Adsorption of highly charged Gaussian polyelectrolytes onto oppositely charged surfaces.

In many biological processes highly charged biopolymers are adsorbed onto oppositely charged surfaces of macroions and membranes. They form strongly correlated structures close to the surface which cannot be explained by the conventional Poisson-Boltzmann theory. In this work strong coupling theory is used to study the adsorption of highly charged Gaussian polyelectrolytes. Two cases of adsorptions are considered, when the Gaussian polyelectrolytes are confined (a) by one charged wall, and (b) between two charged walls. The effects of salt and the geometry of the polymers on their adsorption-depletion transitions in the strong coupling regime are discussed.

Shell formation in short like-charged polyelectrolytes in a harmonic trap.

Inspired by recent experiments and simulations on pattern formation in biomolecules by optical tweezers, a theoretical description based on the reference interaction site model (RISM) is developed to calculate the equilibrium density profiles of small polyelectrolytes in an external potential. The formalism is applied to the specific case of a finite number of Gaussian and rodlike polyelectrolytes trapped in a harmonic potential. The density profiles of the polyelectrolytes are studied over a range of lengths and numbers of polyelectrolytes in the trap, and the strength of the trap potential. For smaller polymers we recover the results for point charges. In the mean field limit the longer polymers, unlike point charges, form a shell at the boundary layer. When the interpolymer correlations are included, the density profiles of the polymers show sharp shells even at weaker trap strengths. The implications of these results are discussed.

Strong-coupling electrostatic theory of polymer counterions close to planar charges.

Strong-coupling phenomena, such as like-charge macroion attraction, opposite-charged macroion repulsion, charge renormalization, and charge inversion, are known to be mediated by multivalent counterions. Most theories treat the counterions as point charges and describe the system by a single coupling parameter that measures the strength of the Coulomb interactions. In many biological systems, the counterions are highly charged and have finite sizes and can be well-described by polyelectrolytes. The shapes and orientations of these polymer counterions play a major role in the thermodynamics of these systems. In this work we apply a field-theoretic description in the strong-coupling regime to the polymer counterions in the presence of a fixed charge distribution. We work out the special cases of rodlike polymer counterions confined by one, and two charged walls, respectively. The effects of the geometry of the rodlike counterions and the excluded volume of the walls on the density, pressure, and free energy of the rodlike counterions are discussed.

Hydration of ions in two-dimensional water.

We present a two-dimensional lattice model of water to study the effects of ion hydration on the properties of water. We map the water molecules as lattice particles consisting of a single oxygen atom at the center of a site and two hydrogen atoms on each side. The internal state of the system, such as the dipole moment at a site, is defined with respect to the location of the hydrogen atoms at the site depending on their role in hydrogen bonds (H bonds) being a donor or an acceptor. We study the influence of the charge and the radius of the ion on the insertion energy and on the H bonds in the first and second hydration layers around the ion and in the bulk. In particular we analyze how the competing interactions of the short-ranged H bonds and the long-ranged electrostatics influence the hydration properties. The role of the ion both as a source of the electrostatic interactions as well as a defect is also discussed. Our model also shows the well-known fact that the polarizability of the water molecules destroys the hydrogen bond network and increases the dipole moment of the molecules near the ion.

Effect of charge inhomogeneity and mobility on colloid aggregation.

The aggregation of inhomogeneously charged colloids with the same average charge is analyzed using Monte Carlo simulations. We find aggregation of colloids for sizes in the range 10-200 nm, which is similar to the range in which aggregation is observed in several experiments. The attraction arises from the strongly correlated electrostatic interactions associated with the increase in the counterion density in the region between the particles; this effect is enhanced by the discreteness and mobility of the surface charges. Larger colloids attract more strongly when their surface charges are discrete. We study the aggregation as functions of the surface charge density, counterion valence, and volume fraction.

Long-range interaction between heterogeneously charged membranes.

Despite their neutrality, surfaces or membranes with equal amounts of positive and negative charge can exhibit long-range electrostatic interactions if the surface charge is heterogeneous; this can happen when the surface charges form finite-size domain structures. These domains can be formed in lipid membranes where the balance of the different ranges of strong but short-ranged hydrophobic interactions and longer-ranged electrostatic repulsion result in a finite, stable domain size. If the domain size is large enough, oppositely charged domains in two opposing surfaces or membranes can be strongly correlated by the electrostatic interactions; these correlations give rise to an attractive interaction of the two membranes or surfaces over separations on the order of the domain size. We use numerical simulations to demonstrate the existence of strong attractions at separations of tens of nanometers. Large line tensions result in larger domains but also increase the charge density within the domain. This promotes correlations and, as a result, increases the intermembrane attraction. On the other hand, increasing the salt concentration increases both the domain size and degree of domain anticorrelation, but the interactions are ultimately reduced due to increased screening. The result is a decrease in the net attraction as salt concentration is increased.

Monte carlo simulations of tau proteins: effect of phosphorylation.

We perform Monte Carlo simulations of tau proteins bound to a cylinder that mimics a microtubule (MT), and then study them in solution. Tau protein binds to a highly anionic MT surface to stabilize the cylindrical structure of MT. The negatively charged tail domain floats away from the anionic MT surface while positively charged tau segments localize near the MT surface. Monte Carlo simulations demonstrate that, in 3RS tau isoform (which has three imperfect repeats (R) short (S) isoform), amino acids are more condensed near a highly charged interface compared to 4RL isoform (which has four imperfect repeats (R) long (L) isoform). In 4RL isoform, amino acids in tail domain stay mostly apart from the MT surface. In the bulk solution, dephosphorylated taus are separated due to Coulomb repulsion between similarly charged isoforms. Moderate phosphorylation of 3RS isoform decreases average intermolecular distance between dephosphorylated and phosphorylated taus and lead to their overlap. Further phosphorylation does not change noticeably the intermolecular distances.

Lamellar phase coexistence induced by electrostatic interactions.

Membranes containing highly charged biomolecules can have a minimal free-energy state at small separations that originates in the strongly correlated electrostatic interactions mediated by counterions. This phenomenon can lead to a condensed, lamellar phase of charged membranes that coexists in thermodynamic equilibrium with a very dilute membrane phase. Although the dilute phase is mostly water, entropy dictates that this phase must contain some membranes and counterions. Thus, electrostatics alone can give rise to the coexistence of a condensed and an unbound lamellar phase. We use numerical simulations to predict the nature of this coexistence when the charge density of the membrane is large, for the case of multivalent counterions and for a membrane charge that is characteristic of biomolecules. We also investigate the effects of counterion size and salt on the two coexisting phases. With increasing salt concentration, we predict that electrostatic screening by salt can destroy the phase separation.

The role of multipoles in counterion-mediated interactions between charged surfaces: strong and weak coupling.

We present general arguments for the importance, or lack thereof, of structure in the charge distribution of counterions for counterion-mediated interactions between bounding symmetrically charged surfaces. We show that on the mean field or weak coupling level, the charge quadrupole contributes the lowest order modification to the contact value theorem and thus to the intersurface electrostatic interactions. The image effects are non-existent on the mean field level even with multipoles. On the strong coupling level the quadrupoles and higher order multipoles contribute additional terms to the interaction free energy only in the presence of dielectric inhomogeneities. Without them, the monopole is the only multipole that contributes to the strong coupling electrostatics. We explore the consequences of these statements in all their generality.

A numerical study of the electrostatic properties of two finite-width charged dielectric slabs in water.

A numerical algorithm based on the image charge method is introduced to calculate the electrostatic potential, energy, and forces present in systems involving multiple point charges embedded in an inhomogeneous dielectric environment composed of five parallel dielectric slabs. The methodology is implemented within Monte Carlo simulations to calculate the thermal properties of two charged dielectric plates of finite thickness immersed in water.

Strong-coupling electrostatics in the presence of dielectric inhomogeneities.

We study the strong-coupling (SC) interaction between two like-charged membranes of finite thickness embedded in a medium of higher dielectric constant. A generalized SC theory is applied along with extensive Monte Carlo simulations to study the image charge effects induced by multiple dielectric discontinuities in this system. These effects lead to strong counterion crowding in the central region of the intersurface space upon increasing the solvent-membrane dielectric mismatch and change the membrane interactions from attractive to repulsive at small separations. These features agree quantitatively with the SC theory at elevated couplings or dielectric mismatch where the correlation hole around counterions is larger than the thickness of the central counterion layer.

Effects of dielectric discontinuities on two charged plates.

Counterions in a biological system are charged in water and interact with charged macroions, which are generally made up of hydrocarbons. The dielectric difference between water and the hydrocarbon substrates occurs naturally, and may greatly affect the electrostatic properties of biological systems. Particularly for a slab geometry, bulk counterions that are dissolved in water are driven to the midplane of the slab because of their repulsive interaction with their image charges. The pressure between two charged plates becomes less repulsive since the low dielectric constant of the hydrocarbon substrate creates stronger association between counterions and surface charges as compared to the case of no dielectric discontinuity.

Interaction between two inhomogeneously charged parallel surfaces in the strong coupling regime.

The counterion density profile and pressure between two inhomogenously charged parallel plates are analyzed analytically and numerically in the strong-coupling regime. Point charges are used and the surface charges are immobile. It is found that when the surface charge distribution is inhomogeneous, the charge coupling effect becomes stronger, the counterion spatial distribution is more localized toward the plate surfaces, and, thus, the pressure between two plates becomes lower than in the case when the surface charge distribution is homogeneous.