties. Finally, we show that ion-ligand transferability errors in the MM model can be reduced significantly from 10.3 kcal/mol to 1.2 kcal/mol by correcting the ligand's polarization term and by introducing Lennard-Jones cross-terms. In general, this work sets up systematic approaches to evaluate and improve molecular models of ions binding to proteins.

Evaluation of the AMOEBA force field for simulating metal halide perovskites in the solid state and in solution

In this work, we compare the existing nonpolarizable force fields developed to study the solid or solution phases of hybrid organic-inorganic halide perovskites with the AMOEBA polarizable force field. The aim is to test whether more computationally expensive polarizable force fields like AMOEBA offer better transferability between solution and solid phases, with the ultimate goal being the study of crystal nucleation, growth, and other interfacial phenomena involving these ionic compounds. In the context of hybrid perovskites, AMOEBA force field parameters already exist for several elements in solution, and we decided to leave them unchanged and to only parameterize the missing ones (Pb²⁺ and CH₃NH₃ ⁺ ions) in order to maximize transferability and avoid overfitting to the specific examples studied here. Overall, we find that AMOEBA yields accurate hydration free energies (within 5%) for typical ionic species while showing the correct ordering of stability for the different crystal polymorphs of CsPbI₃ and CH₃NH₃PbI₃. Although the existing parameters do not accurately reproduce all transition temperatures and lattice parameters, AMOEBA offers better transferability between solution and solid states than existing nonpolarizable force fields.

Accurate Biomolecular Simulations Account for Electronic Polarization

In this perspective, we discuss where and how accounting for electronic many-body polarization affects the accuracy of classical molecular dynamics simulations of biomolecules. While the effects of electronic polarization are highly pronounced for molecules with an opposite total charge, they are also non-negligible for interactions with overall neutral molecules. For instance, neglecting these effects in important biomolecules like amino acids and phospholipids affects the structure of proteins and membranes having a large impact on interpreting experimental data as well as building coarse grained models. With the combined advances in theory, algorithms and computational power it is currently realistic to perform simulations with explicit polarizable dipoles on systems with relevant sizes and complexity. Alternatively, the effects of electronic polarization can also be included at zero additional computational cost compared to standard fixed-charge force fields using the electronic continuum correction, as was recently demonstrated for several classes of biomolecules.

Molecular Dynamics Simulations of Ionic Liquids and Electrolytes Using Polarizable Force Fields

Many applications in chemistry, biology, and energy storage/conversion research rely on molecular simulations to provide fundamental insight into structural and transport properties of materials with high ionic concentrations. Whether the system is comprised entirely of ions, like ionic liquids, or is a mixture of a polar solvent with a salt, e.g., liquid electrolytes for battery applications, the presence of ions in these materials results in strong local electric fields polarizing solvent molecules and large ions. To predict properties of such systems from molecular simulations often requires either explicit or mean-field inclusion of the influence of polarization on electrostatic interactions. In this manuscript, we review the pros and cons of different treatments of polarization ranging from the mean-field approaches to the most popular explicit polarization models in molecular dynamics simulations of ionic materials. For each method, we discuss their advantages and disadvantages and emphasize key assumptions as well as their adjustable parameters. Strategies for the development of polarizable models are presented with a specific focus on extracting atomic polarizabilities. Finally, we compare simulations using polarizable and nonpolarizable models for several classes of ionic systems, discussing the underlying physics that each approach includes or ignores, implications for implementation and computational efficiency, and the accuracy of properties predicted by these methods compared to experiments.

Improving the description of solvent pairwise interactions using local solute/solvent three-body functions. The case of halides and carboxylates in aqueous environment

We propose a general strategy to remediate force-field artifacts in describing pairwise interactions among similar molecules M in the vicinity of another chemical species, C, like water molecules interacting at short distance from a monoatomic ion. This strategy is based on introducing a three-body potential energy term that alters the pairwise interactions among M-type molecules when they lie at short range from the species C. In other words the species C is the center of a space domain where the pairwise interactions among the molecules M is altered. Here, we apply it to improve the description of the water interactions provided by the polarizable water model TCPE/2013 in the vicinity of halides, from F^- to At^- , and of the prototypical carboxylate anion CH₃ COO^- . We show the accuracy and the transferability of such an approach to investigate not only the hydration process of single anions but also of a salt solution NH 4 + / Cl - in aqueous phase. This strategy can be used to remediate the drawbacks of any kind of force fields. © 2019 Wiley Periodicals, Inc.

Ion-Hydroxyl Interactions: From High-Level Quantum Benchmarks to Transferable Polarizable Force Fields

Ion descriptors in molecular mechanics models are calibrated against reference data on ion-water interactions. It is then typically assumed that these descriptors will also satisfactorily describe interactions of ions with other functional groups, such as those present in biomolecules. However, several studies now demonstrate that this transferability assumption produces, in many different cases, large errors. Here we address this issue in a representative polarizable model and focus on transferability of cationic interactions from water to a series of alcohols. Both water and alcohols use hydroxyls for ion-coordination, and, therefore, this set of molecules constitutes the simplest possible case of transferability. We obtain gas phase reference data systematically from "gold-standard" quantum Monte Carlo and CCSD(T) methods, followed by benchmarked vdW-corrected DFT. We learn that the original polarizable model yields large gas phase water → alcohol transferability errors - the RMS and maximum errors are 2.3 and 5.1 kcal/mol, respectively. These errors are, nevertheless, systematic in that ion-alcohol interactions are overstabilized, and systematic errors typically imply that some essential physics is either missing or misrepresented. A comprehensive analysis shows that when both low- and high-field responses of ligand dipole polarization are described accurately, then transferability improves significantly - the RMS and maximum errors in the gas phase reduce, respectively, to 0.9 and 2.5 kcal/mol. Additionally, predictions of condensed phase transfer free energies also improve. Nevertheless, within the limits of the extrathermodynamic assumptions necessary to separate experimental estimates of salt dissolution into constituent cationic and anionic contributions, we note that the error in the condensed phase is systematic, which we attribute, at least, partially to the parametrization in long-range electrostatics. Overall, this work demonstrates a rational approach to boosting transferability of ionic interactions that will be applicable broadly to improving other polarizable and nonpolarizable models.

Polarizable Force Fields for Biomolecular Simulations: Recent Advances and Applications

Realistic modeling of biomolecular systems requires an accurate treatment of electrostatics, including electronic polarization. Due to recent advances in physical models, simulation algorithms, and computing hardware, biomolecular simulations with advanced force fields at biologically relevant timescales are becoming increasingly promising. These advancements have not only led to new biophysical insights but also afforded opportunities to advance our understanding of fundamental intermolecular forces. This article describes the recent advances and applications, as well as future directions, of polarizable force fields in biomolecular simulations.

Infrared Spectra of Deprotonated Dicarboxylic Acids: IRMPD Spectroscopy and Empirical Valence‐Bond Modeling

Experimental infrared multiple-photon dissociation (IRMPD) spectra recorded for a series of deprotonated dicarboxylic acids, HO₂ (CH₂ )_n CO 2 - (n=2-4), are interpreted using a variety of computational methods. The broad bands centered near 1600 cm^-1 can be reproduced neither by static vibrational calculations based on quantum chemistry nor by a dynamical description of individual structures using the many-body polarizable AMOEBA force field, strongly suggesting that these molecules experience dynamical proton sharing between the two carboxylic ends. To confirm this assumption, AMOEBA was combined with a two-state empirical valence-bond (EVB) model to allow for proton transfer in classical molecular dynamics simulations. Upon suitable parametrization based on ab initio reference data, the EVB-AMOEBA model satisfactorily reproduces the experimental infrared spectra, and the finite temperature dynamics reveals a significant amount of proton sharing in such systems.

Decomposition of molecular properties

We review recent work on property decomposition techniques using quantum chemical methods and discuss some topical applications in terms of quantum mechanics-molecular mechanics calculations and the constructing of properties of large molecules and clusters. Starting out from the so-called LoProp decomposition scheme [Gagliardi et al., J. Chem. Phys., 2004, 121, 4994] for extracting atomic and inter-atomic contributions to molecular properties we show how this method can be generalized to localized frequency-dependent polarizabilities, to localized hyperpolarizabilities and to localized dispersion coefficients. Some applications of the generalized decomposition technique are reviewed - calculations of frequency-dependent polarizabilities, Rayleigh scattering of large clusters, and calculations of hyperpolarizabilities of proteins.

Force Fields for Small Molecules

Molecular dynamics (MD) simulations have been widely applied to computer-aided drug design (CADD). While MD has been used in a variety of applications such as free energy perturbation and long-time simulations, the accuracy of the results from those methods depends strongly on the force field used. Force fields for small molecules are crucial, as they not only serve as building blocks for developing force fields for larger biomolecules but also act as model compounds that will be transferred to ligands used in CADD. Currently, a wide range of small molecule force fields based on additive or nonpolarizable models have been developed. While these nonpolarizable force fields can produce reasonable estimations of physical properties and have shown success in a variety of systems, there is still room for improvements due to inherent limitations in these models including the lack of an electronic polarization response. For this reason, incorporating polarization effects into the energy function underlying a force field is believed to be an important step forward, giving rise to the development of polarizable force fields. Recent simulations of biological systems have indicated that polarizable force fields are able to provide a better physical representation of intermolecular interactions and, in many cases, better agreement with experimental properties than nonpolarizable, additive force fields. Therefore, this chapter focuses on the development of small molecule force fields with emphasis on polarizable models. It begins with a brief introduction on the importance of small molecule force fields and their evolution from additive to polarizable force fields. Emphasis is placed on the additive CHARMM General Force Field and the polarizable force field based on the classical Drude oscillator. The theory for the Drude polarizable force field and results for small molecules are presented showing their improvements over the additive model. The potential importance of polarization for their application in a wide range of biological systems including CADD is then discussed.

Polarizable ab initio QM/MM Study of the Reaction Mechanism of N-tert-Butyloxycarbonylation of Aniline in [EMIm][BF₄]

N-t e r t-butoxycarbonylation of amines in solution (water, organic solvents, or ionic liquids) is a common reaction for the preparation of drug molecules. To understand the reaction mechanism and the role of the solvent, quantum mechanical/molecular mechanical simulations using a polarizable multipolar force field with long⁻range electrostatic corrections were used to optimize the minimum energy paths (MEPs) associated with various possible reaction mechanisms employing the nudged elastic band (NEB) and the quadratic string method (QSM). The calculated reaction energies and energy barriers were compared with the corresponding gas-phase and dichloromethane results. Complementary Electron Localization Function (ELF)/NCI analyses provide insights on the critical structures along the MEP. The calculated results suggest the most likely path involves a sequential mechanism with the rate⁻limiting step corresponding to the nucleophilic attack of the aniline, followed by proton transfer and the release of CO 2 without the direct involvement of imidazolium cations as catalysts.

Many-body effect determines the selectivity for Ca2+ and Mg2+ in proteins

Calcium ion is a versatile messenger in many cell-signaling processes. To achieve their functions, calcium-binding proteins selectively bind Ca2+ against a background of competing ions such as Mg2+ The high specificity of calcium-binding proteins has been intriguing since Mg2+ has a higher charge density than Ca2+ and is expected to bind more tightly to the carboxylate groups in calcium-binding pockets. Here, we showed that the specificity for Ca2+ is dictated by the many-body polarization effect, which is an energetic cost arising from the dense packing of multiple residues around the metal ion. Since polarization has stronger distance dependence compared with permanent electrostatics, the cost associated with the smaller Mg2+ is much higher than that with Ca2+ and outweighs the electrostatic attraction favorable for Mg2+ With the AMOEBA (atomic multipole optimized energetics for biomolecular simulation) polarizable force field, our simulations captured the relative binding free energy between Ca2+ and Mg2+ for proteins with various types of binding pockets and explained the nonmonotonic size dependence of the binding free energy in EF-hand proteins. Without electronic polarization, the smaller ions are always favored over larger ions and the relative binding free energy is roughly proportional to the net charge of the pocket. The many-body effect depends on both the number and the arrangement of charged residues. Fine-tuning of the ion selectivity could be achieved by combining the many-body effect and geometric constraint.

Classical Drude Polarizable Force Field Model for Methyl Phosphate and Its Interactions with Mg2

Phosphate groups are essential components of nucleic acids and proteins, whose interactions with solvent, metal ions, and ionic side chains help control folding and binding. Methyl phosphate (MP) represents a simple analog of phosphate moieties that are post-translation modifications in proteins and present at the termini of nucleic acids, among other environments. In the present study, we optimized parameters for use in polarizable molecular dynamics simulations of MP in its mono- and dianionic forms, MP- ≡ CH3HPO4- and MP2- ≡ CH3PO42-, along with P i2- ≡ HPO42-, in the context of the classical Drude oscillator model. Parameter optimization was done in a manner consistent with the remainder of the Drude molecular mechanics force field, choosing atomic charges and polarizabilities to reproduce molecular properties from quantum mechanics as well as experimental hydration free energies. Optimized parameters were similar to existing dimethyl phosphate parameters, with a few significant differences. The developed parameters were then used to compute magnesium binding affinities in aqueous solution, using alchemical molecular dynamics free energy simulations. Good agreement with experiment was obtained, and outer sphere binding was shown to be predominant for MP- and MP2-.

A Kirkwood-Buff derived force field for alkaline earth halide salts

The activity and function of many macromolecules in cellular environments are coupled with the binding of divalent ions such as calcium or magnesium. In principle, computer simulations can be used to understand the molecular level aspects of how many important macromolecules interact with ions. However, most of the force fields currently available often fail to accurately reproduce the properties of divalent ions in aqueous environments. Here we develop classical non-polarizable force fields for the aqueous alkaline earth metal halides (MX₂), where M = Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺ and X = Cl^-, Br^-, I^-, which can be used in bimolecular simulations and which are compatible with the Simple Point Charge/Extended (SPC/E) water model. The force field parameters are specifically developed to reproduce the experimental Kirkwood-Buff integrals for aqueous solutions and thereby the experimental activity derivatives, partial molar volumes, and excess coordination numbers. This ensures that a reasonable balance between ion-ion, ion-water, and water-water distributions is obtained. However, this requires a scaling of the cation to water oxygen interaction strength in order to accurately reproduce the integrals. The scaling factors developed for chloride salts are successfully transferable to the bromide and iodide salts. Use of these new models leads to reasonable diffusion constants and dielectric decrements. However, the performance of the models decreases with increasing salt concentration (>4m), and simulations of the pure crystals exhibited unstable behavior.

Molecular dynamics investigation of water-exchange reactions on lanthanide ions in water/1-ethyl-3-methylimidazolium trifluoromethylsufate ([EMIm][OTf])

We report a kinetic study of the water exchange on lanthanide ions in water/[1-ethyl-3-methylimidazolium][trifluoromethylsufate] (water/[EMIm][OTf]). The results from ¹⁷O-NMR measurements show that the water-exchange rates in water/[EMIm][OTf] increase with decreasing size of the lanthanide ions. This trend for water-exchange is similar to the previously reported trend in water/1-ethyl-3-methylimidazolium ethyl sulfate (water/[EMIm][EtSO₄]) but opposite to that in water. To gain atomic-level insight into these water-exchange reactions, molecular dynamics simulations for lanthanide ions in water/[EMIm][OTf] have been performed using the atomic-multipole-optimized-energetics-for-biomolecular-application polarizable force field. Our molecular dynamics simulations reproduce the experimental water-exchange rates in terms of the trend and provide possible explanations for the observed experimental behavior. The smaller lanthanide ions in water/[EMIm][OTf] undergo faster water exchange because the smaller lanthanide ions coordinate to the first shell [OTf]^- anions more tightly, resulting in a stronger screening effect for the second-shell water. The screening effect weakens the interaction of the lanthanide ions with the second-shell water molecules, facilitating the dissociation of water from the second-shell and subsequent association of water molecules from the outer solvation shells.

Computer simulations of alkali-acetate solutions: Accuracy of the forcefields in difference concentrations

When proteins are solvated in electrolyte solutions that contain alkali ions, the ions interact mostly with carboxylates on the protein surface. Correctly accounting for alkali-carboxylate interactions is thus important for realistic simulations of proteins. Acetates are the simplest carboxylates that are amphipathic, and experimental data for alkali acetate solutions are available and can be compared with observables obtained from simulations. We carried out molecular dynamics simulations of alkali acetate solutions using polarizable and non-polarizable forcefields and examined the ion-acetate interactions. In particular, activity coefficients and association constants were studied in a range of concentrations (0.03, 0.1, and 1M). In addition, quantum-mechanics (QM) based energy decomposition analysis was performed in order to estimate the contribution of polarization, electrostatics, dispersion, and QM (non-classical) effects on the cation-acetate and cation-water interactions. Simulations of Li-acetate solutions in general overestimated the binding of Li⁺ and acetates. In lower concentrations, the activity coefficients of alkali-acetate solutions were too high, which is suggested to be due to the simulation protocol and not the forcefields. Energy decomposition analysis suggested that improvement of the forcefield parameters to enable accurate simulations of Li-acetate solutions can be achieved but may require the use of a polarizable forcefield. Importantly, simulations with some ion parameters could not reproduce the correct ion-oxygen distances, which calls for caution in the choice of ion parameters when protein simulations are performed in electrolyte solutions.

Chemical shift extremum of 129Xe(aq) reveals details of hydrophobic solvation

The ¹²⁹Xe chemical shift in an aqueous solution exhibits a non-monotonic temperature dependence, featuring a maximum at 311 K. This is in contrast to most liquids, where the monotonic decrease of the shift follows that of liquid density. In particular, the shift maximum in water occurs at a higher temperature than that of the maximum density. We replicate this behaviour qualitatively via a molecular dynamics simulation and computing the ¹²⁹Xe chemical shift for snapshots of the simulation trajectory. We also construct a semianalytical model, in which the Xe atom occupies a cavity constituted by a spherical water shell, consisting of an even distribution of solvent molecules. The temperature dependence of the shift is seen to result from a product of the decreasing local water density and an increasing term corresponding to the energetics of the Xe-H₂O collisions. The latter moves the chemical shift maximum up in temperature, as compared to the density maximum. In water, the computed temperature of the shift maximum is found to be sensitive to both the details of the binary chemical shift function and the coordination number. This work suggests that, material parameters allowing, the maximum should be exhibited by other liquids, too.

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.

On the Computational Characterization of Charge-Transfer Effects in Noncovalently Bound Molecular Complexes

Charge-transfer (CT) is an important binding force in the formation of intermolecular complexes, and there have been a variety of theoretical models proposed to quantify this effect. These approaches, which typically rely on a definition of a "CT-free" state based on a partition of the system, sometimes yield significantly different results for a given intermolecular complex. Two widely used definitions of the "CT-free" state, the absolutely localized molecular orbitals (ALMO) method (where only on-fragment orbital mixings are permitted) and the constrained density functional theory (CDFT) approach (where fragment electron populations are fixed), are carefully examined in this work. Natural bond orbital (NBO) and the regularized symmetry-adapted perturbation theory (SAPT) are also briefly considered. Results for the ALMO and CDFT definitions of CT are compared on a broad range of model systems, including hydrogen-bonding systems, borane complexes, metal-carbonyl complexes, and complexes formed by water and metal cations. For most of these systems, CDFT yields a much smaller equilibrium CT energy compared to that given by the ALMO-based definition. This is mainly because the CDFT population constraint does not fully inhibit CT, which means that the CDFT "CT-free" state is in fact CT-contaminated. Examples of this contamination include (i) matching forward and backward donation (e.g., formic acid dimer) and (ii) unidirectional CT without changing fragment populations. The magnitude of the latter effect is quantified in systems such as the water dimer by employing a 3-space density constraint in addition to the orbital constraint. Furthermore, by means of the adiabatic EDA, it is shown that several observable effects of CT, such as the "pyramidalization" of the planar BH₃ molecule upon the complexation with Lewis bases, already appear on the "CT-free" CDFT surface. These results reveal the essential distinctions between the ALMO and CDFT definitions of CT and suggest that the former is more consistent with accepted understanding of the role of CT in intermolecular binding.

Temperature effect on the structure and conformational fluctuations in two zinc knuckles from the mouse mammary tumor virus

Zinc fingers are small protein domains in which zinc plays a structural role, contributing to the stability of the zinc-peptide complex. Zinc fingers are structurally diverse and are present in proteins that perform a broad range of functions in various cellular processes, such as replication and repair, transcription and translation, metabolism and signaling, cell proliferation, and apoptosis. Zinc fingers typically function as interaction modules and bind to a wide variety of compounds, such as nucleic acids, proteins, and small molecules. In this study, we investigated the structural properties, in solution, of the proximal and distal zinc knuckles of the nucleocapsid (NC) protein from the mouse mammary tumor virus (MMTV) (MMTV NC). For this purpose, we performed a series of molecular dynamics simulations in aqueous solution at 300 K, 333 K, and 348 K. The temperature effect was evaluated in terms of root mean square deviation of the backbone atoms and root mean square fluctuation of the coordinating residue atoms. The stability of the zinc coordination sphere was analyzed based upon the time profile of the interatomic distances between the zinc ions and the chelator atoms. The results indicate that the hydrophobic character of the proximal zinc finger is dominant at 333 K. The low mobility of the coordinating residues suggests that the strong electrostatic effect exerted by the zinc ion on its coordinating residues is not influenced by the increase in temperature. The evolution of the structural parameters of the coordination sphere of the distal zinc finger at 300 K gives us a reasonable picture of the unfolding pathway, as proposed by Bombarda and coworkers (Bombarda et al., 2005), which can predict the binding order of the four conserved ligand-binding residues. Our results support the conclusion that the structural features can vary significantly between the two zinc knuckles of MMTV NC.

Physics-based all-atom modeling of RNA energetics and structure

The database of RNA sequences is exploding, but knowledge of energetics, structures, and dynamics lags behind. All-atom computational methods, such as molecular dynamics, hold promise for closing this gap. New algorithms and faster computers have accelerated progress in improving the reliability and accuracy of predictions. Currently, the methods can facilitate refinement of experimentally determined nuclear magnetic resonance and x-ray structures, but are 'unreliable' for predictions based only on sequence. Much remains to be discovered, however, about the many molecular interactions driving RNA folding and the best way to approximate them quantitatively. The large number of parameters required means that a wide variety of experimental results will be required to benchmark force fields and different approaches. As computational methods become more reliable and accessible, they will be used by an increasing number of biologists, much as x-ray crystallography has expanded. Thus, many fundamental physical principles underlying the computational methods are described. This review presents a summary of the current state of molecular dynamics as applied to RNA. It is designed to be helpful to students, postdoctoral fellows, and faculty who are considering or starting computational studies of RNA. WIREs RNA 2017, 8:e1422. doi: 10.1002/wrna.1422.

Energy decomposition analysis in an adiabatic picture

Energy decomposition analysis (EDA) of electronic structure calculations has facilitated quantitative understanding of diverse intermolecular interactions. Nevertheless, such analyses are usually performed at a single geometry and thus decompose a "single-point" interaction energy. As a result, the influence of the physically meaningful EDA components on the molecular structure and other properties are not directly obtained. To address this gap, the absolutely localized molecular orbital (ALMO)-EDA is reformulated in an adiabatic picture, where the frozen, polarization, and charge transfer energy contributions are defined as energy differences between the stationary points on different potential energy surfaces (PESs), which are accessed by geometry optimizations at the frozen, polarized and fully relaxed levels of density functional theory (DFT). Other molecular properties such as vibrational frequencies can thus be obtained at the stationary points on each PES. We apply the adiabatic ALMO-EDA to different configurations of the water dimer, the water-Cl^- and water-Mg²⁺/Ca²⁺ complexes, metallocenes (Fe²⁺, Ni²⁺, Cu²⁺, Zn²⁺), and the ammonia-borane complex. This method appears to be very useful for unraveling how physical effects such as polarization and charge transfer modulate changes in molecular properties induced by intermolecular interactions. As an example of the insight obtained, we find that a linear hydrogen bond geometry for the water dimer is preferred even without the presence of polarization and charge transfer, while the red shift in the OH stretch frequency is primarily a charge transfer effect; by contrast, a near-linear geometry for the water-chloride hydrogen bond is achieved only when charge transfer is allowed.

Tinker-HP: a massively parallel molecular dynamics package for multiscale simulations of large complex systems with advanced point dipole polarizable force fields

We present Tinker-HP, a massively MPI parallel package dedicated to classical molecular dynamics (MD) and to multiscale simulations, using advanced polarizable force fields (PFF) encompassing distributed multipoles electrostatics. Tinker-HP is an evolution of the popular Tinker package code that conserves its simplicity of use and its reference double precision implementation for CPUs. Grounded on interdisciplinary efforts with applied mathematics, Tinker-HP allows for long polarizable MD simulations on large systems up to millions of atoms. We detail in the paper the newly developed extension of massively parallel 3D spatial decomposition to point dipole polarizable models as well as their coupling to efficient Krylov iterative and non-iterative polarization solvers. The design of the code allows the use of various computer systems ranging from laboratory workstations to modern petascale supercomputers with thousands of cores. Tinker-HP proposes therefore the first high-performance scalable CPU computing environment for the development of next generation point dipole PFFs and for production simulations. Strategies linking Tinker-HP to Quantum Mechanics (QM) in the framework of multiscale polarizable self-consistent QM/MD simulations are also provided. The possibilities, performances and scalability of the software are demonstrated via benchmarks calculations using the polarizable AMOEBA force field on systems ranging from large water boxes of increasing size and ionic liquids to (very) large biosystems encompassing several proteins as well as the complete satellite tobacco mosaic virus and ribosome structures. For small systems, Tinker-HP appears to be competitive with the Tinker-OpenMM GPU implementation of Tinker. As the system size grows, Tinker-HP remains operational thanks to its access to distributed memory and takes advantage of its new algorithmic enabling for stable long timescale polarizable simulations. Overall, a several thousand-fold acceleration over a single-core computation is observed for the largest systems. The extension of the present CPU implementation of Tinker-HP to other computational platforms is discussed.

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.

Ionic Solution: What Goes Right and Wrong with Continuum Solvation Modeling

Solvent-mediated electrostatic interactions were well recognized to be important in the structure and function of molecular systems. Ionic interaction is an important component in electrostatic interactions, especially in highly charged molecules, such as nucleic acids. Here, we focus on the quality of the widely used Poisson-Boltzmann surface area (PBSA) continuum models in modeling ionic interactions by comparing with both explicit solvent simulations and the experiment. In this work, the molality-dependent chemical potentials for sodium chloride (NaCl) electrolyte were first simulated in the SPC/E explicit solvent. Our high-quality simulation agrees well with both the previous study and the experiment. Given the free-energy simulations in SPC/E as the benchmark, we used the same sets of snapshots collected in the SPC/E solvent model for PBSA free-energy calculations in the hope to achieve the maximum consistency between the two solvent models. Our comparative analysis shows that the molality-dependent chemical potentials of NaCl were reproduced well with both linear PB and nonlinear PB methods, although nonlinear PB agrees better with SPC/E and the experiment. Our free-energy simulations also show that the presence of salt increases the hydrophobic effect in a nonlinear fashion, in qualitative agreement with previous theoretical studies of Onsager and Samaras. However, the lack of molality-dependency in the nonelectrostatics continuum models dramatically reduces the overall quality of PBSA methods in modeling salt-dependent energetics. These analyses point to further improvements needed for more robust modeling of solvent-mediated interactions by the continuum solvation frameworks.

Metal Ion Modeling Using Classical Mechanics

Metal ions play significant roles in numerous fields including chemistry, geochemistry, biochemistry, and materials science. With computational tools increasingly becoming important in chemical research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aqueous, and solid phases. Herein, we review both quantum and classical modeling strategies for metal ion-containing systems that have been developed over the past few decades. This Review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond-based models. Quantum mechanical studies of metal ion-containing systems at the semiempirical, ab initio, and density functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion-containing systems.

Polarizable Multipole-Based Force Field for Aromatic Molecules and Nucleobases

Aromatic molecules with π electrons are commonly involved in chemical and biological recognitions. For example, nucleobases play central roles in DNA/RNA structure and their interactions with proteins. The delocalization of the π electrons is responsible for the high polarizability of aromatic molecules. In this work, the AMOEBA force field has been developed and applied to 5 regular nucleobases and 12 aromatic molecules. The permanent electrostatic energy is expressed as atomic multipole interactions between atom pairs, and many-body polarization is accounted for by mutually induced atomic dipoles. We have systematically investigated aromatic ring stacking and aromatic-water interactions for nucleobases and aromatic molecules, as well as base–base hydrogen-bonding pair interactions, all at various distances and orientations. van der Waals parameters were determined by comparison to the quantum mechanical interaction energy of these dimers and fine-tuned using condensed phase simulation. By comparing to quantum mechanical calculations, we show that the resulting classical potential is able to accurately describe molecular polarizability, molecular vibrational frequency, and dimer interaction energy of these aromatic systems. Condensed phase properties, including hydration free energy, liquid density, and heat of vaporization, are also in good overall agreement with experimental values. The structures of benzene liquid phase and benzene-water solution were also investigated by simulation and compared with experimental and PDB structure derived statistical results.

Local decomposition of imaginary polarizabilities and dispersion coefficients

We present a new way to compute the two-body contribution to the dispersion energy using ab initio theory.

Characterization of Mg2+ Distributions around RNA in Solution

Binding of metal ions is an important factor governing the folding and dynamics of RNA. Shielding of charges in the polyanionic backbone allows RNA to adopt a diverse range of folded structures that give rise to their many functions within the cell. Some RNA sequences fold only in the presence of Mg²⁺, which may be bound via direct interactions or occupy the more diffuse "ion atmosphere" around the RNA. To understand the driving forces for RNA folding, it is important to be able to fully characterize the distribution of metal ions around the RNA. In this work, a combined Grand Canonical Monte Carlo-Molecular Dynamics (GCMC-MD) method is applied to characterize Mg²⁺ distributions around folded RNA structures. The GCMC-MD approach identifies known inner- and outer-shell Mg²⁺ coordination, while also predicting new regions occupied by Mg²⁺ that are not observed in crystal structures but that may be relevant in solution, including the case of the Mg²⁺ riboswitch, for which alternate Mg²⁺ binding sites may have implications for its function. This work represents a significant step forward in establishing a structural and thermodynamic description of RNA-Mg²⁺ interactions and their role in RNA structure and function.

Balancing the Interactions of Mg2+ in Aqueous Solution and with Nucleic Acid Moieties For a Polarizable Force Field Based on the Classical Drude Oscillator Model

Mg²⁺ ions are important in biological systems, particularly in stabilizing compact RNA folds. Mg²⁺ is strongly polarizing, and representing its interactions in heterogeneous environments is a challenge for empirical force field development. To date, the most commonly used force fields in molecular dynamics simulations utilize a pairwise-additive approximation for electrostatic interactions, which cannot account for the significant polarization response in systems containing Mg²⁺. In the present work, we refine the interactions of Mg²⁺ with water, Cl^- ions, and nucleic acid moieties using a polarizable force field based on the classical Drude oscillator model. By targeting gas-phase quantum mechanical interaction energies and geometries of hydrated complexes, as well as condensed-phase osmotic pressure calculations, we present a model for Mg²⁺ that yields quantitative agreement with experimental measurements of water dissociation free energy and osmotic pressure across a broad range of concentrations. Notable is the direct modeling of steric repulsion between the water Drude oscillators and Mg²⁺ to treat the Pauli exclusion effects associated with overlap of the electron clouds of water molecules in the first hydration shell around Mg²⁺. Combined with the refined interactions with nucleic acid moieties, the present model represents a significant advancement in simulating nucleic acid systems containing Mg²⁺.