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.     

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.     

Study of the DNA/ethidium bromide interactions on mica surface by atomic force microscope: influence of the surface friction

The influence of mica surface on DNA/ethidium bromide interactions is investigated by atomic force microscopy (AFM). We describe the diffusion mechanism of a DNA molecule on a mica surface by using a simple analytical model. It appears that the DNA diffusion on a mica surface is limited by the surface friction due to the counterion correlations between the divalent counterions condensed on both mica and DNA surfaces. We also study the structural changes of linear DNA adsorbed on mica upon ethidium bromide binding by AFM. It turns out that linear DNA molecules adsorbed on a mica surface are unable to relieve the topological constraint upon ethidium bromide binding. In particular, strongly adsorbed molecules tend to be highly entangled, while loosely bound DNA molecules appear more extended with very few crossovers. Adsorbed DNA molecules cannot move freely on the surface because of the surface friction. Therefore, the topological constraint increases due to the ethidium bromide binding. Moreover, we show that ethidium bromide has a lower affinity for strongly bound molecules due to the topological constraint induced by the surface friction.     

Electron and scanning force microscopy studies of alterations in supercoiled DNA tertiary structure.

The configuration of supercoiled DNA (scDNA) was investigated by electron microscopy and scanning force microscopy. Changes in configuration were induced by varying monovalent/divalent salt concentrations and manifested by variation in the number of nodes (crossings of double helical segments). A decrease in the concentration of monovalent cations from 50 mM to approximately 1 mM resulted in a significant change of apparent configuration of negatively supercoiled DNA from a plectonemic form with virtually approximately 15 nodes (the value expected for molecules of approximately 3000 bp) to one or two nodes. This result was in good agreement with values calculated using an elastic rod model of DNA and salt concentration in the range of 5-50 mM. The effect did not depend on the identity of the monovalent cation (Na(+), K(+)) or the nature of the support used for electron microscopy imaging (glow-discharged carbon film, polylysine film). At very low salt concentrations, a single denatured region several hundred base-pairs in length was often detected. Similarly, at low concentrations of divalent cations (Mg(2+), Ca(2+), Zn(2+)), scDNA was apparently relaxed, although the effect was slightly dependent on the nature of the cation. Positively supercoiled DNA behaved in a manner different from that of its negative counterpart when the ion concentration was varied. As expected for these molecules, an increase in salt concentration resulted in an apparent relaxation; however, a decrease in salt concentration also led to an apparent relaxation manifested by a slight decrease in the number of nodes. Scanning force microscopy imaging of negatively scDNA molecules deposited onto a mica surface under various salt conditions also revealed an apparent relaxation of scDNA molecules. However, due to weak interactions with the mica surface in the presence of a mixture of mono/divalent cations, the effect occurred under conditions differing from those used for electron microscopy. We conclude that the observed changes in scDNA configuration are inherent to the DNA structure and do not reflect artifacts arising from the method(s) of sample preparation.     

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.     

Plasmid DNA adsorption on silica: kinetics and conformational changes in monovalent and divalent salts

A quartz crystal microbalance with dissipation (QCM-D) is used to determine the adsorption rate of a supercoiled plasmid DNA onto a quartz surface and the structure of the resulting adsorbed DNA layer. To better understand the DNA adsorption mechanisms and the adsorbed layer physicochemical properties, the QCM-D data are complemented by dynamic light scattering measurements of diffusion coefficients of the DNA molecules as a function of solution ionic composition. The data from simultaneous monitoring of variations in frequency and dissipation energy with the QCM-D suggest that the adsorbed DNA layer is more rigid in the presence of divalent (calcium) cations compared to monovalent (sodium) cations. Adsorption rates are significantly higher in the presence of calcium, attaining a transport-limited rate at about 1 mM Ca2+. Results further suggest that in low ionic strength solutions containing 1 mM Ca2+ and in moderately high ionic strength solutions containing 300 mM NaCl, plasmid DNA adsorption to negatively charged mineral surfaces is irreversible.     

Molecular Forces for the Binding and Condensation of DNA Molecules

Atomic force microscopy has been used to investigate the binding between a double-stranded DNA and bilayers of cationic lipids and zwitterionic lipids in low ionic-strength solutions. The binding of a DNA molecule to freshly cleaved mica surface in solution has also been measured. The binding of DNA molecules to cationic lipid bilayers has a minimal strength of ∼45 pN. On zwitterionic lipid bilayers and mica surface, the minimal binding strength is approximately twice that value. The binding also has a dynamic nature, with only a certain percentage of recorded force curves containing the binding characteristics. Divalent Mg²⁺ ions enhance the binding by increasing that percentage without any effect on the binding strength. We have also observed a long-range attraction between DNA molecules and cationic lipid bilayers with a strength much larger than the minimum force and a range well over 50 nm, possibly related to the driving force responsible for the two-dimensional condensation of DNA.     

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.

     

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.     

Atomic force microscopy imaging of DNA under macromolecular crowding conditions

Studying the influence of macromolecular crowding at high ionic strengths on assemblies of biomolecules is of particular interest because these are standard intracellular conditions. However, up to now, no techniques offer the possibility of studying the effect of molecular crowding at the single molecule scale and at high resolution. We present a method to observe double-strand DNA under macromolecular crowding conditions on a flat mica surface by atomic force microscope. By using high concentrations of monovalent salt ([NaCl] > 100 mM), we promote DNA adsorption onto NiCl 2 pretreated muscovite mica. It therefore allows analysis of DNA conformational changes and DNA compaction induced by polyethylene glycol (PEG), a neutral crowding agent, at physiological concentrations of monovalent salt.     

Divalent cation-induced surface tension increase in acidic phospholipid membranes: Ion binding and membrane fusion

Chelation binding of divalent cations to phospholipid membranes may cause deformation in the headgroup regions of these lipid molecules. This deformation may be responsible for the observed large increase in surface tension of acidic phospholipid membranes induced by divalent cations. On the other hand, simple binding of monovalent cations without being followed by such a deformation of membrane molecules, does not result in a large surface tension increase in the membrane. A theoretical explanation for the above situation is given and the divalent cation-induced acidic phospholipid membrane fusion as well as other lipid membrane fusions are discussed in terms of the increased surface energy of membranes.     

Self-assembly effect during the adsorption of polynucleotides on stearic acid langmuir-blodgett monolayer

Interaction of polyadenylic acid, poly(A), with stearic acid Langmuir-Blodgett (LB) monolayer was studied in different electrolyte surroundings. For this purpose LB films of stearic acid, transferred on the mica substrate from poly(A) containing subphase, were analyzed with atomic force microscopy (AFM). The density of polynucleotides surface coverage is ruled by the monovalent electrolyte concentration in the subphase that is in good agreement with previous results. Divalent cations in the subphase are needed to stabilize poly(A) molecules on the surface through formation of "salt bridges". At the very low divalent electrolyte concentration polynucleotides adsorb on the LB film to domains in which the effect of self-assembly is observed. Increase of divalent electrolyte concentration leads to the loss of this orientation effect. The explanation of this effect is proposed.     

The iso-competition point for counterion competition binding to DNA: calculated multivalent versus monovalent cation binding equivalence.

In this paper we introduce an important parameter called the iso-competition point (ICP), to characterize the competition binding to DNA in a two-cation-species system. By imposing the condition of charge neutralization fraction equivalence theta1 = ZthetaZ upon the two simultaneous equations in Manning's counterion condensation theory, the ICPs can be calculated. Each ICP, which refers to a particular multivalent concentration where the charge fraction on DNA neutralized from monovalent cations equals that from the multivalent cations, corresponds to a specific ionic strength condition. At fixed ionic strength, the total DNA charge neutralization fractions thetaICP are equal, no matter whether the higher valence cation is divalent, trivalent, or tetravalent. The ionic strength effect on ICP can be expressed by a semiquantitative equation as ICPZa/ICPZb = (Ia/Ib)Z, where Ia, Ib refers to the instance of ionic strengths and Z indicates the valence. The ICP can be used to interpret and characterize the ionic strength, valence, and DNA length effects on the counterion competition binding in a two-species system. Data from our previous investigations involving binding of Mg2+, Ca2+, and Co(NH3)63+ to lambda-DNA-HindIII fragments ranging from 2.0 to 23.1 kbp was used to investigate the applicability of ICP to describe counterion binding. It will be shown that the ICP parameter presents a prospective picture of the counterion competition binding to polyelectrolyte DNA under a specific ion environment condition.     

Thermodynamics of cation-induced DNA condensation.

An estimation of the various free energy contributions to DNA collapse into toroidal particles is made, considering DNA bending and segment mobility, electrostatic repulsions between DNA chains, and attractive forces resulting from correlated counterion fluctuations. It is shown that the process of DNA condensation becomes spontaneous in the presence of divalent cations in methanol, and in the presence of tri- or tetravalent cations in water media. This is a consequence of the large decrease in the electrostatic repulsion between charged DNA segments, allowing the attractive force resulting from correlated fluctuations of bound counterions to become dominant. Our calculations indicate that short DNA fragments would condense into multimolecular particles in order to maximize the attractive force due to counterion fluctuations.     

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.     

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.     

High-resolution AFM imaging of single-stranded DNA-binding (SSB) protein--DNA complexes

DNA in living cells is generally processed via the generation and the protection of single-stranded DNA involving the binding of ssDNA-binding proteins (SSBs). The studies of SSB-binding mode transition and cooperativity are therefore critical to many cellular processes like DNA repair and replication. However, only a few atomic force microscopy (AFM) investigations of ssDNA nucleoprotein filaments have been conducted so far. The point is that adsorption of ssDN A-SSB complexes on mica, necessary for AFM imaging, is not an easy task. Here, we addressed this issue by using spermidine as a binding agent. This trivalent cation induces a stronger adsorption on mica than divalent cations, which are commonly used by AFM users but are ineffective in the adsorption of ssDNA-SSB complexes. At low spermidine concentration (<0.3 mM), we obtained AFM images of ssDNA-SSB complexes (E. coli SSB, gp32 and yRPA) on mica at both low and high ionic strengths. In addition, partially or fully saturated nucleoprotein filaments were studied at various monovalent salt concentrations thus allowing the observation of SSB-binding mode transition. In association with conventional biochemical techniques, this work should make it possible to study the dynamics of DNA processes involving DNA-SSB complexes as intermediates by AFM.     

Electrostatics of membrane adhesion.

We consider electrical double layer interaction under the conditions typically encountered during membrane fusion. Within the physiological concentration range of monovalent electrolytes the interaction is repulsive and the Poisson-Boltzmann calculation may be used to evaluate the force. When divalent counterions are added, strong ion-ion correlations make the Poisson-Boltzmann approximation inapplicable. We use the anisotropic hypernetted chain method to show that in the presence of small amounts of divalent counterions in adsorption equilibrium with the surfaces, the double layer interaction turns into attraction. This attractive electrostatic force may be the balancing contribution controlling membrane adhesion.     

Specific interactions versus counterion condensation. 2. Theoretical treatment within the counterion condensation theory

Polyuronates such as pectate and alginate are very well-known examples of biological polyelectrolytes undergoing, upon addition of divalent cations, an interchain association that acts as the junction of an eventually formed stable hydrogel. In the present paper, a thermodynamic model based on the counterion condensation theory has been developed to account for this cation-induced chain pairing of negatively charged polyelectrolytes. The strong interactions between cross-linking ions and uronate moieties in the specific binding site have been described in terms of chemical bonding, with complete charge annihilation between the two species. The chain-pairing process is depicted as progressively increasing with the concentration of cross-linking counterions and is thermodynamically defined by the fraction of each species. On these bases, the total Gibbs energy of the system has been expressed as the sum of the contributions of the Gibbs energy of the (single) chain stretches and of the (associated) dimers, weighted by their respective fractions 1 - theta and theta. In addition, the model assumes that the condensed divalent counterions exhibit an affinity free-energy for the chain, G(C)(aff,0), and the junction, G(D)(aff,0), respectively. Moreover, a specific Gibbs energy of chemical bonding, G(bond,0), has been introduced as the driving force for the formation of dimers. The model provides the mathematical formalism for calculating the fraction, theta, of chain dimers formed and the amount of ions condensed and bound onto the polyelectrolyte when two different types of counterions (of equal or different valence) are present. The effect of the parameter G(bond,0) has been investigated and, in particular, its difference from G(C,D)(aff,0) was found to be crucial in determining the distribution of the ions into territorial condensation and chemical bonding, respectively. Finally, the effect of the variation of the molar ratio between cross-linking ions and uronic groups in the specific binding sites, sigma0, was evaluated. In particular, a remarkable decrease in the amount of condensed counterions has been pointed out in the case of sigma0 = 1/3, with respect to the value of sigma0 = 1/4, characterizing the traditional "egg-box" structure, as a result of the drop of the charge density of the polyelectrolyte induced by complete charge annihilation.     

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.