Polyelectrolyte–protein interaction at low ionic strength: required chain flexibility depending on protein average charge

The effect of low ionic strength leading to reduced polyelectrolyte–protein interactions has been shown by in silico and in vitro experiments, suggesting polyelectrolyte rigidity increasing at low ionic strength, thus leading to reduced interactions with proteins. This contribution elucidates polyelectrolyte–protein precipitation in the 0–2.6-mS?cm^?1 ionic strength regime with polyelectrolyte rigidity determinations, using viscosimetry at these conditions, also considering protein charge distributions, using different proteins. Precipitation yields increased from 5 to 40 % at low ionic strength to up to 90 % at intermediate ionic strength, depending on protein and polyelectrolyte type, using lysozyme and three different monoclonal antibodies. Comparing precipitation behavior of the monoclonal antibodies, a qualitative correlation between required polyelectrolyte flexibility to enhance protein precipitation and protein average charge as well as hydrophobicity of the antibodies was discovered. Antibodies with lower average charge and less hydrophobicity required more flexible polyelectrolytes to enhance precipitation behavior by allowing interaction of the polyelectrolytes with proteins, attaching to positively charged protein patches while “circumnavigating” negatively charged protein areas. In contrast, antibodies with higher protein average charge showed increasing precipitation yields up to 90 % already at lower ionic strength, associated with then more rigid polyelectrolyte structures. Therefore, designing polyelectrolytes with specific chain flexibility could help to improve precipitation behavior toward specific target proteins in polyelectrolyte-driven purification techniques.     

Complexation and coacervation of polyelectrolytes with oppositely charged colloids

Polyelectrolyte-colloid coacervation could be viewed as a sub-category of complex coacervation, but is unique in (1) retaining the structure and properties of the colloid, and (2) reducing the heterogeneity and configurational complexity of polyelectrolyte-polyelectrolyte (PE-PE) systems. Interest in protein-polyelectrolyte coacervates arises from preservation of biofunctionality; in addition, the geometric and charge isotropy of micelles allows for better comparison with theory, taking into account the central role of colloid charge density. In the context of these two systems, we describe critical conditions for complex formation and for coacervation with regard to colloid and polyelectrolyte charge densities, ionic strength, PE molecular weight (MW), and stoichiometry; and effects of temperature and shear, which are unique to the PE-micelle systems. The coacervation process is discussed in terms of theoretical treatments and models, as supported by experimental findings. We point out how soluble aggregates, subject to various equilibria and disproportionation effects, can self-assemble leading to heterogeneity in macroscopically homogeneous coacervates, on multiple length scales.     

Polyelectrolyte–particle complex formation. Polyelectrolyte linear charge density and ionic concentration effects. Monte Carlo simulations

The influence of the linear charge density (LCD) of a polyelectrolyte on its adsorption on an oppositely charged colloidal particle is investigated by Monte Carlo simulations. Adsorption characteristics are studied at different linear charge densities and ionic concentrations and for a given polyelectrolyte/particle size ratio so that particle curvature has full effect. The isolated polyelectrolyte goes through a smooth transition from a collapsed structure to an extended rod-like conformation with increasing the linear charge density in the low ionic concentration regime. In the high ionic concentration regime, the polyelectrolyte is less sensitive to the increase in the linear charge density and adopts a coil conformation. We found that complex formation is promoted by decreasing the ionic concentration and increasing the linear charge density and that large changes in the polymer dimensions are observed at the adsorption-desorption limit. By adjusting the linear charge density and ionic strength, we demonstrate that the adsorption-desorption limit corresponds to a sharp transition from non-adsorbed to adsorbed conformations and that the mean adsorption energy per monomer has to be less than -0.4 kT to achieve adsorption. We calculated that the linear charge density at the adsorption-desorption limit is related to the Debye-Hückel length according to LCD^crit ~3². At small values of the linear charge density and low ionic strength (no adsorption is observed at high ionic strength), a large amount of monomers are present in loops and tails. By increasing LCD, the amount of monomers in trains reaches a maximum value and the polyelectrolyte adopt flat conformation at the surface of the particle.     

Release of lysozyme from the branched polyelectrolyte-lysozyme complexation

On the basis of the discretely charged sphere model of lysozyme, the release behavior of lysozyme from the branched polyelectrolyte-lysozyme complexation is investigated by adding salt and changing the pH values of the solution. It is found that, with the increase of the salt ionic strength of the solution, the lysozymes are gradually released from the oppositely charged polyelectrolyte as a result of the screening of electrostatic attraction between the two ionic species by adding the salt. Interestingly, there exists a critical salt ionic strength at which all proteins are released from the branched polyelectrolyte, and the polyelectrolyte-protein complexation is broken completely. Beyond the critical value, the increase of the salt ionic strength causes self-association of the proteins released from the branched polyelectrolyte-protein complexation. The self-association of the protein is detrimental in biological systems. By calculating the second virial coefficient, we found that the optimal salt content for the dispersion of proteins coincides with the critical ionic strength, because the second virial coefficient reaches its maximum at the critical ionic strength. Similarly, increasing the pH value of the solution can also release the lysozymes from the polyelectrolyte, because the increase of pH value of the solution changes the charge distribution and net charge of the lysozyme, weakens the attraction between lysozymes mediated by polyelectrolyte, and finally leads to the dissolution of the complexation of branched polyelectrolyte with lysozymes in strong alkaline solution. In addition, by exploring the effect of architecture of the polyelectrolyte on the release behavior of proteins, we found that it is more difficult to release proteins from the branched polyelectrolyte than from the linear polyelectrolyte.     

On the mechanism of uptake of globular proteins by polyelectrolyte brushes: a two-gradient self-consistent field analysis

We present model calculations for the interaction of a protein-like inhomogeneously charged nanoscale object with a layer of densely grafted polyelectrolytes ("polyelectrolyte brush"). The motivation of this work is the recent experimental observation that proteins that carry an overall negative charge are absorbed into negatively charged polyelectrolyte brushes. Two-gradient self-consistent field (2G-SCF) calculations have been performed to unravel the physical mechanism of the uptake of protein thus effected. Our results prove that an overall neutral, protein-like object can electrostatically be attracted and therefore spontaneously driven into a polyelectrolyte brush when the object has two faces (patches, domains), one with a permanent positive charge and the other with a permanent negative charge. Using a 2G-SCF analysis, we evaluate the free energy of insertion, such that the electric dipole of the inclusion is oriented parallel to the brush surface. An electroneutral protein-like object is attracted into the brush because the polyelectrolyte brush interacts asymmetrically with the charged patches of opposite sign. At high ionic strength and low charge density on the patches, the attraction cannot compete with the repulsive excluded-volume interaction. However, for low ionic strengths and sufficiently high charge density on the patches, a gain on the order of k(B)T per charge becomes possible. Hence, the asymmetry of interaction for patches of different charges may result in a total attractive force between the protein and the brush. All results obtained herein are in excellent agreement with recent experimental data.     

Proteins and polyelectrolytes: A charged relationship

We review the interaction of charged polymeric systems with proteins. In solutions of low ionic strength there are many examples of proteins attracted to polyelectrolytes even if both systems carry the same overall charge. This attractive interaction is widespread, having been observed for single polyelectrolyte chains as well as for polyelectrolytes grafted to surfaces (polyelectrolyte brushes) and charged polymeric networks. In all cases, adding salt weakens the interaction considerably. We discuss the suggestion that the attractive force at low salinity originates from the asymmetry of interaction between charged polymer segments and charged patches on the surface of the protein globule. This can be explained if the attractive force is mainly due to a counterion release force, i.e., the polyelectrolyte chains become the multivalent counterions for the patches of opposite charge localized on the surface of the proteins. We review a selection of simple models that lead to semi-quantitative estimates of this force as the function of salt concentration.     

Poisson-Boltzmann theory of the charge-induced adsorption of semi-flexible polyelectrolytes

A model is suggested for the structure of an adsorbed layer of a highly charged semi-flexible polyelectrolyte on a weakly charged surface of opposite charge sign. The adsorbed phase is thin, owing to the effective reversal of the charge sign of the surface upon adsorption, and ordered, owing to the high surface density of polyelectrolyte strands caused by the generally strong binding between polyelectrolyte and surface. The Poisson-Boltzmann equation for the electrostatic interaction between the array of adsorbed polyelectrolytes and the charged surface is solved for a cylindrical geometry, both numerically, using a finite element method, and analytically within the weak curvature limit under the assumption of excess monovalent salt. For small separations, repulsive surface polarization and counterion osmotic pressure effects dominate over the electrostatic attraction and the resulting electrostatic interaction curve shows a minimum at nonzero separations on the Angstrom scale. The equilibrium density of the adsorbed phase is obtained by minimizing the total free energy under the condition of equality of chemical potential and osmotic pressure of the polyelectrolyte in solution and in the adsorbed phase. For a wide range of ionic conditions and charge densities of the charged surface, the interstrand separation as predicted by the Poisson-Boltzmann model and the analytical theory closely agree. For low to moderate charge densities of the adsorbing surface, the interstrand spacing decreases as a function of the charge density of the charged surface. Above about 0.1 M excess monovalent salt, it is only weakly dependent on the ionic strength. At high charge densities of the adsorbing surface, the interstrand spacing increases with increasing ionic strength, in line with the experiments by Fang and Yang [J. Phys. Chem. B 101, 441 (1997)].     

Light scattering study of complex formation between protein and polyelectrolyte at various ionic strengths

Formation of protein-polyelectrolyte complexes (PPCs) between bovine serum albumin (BSA) and potassium poly (vinyl alcohol) sulfate (KPVS) was studied at pH 3 as a function of ionic strength. Turbidimetric titration was employed by a combination of dynamic light scattering (DLS) and electrophoretic light scattering (ELS). The formal charge (Z(PPC)) of the resulting PPCs at different ionic strengths were estimated from ELS data by assuming the free draining and the non-free draining model. The radius of a BSA molecule in the complex was used in the former model for calculation of Z(PPC) with the Henry's equation, while in the latter case the hydrodynamic radius of a PPC particle determined from DLS was employed. The results obtained were compared with the Z(PPC) values calculated using a relation of Z(PPC)=n(b)Z(BSA)+alphaZ(KPVS), where Z(BSA) (> or =0) and Z(KPVS) (< or =0) denote the formal charge of BSA and KPVS, respectively. Moreover, n(b) is the number of bound proteins per complex composed of alpha polymer chains. It was suggested that the PPC between BSA and KPVS behaves as a free draining molecule during the electrophoresis, at least at a high ionic strength. Also suggested is that the PPC formation at low ionic strength follows a 1:1 stoichiometry in the charge neutralization.     

Light-scattering study of polyelectrolyte complexes: Heparin with partially aminoacetalized poly(vinyl alcohol) in aqueous solution

The structure of soluble polyelectrolyte complexes composed of heparin (Hep) and partially aminoacetalized poly(vinyl alcohol) (PVAA) in aqueous solution was investigated by light scattering. The pH was fixed at 3.2 while the ionic strength and mixing ratio were varied. At high ionic strength (0.5), polyelectrolyte complexes were not formed owing to the screening effect of simple salts on polyion charges. At low ionic strength (0.005), polyelectrolyte complexes formed were stable and dispersed when either the polycation or the polyanion was in great excess, whereas the complexes became unstable and coagulated when the concentrations of polycation and polyanion approached each other. At intermediate ionic strength (0.1), when PVAA was in excess, complex formation was similar to that at low ionic strength (0.005); but with an excess of Hep, polyelectrolyte complexes with similar structure (i.e., roughly spherical with average diameters about 2,700 Å) were formed over a wide range of mixing ratio. This observation is of interest in connection with the physiological activity of Hep in vivo.     

Lateral mobility of polyelectrolyte chains in multilayers

In this work, the lateral mobility of polyelectrolyte multilayers was investigated by means of the fluorescence recovery after photobleaching (FRAP) technique, with special attention to the effect of relevant parameters during and after preparation. Different polyelectrolytes with respect to charge density, stiffness, and hydrophilicity were compared. From the experimental results emerged that the density of charged sites along the polymer is the most important parameter controlling the formation of polymer complexes. At higher charge density, more complexes are formed, and the diffusion coefficient decreases. It was observed that the intrinsic backbone stiffness reduces the interpenetration of polyelectrolyte layers and the formation of complexes promoting the lateral mobility. In addition, the lateral mobility increases with increasing ionic strength and with decreasing hydration shell of the added anion in the polyelectrolyte solution. The effect of heating or annealing in electrolyte solution after preparation was also investigated along with the embedding of the probing layer at controlled distances to the multilayer surface.     

Single ion diffusive transport within a Poly(styrene sulfonate) polymer brush matrix probed by fluorescence correlation spectroscopy

Diffusive transport within complex environments is a critical piece of the chemistry occurring in such diverse membrane systems as proton exchange and bilayer lipid membranes. In the present study, fluorescence correlation spectroscopy was used to evaluate diffusive charge transport within a strong polyelectrolyte polymer brush. The fluorescent cation rhodamine-6G was used as a counterion probe molecule, and the strong polyelectrolyte poly(styrene sulfonate) was the polymer brush. Such strong polyelectrolyte brushes show promise for charge storage applications, and thus it is important to understand and tune their transport efficiencies. The polymer brush demonstrated preferential solvation of the probe counterion as compared to solvation by the aqueous solvent phase. Additionally, diffusion within the polymer brush was strongly inhibited, as evidenced by a decrease in diffusion constant of 4 orders of magnitude. It also proved possible to tune the transport characteristics by controlling the solvent pH, and thus the ionic strength of the solvent. The diffusion characteristics within the charged brush system depend on the brush density as well as the effective interaction potential between the probe ions and the brush. In response to changes in ionic strength of the solution, it was found that these two properties act in opposition to each other within this strong polyelectrolyte polymer brush environment. A stochastic random walk model was developed to simulate interaction of a diffusing charged particle with a periodic potential, to show the response of characteristic diffusion times to electrostatic field strengths. The combined results of the experiments and simulations demonstrate that responsive diffusion characteristics in this brush system are dominated by changes in Coulombic interactions rather than changes in brush density. More generally, these results support the use of FCS to evaluate local charge transport properties within polyelectrolyte brush systems, and demonstrate that the technique shows promise in the development of novel polyelectrolyte films for charge storage/transport materials.     

Complexation between low-molecular-weight cationic ligands and negatively charged polymers as studied by capillary electrophoresis frontal analysis

The potential of using capillary electrophoresis frontal analysis for the study of low-molecular-weight ligand-polyelectrolyte interactions was assessed. The interaction of the ligands 1-propylpyridinium bromide, 2-propylisochinolinium bromide, and paraquat with the polymer dextran sulfate was investigated as a function of polymer concentration and ionic strength of the buffer solution. Linear binding isotherms were obtained and association constants were determined. The complex formation was independent of the dextran sulfate concentration at low ionic strength. Ligand-polyelectrolyte interactions were strongly dependent on the ionic strength. The interaction of the divalent cation paraquat with the dextran sulfate was much stronger than the interactions of the monovalent cationic ligands with the polyelectrolyte. The binding data obtained were in accord with results obtained by equilibrium dialysis. Capillary electrophoresis frontal analysis has the potential to become a valuable tool for characterization of ligand-polyelectrolyte interactions in drug design as well as in other areas.     

Unfolding and refolding details of lysozyme in the presence of β-casein micelles

In this work, we selected a small globular protein, lysozyme, to study how it unfolds and refolds in the presence of micelles composed of the unstructured β-casein proteins by using microcalorimetry and circular dichroism spectroscopy. It was found that a partially unfolded structure of lysozyme starts to form when the β-casein/lysozyme molar ratio is above 0.7, and the structure forms exclusively when the β-casein/lysozyme molar ratio is above 1.6. This partially unfolded state of lysozyme loses most of its tertiary structure and after heating, the denatured lysozyme molecules are trapped in the charged coatings of β-casein micelles and cannot refold upon cooling. The thus obtained protein complex can be viewed as a kind of special polyelectrolyte complex micelle. The net charge ratios of the two proteins and the ionic strength of the dispersions can significantly modulate the electrostatic and hydrophobic interactions between the two proteins. Our present work may have implications for the nanoparticle protein engineering therapy in the biomedicine field and may provide a better understanding of the principles governing the protein-protein interactions. Besides, the heating-cooling-reheating procedure employed in this work can also be used to study the unfolding and refolding details of the target protein in other protein-protein, protein-polymer and protein-small solute systems.     

Counterions in poly(allylamine hydrochloride) and poly(styrene sulfonate) layer-by-layer films

The amount of counterions in layer-by-layer (LBL) films of poly(allylamine hydrochloride) (PAH) and poly(styrene sulfonate) (PSS) has been determined with X-ray photoelectron spectroscopy (XPS) for films prepared from solutions with various NaCl concentrations. Sodium and chloride counterions are present in LBL films produced from salt solutions, which are located at the surface and in the bulk of the films. The percentage of bulk counterions increases with the ionic strength of the polyelectrolyte before reaching a constant value. The bulk sodium/sulfur percentage ratios tend to 0.8 for samples washed with pure water and for samples washed with NaCl aqueous solutions, while the bulk chlorine/nitrogen percentage ratios tend to 0.5 for the same samples. The ratio between the percentages of polyelectrolyte ionic groups lies close to unity for all samples, indicating that counterions do not contribute to charge compensation in the polyelectrolyte during the adsorption process. The presence of counterions in LBL films is explained by Manning condensation near the polyelectrolyte ionic groups, leading to inter-polyelectrolyte ionic bondings via ionic networks. It is believed that condensation leads to the formation of NaCl crystallites in these LBL films, which was confirmed by X-ray diffraction measurements.     

Colloidal interactions between monoclonal antibodies in aqueous solutions

Colloidal interactions between proteins determine the behavior and stability of globular proteins such as monoclonal antibodies (mAbs) against their propensity to cluster formation in solution. We study interactions between these proteins through their dilute solution behavior. Experiments to quantify intermolecular interactions were done using Dynamic and Static Light Scattering (DLS and SLS) in a high-throughput manner in parallel with zeta potential measurements with Laser Doppler Electrophoresis method (M3-PALS). This approach offers a rapid indirect determination of colloidal interactions through their measured second virial coefficient. Electrostatic part of the DLVO interaction was conveniently parameterized via the corresponding surface charge and/or surface potential, while the van der Waals interactions were parameterized via their Hamaker coefficient, both as functions of ionic strength and pH of the bathing solution. This parametrization of protein-protein interactions improves our understanding of mAb assembly and provides a means for its control by solution parameter variation. Additionally, our results also provide a consistency check and validation of applicability of the DLVO theory in mAbs solution assembly processes.     

Mixed systems of hydrophobically modified polyelectrolytes: controlling rheology by charge and hydrophobe stoichiometry and interaction strength

Rheology and phase separation were investigated for aqueous mixtures of two oppositely charged hydrophobically modified polyelectrolytes. The typical phase separation, normally seen for oppositely charged polymer mixtures, is dramatically reduced by the presence of hydrophobic modification, and phase separation is only detected close to the point of charge neutralization. While the two polyelectrolytes separately can give high viscosities and a gel-like behavior, a pronounced maximum in viscosity and storage modulus with the mixing ratio of the polyelectrolytes is observed; the maximum is located between the points of charge and hydrophobe stoichiometry and reflects a combination of hydrophobic and electrostatic association. Lowering the charge density of the anionic polymer leads to a strengthened association at first, but at lower charge densities there is a weakened association due to the onset of phase separation. The strength of the electrostatic interaction was modified by adding salt. Increased ionic strength can lead to phase separation and to increased or decreased viscosity depending on the polyelectrolyte mixing ratio.     

Polyelectrolyte complexes of soluble poly-2-[(methacryloyloxy)ethyl]trimethylammonium chloride and its hydrogels with poly(acrylic acid)

The complex formation of poly-2-[(methacryloyloxy)-ethyl]trimethylammonium chloride (PMADQUAT) with poly(acrylic acid) (PAA) of different molecular weights has been studied in aqueous solutions by potentiometric, viscometric, turbidimetric and FTIR spectroscopic methods. The formation of insoluble non-stoichiometric polyelectrolyte complexes has been shown. The stability of polyelectrolyte complexes in solutions of different pH and ionic strength has been evaluated. The formation of polyelectrolyte complexes between hydrogels of PMADQUAT and linear PAA of different molecular weights has been studied. It was shown that the molecular weight of PAA considerably affects the kinetics of interaction as well as the final state of gel-polymer complex.     

Interactions of poly(2-methacryloyloxyethyl phosphorylcholine) with various salts studied by size exclusion chromatography

The objective of this research is to develop a relationship between salt type and concentration to poly(2-methacyloyloxyethyl phosphorylcholine) (PMPC) zwitterionic polymer solution behaviors. In particular, polyelectrolyte hydrodynamic volumes were analyzed through size exclusion chromatography in relation to the addition of various salts at various concentrations. The salt properties examined were salt concentration, ionic strength, solution pH, cation type/size, anion type/size, valency, and configuration. It was found that the effect of ion properties is related to mechanisms associated with the geometry of the polyelectrolyte. The negative charge group of the polyelectrolyte situated closer to the backbone (inside) is less important to the change in hydrodynamic volume than the positive charge group situated at the end of the side chain (outside). The extensive amount of data generated in this study provides a strong background for possible accurate formulation of a theory based on the salt effect on PMPC polyelectrolyte solution behavior.     

Ionic effects in collapse of polyelectrolyte brushes

We investigated the effect of counterion valence on the structure and swelling behavior of polyelectrolyte brushes using a nonlocal density functional theory that accounts for the excluded-volume effects of all ionic species and intrachain and electrostatic correlations. It was shown that charge correlation in the presence of multivalent counterions results in collapse of a polyelectrolyte brush at an intermediate polyion grafting density. At high grafting density, the brush reswells in a way similar to that in a monovalent ionic solution. In the presence of multivalent counterions, the nonmonotonic swelling of a polyelectrolyte brush in response to the increase of the grafting density can be attributed to a competition of the counterion-mediated electrostatic attraction between polyions with the excluded-volume effect of all ionic species. While a polyelectrolyte brush exhibits an "osmotic brush" regime at low salt concentration and a "salted brush" regime at high salt concentration regardless of the counterion valence, we found a smoother transition as the valence of the counterions increases. As observed in recent experiments, a quasi-power-law dependence of the brush thickness on the concentration ratio can be identified when the monovalent counterions are replaced with trivalent counterions at a fixed ionic strength.     

A modified box model including charge regulation for protein adsorption in a spherical polyelectrolyte brush

Recent experiments showed significant adsorption of bovine serum albumin (BSA) in spherical polyelectrolyte brushes (SPB) consisting of polyacrylic acid, even for pH values above the isoelectric point of the protein, when both protein and polyion are negatively charged. To describe these experimental findings theoretically, we have constructed a spherical box model for an annealed brush consisting of a weak polyelectrolyte that includes the adsorption of BSA. At equilibrium the chemical potential of BSA in solution equals that at each location in the brush, while the net force on the polyions (including osmotic, stretching, and excluded volume terms) is zero at each location. Protein adsorption is predicted above the isoelectric point and--in agreement with experimental data--is a strong function of ionic strength and pH. Adsorption of protein in the brush is possible because the pH in the brush is below the isoelectric point and protein reverses its charge from negative to positive when it adsorbs.