Étude,par diffusion centrale des Rayons X,des polyelectrolytes rigides en solution. Cas des sels de Li,Na et Cs du DNA

The study of polyelectrolytes in solution by small-angle x-ray scattering techniques involves special problems, raised by the presence of several species: solvent, macroions, counterions, and possibly the ions of an additional electrolyte. A theoretical treatment of this problem is developed, based upon geometric concepts; the treatment applies to globular and to rodlike particles for the case of x-ray experiments carried out on an absolute scale. The equation obtained involves several parameters: mass and radius of gyration for globular particles; mass per unit length and axial radius of gyration for rodlike particles; partial specific volumes of the neutral macromolecular component of the counterions and of the added electrolyte; solvation of the macromolecular species; fraction of the counterions osmotically free. The equation is used to interpret a series of experiments performed with the Li, Na, and Cs salts of DNA in solution in water containing variable amounts of the chlorides of each cation. The effects of concentration are first eliminated by extrapolating to infinite dilution the experiments carried out at different concentrations; then the effects of the solvation are eliminated by extrapolating to pure water the results obtained at different electrolyte concentration. The parameters still involved at this stage are the mass per unit length, the partial specific volumes of the DNA and of the counterions, and the fraction of the counterions osmotically free. If the partial specific volumes are chosen in agreement with other data of the literature, and if the fraction of the counterions osmotically free is assumed to be 0.30 for the three salts, as suggested by other workers, the structure of the DNA molecules turns out to be the same for three cations, and to agree with the Watson-Crick model. These results are confirmed by the study of the liquid–crystalline gels, obtained at higher concentration, that lead to a direct determination of the mass per unit length of the rods. Moreover the solvation of the DNA molecules is determined as is shown to be different for each of the three cations. These results are in excellent agreement with those obtained by other techniques.     

Myoplasmic fixed charges of the barnacle muscle fiber (author's transl)]

The experimental model used to study diffusion and electrical conduction in the cytoplasm of large muscle fibers was adapted to evaluate the myoplasmic density of fixed charges. Membranes of myoplasm were prepared and phi X, the myoplasmic thermodynamically effective charge density, was calculated from the membrane potential (Kamo, N., Toyoshima, Y. and Kobatake, Y. (1971) Kolloid Z.u.Z. Polymère 1061--1068) when these membranes were used as the partition between two electrolyte solutions. The dilution of KCl in the external solutions reduced phi X, which increases with the reduction of the water content in the membrane of myoplasm. With a water content of 73.0 ml/100 g KCl concentration in the external medium equal to 0.15 M, phi X was evaluated to 0.058 equiv/l. The substitution of KCl by NaCl introduces a reduction in phi X of 20--50% depending on E1KCl] in the external solutions. The addition of ATP, Mg2+, and Ca2+ also causes a reduction of phi B by 30--50% according to the experimental conditions. These results indicate that the fraction of counterions dissociated from the myoplasmic macromolecules is reduced when the concentration of the counterions is diminished or when CKl is replaced by Nal. It also suggests a reduction of phi X during muscular contraction.     

Stability of Keplerate polyoxometalate macroanionic assemblies in salt-containing aqueous solutions

The solution stability of hydrophilic Keplerate polyoxometalate {Mo₇₂Fe₃₀} macroions was investigated at various ionic strengths. The solution stability varies with the type of monovalent cations with the lowest stability with large, weakly hydrated monovalent cations. Even lower stability was observed when the counter-cations were multivalent cations. Interestingly, the stability of {Mo₇₂Fe₃₀} solutions was found to increase with increasing POM concentration. The close association of monovalent counter-ions around macroions exists in aqueous solution and is likely enhanced at higher macroion concentrations. This behavior can further decrease the net charge on the macroions leading to a decreased electrostatic repulsion, which decreases the screening length of the macroions and causes them to irreversibly precipitate.     

Charges fixes du protoplasme des fibres musculaires de balaneMyoplasmic fixed charges of the barnacle muscle fiber

The experimental model used to study diffusion and electrical conduction in the cytoplasm of large muscle fibers was adapted to evaluate the myoplasmic density of fixed charges. Membranes of myoplasm were prepared and øX, the myoplasmic thermodynamically effective charge density, was calculated from the membrane potential (Kamo, N., Toyoshima, Y. and Kobatake, Y. (1971) Kolloid Z.u.Z. Polymère 1061–1068) when these membranes were used as the partition between two electrolyte solutions. The dilution of KCl in the external solutions reduced øX, which increases with the reduction of the water content in the membrane of myoplasm. With a water content of 73.0 ml/100g KCl concentration in the external medium equal to 0.15 M, øX was evaluated to 0.058 equiv/l. The substitution of KCl by NaCl introduces a reduction in øX of 20–50% depending on [KCl] in the external solutions. The addition of ATP, Mg²⁺ and Ca²⁺ also causes a reduction of øX by 30–50% according to the experimental conditions. These results indicate that the fraction of counterions dissociated from the myoplasmic macromolecules is reduced when the concentration of the counterions is diminished or when KCl is replaced by NaCl. It also suggests a reduction of øX during muscular contraction.     

Effect of polyelectrolytes on the kinetics of ionic reactions. III. Hydrolysis of pyrophosphate in poly-(ethyleneimine) solutions

The effect of the weak polyelectrolyte poly(ethyleneimine) on the rate of hydrolysis of pyrophosphate has been studied as a function of pH at 70°C. Inhibition by the macroions was observed at pH ? 2, the inhibition becomes stronger as pH increases. At pH > 7 the hydrolysis in the presence of polyions becomes undetectable. Addition of NaCl to the solutions reduces the inhibitory effect of the polyelectrolyte.Electrostatic interactions between macroions and substrate ions cause the observed inhibition, therefore this is another manifestation of the polyelectrolyte effect due to the large charge density on the polycations.     

Effect of cation and anion of an electrolyte on apparent molar volume, isentropic compressibility and refractive index of glycine in aqueous solutions

Experiments at 298.15 K have been performed to measure the density, velocity of sound and refractive index in three water+glycine+electrolyte systems. The electrolytes studied were KCl, KNO3 and NaNO3. The values of apparent molar volume and isentropic compressibility of glycine in aqueous electrolyte solutions were calculated from the measured data. The results obtained in this study and those reported previously for water+glycine+NaCl system have been comparatively studied. The results show that the nature of both the cation and the anion of an electrolyte influence the behaviour of glycine in aqueous solutions. For all four electrolytes studied, the comparison shows a positive volume transfer for glycine from an electrolyte solution to a more concentrated solution of the same electrolyte. The results also show a negative apparent isentropic compressibility for glycine in the presence of the electrolytes studied. These effects indicate that the volume of a glycine molecule is larger in solutions with higher electrolyte concentration and the water molecules around the glycine molecules are less compressible than the water molecules in the bulk solution. These effects were attributed to the doubly charged behaviour of glycine and to the formation of physically bonded ion-pairs between the charged groups of glycine and the cation and the anion of the electrolyte.     

The polyelectrolyte behavior of actin filaments: a 25Mg NMR study.

Under physiological conditions, filamentous actin (F-actin) is a polyanionic protein filament. Key features of the behavior of F-actin are shared with other well-characterized polyelectrolytes, in particular, duplex DNA. For example, the bundle formation of F-actin by polyvalent cations, including divalent metal ions such as Mg2+, has been proposed to be a natural consequence of the polyelectrolyte nature of actin filaments [Tang and Janmey (1996) J. Biol. Chem. 271, 8556-8563]. This recently proposed model also suggests that weak interactions between F-actin and Mg2+ ions reflect a nonspecific trapping of counterions in the electric field surrounding F-actin due to its polyelectrolyte nature. To test this hypothesis, we have performed 25Mg NMR measurements in F-actin solutions. Based on the NMR data, we estimate that the rotational correlation times of Mg2+ are independent of the overall rotational dynamics of the actin filaments. Moreover, competitive binding experiments demonstrate a facile displacement of F-actin-bound Mg2+ by Co(NH3)63+. At higher Co(NH3)63+ concentrations, a fraction of the magnesium ions are trapped as actin filaments aggregate. ATP also competes effectively with actin filaments for binding to Mg2+. These results support the hypothesis that magnesium ions bind loosely and nonspecifically to actin filaments, and thus show a behavior typical of counterions in polyelectrolyte solutions. The observed features mimic to some extent the well-documented behavior of counterions in DNA solutions.     

Phase transitions of concentrated DNA solutions in low concentrations of 1:1 supporting electrolyte

Transitions between isotropic and liquid crystalline phases of concentrated solutions of DNA with an average contour length (500 A) near the persistence length were examined in 0.01 M supporting 1:1 electrolyte (predominantly NaCl). A quantitative phase diagram describing the transitions occurring over a DNA concentration range from 100 to 290 mg/mL and temperatures from 20 to 60 degrees C was constructed from solid-state 31P-nmr data and examination of the morphologies of the mesophases by polarized light microscopy. Three anisotropic phases were observed in solutions with DNA concentrations of 160-290 mg/mL: an unidentified, weakly birefringent phase termed "precholesteric," a true cholesteric phase with pitch approximately 2 microns, and a third, presumably more highly ordered phase. Comparison with previous studies showed that the critical concentration for anisotropic phase formation and the nature of the phases formed by these DNA molecules are not strongly affected by decreasing the supporting electrolyte concentration from approximately 0.2 M to 10 mM. There are, however, profound effects of decreasing the supporting electrolyte concentration on the width of the transition from isotropic to totally anisotropic solutions, and the nature of the transitions between phases. Decreasing the supporting electrolyte concentration significantly increases the concentration range of persistence of the isotrophic phase, and results in the formation of triphasic solutions (isotropic and two liquid crystalline phases). Values of the critical DNA concentrations for anisotropic phase formation from the theory of A. Stroobants et al. [(1986) Macromolecules 19, 2232 to 2238] were found to be significantly lower than the observed values for any reasonable estimate of the effective radius, probably because of the relatively short lengths of DNA fragments examined in the present study. Comparison of the experimentally determined DNA concentrations required for anisotropic phase formation with the values predicted from Flory's lattice statistics theory, which explicitly considers the rod length, permitted estimation of the effective DNA radius. The estimated radius was inconsistent with effective radii calculated from Poisson-Boltzmann (P-B) theory based on a supporting electrolyte concentration of 10 mM, but was in fair agreement with P-B theory assuming that Na+ DNA contributes approximately 0.24 Na+ counterions/nucleotide to the effective free sodium ion concentration.     

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.     

The equivalent conductivity of aqueous salt-free solutions of DNA: Influence of univalent counterions

The equivalent conductivity of salt-free solutions of deoxyribonucleates of alkali metals and ammonium obtained by filtering an isoionic DNA solution through a cation exchanger in the corresponding form has been investigated in the concentrations range of 1 × 10^?4 to 4 × 10^?3M. For all counterions investigated there is a linear dependence of the equivalent conductivity on \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {C_p} $\end{document}, where C_p is the nucleic phosphorus concentration. The limiting equivalent conductivity of deoxyribonucleates increases linearly with the limiting mobility of a counterion. By extrapolation to the zero mobility of the counterion, we have obtained the limiting mobility of a macroion, which is equal to 19 × 10^?4 Sm m² equiv.^?1, which is in good agreement with the literature data for denatured DNA obtained by the method of a moving boundary. It is shown that the degree of binding of counterions calculated from the conductometric data in diluted DTA solutions in independent of the nature of the univalent counterion. The degree of dissociation of H⁺-DNA in the isoionic solution calculated with allowance for the fraction of unprotonated bases practically coincides with this value for salts of DNA. The parameter of Manning's theory calculated from the experimental data corresponds to the distance between phosphates along the chain of the macroion, which is equal to 6.7 Å. We attribute the smaller value of this distance as compared with the theoretical one for denatured DNA to the aggregation of macroions.     

Polyelectrolyte behavior of carrageenans in aqueous solutions

Osmotic coefficients of sodium, potassium, and calcium counterions have been determined in aqueous solutions on kappa-, iota-, and lambda-carrageenans at 25°C. The experimental results are correlated with the calculated ones from the limiting law of Manning. An orderd secondary structure exists in kappa- and iota-carrageenans. Its stability is discussed as a function of temperature, ionic strength, and the nature of the counterions.     

Activity coefficients of counterions in solutions of diethylaminoethyl dextran hydrochloride

Activity coefficients of counterions in solutions of diethylaminoethyl dextran hydrochloride have been determined. It has been observed that they increase with decreasing concentration of the polyelectrolyte. The experimental values have been compared with those calculated using Oosawa's theory of activity coefficients. The calculated values are higher than those observed, which suggests that the rodlike model on which Oosawa's theory is based is inadequate for the present case. Activity coefficients of counterions of some solutions containing NaCl and KC1, respectively, have also been determined. It has been found that the additivity rule for activity of counterions applies for these solutions.     

Thermal membrane potential through charged membranes in electrolyte solutions.

Measurements of the thermal membrane potential across cation and anion exchange membranes were carried out by using the same solution of various 1-1 electrolytes on both sides of the membrane. In all cases a good linear relationship was observed between the thermal membrane potential increment psi and the temperature difference increment T. The slope of the linear plot varied with the concentration of the electrolyte. The value of increment psi/increment T versus logarithmic activity of the electrolyte plot was linear with a slope of +/- R/F if the transport number of counterion was unity. The magnitude of increment psi/increment T was independent of coion species but dependent on counterions. These experimental results are in agreement with a theory presented previously. The thermal membrane potential caused by the direct effect of temperature differences and that by the indirect effect arising from the changes in ionic and water chemical potentials due to the temperature difference are separately discussed.     

Monte Carlo and Poisson–Boltzmann calculations of the fraction of counterions bound to DNA

The counterion density and the condensation region around DNA have been examined as functions of both ion size and added-salt concentration using Metropolis Monte Carlo (MC) and Poisson–Boltzmann (PB) methods. Two different definitions of the “bound” and “free” components of the electrolyte ion atmosphere were used to compare these approaches. First, calculation of the ion density in different spatial regions around the polyelectrolyte molecule indicates, in agreement with previous work, that the PB equation does not predict an invariance of the surface concentration of counterions as electrolyte is added to the system. Further, the PB equation underestimates the counterion concentration at the DNA surface, compared to the MC results, the difference being greatest in the grooves, where ionic concentrations are highest. If counterions within a fixed radius of the helical axis are considered to be bound, then the fraction of polyelectrolyte charge neutralized by counterions would be predicted to increase as the bulk electrolyte concentration increases. A second categorization—one in which monovalent cations in regions where the average electrostatic potential is ledd than ?kT are considered to be bound—provides an informative basis for comparison of MC and PB with each other and with counterion-condensation theory. By this criterion, PB calculations on the B from of DNA indicate that the amount of bound counterion charge per phosphate group is about .67 and is independent of salt concentration. A particularly provocative observatiob is that when this binding criterion is used, MC calculations quantitatively reproduce the bound fraction predicated by counterion-condensation theory for all-atom models of B-DNA and A-DNA as well as for charged cylindera of varying lineat charge densities. For example, for B-DNA and A-DNA, the fractions of phosphate groups neutralized by 2 Å hard sphere counterions are 0.768 and .817, respectively. For theoretical studies, the rediys enclosing the region in which the electrostatic potential is calculated studies, the radius enclosing the region in which the electrostatic potential is calculated to be less than ?kT is advocated s a more suitable binding or condensation radius that enclosing the fraction of counterions given by (1 – ξ^?1). A comparsion of radii calculated using both of these definitions is presented. © 1994 John Wiley & Sons, Inc.     

Transport phenomena and ion binding in solutions of sodium polystyrenesulphonate

The results of transference and conductance measurements on solutions of sodium polystyrenesulpnonate, in the concentration range from 0.0025 to 0.075 monomolar, are presented. The fraction of free Counterions calculated from experimental data is found to he independent of molecular weight of the polyelectrolyte within the range of degree of polymerization from 200 to 2400. The experimental data, combined with the cell model, are used to calculate the electrostatic potential at a cylindrical surface Which surrounds the polyion and divides the counterions into bound and free. The same value for this potential is found for the whole concentration range investigated, which lends support to the assumption of cylindrical distribution of counterions in polyelectrolyte solutions.     

Studies with Composite Membranes: II. Measurement of Asymmetric Properties

Electrical potentials arising across composite membranes when they separate the same concentration of a (1:1) electrolyte or electrolytes have been measured. These potentials have been shown to arise from differences in the transport number of counterions contacting the two faces of the membrane which contained in its body a high concentration of electrolyte and polyelectrolyte. When the concentration of this trapped electrolyte or polyelectrolyte is low, the asymmetry potentials are small. Although measurements of current-voltage relations provided evidence for the existence of asymmetry between the two faces of the membrane, osmotic flow of water in either direction across the membrane and the salt flow in the two directions were symmetrical. These solvent and solute flux measurements lasted more than 30 hr. Short-term (about 4 hr) flux measurements, however, using tritiated water (THO), gave flows which were different in the two directions. Similarly, the salt flows measured using ²²Na isotope were different in the two directions. The usefulness of the present system as a model to use for studies concerned with carrier transport problems in biology has been pointed out.     

Condensation of Co++ ions on chondroitin sulfate from transport coefficients and proton NMR measurements in aqueous solutions

The “condensed” counterions which characterize high-charge-density polyelectrolyte solutions can be analyzed into two subpopulations: (1) site-bound counterions and (2) atmospherically entrapped counterions. The distinction is achieved experimentally by combining the data from self-diffusion coefficient or electrical mobility measurements, which give the amount of “condensed” ions, and those from nmr, chemical shift measurements, which indicate the amount of site-bound ions. In the case of a solution of chondroitin sulfate with excess Co⁺⁺ counterions, it can be estimated that 20% of the structural charge of the polyion is neutralized by site-bound, dehydrated, condensed counterions, while a further 30% is neutralized by atmospherically entrapped, hydrated counterions.     

Magnetic resonance distinction between site bound and atmospherically bound paramagnetic counterions in polyelectrolyte solutions.

A combination of the water protons NMR chemical shifts, longitudinal and transversal relaxation rates and of the paramagnetic counterion EPR signal is shown to provide a clear distinction between site binding, atmospheric trapping and free counterions in solutions of polyelectrolyte TMA salts with increasing concentrations of the divalent counterions Co++ and Mn++. Site binding is defined by the loss of water in the counterion first hydration shell while atmospheric binding results in a change in the counterion correlation time as compared to a free ion.     

Divalent paramagnetic counterions site binding in polyelectrolyte solutions. Analysis of the frequency dependence of the water protons magnetic relaxation and the characteristic parameters of "site binding"

Chemical shift and relaxation time measurements on the water protons in polyelectrolyte solutions containing divalent paramagnetic counterions have shown the existence of three types of counterions: - site bound with loss of water molecules and partial or complete release of the electrostriction in the first hydration sphere, - atmospherically trapped with no change in hydration, - free. The overall stoichiometry of the two former is in agreement with Manning's fraction of condensed counterions. A complete analysis of the frequency dependent contribution of site bound counterions to the water protons relaxation times leads us to interesting conclusions on the modifications of the first hydration shell and on the life time of site binding.