Effect of salt identity on the phase diagram for a globular protein in aqueous electrolyte solution

Monte Carlo simulations are used to establish the potential of mean force between two globular proteins in an aqueous electrolyte solution. This potential includes nonelectrostatic contributions arising from dispersion forces first, between the globular proteins, and second, between ions in solution and between each ion and the globular protein. These latter contributions are missing from standard models. The potential of mean force, obtained from simulation, is fitted to an analytic equation. Using our analytic potential of mean force and Barker-Henderson perturbation theory, we obtain phase diagrams for lysozyme solutions that include stable and metastable fluid-fluid and solid-fluid phases when the electrolyte is 0.2 M NaSCN or NaI or NaCl. The nature of the electrolyte has a significant effect on the phase diagram.     

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.     

Interaction of nanometric clay platelets

The free energy of interaction between two nanometric clay platelets immersed in an electrolyte solution has been calculated using Monte Carlo simulations as well as direct integration of the configurational integral. Each platelet has been modeled as a collection of charged spheres carrying a unit charge the face of a platelet contains negative charges, and the edge, positive charges. The calculations predict that a configuration of "overlapping coins" is the global free energy minimum at intermediate salt concentrations (10-100 mM). A second weaker minimum, corresponding to the well-known "house of cards" configuration, also appears in this salt interval. At low salt concentrations the electrostatic repulsion dominates, while at intermediate concentrations electrostatic interactions alone can create a net attraction between the platelets. At sufficiently high salt content (>200 mM), the van der Waals interaction takes over and the net interaction becomes attractive at essentially all separations. From the calculated free energy and its derivative, we can derive a yield stress and elasticity modulus in fair agreement with experiment. The roughness of the platelets affects the quantitative behavior of the free energy of interaction but does not alter the results in a qualitative way. From the variation of the free energy of interaction, we would tentatively describe the phase behavior as follows: At low salt, the interaction is strongly repulsive and the dispersion should appear as a solid ("repulsive gel"). With increasing salt concentration, the repulsion is weakened and a liquid phase appears ("sol"). A further increase of the salt content leads a second solid phase ("attractive gel") governed by attractive interactions between the platelets. Finally, at sufficiently high salinity, the clay precipitates due to van der Waals forces.     

Colloidal systems with a short-range attraction and long-range repulsion: Phase diagrams,structures, and dynamics

Colloidal systems with both a short-range attraction and long-range repulsion (SALR) have rich phases compared with the traditional hard sphere systems or sticky hard sphere systems. The competition between the short-range attraction and long-range repulsion results in the frustrated phase separation, which leads to the formation of intermediate range order (IRO) structures and introduces new phases to both equilibrium and nonequilibrium phase diagrams, such as clustered fluid, cluster percolated fluid, Wigner glass, and cluster glass. One hallmark feature of many SALR systems is the appearance of the IRO peak in the interparticle structure factor, which is associated with different types of IRO structures. The relationship between the IRO peak and the clustered fluid state has been careful investigated. Not surprisingly, the morphology of clusters in solutions can be affected and controlled by the SALR potential. And the effect of the SALR potential on the dynamic properties is also reviewed here. Even though much progress has been made in understanding SALR systems, many future works are still needed to have quantitative comparisons between experiments and simulations/theories and understand the differences from different experimental systems. Owing to the large parameter space available for SALR systems, many exciting features of SALR systems are not fully explored yet. Because proteins in low-salinity solutions have SALR interactions, the understanding of SALR systems can greatly help understand protein behavior in concentrated solutions or crowded conditions.     

Effects of ammonium sulfate and sodium chloride concentration on PEG/protein liquid-liquid phase separation

When added to protein solutions, poly(ethylene glycol) (PEG) creates an effective attraction between protein molecules due to depletion forces. This effect has been widely used to crystallize proteins, and PEG is among the most successful crystallization agents in current use. However, PEG is almost always used in combination with a salt at either low or relatively high concentrations. Here the effects of sodium chloride and ammonium sulfate concentration on PEG 8000/ovalbumin liquid-liquid (L-L) phase separation are investigated. At low salt the L-L phase separation occurs at decreasing protein concentration with increasing salt concentration, presumably due to repulsive electrostatic interactions between proteins. At high salt concentration, the behavior depends on the nature of the salt. Sodium chloride has little effect on the L-L phase separation, but ammonium sulfate decreases the protein concentration at which the L-L phase separation occurs. This trend is attributed to the effects of critical fluctuations on depletion forces. The implications of these results for designing solution conditions optimal for protein crystallization are discussed.     

Specific ion effects: Interaction between nanoparticles in electrolyte solutions

Dependence of colloidal interactions on salt identity, observed frequently in experiments, can be accounted for once ion specific non-electrostatic forces are included in the theory. Ability to predict the effect of added salt on the phase diagram of colloid dispersions is essential for the design of processes involving nanocolloids. The Ornstein–Zernike equation with hypernetted chain closure approximation provides a viable first estimate for the potential of mean force between ionized nanoparticles like alumina aggregates in aqueous electrolytes subject to dispersion interactions with hydrated simple ions. Calculated potentials of mean force enable the prediction of osmotic second virial coefficients and phase diagrams showing a dramatic dependence on ion type. The choice of salt therefore provides an efficient, non-intrusive way to tune the phase behavior of nanoparticle dispersions.     

The nonmonotonic concentration dependence of the mean activity coefficient of electrolytes is a result of a balance between solvation and ion-ion correlations

We propose a simple model to explain the nonmonotonic concentration dependence of the mean activity coefficient of simple electrolytes without using any adjustable parameters. The primitive model of electrolytes is used to describe the interaction between ions computed by the adaptive grand canonical Monte Carlo method. For the dielectric constant of the electrolyte, we use experimental concentration dependent values. This is included through a solvation term in our treatment to describe the interaction between ions and water that changes as the dielectric constant changes with concentration. This term is computed by a Born-treatment fitted to experimental hydration energies. Our results for LiCl, NaCl, KCl, CsCl, NaBr, NaI, MgCl(2), CaCl(2), SrCl(2), and BaCl(2) demonstrate that the principal reason of the nonmonotonic behavior of the activity coefficient is a balance between the solvation and ion-ion correlation terms. This conclusion differs from previous studies that assumed that it is the balance of hard sphere repulsion and electrostatic attraction that produces the nonmonotonic behavior. Our results indicate that the earlier assumption that solvation can be taken into account by a larger, "solvated" ionic radius should be reconsidered. To explain second order effects (such as dependence on ionic size), we conclude that explicit water models are needed.     

Interparticle interactions and direct imaging of colloidal phases assembled from microsphere-nanoparticle mixtures

We investigate the interparticle interactions, phase behavior, and structure of microsphere-nanoparticle mixtures that possess high size and charge asymmetry. We employ a novel Monte Carlo simulation scheme to calculate the effective microsphere interactions in suspension, yielding new insight into the origin of the experimentally observed behavior. The initial settling velocity, final sediment density, and three-dimensional structure of colloidal phases assembled from these binary mixtures via gravitational settling of silica microspheres in water and index-matched solutions exhibit a strong compositional dependence. Confocal laser scanning microscopy is used to directly image and quantify their structural evolution during assembly. Below a lower critical nanoparticle volume fraction (phi(nano) < phi(L,C)), the intrinsic van der Waals attraction between microspheres leads to the formation of colloidal gels. These gels exhibit enhanced consolidation as phi(nano) approaches phi(L,C). When phi(nano) exceeds phi(L,C), an effective repulsion arises between microspheres due to the formation of a dynamic nanoparticle halo around the colloids. From this stable fluid phase, the microspheres settle into a crystalline array. Finally, above an upper critical nanoparticle volume fraction (phi(nano) > phi(U,C)), colloidal gels form whose structure becomes more open with increasing nanoparticle concentration due to the emergence of an effective microsphere attraction, whose magnitude exhibits a superlinear dependence on phi(nano).     

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.     

Visualizing worm micelle dynamics and phase transitions of a charged diblock copolymer in water

Assemblies of block copolymer amphiphiles are sometimes viewed as glassy, frozen, or static colloids, especially in strongly segregating solutions. Here, we visualize by fluorescence microscopy and AFM the dynamics and transitions of single cylindrical micelles and vesicles composed of a charged diblock copolymer in water. In mapping the salt- and pH-dependent phase diagrams of a near-symmetric diblock of poly(acrylic acid)-polybutadiene, low pH and high salt (NaCl, CaCl2) neutralize and screen the charged corona sufficiently to foster membrane formation and generate vesicles. Decreased salt and neutral pH increases intra-coronal repulsion and drives a transition to multi-branched cylinders and highly stable, but fluid and flexible, worm micelles. Ca2+ both stiffens cylinders and stabilizes them relative to spheres. Further increase of intra-coronal repulsion generates spherical micelles by fragmentation and pinch-off at the ends of worms. Both the transition kinetics and phase diagrams indicate divalent cation is about 5-10-fold more effective than monovalent in stabilizing all nonspherical morphologies.     

Why pH titration in protein solutions follows a Hofmeister series

Measurements of pH in single-phase cytochrome c suspensions are reported. The pH, as determined by a glass electrode, has a fixed value. With the addition of salt, the supposedly fixed pH changes strongly. The pH depends on salt type and concentration and follows a Hofmeister series. A theoretical interpretation is given that provides insights into such Hofmeister effects. These occur generally in protein solutions. While classical electrostatic models provide partial understanding of such trends in protein solutions, they fail to explain the observed ion specificity. Such models neglect electrodynamic fluctuation (dispersion) forces acting between ions and proteins. We use a Poisson-Boltzmann cell model that takes these ionic dispersion potentials between ions and proteins into account. The observed ion specificity can then be accounted for. Proteins act as buffers that display similar salt-dependent pH trends not previously explained.     

Solubility of lysozyme in the presence of aqueous chloride salts: common-ion effect and its role on solubility and crystal thermodynamics

Understanding protein solubility is important for a rational design of the conditions of protein crystallization. We report measurements of lysozyme solubility in aqueous solutions as a function of NaCl, KCl, and NH4Cl concentrations at 25 degrees C and pH 4.5. Our solubility results are directly compared to preferential-interaction coefficients of these ternary solutions determined in the same experimental conditions by ternary diffusion. This comparison has provided new important insight on the dependence of protein solubility on salt concentration. We remark that the dependence of the preferential-interaction coefficient as a function of salt concentration is substantially shaped by the common-ion effect. This effect plays a crucial role also on the observed behavior of lysozyme solubility. We find that the dependence of solubility on salt type and concentration strongly correlates with the corresponding dependence of the preferential-interaction coefficient. Examination of both preferential-interaction coefficients and second virial coefficients has allowed us to demonstrate that the solubility dependence on salt concentration is substantially affected by the corresponding change of protein chemical potential in the crystalline phase. We propose a simple model for the crystalline phase based on salt partitioning between solution and the hydrated protein crystal. A novel solubility equation is reported that quantitatively explains the observed experimental dependence of protein solubility on salt concentration.     

Phase behavior of self-associating fluids with weaker dispersion interactions between bonded particles

In this study, we explore the global phase behavior of a simple model for self-associating fluids where association reduces the strength of the dispersion interactions between bonded particles. Recent research shows that this type of behavior likely explains the thermodynamic properties of strongly polar fluids and certain micellar solutions. Based on Wertheim's theory of associating liquids [M. S. Wertheim, J. Stat. Phys. 42, 459 (1986); 42, 477 (1986)], our model takes into account the effect that dissimilar particle interactions have on the equilibrium constant for self-association in the system. We find that weaker interactions between bonded molecules tend to favor the dissociation of chains at any temperature and density. This effect stabilizes a monomeric liquid phase at high densities, enriching the global phase behavior of the system. In particular, for systems in which the energy of mixing between bonded and unbonded species is positive, we find a triple point involving a vapor, a dense phase of chain aggregates, and a monomeric liquid. Phase coexistence between the vapor and the monomeric fluid is always more stable at temperatures above the triple point, but a highly associated fluid may exist as a metastable phase under these conditions. The presence of this metastable phase may explain the characteristic nucleation behavior of the liquid phase in strongly dipolar fluids.     

Simple model of membrane proteins including solvent

We report a numerical simulation for the phase diagram of a simple two-dimensional model, similar to the one proposed by Noro and Frenkel [J. Chem. Phys. 114, 2477 (2001)] for membrane proteins, but one that includes the role of the solvent. We first use Gibbs ensemble Monte Carlo simulations to determine the phase behavior of particles interacting via a square-well potential in two dimensions for various values of the interaction range. A phenomenological model for the solute-solvent interactions is then studied to understand how the fluid-fluid coexistence curve is modified by solute-solvent interactions. It is shown that such a model can yield systems with liquid-liquid phase separation curves that have both upper and lower critical points, as well as closed loop phase diagrams, as is the case with the corresponding three-dimensional model.     

粘度法研究外加盐对离子聚合物在水中形态的影响

本文考察外加盐浓度、反离字半径和价数对6, 10Br大分子形态的影响。计算表征分子尺寸的各种参数。表明6, 10Br分子形态的转变是主链上正氮离子的静电斥力和—CH_3之间亲合力协同作用的结果。对大分子卷曲的影响是: I~->Br~->Cl~-。在KI溶液中, 6, 10Br转变为6, 10I而导致沉淀, 估计与I~-的极化率大易变形有关, 也与6, 10Br主链的结构特点有关。多价反离子(SO~(2-)_4, PO~(3-)_4)对大分子形态的影响与Cl~-和Br~-没有明显不同。     

Combined effect of spin speed and ionic strength on polyelectrolyte spin assembly

Polyelectrolyte spin assembly (PSA) of multilayers is a sequential process featuring adsorption of oppositely charged polyelectrolytes from dilute solutions undergoing spin-coating flow. Here, we report on the dependence of PSA multilayer buildup of poly(sodium 4-styrenesulfonate) and poly(allylamine hydrochloride) on solution ionic strength and spin speed. We observed that at a given spin speed, the PSA coating growth rate (thickness/bilayer) and polymer surface coverage shows a nonmonotonic dependence on salt concentration, first increasing and then decreasing with increasing solution ionic strength. This is argued to be a manifestation of two competing mechanisms responsible for the layer formation. At low salt concentrations, the electrostatic interactions control the multilayer assembly process, while at high salt concentrations it is dominated by shear flow. We explain this nonmonotonic behavior in the framework of a Flory-like theory of multilayer formation from polyelectrolyte solution under shear flow. Additionally, the PSA process led to multilayer coatings with a radial dependence on thickness at lower spin speed in the shear-dominated regime. On increasing spin speed, such radial dependence subsided, eventually leading to uniform coatings by planarization. The surface topography of the multilayered coatings adsorbed at salt concentration less than 0.1 M was flat and featureless for all studied spin speeds. Unique morphological features in the films were formed at salt concentration higher than 0.1 M, the size of which depended on the spin speed and solution ionic strength.     

pH-responsive non-surface-active/surface-active transition of weakly ionic amphiphilic diblock copolymers

The weakly ionic amphiphilic diblock copolymer polystyrene-b-poly(acrylic acid) was synthesized by nitroxy radical-mediated living radical polymerization with precise control of block length, block ratio, and polydispersity. Systematical surface tension experiments and foam formation observations revealed that this polymer was non-surface active under neutral and alkaline (pH 10) conditions, while it was surface active under an acidic condition (pH 3). This result supports our proposed origin of non-surface activity; the image charge repulsion at the air/water interface is essential in addition to very stable micelle formation in the bulk solution. At a higher pH (pH 12), the polymer showed slight surface activity since the added NaOH played a role as an added salt. The critical micelle concentration (cmc) was estimated by static light scattering. Cmc increased with increasing added salt (NaCl) concentration as was observed for other strongly ionic non-surface-active polymers. Hence, this trend is characteristic for non-surface-active polymers. The pH dependence of cmc was minimum at pH 8–10. Since the acrylic acid block is fully ionized under this condition, the strong image charge repulsion at this condition accelerated micelle formation at a low polymer concentration, which consequently decreased cmc. Micelles in bulk solution were confirmed by dynamic light scattering, and the salt concentration and pH dependencies of the hydrodynamic radius of the micelles were also estimated. The pH-responsive non-surface-active/surface-active transition observed in this study strongly supports the fact that the image charge repulsion is an essential factor for non-surface activity in addition to stable micelle formation in solution.     

Anomalous corresponding-states surface tension of hydrogen fluoride and of the Onsager model

In a corresponding-states analysis of the liquid-vapor surface tension originally suggested by Guggenheim, we study the behavior of different simple (i.e., nonpolar), polar and ionic fluids. The results are compared to the corresponding ones for model fluids of each of the three types. For simple and weakly polar fluids (both real and model), the data map onto a master curve, as demonstrated by Guggenheim. For strongly dipolar, associating fluids, which also exhibit hydrogen bonding, one finds deviations from the master curve at low temperatures and, thus, observes the characteristic sigmoid behavior of the reduced surface tension as a function of temperature. The same is obtained for the model ionic fluid, the restricted primitive model. Truly exceptionally low values of the reduced surface tension are found for hydrogen fluoride and for the Onsager model of dipolar fluids, the surface tension of which we evaluate using an approximate hypernetted chain relation to obtain the square-gradient term in a modified van der Waals theory. Remarkably, in the corresponding-states plot, the surface tensions of HF and of the Onsager model agree very closely, while being well separated from the values for the other fluids. We also study the gradual transition of a model fluid from a simple fluid to a strongly dipolar one by varying the relative strength of dipolar and dispersion forces.