Interaction Between Equally Charged Membrane Surfaces Mediated by Positively and Negatively Charged Macro-Ions

In biological systems, charged membrane surfaces are surrounded by charged molecules such as electrolyte ions and proteins. Our recent experiments in the systems of giant phospholipid vesicles indicated that some of the blood plasma proteins (macro-ions) may promote adhesion between equally charged membrane surfaces. In this work, theory was put forward to describe an IgG antibody-mediated attractive interaction between negatively charged membrane surfaces which was observed in experiments on giant phospholipid vesicles with cardiolipin-containing membranes. The attractive interactions between negatively charged membrane surfaces in the presence of negatively and positively charged spherical macro-ions are explained using functional density theory and Monte Carlo simulations. Both, the rigorous solution of the variational problem within the functional density theory and the Monte Carlo simulations show that spatial and orientational ordering of macro-ions may give rise to an attractive interaction between negatively charged membrane surfaces. It is also shown that the distinctive spatial distribution of the charge within the macro-ions (proteins) is essential in this process.     

Donnan potential and surface potential of a charged membrane.

A model is presented for the electrical potential distribution across a charged biological membrane that is in equilibrium with an electrolyte solution. We assume that a membrane has charged surface layers of thickness d on both surfaces of the membrane, where the fixed charges are distributed at a uniform density N within the layers, and that these charged layers are permeable to electrolyte ions. This model unites two different concepts, that is, the Donnan potential and the surface potential (or the Gouy-Chapman double-layer potential). Namely, the present model leads to the Donnan potential when d much greater than 1/k' (k' is the Debye-Hückel parameter of the surface charge layer) and to the surface potential as d----0, keeping the product Nd constant. The potential distribution depends significantly on the thickness d of the surface charge layer when d less than or approximately equal to 1/k'.     

The effect of lipid demixing on the electrostatic interaction of planar membranes across a salt solution

We study the effect of lipid demixing on the electrostatic interaction of two oppositely-charged membranes in solution, modeled here as an incompressible two-dimensional fluid mixture of neutral and charged mobile lipids. We calculate, within linear and nonlinear Poisson-Boltzmann theory, the membrane separation at which the net electrostatic force between the membranes vanishes, for a variety of different system parameters. According to Parsegian and Gingell, contact between oppositely-charged surfaces in an electrolyte is possible only if the two surfaces have exactly the same charge density (sigma(1) = -sigma(2)). If this condition is not fulfilled, the surfaces can repel each other, even though they are oppositely charged. In our model of a membrane, the lipidic charge distribution on the membrane surface is not homogeneous and frozen, but the lipids are allowed to freely move within the plane of the membrane. We show that lipid demixing allows contact between membranes even if there is a certain charge mismatch, /sigma(1)/ not equal /sigma(2)/, and that in certain limiting cases, contact is always possible, regardless of the value of sigma(1)/sigma(2) (if sigma(1)/sigma(2) < 0). We furthermore find that of the two interacting membranes, only one membrane shows a major rearrangement of lipids, whereas the other remains in exactly the same state it has in isolation and that, at zero-disjoining pressure, the electrostatic mean-field potential between the membranes follows a Gouy-Chapman potential from the more strongly charged membrane up to the point of the other, more weakly charged membrane.     

Model films from native cellulose nanofibrils. Preparation, swelling, and surface interactions

Native cellulose model films containing both amorphous and crystalline cellulose I regions were prepared by spin-coating aqueous cellulose nanofibril dispersions onto silica substrates. Nanofibrils from wood pulp with low and high charge density were used to prepare the model films. Because the low charged nanofibrils did not fully cover the silica substrates, an anchoring substance was selected to improve the coverage. The model surfaces were characterized using atomic force microscopy (AFM) and X-ray photoelectron spectroscopy (XPS). The effect of nanofibril charge density, electrolyte concentration, and pH on swelling and surface interactions of the model film was studied by quartz crystal microbalance with dissipation (QCM-D) and AFM force measurements. The results showed that the best coverage for the low charged fibrils was achieved by using 3-aminopropyltrimethoxysilane (APTS) as an anchoring substance and hence it was chosen as the anchor. The AFM and XPS measurements showed that the fibrils are covering the substrates. Charge density of the fibrils affected the morphology of the model surfaces. The low charged fibrils formed a network structure while the highly charged fibrils formed denser film structure. The average thickness of the films corresponded to a monolayer of fibrils, and the average rms roughness of the films was 4 and 2 nm for the low and high charged nanofibril films, respectively. The model surfaces were stable in QCM-D swelling experiments, and the behavior of the nanofibril surfaces at different electrolyte concentrations and pHs correlated with other studies and the theories of Donnan. The AFM force measurements with the model surfaces showed well reproducible results, and the swelling results correlated with the swelling observed by QCM-D. Both steric and electrostatic forces were observed and the influence of steric forces increased as the films were swelling due to changes in pH and electrolyte concentration. These films differ from previous model cellulose films due to their chemical composition (crystalline cellulose I and amorphous regions) and fibrillar structure and hence serve as excellent models for the pulp fiber surface.     

Imaging the electrostatic potential of transmembrane channels: atomic probe microscopy of OmpF porin

The atomic force microscope (AFM) was used to image native OmpF porin and to detect the electrostatic potential generated by the protein. To this end the OmpF porin trimers from Escherichia coli was reproducibly imaged at a lateral resolution of approximately 0.5 nm and a vertical resolution of approximately 0.1 nm at variable electrolyte concentrations of the buffer solution. At low electrolyte concentrations the charged AFM probe not only contoured structural details of the membrane protein surface but also interacted with local electrostatic potentials. Differences measured between topographs recorded at variable ionic strength allowed mapping of the electrostatic potential of OmpF porin. The potential map acquired by AFM showed qualitative agreement with continuum electrostatic calculations based on the atomic OmpF porin embedded in a lipid bilayer at the same electrolyte concentrations. Numerical simulations of the experimental conditions showed the measurements to be reproduced quantitatively when the AFM probe was included in the calculations. This method opens a novel avenue to determine the electrostatic potential of native protein surfaces at a lateral resolution better than 1 nm and a vertical resolution of approximately 0.1 nm.     

Polynucleotide adsorption to negatively charged surfaces in divalent salt solutions

Polynucleotide adsorption to negatively charged surfaces via divalent ions is extensively used in the study of biological systems. We analyze here the adsorption mechanism via a self-consistent mean-field model that includes the pH effect on the surface-charge density and the interactions between divalent ions and surface groups. The adsorption is driven by the cooperative effect of divalent metal ion condensation along polynucleotides and their reaction with the surface groups. Although the apparent reaction constants are enhanced by the presence of polynucleotides, the difference between reaction constants of different divalent ions at the ideal condition explains why not all divalent cations mediate DNA adsorption onto anionic surfaces. Calculated divalent salt concentration and pH value variations on polynucleotide adsorption are consistent with atomic force microscope results. Here we use long-period x-ray standing waves to study the adsorption of mercurated-polyuridylic acid in a ZnCl2 aqueous solution onto a negatively charged hydroxyl-terminated silica surface. These in situ x-ray measurements, which simultaneously reveal the Hg and Zn distribution profiles along the surface normal direction, are in good agreement with our model. The model also provides the effects of polyelectrolyte line-charge density and monovalent salt on adsorption.     

Dielectric saturation of the aqueous boundary layers adjacent to charged bilayer membranes

Summary The surface charge density resulting from the adsorption of hydrophobic anions of dipicrylamine onto dioleyl-lecithin bilayer membranes has been measured directly using a high field pulse method. The surface charge density increases linearly with adsorbate concentration in the water until electrostatic repulsion of impinging hydrophobic ions by those already adsorbed becomes appreciable. Then Gouy-Chapman theory predicts that surface charge density will increase sublinearly, with the power [z ⁺/(z ⁺+2)] of the adsorbate concentration, wherez ⁺ is the cation valence of the indifferent electrolyte screening the negatively charged membrane surface. The predicted 1/3 and 1/2 power laws for univalent and divalent cations, respectively, have been observed in these experiments using Na⁺, Mg⁺⁺, and Ba⁺⁺ ions. Gouy-Chapman theory predicts further that the change from linear to sublinear dependence takes place at a surface charge density governed by the static dielectric constant of water and the concentration of indifferent electrolyte. Quantitative agreement with experiment is obtained at electrolyte concentrations of 10^–4 m and 10^–3 m, but can be maintained at higher concentrations only if the aqueous dielectric constant is decreased. A transition field model is proposed in which the Gouy-Chapman theory is modified to take account of dielectric saturation of water in the intense electric fields adjacent to charged membrane surfaces.     

Langevin Poisson-Boltzmann equation: point-like ions and water dipoles near a charged surface

Water ordering near a charged membrane surface is important for many biological processes such as binding of ligands to a membrane or transport of ions across it. In this work, the mean-field Poisson-Boltzmann theory for point-like ions, describing an electrolyte solution in contact with a planar charged surface, is modified by including the orientational ordering of water. Water molecules are considered as Langevin dipoles, while the number density of water is assumed to be constant everywhere in the electrolyte solution. It is shown that the dielectric permittivity of an electrolyte close to a charged surface is decreased due to the increased orientational ordering of water dipoles. The dielectric permittivity close to the charged surface is additionally decreased due to the finite size of ions and dipoles.     

Size-asymmetric competition and size-asymmetric growth in a spatially explicit zone-of-influence model of plant competition

Size-asymmetric competition among plants is usually defined as resource pre-emption by larger individuals, but it is usually observed and measured as a disproportionate size advantage in the growth of larger individuals in crowded populations (“size-asymmetric growth”). We investigated the relationship between size-asymmetric competition and size-asymmetric growth in a spatially explicit, individual-based plant competition model based on overlapping zones of influence (ZOI). The ZOI of each plant is modeled as a circle, growing in two dimensions. The size asymmetry of competition is reflected in the rules for dividing up the overlapping areas. We grew simulated populations with different degrees of size-asymmetric competition and at different densities and analyzed the size dependency of individual growth by fitting coupled growth functions to individuals. The relationship between size and growth within the populations was summarized with a parameter that measures the size asymmetry of growth. Complete competitive symmetry (equal division of contested resources) at the local level results in a very slight size asymmetry in growth. This slight size asymmetry of growth did not increase with increasing density. Increased density resulted in increased growth asymmetry when resource competition at the local level was size asymmetric to any degree. Size-asymmetric growth can be strong evidence that competitive mechanisms are at least partially size asymmetric, but the degree of size-asymmetric growth is influenced by the intensity as well as the mode of competition. Intuitive concepts of size-asymmetric competition among individuals in spatial and nonspatial contexts are very different.     

Ion flux across lipid bilayer membranes with charged surfaces

Summary In this paper we derive expressions for the ion flux across lipid bilayer membranes with charged surfaces treating the membrane as a continuous phase interposed between two electrolyte solutions and calculating the ion flux with the Nernst-Planck equations. The theoretical results are compared with experiments of Seufert and Hashimoto on lipid bilayer membranes with charged surface active agents added to the membranes. If the charge of both membrane surfaces has the same sign the flux of the gegenions is greatly increased whereas the flux of the coions decreases to a small amount. For oppositely charged membrane surfaces the membrane behaves like a np semiconductor and typical rectification voltage-current characteristics are obtained.     

Measuring electrostatic, van der Waals, and hydration forces in electrolyte solutions with an atomic force microscope

In atomic force microscopy, the tip experiences electrostatic, van der Waals, and hydration forces when imaging in electrolyte solution above a charged surface. To study the electrostatic interaction force vs distance, curves were recorded at different salt concentrations and pH values. This was done with tips bearing surface charges of different sign and magnitude (silicon nitride, Al₂O₃, glass, and diamond) on negatively charged surfaces (mica and glass). In addition to the van der Waals attraction, neutral and negatively charged tips experienced a repulsive force. This repulsive force depended on the salt concentration. It decayed exponentially with distance having a decay length similar to the Debye length. Typical forces were about 0.1 nN strong. With positively charged tips, purely attractive forces were observed. Comparing these results with calculations showed the electrostatic origin of this force.

In the presence of high concentrations (> 3 M) of divalent cations, where the electrostatic force can be completely ignored, another repulsive force was observed with silicon nitride tips on mica. This force decayed roughly exponentially with a decay length of 3 nm and was ~0.07-nN strong. This repulsion is attributed to the hydration force.

     

Monte Carlo simulation of the double layer at an electrode including the effect of a dielectric boundary

Monte Carlo values of the density profiles and related properties of the double layer formed by an electrolyte near a charged electrode are reported for the cases where the electrode has a dielectric coefficient greater, equal, and smaller than that of the electrolyte that causes a surface polarization that can be represented by electrostatic images. As expected, compared to the case where there is no dielectric boundary the ions near the electrode are attracted or repelled by the electrode if the dielectric coefficient is greater or smaller, respectively, than that of the electrolyte. This effect is most pronounced near the electrode and is stronger for 2:2 electrolytes than for 1:1 electrolytes. For both monovalent and divalent ions the effect of the dielectric boundary is stronger at low concentrations.     

The osmotic flow of an electrolyte through a charged porous membrane

A pore model in which the pore wall has a continuous distribution of electrical charge is used to investigate the osmotic flow through a charged permeable membrane separating electrolyte solutions of unequal concentrations. The pore is treated as a long, circular, cylindrical duct. The analysis is based on a continuum formulation in which a dilute electrolyte solution is described by the coupled Nernst-Planck/Poisson creeping flow equations. Account is taken of the significant size of the electrolyte ions (assumed to be rigid spheres) when compared with the diameter of the membrane pores. Analytical solutions for the ion concentrations, hydrostatic pressure and electrostatic potential in the electrolyte solutions are given and an intra-pore flow solution is derived. A mathematical expression for the osmotic reflection coefficient as a function of the solute ion: pore diameter ratio λ and the solute fluxes is obtained. Approximate solutions are quoted which relate the solute fluxes and the solution electrostatic potentials at the membrane surfaces to the bulk solution concentrations, the membrane pore charge and pore geometry. The osmotic reflection coefficient is thus determined as a function of these parameters.     

A thermodynamic analysis of calcium–alginate gel formation in the presence of inert electrolyte

The effect of mixed salt (1:1 and 2:1 electrolyte) on alginate (a charged polysaccharide) gel formation is analyzed within the Poisson-Boltzmann cell model utilizing experimental data from the literature. The concentration of calcium ions needed to induce gelation of alginate goes through a minimum as 1 : 1 electrolyte is added. The theoretical model can account for this in a qualitative manner. According to the theoretical model, however, it is only in terms of concentrations that the minimum exists. In terms of chemical potentials for the ions (or salt) the curve is monotonic. The effect is due to the highly nonideal interactions in polyelectrolyte solutions when the total salt content is low. © 1992 John Wiley & Sons, Inc.     

AFM Imaging and Analysis of Electrostatic Double Layer Forces on Single DNA Molecules

Electrical double layer (EDL) forces develop between charged surfaces immersed in an electrolyte solution. Biological material surrounded by its physiological medium constitutes a case where these forces play a major role. Specifically, this work is focused on the study of the EDL force exerted by DNA molecules, a standard reference for the study of single biomolecules of nanometer size. The molecules deposited on plane substrates have been characterized by means of the atomic force microscope operated in the force spectroscopy imaging mode. Force spectroscopy imaging provides images of the topography of the DNA molecules, and of the EDL force spectrum. Due to the size of the molecule being much smaller than that of the tip, both the tip-substrate and tip-molecule interactions need to be considered in the analysis of the experimental results. We solve this problem by linearly superposing the two contributions. EDL force images are presented where DNA molecules are clearly resolved. The lateral resolution of the EDL force is discussed and compared with that of the topography. The method also allows the estimation of the DNA surface charge density, thereby obtaining reasonable values.     

Positively charged surfaces increase the flexibility of DNA

Many proteins "bind" DNA through positively charged amino acids on their surfaces. However, to overcome significant energetic and topological obstacles, proteins that bend or package DNA might also modulate the stiffness that is generated by repulsions between phosphates within DNA. Much previous work describes how ions change the flexibility of DNA in solution, but when considering macromolecules such as chromatin in which the DNA contacts the nucleosome core each turn of the double helix, it may be more appropriate to assess the flexibility of DNA on charged surfaces. Mica coated with positively charged molecules is a convenient substrate upon which the flexibility of DNA may be directly measured with a scanning force microscope. In the experiments described below, the flexibility of DNA increased as much as fivefold depending on the concentration and type of polyamine used to coat mica. Using theory that relates charge neutralization to flexibility, we predict that phosphate repulsions were attenuated by approximately 50% in the most flexible DNA observed. This simple method is an important tool for investigating the physiochemical causes and molecular biological effects of DNA flexibility, which affects DNA biochemistry ranging from chromatin stability to viral encapsulation.     

Atomic force microscope measurements of long-range forces near lipid-coated surfaces in electrolytes.

The interaction of DMPC (L-alpha-dimyristoyl-1,2-diterradecanoyl-sn-glycero-3-phosphoch oli ne, C36H72NO8P) lipid-coated Si3N4 surfaces immersed in an electrolyte was investigated with an atomic force microscope. A long-range interaction was observed, even when the Si3N4 surfaces were covered with nominally neutral lipid layers. The interaction was attributed to Coulomb interactions of charges located at the lipid surface. The experimental force curves were compared with solutions for the linearized as well as with exact solutions of the Poisson-Boltzmann equation. The comparison suggested that in 0.5 mM KCl electrolyte the DMPC lipids carried about one unit of charge per 100 lipid molecules. The presence of this surface charge made it impossible to observe an effective charge density recently predicted for dipole layers near a dielectric when immersed in an electrolyte. A discrepancy between the theoretical results and the data at short separations was interpreted in terms of a decrease in the surface charge with separation distance.     

Molecular-dynamic simulation of phospholipid bilayers: Ion distribution at the surface of neutral and charged bilayer in the liquid crystalline state

The electric field and ion distribution at the surface of neutral and charged lipid bilayers (BeCl₂ and dipalmitoyl phosphatidylcholine/dipalmitoyl phosphatidylserine (DPPC/DPPS) + KCl) were studied with molecular dynamic (MD) methods. It is shown that the contributions of lipid molecules, water and ions to the electric potential compensate each other in the region of the diffuse double layer and decrease the potential value close to zero. It is also demonstrated that the ion distribution at the charged surface is determined not only by the electrostatic ion-medium interaction. The total energy of this interaction was compared with the potential of mean ion force. It was shown that cations and anions have a different effect on the state of water molecules at the surface. The order parameter of water in the system DPPC + BeCl₂ and the Clion distribution have the extremum at the distance of 10 α atoms of the phospholipid glycerol. This position was chosen as the “electrical” interface of the electrical double layer (EDL) for all lipid systems studied. The potential of mean force of counter ions in EDL allows us to obtain the value of potential at the lipid surface suitable for experimental test of the MD data. This surface potential and surface charge density was found from MD simulation different electrolyte concentrations and DPPS content of 20, 40 and 60% in the mixture with DPPC and was shown to be in a good agreement with the Gouy-Chapman-Stern model upon fitting parameters close to their experimental values.     

Cation binding to membranes: Competition between mono-, di- and trivalent cations

The binding of mono-, di- and trivalent cations to negatively charged surfaces is studied within the framework of a modified Gouy-Chapman equation. For any given combination of ions of the above valences, the existence and uniqueness of the solution for the surface potential is shown. The treatment provides the surface potential and charge density. For a system containing only monovalent and divalent ions, analytical solutions are given. When trivalent ions are also present, a procedure based on numerical integration is described. The distance dependence of the electrostatic potential for planar surfaces is given. The calculations provide the amount of cations tightly bound and the amount trapped in the double layer region. The competition between cations for binding to surfaces is elucidated.     

Surface charge measurements on Micrococcus lysodeikticus and the catalytic implications for lysozyme

Electrophoresis measurements on Micrococcus lysodeikticus have shown that the net surface charge density on the cell wall is constant at around -1.5 microC/cm2 for the pH range 4-8. This result has enabled a quantitative analysis to be made of how the electrostatic field associated with the negatively charged cell wall influences the ionic strength and pH dependency of the lytic activity of lysozyme towards M. lysodeikticus. A dominant effect is the creation of a local pH gradient at the cell wall, and at high ionic strengths the lytic activity is found to be controlled by an electrostatic force of attraction between the lysozyme molecule and the cell wall. As the ionic strength of the supporting electrolyte is decreased, however, an electrostatic force of repulsion becomes dominant and is associated with a negative charge carried by the lysozyme molecule, which could possibly be the ionized Asp-52 residue at the active site. This is considered to arise from the fact that at low ionic strengths the fine details of the heterogeneous charge distribution on the cell wall and lysozyme molecule are only partially screened by counter ions.