Hydrated Anions: From Clusters to Bulk Solution with Quasi-Chemical Theory

On the stability constants of metal-nitrate complexes in aqueous solutions

Stability constants of simple reactions involving addition of the NO3- ion to hydrated metal complexes, [M(H2O)x]n+ are calculated with a computational workflow developed using cloud computing resources. The computational workflow performs conformational searches for metal complexes at both low and high levels of theories in conjunction with a continuum solvation model (CSM). The low-level theory is mainly used for the initial conformational searches, which are complemented with high-level density functional theory conformational searches in the CSM framework to determine the coordination chemistry relevant for stability constant calculations. In this regard, the lowest energy conformations are found to obtain the reaction free energies for the addition of one NO3- to [M(H2O)x]n+ complexes, where M represents Fe(II), Fe(III), Sr(II), Ce(III), Ce(IV), and U(VI), respectively. Structural analysis of hundreds of optimized geometries at high-level theory reveals that NO3- coordinates with Fe(II) and Fe(III) in either a monodentate or bidentate manner. Interestingly, the lowest-energy conformations of Fe(II) metal-nitrate complexes exhibit monodentate or bidentate coordination with a coordination number of 6 while the bidentate seven-coordinated Fe(II) metal-nitrate complexes are approximately 2 kcal mol-1 higher in energy. Notably, for Fe(III) metal-nitrate complexes, the bidentate seven-coordinated configuration is more stable than the six-coordinated Fe(II) complexes (monodentate or bidentate) by a few thermal energy units. In contrast, Sr(II), Ce(III), Ce(IV), and U(VI) metal ions predominantly coordinate with NO3- in a bidentate manner, exhibiting typical coordination numbers of 7, 9, 9, and 5, respectively. Stability constants are accordingly calculated using linear free energy approaches to account for the systematic errors and good agreements are obtained between the calculated stability constants and the available experimental data.

QM Investigation of Rare Earth Ion Interactions with First Hydration Shell Waters and Protein-Based Coordination Models

Conventional methods for extracting rare earth metals (REMs) from mined mineral ores are inefficient, expensive, and environmentally damaging. Recent discovery of lanmodulin (LanM), a protein that coordinates REMs with high-affinity and selectivity over competing ions, provides inspiration for new REM refinement methods. Here, we used quantum mechanical (QM) methods to investigate trivalent lanthanide cation (Ln3+) interactions with coordination systems representing bulk solvent water and protein binding sites. Energy decomposition analysis (EDA) showed differences in the energetic components of Ln3+ interaction with representatives of solvent (water, H2O) and protein binding sites (acetate, CH3COO-), highlighting the importance of accurate description of electrostatics and polarization in computational modeling of REM interactions with biological and bioinspired molecules. Relative binding free energies were obtained for Ln3+ with coordination complexes originating from binding sites in PDB structures of a lanthanum binding peptide (PDB entry 7CCO) and LanM, with explicit consideration of the first hydration shell waters, according to quasi-chemical theory (QCT). Beyond the first shell, the bulk solvent environment was represented with an implicit continuum model. Ln3+ interactions with (H2O)9 and both binding site models became more favorable, moving down the periodic series. This trend was more pronounced with the protein binding site models than with water, resulting in affinity increasing with periodic number, except for the last REM, Lu3+, which bound less favorably than the preceding element, Yb3+. Using the truncated 7CCO binding site model, the magnitude and trend of the experimental Ln3+ relative binding free energies for the whole 7CCO peptide were reproduced. Conversely, the previously reported experimental data for LanM show a preference for the earlier lanthanides; this is likely due to longer-range interactions and cooperative effects, which are not represented by the reduced models. Using the truncated 7CCO binding site model, the magnitude and trend of the experimental Ln3+ relative binding free energies for the whole 7CCO peptide were reproduced. In contrast to the previously reported experimental data for LanM, the peptide preferentially binds the earlier lanthanides. This difference likely arises due to longer-range interactions and cooperative effects not represented by the peptide. Further investigation of Ln3+ interactions with whole proteins using polarizable molecular mechanics models with explicit solvent is warranted to understand the influence of longer-ranged interactions, cooperativity, and bulk solvent. Nevertheless, the present work provides new insights into Ln3+ interactions with biomolecules and presents an effective computational platform for designing specific single-site REM binding peptides more efficiently.

Binding of Sulfates and Water to Monovalent Cations

The binding of the sulfate ligand group to monovalent cations in the presence of water is important for many systems. To understand the structure and energetics of sulfate complexes, we use density functional theory to study ethyl sulfate binding to the monovalent cations Li+, Na+, and K+, and to water. The free energies of binding and optimal structures are calculated for a range of the number of ethyl sulfates and waters. Without water, the most optimal structure for all the cations is bidentate binding by two ethyl sulfates, yielding a 4-fold coordination. With water, the lowest free energy structures also have two ethyl sulfates, but the coordination varies with cations. For complexes with water, the four oxygen atoms in the sulfate group enable multiple binding geometries for the cations and for hydrogen bonding with water. Many of these geometries differ in free energy by only a small amount (1-2 kcal/mol), meaning there will be multiple binding configurations in bulk solution. In comparison to the optimal structures for binding to the carboxylate group, there is more variation for binding to the sulfate group as a function of cation type and the number of waters. The polarization of the atoms is significant and varies among the sulfate oxygen atoms. The water oxygen charge is often larger than that of sulfate oxygen, which plays a role in the preference for monodentate ligand binding to cations in the presence of water.

Ion Effects on Terahertz Spectra of Microsolvated Clusters

Water clusters containing Na+ and Cl- ions play a key role in the atmospheric chemistry of sea salt aerosols. While Na+ is clearly buried deep inside, Cl- appears to be a chameleon since evidence for both surface-localized and interior solvation states are reported. Thus, disclosing the preferred location of Cl- within clusters remains challenging. Here, we investigate whether THz spectroscopy, a powerful tool for directly probing hydrogen bonds in water, provides insights into the location of Cl- ions in water clusters. We performed ab initio molecular dynamics simulations on water clusters containing a single Cl- ion and up to 64 water molecules to compute the THz spectra with reference to Na+ and bulk. The THz spectrum of the 64-water Cl- cluster closely agrees with that of the bulk solution. Surprisingly, this match is not caused by bulk-like solvation of Cl- as suggested by phenomenological line shape analyses. Instead, the similarity stems from Cl- being mostly located at the cluster surface, thus leaving the water-water interactions largely unperturbed.

Hydrates of N-((10-Chloroanthracen-9-yl)methyl)-3-(1H-imidazol-1-yl)propan-1-ammonium Cobalt(II), Copper(II), and Zinc(II) 2,6-Pyridinedicarboxylate: Reversible Crystallization

In a quest to explore interconvertible assemblies of hydrates of cobalt(II), copper(II), and zinc(II) 2,6-pyridinedicarboxylate (26-pdc), complexes having cation of a chloro-substituted analogue N-{(10-chloroanthracen-9-yl)methyl}-3-(1H-imidazol-1-yl)propan-1-amine were investigated. In the case of cobalt and copper complexes, a crystallized stable hydrate and a less stable methanol hydrate were guided by concentration-dependent crystallizations. The unit-cells of the crystals of the methanol hydrates of the two cobalt and copper complexes each belong to the P1̅ space group but have different stoichiometries as well as large differences in packing. These hydrates could be reversibly crystallized in a predictable manner. The unit-cell volumes of the methanol hydrate of the cobalt complex were four-times smaller than that of the respective stable form (C2/c space group), whereas similar hydrates of the copper complex had a two-times smaller unit-cell volume than that of the stable form. The cations of the stable forms assembled together and formed zigzag ladder-like chains. The spaces present in between the assembled chains were filled with clusters of face to face stacked anions. The transformation to stable form required a bottom-up building process of the unit-cell starting from a smaller unit-cell of the less stable hydrates. Fluorescence spectroscopic studies showed the possibility of two forms of assemblies of the zinc-complex in solution, but crystallization had yielded only the stable form.

Electronic Polarizability Tunes the Function of the Human Bestrophin 1 Cl- Channel

Mechanisms of anion permeation within ion channels and nanopores remain poorly understood. Recent cryo-electron microscopy structures of the human bestrophin 1 Cl- channel (hBest1) provide an opportunity to evaluate ion interactions predicted by molecular dynamics (MD) simulations against experimental observations. Here, we implement the fully polarizable forcefield AMOEBA in MD simulations on different conformations of hBest1. This forcefield models multipole moments up to the quadrupole; therefore, it captures induced dipole and anion-π interactions. We show that key biophysical properties of the channel can only be simulated when electronic polarization is included in the molecular models and that Cl- permeation through the neck of the pore is achieved through hydrophobic solvation concomitant with partial ion dehydration. Furthermore, we demonstrate how such polarizable simulations can help determine the identity of ion-like densities within high-resolution cryo-EM structures and that neglecting polarization places Cl- at positions that do not correspond with their experimentally resolved location. Overall, our results demonstrate the importance of including electronic polarization in realistic and physically accurate models of biological systems, especially channels and pores that selectively permeate anions.

Impact of Nuclear Quantum Effects on the Structural Properties of Protonated Water Clusters

Nuclear quantum effects (NQEs) play a crucial role in hydrogen-bonded systems due to quantum tunneling and proton fluctuation. Our understanding of how NQEs affect microstructures mainly focuses on bulk phases of liquids and solids but remains deficient for water clusters, including their hydrogen nuclei, hydrogen-bonded configurations, and temperature dependence. Here, we conducted ab initio molecular dynamics (MD) and path integral MD simulations to investigate the influence of NQEs on the structural properties of protonated water clusters H+(H2O)n (n = 3, 6, 9, 12). The results reveal that the NQEs become less evident as the cluster size increases due to the competition between NQEs and electrostatic interactions. Simulations of several H+(H2O)6 isomers at different temperatures indicate that the effect of elevated temperature on proton transfer is related to the initial structure. Interestingly, the process of proton transfer also involves the interconversion between Zundel-type and Eigen-type isomers. These findings significantly deepen our understanding of ion-water and water-water interactions, opening new avenues for the study of hydrated ion clusters and related systems.

Recognition of anion-water clusters by peptide-based supramolecular capsules

The biological and technological importance of anion-mediated processes has made the development of improved methods for the selective recognition of anions one of the most relevant research topics today. The hydration sphere of anions plays an important role in the functions performed by anions by forming a variety of cluster complexes. Here we describe a supramolecular capsule that recognizes hydrated anion clusters. These clusters are most likely composed of three ions that form hydrated C3 symmetry complexes that are entrapped within the supramolecular capsule of the same symmetry. The capsule is made of self-assembled α,γ-cyclic peptide containing amino acid with by five-membered rings and equipped with a tris(triazolylethyl)amine cap. To recognise the hydrated anion clusters, the hexapeptide capsule must disassemble to entrap them between its two subunits.

Encapsulation of charged halogens by the 512 water cage

This study focuses on the encapsulation of the entire series of halides by the 512 cage of twenty water molecules and on the characterization of water to water and water to anion interactions. State-of-the-art computations are used to determine equilibrium geometries, energy related quantities, and thermal stability towards dissociation and to dissect the nature and strength of intermolecular interactions holding the clusters as stable units. Two types of structures are revealed: heavily deformed cages for F- indicating a preference for microsolvation, and slightly deformed cages for the remaining anions indicating a preference for encapsulation. The primary variable dictating the properties of the clusters is the charge density of the central halide, with the most severe effects observed for the F- case. For the remaining halides, the anion may be safely viewed as a sort of "big electron" with little local disruptive power, enough to affect the network of non-covalent hydrogen bonds in the cage, but not enough to break it. Gibbs energies for dissociation either into cavity and halide or into water molecules and halide suggest that, in a similar way as to methane clathrate, a more weakly bonded complex that has been detected in the gas phase, all halide containing clathrate-like structures should be amenable to experimental detection in the gas phase at moderate temperature and pressure conditions.

The multi-scale polarizable pseudo-particle solvent coarse-grained approach: From NaCl salt solutions to polyelectrolyte hydration

We discuss key parameters that affect the reliability of hybrid simulations in the aqueous phase based on an efficient multi-scale coarse-grained polarizable pseudo-particle approach, denoted as pppl, to model the solvent water, whereas solutes are modeled using an all atom polarizable force field. Among those parameters, the extension of the solvent domain (SD) at the solute vicinity (domain in which each solvent particle corresponds to a single water molecule) and the magnitude of solute/solvent short range polarization damping effects are shown to be pivotal to model NaCl salty aqueous solutions and the hydration of charged systems, such as the hydrophobic polyelectrolyte polymer that we have recently investigated [Masella et al., J. Chem. Phys. 155, 114903 (2021)]. Strong short range damping is pivotal to simulate aqueous salt NaCl solutions at moderate concentration (up to 1.0M). The SD extension (as well as short range damping) has a weak effect on the polymer conformation; however, it plays a pivotal role in computing accurate polymer/solvent interaction energies. As the pppl approach is up to two orders of magnitude computationally more efficient than all atom polarizable force field methods, our results show it to be an efficient alternative route to investigate the equilibrium properties of complex charged molecular systems in extended chemical environments.

The Missing Chalcogen Bonding Donor: Strongly Polarized Oxygen of Water

A biscyclen molecular cabin, synthesized by connecting two cyclen macrocycles with four linkages, entraps a Li+···H2O···Li+ trimer with a water molecule clamped by two Li+ ions. This configuration results in strongly polarized water, characterized by a water proton resonance shift of up to 10.00 ppm. The arrangement facilitates unprecedented O-centered chalcogen bonds between the lone pairs of pyridinyl nitrogen atoms and polarized water oxygen, as confirmed by X-ray crystallography, NMR spectroscopy, and theoretical calculations. Further observation of O-centered chalcogen bonding in a H2O·(LiCl)2 cluster suggests its widespread presence in hydrated salt systems.

Insight into the K channel's selectivity from binding of K+, Na+ and water to N-methylacetamide

In potassium channels that conduct K+ selectively over Na+, which sites are occupied by K+ or water and the mechanism of selectivity are unresolved questions. The combination of the energetics and the constraints imposed by the protein structure yield the selective permeation and occupancy. To gain insight into the combination of structure and energetics, we performed density functional theory (DFT) calculations of multiple N-methyl acetamide (NMA) ligands binding to K+ and Na+, relative to hydrated K+ and Na+. NMA is an analogue of the amino acid backbone and provides the carbonyl binding to the ions that occurs in most binding sites of the K+ channel. Unconstrained optimal structures are obtained through geometry optimization calculations of the NMA ligand binding. The complexes formed by 8 NMA binding to the cations have the O atoms positioned in nearly identical locations as the O atoms in the selectivity filter. The transfer free energies between bulk water and K+ or Na+ bound to 8 NMA are almost identical, implying there is no selectivity by a single site. For water optimized with 8 NMA, binding is weak and O atoms are not positioned as in the K+ channel selectivity filter, suggesting that the ions are much more favored than water. Optimal structures of 8 NMA binding with two cations (K+ or Na+) are stable and have lower binding free energy than the optimal structures with just one cation. However, in the Na+ case, the optimal structure deforms and does not match the K+ channel; that is, two bound Na+ are destabilizing. In contrast, the two K+ structure is stabilized and the selectivity free energy favors K+. Overall, this study shows that binding site occupancy and the mechanism for K+ selectivity involves multiple K+ binding in multiple neighboring layers or sites of the K+ channel selectivity filter.

Binding of Li+ to Negatively Charged and Neutral Ligands in Polymer Electrolytes

Conceptually, single-ion polymer electrolytes (SIPE) with the anion bound to the polymer could solve major issues in Li-ion batteries, but their conductivity is too low. Experimentally, weakly interacting anionic groups have the best conductivity. To provide a theoretical basis for this result, density functional theory calculations of the optimized geometries and energies are performed for charged ligands used in SIPE. Comparison is made to neutral ligands found in dual-ion conductors, which demonstrate higher conductivity. The free energy differences between adding and subtracting a ligand are small enough for the neutral ligands to have the conductivity seen experimentally. However, charged ligands have large barriers, implying that lithium transport will coincide with the slow polymer diffusion, as observed in experiments. Overall, SIPE will require additional solvent to achieve a sufficiently high conductivity. Additionally, the binding of mono- and bidentate geometries varies, providing a simple and clear reason that polarizable force fields are required for detailed interactions.

Binding of carboxylate and water to monovalent cations

The interactions of carboxylate anions with water and cations are important for a wide variety of systems, both biological and synthetic. To gain insight on properties of the local complexes, we apply density functional theory, to treat the complex electrostatic interactions, and investigate mixtures with varied numbers of carboxylate anions (acetate) and waters binding to monovalent cations, Li+, Na+ and K+. The optimal structure with overall lowest free energy contains two acetates and two waters such that the cation is four-fold coordinated, similar to structures found earlier for pure water or pure carboxylate ligands. More generally, the complexes with two acetates have the lowest free energy. In transitioning from the overall optimal state, exchanging an acetate for water has a lower free energy barrier than exchanging water for an acetate. In most cases, the carboxylates are monodentate and in the first solvation shell. As water is added to the system, hydrogen bonding between waters and carboxylate O atoms further stabilizes monodentate structures. These structures, which have strong electrostatic interactions that involve hydrogen bonds of varying strength, are significantly polarized, with ChelpG partial charges that vary substantially as the bonding geometry varies. Overall, these results emphasize the increasing importance of water as a component of binding sites as the number of ligands increases, thus affecting the preferential solvation of specific metal ions and clarifying Hofmeister effects. Finally, structural analysis correlated with free energy analysis supports the idea that binding to more than the preferred number of carboxylates under architectural constraints are a key to ion transport.

Limitations of non-polarizable force fields in describing anion binding poses in non-polar synthetic hosts

Transmembrane anion transport by synthetic ionophores has received increasing interest not only because of its relevance for understanding endogenous anion transport, but also because of potential implications for therapeutic routes in disease states where chloride transport is impaired. Computational studies can shed light on the binding recognition process and can deepen our mechanistic understanding of them. However, the ability of molecular mechanics methods to properly capture solvation and binding properties of anions is known to be challenging. Consequently, polarizable models have been suggested to improve the accuracy of such calculations. In this study, we calculate binding free energies for different anions to the synthetic ionophore, biotin[6]uril hexamethyl ester in acetonitrile and to biotin[6]uril hexaacid in water by employing non-polarizable and polarizable force fields. Anion binding shows strong solvent dependency consistent with experimental studies. In water, the binding strengths are iodide > bromide > chloride, and reversed in acetonitrile. These trends are well captured by both classes of force fields. However, the free energy profiles obtained from potential of mean force calculations and preferred binding positions of anions depend on the treatment of electrostatics. Results from simulations using the AMOEBA force-field, which recapitulate the observed binding positions, suggest strong effects from multipoles dominate with a smaller contribution from polarization. The oxidation status of the macrocycle was also found to influence anion recognition in water. Overall, these results have implications for the understanding of anion host interactions not just in synthetic ionophores, but also in narrow cavities of biological ion channels.

Influence of electronic polarization on the binding of anions to a chloride-pumping rhodopsin

The functional properties of some biological ion channels and membrane transport proteins are proposed to exploit anion-hydrophobic interactions. Here, we investigate a chloride-pumping rhodopsin as an example of a membrane protein known to contain a defined anion binding site composed predominantly of hydrophobic residues. Using molecular dynamics simulations, we explore Cl- binding to this hydrophobic site and compare the dynamics arising when electronic polarization is neglected (CHARMM36 [c36] fixed-charge force field), included implicitly (via the prosECCo force field), or included explicitly (through the polarizable force field, AMOEBA). Free energy landscapes of Cl- moving out of the binding site and into bulk solution demonstrate that the inclusion of polarization results in stronger ion binding and a second metastable binding site in chloride-pumping rhodopsin. Simulations focused on this hydrophobic binding site also indicate longer binding durations and closer ion proximity when polarization is included. Furthermore, simulations reveal that Cl- within this binding site interacts with an adjacent loop to facilitate rebinding events that are not observed when polarization is neglected. These results demonstrate how the inclusion of polarization can influence the behavior of anions within protein binding sites and can yield results comparable with more accurate and computationally demanding methods.

Development of AMOEBA Polarizable Force Field for Rare-Earth La3+ Interaction with Bioinspired Ligands

Rare-earth metals (REMs) are crucial for many important industries, such as power generation and storage, in addition to cancer treatment and medical imaging. One promising new REM refinement approach involves mimicking the highly selective and efficient binding of REMs observed in relatively recently discovered proteins. However, realizing any such bioinspired approach requires an understanding of the biological recognition mechanisms. Here, we developed a new classical polarizable force field based on the AMOEBA framework for modeling a lanthanum ion (La3+) interacting with water, acetate, and acetamide, which have been found to coordinate the ion in proteins. The parameters were derived by comparing to high-level ab initio quantum mechanical (QM) calculations that include relativistic effects. The AMOEBA model, with advanced atomic multipoles and electronic polarization, is successful in capturing both the QM distance-dependent La3+-ligand interaction energies and experimental hydration free energy. A new scheme for pairwise polarization damping (POLPAIR) was developed to describe the polarization energy in La3+ interactions with both charged and neutral ligands. Simulations of La3+ in water showed water coordination numbers and ion-water distances consistent with previous experimental and theoretical findings. Water residence time analysis revealed both fast and slow kinetics in water exchange around the ion. This new model will allow investigation of fully solvated lanthanum ion-protein systems using GPU-accelerated dynamics simulations to gain insights on binding selectivity, which may be applied to the design of synthetic analogues.