Charge Inversion Phenomena Research Articles

Phosphatidic Acid Domains in Membranes: Effect of Divalent Counterions

Phosphatidic acid (PA) is emerging as a key phospholipid in a wide range of biological processes such as signal transduction, secretion, or membrane fusion. In most cases, the biological functionality of PA is associated with the presence of micromolar to millimolar calcium concentrations. It has been argued that PA can create defects in the packing of lipids in membranes due to lateral phase separation by divalent ions, which in turn aggregate proteins with high affinity for PA. In this article, we present a detailed investigation of the properties of PA domains in the presence of divalent ions by a combination of molecular dynamics simulations and theoretical methods. Our results show that PA is extremely effective in binding divalent ions through its oxygen atoms, with a broad distribution of binding constants and exhibiting the phenomenon of charge inversion (a total number of bound counterion charges that exceeds the negative PA charge). We predict that a PA-rich domain undergoes a drastic reorganization when divalent cations reach micromolar concentrations (i.e., typical physiological conditions), as PA lipids become doubly charged by releasing their protons. We also present a detailed investigation of the properties of interfacial water, which determine the binding of proteins or other molecules. We conclude with a discussion of the implications of our results in the context of recent experimental studies in model systems and in real cells.

Electrophoretic properties of highly charged colloids: A hybrid molecular dynamics∕lattice Boltzmann simulation study

Using computer simulations, the electrophoretic motion of a positively charged colloid (macroion) in an electrolyte solution is studied in the framework of the primitive model. In this model, the electrolyte is considered as a system of negatively and positively charged microions (counterions and coions, respectively) that are immersed into a structureless medium. Hydrodynamic interactions are fully taken into account by applying a hybrid simulation scheme, where the charged ions (i.e., macroion and electrolyte), propagated via molecular dynamics, are coupled to a lattice Boltzmann (LB) fluid. In a recent electrophoretic experiment by Martin-Molina et al. [J. Phys. Chem. B 106, 6881 (2002)], it was shown that, for multivalent salt ions, the mobility mu initially increases with charge density sigma, reaches a maximum, and then decreases with further increase of sigma. The aim of the present work is to elucidate the behavior of mu at high values of sigma. Even for the case of monovalent microions, a decrease of mu with sigma is found. A dynamic Stern layer is defined that includes all the counterions that move with the macroion while subjected to an external electrical field. The number of counterions in the Stern layer, q(0), is a crucial parameter for the behavior of mu at high values of sigma. In this case, the mobility mu depends primarily on the ratio q(0)/Q (with Q the valency of the macroion). The previous contention that the increase in the distortion of the electric double layer (EDL) with increasing sigma leads to the lowering of mu does not hold for high sigma. In fact, it is shown that the deformation of the EDL decreases with the increase of sigma. The role of hydrodynamic interactions is inferred from direct comparisons to Langevin simulations where the coupling to the LB fluid is switched off. Moreover, systems with divalent counterions are considered. In this case, at high values of sigma the phenomenon of charge inversion is found.

Testing one component plasma models on colloidal overcharging phenomena

In this paper, the mechanisms of overcharging of a colloidal macroion in the presence of multivalent counterions are investigated by means of Monte Carlo simulations. This computational technique appears as a powerful tool for probing the validity of semianalytical models developed for this issue. In particular, the simulations performed are compared with the predictions of two different models based on the one component plasma (OCP) theory. Therein, the multivalent ionic atmosphere confined at the macroion surface is approximated by a two-dimensional Wigner crystal. These kinds of models are largely used in the literature since (in some cases) they present quite simple equations to describe the electric double layer (EDL) of macroions with different geometries in the presence of much smaller (but still multivalent) ions. In this sense, charge inversion phenomena of membranes, polyelectrolytes, DNA molecules, etc., are straightforwardly predicted in terms of these expressions. Unfortunately, comparisons between these predictions and experimental results are scarce, mostly due to the difficulty to reproduce the experimental conditions in the laboratory. Accordingly, the goal of the present paper is to simulate EDLs under real conditions (in which overcharging phenomena are expected to happen) and use the results obtained in this way for comparing with those obtained from OCP models.

Nonlinear screening on the charged surfaces with trivalent and tetravalent salt ions: Monte Carlo simulations

We investigate the electrostatic screening phenomena with divalent, trivalent and tetravalent salt ions on charged surfaces. The integrated charge distribution function is studied to clarify the structure of the electric double-layers on spherical colloids and charged rods by Monte Carlo simulations. The profiles of electric double-layers show that the charge inversion phenomena with divalent salt are sensitive to the size of microions. These results reflect the importance of the nonlinearity and excluded-volume effect on strongly charged systems in an aqueous solution.

Permeation of mixed-salt solutions with commercial and pore-filled nanofiltration membranes: membrane charge inversion phenomena

This paper presents experimental observations on the permeation of mixed-salt solutions through commercial and McMaster pore-filled nanofiltration membranes. Two types of mixed-salt solutions are analyzed (common co-ions and common counter-ions). The permeation of solutions with common counter-ions can be explained from theory and has been predicted accurately in previous work. However, the performance of these membranes when common co-ions are present does not directly follow the behavior expected from normal electrostatic and steric exclusion mechanisms. The membranes behave as if the charge has been inverted. Multivalent counter-ion adsorption is believed to play an important role in the inversion of the effective charge of the membrane, and the subsequent anomalous permeation of counter-ions.

Structure of Polyelectrolyte Solutions at a Charged Surface

The structure of polyelectrolyte solutions at a charged surface is studied using density functional theory and Monte Carlo simulations. The polymer molecules are modeled as freely jointed chains of charged hard spheres, the counterions and co-ions as charged hard spheres, and the surface is a planar, impenetrable hard wall with a uniform surface charge density. The density functional theory treats the ideal gas contribution exactly, uses a weighted density approximation for the hard sphere contribution, and a generalized van der Waals approximation for the electrostatic contribution. At a fixed surface charge density, with increasing concentration of the polyion, the simulations show layering as well as charge inversion phenomena resulting from an interplay between excluded volume and electrostatic interactions. The integrated surface excess is a monotonically decreasing function of polymer concentration at high surface charge densities, but a nonmonotonic function of polymer concentration at lower surfac...

Electrophoresis of a rod macroion under polyelectrolyte salt: is mobility reversed forDNA?

By molecular dynamics simulation, we study the charge inversion phenomenon of a rodmacroion in the presence of polyelectrolyte counterions. We simulate electrophoresis of themacroion under an applied electric field. When both counterions and coions arepolyelectrolytes, charge inversion occurs if the line charge density of the counterions islarger than that of the coions. For the macroion of surface charge density equal to that ofthe DNA, the reversed mobility is realized either with adsorption of the multivalentcounterion polyelectrolyte or the combination of electrostatics and other mechanismsincluding the short-range attraction potential or the mechanical twinning of polyelectrolytearound the rod axis.

Charge Inversion and Flow Reversal in a Nanochannel Electro-osmotic Flow

Ion distribution and velocity profiles for electro-osmotic flow in a 3.49 nm wide slit channel with a surface charge density of -0.285 C/m(2) are studied using molecular dynamics simulations. Simulation results indicate that the concentration of the co-ion exceeds that of the counterion in the region 0.53 nm away from the channel wall, and the electro-osmotic flow is in the opposite direction to that predicted by the classical continuum theory. The charge inversion is mainly caused by the molecular nature of water and ions. The flow reversal is caused by the immobilization of counterions adsorbed on the channel wall and due to the charge inversion phenomena.

Density-functional theory of spherical electric double layers and zeta potentials of colloidal particles in restricted-primitive-model electrolyte solutions.

A density-functional theory is proposed to describe the density profiles of small ions around an isolated colloidal particle in the framework of the restricted primitive model where the small ions have uniform size and the solvent is represented by a dielectric continuum. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-sphere repulsion and a quadratic functional Taylor expansion for the electrostatic interactions. The theoretical predictions are in good agreement with the results from Monte Carlo simulations and from previous investigations using integral-equation theory for the ionic density profiles and the zeta potentials of spherical particles at a variety of solution conditions. Like the integral-equation approaches, the density-functional theory is able to capture the oscillatory density profiles of small ions and the charge inversion (overcharging) phenomena for particles with elevated charge density. In particular, our density-functional theory predicts the formation of a second counterion layer near the surface of highly charged spherical particle. Conversely, the nonlinear Poisson-Boltzmann theory and its variations are unable to represent the oscillatory behavior of small ion distributions and charge inversion. Finally, our density-functional theory predicts charge inversion even in a 1:1 electrolyte solution as long as the salt concentration is sufficiently high.

Effects of asymmetric salt and a cylindrical macroion on charge inversion: electrophoresis by molecular dynamics simulations.

The charge inversion phenomenon is studied by molecular dynamics simulations, focusing on size and valence asymmetric salts, and a threshold of surface charge density for charge inversion. The charge inversion criteria by the electrophoretic mobility and the radial distribution functions of ions coincide except around the charge inversion threshold. The reversed electrophoretic mobility increases with the ratio of coion to counterion radii, a(-)/a(+), while it decreases with the ratio of coion to counterion valences, Z(-)/Z(+). The monovalent salt enhances charge inversion of a strongly charged macroion at small salt ionic strength, while it reduces reversed mobility otherwise. A cylindrical macroion is more persistent to monovalent salt than a spherical macroion of the same radius and surface charge density.

Charge inversion of colloidal particles in an aqueous solution: screening by multivalent ions.

We investigate the structure of the electric double layer on charged colloids by Monte Carlo simulations. Using the primitive model of asymmetric electrolytes, the integrated charge distribution function on a spherical colloidal particle are also studied. With high concentrations of divalent ions, numerical results predict charge oscillation and charge inversion phenomena, which the traditional Derjaguin-Landau-Verwey-Overbeek theory cannot reproduce.

Effective interactions between like-charged macromolecules

We investigate, within a local density functional theory formalism, the interactions between like-charged polyions immersed in a confined electrolyte. We obtain a simple condition for a repulsive effective pair potential, which can be related to the thermodynamic stability criterion of the uncharged counterpart of microscopic species constituting the electrolyte. Under the same condition, the phenomenon of charge inversion (over-charging), where the polyion bare charge is over-screened by its electric double layer, is shown to be impossible. These results hold beyond standard mean-field theories (such as Poisson-Boltzmann or modified Poisson-Boltzmann approaches).

Structure of electric double layers: A simple weighted density functional approach

A simple weighted density functional approach is developed for inhomogeneous ionic fluids and applied to the structure of the electric double layer using the restricted primitive model where the ions are considered to be charged hard spheres of equal diameter. The formalism is nonperturbative with both hard-sphere and electrical contributions to the one-particle correlation function evaluated through a suitably averaged weighted density, the only input being the second-order direct correlation functions of the corresponding uniform system. The approach is designed in such a way, that the calculation of the weight function is decoupled from the weighted density. Numerical results on the ionic density profile and the mean electrostatic potential near a hard wall at several surface charge densities are shown to compare well with available simulation results. The corresponding results for the nonprimitive molecular solvent model provide insight into the layering effect and the charge inversion phenomena.

A nonlocal density-functional theory of electric double layer: Charge-asymmetric electrolytes

A nonlocal density-functional theory of inhomogeneous ionic fluids proposed by us recently [J. Chem. Phys. 100, 5219 (1994)] for symmetric electrolytes is extended to study the structure of electric double layer for a charge-asymmetric (2:1) situation involving hard sphere ions of equal diameter with a continuum or neutral hard sphere model for the solvent. The hard sphere contributions to the excess free energy density and its derivatives for the inhomogeneous system are evaluated nonperturbatively through a position-dependent effective weighted density, which is also used to obtain the corresponding ionic contributions through a second-order functional Taylor expansion. The calculated results for the continuum solvent model show reasonably good agreement with the available simulation results, while the layering effect due to hard sphere exclusion and the charge inversion phenomena are some of the interesting consequences arising from the molecular nature of the solvent.

A nonlocal density functional theory of electric double layer: Symmetric electrolytes

The density functional theory of inhomogeneous classical neutral fluids is extended to study the structure of electric double layer using the restricted primitive model as well as the nonprimitive three-component molecular solvent model. The formalism is based on a weighted density approach where the hard-sphere contributions to the excess free energy density and the one-particle correlation function are evaluated nonperturbatively using a position-dependent effective density while the corresponding ionic part is obtained through a second-order functional Taylor expansion around this effective density. The calculated results for the density profiles of the ions and the mean electrostatic potential are in good agreement with the available simulation results for the continuum solvent primitive model. The corresponding results for the nonprimitive molecular solvent model provide insight into the layering effect due to hard-sphere exclusion and the charge inversion phenomena.

Non-local free-energy density-functional theory applied to the electrical double layer

A theoretical study of the restricted primitive model of the electrical double layer using a free-energy density-functional theory is presented. The ion-ion hard-core repulsive contribution to the free energy is incorporated through a non-local excess hard-sphere free-energy density functional. The electrostatic part of the ion-ion direct correlation function of the inhomogeneous electrolyte in the interfacial region is approximated by that of the homogeneous bulk electrolyte. The generalized van der Waals model and the Tarazona model are used to construct the respective excess hard-sphere free-energy density functionals and compared with each other. Each model requires as input a hard-sphere equation of state. The Carnahan-Starling equation of state is chosen. The theory correctly predicts the layering effect of the counterions and the charge-inversion phenomenon. The results for 1:1 and 2:2 electrolytes agree well with Monte Carlo simulations. The Tarazona model gives results in closer agreement with Monte Carlo data than does the generalized van der Waals model. The diffuse-layer potentials predicted by the Tarazona model are not as accurate as those predicted by the generalized hard-rod model, which has been applied to the same problem in a previous study.