Dezső Boda

Monte Carlo simulation of an ion-dipole mixture as a model of an electrical double layer

Canonical Monte Carlo simulations were performed for a nonprimitive model of an electrical double layer. The ions and the solvent molecules are modeled as charged and dipolar hard spheres, respectively, while the electrode as a hard, impenetrable wall carrying uniform surface charge. We found that the ion-dipole model gives a reasonable description of the double layer for partially charged ions with small to moderate dipole moments, or equivalently for an “effective” dielectric constant. Density, polarization and mean electrostatic potential profiles are reported. Strong layering structure, and at higher charges, charge inversion in the second layer were found. With appropriate choices of charge and solvent parameters, states corresponding to the primitive or the solvent primitive model can be produced, and the results agreed well with literature data. At higher effective charges and dipole moments, the dipolar solvent has difficulties in preventing the ions from clustering. More realistic models of water...

Monte Carlo study of the capacitance of the double layer in a model molten salt

Monte Carlo simulations are reported for charged hard spheres at high density near a charged wall. This system is a simple model for a molten salt double layer. Unfortunately, the reduced temperatures that correspond to experiment are very small. This results in a large Boltzmann factor. As a result, we are unable to obtain meaningful results for such low values and report results only for moderately low values of the reduced temperature. Even so, our results should be a useful benchmark. Further, we are able to give a qualitative answer to an interesting question. We find that at low temperatures the capacitance near the point of zero charge increases with increasing temperature. This agrees with experiment for molten salts and disagrees with the behavior of double layer in dissolved salts, which can be modeled with low density and high temperature charged hard spheres near a wall. This also disagrees with the predictions of the Gouy–Chapman theory and the mean spherical approximation. It appears that it...

Insights from theory and simulation on the electrical double layer.

Despite the fact that our conceptual understanding of the electrical double layer has advanced during the past few decades, the interpretation of experimental and applied work is still largely based on the venerable Poisson-Boltzmann theory of Gouy, Chapman and Stern. This is understandable since this theory is simple and analytic. However, it is not very accurate because the atomic/molecular nature of the ions/solvent and their correlations are ignored. Simulation and some theoretical studies by ourselves and others that have advanced our understanding are discussed. These studies show that the GCS theory predicts a narrow double layer with monotonic profiles. This is not correct. The double layer is wider, and there can be substantial layering that would be even more pronounced if explicit solvent molecules are considered. For many years, experimental studies of the double layer have been directed to the use of electrochemistry as an analytical tool. This is acceptable for analytic chemistry studies. However, the understanding of electrochemical reactions that typically occur at the electrode surface, where simulation and theory indicate that the GCS theory can have substantial errors, requires modern approaches. New, fundamental experimental studies that would lead to deeper insights using more novel systems would be desirable. Further, biophysics is an interesting field. Recent studies of the selectivity of ion channels and of the adsorption of ions in a binding sites of a protein have shown that the linearized GCS theory has substantial errors.

The effect of protein dielectric coefficient on the ionic selectivity of a calcium channel.

Calcium-selective ion channels are known to have carboxylate-rich selectivity filters, a common motif that is primarily responsible for their high Ca(2+) affinity. Different Ca(2+) affinities ranging from micromolar (the L-type Ca channel) to millimolar (the ryanodine receptor channel) are closely related to the different physiological functions of these channels. To understand the physical mechanism for this range of affinities given similar amino acids in their selectivity filters, we use grand canonical Monte Carlo simulations to assess the binding of monovalent and divalent ions in the selectivity filter of a model Ca channel. We use a reduced model where the electolyte is modeled by hard-sphere ions embedded in a continuum dielectric solvent, while the interior of protein surrounding the channel is allowed to have a dielectric coefficient different from that of the electrolyte. The induced charges that appear on the protein/lumen interface are calculated by the induced charge computation method [Boda et al., Phys. Rev. E 69, 046702 (2004)]. It is shown that decreasing the dielectric coefficient of the protein attracts more cations into the pore because the proteins carboxyl groups induce negative charges on the dielectric boundary. As the density of the hard-sphere ions increases in the filter, Ca(2+) is absorbed into the filter with higher probability than Na(+) because Ca(2+) provides twice the charge to neutralize the negative charge of the pore (both structural carboxylate oxygens and induced charges) than Na(+) while occupying about the same space (the charge/space competition mechanism). As a result, Ca(2+) affinity is improved an order of magnitude by decreasing the protein dielectric coefficient from 80 to 5. Our results indicate that adjusting the dielectric properties of the protein surrounding the permeation pathway is a possible way for evolution to regulate the Ca(2+) affinity of the common four-carboxylate motif.

Low temperature anomalies in the properties of the electrochemical interface

Abstract Some features of the adsorption isotherms and electrochemical capacitance of electrolytes in solvents at low temperatures are studied by means of computer simulations. The so-called restricted primitive model where the ions are represented as charged hard spheres of equal diameter and the solvent is represented by a uniform dielectric constant is used. It is found that at low temperatures the capacitance of double layers in dissolved electrolytes decreases with decreasing temperatures. This is similar to the behaviour of the capacitance of molten salt double layers but opposite to the behaviour of double layers in dissolved electrolytes at room temperature. Further, we find a maximum in the adsorption isotherm near the critical point of the electrolyte. This quantity may well be singular at the critical point.

Temperature dependence of the double layer capacitance for the restricted primitive model of an electrolyte solution from a density functional approach

We apply a different version of the density functional theory, given by Pizio, Patrykiejew, and Sokolowski [J. Chem. Phys. 121, 11957 (2004)], for a nonuniform restricted primitive model of an electrolyte solution to evaluate the temperature dependence of the capacitance of an electric double layer. We show that this theory is capable of reproducing the computer simulation data at a quantitative level. In particular, the reversal of the temperature dependence of the capacitance at low temperatures is predicted. This phenomenon has been difficult to predict from theory. Further, this theory also leads to an accurate description of the double layer structure.

Ionic selectivity in L-type calcium channels by electrostatics and hard-core repulsion

A physical model of selective “ion binding” in the L-type calcium channel is constructed, and consequences of the model are compared with experimental data. This reduced model treats only ions and the carboxylate oxygens of the EEEE locus explicitly and restricts interactions to hard-core repulsion and ion–ion and ion–dielectric electrostatic forces. The structural atoms provide a flexible environment for passing cations, thus resulting in a self-organized induced-fit model of the selectivity filter. Experimental conditions involving binary mixtures of alkali and/or alkaline earth metal ions are computed using equilibrium Monte Carlo simulations in the grand canonical ensemble. The model pore rejects alkali metal ions in the presence of biological concentrations of Ca2+ and predicts the blockade of alkali metal ion currents by micromolar Ca2+. Conductance patterns observed in varied mixtures containing Na+ and Li+, or Ba2+ and Ca2+, are predicted. Ca2+ is substantially more potent in blocking Na+ current than Ba2+. In apparent contrast to experiments using buffered Ca2+ solutions, the predicted potency of Ca2+ in blocking alkali metal ion currents depends on the species and concentration of the alkali metal ion, as is expected if these ions compete with Ca2+ for the pore. These experiments depend on the problematic estimation of Ca2+ activity in solutions buffered for Ca2+ and pH in a varying background of bulk salt. Simulations of Ca2+ distribution with the model pore bathed in solutions containing a varied amount of Li+ reveal a “barrier and well” pattern. The entry/exit barrier for Ca2+ is strongly modulated by the Li+ concentration of the bath, suggesting a physical explanation for observed kinetic phenomena. Our simulations show that the selectivity of L-type calcium channels can arise from an interplay of electrostatic and hard-core repulsion forces among ions and a few crucial channel atoms. The reduced system selects for the cation that delivers the largest charge in the smallest ion volume.

Volume Exclusion in Calcium Selective Channels

Another research group has proposed an interesting model for calcium channel selectivity. However, on the basis of their reported results we find it impossible to assess the merits of their model because their results and claims concerning selectivity are based on an extrapolation over four orders of magnitude to low Ca(2+) concentration. Their results and claims have been presented in several articles and reviews in several journals and, thus, need attention. In this article, we first establish that we obtain results on electrostatics and channel occupancies similar to the high-concentration simulations they present. We then perform grand canonical ensemble simulations that enable us to study micromolar Ca(2+) concentrations. We find that their model channel is only weakly Ca(2+) selective. A crucial problem with their model appears to be the placement of the negatively charged glutamate structural elements in fixed positions inside the protein rather than as flexible units inside the filter.

Synthetic Nanopores as a Test Case for Ion Channel Theories: The Anomalous Mole Fraction Effect without Single Filing

The predictions of a theory for the anomalous mole fraction effect (AMFE) are tested experimentally with synthetic nanopores in plastic. The negatively charged synthetic nanopores under consideration are highly cation selective and 50 A in diameter at their smallest point. These pores exhibit an AMFE in mixtures of Ca(2+) and monovalent cations. An AMFE occurs when the conductance through a pore is lower in a mixture of salts than in the pure salts at the same concentration. For ion channels, the textbook interpretation of the AMFE is that multiple ions move through the pore in coordinated, single-file motion. However, because the synthetic nanopores are so wide, their AMFE shows that single filing is not necessary for the AMFE. It is shown that the AMFE in the synthetic nanopores is explained by a theory of preferential ion selectivity. The unique properties of the synthetic nanopores allow us to experimentally confirm several predictions of this theory. These same properties make synthetic nanopores an interesting new platform to test theories of ion channel permeation and selectivity in general.

The effects of deviations from Lorentz-Berthelot rules on the properties of a simple mixture

Generally, the parameters in the interaction potential between like molecules in a mixture can be determined in a relatively straightforward manner from the properties of the pure components. However, the determination of the parameters in the interaction potential between the unlike pairs in the mixtures is more difficult. As a result, these parameters are usually estimated from averages of the like parameters. The most common recipes are the Lorentz–Berthelot mixing rules, where the energy and molecular size parameters are presumed to be geometric and arithmetic averages, respectively. There have been some studies of the consequences of deviations from the energy rule but almost no studies of the consequences of deviations from the size rule. Here, we study the effects of deviations from both rules on the radial distribution functions of a simple mixture. We find from simulations that, for this mixture, the effect of deviations from the energy rule on the radial distribution function are rather small but that the effect of deviations from the size rule can be significant and are interesting.