Electrostatics of phosphoinositide bilayer membranes. Theoretical and experimental results.

We made fluorescence, electron paramagnetic resonance (EPR), electrophoretic mobility, and ionizing electrode measurements to study the effect of the monovalent lipid phosphatidylinositol (PI) and the trivalent lipid phosphatidylinositol 4,5-bisphosphate (PIP2) on the electrostatic potential adjacent to bilayer membranes. When the membranes were formed from mixtures of PI and the zwitterionic lipid phosphatidylcholine (PC), the Gouy-Chapman-Stern (GCS) theory described adequately the dependence of potential on distance (0, 1, 2 nm) from the membrane, mole % negative lipid, and [KCI]. Furthermore, all EPR and fluorescence probes reported identical surface potentials with a PC/PI membrane. With PC/PIP2 membranes, however, the anionic (coion) probes reported less negative potentials than the cationic (counterion) probes; the deviations from the GCS theory were greater for the coions than the counterions. Discreteness-of-charge theories based on the Poisson-Boltzmann equation incorrectly predict that deviations from the GCS theory should be greater for counterions than for coions. We discuss a consistent statistical mechanical theory that takes into account three effects ignored in the GCS theory: the finite size of the ions in the double layer, the electrical interaction between pairs of ions (correlation effects), and the mobile discrete nature of the surface charges. This theory correctly predicts that deviations from GCS theory should be negligible for monovalent lipids, significant for trivalent lipids, and greater for coions than for counterions.     

Limiting-laws of polyelectrolyte solutions. Ionic distribution in mixed-valency counterions systems. II. A comparison of conductometric data and theoretical predictions

The competitive binding of monovalent and divalent counterions (M+ and M2+, respectively) has been studied by a conductometric procedure as described by De Jong et al. (Biophysical Chemistry 27 (1987) 173) for aqueous solutions of alkali metal polymethacrylates in the presence of Ca (NO3)2 or Mg(NO3)2. The experimentally obtained fractions of conductometrically free counterions are compared with theoretical values computed according to a new thermodynamic model recently developed by Paoletti et al. (Biophysical Chemistry, 41 (1991) 73). For the systems studied, the fractions of free monovalent and divalent counterions can be fairly well described by the theory. In fact, the results support the assumption that under the present conditions the conductometrically obtained distribution parameters (l) and (2) approximate the equilibrium fractions of free monovalent and divalent counterions. For a degree of neutralization of 0.8 and a molar concentration ratio of divalent counterions and charged groups on the polyion up to 0.25, the mean M+/M2+, exchange ratio nu has been found to be 1.39 +/- 0.03 and 1.33 +/- 0.03 for the alkali metal/Ca/PMA and alkali metal/Mg/PMA systems, respectively. These values agree well with the theoretical value, which for this particular case is 1.38.     

Adsorption of DNA to mica mediated by divalent counterions: a theoretical and experimental study

The adsorption of DNA molecules onto a flat mica surface is a necessary step to perform atomic force microscopy studies of DNA conformation and observe DNA-protein interactions in physiological environment. However, the phenomenon that pulls DNA molecules onto the surface is still not understood. This is a crucial issue because the DNA/surface interactions could affect the DNA biological functions. In this paper we develop a model that can explain the mechanism of the DNA adsorption onto mica. This model suggests that DNA attraction is due to the sharing of the DNA and mica counterions. The correlations between divalent counterions on both the negatively charged DNA and the mica surface can generate a net attraction force whereas the correlations between monovalent counterions are ineffective in the DNA attraction. DNA binding is then dependent on the fractional surface densities of the divalent and monovalent cations, which can compete for the mica surface and DNA neutralizations. In addition, the attraction can be enhanced when the mica has been pretreated by transition metal cations (Ni(2+), Zn(2+)). Mica pretreatment simultaneously enhances the DNA attraction and reduces the repulsive contribution due to the electrical double-layer force. We also perform end-to-end distance measurement of DNA chains to study the binding strength. The DNA binding strength appears to be constant for a fixed fractional surface density of the divalent cations at low ionic strength (I < 0.1 M) as predicted by the model. However, at higher ionic strength, the binding is weakened by the screening effect of the ions. Then, some equations were derived to describe the binding of a polyelectrolyte onto a charged surface. The electrostatic attraction due to the sharing of counterions is particularly effective if the polyelectrolyte and the surface have nearly the same surface charge density. This characteristic of the attraction force can explain the success of mica for performing single DNA molecule observation by AFM. In addition, we explain how a reversible binding of the DNA molecules can be obtained with a pretreated mica surface.     

Thermal membrane potential across charged membranes in 2-1 and 1-2 electrolyte solutions

Measurements of thermal membrane potential across cation exchange membranes in MgCl2, CaCl2 and BaCl2 solutions and across anion exchange membranes in K2SO4, Na2SO4 and K2CO3 solutions were carried out. The magnitude of the thermal membrane potential for divalent counterions is lower than that for monovalent counterions. If the transport number of counterions in the membrane phase is unity, the slopes of the temperature coefficient of thermal membrane potential against logarithmic activities of counterion in the external solution are predicted to be--R/2F for 2-1 electrolytes with cation exchange membranes and R/2F for 1-2 electrolytes with anion exchange membranes, respectively.     

Adsorption of monovalent and divalent cations by phospholipid membranes. The monomer-dimer problem.

A generalization of the Stern theory is derived to treat the simultaneous adsorption of monovalent cations and divalent cations by single-component phospholipid membranes, where the ion:phospholipid binding stoichiometries are 1:1 for the monovalent cations and 1:1 and/or 1:2 for the divalent cations. This study treats both the situation in which the monovalent and divalent cations compete for membrane binding sites and that in which they do not compete. The general formalism of the screening/binding problem is reviewed, and it is shown how the adsorption problem can be isolated from the electrostatics. The statistical mechanics of mixed 1:1- and 1:2-stoichiometric adsorption (the monomer-dimer problem) is treated, and the problem of simultaneous 1:1 and 1:2 binding is solved. A simple expression for this solution, given in the Bethe approximation, is combined with the electrostatics to yield an adsorption isotherm encompassing both 1:1 monovalent-cation, and 1:1 and 1:2 divalent-cation, binding to charged membranes. A comparison with the simplified treatment of previous authors is made and the significance of their assumptions clarified in light of the present result. The present and previous treatments are plotted for a representative case of Na+ and Ca++ binding to a phosphatidylserine membrane. Criteria are established to permit unambiguous experimental testing of the present vs. previous treatments.     

Clustering of macroions in solutions of highly asymmetric electrolytes

In this paper, we present results of computer simulations for a primitive model of asymmetric electrolyte solutions containing macroions, counterions and in a few cases, also co-ions. The results show that the valency of counterions plays an important role in shaping the net interaction between the macroions. For solutions with monovalent counterions, the macroions are distributed at larger distances, and in solutions with divalent counterions, the macroions come closer to each other and share a layer of counterions, whereas, in solutions with trivalent counterions, the macroions form clusters. These clusters dissolve upon dilution or addition of a simple electrolyte. These findings suggest a mechanism whereby the nonuniform distribution of macroions observed experimentally in charged systems may occur.     

Large divalent cations and electrostatic potentials adjacent to membranes. A theoretical calculation

We have extended the Gouy-Chapman theory of the electrostatic diffuse double layer by considering the finite size of divalent cations in the aqueous phase adjacent to a charged surface. The divalent cations are modeled as either two point charges connected by an infinitely thin, rigid "rod" or two noninteracting point charges connected by an infinitely thin, flexible "string." We use the extended theory to predict the effects of a cation of length 10 A (1 nm) on the zeta and surface potentials of phospholipid bilayer membranes. The predictions of the rod and string models are similar to one another but differ markedly from the predictions of the Gouy-Chapman theory. Specifically, the extended model predicts that a large divalent cation will have a smaller effect on the potential adjacent to a negatively charged bilayer membrane than a point divalent cation, that the magnitude of this discrepancy will decrease as the Debye length increases, and that a large divalent cation will produce a negative zeta potential on a membrane formed from zwitterionic lipids. These predictions agree qualitatively with the experimental results obtained with the large divalent cation hexamethonium. We discuss the biological relevance of our calculations in the context of the interaction of cationic drugs with receptor sites on cell membranes.     

Flexible charged macromolecules on mixed fluid lipid membranes: theory and Monte Carlo simulations

Fluid membranes containing charged lipids enhance binding of oppositely charged proteins by mobilizing these lipids into the interaction zone, overcoming the concomitant entropic losses due to lipid segregation and lower conformational freedom upon macromolecule adsorption. We study this energetic-entropic interplay using Monte Carlo simulations and theory. Our model system consists of a flexible cationic polyelectrolyte, interacting, via Debye-Hückel and short-ranged repulsive potentials, with membranes containing neutral lipids, 1% tetravalent, and 10% (or 1%) monovalent anionic lipids. Adsorption onto a fluid membrane is invariably stronger than to an equally charged frozen or uniform membrane. Although monovalent lipids may suffice for binding rigid macromolecules, polyvalent counter-lipids (e.g., phosphatidylinositol 4,5 bisphosphate), whose entropy loss upon localization is negligible, are crucial for binding flexible macromolecules, which lose conformational entropy upon adsorption. Extending Rosenbluth's Monte Carlo scheme we directly simulate polymer adsorption on fluid membranes. Yet, we argue that similar information could be derived from a biased superposition of quenched membrane simulations. Using a simple cell model we account for surface concentration effects, and show that the average adsorption probabilities on annealed and quenched membranes coincide at vanishing surface concentrations. We discuss the relevance of our model to the electrostatic-switch mechanism of, e.g., the myristoylated alanine-rich C kinase substrate protein.     

A test of discreteness-of-charge effects in phospholipid vesicles: measurements using paramagnetic amphiphiles

A new series of negatively charged, paramagnetic alkylsulfonate probes was synthesized and can be used to measure both the internal and the external surface potentials of model membrane systems. We tested for discreteness-of-charge effects in lipid membranes by comparing the surface potentials, estimated by use of these negatively charged amphiphiles, with that of a series of positively charged alkylammonium nitroxides in charged membranes. From the partitioning of these probes, the membrane surface potential was estimated in phosphatidylcholine membranes containing either phosphatidylserine or didodecyldimethylammonium bromide. The surface potentials, estimated with either positive or negative probes, were identical, within experimental error, in either positive or negative membranes, and they were well accounted for by a simple Gouy-Chapman-Stern theory. This symmetry, with respect to the sign of the charge, indicates that discreteness-of-charge effects are not significant in determining the potential-sensitive phase partitioning of these probes in model membranes. Thus, despite the fact that charge on membranes is discrete, models that assume a uniform density of charge in the plane of the membrane adequately account for the potentials measured by these amphiphilic probes.     

Effect of finite ionic size on the solution of the Poisson-Boltzmann equation: Application to the binding of divalent metal ions to DNA

The nonlinear Poisson-Boltzmann equation is solved for a cylindrical polyelectrolyte solution containing mono- and divalent counterions and monovalent coions. The finite size of the ions is taken into account by the introduction of the distances of closest approach between the ionic charges and the surface of the polyelectrolyte. The choice of these distances is based on the physicochemical properties of the polyelectrolyte and ions in solution. The effects of the finite ionic size on the distribution of the counterions around the polyelectrolyte and on the local ion concentration and the integrated charge fraction of the divalent cations in the vicinity of the polyelectrolyte are discussed. Theoretical predictions regarding the overall extent of binding and the extent of inner-sphere binding of divalent counterions to rodlike polyions are compared with the results of nmr studies of the binding of divalent metal ions to DNA.     

Kinetics of prothrombin-mediated binding of lupus anticoagulant antibodies to phosphatidylserine-containing phospholipid membranes: an ellipsometric study

Antiphospholipid antibodies interact with phospholipid membranes via lipid binding plasma proteins, mostly, prothrombin and beta(2)-glycoprotein I. Using ellipsometry, we characterized prothrombin-mediated binding of lupus anticoagulant (LA) positive IgG, isolated from patients with antiphospholipid syndrome, to phosphatidylserine (PS)-containing membranes. LA IgG did not bind to membranes in the absence of prothrombin, but addition of prothrombin resulted in high-affinity binding of prothrombin-LA IgG complexes; half-maximal binding was attained at IgG and prothrombin concentrations of 10 microg/mL and 4 nM, respectively. Adsorption to membranes containing 10-40 mol % PS revealed that membrane-bound rather than solution-phase prothrombin determines the adsorption kinetics. Depletion of prothrombin and LA IgG from the solution results in rapid desorption which is strongly inhibited by addition of prothrombin but not of LA IgG. Prothrombin-mediated adsorption of monovalent Fab1 fragments prepared from patient LA IgG was negligible, indicating that monovalent interaction between prothrombin and LA IgG is weak. The kinetics of adsorption and desorption indicate that divalent binding of LA IgG to prothrombin at the lipid membrane occurs.     

Interactions of mono- and divalent counterions with alkali- and enzyme-deesterified pectins in salt-free solutions

The free fractions of monovalent and divalent counterions were determined on salt-free solutions of pectins. The effects of charge density, distribution of the carboxyl groups, polymer concentration, and the nature of the counterion were investigated by determinating the calcium and sodium activity coefficients (with specific electrodes) and by measuring the transport parameters (by conductimetry). Poor agreement for calcium ions was found with the Manning theory. The strong binding of these ions to highly charged polymers, which is ascribed to a dimerization process was demonstrated in very dilute solutions.     

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.     

Intrinsic binding effects in mixed counterionic polyelectrolyte systems: extension of condensation theory and comparison with voltammetric data

Voltammetric speciation data for the potassium/zinc/polymethacrylate system, recently obtained for various charge densities of the polyelectrolyte (Díaz-Cruz et al., Anal. Chim. Acta, 264 (1992) 163) and for different concentrations of monovalent counterions (van den Hoop and van Leeuwen, Anal. Chim. Acta, 273 (1993) 275), are compared with theoretical predictions computed according to a new thermodynamic model developed by Paoletti et al. (Biophys. Chem., 41 (1991) 73) and recently extended by Benegas and Paoletti (in preparation). The model allows: (i) the simultaneous condensation of both monovalent and divalent counterions and (ii) can account for a certain specific affinity of the polyelectrolyte for one type of the counterion over the other. For various charge densities of the polyelectrolyte, experimentally obtained speciation data for the K/Zn/PMA system agree well with theoretical predictions by considering an extra reduced molar affinity energy of -4RT for the Zn(2+) polyelectrolyte binding. The agreement between experimental and theoretical values for the distribution of Zn(2+) ions over the free and bound state becomes less perfect for relatively high concentrations of monovalent counterions.     

Influence of monovalent and divalent cations on the surface area of phosphatidylglycerol monolayers

A theory is presented on the electrostatic properties of the surface area of phosphatidyl-glycerol monolayers spreading at an air-water interface in the presence of monovalent and divalent cations. In the present theory, the adsorption of monovalent and divalent cations to the membranes is taken into account, besides the dissociation of protons, as a possible cause of the change of surface charge density with the variation of pH or ion concentrations. It is also pointed out that, in the presence of structure-making ions such as Li⁺ and Na⁺, the nearest-neighbour interactions between proton dissociation sites become important for the monolayers in the gel state to yield a sharp expansion of the surface area with the increase of pH. The present theory shows quantitative agreements with previously-observed data.     

Divalent cations and the electrostatic potential around DNA: Monte Carlo and Poisson-Boltzmann calculations

The predictions of counterion condensation theory for divalent ions were tested by comparison with the results of Monte Carlo calculations on an all-atom model of DNA. Monovalent-divalent competition at the polyelectrolyte surface was investigated by varying the partial molar volume of divalent ions. To assess the viability of using Poisson-Boltzmann (PB) calculations for determining divalent ion concentrations at DNA surfaces, Monte Carlo (MC) calculations were compared with PB calculations using different models of the dielectric continuum. It was determined that, while standard PB calculations of divalent ion surface densities are about 25-30% below those predicted by MC techniques, and somewhat larger than errors previously determined for monovalent ions, errors due to the use of the mean-field approximation of PB theory are smaller than those arising from common assumptions regarding the dielectric continuum.     

The involvement of the electrical double layer in the quenching of 9-aminoacridine fluorescence by negatively charged surfaces.

The addition of 9-aminoacridine monohydrochloride to carboxymethyl-cellulose particles or azolectin liposomes suspended in a low cation medium results in a quenching of its fluorescence. This quenching can be released on the addition of cations. The effectiveness of cations is related only to their valency in the series of salts tested, being monovalent less than divalent less than trivalent, and is independent of the associated anions. These results indicate an electrical rather than a chemical effect, and the relative effectiveness of the various cations can be predicted by the application of classical electrical double layer theory. Fluorescence quenching can also be released on protonation of the fixed negatively charged ionisable groups, and the quenching release curve follows the ionisation curve of these groups. We postulate that when 9-aminoacridine molecules are in the electrical diffuse layer adjacent to the charged surface their fluorescence is quenched, probably due to aggregate formation. As cations are added the 9-aminoacridine concentration at the surface falls as it is displaced into the bulk solution, where it shows a high fluorescence yield with a fluorescence lifetime of 16.3 ns. The fluorescence quenching is associated with an absorbance decrease, which is pronounced with carboxymethyl-cellulose particles and can probably be attributed to self-shielding. The negative charges carried by lipoprotein membranes are primarily due to carboxyl and phosphate groups. Therefore these results with carboxymethyl-cellulose (carboxyl) and azolectin (phosphate) support our earlier suggestion that 9-aminoacridine may be used to probe the electrical double layer associated with negatively charged biological membranes.     

Limiting-laws of polyelectrolyte solutions. Ionic distribution in mixed-valency counterions systems. I: The model

An extension of the counterion-condensation (CC) theory of linear polyelectrolytes has been developed for the case of a system containing a mixture of counterions of different valency, i and j. The main assumption in the derivation of the model is that the relative amount of the condensed counterions of the type i and j is strongly correlated and it is determined by the overall physical bounds of the system. The results predicted by the model are consistent, in the limiting cases of single species component, with those of the original CC theory. The most striking results are obtained for the cases of low charge density and excess of counterion species: in particular, an apparent positive "binding" cooperativity of divalent ions is revealed for small, increasing additions of M2+ ions to a solution containing a swamping amount of monovalent salt and a polyelectrolyte of low charge density. Apparent "competitive binding" of mono- and divalent ions derives as a bare consequence of the electrostatic interactions. Theoretical calculations of experimentally accessible quantities, namely single-(counter) ion activity coefficients, confirm the surprising predictions at low charge density, which qualitatively agree with the measured quantities.     

Site-specific counterion binding and pectic chains conformational transitions in the Nitella cell wall

The types of binding of different mono- and divalent ions to sites of the constitutive pectic acids of the Nitella cell walls were investigated by performing ion exchanges at different pH. The experimental results were then analysed in the framework of a model derived from the polyelectrolyte theory in which the competitive process of dissociation of the exchange sites and their complexation by counterions are taken into account. Divalent ions Ca²⁺ and Mn²⁺ interacted specifically with the exchange sites to give rise to strong thermodynamic association constants. They also induced conformational transitions of the pectic acids which allowed some site-specific association with monovalent ions, although the latter, in the absence of divalent ions, interacted only in a purely electrostatic manner with the charged sites. The complexation phenomenon of the monovalent ions also results in a feedback process which enhances or depletes the site-specific interactions of the divalent counterions. Changes in the counterion association with the wall exchange sites will take place without modification in the wall electrostatic field, when divalent ions are present at the usual pH. These specific interactions are supported by the values of the residual interaction energy, calculated from the variations of the apparent pKa of the polygalacturonic acids with their degree of protonation.     

DNA like-charge attraction and overcharging by divalent counterions in the presence of divalent co-ions

Strongly correlated electrostatics of DNA systems has drawn the interest of many groups, especially the condensation and overcharging of DNA by multivalent counterions. By adding counterions of different valencies and shapes, one can enhance or reduce DNA overcharging. In this paper, we focus on the effect of multivalent co-ions, specifically divalent co-ions such as SO\(_{4}^{2-}\). A computational experiment of DNA condensation using Monte Carlo simulation in grand canonical ensemble is carried out where the DNA system is in equilibrium with a bulk solution containing a mixture of salt of different valency of co-ions. Compared to systems with purely monovalent co-ions, the influence of divalent co-ions shows up in multiple aspects. Divalent co-ions lead to an increase of monovalent salt in the DNA condensate. Because monovalent salts mostly participate in linear screening of electrostatic interactions in the system, more monovalent salt molecules enter the condensate leads to screening out of short-range DNA–DNA like charge attraction and weaker DNA condensation free energy. The overcharging of DNA by multivalent counterions is also reduced in the presence of divalent co-ions. Strong repulsions between DNA and divalent co-ions and among divalent co-ions themselves lead to a depletion of negative ions near the DNA surface as compared to the case without divalent co-ions. At large distances, the DNA–DNA repulsive interaction is stronger in the presence of divalent co-ions, suggesting that divalent co-ions’ role is not only that of simple stronger linear screening.