Protein Association in Solution: Statistical Mechanical Modeling.

Protein molecules associate in solution, often in clusters beyond pairwise, leading to liquid phase separations and high viscosities. It is often impractical to study these multi-protein systems by atomistic computer simulations, particularly in multi-component solvents. Instead, their forces and states can be studied by liquid state statistical mechanics. However, past such approaches, such as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, were limited to modeling proteins as spheres, and contained no microscopic structure-property relations. Recently, this limitation has been partly overcome by bringing the powerful Wertheim theory of associating molecules to bear on protein association equilibria. Here, we review these developments.

Behaviour of the model antibody fluid constrained by rigid spherical obstacles: Effects of the obstacle-antibody attraction.

This study investigates the behaviour of a fluid of monoclonal antibodies (mAbs) when trapped in a confinement represented by rigid spherical obstacles that attract antibodies. The antibody molecule is depicted as an assembly of seven hard spheres (7-bead model), organized to resemble a Y-shaped object. The model antibody has two Fab and one Fc domains located in the corners of letter Y. In this calculation, only the Fab-Fab and Fab-Fc attractive pairs of interactions are effective. The confinement is formed by the randomly distributed hard-spheres fixed in space. The spherical obstacles, besides the size exclusion, interact with beads of the antibody molecules via the Yukawa attractive potential. We applied the combination of the scaled particle theory, replica Ornstein-Zernike equations, Wertheim's thermodynamic perturbation approach and the Flory-Stockmayer theory to calculate: (i) the phase diagram of the liquid-liquid phase separation and the percolation threshold, (ii) the cluster size distributions, and (iii) the second virial coefficient of the protein fluid distributed among the obstacles. All these quantities were calculated as functions of the strength of the attraction between the monoclonal antibodies, and the monoclonal antibodies and obstacles. The conclusion is that while the hard-sphere obstacles decrease the critical density and the critical temperature of the mAbs fluid, the effect of the protein-obstacle attraction is more complex. Adding an attractive potential to the obstacle-mAbs interaction first increases the wideness of the T*-ρ envelope. However, with the further increase of the obstacle-mAbs attraction intensity, we observe reversal of the effect, the T*-ρ curves become narrower. At some point, depending on the obstacle-mAbs interaction, the situation is observed where two different temperatures have the same fluid density (re-entry point). In all the cases shown here the critical point decreases below the value for the neat fluid, but the behaviour with respect to an increase of the strength of the obstacle-mAbs attraction is not monotonic. Yet another interesting phenomenon, known in the literature as an approach toward the "empty liquid" state, is observed. The stability of the "protein droplets", formed by the liquid-liquid phase separation, depends on their local environment and temperature.

Phase stability of aqueous mixtures of bovine serum albumin with low molecular mass salts in presence of polyethylene glycol.

The stability of bovine serum albumin (BSA) solutions against phase separation caused by cooling the system is studied under the combined influence of added poly(ethylene glycol) (PEG) and alkali halide salts in water as solvent. The phase stability of the system depends on the concentration of the added PEG and its molecular mass, the concentration of the low molecular mass electrolyte and its nature, as also on the pH of the solution. More specifically, the addition of NaCl to the BSA-PEG mixture promotes phase separation at pH = 4.0, where BSA carries the net positive charge in aqueous solution, and it increases the stability of the solution at pH=4.6, i.e., near the isoionic point of the protein. Moreover, at pH = 4.6, the cloud-point temperature decreases in the order from NaF to NaI and from LiCl to CsCl. The order of the salts at pH = 4.0 is exactly reversed: LiCl and NaF show the weakest effect on the cloud-point temperature and the strongest decrease in stability is caused by RbCl and NaNO3. An attempt is made to correlate these observations with the free energies of hydration of the added salt ions and with the effect of adsorption of salt ions on the protein surface on the protein-protein interactions. Kosmotropic salt ions decrease the phase stability of BSA-PEG-salt solutions at pH < pI, while exactly the opposite is true at pH = pI.

Multiscale Water Dynamics on Protein Surfaces: Protein-Specific Response to Surface Ions.

Proteins function in crowded aqueous environments, interacting with a diverse range of compounds, and among them, dissolved ions. These interactions are water-mediated. In the present study, we combine field-dependent NMR relaxation (NMRD) and theory to probe water dynamics on the surface of proteins in concentrated aqueous solutions of hen egg-white lysozyme (LZM) and bovine serum albumin (BSA). The experiments reveal that the presence of salts (NaCl or NaI) leads to an opposite ion-specific response for the two proteins: an addition of salt to LZM solutions increases water relaxation rates with respect to the salt-free case, while for BSA solutions, a decrease is observed. The magnitude of the change depends on the ion identity. The developed model accounts for the non-Lorentzian shape of the NMRD profiles and reproduces the experimental data over four decades in Larmor frequency (10 kHz to 110 MHz). It is applicable up to high protein concentrations. The model incorporates the observed ion-specific effects via changes in the protein surface roughness, represented by the surface fractal dimension, and the accompanying changes in the surface water residence times. The response is protein-specific, linked to geometrical aspects of the individual protein surfaces, and goes beyond protein-independent Hofmeister-style ordering of ions.

Aggregation, liquid-liquid phase separation, and percolation behaviour of a model antibody fluid constrained by hard-sphere obstacles.

This study is concerned with the behaviour of proteins within confinement created by hard-sphere obstacles. An individual antibody molecule is depicted as an assembly of seven hard spheres, organized to resemble a Y-shaped (on average) antibody (7-bead model) protein. For comparison with other studies we, in one case, model the protein as a hard sphere decorated by three short-range attractive sites. The antibody has two Fab and one Fc domains located in the corners of the letter Y. In this calculation, only the Fab-Fab and Fab-Fc attractive pair interactions are possible. The confinement is formed by the randomly distributed hard-sphere obstacles fixed in space. Aside from size exclusion, the obstacles do not interact with antibodies, but they affect the protein-protein correlation. We used a combination of the scaled-particle theory, Wertheim's thermodynamic perturbation theory and the Flory-Stockmayer theory to calculate: (i) the second virial coefficient of the protein fluid, (ii) the percolation threshold, (iii) cluster size distributions, and (iv) the liquid-liquid phase separation as a function of the strength of the various pair interactions of the protein and the model parameters, such as protein concentration and the packing fraction of obstacles. The conclusion is that hard-sphere obstacles strongly decrease the critical density and also, but to a much lesser extent, the critical temperature. Also, the confinement enhances clustering, making the percolating region broader. The effect depends on the model parameters, such as the packing fraction of obstacles η0, the inter-site interaction strength εIJ, and the ratio between the size of the obstacle σ0 and the size of one bead of the model antibody σhs; the value of this ratio is varied here from 2 to 5. Interestingly, at low to moderate packing fractions of obstacles, the second virial coefficient first slightly decreases (destabilization), and the slope depends on the observation temperature, but then at higher values of η0 it increases. The calculated values of the second virial coefficient also depend on the size of the obstacles.

Ion-specificity and surface water dynamics in protein solutions.

Ion-specific effects at the protein surface are investigated here in light of the changes they infer to surface water dynamics, as observed by 1H NMR relaxation (at 20 MHz). Two well-known proteins, hen egg-white lysozyme (LZM) and bovine serum albumin (BSA), show qualitatively opposite trends in the transverse relaxation rate, R2(1H), along a series of different monovalent salt anions in the solution. Presence of salt ions increases R2(1H) in the case of lysozyme and diminishes it in the case of BSA. The effect magnifies for larger and more polarizable ions. The same contrasting effect between the two proteins is observed for protein-solvent proton exchange. This hints at subtle effects ion-binding might have on the accessibility of water surface sites on the protein. We suggest that the combination of the density of surface charge residues and surface roughness, at the atomic scale, dictates the response to the presence of salt ions and is proper to each protein. Further, a dramatic increase in R2(1H) is found to correlate closely with the formation of protein aggregates. The same ordering of salts in their ability to aggregate lysozyme, as seen previously by cloud point measurements, is reproduced here by R2(1H). 1H NMR relaxation data is supplemented by 35Cl and 14N NMR relaxation for selected salt ions to probe the ion-binding itself.

Theory for the Liquid-Liquid Phase Separation in Aqueous Antibody Solutions.

This study presents the theory for liquid-liquid phase separation for systems of molecules modeling monoclonal antibodies. Individual molecule is depicted as an assembly of seven hard spheres, organized to mimic the Y-shaped antibody. We consider the antibody-antibody interactions either through Fab, Fab' (two Fab fragments may be different), or Fc domain. Interaction between these three domains of the molecule (hereafter denoted as A, B, and C, respectively) is modeled by a short-range square-well attraction. To obtain numerical results for the model under study, we adapt Wertheim's thermodynamic perturbation theory. We use this model to calculate the liquid-liquid phase separation curve and the second virial coefficient B2. Various interaction scenarios are examined to see how the strength of the site-site interactions and their range shape the coexistence curve. In the asymmetric case, where an attraction between two sites is favored and the interaction energies for the other sites kept constant, critical temperature first increases and than strongly decreases. Some more microscopic information, for example, the probability for the particular two sites to be connected, has been calculated. Analysis of the experimental liquid-liquid phase diagrams, obtained from literature, is presented. In addition, we calculate the second virial coefficient under conditions leading to the liquid-liquid phase separation and present this quantity on the graph B2 versus protein concentration.

Calorimetric studies of interactions between low molecular weight salts and bovine serum albumin in water at pH values below and above the isoionic point.

Isothermal titration calorimetry was used to determine the temperature and salt concentration dependence of the enthalpy of mixing, Δmix H, of bovine serum albumin (BSA) in aqueous buffer solutions with several low molecular weight salts. Three buffers were used: acetate (pH = 4.0), MOPS (7.2), and borate (9.2). Since the isoionic point of BSA is at pI ≈ 4.7, the net charge of BSA in acetate buffer was positive (≈ +20), while in the other two buffer solutions it was negative (≈ -15 in MOPS and ≈ -25 in borate). The majority of the recorded heat effects were exothermic, while only at pH = 9.2 a weak endothermic effect upon mixing BSA with LiCl, NaCl, and KCl was observed. For all buffer solutions the absolute values of Δmix H of sodium salts followed the order: NaCl < NaBr < NaNO3 < NaI < NaSCN, which is the reverse Hofmeister series for anions. The magnitude of the effects was the largest in acetate buffer and decreased with an increasing pH value of the solution. While the effect of varying the anion of the added salts was strongly pronounced at all pH values, the effect of the cation (LiCl, NaCl, KCl, RbCl and CsCl salts) was weak. The most interesting feature of the results obtained for pH > pI was the fact that Δmix H were considerably more sensitive to the anion (co-ion to the net BSA charge) than to the cation species. This indicated that anions interacted quite strongly with the BSA even at pH values where the net charge of the protein was negative. We showed that Δmix H at high addition of salts correlated well with the enthalpy of hydration of the corresponding salt anion. This finding suggested, consistently with some previous studies, that a part of the exothermic contribution to Δmix H originated from the hydration changes upon the protein-salt interaction. Theoretical analysis, based on the primitive model of highly asymmetric electrolyte solutions solved within the mean spherical approximation, was used to estimate Coulomb effects upon mixing.

Controlling the viscosities of antibody solutions through control of their binding sites.

For biotechnological drugs, it is desirable to formulate antibody solutions with low viscosities. We go beyond previous colloid theories in treating protein-protein self-association of molecules that are antibody-shaped and flexible and have spatially specific binding sites. We consider interactions either through fragment antigen (Fab-Fab) or fragment crystalizable (Fab-Fc) binding. Wertheim's theory is adapted to compute the cluster-size distributions, viscosities, second virial coefficients, and Huggins coefficients, as functions of antibody concentration. We find that the aggregation properties of concentrated solutions can be anticipated from simpler-to-measure dilute solutions. A principal finding is that aggregation is controllable, in principle, through modifying the antibody itself, and not just the solution it is dissolved in. In particular: (i) monospecific antibodies having two identical Fab arms can form linear chains with intermediate viscosities. (ii) Bispecific antibodies having different Fab arms can, in some cases, only dimerize, having low viscosities. (iii) Arm-to-Fc binding allows for three binding partners, leading to networks and high viscosities.

Modeling phase transitions in mixtures of ß-γ lens crystallins.

We analyze the experimentally determined phase diagram of a γD-ßB1 crystallin mixture. Proteins are described as dumbbells decorated with attractive sites to allow inter-particle interaction. We use thermodynamic perturbation theory to calculate the free energy of such mixtures and, by applying equilibrium conditions, also the compositions and concentrations of the co-existing phases. Initially we fit the Tcloudversus packing fraction η measurements for a pure (x2 = 0) γD solution in 0.1 M phosphate buffer at pH = 7.0. Another piece of experimental data, used to fix the model parameters, is the isotherm x2vs. η at T = 268.5 K, at the same pH and salt content. We use the conventional Lorentz-Berthelot mixing rules to describe cross interactions. This enables us to determine: (i) model parameters for pure ßB1 crystallin protein and to calculate; (ii) complete equilibrium surface (Tcloud-x2-η) for the crystallin mixtures. (iii) We present the results for several isotherms, including the tie-lines, as also the temperature-packing fraction curves. Good agreement with the available experimental data is obtained. An interesting result of these calculations is evidence of the coexistence of three phases. This domain appears for the region of temperatures just out of the experimental range studied so far. The input parameters, leading good description of experimental data, revealed a large difference between the numbers of the attractive sites for γD and ßB1 proteins. This interesting result may be related to the fact that γD has a more than nine times smaller quadrupole moment than its partner in the mixture.

Explicit-water theory for the salt-specific effects and Hofmeister series in protein solutions.

Effects of addition of salts on stability of aqueous protein solutions are studied theoretically and the results are compared with experimental data. In our approach, all the interacting species, proteins, ions, and water molecules, are accounted for explicitly. Water molecules are modeled as hard spheres with four off-center attractive square-well sites. These sites serve to bind either another water or to solvate the ions or protein charges. The ions are represented as charged hard spheres, and decorated by attractive sites to allow solvation. Spherical proteins simultaneously possess positive and negative groups, represented by charged hard spheres, attached to the surface of the protein. The attractive square-well sites, mimicking the protein-protein van der Waals interaction, are located on the surface of the protein. To obtain numerical results, we utilized the energy route of Wertheim's associative mean spherical approximation. From measurable properties, we choose to calculate the second virial coefficient B2, which is closely related to the tendency of proteins to aggregate and eventually crystalize. Calculations are in agreement with experimental trends: (i) For low concentration of added salt, the alkali halide salts follow the inverse Hofmeister series. (ii) At higher concentration of added salt, the trend is reversed. (iii) When cations are varied, the salts follow the direct Hofmeister series. (iv) In contrast to the colloidal theories, our approach correctly predicts the non-monotonic behavior of B2 upon addition of salts. (v) With respect to anions, the theory predicts for the B2 values to follow different sequences below and above the iso-ionic point, as also confirmed experimentally. (vi) A semi-quantitative agreement between measured and calculated values for the second virial coefficient, as functions of pH of solution and added salt type and concentration, is obtained.

Effects of Translational and Rotational Degrees of Freedom on the Hydration of Ionic Solutes as Seen by the Popular Water Models.

We employed molecular dynamics simulations with separate thermostats for translational and rotational temperatures in order to study the effects of these degrees of freedom on the hydration of ions. In this work we examine how water models, differing in charge distribution, respond to the rise of rotational temperature. The study shows that, with respect to the distribution of negative charge, popular water models lead to different responses upon an increase of the rotational temperature. The differences arise in hydration of cations, as the negative charge distribution on the model solvent represents the determining factor in such cases. The cation-water correlation increases with the increasing rotational temperature if negative charge is placed in (or close to) the centre of the water molecule (a typical example is the SPC water model) and decreases, when the negative charge is shifted from the centre (as in the TIP5P model of water). Because all the water models examined here have similar distributions of positive charge, they all exhibit similar trends in solvation of anions. In contrast to above, the effect of translational temperature variation is similar for all water-solute pairs; any increase in translational temperature decreases the solute-water correlations.

Protein aggregation in salt solutions.

Protein aggregation is broadly important in diseases and in formulations of biological drugs. Here, we develop a theoretical model for reversible protein-protein aggregation in salt solutions. We treat proteins as hard spheres having square-well-energy binding sites, using Wertheim's thermodynamic perturbation theory. The necessary condition required for such modeling to be realistic is that proteins in solution during the experiment remain in their compact form. Within this limitation our model gives accurate liquid-liquid coexistence curves for lysozyme and γ IIIa-crystallin solutions in respective buffers. It provides good fits to the cloud-point curves of lysozyme in buffer-salt mixtures as a function of the type and concentration of salt. It than predicts full coexistence curves, osmotic compressibilities, and second virial coefficients under such conditions. This treatment may also be relevant to protein crystallization.

On the crossroads of current polyelectrolyte theory and counterion-specific effects.

Aqueous solutions of polyelectrolytes are studied here by means of neutron scattering, with emphasis on backbone hydrophobicity and counter ion specific effects. Ionene polyelectrolytes with varying chain charge density and different counter ions are considered. Their neutron scattering data feature a number of aspects and trends that clearly deviate from the predictions of the existing theory. Ionenes challenge the current hydrophilic-hydrophobic classification of water-soluble polyelectrolytes. The hydrophobic character of their hydrocarbon backbone emerges only for very low chain charge densities (at 15% of charged monomers), which is significantly lower than for other polyelectrolytes with a more complex structure. Universality in the counter ion specific effect seen in ionene solutions with Br(-) or F(-) counterions is established. The polyelectrolyte peak in the scattering spectra of Br-ionenes disappears beyond a specific charge concentration, which is identical across all ionene chain charge densities. In addition, scattering spectra of Br-ionenes and F-ionenes feature contrasting temperature trends, which are accentuated with decreasing chain charge density. Our interpretation of the F-Br effect, based on the different hydration properties of the counter ions, is supported by additional NMR measurements on ionenes with mixed counter ion clouds. Overall, the study of ionene polyelectrolytes points clearly to the need for combining the scaling concepts with those of ion specificity, to obtain a theoretical framework encompassing the wealth of phenomena occurring in polyelectrolyte solutions.

Fast rotational motion of water molecules increases ordering of hydrophobes in solutions and may cause hydrophobic chains to collapse.

Using the molecular dynamics simulations with separate thermostats for translational and rotational degrees of freedom, we investigate the effects of water's rotational motion on the interaction among Lennard-Jones solutes. The situation with rotational temperature higher than the translational one (TR > TT) is mimicking the effects of microwaves on model solutions. Molecular dynamics simulations suggest that solutions of Lennard-Jones solutes become increasingly more structured with the rise in TR, while keeping the TT constant. This is evidenced by an increase of the first and the second peak of the solute-solute radial distribution function. In addition, the first peak moves toward slightly larger distances; the effect seems to be caused by the destabilization of water molecules in the first hydration shell around hydrophobic solutes. More evidence of strong effects of the rotationally excited water is provided by the simulations of short hydrophobic polymers, which upon an increase in TR assume more compact conformations. In these simulations, we see the re-distribution of water molecules, which escape from hydrophobic "pockets" to better solvate the solvent exposed monomers.

Salt-specific effects observed in calorimetric studies of alkali and tetraalkylammonium salt solutions of poly(thiophen-3-ylacetic acid).

The enthalpies of dilution ΔHdil of aqueous solutions of a conjugated polyelectrolyte, poly(thiophen-3-ylacetic acid), neutralized by lithium, sodium, cesium, tetramethyl-, tetraethyl-, tetrapropyl-, and tetrabutylammonium hydroxides, were determined in the concentration range from cp = 2 × 10(-3) to 1 × 10(-1) monomol dm(-3) and for T = 278.15, 298.15, and 318.15 K. At low concentrations the dilution of the alkali PTAA salts yields an endothermic effect, which is in part a consequence of the hydrolysis. An exception is PTALi at 278.15 K, where ΔHdil < 0. In the case of tetraalkylammonium salts the enthalpies of dilution increase in the order TBA < TPA < TEA < TMA. Only the TBA salt of PTAA yields an exothermic effect upon dilution in the whole temperature range. In the second part of the study we measured the enthalpies of mixing, ΔHmix, of various salts of poly(thiophen-3-ylacetic acid) with LiCl, NaCl, KCl, and CsCl solutions in water. When lithium salt of PTAA is mixed with LiCl ΔHmix is positive. For mixing experiments with other alkali chlorides the effect is exothermic. In addition, the enthalpies of mixing of PTALi with tetramethyl-, tetraethyl-, tetrapropyl-, and tetrabutylammonium chloride were measured at T = 278.15 K, 298.15 K, and 318.15 K. Popular polyelectrolyte theories, such as Manning's limiting law, predict for the heat to be released upon dilution, and consumed upon mixing; the agreement between this purely electrostatic theory and experiments is at best qualitative. The ΔHmix values are correlated with the enthalpies of hydration of the cations of the low molecular mass salts added to the solution.

Effects of the translational and rotational degrees of freedom on the hydration of simple solutes.

Molecular dynamics simulations with separate thermostats for rotational and translational motion were used to study the effect of these degrees of freedom on the structure of water around model solutes. To describe water molecules we used the SPC/E model. The simplest solute studied here, the hydrophobe, was represented as a Lennard-Jones particle. Since direct interaction between the hydrophobe and water molecules has no angular dependence the influence of the increase of the rotational temperature on the solvation of a hydrophobe is only indirect. In the next step the central solute was assumed to be charged with either a positive or a negative charge to mimic an ion in water. Hence, depending on the charge of the ion, the neighboring water molecules assumed different angular distributions. The principal conclusions of this work are: (i) an increase of the translational temperature always decreases the height of the first peak in the solute-water radial distribution function; (ii) an increase of the rotational temperature yields an increase in the first peak in the solute-water radial distribution function for hydrophobes and cations; (iii) in contrast to this, the solvation peak decreases around ions with sufficiently large negative charge; and (iv) an increase of the rotational temperature affects cations in an opposite way to anions. For this reason complex molecules with a small net charge may not be very sensitive to variation of the rotational temperature.

Presence of hydrophobic groups may modify the specific ion effect in aqueous polyelectrolyte solutions.

Enthalpies of dilution of aqueous solutions of aliphatic 6,12- and 12,12-ionene bromides and fluorides and enthalpies of mixing with low molecular-weight salts, such as sodium fluoride and bromide, are determined. In the second part of the study, the various x,y-ionenes (x, y are numbers of methylene groups between the adjacent charges) with fluoride, bromide, and iodide counterions are mixed with aqueous sodium sulfate solution. The polyelectrolytes examined in this part of the work are 3,3-, 6,9-, 6,12-, and 12,12-ionenes. A comparison with theoretical results, based on the Poisson-Boltzmann cell model, is presented. The theory predicts for the enthalpy of dilution to be exothermic and the enthalpy of mixing endothermic, while experiments show that signs of the heat effects depend on the nature of the counterion of the added salt, as also on the hydrophobicity (numbers x, y of methylene groups) of the ionene. We show that the salts when ordered by heat effects produced by mixing of NaF and NaBr with 3,3-, 6,9-, or 6,12-ionene fluorides and bromides follow the opposite ordering than in the case when the same alkali halide salts are mixed with more hydrophobic 12,12-ionene salts. The results for the enthalpy of mixing of ionenes under study with Na2SO4 follow the same order as obtained for monovalent salts.

Self-diffusion and activity coefficients of ions in charged disordered media.

Self-diffusion and single ion activity coefficients of ions of size symmetric electrolytes were studied in the presence of a collection of charged obstacles (called matrix) within a "soft" version of the primitive model of electrolyte solutions. The matrix subsystem possesses a net charge, depending on the concentration and charge of obstacles. The brownian dynamics method was used to calculate the self-diffusion coefficients of mobile species. The replica Ornstein-Zernike theory for the partly quenched systems was used to calculate the individual activity coefficients of mobile ionic species. The results reflect the competition between attractive (obstacle-counterion, co-ion-counterion), and repulsive (obstacle-co-ion) interactions in these model systems. For the simplest possible system of symmetric monovalent ions the latter effect wins: Co-ions are excluded from the area around obstacles, and this slows down their diffusion compared to that of counterions. Introduction of divalent charges into the system changes this result when the concentration of obstacles is low. We compare these results to those obtained for the corresponding fully annealed systems, i.e., where all the species are mobile. In most cases the self-diffusion and activity coefficients of counterions and co-ions in the presence of charged obstacles follow the trends of the fully annealed solution, which are dictated by the composition of the mixture. In few situations, however, the presence of charged obstacles modifies these trends. Our study allows us to clearly identify the effects due to obstacles, and to separate them from those arising from the composition of the solution. In the case of charge and size symmetric systems, the results for the individual activity coefficients fully support the hypothesis of the "electrostatic excluded volume". Thermodynamic and dynamic results are consistent in explaining the behavior of the systems studied.

Aqueous solutions of ionenes: interactions and counterion specific effects as seen by neutron scattering.

Aqueous solutions of ionenes with bromide and fluoride counterions have been investigated using small angle neutron scattering for the first time. Ionenes are a class of cationic polyelectrolytes based on quaternary ammonium atoms and, considering the very low solubility of their uncharged part (hydrocarbon chain), would be formally classified as hydrophobic. Ionenes present important structural differences over previously studied polyelectrolytes: (a) charge is located on the polyelectrolyte backbone, (b) the distance between charges is regular and tunable by synthesis, (c) hydrophobicity comes from methylene groups of the backbone and not from bulky side groups. Results for Br ionenes feature a disappearance of the well-known polyelectrolyte peak beyond a given monomer concentration. Below this concentration, the position of the peak depends on the chain charge density, f(chem), and scales as f(chem)(0.30±0.04). This is an indication of a hydrophilic character of the ionene backbone. In addition, osmotic coefficients of ionene solutions resemble again other hydrophilic polyelectrolytes, featuring no unusual increase in the water activity (or a significant counterion condensation). We conclude that despite the hydrophobicity of the hydrocarbon chain separating charged centers on ionenes, these chains behave as hydrophilic. In contrast to Br ionenes, the polyelectrolyte peak remains at all concentrations studied for the single F ionene investigated. This strong counterion effect is rationalized in terms of the different hydrating properties and ion pairing in the case of bromide and fluoride ions.