Ca2+ -Cl- Association in Water Revisited: the Role of Cation Hydration

Mechanism of Calcium Permeation in a Glutamate Receptor Ion Channel

The α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (AMPARs) are neurotransmitter-activated cation channels ubiquitously expressed in vertebrate brains. The regulation of calcium flux through the channel pore by RNA-editing is linked to synaptic plasticity while excessive calcium influx poses a risk for neurodegeneration. Unfortunately, the molecular mechanisms underlying this key process are mostly unknown. Here, we investigated calcium conduction in calcium-permeable AMPAR using Molecular Dynamics (MD) simulations with recently introduced multisite force-field parameters for Ca²⁺. Our calculations are consistent with experiment and explain the distinct calcium permeability in different RNA-edited forms of GluA2. For one of the identified metal binding sites, multiscale Quantum Mechanics/Molecular Mechanics (QM/MM) simulations further validated the results from MD and revealed small but reproducible charge transfer between the metal ion and its first solvation shell. In addition, the ion occupancy derived from MD simulations independently reproduced the Ca²⁺ binding profile in an X-ray structure of an NaK channel mimicking the AMPAR selectivity filter. This integrated study comprising X-ray crystallography, multisite MD, and multiscale QM/MM simulations provides unprecedented insights into Ca²⁺ permeation mechanisms in AMPARs, and paves the way for studying other biological processes in which Ca²⁺ plays a pivotal role.

Local Molecular Field Theory for Coulomb Interactions in Aqueous Solutions

Coulomb interactions play a crucial role in a wide array of processes in aqueous solutions but present conceptual and computational challenges to both theory and simulations. We review recent developments in an approach addressing these challenges─local molecular field (LMF) theory. LMF theory exploits an exact and physically suggestive separation of intermolecular Coulomb interactions into strong short-range and uniformly slowly varying long-range components. This allows us to accurately determine the averaged effects of the long-range components on the short-range structure using effective single particle fields and analytical corrections, greatly reducing the need for complex lattice summation techniques used in most standard approaches. The simplest use of these ideas in aqueous solutions leads to the short solvent (SS) model, where both solvent-solvent and solute-solvent Coulomb interactions have only short-range components. Here we use the SS model to give a simple description of pairing of nucleobases and biologically relevant ions in water.

Solvation structures of calcium and magnesium ions in water with the presence of hydroxide: a study by deep potential molecular dynamics

The solvation structures of calcium (Ca²⁺) and magnesium (Mg²⁺) ions with the presence of hydroxide (OH^-) ion in water are essential for understanding their roles in biological and chemical processes but have not been fully explored. Ab initio molecular dynamics (AIMD) is an important tool to address this issue, but two challenges exist. First, an accurate description of OH^- from AIMD needs an appropriate exchange-correlation functional. Second, a long trajectory is needed to reach an equilibrium state for the Ca²⁺-OH^- and Mg²⁺-OH^- ion pairs in aqueous solutions. Herein, we adopt a deep potential molecular dynamics (DPMD) method to simulate 1 ns trajectories for the Ca²⁺-OH^- and Mg²⁺-OH^- ion pairs in water; the DPMD method provides efficient machine-learning-based models that have the accuracy of the SCAN exchange-correlation functional within the framework of density functional theory. The solvation structures of the cations and the OH^- in terms of three different species have been systematically investigated. On the one hand, we find that OH^- have more significant effects on the solvation structure of Ca²⁺ than that of Mg²⁺. We observe that the OH^- substantially affects the orientation angles of water molecules surrounding the cation. Through the time correlation functions, we conclude that the water molecules in the first solvation shell of Ca²⁺ change their preferred orientation faster than those of Mg²⁺. On the other hand, with the presence of the cation in the first solvation shell of OH^-, we find that the hydrogen bonds of OH^- are severely altered, and the adjacent water molecules of OH^- are squeezed. The two cations have substantially different effects on the solvation structure of OH^-. Our work provides new insight into the solvation structures of Ca²⁺ and Mg²⁺ in water with the presence of OH^-.

Thermodynamic and Kinetic Studies on the Conversion of Solvent-Shared to Contact Ion Pairs in Sparingly Soluble MF2 (M = Mg2+ and Ca2+) Aqueous Solutions: Implications for Understanding Supersaturated Behavior and Association Constant Determination

The thermodynamic and kinetic behaviors of Mg²⁺-F^- ion pairing in aqueous solution are investigated theoretically and experimentally and are contrasted to those of Ca²⁺-F^-. Thermodynamically, similar to CaF_x(H₂O)₁₄^2-x (x = 1 and 2), MgF(H₂O)_y⁺ (y = 14-20) contact ion pairs (CIPs) are more stable than their solvent-shared ion pairs (SSIPs), whereas the CIPs and SSIPs of MF₂(H₂O)_y are almost isoenergetic. However, in kinetics, the conversion of SSIPs to CIPs for M²⁺-F^- (M = Mg²⁺ and Ca²⁺) ion pairing must overcome a high energy barrier due to the strong hydration of Mg²⁺ and F^-. The kinetics dominate after the thermodynamics and kinetics are balanced, which hinders the formation of M²⁺-F^- CIPs in practical MF₂ aqueous solutions (less than or equal to saturated concentrations). This result is also supported by the ¹⁹F nuclear magnetic resonance spectra of saturated MF₂ solutions. Although the interaction between Mg²⁺ and F^- is slightly stronger than that between Ca²⁺ and F^- due to the smaller radius of Mg²⁺, the formation of Mg²⁺-F^- CIPs needs to go through two rate-limiting steps, the dehydration and entrance of F^- (i.e., via exchange mode) with a higher energy barrier, due to the ability of strongly bound water molecules and rigorous octahedral coordinated configuration of Mg²⁺, while the formation of Ca²⁺-F^- CIPs only goes through a single rate-limiting step, the entrance of F^- (i.e., via swinging mode) with a lower energy barrier, due to the flexible coordination configuration of Ca²⁺. This is responsible for precipitation in MgF₂ aqueous solution requiring a larger supersaturation degree and a lower precipitation rate than in CaF₂. These kinetic factors lead to the association constants previously reported for MF⁺ determined by a fluoride ion-selective electrode (ISE) combined with the titration method, where the MF₂ solutions were always unsaturated at the titration end point, which actually corresponds to those of the ligand process going from completely free M²⁺ and F^- to their SSIPs. A possible strategy to accurately determine the association constants of MF⁺ and MF₂(aq) CIPs by fluoride ISEs is proposed. The present results suggest that judging the formation of M²⁺-F^- CIPs in practical solutions from a theoretical calculation perspective requires significant consideration of the kinetic factors, except for the thermodynamic factors.

Short solvent model for ion correlations and hydrophobic association

Coulomb interactions play a major role in determining the thermodynamics, structure, and dynamics of condensed-phase systems, but often present significant challenges. Computer simulations usually use periodic boundary conditions to minimize corrections from finite cell boundaries but the long range of the Coulomb interactions generates significant contributions from distant periodic images of the simulation cell, usually calculated by Ewald sum techniques. This can add significant overhead to computer simulations and hampers the development of intuitive local pictures and simple analytic theory. In this paper, we present a general framework based on local molecular field theory to accurately determine the contributions from long-ranged Coulomb interactions to the potential of mean force between ionic or apolar hydrophobic solutes in dilute aqueous solutions described by standard classical point charge water models. The simplest approximation leads to a short solvent (SS) model, with truncated solvent-solvent and solute-solvent Coulomb interactions and long-ranged but screened Coulomb interactions only between charged solutes. The SS model accurately describes the interplay between strong short-ranged solute core interactions, local hydrogen-bond configurations, and long-ranged dielectric screening of distant charges, competing effects that are difficult to capture in standard implicit solvent models.