Biblioteca Digital

A major contribution to the binding free energy associated with most protein-nucleic acid complexes is the increase in entropy due to counterion release from the nucleic acid that results from electrostatic interactions. To examine this quantitatively, we have measured the thermodynamic extent of counterion release that results from the interaction between single-stranded homopolynucleotides and a series of oligolysines, possessing net charges z = 2-6, 8, and 10. This was accomplished by measuring the salt dependence of the intrinsic equilibrium binding constants--i.e., (delta log Kobs/delta log[K+])--over the range from 6 mM to 0.5 M potassium acetate. These data provide a rigorous test of linear polyelectrolyte theories that have been used to interpret the effects of changes in bulk salt concentration on protein-DNA binding equilibria, since single-stranded nucleic acids have a lower axial charge density than duplex DNA. Upon binding to poly(U), the thermodynamic extent of counterion release per oligolysine charge, z, is 0.71 +/- 0.03, which is significantly less than unity and less than that measured upon binding duplex DNA. These results are most simply interpreted using the limiting law predictions of counterion condensation and cylindrical Poisson-Boltzmann theories...

The effect of different organic osmolytes on the DNA counterion condensation layer has been investigated by 23Na NMR relaxation measurements. The zwitterionic compounds glycine, beta-alanine, 4-aminobutyric acid, and 6-aminocaproic acid have shown an increasing capacity to decrease the amount of sodium ions in the vicinity of the macromolecule. The experimental data have been correlated with the dielectric constant increase in their corresponding solutions and have been compared with the prediction of counterion condensation theory. Polyols (sorbitol and mannitol) did not display the same effect. These compounds largely increase the relaxation rate of sodium ions in the proximity of DNA, unlike the zwitterionic compounds. This probably results from a perturbation of the water dynamic around the macromolecule, of the primary or secondary hydration shell of the sodium nuclei involved, or both.

We compare free energies of counterion distributions in polyelectrolyte solutions predicted from the cylindrical Poisson-Boltzmann (PB) model and from the counterion condensation theories of Manning: CC1 (Manning, 1969a, b), which assumes an infinitely thin region of condensed counterions, and CC2 (Manning, 1977), which assumes a region of finite thickness. We consider rods of finite radius with the linear charge density of B-DNA in 1-1 valent and 2-2 valent salt solutions. We find that under all conditions considered here the free energy of the CC1 and the CC2 models is higher than that of the PB model. We argue that counterion condensation theory imposes nonphysical constraints and is, therefore, a poorer approximation to the underlying physics based on continuum dielectrics, point-charge small ions, Poisson electrostatics, and Boltzmann distributions. The errors in counterion condensation theory diminish with increasing distance from, or radius of, the polyion.

The use of linear theory, in particular, counterion condensation (CC) theory, in describing electrophoresis of polyelectrolyte chains, is criticized on several grounds. First, there are problems with CC theory in describing the equilibrium distribution of ions around polyelectrolytes. Second, CC theory is used to treat ion relaxation in a linear theory with respect to the polyion charge despite the fact that ion relaxation arises as a consequence of nonlinear charge effects. This nonlinearity has been well established by several investigators over the last 70 years for spherical, cylindrical, and arbitrarily shaped model polyions. Third, current use of CC theory ignores the electrophoretic hindrance as well as the ion relaxation for condensed counterions and only includes such interactions for uncondensed counterions. Because most of the condensed counterions lie outside the shear surface of the polyion (in the example of DNA), the assumption of ion condensation is artificial and unphysical. Fourth, the singular solution, based on a screened Oseen tensor, currently used in the above mentioned theories is simply wrong and fails to account for the incompressibility of the solvent. The actual singular solution, which has long been available...

In the presence of condensing agents, single chains of giant double-stranded DNA undergo a first-order phase transition between an elongated coil state and a folded compact state. To connect this like-charged attraction phenomenon to counterion condensation, we performed a series of single-chain experiments on aqueous solutions of DNA, where we varied the extent of counterion condensation by varying the relative dielectric constant ɛr from 80 to 170. Single-chain observations of changes in the conformation of giant DNA were performed by transmission electron microscopy and fluorescence microscopy, with tetravalent spermine (SPM4+) as a condensing agent. At a fixed dielectric constant, single DNA chains fold into a compact state upon the addition of spermine, whereas at a constant spermine concentration single DNA chains unfold with an increase in ɛr. In both cases, the transition is largely discrete at the level of single chains. We found that the critical concentration of spermine necessary to induce the single-chain folding transition increases exponentially as the dielectric constant increases, corresponding to 87–88% of the DNA charge neutralized at the onset of the transition. We also observed that the toroidal morphology of compact DNA partially unfolds when ɛr is increased.

A two-sided model for DNA is employed to analyze fluctuations of the spatial distribution of condensed counterions and the effect of these fluctuations on transient bending. We analyze two classes of fluctuations. In the first, the number of condensed counterions on one side of the DNA remains at its average value, while on the other side, counterions are lost to bulk solution or gained from it. The second class of fluctuations is characterized by movement of some counterions from one side of the DNA to the other. The root-mean-square fluctuation for each class is calculated from counterion condensation theory. The amplitude of the root-mean-square fluctuation depends on the ionic strength as well as the length of the segment considered and is of the order 5–10%. Both classes of fluctuation result in transient bends toward the side of greater counterion density. The bending amplitudes are ∼15% of the total root-mean-square bends associated with the persistence length of DNA. We are thus led to suggest that asymmetric fluctuations of counterion density contribute modestly but significantly toward the aggregate of thermalized solvent fluctuations that cause bending deformations of DNA free in solution. The calculations support the idea that counterions may exert some modulating influence on the fine structure of DNA.

We present experiments on the bias-induced release of immobilized, single-stranded (ss) 24-mer oligonucleotides from Au-surfaces into electrolyte solutions of varying ionic strength. Desorption is evidenced by fluorescence measurements of dye-labeled ssDNA. Electrostatic interactions between adsorbed ssDNA and the Au-surface are investigated with respect to 1), a variation of the bias potential applied to the Au-electrode; and 2), the screening effect of the electrolyte solution. For the latter, the concentration of monovalent salt in solution is varied from 3 to 1600 mM. We find that the strength of electric interaction is predominantly determined by the effective charge of the ssDNA itself and that the release of DNA mainly occurs before the electrochemical double layer has been established at the electrolyte/Au interface. In agreement with Manning's condensation theory, the measured desorption efficiency (ηrel) stays constant over a wide range of salt concentrations; however, as the Debye length is reduced below a value comparable to the axial charge spacing of the DNA, ηrel decreases substantially. We assign this effect to excessive counterion condensation on the DNA in solutions of high ionic strength. In addition, the relative translational diffusion coefficient of ssDNA in solution is evaluated for different salt concentrations.

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.

The phenomenon of Manning-Oosawa counterion condensation is given an explicit statistical mechanical and qualitative basis via a dressed polyelectrolyte formalism in connection with the topology of the electrostatic free-energy surface and is derived explicitly in terms of the adsorption excess of ions about the polyion via the nonlinear Poisson-Boltzmann equation. The approach is closely analogous to the theory of ion binding in micelles. Our results not only elucidate a Poisson-Boltzmann analysis, which shows that a fraction of the counterions lie within a finite volume around the polyion even if the volume of the system tends towards infinity, but also provide a direct link between Manning's theta-the number of condensed counterions for each polyion site-and a statistical thermodynamic quantity, namely, the adsorption excess per monomer.

Using a generalization of the Poisson-Boltzmann equation, dynamics of counterion condensation is studied. For a single charged plate in the presence of counterions, it is shown that the approach to equilibrium is diffusive. In the far from equilibrium case of a moving charged plate, a dynamical counterion condensation transition occurs at a critical velocity. The complex dynamic behavior of the counterion cloud is shown to lead to a novel nonlinear force-velocity relation for the moving plate.; Comment: 5 pages, 1 ps figure included using epsf

A highly-charged spherical colloid in a salt-free environment exerts such a powerful attraction on its counterions that a certain fraction condenses onto the surface of a particle. The degree of condensation depends on the curvature of the surface. So, for instance, condensation is triggered on a highly-charged sphere only if the radius exceeds a certain critical radius $\collrad^{*}$. $\collrad^{*}$ is expected to be a simple function of the volume fraction of particles. To test these predictions, we prepare spherical particles which contain a covalently-bound ionic liquid, which is engineered to dissociate efficiently in a low-dielectric medium. By varying the proportion of ionic liquid to monomer we synthesise nonpolar dispersions of highly-charged spheres which contain essentially no free co-ions. The only ions in the system are counterions generated by the dissociation of surface-bound groups. We study the electrophoretic mobility of this salt-free system as a function of the colloid volume fraction, the particle radius, and the bare charge density and find evidence for extensive counterion condensation. At low electric fields, we observe excellent agreement with Poisson-Boltzmann predictions for counterion condensation on spheres. At high electric fields however...

The low-frequency limit of the electrical conductivity (d.c. conductivity) of differently flexible polyions in aqueous solutions has been measured over an extended polyion concentration range, covering both the dilute and semidilute (entangled and unentangled) regime, up to the concentrated regime. The data have been analyzed taking into account the different flexibility of the polymer chains according to the scaling theory of polyion solutions, in the case of flexible polyions, and according to the Manning model, in the case of rigid polyions. In both cases, the fraction f of free counterions, released into the aqueous phase from the ionizable polyion groups, has been evaluated and its dependence on the polyion concentration determined. Our results show that the counterion condensation follows at least three different regimes in dependence on the polyion concentration. The fraction f of free counterions remains constant only in the semidilute regime (a region that we have named the Manning regime), while there is a marked dependence on the polyion concentration both in the dilute and in the concentrated regime. These results are briefly discussed at the light of the aqueous ionic solutions.; Comment: 9 pages, 8 figures

A comparison between the Kosterlitz-Thouless theory of metal insulator transition in a two dimensional plasma and a counterion condensation in a polyelectrolyte solution is made. It is demonstrated that, unlike some of the recent suggestions, the counterion condensation and the Kosterlitz-Thouless transition are distinct.; Comment: 3 pages, uses multicol.sty, accepted to Physica A

A new quantitative theory for polyelectrolytes in salt free dilute solutions is developed. Depending on the electrostatic interaction strength, polyelectrolytes in solutions can undergo strong stretching (with polyelectrolyte dimension R_g\sim l_B^{1/3}N, where l_B is the Bjerrum length and N is the number of the chain segments) or strong compression (with R_g\sim l_B^{-1/2}N^{1/3}). A strong polymer collapse occurs as a first-order phase transition due to accompanying counterion condensation.; Comment: 4 pages, 2 figures

Light scattering and viscometric measurements on weak polyelectrolytes show two important aspects of counterion condensation, namely, non-monotonic variation in the polyelectrolyte size with the increase in the electrostatic strength, and, monovalent counterion selectivity in determining the nature of collapse transition at high electrostatic strengths. Here, we present a self-consistent variational theory for weak polyelectrolytes which includes the effects of the polarizability of monovalent counterions. Our theory reproduces several experimental findings including non-monotonic conformational size with the variation in the electrostatic strength and a shift from a continuous to a discontinuous collapse transition with the increase in the dipole strength of condensed ions. At low dipole strength and high electrostatic strength, our theory predicts a series of solvent quality driven size transitions spanning the re-entrant poor, theta and good solvent regimes. At high dipole strength, the size remains that of a compact globule independent of solvent quality. The dipole strength of the ion-pair formed due to counterion condensation, which depends on the size and polarizability of the monovalent counterions, is found to be an important molecular parameter in determining the nature of collapse transition...

We consider an overall neutral system consisting of two similarly charged plates and their oppositely charged counterions and analyze the electrostatic interaction between the two surfaces beyond the mean-field Poisson-Boltzmann approximation. Our physical picture is based on the fluctuation-driven counterion condensation model, in which a fraction of the counterions is allowed to ``condense'' onto the charged plates. In addition, an expression for the pressure is derived, which includes fluctuation contributions of the whole system. We find that for sufficiently high surface charges, the distance at which the attraction, arising from charge fluctuations, starts to dominate can be large compared to the Gouy-Chapmann length. We also demonstrate that depending on the valency, the system may exhibit a novel first-order binding transition at short distances.; Comment: 15 pages, 8 figures, to appear in PRE

We study the counterion condensation on a two dimensional charged disc in the limit of infinite dilution, and compare the energy-temperature relation obtained from the canonical free energy and microcanonical entropy. The microcanonical entropy is piecewise linear in energy, and is shown to be concave for all energies. As a result, even though the interactions are long-ranged, the energy-temperature relation and hence the counterion condensation transition points are identical in both the ensembles.; Comment: 4 pages, 2 figures

We address the critical and universal aspects of counterion-condensation transition at a single charged cylinder in both two and three spatial dimensions using numerical and analytical methods. By introducing a novel Monte-Carlo sampling method in logarithmic radial scale, we are able to numerically simulate the critical limit of infinite system size (corresponding to infinite-dilution limit) within tractable equilibration times. The critical exponents are determined for the inverse moments of the counterionic density profile (which play the role of the order parameters and represent the inverse localization length of counterions) both within mean-field theory and within Monte-Carlo simulations. In three dimensions (3D), correlation effects (neglected within mean-field theory) lead to an excessive accumulation of counterions near the charged cylinder below the critical temperature (condensation phase), while surprisingly, the critical region exhibits universal critical exponents in accord with the mean-field theory. In two dimensions (2D), we demonstrate, using both numerical and analytical approaches, that the mean-field theory becomes exact at all temperatures (Manning parameters), when number of counterions tends to infinity. For finite particle number...

We present results of molecular dynamics simulations of strong, flexible polyelectrolyte chains in solution with added salt. The effect of added salt on the polyelectrolyte chain structure is fully treated for the first time as a function of polymer density. Systems above and below the Manning condensation limit are studied. The chain contraction due to added salt is weaker than expected from simple screening arguments. The chain structure is intimately tied to the ion density near the chain even for chains in the counterion condensation regime. In contradiction to Manning counterion condensation theory, the ion density near the polymer chain depends on the amount of added salt, and above the condensation limit the chains significantly contract due to added salt.; Comment: Revtex, 4 pages, 3 eps figures

The prevalent theories for polyelectrolytes have not been able to describe the experimentally observed ion specificity found at high ion concentrations for counterion condensation and conformational transitions. One important source of ion specificity missed in these theories is the dispersion force that acts between an ion and the cylindrical polyion surface. Here, we solve the cylindrical Poisson-Boltzmann equation numerically in the presence of ionic dispersion potentials. We demonstrate that ionic dispersion forces have important influences on ionic distributions and potentials. This influence increases with increasing concentration reflecting that specific ion effects are observed only at high concentrations.