Electrophoretic light scattering studies of poly(L‐lysine) in the ordinary and extraordinary phase. Effects of salt, molecular weight, and polyion concentration

Dilute polyelectrolyte solutions: recent progress and open questions

Polyelectrolytes are a class of polymers possessing ionic groups on their repeating units. Since counterions can dissociate from the polymer backbone, polyelectrolyte chains are strongly influenced by electrostatic interactions. As a result, the physical properties of polyelectrolyte solutions are significantly different from those of electrically neutral polymers. The aim of this article is to highlight key results and some outstanding questions in the polyelectrolyte research from recent literature. We focus on the influence of electrostatics on conformational and hydrodynamic properties of polyelectrolyte chains. A compilation of experimental results from the literature reveals significant disparities with theoretical predictions. We also discuss a new class of polyelectrolytes called poly(ionic liquid)s that exhibit unique physical properties in comparison to ordinary polyelectrolytes. We conclude this review by listing some key research challenges in order to fully understand the conformation and dynamics of polyelectrolytes in solutions.

Dipole-driven interlude of mesomorphism in polyelectrolyte solutions

Uniformly charged polyelectrolyte molecules disperse uniformly in aqueous electrolyte solutions, due to electrostatic repulsion between them. In stark contrast to this well-established result of homogeneous polyelectrolyte solutions, we report a phenomenon where an aqueous solution of positively charged poly(L-lysine) (PLL) exhibits precipitation of similarly charged macromolecules at low ionic strength and a homogeneous solution at very high ionic strength, with a stable mesomorphic state of spherical aggregates as an interlude between these two limits. The precipitation at lower ionic strengths that is orthogonal to the standard polyelectrolyte behavior and the emergence of the mesomorphic state are triggered by the presence of a monovalent small organic anion, acrylate, in the electrolyte solution. Using light scattering, we find that the hydrodynamic radius R_h of isolated PLL chains shrinks upon a decrease in electrolyte (NaBr) concentration, exhibiting the "anti-polyelectrolyte effect." In addition, R_h of the aggregates in the mesomorphic state depends on PLL concentration c_p according to the scaling law, [Formula: see text]. Furthermore, at higher PLL concentration, the mesomorphic aggregates disassemble by a self-poisoning mechanism. We conjecture that all these findings can be attributed to both intra- and interchain dipolar interactions arising from the transformation of polycationic PLL into a physical polyzwitterionic PLL at higher concentrations of acrylate. The reported phenomenon of PLL exhibiting dipole-directed assembly of mesomorphic states and the anti-polyelectrolyte effect are of vital importance toward understanding more complex situations such as coacervation and formation of biomolecular condensates.

Using capillary electrophoresis to characterize the hydrodynamic and electrostatic properties of DNA in solutions containing various monovalent cations

This review describes the results obtained by using free-solution capillary electrophoresis to probe the electrostatic and hydrodynamic properties of DNA in solutions containing various monovalent cations. In brief, we found that the mobilities of double-stranded DNAs (dsDNAs) increase with increasing molecular weight before leveling off and becoming constant at molecular weights ≥400 bp. The mobilities of single-stranded DNAs (ssDNAs) go through a maximum at ∼10-20 nucleotides before decreasing and becoming constant for oligomers larger than ∼30-50 bases. The mobilities of both ss- and dsDNAs increase linearly with the logarithm of increasing charge per unit length and decrease linearly with the logarithm of increasing ionic strength. Surprisingly, ss- and dsDNA mobilities level off and become nearly constant at ionic strengths ≥0.6 M. The thermal stabilities of dsDNAs decrease linearly with increasing solution viscosity. The diffusion coefficients of dsDNA are modulated by the diffusion coefficients of their counterions because of electrostatic DNA-cation coupling interactions. Finally, the anomalously slow mobilities observed for A-tract-containing DNAs can be attributed both to differences in shape and to the preferential localization of small cations in the A-tract minor groove. Since many of these results are mirrored in other polyion-counterion systems, free-solution electrophoresis can be viewed as a reporter of the electrostatics and hydrodynamics of highly charged polyions. New results describing the mobilities of dsDNA analogues of a microRNA-messenger RNA complex are also presented.

Effect of Salt on the Ordinary-Extraordinary Transition in Solutions of Charged Macromolecules

Using dynamic light scattering technique, we address the role of added salt at higher concentrations on the "ordinary-extraordinary" transition in solutions of charged macromolecules. The "ordinary" behavior has previously been associated with a "fast" diffusion coefficient which is independent of salt concentration C_s and polymer concentration C_p if the ratio C_p/ C_s is above a threshold value. The "extraordinary" transition is associated with formation of aggregates, with a "slow" diffusion coefficient, formed from similarly charged macromolecules. By investigating aqueous solutions of sodium poly(styrenesulfonate) and sodium chloride with variations in C_p, C_s, and polymer molecular weight, M_w, we report the emergence of a new diffusive "fast" relaxation mode at higher values of C_p, C_s, and M_w, in addition to the previously known "fast" and "slow" relaxation modes. Furthermore, we find that M_w plays a crucial role on the collective dynamics of polyelectrolyte solutions with salt, instead of just the C_p/ C_s ratio as previously postulated. As M_w is progressively decreased, the salty solution exhibits dynamical transitions from three modes to two modes and then to one mode of relaxation. The emergence of the new fast mode and the dynamical transitions are in marked departure from the general premise of the ordinary-extraordinary transition developed over several decades. In an effort to rationalize our experimental findings we present a theory for the collective dynamics of polyelectrolyte solutions with salt by addressing the coupling between the relaxations of polyelectrolyte chains, counterions from the polymer and added salt, and co-ions from the salt. The predictions are in qualitative agreement with experimental findings. The present combined work of experiments and theory forms the basis for accurately characterizing dynamics of charged macromolecules in salty solutions, which are ubiquitous in biological systems and polyelectrolyte-based technologies.

Ordinary-extraordinary transition in dynamics of solutions of charged macromolecules

The occurrence of the ubiquitous and intriguing "ordinary-extraordinary" behavior of dynamics in solutions of charged macromolecules is addressed theoretically by explicitly considering counterions around the macromolecules. The collective and coupled dynamics of macromolecules and their counterion clouds in salt-free conditions are shown to lead to the "ordinary" behavior (also called the "fast" mode) where diffusion coefficients are independent of molar mass and polymer concentration and are comparable to those of isolated metallic ions in aqueous media, in agreement with experimental facts observed repeatedly over the past four decades. The dipoles arising from adsorbed counterions on polymer backbones can form many pairwise physical cross-links, leading to microgel-like aggregates. Balancing the swelling from excluded volume effects and counterion pressure with elasticity of the microgel, we show that there is a threshold value of a combination of polymer concentration and electrolyte concentration for the occurrence of the "extraordinary" phase (also called the "slow" mode) and the predicted properties of diffusion coefficient for this phase are in qualitative agreement with well-known experimental data.

Interactions of cationic ligands and proteins with small nucleic acids: analytic treatment of the large coulombic end effect on binding free energy as a function of salt concentration

For nonspecific binding of oligopeptides and other cationic ligands, including proteins, to nucleic acid oligomers, we develop a model capable of quantifying and predicting the salt concentration dependence of the binding free energy (deltaG(o)obs) by way of an analytic treatment of the Coulombic end effect (CEE). Ligands, nucleic acids, and their complexes (species j of valence Zj) are modeled as finite lattices with absolute value(Zj) charged residues; the CEE is quantified by its characteristic length Ne (specified in charged residues) and its consequences for the free energy and ion association of the oligomer. Expressions are developed for the individual site binding constants Ki as a function of position (site number i) of a bound ligand on a nucleic acid and for the observed binding constant Kobs as an ensemble average of Ki. Analysis of deltaG(o)obs = -RT ln Kobs and Sa Kobs identical with (partial differential ln Kobs)/(partial differential ln a(+/-)) for binding of the oligopeptide KWK6 (ZL = +8) to single-stranded (ss) dT(pdT)(absolute value(ZD) oligomers (dT-mers) where ZD = {-6, -10, -11, -14, -15} in the range 0.1-0.25 M Na+ yields Ne = 9.0 +/- 0.8 residues at each end, demonstrating that both KWK6 and the above dT-mers are sufficiently short so that the CEE extends over the entire molecule. The dependences of Kobs and of Sa Kobs on absolute value(ZD) for a given ZL are determined by the difference between 2Ne and the net number of charged residues Q in the complex (Q identical with absolute value(ZD) - ZL). For Q < 2Ne, characteristic of complexes of KWK6 with this set of dT-mers, the distribution of binding free energies deltaG(o)obs = -RT ln Ki for sites along the DNA oligomer is parabolic, and Kobs and Sa Kobs are strongly dependent on absolute value(ZD). For Q > or = 2Ne, the distribution of binding free energies deltaG(o)obs is trapezoidal, and the dependence of Kobs and Sa Kobs on absolute value(ZD) is weaker. Application of the model to nonspecific binding of human DNA polymerase beta to ssDNA demonstrates the significance of the CEE in determining Kobs and Sa Kobs of binding of a cationic site on a protein to a DNA oligomer.

Real-time monitoring of the origination of multimacroion domains in a polyelectrolyte solution

First real-time monitoring of the origination of multimacroion domains in an initially homogeneous polyelectrolyte solution was performed. Domains were generated by pH-induced increase of macroion charge in solution of poly(methacrylic acid). Monitoring was performed by static and dynamic light scatterings, in which scattering contributions from individual polyions and growing multimacroion domains were separated, such that amplitudes of both modes were expressed in absolute units. Kinetic results also yield new information regarding the nature of multimacroion domains.

Nonaqueous and aqueous capillary electrophoresis of synthetic polymers

In this work, the use of capillary electrophoresis (CE) to analyze synthetic polymers is reviewed including works published till February 2004. The revised works have been classified depending on the CE mode (e.g., free solution capillary electrophoresis, capillary gel electrophoresis, etc.) and type of buffer (i.e., nonaqueous, aqueous and hydro-organic background electrolytes) employed to separate synthetic macromolecules. Advantages and drawbacks of these different separation procedures for polymer analysis are discussed. Also, physicochemical studies of complex polymer systems by CE are reviewed, including drug release studies, synthetic polyampholytes, dendrimers, fullerenes, carbon nanotubes and associative copolymers.

Association Behavior of Biotinylated and Non-Biotinylated Poly(ethylene oxide)-b-poly(2-(diethylamino)ethyl methacrylate)

Biotinylated and non-biotinylated copolymers of poly(ethylene oxide) (PEO) and poly(2-(diethylamino)ethyl methacrylate) (PDEAEMA) were synthesized by the atom transfer radical polymerization technique. The chemical compositions of the copolymers as determined by NMR are represented by PEO(113)PDEAEMA(70) and biotin-PEO(104)PDEAEMA(93), respectively. The aggregation behavior of these polymers in aqueous solutions at different pHs and ionic strengths was studied using a combination of potentiometric titration, dynamic light scattering, static light scattering, and transmission electron microscopy. Both PEO-b-PDEAEMA and biotin-PEO-b-PDEAEMA diblock copolymers form micelles at high pH with hydrodynamic radii (R(h)) of about 19 and 23 nm, respectively. At low pH, the copolymers are dispersed as unimers in solution with R(h) values of about 6-7 nm. However, at a physiological salt concentration (c(s)) of about 0.16 M NaCl and a pH of 7-8, the copolymers form large loosely packed Gaussian chains, which were not present at the low c(s) of 0.001 M NaCl. The critical micelle concentrations (cmc's) and the cytotoxicities of the copolymers were investigated to determine a suitable polymer concentration range for future biological applications. Both PEO-b-PDEAEMA and biotin-PEO-b-PDEAEMA diblock copolymers possess identical cmc values of about 0.0023 mg/g, while the cytotoxicity test indicated that the copolymers are not toxic up to 0.05 mg/g (>83% cell survival at this concentration).

The free solution mobility of DNA

The free solution mobility of DNA has been measured by capillary electrophoresis in the two buffers most commonly used for DNA gel electrophoresis, Tris-borate-EDTA (TBE) and Tris-acetate-EDTA (TAE). The capillaries were coated with polymers of either of two novel acrylamide monomers, N-acryloylaminoethoxyethanol or N-acryloylaminopropanol, both of which are stable at basic pH and effectively eliminate the electroendosmotic mobility due to the capillary walls. The free solution mobility of DNA in TAE buffer was found to be (3.75 +/- 0.04) x 10(-4) cm2 V-1 s-1 at 25 degrees C, independent of DNA concentration, sample size, electric field strength, and capillary coating, and in good agreement with other values in the literature. The free solution mobility was independent of DNA molecular weight from approximately 400 base pairs to 48.5 kilobase pairs, but decreased monotonically with decreasing molecular weight for smaller fragments. Surprisingly, the free solution mobility of DNA in TBE buffer was found to be (4.5 +/- 0.1) x 10(-4) cm2 V-1 s-1, about 20% larger than observed in TAE buffer, presumably because of the formation of nonspecific borate-deoxyribose complexes.

Electrostatic Interactions and Stability of Poly-l -lysine Covered Polystyrene Latex Particles Investigated by Dynamic Light Scattering

Adsorption isotherms of the pH dependent positively charged polyelectrolyte poly-l -lysine (PLL) on negatively and positively charged polystyrene latices are determined. With photon correlation spectrometry (PCS) the influence of the fluctuating PLL domaines in solution on the diffusion coefficient is observed at low salt concentrations c NaBr < 10(-3) M with lambda = c PE /c NaBr < 0.1 (c PE = concentration of the polyelectrolyte units). Screening of the charged layer by increasing electrolyte concentration results in large adsorbed amounts and layer thicknesses. At low molar mass of PLL the suspensions become unstable and the state and kinetic of flocculation is followed by the decreasing diffusion coefficient. PLL of higher molar mass (M w >/= 100 000) stabilizes the particles sterically and the adsorbed layer thicknesses can be determined. The conclusions drawn from PCS features are confirmed directly by raster electron micrographs of the filtered particles.