Ion atmosphere around nucleic acid

The poyion-ion preferential interaction coefficient Gamma describes the exclusion of coions and accumulations of counterions in the vicinity of a polyion in an aqueous solution. We give tight upper and lower bounds for Gamma when the polyion can be modeled by a cylinder of infinite length but of arbitrary charge density. This case can be used as a model for long strands of DNA or RNA in an aqueous solution containing univalent cations. The salt dependence of Gamma is predicted from low to intermediate and high salt concentrations. We also indicate how the bounds for the infinite polyion can be exploited to place bounds for polyions of length greater than a constant on the order of the inverse Debye screening length.     

Ionic correlations in the inhomogeneous atmosphere surrounding cylindrical polyions: catalytic effects of polyions

The structural properties of linear polyelectrolyte solutions in the presence of a salt as evidenced through ionic correlations in the inhomogeneous atmosphere around a polyion and their consequence such as the catalytic potential are studied by using Monte Carlo simulation techniques. The simulations are performed on the cylindrical cell model where a uniformly charged hard cylinder mimics the linear polyion, which is caged in its own cylindrical cell containing counterions and salt. The cell (volume) average of the interionic correlations is presented as a function of the polyion and salt concentrations and ion radius. These results are utilized to study the catalytic effects of polyions as manifested through the changes in the collision frequency between ions in the double layer surrounding the polyion relative to that in the pure electrolyte solution. The reported results suggest a strong influence of the added salt/polyelectrolyte concentration ratio on the structural properties of the solution and hence on ion-ion collision frequency. The machine simulations are supplemented by nonlinear Poisson-Boltzmann results. Fair agreement between two different theoretical methods of calculating the collision frequency is obtained.     

Interactions between charged surfaces immersed in a polyelectrolyte solution

With grand canonical simulations invoking a configurationally weighted scheme, we have calculated interactions between charged surfaces immersed in a polyelectrolyte solution. In contrast to previous simulations of such systems, we have imposed full equilibrium conditions (i.e., we have included diffusive equilibrium with a bulk solution). This has a profound impact on the resulting interactions: even at modest surface charge densities, oppositely charged chains will, at sufficiently large separations, adsorb strongly enough to overcompensate for the nominal surface charge. This phenomenon, known as charge inversion, generates a double-layer repulsion and a free-energy barrier. Simpler canonical approaches, where the chains are assumed to neutralize the surfaces perfectly, will not capture this stabilizing barrier. The barrier height increases with the length of the polyions. Interestingly enough, the separation at which the repulsion becomes attractive is independent of chain length. The short chains here are unable to reach across from one surface to the other. We therefore conclude that the transition to an attractive regime is not provided by the formation of such "intersurface" bridges. With long chains and at large separations, charge inversion displays decaying oscillatory behavior (i.e., the apparent surface charge switches sign once again). This is due to polyion packing effects. We have also investigated responses to salt addition and changes in polyelectrolyte concentration. Our results are in qualitative and semiquantitative agreement with experimental findings, although it should be noted that our chains are comparatively short, and the experimental surface charge density is poorly established.     

Explicit ions condensation around strongly charged polyelectrolytes and spherical macroions: the influence of salt concentration and chain linear charge density. Monte Carlo simulations

The condensation of monovalent counterions and trivalent salt particles around strong rigid and flexible polyelectrolyte chains as well as spherical macroions is investigated by Monte Carlo simulations. The results are compared with the condensation theory proposed by Manning. Considering flexible polyelectrolyte chains, the presence of trivalent salt is found to play an important role by promoting chain collapse. The attraction of counterions and salt particles near the polyelectrolyte chains is found to be strongly dependent on the chain linear charge density with a more important condensation at high values. When trivalent salt is added in a solution containing monovalent salt, the trivalent cations progressively replace the monovalent counterions. Ion condensation around flexible chains is also found to be more efficient compared with rigid rods due to monomer rearrangement around counterions and salt cations. In the case of spherical macroions, it is found that a fraction of their bare charge is neutralized by counterions and salt cations. The decrease of the Debye length, and thus the increase of salt concentration, promotes the attraction of counterions and salt particles at the macroion surface. Excluded volume effects are also found to significantly influence the condensation process, which is found to be more important by decreasing the ion size.     

Theory of polyelectrolyte adsorption onto surfaces patterned with charge and topography

Mean-field theory is used to derive criteria for the adsorption of a weakly charged polyelectrolyte molecule from salt solution onto surfaces patterned with charge and topography. For flat surfaces patterned with periodic arrays of charged patches, the adsorbed layer thickness predicted using mean-field theory and that found by Brownian dynamics simulations are in quantitative agreement in the strong-adsorption regime, which corresponds to sufficiently small kappa or sufficiently large |sigma(eff)q|, where kappa is the inverse Debye screening length, sigma(eff) is an effective surface charge density, and q is the charge on each segment of the polyelectrolyte. Qualitative agreement is obtained in the weak-adsorption regime, and for the case where surfaces are patterned with both charge and topography. For uniformly charged, sinusoidally corrugated surfaces, the theory predicts that the critical temperature required for adsorption can be greater than or less than the corresponding value for a flat surface depending on the relative values of kappa and the corrugation wave number. If the surface charge is also allowed to vary sinusoidally, then adsorption is predicted to occur only when the topography crests have a surface charge opposite to that of the polyelectrolyte. Surfaces patterned with rectangular indentations having charged bottoms which are separated by flat charged plateaus are investigated as well. Adsorption is predicted to occur even when the net surface charge is zero, provided that the plateaus have a charge opposite to that of the polyelectrolyte. If the charge on the plateaus and polyelectrolyte is the same, adsorption may still occur if electrostatic attraction from the indentation bottoms is sufficiently strong.     

Counterion-counterion correlation in the double layer around cylindrical polyions: counterion size and valency effects

Monte Carlo simulation and Poisson-Boltzmann results on some aspects of structure and thermodynamics of aqueous polyelectrolyte solutions are presented. The polyelectrolyte solution is described by an infinitely long cylindrical polyion surrounded by counterions modeled as rigid ions moving in a continuum dielectric. Ion-ion correlations in the form of volume average of the counterion-counterion distribution function in the double layer surrounding the polyion are reported for mono- and divalent counterions and for a range of polyion concentrations and charge density parameters in each case. These results confirm again strong influence of the charge density parameter of polyions on properties of polyelectrolyte solutions. The structural information is supplemented by the calculated thermodynamic properties such as osmotic coefficients and heats of dilutions; the latter quantity has not been examined yet in detail by computer simulations. The results are discussed in view of the existing experimental data from the literature for these properties.     

Self-diffusion in solutions of a 20 base pair oligonucleotide: effects of concentration and ionic strength

The long-time self-diffusion coefficients of a 20 base pair duplex oligonucleotide are measured as functions of 20-mer and added NaCl salt concentrations. The self-diffusion coefficients decrease monotonically with increasing 20-mer concentrations for the high-added salt sample and display non-monotonically decreasing 20-mer concentration dependences at lower added salt concentrations. The non-monotonic behavior is attributed to the opposing effects of the tendency to increase the interactions between 20-mers as the concentration is increased and to a decrease in the extent of the Coulomb forces as counterions from the 20-mer increasingly screen them. Attempts to account for the effect of the Coulomb forces on the self-diffusion coefficients by using effective dimensions in the hard rod theory give good agreement with experiment at the highest salt concentration studied. For the lower salt concentrations there appear to be two scaling regimes--one at low polyion concentration in which the high salt scaling of the rod dimensions by adding the Debye screening to the length and diameter of the rod is appropriate and one at high polyion concentrations where the scaling of the dimensions is the addition of 1/2 the Debye screening length. Estimates of the "overlap" concentration C*=1/L(eff) indicate that the non-monotonic decrease occurs at concentrations lower than C*. Finally, the fluorescence correlation spectroscopy self-diffusion coefficients measured here are compared with the mutual diffusion coefficients measured by dynamic light scattering.     

Stoichiometric polyelectrolyte complexes of ionic block copolymers and oppositely charged polyions

Micellization in dilute solutions of diblock copolymers with a polyelectrolyte and a hydrophilic nonionic blocks and oppositely charged polyions is studied using mean-field theory. In aqueous solutions the micelle core consists of the polyelectrolyte complex (PEC) while the corona is formed by hydrophilic blocks of the block copolymers. Describing PEC as a globule in the framework of the Lifshitz [Zh. Eksp. Teor. Fiz. 55, 2408 (1968)] globule theory we calculate the surface tension of the micellar core/solvent interface as a function of the polyion degree of ionization, solvent quality, and concentration of low-molecular-mass salt. The equilibrium aggregation number of starlike micelles formed by block copolymers and homopolymers of opposite charge at stoichiometric mixture compositions is found as a function of the system parameters. It is shown that micelles disintegrate upon addition of salt.     

Dynamics and Structure of Biopolyelectrolytes Characterized by Dielectric Spectroscopy

Structural properties of Na-DNA and Na-HA aqueous solutions can be quantified using dielectric spectroscopy in the frequency range 100 Hz–100 MHz. Two relaxation modes are typically detected that can be attributed to diffusive motion of polyion counterions. The overall study as a function of polyion length, concentration and added salt concentration demonstrates that the motion of polyion counterions detected at MHz frequencies probes collective properties, whereas the motion at kHz range probes single-chain properties of polyelectrolytes. Fundamental length scales found to characterize the polyelectrolyte structure differ for the dilute and semidilute regime and also depend on the strength of electrostatic interactions and the flexibility. Characteristic length scales detected in the dielectric spectroscopy measurements compare well with the fundamental length scales predicted by theory and comply with those extracted from small-angle X-ray scattering.     

Counterion condensation on charged spheres, cylinders, and planes

We use the framework of counterion condensation theory, in which deviations from linear electrostatics are ascribed to charge renormalization caused by collapse of counterions from the ion atmosphere, to explore the possibility of condensation on charged spheres, cylinders, and planes immersed in dilute solutions of simple salt. In the limit of zero concentration of salt, we obtain Zimm-Le Bret behavior: a sphere condenses none of its counterions regardless of surface charge density, a cylinder with charge density above a threshold value condenses a fraction of its counterions, and a plane of any charge density condenses all of its counterions. The response in dilute but nonzero salt concentrations is different. Spheres, cylinders, and planes all exhibit critical surface charge densities separating a regime of counterion condensation from states with no condensed counterions. The critical charge densities depend on salt concentration, except for the case of a thin cylinder, which exhibits the invariant criticality familiar from polyelectrolyte theory.     

Neutron scattering from polyelectrolyte solutions

The neutron scattering intensity from polyelectrolyte solutions is calculated using an asymmetric primitive model electrolyte for the computation of the partial structure factors and a Debye function for the polyion form factor. The variation of the intensity with wavevector and concentration agrees with experimental results.     

Complexation of anionic polyelectrolytes with cationic liposomes: evidence of reentrant condensation and lipoplex formation

We have studied the complexation process taking place in cationic liposomes in the presence of anionic polyelectrolytes, in the polyion concentration range from the dilute to the concentrated regime, by combining dynamic light scattering and transmission electron microscopy techniques. We employed as the cationic lipid a two-chained amphiphile (Dioleoyltrimethylammoniumpropane) and sodium polyacrylate salt as the flexible anionic polyelectrolyte. The results evidence a variety of different structures, mainly depending on the liposome-polyion charge ratio, whose peculiar dynamical and structural features are briefly described. In particular, three different polyion concentration regions are found, within which a monomodal or bimodal distribution of aggregates, with a well-defined time evolution, is present. At low polyion content, close to the isoelectric point, large aggregates are formed, deriving from the collapse of the liposomal bilayers into extended charged surfaces, where adsorbed polyions form a two-dimensional strongly correlated array and organize into a two-dimensional Wigner liquid. At high polyion content, above a critical concentration, the size distributions of the complexes are clearly bimodal and a large-component aggregate, continuously increasing with time, coexists with a population of smaller-size aggregates. At an intermediate polyion concentration, spherical, small-size vesicular structures are reformed, connected in a network by polymer chains. A brief discussion tries to summarize our results into a consistent picture.     

Counterion release from adsorbed highly charged polyelectrolyte: an electrooptical study

The adsorption of sodium poly(4-styrene sulfonate) on oppositely charged beta-FeOOH particles is studied by electrooptics. The focus of this paper is on the release of condensed counterions from adsorbed polyelectrolyte upon surface charge overcompensation. The fraction of condensed Na+ counterions on the adsorbed polyion surface is estimated according to the theory of Sens and Joanny and it is compared with the fraction of condensed counterions on nonadsorbed polyelectrolyte. The relaxation frequency of the electrooptical effect from the polymer-coated particle is found to depend on the polyelectrolyte molecular weight. This is attributed to polarization of the layer from condensed counterions on the polyion surface, being responsible for creation of the effect from particles covered with highly charged polyelectrolyte. The number of the adsorbed chains is calculated also assuming counterion condensation on the adsorbed polyelectrolyte and semiquantative agreement is found with the result obtained from the condensed counterion polarizability of the polymer-coated particle. Our findings are in line with theoretical predictions that the fraction of condensed counterions remains unchanged due to the adsorption of highly charged polyelectrolyte onto weakly charged substrate.     

Phenomenological surface characterization of cationic-lipid monolayers in the presence of oppositely charged polyions

The thermodynamic properties of monolayers of double chain cationic lipids DOTAP at the air–water interface have been investigated by means of surface pressure and surface potential measurements. We studied the interfacial properties of the film in the liquid-expanded regime during the isothermal compression in the presence of oppositely charged linear polyions (poly(acrylate)sodium salt, [NaPA]) of different molecular weights. The influence of the ionic character of the aqueous subphase on the polyion adsorption has been studied in different environmental conditions, considering different subphase compositions, ranging from a polyion solution at different concentrations to a salty polyion solution, containing different amount of simple added salt [NaCl]. The data are compared to the ones when only NaCl salt is present in the subphase. The results have been analyzed according to an osmotic-type equation of state and the characteristic parameter associated with the water activity has been evaluated as a function the different molecular weight polyion content. The influence of the simple salt in the adsorption process has been discussed in the light of current scaling theories of polyelectrolyte solutions and the critical salt concentrations inducing a polyion desorption in the different experimental conditions investigated have been estimated.     

Packaging of a flexible polyelectrolyte inside a viral capsid: effect of salt concentration and salt valence

The effect of salt on the location and structure of a flexible polyelectrolyte confined inside a viral capsid and the Donnan equilibrium of the salt across the capsid have been examined using a coarse-grained model solved by Monte Carlo simulations. The polyelectrolyte was represented by a linear jointed chain of charged beads, and the capsid was represented by a spherical shell with embedded charges. At low salt concentration, the polyelectrolyte was strongly adsorbed onto the inner capsid surface, whereas at high salt concentration it was located preferentially in the central part of the capsid. Under the condition of equal Debye screening length, the electrostatic screening increased as the valence of the polyelectrolyte counterion was increased. The distribution of the small cations and anions was unequal across the capsid. An excess of polyelectrolyte counterions occurred inside the capsid, and the excess increased with the salt concentration. A simplified representation of the small ions through the use of the screened Coulomb potential provided only a qualitatively correct picture; the electrostatic screening originating from the small ions was exaggerated.     

Increased layer interdiffusion in polyelectrolyte films upon annealing in water and aqueous salt solutions

As-deposited films of multilayered polyelectrolytes are considered to be non-equilibrium structures. Due to the strong attraction between oppositely charged polyions, polyelectrolyte interdiffusion is thought to be suppressed during the adsorption process. Equilibration is promoted by a decrease of the electrostatic attraction between polyion pairs. We have used neutral impact collision ion scattering spectroscopy to investigate the influence of polyelectrolyte multilayer annealing in water and aqueous 1 M NaCl solutions at different temperatures (20 and 70 degrees C) on the increase in interpenetration of a single polyelectrolyte layer throughout the whole film. The multilayers were composed of poly(4-vinylpyridinium) and poly(4-styrenesulfonate). Contrast between neighboring layers was established by labelling the layer in question with the heavy atom ruthenium. It is found that both temperature and salt increase layer interpenetration, whereas salt has a stronger influence than temperature. From numerical simulations polyelectrolyte diffusion coefficients were evaluated for the different annealing conditions. The influence of temperature and salt on the equilibration of the film is interpreted in terms of increased screening of polyion charges and binding of small counterions to polyion monomeric units.     

The Formation and Salt Induced Melting of a Highly Viscoelastic Mixture of Two Oppositely Charged Polyelectrolytes

A quick and convenient route to prepare a highly viscoelastic mixture of two oppositely charged polyelectrolytes is presented. The investigation was essentially performed at a fixed total polyelectrolyte concentration. The phase behaviour was studied at varying ratios between the two oppositely charged polyions. The mixtures phase separated associatively at mixing ratios in the vicinity of overall charge neutrality, while by screening the attractive forces with NaCl the precipitate could be dissolved. At certain mixing ratios off charge neutrality the mixtures were highly viscoelastic single-phase solutions in the absence of screening electrolyte. When NaCl was added to such a solution the viscoelasticity decreased strongly since the attractive forces between the oppositely charged polyions were screened. Therefore, by contacting an initially salt free mixture of polyions with a brine solution of known concentration, the diffusion of salt into the polyion matrices could be monitored by following the rheology of the mixture as a function of the contact time. It is shown that the transport of NaCl inside the polyion matrices was diffusion controlled.     

On the phase behavior and structural properties of polyelectrolyte solutions

Correlations between structural properties and phase behavior of polyelectrolyte solutions were discussed along the line of the work reported by Châtellier and Joanny [Joanny JF, Châtellier X. J Phys France II 1996;6:1669]. A multicomponent system made of polyions, salt ions and counterions was considered under poor solvent conditions. Unlike this reference, partial structure factors were derived from the celebrated Zimm’s formula written in the matrix form including the effects of finite chain length. These effects were found to generate significant shifts in phase diagrams and qualitative changes in structural properties. The presence of a charged solid surface was briefly discussed. Here also, the phase diagram was found to shift with an increasing amount as the polyion chain length decreased.