Barbara Hribar-Lee

Protein aggregation in salt solutions

Significance Protein aggregation is a problem in amyloid and other diseases, and it is a challenge when formulating solutions of biological drugs, such as monoclonal antibodies. The physical processes of aggregation, especially in salt solutions, are not well understood. We model a protein as having multiple binding sites to other proteins, leading to orientational variations, dependent on salt. With few parameters and with knowledge of the cloud-point temperatures as a function of added salt, the model gives good predictions for properties including the liquid–liquid coexistence curves, the second virial coefficients, and others for lysozyme and gamma-crystallin. 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.

Simple Model of Hydrophobic Hydration

Water is an unusual liquid in its solvation properties. Here, we model the process of transferring a nonpolar solute into water. Our goal was to capture the physical balance between waters hydrogen bonding and van der Waals interactions in a model that is simple enough to be nearly analytical and not heavily computational. We develop a 2-dimensional Mercedes-Benz-like model of water with which we compute the free energy, enthalpy, entropy, and the heat capacity of transfer as a function of temperature, pressure, and solute size. As validation, we find that this model gives the same trends as Monte Carlo simulations of the underlying 2D model and gives qualitative agreement with experiments. The advantages of this model are that it gives simple insights and that computational time is negligible. It may provide a useful starting point for developing more efficient and more realistic 3D models of aqueous solvation.

Receptacle model of salting-in by tetramethylammonium ions.

Water is a poor solvent for nonpolar solutes. Water containing ions is an even poorer solvent. According to standard terminology, the tendency of salts to precipitate oils from water is called salting-out. However, interestingly, some salt ions, such as tetramethylammonium (TMA), cause instead the salting-in of hydrophobic solutes. Even more puzzling, there is a systematic dependence on solute size. TMA causes the salting-out of small hydrophobes and the salting-in of larger nonpolar solutes. We study these effects using NPT Monte Carlo simulations of the Mercedes-Benz (MB) + dipole model of water, which was previously shown to account for hydrophobic effects and ion solubilities in water. The present model gives a structural interpretation for the thermodynamics of salting-in. The TMA structure allows deep penetration by a first shell of waters, the dipoles of which interact electrostatically with the ion. This first water shell sets up a second water shell that is shaped to act as a receptacle that binds the nonpolar solute. In this way, a nonpolar solute can actually bind more tightly to the TMA ion than to another hydrophobe, leading to the increased solubility and salting-in. Such structuring may also explain why molecular ions do not follow the same charge density series as atomic ions do.

How Water’s Properties Are Encoded in Its Molecular Structure and Energies

How are water’s material properties encoded within the structure of the water molecule? This is pertinent to understanding Earth’s living systems, its materials, its geochemistry and geophysics, and a broad spectrum of its industrial chemistry. Water has distinctive liquid and solid properties: It is highly cohesive. It has volumetric anomalies—water’s solid (ice) floats on its liquid; pressure can melt the solid rather than freezing the liquid; heating can shrink the liquid. It has more solid phases than other materials. Its supercooled liquid has divergent thermodynamic response functions. Its glassy state is neither fragile nor strong. Its component ions—hydroxide and protons—diffuse much faster than other ions. Aqueous solvation of ions or oils entails large entropies and heat capacities. We review how these properties are encoded within water’s molecular structure and energies, as understood from theories, simulations, and experiments. Like simpler liquids, water molecules are nearly spherical and interact with each other through van der Waals forces. Unlike simpler liquids, water’s orientation-dependent hydrogen bonding leads to open tetrahedral cage-like structuring that contributes to its remarkable volumetric and thermal properties.

Tuning the Hydrophobic Interaction: Ultrafast Optical Kerr Effect Study of Aqueous Ionene Solutions

The molecular origin of the hydrophobic effect continues to be widely studied. Here we design an experiment to tune independently hydrophilic and hydrophobic interactions through the study of a series of aqueous ionene solutions. The dynamics of these solutions are probed using the ultrafast optical Kerr effect, which measures polarizability anisotropy relaxation. Analysis of these data yields information on both structural dynamics within the water hydrogen-bonded network and the low frequency intermolecular bending and stretching H-bond modes. In all cases the ionene solute retards the structural dynamics compared to bulk water. However, the effect is small and cannot be assigned specifically to water-hydrophobe interactions. There is no evidence for a dramatic slowdown of the water dynamics observed by the optical Kerr effect when water is in the solvation shell of a hydrophobic group. The low frequency spectrum was recorded as a function of ionene concentration. Again the effect of the solute was small, and could be assigned mainly to the effect of anion solvation.

Primitive model electrolytes. A comparison of the HNC approximation for the activity coefficient with Monte Carlo data

Accuracy of the mean activity coefficient expression (Hansen-Vieillefosse-Belloni equation), valid within the hypernetted chain (HNC) approximation, was tested in a wide concentration range against new Monte Carlo (MC) data for +1:−1 and +2:−2 primitive model electrolytes. The expression has an advantage that the excess chemical potential can be obtained directly, without invoking the time consuming Gibbs-Duhem calculation. We found the HNC results for the mean activity coefficient to be in good agreement with the machine calculations performed for the same model. In addition, the thermodynamic consistency of the HNC approximation was tested. The mean activity coefficients, calculated via the Gibbs-Duhem equation, seem to follow the MC data slightly better than the Hansen-Vieillefosse-Belloni expression. For completeness of the calculation, the HNC excess internal energies and osmotic coefficients are also presented. These results are compared with the calculations based on other theories commonly used to describe electrolyte solutions, such as the mean spherical approximation, Pitzer’s extension of the Debye-Huckel theory, and the Debye-Huckel limiting law.

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.

Self-diffusion of ions in charged nanoporous media

Self-diffusion coefficients of ions of a charge and size symmetric +1 : −1 electrolyte were studied in the presence of ionic obstacles carrying ten negative elementary charges within a “soft” version of the primitive model of electrolytes. The Brownian dynamics method was used to calculate the diffusion coefficients of mobile species. Simulations were complemented with the replica Ornstein–Zernike theory for partly-quenched systems to calculate the activity coefficients of individual ions and the Donnan exclusion coefficient. We study the influence of (i) the size of the pores, which varies with the concentration of quenched charged nanoparticles, and (ii) the presence of added salt on the mobility and thermodynamics of small ions. We show that for dilute matrices (low concentration of charged obstacles) the diffusion coefficient of counterions is smaller or equal to that of co-ions. The opposite is true for concentrated matrices: here counterions are considerably faster than co-ions. In dilute matrices, where obstacles are distributed at larger distances, the counterions are strongly attracted by fixed obstacles. As a consequence, they are slowed down in comparison with the co-ions. In concentrated matrices, where the average size of the pores is small, the counterions can take advantage of hopping from one obstacle to another, whereas the co-ions, repelled by the obstacles, need to diffuse in the space between the layers of counterions surrounding the obstacles. Thermodynamic calculations are consistent with the Brownian dynamics results.

The application of the thermodynamic perturbation theory to study the hydrophobic hydration

The thermodynamic perturbation theory was tested against newly obtained Monte Carlo computer simulations to describe the major features of the hydrophobic effect in a simple 3D-Mercedes-Benz water model: the temperature and hydrophobe size dependence on entropy, enthalpy, and free energy of transfer of a simple hydrophobic solute into water. An excellent agreement was obtained between the theoretical and simulation results. Further, the thermodynamic perturbation theory qualitatively correctly (with respect to the experimental data) describes the solvation thermodynamics under conditions where the simulation results are difficult to obtain with good enough accuracy, e.g., at high pressures.

Structural and thermodynamical properties of charged hard spheres in a mixture with core-softened model solvent

The canonical Monte Carlo computer simulations and integral equation theory were applied to examine the structural and thermodynamic properties of a mixture of ions and a core-softened fluid molecules. The positive and negative ions forming a +1:-1 salt were modeled as charged hard spheres, immersed in the dielectric medium. It was shown previously that the core-softened fluid under study is characterized by a set of structural, thermodynamic, and dynamic anomalies. The principal objective of this work was to elucidate how the presence of ions alters this behavior. The structural properties of the mixtures are discussed in terms of the pair distribution functions; in addition, the pair contribution to the excess entropy was calculated. Thermodynamic properties are investigated by using the dependencies of energy and compressibility factor on density, composition of the mixture, and reduced temperature. The heat capacity was also evaluated. Our principal findings concern the description of structural anomalies in the mixture, the dependence of the temperature of maximum density on the ionic concentration, and establishing the regions delimiting the structural and thermodynamic anomalies of the model mixture.