An ionic concentration and size dependent dielectric permittivity Poisson-Boltzmann model for biomolecular solvation studies

Microwave Dielectric Relaxation of Univalent and Bivalent Electrolyte Solutions

The microwave dielectric relaxation of aqueous solutions of univalent (KCl, NaCl, NaI) and bivalent (CaCl2, MgCl2) electrolytes at concentrations between 0.1 and 1 M at 25 °C was investigated using a vector network analyzer (0.5≤ ν ≤ 40 GHz). The spectra of these electrolyte systems are characterized by a symmetrical broadening of the main relaxation peak and were fitted using the Cole-Cole equation. In our analysis, we provide insights into the underlying physics of the relaxation events at microscopic and mesoscopic scales by using a 3D phase space trajectory that is based on the interactions of the relaxing dipole units with their surroundings and Frohlich's B function. The effect of the solutes on the H-bond network of water with increasing concentration is evident in the microwave dielectric spectra through decreasing dielectric strengths and relaxation times. It was found that the number of perturbed water molecules is higher in the case of bivalent electrolytes and appears to be proportional to the ionic radius. In our approach, the particular dependence between the broadening parameter α and the relaxation times τ reflects the rate of interactions between the elementary dipole units and their surroundings. We provide a quantitative analysis of the level of perturbation caused by the presence of ions in the hydrogen-bond network of water. It was found that the H-bonded network of water is highly perturbed in univalent systems compared to bivalent systems due to weaker bonded hydration shells. Finally, we found significant differences between the dielectric response of NaCl and NaI. The differences, originating in the counterions Cl- and I-, which are characterized by large ionic radii and consequently weaker electric fields in their vicinity, confirm that the effect of weakly hydrated ions should not be neglected in microwave dielectric spectra analysis.

Fast Calculation of Electrostatic Solvation Free Energy in Simple Ionic Fluids Using an Energy-Scaled Debye-Hückel Theory

Continuum theories are useful to compute the solvation free energy in ionic fluids. Herein, the electrostatic solvation free energy (ESFE) in simple ionic fluids is studied with an energy-scaled Debye-Hückel (ESDH) theory. Given the ESFEs of simple spherical ions as input, the ESDH theory is applicable to molecules with various complex geometries and charge distributions. Specifically, the ESDH theory is applied to molecules in a molten salt system, where the predicted ESFEs are in good agreement with molecular dynamics simulation results. Our study sheds light on accurately predicting the ESFE in ionic fluids with phenomenological continuum theories.

Dielectric response in the vicinity of an ion: A nonlocal and nonlinear model of the dielectric properties of water

The goal of this work is to propose a simple continuous model that captures the dielectric properties of water at the nanometric scale. We write an electrostatic energy as a functional of the polarisation field containing a term in P⁴ and non-local Gaussian terms. Such a hamiltonian can reproduce two key properties of water: the saturation of the polarisation response of water in the presence of a strong electrostatic field and the nanometric dipolar correlations of the solvent molecules modifying the long range van der waals interaction. This model explores thus two fundamental aspects that have to be included in implicit models of electrolytes for a relevant description of electrostatic interactions at nanometric scales.

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.

Incorporating Born solvation energy into the three-dimensional Poisson-Nernst-Planck model to study ion selectivity in KcsA K^{+} channels

Potassium channels are much more permeable to potassium than sodium ions, although potassium ions are larger and both carry the same positive charge. This puzzle cannot be solved based on the traditional Poisson-Nernst-Planck (PNP) theory of electrodiffusion because the PNP model treats all ions as point charges, does not incorporate ion size information, and therefore cannot discriminate potassium from sodium ions. The PNP model can qualitatively capture some macroscopic properties of certain channel systems such as current-voltage characteristics, conductance rectification, and inverse membrane potential. However, the traditional PNP model is a continuum mean-field model and has no or underestimates the discrete ion effects, in particular the ion solvation or self-energy (which can be described by Born model). It is known that the dehydration effect (closely related to ion size) is crucial to selective permeation in potassium channels. Therefore, we incorporated Born solvation energy into the PNP model to account for ion hydration and dehydration effects when passing through inhomogeneous dielectric channel environments. A variational approach was adopted to derive a Born-energy-modified PNP (BPNP) model. The model was applied to study a cylindrical nanopore and a realistic KcsA channel, and three-dimensional finite element simulations were performed. The BPNP model can distinguish different ion species by ion radius and predict selectivity for K^{+} over Na^{+} in KcsA channels. Furthermore, ion current rectification in the KcsA channel was observed by both the PNP and BPNP models. The I-V curve of the BPNP model for the KcsA channel indicated an inward rectifier effect for K^{+} (rectification ratio of ∼3/2) but indicated an outward rectifier effect for Na^{+} (rectification ratio of ∼1/6).

Fractional Poisson-Nernst-Planck Model for Ion Channels I: Basic Formulations and Algorithms

In this work, we propose a fractional Poisson-Nernst-Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker-Planck equation. Then, it is generalized to the macroscopic fractional Poisson-Nernst-Planck model for ionic concentrations. Necessary computational algorithms are designed to implement numerical simulations for the proposed model, and the dynamics of gating current is investigated. Numerical simulations show that the fractional PNP model provides a more qualitatively reasonable match to the profile of gating currents from experimental observations. Meanwhile, the proposed model motivates new challenges in terms of mathematical modeling and computations.

Dependence of the dielectric constant of electrolyte solutions on ionic concentration: A microfield approach

We present a microfield approach for studying the dependence of the orientational polarization of the water in aqueous electrolyte solutions upon the salt concentration and temperature. The model takes into account the orientation of the solvent dipoles due to the electric field created by ions, and the effect of thermal fluctuations. The model predicts a dielectric functional dependence of the form ɛ(c)=ɛ_{w}-βL(3αc/β),β=ɛ_{w}-ɛ_{ms}, where L is the Langevin function, c is the salt concentration, ɛ_{w} is the dielectric of pure water, ɛ_{ms} is the dielectric of the electrolyte solution at the molten salt limit, and α is the total excess polarization of the ions. The functional form gives a remarkably accurate description of the dielectric constant for a variety of salts and a wide range of concentrations.