Polyanionic characteristics of purified sulphated homofucans from brown algae

Sulphated fucans were fractionated from different brown algae using quaternary ammonium detergents. Purified fractions from different species had the same general chemical composition, that of a typical sulphated homofucans, or fucoidan. The interaction of univalent and divalent counter-ions with fucoidan was investigated by viscometry and polarimetry, and by measuring the counter-ion activites and conductance coefficients in salt-free solutions. The activity and conductance coefficients were found to be independent of the polyanion concentration and approximately the same within each family of counter-ions. This indicates that cation binding in salt-free solutions of fucoidan is purely electrostatic. The conductivity results were in good agreement with the Manning's condensation polyelectrolyte model. The density charge parameter was 2.08 and the mean length of the monomeric unit was 4.5 Å. Both the reduced viscosity and the optical rotation were dependent on the valency of the counter-ions used. Coupled with the data obtained from light-scattering measurements. ( and R_g = 1760 Å), our results suggest that fucoidan in aqueous solution is an extended, flexible coil.     

Biological ion exchanger resins. VII. Counter-ion activity coefficients in solutions of biological polyelectrolytes.

The single ion activity coefficients of K+ and Cl- counter-ions were determined in concentrated polyelectrolyte solutions. The polyelectrolytes investigated included DNA and several proteins. Results indicate that ion gradients of up to 40:1 do not lower the counter-ion activity coefficient below 0.5. Thus, published values of the intracellular activity coefficient of K+ are not incompatible with cellular models utilizing cytoplasmic ion exchange.     

Limiting laws and counterion condensation in polyelectrolyte solutions: IV. The approach to the limit and the extraordinary stability of the charge fraction

The limiting laws for polyelectrolyte solutions developed in previous papers of this series have been amply confirmed by measurement. A surprising result of the accumulated data is that the limiting polyelectrolyte charge fraction (fraction of fixed charges uncompensated by condensed counterions in the limit of zero concentration), persists up to concentrations of 0.1 M or even higher. Here the theory is extended in a simple manner to finite concentrations, and the stability of the charge fraction is found to be firmly based on consequences of the long-range polyelectrolyte field. The associated counterions are assumed to translate freely in a region centered on the contour axis of the polyion. The numerical value of the free volume is determined self-consistently from the axial charge density of the polyelectrolyte and is used as the general framework within which specific binding effects are treated.     

Properties of Double-Stranded DNA as a Polyelectrolyte

The stability of the structure of double-stranded DNA in the salt-free solution is discussed on the basis of the polyelectrolyte theory. Assuming that DNA is an infinitely long rod, and the formation of double strands is divided into combining process and folding process, the free energy changes required in these processes are calculated by the use of the exact solutions of two-dimensional Poisson-Boltzmann equation for the one rod and the two rod systems.

By strong depression of electrostatic interaction due to counter-ion condensation phenomena, the free energy change is remarkably decreased so that the double-stranded structure of DNA can be stabilized by energy of hydrogen bonds between base pairs. The increase of the activity coefficient of a counterion upon heat denaturation of DNA is also explained.

     

Polyelectrolyte Charge Corrected Molecular Weight and Effective Charge by Sedimentation

Ionic charge on a macromolecule complicates the determination of its molecular weight in solution due to the Donnan effect. Compensation for it can be made if one knows the value of the effective charge, which can be found by dialysis equilibrium across a semipermeable membrane. A moving boundary of molecules sedimenting in a centrifugal field can act as a membrane, obviating some of the disadvantages (such as selective adsorption) of a real membrane. Interference optics are used to monitor the reverse gradient of the salt due to the Donnan effect, hence facilitating the determination of the effective charge. The apparent molecular weight obtained from a conventional sedimentation equilibrium can then be corrected to yield the true molecular weight. The effective charge is valuable in revealing macromolecular structural features when related to the titratable charge through the Manning counter-ion condensation theory. Agreement between the values of the backbone molecular weights for the Na, Cs, and Ca salts of heparin indicated the validity of the approach. The effective charge ratio and the axial charge spacing for the Na and Ca heparin agreed with the literature, whereas the results for Cs indicated a degree of binding in excess of that due to counter-ion condensation.     

The release of monovalent counterions by addition of divalent counterions in coulombic interaction system

The additivity rule of counterion activity or osmotic pressure in rodlike polyelectrolyte solutions has been discussed on the basis of the Fokker-Planck and Poisson equations in relation to the fluctuation of counterion distribution. This new theory has concluded that the additivity rule of counterion activity is less applicable than that of osmotic pressure due to the electric expansion force acting on the free-volume surface resulting from the fluctuation of counterion distribution. The theory has introduced an approximate relation between the counterion activities in the mixture solution of divalent and monovalent counterions, such that Deltaa+ = DeltaC++ - Deltaa++, in which Deltaa+ represents the increase of activity of monovalent counter-ions resulting from the addition of divalent counterionsDeltaC++, (in molar) to the solution, and Deltaa++ means the increase of the divalent counterion activity (in molar) in this process. This relation has been experimentally examined for Na-PSS solutions in the process of Cu2+ ion addition by the use of Na+ and Cu2+ sensitive electrodes, and it has been turned out that the relation is established in the low charge state of polyion.     

Interpreting protein/DNA interactions: distinguishing specific from non-specific and electrostatic from non-electrostatic components

We discuss the effectiveness of existing methods for understanding the forces driving the formation of specific protein-DNA complexes. Theoretical approaches using the Poisson-Boltzmann (PB) equation to analyse interactions between these highly charged macromolecules to form known structures are contrasted with an empirical approach that analyses the effects of salt on the stability of these complexes and assumes that release of counter-ions associated with the free DNA plays the dominant role in their formation. According to this counter-ion condensation (CC) concept, the salt-dependent part of the Gibbs energy of binding, which is defined as the electrostatic component, is fully entropic and its dependence on the salt concentration represents the number of ionic contacts present in the complex. It is shown that although this electrostatic component provides the majority of the Gibbs energy of complex formation and does not depend on the DNA sequence, the salt-independent part of the Gibbs energy--usually regarded as non-electrostatic--is sequence specific. The CC approach thus has considerable practical value for studying protein/DNA complexes, while practical applications of PB analysis have yet to demonstrate their merit.     

The role of the ionic environment in the orientation of nucleic acids in electric fields

The relationship between polyelectrolyte theories based on linear charge density models and the electric-field induced orientation of the polyelectrolytes, poly(A), poly(C) and DNA is examined by varying their ionic environment with respect to ionic strength and acidity. The degree of counterion condensation on the polyelectrolytes predicted by the theories of Manning and Record is shown to be related linearly to the orientation as measured by their dichroism in the field. Micro-structural differences between poly(A) and poly(C) account for the differences in their dependence on the pH of the medium which affects the counterion condensation and thus the polarization in the orienting electric fields. The results consequently support recent treatments of linear polyelectrolytes having a high charge density which model them as smoothly charged linear polyions, but indicate that these models are insufficient to account for some of the effects of microstructural variations.     

Relaxation and electrophoretic effects in polyelectrolyte solutions. I. Salt-free solutions

Relations between relaxation and electrophoretic effects in salt-free polyelectrolyte solutions are studied in terms of nonequilibrium thermodynamics and of binary friction coefficients. The significance and the method of determining these coefficients are explained. Consideration of experimental results and of long- and short-range interactions suggests that the concept of “ion condensation” is needed to provide a consistent desciption of transport processes for linear flexible polyelectrolytes. Empirical relations previously used are shown to have only limited validity.     

Light scattering,CD, and ligand binding studies of ferrihemoglobin–polyelectrolyte complexes

Quasi‐elastic light scattering (QELS), electrophoretic light scattering (ELS), CD spectroscopy, and azide binding titrations were used to study the complexation at pH 6.8 between ferrihemoglobin and three polyelectrolytes that varied in charge density and sign. Both QELS and ELS show that the structure of the soluble complex formed between ferrihemoglobin and poly(diallyldimethylammonium chloride) [PDADMAC] varies with protein concentration. At fixed 1.0 mg/mL polyelectrolyte concentration, protein addition increases complex size and decreases complex mobility in a tightly correlated manner. At 1.0 mg/mL or greater protein concentration, a stable complex is formed between one polyelectrolyte chain and many protein molecules (i.e., an intra‐polymer complex) with apparent diameter approximately 2.5 times that of the protein‐free polyelectrolyte. Under conditions of excess polyelectrolyte, each of the three ferrihemoglobin–polyelectrolyte solutions exhibits a single diffusion mode in QELS, which indicates that all protein molecules are complexed. CD spectra suggest little or no structural disruption of ferrihemoglobin upon complexation. Azide binding to the ferrihemoglobin–poly(2‐acrylamide‐2‐methylpropanesulfonate) [PAMPS] complex is substantially altered relative to the polyelectrolyte‐free protein, but minimal change is induced by complexation with an AMPS‐based copolymer of reduced linear charge density. The change in azide binding induced by PDADMAC is intermediate between that of PAMPS and its copolymer. © 1999 John Wiley & Sons, Inc. Biopoly 50: 153–161, 1999     

Evaluation of the counterion condensation theory of polyelectrolytes.

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.     

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.     

The effect of salt on oligocation-induced chromatin condensation

Condensation of model chromatin in the form of fully saturated 12-mer nucleosome arrays, induced by addition of cationic ligands (ε-oligolysines with charge varied from +4 to +11), was studied in a range of KCl concentrations (10-500mM) using light scattering and precipitation assay titrations. The dependence of EC(50) (ligand concentration at the midpoint of the array condensation) on C(KCl) displays two regimes, a salt-independent at low C(KCl) and a salt-dependent at higher salt concentrations. In the salt-dependent regime EC(50) rises sharply with increase of C(KCl). Increase of ligand charge shifts the transition from the salt-independent to salt-dependent regime to higher salt. In the nucleosome array system, due to the partial neutralization of the DNA charge by histones, a lower oligocation concentration is needed to provoke condensation in the salt-independent regime compared to the related case of DNA condensation by the same cation. In the physiological range of salt concentrations (C(KCl)=50-300mM), K(+) ions assist array condensation by shifting EC(50) of the ε-oligolysines to lower values. At higher C(KCl), K(+) competes with the cationic ligands, which leads to increase of EC(50). Values of salt-dependent dissociation constant for the ε-oligolysine-nucleosome array interaction were obtained, by fitting to a general equation developed earlier for DNA, describing the dependence of EC(50) on dissociation constant, salt and polyelectrolyte concentrations.     

Extent of charge screening in aqueous polysaccharide solutions

The absorption optical system of a Beckman XL-I ultracentrifuge has been used to monitor the Donnan distribution of ions in polysaccharide solutions dialyzed against sodium phosphate buffer (pH 6.8, I 0.08) supplemented with 0.2 mM chromate as an indicator ion. For dextran sulfate, heparin, and polygalacturonate, the effective net charges are shown to be only one-third of those deduced from the chemical structures--a reflection of charge screening (counterion condensation) in aqueous polyelectrolyte solutions. Whereas the extent of charge screening for the first two polysaccharides agrees well with theoretical prediction, the disparity in the corresponding comparison for polygalacturonate reflects partial esterification of carboxyl groups, whereupon the experimental parameter refers to the effective charge per hexose residue rather than the effective fractional charge of each carboxyl group.     

Application of polyelectrolyte theories for analysis of DNA melting in the presence of Na+ and Mg2+ ions.

Numerical calculations, using Poisson-Boltzmann (PB) and counterion condensation (CC) polyelectrolyte theories, of the electrostatic free energy difference, DeltaGel, between single-stranded (coil) and double-helical DNA have been performed for solutions of NaDNA + NaCl with and without added MgCl2. Calculations have been made for conditions relevant to systems where experimental values of helix coil transition temperature (Tm) and other thermodynamic quantities have been measured. Comparison with experimental data has been possible by invoking values of Tm for solutions containing NaCl salt only. Resulting theoretical values of enthalpy, entropy, and heat capacity (for NaCl salt-containing solutions) and of Tm as a function of NaCl concentration in NaCl + MgCl2 solutions have thus been obtained. Qualitative and, to a large extent, quantitative reproduction of the experimental Tm, DeltaHm, DeltaSm, and DeltaCp values have been found from the results of polyelectrolyte theories. However, the quantitative resemblance of experimental data is considerably better for PB theory as compared to the CC model. Furthermore, some rather implausible qualitative conclusions are obtained within the CC results for DNA melting in NaCl + MgCl2 solutions. Our results argue in favor of the Poisson-Boltzmann theory, as compared to the counterion condensation theory.     

Charge patch attraction and reentrant condensation in DNA-liposome complexes

We investigated the formation of complexes between cationic liposomes built up by DOTAP and three linear anionic polyions, with different charge density and flexibility, such as a single-stranded ssDNA, a double-stranded dsDNA and the polyacrylate sodium salt [NaPAA] of three different molecular weights. Our aim is to gain further insight into the formation mechanism of polyion-liposome aggregates of different sizes (lipoplexes), by comparing the behavior of DNA with a model polyelectrolyte, such as NaPAA, with approximately the same charge density but with a higher flexibility. We employed dynamic light scattering (DLS) and transmission electron microscopy (TEM) measurements, in order to explore both the hydrodynamic and structural properties of the aggregates resulting from polyion-liposome interaction and to present a comprehensive picture of the complexation process. The phenomenology can be summarized in a charge ratio-dependent scenario, where the main feature is the formation of large equilibrium clusters due to the aggregation of intact polyion-coated vesicles. At increasing polyion-liposome ratio, the size of the clusters continuously increases, reaching a maximum at a well-defined value of this ratio, and then decreases (“reentrant” condensation). The aggregation mechanism and the role of the polyion charge density in the complex formation are discussed in the light of the recent theories on the correlated adsorption of polyelectrolytes at charged interfaces. Within this framework, the phenomena of charge inversion and the reentrant condensation, peaked at the isoelectric point, finds a simple explanation.     

Inhibitory effects of multicomponent, phosphonate-grafted, zwitterionic chitosan biomacromolecules on silicic acid condensation

This article reports the inhibitory effects of phosphonated chitosan (PCH, synthesized from chitosan (CHS) by a Mannich-type reaction) on the in vitro silicic acid condensation. In particular, the ability of PCH to retard silicic acid condensation in aqueous supersaturated solutions at circumneutral pH is studied. Furthermore, the effect of anionic carboxymethyl inulin (CMI) polyelectrolyte on the inhibitory activity of PCH is systematically studied. It was discovered that when PCH is added in dosages up to 150 ppm, it can inhibit silicic acid condensation, thereby maintaining soluble silicic acid up to 300 ppm (for 8 h, from a 500 ppm initial stock solution). The addition of CMI to working solutions that already contain PCH can further enhance the inhibitory action of PCH. A combination of 150 ppm PCH and 100 ppm CMI maintains 400 ppm soluble silicic acid for 8 h. PCH and CMI combinations also affect colloidal silica particle morphology.     

Charge patch attraction and reentrant condensation in DNA-liposome complexes

We investigated the formation of complexes between cationic liposomes built up by DOTAP and three linear anionic polyions, with different charge density and flexibility, such as a single-stranded ssDNA, a double-stranded dsDNA and the polyacrylate sodium salt [NaPAA] of three different molecular weights. Our aim is to gain further insight into the formation mechanism of polyion-liposome aggregates of different sizes (lipoplexes), by comparing the behavior of DNA with a model polyelectrolyte, such as NaPAA, with approximately the same charge density but with a higher flexibility. We employed dynamic light scattering (DLS) and transmission electron microscopy (TEM) measurements, in order to explore both the hydrodynamic and structural properties of the aggregates resulting from polyion-liposome interaction and to present a comprehensive picture of the complexation process. The phenomenology can be summarized in a charge ratio-dependent scenario, where the main feature is the formation of large equilibrium clusters due to the aggregation of intact polyion-coated vesicles. At increasing polyion-liposome ratio, the size of the clusters continuously increases, reaching a maximum at a well-defined value of this ratio, and then decreases ("reentrant" condensation). The aggregation mechanism and the role of the polyion charge density in the complex formation are discussed in the light of the recent theories on the correlated adsorption of polyelectrolytes at charged interfaces. Within this framework, the phenomena of charge inversion and the reentrant condensation, peaked at the isoelectric point, finds a simple explanation.