Entropy and enthalpy of polyelectrolyte complexation: Langevin dynamics simulations

We report a systematic study by Langevin dynamics simulation on the energetics of complexation between two oppositely charged polyelectrolytes of same charge density in dilute solutions of a good solvent with counterions and salt ions explicitly included. The enthalpy of polyelectrolyte complexation is quantified by comparisons of the Coulomb energy before and after complexation. The entropy of polyelectrolyte complexation is determined directly from simulations and compared with that from a mean-field lattice model explicitly accounting for counterion adsorption. At weak Coulomb interaction strengths, e.g., in solvents of high dielectric constant or with weakly charged polyelectrolytes, complexation is driven by a negative enthalpy due to electrostatic attraction between two oppositely charged chains, with counterion release entropy playing only a subsidiary role. In the strong interaction regime, complexation is driven by a large counterion release entropy and opposed by a positive enthalpy change. The addition of salt reduces the enthalpy of polyelectrolyte complexation by screening electrostatic interaction at all Coulomb interaction strengths. The counterion release entropy also decreases in the presence of salt, but the reduction only becomes significant at higher Coulomb interaction strengths. More significantly, in the range of Coulomb interaction strengths appropriate for highly charged polymers in aqueous solutions, complexation enthalpy depends weakly on salt concentration and counterion release entropy exhibits a large variation as a function of salt concentration. Our study quantitatively establishes that polyelectrolyte complexation in highly charged Coulomb systems is of entropic origin.     

Investigation of the phase behavior of an embedded charge protein model through molecular simulation

The phase behavior of an embedded-charge model for lysozyme developed by Carlsson and co-workers (J. Phys. Chem. B 2001, 105, 9040) is investigated using grand canonical transition matrix Monte Carlo simulation. Within this model, protein-protein interactions are approximated through a combination of hard-sphere repulsion, isotropic hydrophobic attraction, and screened electrostatic interactions through a series of embedded point charges located at the positions of charged amino acid groups within lysozyme. Liquid-liquid phase diagrams are constructed for a wide range of solution conditions and compared with experimental data. Our results indicate that the model is generally capable of describing qualitative trends in the evolution of protein phase behavior with variation of pH and ionic strength. From a quantitative perspective, model estimates for both the change in critical temperature with variation of the solution conditions and the critical concentration do not agree with experimental results. We find the width of model coexistence curves to be independent of solution conditions and narrow relative to experimentally obtained phase envelopes. Connections between the value of the second virial coefficient evaluated at the critical temperature and the location of the liquid-liquid phase envelope are also examined.     

Protein-polyelectrolyte cluster formation and redissolution: a Monte Carlo study

Aqueous solutions of proteins and oppositely charged polyelectrolytes were studied at different polyelectrolyte chain length, ionic strength, and protein-protein interaction potential as a function of the polyelectrolyte concentration. One of the protein models used represented lysozyme in aqueous environment. The model systems were solved by Monte Carlo simulations, and their properties were analyzed in terms of radial distribution functions, structure factors, and cluster composition probabilities. In the system with the strongest electrostatic protein-polyelectrolyte interaction the largest clusters were formed near or at equivalent amount of net protein charge and polyelectrolyte charge, whereas in excess of polyelectrolyte a redissolution appeared. Shorter polyelectrolyte chains and increased ionic strength lead to weaker cluster formation. An inclusion of nonelectrostatic protein-protein attraction promoted the protein-polyelectrolyte cluster formation.     

酪蛋白-g-葡聚糖接枝共聚物对溶菌酶的负载和释放

用溶菌酶作为蛋白质药物模型, 研究了天然大分子对溶菌酶的包埋和释放. 蛋白质为天然的两性聚电解质. 通过Maillard反应制备了无毒且生物相容的β-酪蛋白和葡聚糖的接枝共聚物. 利用β-酪蛋白与溶菌酶之间的静电吸引力制备了以β-酪蛋白/溶菌酶为核, 葡聚糖为壳的胶束. 胶束在低浓度条件下可以稳定存在, 在酸、碱或盐条件下解离. 释放后的溶菌酶分子具有和天然的溶菌酶分子相同的活性. 在胶束中加入Ca2+离子可以使胶束在酸性条件下的稳定性增加. 当用疏水性更强的酪蛋白和葡聚糖接枝共聚物与溶菌酶形成胶束并用Ca2+离子交联后, 胶束在酸性环境下的稳定性显著提高, 在碱性和盐条件下的稳定性也有所增加.     

Comparison of complex coacervate core micelles from two diblock copolymers or a single diblock copolymer with a polyelectrolyte

With light scattering titrations, we show that complex coacervate core micelles (C3Ms) form from a diblock copolymer with a polyelectrolyte block and either an oppositely charged polyelectrolyte, a diblock copolymer with an oppositely charged polyelectrolyte or a mixture of the two. The effect of added salt and pH on both types of C3Ms is investigated. The hydrodynamic radius of mixed C3Ms can be controlled by varying the percentage of oppositely charged polyelectrolyte or diblock copolymer. A simple core-shell model is used to interpret the results from light scattering, giving the same trends as the experiments for both the hydrodynamic radii and the relative scattering intensities. Temperature has only a small effect on the C3Ms. Isothermal titration calorimetry shows that the complexation is mainly driven by Coulombic attraction and by the entropy gain due to counterion release.     

Electrostatic free energy of weakly charged macromolecules in solution and intermacromolecular complexes consisting of oppositely charged polymers

When oppositely charged polyelectrolytes are mixed in water, attraction between oppositely charged groups may lead to the formation of polyelectrolyte complexes (associative phase separation, complex coacervation, interpolymer complexes). Theory is presented to describe the electrostatic free energy change when ionizable (annealed) (macro-)molecules form a macroscopic polyelectrolyte complex. The electrostatic free energy includes an electric term as well as a chemical term that is related to the dissociation of the ionic groups in the polymer. An example calculation for complexation of polyacid with polybase uses a cylindrical diffuse double layer model for free polymer in solution and electroneutrality within the complex and calculates the free energy of the system when the polymer is in solution or in a polyelectrolyte complex. Combined with a term for the nonelectrostatic free energy change upon complexation, a theoretical stability diagram is constructed that relates pH, salt concentration, and mixing ratio, which is in qualitative agreement with an experimental diagram obtained by Bungenberg de Jong (1949) for complex coacervation of arabic gum and gelatin. The theory furthermore explains the increased tendency toward phase separation when the polymer becomes more strongly charged and suggests that complexation of polyacid or polybase with zwitterionic polymer (e.g., protein) of the same charge sign (at the "wrong side" of the iso-electric point) may be due (in part) to an induced charge reversal of the protein.     

Complex formation in mixtures of lysozyme-stabilized emulsions and human saliva

In this paper, we studied the interaction between human unstimulated saliva and lysozyme-stabilized oil-in-water emulsions (10 wt/wt% oil phase, 10 mM NaCl, pH 6.7), to reveal the driving force for flocculation of these emulsions. Confocal scanning laser microscopy (CSLM) showed formation of complexes between salivary proteins and lysozyme adsorbed at the oil-water interface and lysozyme in solution as well. To assess the electrostatic nature of the interaction in emulsion/saliva mixtures, laser-diffraction and rheological measurements were conducted in function of the ionic strength by adding NaCl to the mixture in the range between 0 and 168 mM. Increasing the ionic strength reduced the ability of saliva to induce emulsion flocculation as shown by the decreased floc size and the effect on the viscosity. Turbidity experiments with varying pH (3-7) and ionic strength also showed decreased complex formation in mixtures between saliva and lysozyme in solution upon NaCl addition up to 200 mM. Decreasing the pH increased the turbidity, in line with the increase of the positive net charge on the lysozyme molecule. We conclude that electrostatic attraction is the main driving force for complex formation between saliva components and lysozyme adsorbed at the oil droplets and in solution.     

Controllable immobilization of proteins in quenched spherical polyelectrolyte brushes as observed by fluorescence spectroscopy and small angle X-ray scattering

The immobilization of lysozymes (pI = 11) onto anionic spherical polyelectrolyte brushes (SPB) which consist of a solid polystyrene core and a densely grafted poly(styrene sulfonate) (PSS) shell was systematically studied by fluorescence spectroscopy and small angle X-ray scattering. Results show that the capture of lysozyme by PSS brush is a dynamic process, which involves a quick agglomeration stage and a slow rearrangement one. And lysozyme inclines to immobilize in the inner layer of the brush, and saturation of lysozyme adsorption onto the SPB is gradually reached as the protein concentration increases, proceeding from the inside to the outside of the brush layers. As increasing the pH and ionic strength, the lysozyme previously adsorbed will be partially released and migrate from the inner to the outer layer of SPB. Last competitive adsorption tests between lysozyme and BSA or β-glucosidase were performed, indicating that besides electrostatic interaction counterion release force also plays an important role in protein adsorption. SPB was proved to be ideal candidate for controllable immobilization of protein, which can be extended into various applications, such as drug delivery and protein separation. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1577–1588     

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.     

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.     

Enzyme-polyelectrolyte complex: Salt effects on the reaction of urease with polyallylamine

The effects of inorganic mono- and divalent salts of different types on how the cation polyelectrolyte polyallylamine hydrochloride (PAA) binds with the oligomer enzyme urease were studied. It was shown that in solutions of the monovalent salts NaCl, KCl, and NH₄Cl, polyelectrolyte-protein complexes formed by electrostatic interactions, which decreased monotonically as the salt concentrations increased according to the classic law of statistical physics, correlating the Debye radius with the ionic strength of the solution. In solutions of the divalent salts Na₂SO₄ and (NH₄)2_SO₄, the efficiency of the formation of the polyelectrolyte-protein complexes changed abruptly (the enzyme was drastically activated) at low salt concentrations (∼0.6–0.8 mM), which was not consistent with the classic theory of charge interactions in solutions with different ionic strengths. Turbidimetric titration at different salt concentrations in the given range revealed a high aggregative ability for sulfates and low ability for chlorides. It was concluded that the anomalies in the concentration dependence of the enzyme activity and aggregative ability were related to the formation of stable bonds PAA to the divalent SO₄²⁻ anion, which increased drastically when the ratio of anion concentration to the number of positively charged PAA monomers in solution reached 1: 2.     

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)].     

An extension of the Pitzer equation for the excess Gibbs energy of aqueous electrolyte systems to aqueous polyelectrolyte solutions

Pitzer's equation for the excess Gibbs energy of aqueous solutions of low-molecular electrolytes is extended to aqueous solutions of polyelectrolytes. The model retains the original form of Pitzer's model (combining a long-range term, based on the Debye–Hückel equation, with a short-range term similar to the virial equation where the second osmotic virial coefficient depends on the ionic strength). The extension consists of two parts: at first, it is assumed that a constant fraction of the monomer units of the polyelectrolyte is dissociated, i.e., that fraction does not depend on the concentration of the polyelectrolyte, and at second, a modified expression for the ionic strength (wherein each charged monomer group is taken into account individually) is introduced. This modification is to account for the presence of charged polyelectrolyte chains, which cannot be regarded as punctual charges. The resulting equation was used to correlate osmotic coefficient data of aqueous solutions of a single polyelectrolyte as well as of binary mixtures of a single polyelectrolyte and a salt with low-molecular weight. It was additionally applied to correlate liquid–liquid equilibrium data of some aqueous two-phase systems that might form when a polyelectrolyte and another hydrophilic but neutral polymer are simultaneously dissolved in water. A good agreement between the experimental data and the correlation result is observed for all investigated systems.     

Protein—Protein Interactions in Aqueous Ammonium Sulfate Solutions. Lysozyme and Bovine Serum Albumin (BSA)

Osmotic pressures have been measured to determine lysozyme—lysozyme,BSA—BSA, and lysosyme—BSA interactions for protein concentrations to 100 g-L^–1in an aqueous solution of ammonium sulfate at ambient temperature, as a functionof ionic strength and pH. Osmotic second virial coefficients for lysozyme, forBSA, and for a mixture of BSA and lysozyme were calculated from theosmotic-pressure data for protein concentrations to 40 g-L^–1. The osmotic second virialcoefficient of lysozyme is slightly negative and becomes more negative withrising ionic strength and pH. The osmotic second virial coefficient for BSA isslightly positive, increasing with ionic strength and pH. The osmotic second virialcross coefficient of the mixture lies between the coefficients for lysozyme andBSA, indicating that the attractive forces for a lysozyme—BSA pair areintermediate between those for the lysozyme—lysozyme and BSA—BSA pairs. For proteinconcentrations less than 100 g-L^–1, experimental osmotic-pressure data comparefavorably with results from an adhesive hard-sphere model, which has previouslybeen shown to fit osmotic compressibilities of lysozyme solutions.     

Stabilization of protein-loaded starch microgel by polyelectrolytes

The interaction of biocompatible polyelectrolytes (chargeable poly(amino acids)) with oxidized starch microgel particles has been studied. The aim was to form a polyelectrolyte complex layer around the outer shell of microgel particles filled with functional ingredients to slow down the release of the ingredients from the gel and make this process less sensitive to salt. First, the distribution of positively charged poly(l-lysine) (PLL) of two different molecular weights ("small", 15-30 kDa, and "large", 30-70 kDa) in the negatively charged gel particles was measured. The small PLL distributes homogeneously throughout the gel particles, but the large PLL forms a shell; i.e., its concentration at the outer layer of the particles was found to be much higher than in their core. This shell formation does not occur at a relatively high salt concentration (0.07 M). The large PLL was selected for further study. It was found that upon addition of PLL to lysozyme-loaded gel particles the protein is exchanged by PLL. The exchange rate increases with increasing pH, in line with the increasing electrostatic attraction between the gel and the polyelectrolyte. Therefore, it was decided to use also a negatively charged poly(amino acid), poly(L-glutamic acid) (PGA), to form together with PLL a stable polyelectrolyte complex shell around the gel particles. This approach turned out to be successful, and the PLL/PGA complex layer effectively slows down the release of lysozyme from the microgel particles at 0.05 M salt. In addition, it was found that the PLL/PGA layer protects the gel particle from degradation by α-amylase.     

Sustained and Extended Release with Structural and Activity Recovery of Lysozyme from Complexes with Sodium (Sulfamate Carboxylate) Isoprene/Ethylene Oxide Block Copolymer

The complexation of lysozyme and sodium (sulfamate carboxylate) isoprene/ethylene oxide (SCIEO) at pH = 7.4 and the release of lysozyme from the complexes in the presence of NaCl were investigated. Through electrostatic and hydrophobic interactions, lysozyme and SCIEO form stable complex nanoparticles. The complexation partially disturbs the structure of lysozyme. Some of the hydrophobic residues of lysozyme are exposed to bind with SCIEO. The complexation leads to loss of most of the lysozyme activity. In the presence of NaCl, lysozyme can be released from the complexes. The released lysozyme molecules recover their native structure and activity completely. In the condition of physiological pH and ionic strength, a sustained and extended release of lysozyme was achieved.

     

Water-soluble complexes of star-shaped poly(acrylic acid) with quaternized poly(4-vinylpyridine)

The interaction of star-shaped poly(acrylic acid) having various numbers of arms (5, 8, and 21) and a strong cationic polyelectrolyte, viz., poly( N-ethyl-4-vinylpyridinium bromide), was examined at pH 7 by means of turbidimetry and dynamic light scattering. Mixing aqueous solutions of the oppositely charged polymeric components was found to result in phase separation only if their base-molar ratio Z = [N+]/[COO (-) + COOH] exceeds a certain critical value ZM ( ZM < 1); this threshold value is determined by the number of arms of the star-shaped polyelectrolyte and the ionic strength of the surrounding solution. At Z < ZM, the homogeneous aqueous mixtures of the oppositely charged polymeric components contain two types of complex species clearly differing in their sizes, with the fractions of these species appearing to depend distinctly on the number of arms of the star-shaped poly(acrylic acid), the base-molar ratio of the oppositely charged polymeric components in their mixtures, and the ionic strength of the surrounding solution. The small complex species (major fraction) are assumed to represent the particles of the water-soluble interpolyelectrolyte complex whereas the large complex species (minor fraction) are considered to be complex aggregates.     

Kinetics of Lysozyme Crystallization From Solution

Abstract

We suggest that the growth of molecular aggregates is the rate-controlling step in the crystallization of lysozyme from pH buffered aqueous solutions of strong electrolytes. We propose that the aggregation reaction passes through a charged transition state whose rate of formation is accelerated by Debye-Huckel screening and whose charge is stabilized by ion exchange with the solution. Applying the theory of the “primary kinetic salt effect”, we predict that the half-life for decay of the lysozyme concentration in solution in contact with a growing crystal should decrease linearly with the square root of the ionic strength. This prediction is confirmed experimentally in the case of lysozyme crystals precipitating at 4°C from pH buffered aqueous solutions of sodium chloride.     

Effect of PEG end-group hydrophobicity on lysozyme interactions in solution characterized by light scattering

We compare protein-protein and protein-polymer osmotic virial coefficients measured by static light scattering for aqueous solutions of lysozyme with low-molecular-weight, hydroxy-terminated (hPEG) and methyl-terminated (mPEG) poly(ethylene glycol) at two solution conditions: pH 7.0 and 0.01 M ionic strength, and pH 6.2 and 0.8 M ionic strength. We find that adding PEG to aqueous lysozyme solutions makes a net repulsive contribution to lysozyme-lysozyme interactions, independent of ionic strength and PEG end-group hydrophobicity. PEG end-group hydrophobicity has a profound effect on the magnitude of this contribution, however, at low ionic strength where mPEG-lysozyme attractive interactions become significant. The enhanced attractions promote mPEG-lysozyme preferential interactions at the expense of lysozyme self-interactions, which leads to lysozyme-lysozyme interactions that are more repulsive in the presence of mPEG. These preferential interactions also lead to the preferential exclusion of diffusable ions locally around the protein, which results in a pronounced ionic strength dependence of mPEG-mediated lysozyme-lysozyme interactions.